Structural Analysis of Historical Constructions: SAHC 2023 - Volume 2 (RILEM Bookseries, 46) [1st ed. 2024] 3031394496, 9783031394492
This book gathers the peer-reviewed papers presented at the 13th International Conference on Structural Analysis of Hist
115 101 251MB
English Pages 1349 [1340] Year 2023
Preface
Organisation
Contents
RILEM Publications
Protection of Heritage Structures in Japan and Southeast Asia
Structural Characteristics of Carian Rock-Cut Tombs: The Effect of Discrepancy Between the Connecting Part and the Back Passage
1 The Background of This Study
2 Method
2.1 Outline of the Analytical Model
2.2 Physical Property Values and Boundary Conditions
2.3 Examination of Analysis Patterns
3 Results and Discussion
4 Conclusion
Reference and Notes
The Authenticity and Integrity of the Soil and the Foundation of the Heritage Structure of Bayon Temple, Angkor
1 Bayon Temple, Angkor
2 Foundation System and Ground Conditions
2.1 Trenched Foundation and Ground Condition
2.2 Direct Shallow Foundation
2.3 Foundation Mound with Vertical Shaft at the Center
3 Characteristics of Sandy Soil of the Foundation Mound
3.1 Grainsize Distribution of the Filled Soil
3.2 Weakening Strength with Water Contents
3.3 Mineral Components of the Filled Sand
3.4 Expected Mechanism of Dramatic Change of the Strength and Water Contents
3.5 Field Monitoring of Water Contents by Rain
4 The Authenticity of the Foundation of Main Tower of Bayon
5 Proactive Countermeasures Against the Risk Inherent with Global Warming
5.1 Anticipated Risk to the Heritage Structure with Global Warming
5.2 Proactive Counter Measures Against the Risk of Global Warning to Central Tower of Bayon
5.3 Monitoring the Moisture Change During Rain
6 Conclusions
References
Restoration of Architectural Stone Heritage Damaged by 2011 Great East Japan Earthquake
1 Introduction
2 Overview of Earthquake and Damage of 2011 Great East Japan Earthquake
2.1 Outlines of Earthquake
2.2 Damage to Cultural Properties
3 Description of Fukushima City Museum of Photography
3.1 Building Description
3.2 Earthquake Damage and Process for Restoration
4 Survey for Structural Restoration
4.1 Material Properties Tests
4.2 Microtremore and Earthquake Monitoring
5 Seismic Reinforcement
5.1 Seismic Loads for Designing Reinforcement
5.2 Reinforcement Concept and Decision Making
5.3 Implementation of Reinforcement Utilizing Prestressing Technique
5.4 Strengthening for Structural Connection
5.5 Calculation of Ultimate Lateral Strength
5.6 Another Reinforcement
6 Microtremore Measurement to Verify Reinforcement Implementation
7 Monitoring of Prestressing Force
8 Concluding Remarks
Appendix
References
Study on Evaluation Method of Reinforcement Effect of Dry Masonry in Historical Monuments Applying DDA
1 Introduction
1.1 Outline of Bayon Temple
2 Overview of Analysis Using DDA
2.1 Previous Studies Using DDA
2.2 Outline of DDA Theory
2.3 Quasi-static Analysis of DDA
2.4 Numerical Analysis Model of DDA
2.5 Calculation Results
2.6 Discussion of Evaluation Methods for Analysis Results
3 Conclusions
References
Modern Japanese Pampas Grass Harvest Methods for Thatched Roof Houses Based on Case Studies of Self-procurement of Grasses in Shikoku
1 Introduction
2 Research Methodology
3 Maintenance and Management of Thatch Fields
4 Skills Required for “Kuro”
5 Quantitative Evaluation of Thatch Fields and Thatch
6 Conclusions
References
Estimating the Structural Characteristics of Historic Armenian Church Buildings and Examining Their Strengthening Applications
1 Structural Behavior of St. Hripsime Church
1.1 Analysis Model
1.2 Analysis Results
1.3 Investigation of the Appearance
2 Structural Behavior of Etchimiadzin Cathedral
2.1 Analysis Model
2.2 Analysis Results
2.3 Investigation of the Appearance
2.4 Examination of the Reinforcement Plan
3 Conclusion
References
Vibration Characteristics of Traditional Masonry Buildings in the Kingdom of Bhutan
1 Introduction
2 Shaking Table Tests
2.1 Specimen Configuration
2.2 Outline of Shaking Table Tests
2.3 Results and Discussion
3 Seismic Response Analyses
3.1 Analysis Model
3.2 Analysis Method
3.3 Results and Discussion
4 Conclusions
References
The Introduction and Disappearance of Mixed-Structure Buildings Made from Brick Walls and RC Slabs Between 1900 to 1926 in Japan
1 Introduction
2 Early History of Mixed-Structure Buildings and Fireproof Floor
3 Articles on Mixed-Structure Buildings in the Journal of Architectural Institute of Japan
4 Mixed-Structure Buildings Constructed by the Ministry of Justice Building Division
5 Mixed-Structure Buildings Constructed by the Ministry of Education Building Division
6 Conclusion
References
Snow Load Effect to Vibration Characteristics of Japanese Traditional Wooden Main Temple Building and Three-Story Pagoda Based on Ambient Vibration and Earthquake Observation Records
1 Introduction
2 Outline of the Investigated Buildings: Main Temple Building and Three-Story Pagoda
3 Ambient Vibration Measurement and Earthquake Observation of the Main Temple Building
4 Ambient Vibration Measurement and Earthquake Observation of the Three-Story Pagod
5 Conclusions
References
Proposal of Strength Estimation Formula of Wall Clays Using Multiple Regression Analysis
1 Introduction
2 Strength Tests
2.1 Specimens and Test Methods
2.2 Test Results and Discussion
3 Multiple Regression Analysis
3.1 Analysis Results
4 Conclusions
References
Numerical Investigation of the Properties of Unreinforced and Reinforced Nepalese Historical Brick Masonry Structures
1 Introduction
1.1 Masonry in Earth Mortar
1.2 Numerical Analysis of Masonry in Earth Mortar
2 Materials and Methods
2.1 Description of the Experiment
2.2 Research Methodology
2.3 Results and Discussion
3 Numerical Modeling of URM and Reinforced Masonry Prisms
3.1 Numerical Modeling of Masonry Prism
3.2 Output of URM Model
3.3 Output of Ladder Reinforced Model
3.4 Output of Diagonal Brace Reinforced Model
3.5 Effect of Strut Angle on the Elastic Modulus for Reinforced Masonry Model
3.6 Effect of Elastic Modulus in Compression and Tension in URM Model
4 Conclusions
References
Numerical Modeling and Structural Analysis
Impact Loading Analysis of an Earthen Masonry Structure Using Finite Element Methods
1 Introduction
2 Materials and Models
3 Impact Loading on the Torre de la Vela
3.1 Effects of 16th Century Cannonballs
3.2 Effects of a Hypothetical Impactor
4 Discussion
5 Conclusions
References
Reverse Engineering for the Structural Analysis of Heritage Constructions
1 Introduction
2 Background
2.1 Terrestrial Laser Scanning
2.2 Parametric 3D Modeling
2.3 Reverse Engineering for Improved Built Heritage Structural Knowledge
3 Method
3.1 Methodological Approach
3.2 Method Articulation
4 Case Studies
4.1 Façade Modeling
4.2 Column Modeling
4.3 Timber Truss Modeling
5 Results
5.1 Façade Displacements
5.2 Column Displacements
5.3 Timber Truss Displacements
6 Conclusion
References
Lateral Capacity Assessment of the Main Pyramid of Huaca de la Luna (Peru) Using 2D Finite Element Macroblock Model
1 Introduction
2 Huaca de la Luna
3 Numerical Finite Element (FE) Model
3.1 Geometry and Macroblocks
3.2 Finite Element (FE) Mesh
3.3 Material and Interface Contact Properties
4 Numerical Structural Assessment
4.1 Sequential Structural Analysis
4.2 Energy-Based Approach for Lateral Capacity Estimation
4.3 Sensitivity Analysis: Influence of Friction Coefficient and Number of Macroblocks on Lateral Capacity
5 Conclusion
References
Evaluation of Microscale Behavior and Structural Deformation for Yeonji Wall in Gongsanseong Fortress of the Sixth Century in Korea
1 Introduction
1.1 Background and Purpose
1.2 Subject and Methods
2 Behavior Monitoring
2.1 Annual Micro-behavior
2.2 Environmental Effects
3 3D Image Analysis
3.1 Modeling and Aligning Coordinate Systems
3.2 Deviation Analysis
4 Discussion
5 Conclusion
References
Stability Interpretation for the Tomb of King Muryeong and the Royal Tombs in Baekje Kingdom of Ancient Korea Using 3D Deviation Analysis and Microscale Behavior Measurement
1 Introduction
2 Subject and Methodology
3 Results and Interpretation
3.1 RMS Deviation Analysis
3.2 Displacement Analysis
4 Discussion and Conclusion
References
Structural Analysis of Constructions by Means of Automatic Crack Parameterisation Based on Photographs
1 Introduction
2 The Congruency Algorithm
3 Implementation of the Congruency Algorithm Using Vectorial Autocorrelation of Gradients
4 Example of a Crack Parameterisation
5 Crack Parameterisation in True-to-Scale Image Plans
6 Discussion
7 Outlook
References
Simplified Assessment of the in-Plane Seismic Response of Old Brick Masonry Building Aggregates Using DE Macro-Crack Networks
1 Introduction
2 Preliminary Validation Against Experimental and Micro-modelling Results
3 Numerical Parametric Study Methods
4 DE Macro-Crack Network Numerical Results
4.1 Influence of Material Degradation
4.2 Influence of the Number of Adjacent Buildings
4.3 Influence of Building Height
5 Conclusions
References
Accurate and Efficient 2D Modelling of Historical Masonry Buildings Subjected to Settlements in Comparison to 3D Approaches
1 Introduction
2 Finite Element Models
3 Results
4 Discussion
5 Conclusion
References
Estimation of Load Multipliers in Overturning Mechanisms with Frictional Resistances: Comparison Among Literature Approaches
1 Introduction
2 Literature Approaches for the Evaluation of Collapse Load Multiplier with and Without Friction
2.1 Friction Assessment in Coursed Masonry
2.2 Analytical Formulations
3 Evaluation of Load Multiplier with Frictional Resistances for Overturning Collapse
3.1 Case Study: Castelsantangelo Sul Nera and the Central Italy Earthquake
3.2 Application of Literature Approaches
4 Discussion and Results
5 Conclusions
References
On the Use of Finite Element Method and LEFM to Assess Bearing Capacity of Historic Notched Timber Beams at Arbitrary Location
1 Introduction
2 Methods
2.1 Virtual Crack Closure
2.2 Experimental Work
2.3 Numerical Model
3 Results
3.1 Experimental Work
3.2 Numerical Modeling
4 Discussion
5 Conclusion
References
Influence of Geometric Ratios on the Structural Behaviour of Historic Timber Roof Structures
1 Introduction
2 Analysed Roof Structures
3 Performed Numerical Analysis
3.1 Materials
3.2 Loads
4 Results
4.1 Roof Structure 1
4.2 Roof Structure 2
4.3 Roof Structure 3
5 Conclusions
References
The Effect of a Top Flexible Restraint on a Two-Bodies Vertical Spanning Wall
1 Introduction
2 Description of the Model
3 Parametric Study
3.1 Description of the Parametric Analysis
3.2 Results of the Parametric Analysis
4 Conclusions
References
Investigation of the Structural Performance of Masonry Wharf Cellars in Utrecht Using the Distinct Element Method
1 Introductions
2 Case Study of the Wharf Cellar in Kromme Nieuwegracht
3 Distinct Element Modelling of Utrecht Wharf Cellar
4 Analysis Results
4.1 Safety Assessment of Kromme Nieuwegracht Wharf Cellar System Under BM3 Load
4.2 Failure Load and Failure Mechanism of Kromme Nieuwegracht Wharf Cellar Model
5 Conclusions
References
Analytical Model of Bracket Set Frame in Traditional Chinese Timber Structures
1 Introduction
2 The Proposed Analytical Model of BSF
2.1 Analysis of Structural Form of BSF
2.2 Analytical Model of BSF
3 Validation of Analytical Model
3.1 Solid Element Model of BSF
3.2 Validation of Analytical Model of BSF
4 Mechanical Performances of BSF
4.1 The Effect of Vertical Load on the Load Resistance Capacity of BSF
4.2 The Effect of Section Dimension of Tiaojianliang on the Load Resistance Capacity of BSF
5 Conclusion
Appendix
References
Stability Assessment of an Ancient Roman Heritage Tunnel: The Crypta Neapolitana
1 Introduction
2 Historical Background
3 Ground Conditions
4 Analysis of Static Conditions of the Crypta
5 Seismic Behaviour of the Crypta
6 Conclusions
References
Contributions of Numerical Modelling to the Stability Analysis of Old Masonry Tunnels
1 Introduction
2 Modelling Strategy
2.1 Tunnel Description
2.2 Masonry
2.3 Modelling Stages and Loading
2.4 Soil and Geotechnical Considerations
3 Results: Comparison with Limit Analysis
3.1 Horizontal Earth Pressure State
3.2 Bearing Capacity of the Masonry Tunnel
4 Results: Advantages and Downsides of the FEM Numerical Modelling
4.1 Bearing Capacity: Compressive Strength or Hinge Mechanism?
4.2 Impact of the Soil Properties
4.3 Mesh Sensitivity and Crack Depth
5 Rotational Capacity
6 Conclusions
References
Experimental and Numerical Analysis on the Effect of Joint Deformability and Imperfections on the Response of Masonry Arches Subject to Large Support Displacements
1 Introduction
2 Experimental Tests and Results
3 Numerical Model
4 Comparison Between Numerical and Experimental Results
4.1 Sensitivity Analysis and Comparison for α = 0°
4.2 Comparison for α Between 0° and 90°
5 Conclusions
References
Coupled Deformation and Structural Analysis for the Damage Assessment of Cultural Heritage Buildings: The Case of a Masonry Church Exposed to Slow-Moving Landslides
1 Introduction
2 Nostra Signora Della Bastia Sanctuary in Bastia
3 Damage and Deformations
3.1 Crack Pattern Survey
3.2 Deformation Analysis
4 Structural Analysis
5 Discussion and Conclusions
References
3D Non-periodic Masonry Texture Generation of Cultural Heritage Structures
1 Introduction
2 Masonry Texture Generator
3 Structural Analysis
3.1 Numerical Modelling
3.2 Numerical Results
4 Conclusions
References
Stability of Masonry Vaulted Tunnels in Purely Frictional and Cohesive-Frictional Grounds
1 Introduction
2 Problem Statement and Resolution Method
2.1 System Geometry
2.2 Loadings
2.3 Materials Strength
3 Yield Design Analytical Solutions for Unlined Openings in Cohesive-Frictional Grounds
3.1 “Roof” Failure Mechanism (a)
3.2 “Sides and Roof” Failure Mechanism (b)
3.3 Modelling in Optum CE
3.4 Results
4 Yield Design Analytical Solution for a Masonry Vault Subjected to a Punctual Load
4.1 Mechanism Description
4.2 Upper-Bound Solution
4.3 Results
5 Conclusions
References
Numerical Modelling and Structural Analysis of Armoury Museum at City Palace Udaipur, Rajasthan, India
1 Salehkhana – Armory Museum
1.1 Defect Mapping
1.2 Proposed Interventions
1.3 Numerical Modelling
1.4 Modelling Procedure
1.5 Loads and Boundary Conditions
1.6 Meshing
1.7 Constitutive Material Laws and Mechanical Properties
1.8 Results for Non-linear Analysis Before Intervention
1.9 Numerical Model vs. Defect Map
1.10 Non-linear Structural Analysis After Intervention
1.11 Numerical Modelling
1.12 Results for Non-linear Analysis After Intervention
1.13 Effectiveness of the Intervention Measures
2 Conclusions
References
Numerical Modeling of FRP-Strengthened Masonry Structures Using Equivalent Frame Models
1 Introduction
2 Numerical Modeling Approach
2.1 Increase in Flexural Capacity
2.2 Increase in Shear Capacity
3 Numerical Approach Application
4 Conclusions
References
The Evaluation of the Wooden Structural System in Hijazi Heritage Building via Heritage BIM
1 Introduction
1.1 The Architectural Characteristics of Hijazi Region
2 3D Reality Capture Technique in Heritage
2.1 Terrestrial Laser Scanning “TLS”
2.2 Terrestrial Laser Scanning Data Processing
2.3 Combining Laser Scanning and Digital Images
2.4 Heritage BIM
3 The Evaluation of the Wooden Structural System (the Method)
3.1 Visual Inspections
3.2 Terrestrial Laser Scanning Phase
3.3 HBIM for Structure Simulation
4 Conclusions
References
Modeling of Masonry Bridges in Presence of Damage: The Case Study of San Marcello Pistoiese Bridge
1 Introduction
2 Description of the Bridge
3 3D Modeling of the Structure
3.1 Damage Law Formulation
3.2 Modal Analysis
4 Nonlinear Analyses
4.1 Pushover Analysis
4.2 Time History Analysis
5 Conclusions
References
Macroelement Modelling Based on a Bouc – Wen Formulation with Degradation for the Dynamic Analysis of Masonry Walls
1 Introduction
2 Dynamic Force-Based Macroelement Formulation
2.1 Equivalent Frame Dynamic Formulation
2.2 Hinges Constitutive Law
3 Squat Panel Response
4 Conclusions
References
Structural Analysis of Historic Absorption Building in Turner Valley, Alberta
1 Introduction
2 Methodology
2.1 Geometrical Properties
2.2 Material Properties
2.3 Load Path
2.4 Connections
2.5 Finite Element Model
2.6 Validation
3 Results
4 Discussion
5 Conclusion
References
Sensibility Analysis of Traditional Span Frame
1 Instruction
2 Global Analysis of the Main Frame
2.1 Replica of the Historical Span
2.2 Static Load Test on Full Scale
2.3 Finite-Elements Modelling
3 Investigation of a Traditional Joint
3.1 Experimental Tests
3.2 Characterization of Joint Stiffnesses
3.3 Numerical Twins of the Joint
4 Conclusion
References
Structural Behaviour Assessment of the Anastylosis Reconstruction of the Ruins of Kfar Synagogue in Bar’am (Israel)
1 Introduction
1.1 The Bar’am National Park
1.2 The Current Remains of the Kfar Synagogue
2 Materials and Method
2.1 Distinct Element Model of the Kfar Synagogue
2.2 Material Characterization
2.3 Characterization of the Seismic Action
3 Results
3.1 Reassembled Configuration
3.2 Modal Analysis
3.3 Time-History Analysis
4 Conclusions
References
Discontinuous Dynamics of Santa Maria Annunziata Church Under Seismic Loading: A Non-smooth Contact Dynamics Approach
1 Introduction
2 The Case Study
3 Discrete Element Method: Non-smooth Contact Dynamics Method
4 Numerical Results
5 Conclusions
References
Dynamic Numerical Study of Traditional Dry-Stone Walls with YADE
1 Introduction
2 Wall Configuration
2.1 Longitudinal Section
2.2 Cross Section
3 Damage Level
4 Numerical Model
4.1 Mechanical Properties
4.2 Seismic Signal
5 Configuration Effect
5.1 Effect of Cross-Section
5.2 Effect of Longitudinal Configuration
6 Pseudo-Static Versus Dynamic Results
7 Conclusions
References
Material Characterization, Dynamic Identification and Mechanical Modelling of the Fifth Minaret of Herat, Afghanistan
1 Introduction
1.1 Short Historical Account
1.2 Geometry and Building Technology
2 Experimental Campaign
2.1 Laboratory Tests
2.2 On Site Tests
3 Operational Modal Analysis and Seismic Interferometry
4 Structural Investigation
5 Closing Remarks
References
FE Model Update of a Historic Masonry Building After Restoration. The Case of the Palacio Pereira in Santiago, Chile
1 Introduction
2 Palacio Pereira
2.1 Previous Work
2.2 Main Structural Interventions
3 Dynamic Identification
3.1 Experimental Campaign
3.2 Signal Processing
3.3 Experimental Modes
4 Model Update
4.1 Model Description
4.2 Modal Parameter Identification
4.3 Calibration Process
4.4 Results
5 Conclusions
References
Preliminary Assessment of the Resistance Characteristics and Dynamic Behavior of the San Francisco of Assis Church in Marcapata, Cusco-Perú
1 Introduction
2 Brief Historical Review
2.1 Marcapata Site
2.2 The San Francisco of Assis Church
3 On-Site Visual Inspection
3.1 Visual Inspection and Evaluation Criteria
3.2 Results and Conclusions of the Visual Inspection and Evaluation Criteria
4 Uniaxial Compression Tests
5 Operational Modal Analysis Tests and Calibration of the FE Model
5.1 OMA Tests
5.2 Calibration of the FE Model
6 Conclusions
References
Detailed Numerical Micro-modelling of Masonry TRM Reinforcements
1 Introduction
2 Materials
2.1 Test Setup
2.2 Tensile Tests
3 Numerical Modelling
3.1 Material Properties and Constitutive Equations
3.2 FEM Results
4 Conclusions
References
Parametric Study of In-Plane Collapse Mechanism of Panels with Different Masonry Geometric Bond Patterns
1 Introduction
1.1 Background
1.2 Objectives
2 Masonry Modelling Methodology
2.1 Limit Analysis Approach
3 Parametric Study
3.1 Masonry Wall with Different Loading Conditions
3.2 Masonry Wall with Different Geometric Bond Order
4 Summary and Conclusions
4.1 Parameters Affecting Stability of Masonry Structures
References
A P-Delta Discrete Macro-Element Model for Rocking Masonry Walls
1 Introduction
2 The P-Delta Discrete Macro-Element Method
3 Numerical Application
3.1 Static Nonlinear Simulations
3.2 Dynamic Nonlinear Application
4 Conclusions
References
Numerical Modelling and Structural Health Monitoring for Built Heritage Management: The Case of the Church of Santa Croce in Ravenna
1 Introduction
2 The Case Study: Church of Santa Croce in Ravenna
2.1 Knowledge Path
3 Structural Health Monitoring System
3.1 Real-Time Monitoring System
3.2 Dynamic Identification
4 Numerical Model
4.1 Eigenvalue Analysis
4.2 Nonlinear Analysis
5 Conclusions
References
Micro Modeling of Irregular Stone Masonry Walls Using Mathematical Programming
1 Introduction
2 Method
2.1 Rigid Block Modeling of Mortar-Joint Masonry Structures Using Mathematical Programming
2.2 Automated Model Generation from Images
3 Results
3.1 Material Properties and Reference Simulation
3.2 Influence of the Model Size
3.3 Influence of Various Typologies
4 Conclusion
References
Simulation of Brittle Collapse Mechanisms in Historical Masonry Using Sequentially Linear Analysis (SLA)
1 Introduction
2 Sequentially Linear Analysis: Methodology
3 Structural Masonry Benchmark
3.1 Experiment and Finite Element Model
3.2 SLA Results and Discussion
4 Historical Masonry Benchmark
4.1 Experiment and Finite Element Model
4.2 Results and Discussion
5 Conclusions
References
Numerical Study of Three-Point Bending Fracture Tests for Examination of Wood in Mode II
1 Introduction
2 Material and Methods
2.1 Finite Element Analysis
3 Results
3.1 Influence of Crack Length
3.2 Influence of Span-to-Height Ratio
3.3 Influence of Friction Coefficient
4 Conclusions
References
Thrust Layout Optimization for the Analysis of Historic Masonry Structures
1 Introduction
2 Thrust Layouts
3 Thrust Layout Optimisation (TLO)
4 Examples
4.1 Segmental Arch
4.2 Flying Buttress
4.3 Gothic Cathedral
5 Concluding Remarks
References
Vernacular Constructions: Conservation and Management
Double Quincha in Lima, Peru: Innovation, Adaptation and Comfort in the XVII–XIX Centuries
1 Framework
2 References to the Double Quincha in the Historic Center of the City of Lima
3 The Study
3.1 Constructive Analysis (Case Study 1)
3.2 Thermal Performance Analysis (Case Study 2)
4 Results and Discussion
5 Conclusions
References
Exploration on the Original Architecture of a Vernacular Workshop in East Sichuan Basin of China
1 Introduction
2 Social and Historical Context of the Site
3 Understanding of Information
3.1 Available Information
3.2 Priority of Acceptance
3.3 System of Length Measurement
4 Reasoning of Historic Appearance
4.1 Historic Appearance in 1990s
4.2 Historic Appearance Around 1900
5 Discussion and Conclusion
References
Management of Urban Areas by Preserving the Historic Roofscapes and Timber Traditional Building Technologies
1 Introduction
2 Interdisciplinary Assessment of Roofs-Roof Structures and Their Context
2.1 Historic Urban Development
2.2 Perception of Roofs
2.3 Roof Structure Types
3 Visual Perception, Roof Types, and Construction Details
3.1 Type 1
3.2 Type 2
3.3 Type 3
3.4 Type 4
3.5 Type 5
4 Discussion
5 Conclusion
References
Construction of Traditional Stepped Wells in Rajasthan (India)- Learning from the Past to Conserve for the Future
1 Background
2 Study Area- Rajasthan, India
2.1 Subterranean Structures in the Region
3 Stepped Well
3.1 Variety of Stepped Well in the Study Region
3.2 Construction of Stepped Wells
4 Common Issues with the Conservation of Stepped Well Structures
5 Learnings and Way Forward
References
From the Intervention of a Vernacular Heritage Structure in Oña – Ecuador, to the Improvement of the Cultural Landscape
1 Introduction
1.1 Objectives
1.2 Background
2 The San Francisco de Oña Neighborhood and the “Lara-Espinoza” House
2.1 Maintenance Campaign in the San Francisco Neighborhood
2.2 Methodology
2.3 Results and Discussions
3 Impact of the Campaign on the Urban Planning of the San Francisco De Oña Neighborhood
4 Conclusions
References
The Challenges of the Conservation of Earthen Sites in Seismic Areas
1 The Conservation of Earthen Sites
2 The GCI Vision for the Conservation of Earthen Sites
3 Research for the Conservation of Earthen Sites
4 Professional Exchange and Knowledge Sharing on the Conservation of Earthen Sites
5 Education and Capacity Building
6 Field Projects on the Conservation of Earthen Architecture
6.1 The SRP
7 The Challenges and Opportunities of the Conservation of Earthen Sites in Seismic Areas
References
Post-Earthquake Assessment and Possibilities for Management of Existing Masonry Buildings
The Identity Value of Vernacular Productive Architecture Knowledge, Recovery and Enhancement of the Val D’Agri Water Mills
1 Introduction
2 The Sustainable Vernacular Industry
3 The Role of Knowledge in Enhancement
4 Mills Heritage in Val D’Agri
5 Recovery and Enhancement Strategies
References
1 Introduction
2 Methods and Methodology
2.1 Research Works
3 Value of Information Analysis
4 Decision Problem
5 Conclusion
References
Analysis of Local Mechanical Characteristics and Global Structural Arch Behaviour of Cane (Arundo Donax)
1 Introduction
2 Historic and Modern Cane Construction
3 Material Characterisation
3.1 Moisture Content
3.2 Compression Parallel to the Grain
4 Experimental Campaign
4.1 Arch Construction
4.2 Experimental Procedure
4.3 Results
5 Conclusions and Recommendations
References
Interdisciplinary Projects and Case Studies
Restoration of Cast Iron and Wrought Iron Structures – Case Study: The Restoration of the Orangery at Hof ter Borght in Westmeerbeek (Belgium)
1 Introduction
2 Restoration of the Orangery of Castle “ter Borght”
3 Analysis of the Wrought Iron and Cast Iron Components of the Orangery
3.1 Characterization of Wrought Iron and Cast Iron Samples
3.2 Metallography and Material Testing
4 Structural Analysis and Design of Restoration Interventions
4.1 Structural Analysis
4.2 Reinforcement of Cast Iron Structure
4.3 Reinforcement of Connections
5 Conclusions
References
Comprehensive Study of Brody Bastion Castle
1 Introduction
2 Method
2.1 History of Bastion Castle in Brody
2.2 The Composition of the Complex
2.3 The Composition of the Fortified Ensemble of Brody in the Townscape
2.4 Space Patterns Morphological Analysis
3 Discussions and Conclusions
References
Rehabilitation of Santini Water System in the Plasy Monastery
1 Damp Removal from Historic Buildings
2 Convent of Plasy Monastery
2.1 Convent Foundation Construction
2.2 Description of the Historical Water and Ventilation System of the Convent Building
2.3 Inappropriate Interventions in the Past
2.4 Partial Restoration of the Pressurised Water System
3 Description of Measurements
3.1 Chemical Water Analysis, Experimental Installation of a New Water Source
3.2 Tracking Test (Staining Test)
3.3 Effect of Relative Humidity and Air Temperature
4 Conclusion
References
Restoration of the Moorish Pavilion and Architectural Complex of Manguinhos, in Rio de Janeiro, Brazil
1 Introduction
2 A Brief Historic and Architectural Analysis
3 Transformation Through Time
4 Conclusions
References
Accuracy of Past Analysis: The Steel Frame of the Gillender Building
1 Introduction
2 The Gillender Building
3 Analysis of Tall Frame Buildings in the 1890s
4 Comparative Analysis of the Gillender Building
4.1 General Criteria
4.2 Column End Conditions and Effective Length
4.3 Interaction Between Axial and Bending Loads
4.4 Frame Analysis
4.5 Empirical Loading
4.6 Empirical Bracing
5 Conclusions
References
Two Looks Back to Move Forward. Today’s Evaluation of Opposite Approaches of Concrete Repair in Heritage Preservation
1 The Raw Surface of Concrete Heritage
2 Antoniuskirche Basel
2.1 Renovation or Restoration?
2.2 Realized Options: Localized Repair, Protective Coating, Full-Surface Repair
3 Neue Liederhalle Stuttgart
3.1 Evidence for Minimal Repair
3.2 Aesthetic Optimization as Iterative Process
4 Documentation and Comparison: Photographic Survey and Color Measurement
5 Long-Term Consequences: Reparability, Reversibility, Monitoring
References
The Conservation and Rehabilitation of Listed Buildings in Line with the Relevant Regulations and Community Needs
1 Introduction
2 Description of the Existing Listed Buildings
3 Description of Prevailing Condition
4 The Solution
5 Re-writing the Brief
6 Conclusion
References
Textile-Reinforced Alkali-Activated Mortar for In-Plane Shear Capacity Improvement of Masonry Before and After High Temperature Exposure
1 Introduction
2 Materials and Methods
3 Results and Discussion
3.1 Results of Fire Exposure
3.2 Mechanical Testing Results
4 Conclusions
References
Dilemmas in Upgrade and Use of Railways Heritage: Approaches and Reflections on Structural Interventions
1 Introduction
2 Methodology
3 Railways as Heritage
4 Rhaetian Railway in the Albula/Bernina Landscapes World Heritage Property
4.1 History
4.2 Changing Norms
4.3 Tunnels
5 The Demolition for Reconstruction of the Historic Grzegórzecki Viaduct, Kraków, Poland
5.1 History
5.2 Demolition and Reconstruction
6 Assessing Alternatives
7 Conclusions
References
FRPU Composite Protection of Masonry with Reversible Mineral Interlayer
1 Introduction
2 Experimental Plan and Test Setup
2.1 Materials and Specimen Preparation
2.2 Test Setup
3 Results of the Tests
4 Discussion
5 Conclusions
References
Studies for Sighișoara Citadel Conservation –Ensemble Listed as World Heritage Site
1 Introduction
1.1 Background
1.2 Historical Data and Components
1.3 Argument
2 Tower Presentation
2.1 Geometrical Data
2.2 Tower Load-Bearing Structures. Heritage Value Assessment
2.3 Structural Diagnosis. Non-destructive and Minimally Destructive Tests and Analyses
2.4 Conclusions and Inclusion of the Structures Under Seismic Risk
2.5 Structure Heritage Values
3 Tower Analysis
4 Conclusion
References
Performance Evaluation of Patch Repairs on Historic Concrete Structures (PEPS): Preliminary Results from Two English Case Studies
1 Introduction
2 Case Study I: ENG05
2.1 Background
2.2 Aesthetic Performance
2.3 Technical Performance
3 Case Study II: ENG04
3.1 Backgrounds
3.2 Aesthetic Performance
3.3 Technical Performance
4 Conclusion
References
Base Isolation Technology for Rocking Statues: A Simplified Design Procedure
1 Introduction
2 Review of the Isolated Rigid Rocking Block Model
3 Design Procedure
3.1 Steps of the NRDBD Procedure
4 Validation
4.1 Validation of the NRDBD Procedure
5 Conclusions
References
Tool – Object – Fragment: The Afterlife of Physical Measurement Models
1 Introduction
1.1 The Purpose of Using Measurement Models
1.2 Model Building and Testing Facilities
2 The Olympic Roofs in Munich
2.1 Project
2.2 Model Building and Testing
2.3 Preservation and Condition
2.4 Digital Twins
3 The Sports and Congress Hall in Rostock-Südstadt
3.1 Project
3.2 Model Building and Testing
3.3 Preservation and Condition
3.4 Digital Twin
4 Conclusion
References
Experimental Activities and Structural Analyses for the Restoration and Re-use of the Lazzaretto Vecchio Island in Venice
1 Foreword
2 The Historical Context: The Lazzaretto Island
2.1 History of the Lazaretto Architectural Complex
3 The On-Site Investigation Campaigns
3.1 The Investigation Campaign
3.2 Tests on Timber
3.3 Tests on Masonry & Stone
4 The Structural Analysis
4.1 Introduction
4.2 Seismic & Static Analysis
4.3 Strengthening Interventions Preliminary Design
5 Conclusions
References
Cosmic Rays Pavilion: Candela’s First Experimental Hypars - Analysis of Current
1 Introduction
2 Materials and Methods
3 Analysis and Discussion of Results
4 Conclusions
References
Interventions on Roof Structures as Part of Conservation of Historic Buildings with Local Value
1 Introduction
2 Brief Presentation of the Structure and Its Shortcomings
3 Interventions Approach
4 Structural Analysis
4.1 Current State Analysis
4.2 Analysis of the Intervention Versions
5 Conclusions
References
Is Holism Needed in the Diagnosis of Historical Structures?
1 Introduction
2 Holism in the Diagnosis of Historical Objects
3 Objects
3.1 A Turn-of-The-Century Brick Building in Torun, Chopina Street
3.2 Historic Half-Timbered Building from the Mid-19th Century in Toruń on Bydgoska Street Where a Confluence of Circumstances Unfavorable to the Object Occurred
3.3 Late Gothic Church from the Turn of the 15th and 16th Centuries in Krzynowłoga
3.4 A 1970s Reinforced Concrete Building Constructed Under the Realities of Socialism in Poland
4 Conclusion
References
Exploring AI and Related Technologies in Understanding Cultural Heritage
1 Introduction
2 Literature Survey
3 Methodology
4 Result and Discussion
4.1 Few Test Cases
4.2 Limitation
5 Future Scope
6 Conclusion
References
Application of the Electrical Resistivity Tomography Technique in the Assessment of Historical Buildings in the State of Aguascalientes, Mexico
1 Introduction
1.1 Study Case
1.2 Electrical Resistivity Tomography as Non-destructive Test for Evaluating Historic Buildings
1.3 Research Objectives
2 Materials Y Methods
3 Results and Discussions
3.1 Case 1. Temple “Inmaculada Concepción”
3.2 Case 2. Terán House
4 Conclusions
References
Impact of Environmental Conditions on Rammed Earth Heritage Buildings Seismic Performance
1 Introduction
2 Walls, Materials, Methods and Models
3 Dynamic Simulation and Walls Seismic Performance
4 Conclusions
References
Conservation of Modernism Movement Concrete: Tackling the Compatibility Issue of Retrofit Solutions with the Degraded Substrate
1 Introduction
1.1 Modernism Concrete: Exposure to Aggressive Chloride Environment
1.2 Retrofit Interventions
1.3 Research Objectives
2 Materials and Methods
2.1 Concrete Casting
2.2 Four-Point Bending Cyclic Testing
2.3 Chloride Ingress
2.4 Retrofit Casting
2.5 Inspection Methodology
3 Results
3.1 Test Design and Triggering of Chloride Exposure
3.2 Mechanical Performance After Retrofit
3.3 Interfacial Debonding Phenomena
4 Conclusions
References
Flat Roofs Characterization in Barcelona's Historic Center
1 Introduction
2 Objectives
3 Methodology
4 Results
4.1 Constructive Characterisation
4.2 State of Conservation and Most Frequent Interventions
5 Conclusions and Recommendations
References
Test of Authenticity in the Evaluation of Historic Structures. Theory vs Practice
1 Introduction, Context and Aims
1.1 The Concept of Authenticity; Its Present-Day Relevance
1.2 Authenticity in the International Documents –– Theoretical Issues
1.3 Nara Document on Authenticity and Post-nara Developments
2 Research Focus and Goals
2.1 Research Site
2.2 Definition of Value Indicators
3 Methods of Research
3.1 Data Collection and Sample
3.2 Application – Test of Authenticity
3.3 Limitations
4 Research Results, Recommendation for Theory and Practice
4.1 Discussion of the Research Outcomes
4.2 Recommendations for the Implementation the “Test of Authenticity” in the Practice of Built Heritage Management
References
Vulnerability and Risk Assessment in Natural Hazards and Climate Change
Temporal Variation of Charring Depth of the Wood-Frame Walls in Fire
1 Introduction
2 Research Method
2.1 Preliminary Test Specimens and Heating Conditions
3 Tested Wood Studs and Heat Exposure Experiments
4 Prediction of the Charring Depth of the Wood Stud Specimens
5 Results and Discussion
6 Conclusion
References
Flood Risk Assessment of Traditional Adobe Buildings: Analysis of Case Studies in the River Ebro Basin, Spain
1 Introduction
2 Risk Assessment Methodology
3 Results and Discussion
4 Conclusions
References
The DALIH Database for Recording Disaster Damage and Loss Data in Cultural Heritage
1 Introduction
2 Why Information About Disaster Impacts in Cultural Heritage Is Important?
3 Overview of the DALIH Database for Cultural Heritage
4 Case Study Events Available in DALIH and Analyses that Can Be Performed
5 Conclusion
References
Vulnerability Assessment of Historic Areas to Heat Waves. The Case Study of Bilbao
1 Introduction
2 Purpose and Framework. MIVES and GIS
3 Categorization Method and Decision-Making Tree
3.1 Vulnerability of the Buildings and Public Spaces. Decision Making Tree
3.2 Categorization Process
4 Results for the Bilbao Historic Area
5 Discussion of the Results and Conclusions
References
Development of Refined Data-Driven Stochastic Subspace System Identification for Buildings and Bridges
1 Introduction
2 Mode-by-Mode SSI-DATA Methods
2.1 Mode-by-Mode Method 1
2.2 Mode-by-Mode Method 2
2.3 Mode-by-Mode Method 3
2.4 Mode-by-Mode Method 4
2.5 Implementation of Mode-by-Mode System Identification
3 Numerical Study of Eight-Story Steel-Frame Building
4 Experimental Study of Chillon Viaduct
5 Conclusions
References
A Hybrid Approach for the Assessment of Flood Vulnerability of Historic Constructions and Their Contents
1 Introduction
2 Flood Vulnerability Assessment Method
2.1 Baseline Vulnerability Curve (VC())
2.2 Flood Vulnerability Indicators
3 Application of the Method
3.1 Estimation of the Flood Baseline Vulnerability Curve (VC())
3.2 Calculation of the Flood Vulnerability Index (VIFL)
3.3 Combination of the Baseline Vulnerability Curve with the Vulnerability Index
4 Conclusion
References
Uplift Vulnerability Analysis of Roofing Tiles for Traditional Chinese Timber Buildings Under Strong Wind
1 Introduction
2 Prototype Building
3 Methodology
3.1 CFD Simulation for Determining Wind Loads
3.2 Resistance Calculation
3.3 Simulation of the Failure Probability of Tiles
4 Results and Discussion
5 Conclusion
References
Vulnerability Assessment of Historical Churches in Banat Seismic Region, Romania
1 Introduction
1.1 Opportunity of the Research Theme
1.2 Seismicity of the Area
2 Case Study Churches
2.1 Architectural and Structural System
2.2 Decay
3 Vulnerability Assessment
3.1 Empiric Vulnerability Assessment
3.2 Vulnerability Assessment According to Italian Methodology
4 Conclusion
References
Monitoring the Combined Effects of Induced Earthquakes and Climate Change on a Heritage Building in Groningen
1 Introduction
2 Fraeylemaborg in North Netherlands
3 Induced Earthquakes Affecting the Structure
4 Climate Change Effects and Their Relevance to Damage
5 Conclusions
References
GIS Methodologies for the Management of Seismic Risk and the Damage Prevention on Masonry-Built Heritage
1 Introduction
2 The Empirical Approach
3 The Advantages of the GIS
3.1 GIS as a Post-Event Tool: The Relation Between Building Features, Damage and Seismic Actions
3.2 GIS as a Prognosis/Proactive Tool of the Seismic Risk on Masonry Built Heritage
4 Two Possible Procedural Applications
4.1 Post-Event Database: Protruding Elements and Castles of Central Italy
4.2 Prognostic Database: Fortified Architecture in Emilia (North Italy)
5 Conclusions
References
Towards a Vulnerability Assessment of Historic Timber Barns in the U.S. Midwest Under Severe Windstorms
1 Introduction
2 Methodology
3 Results
3.1 Structural Characteristics
3.2 Condition
3.3 Reflections on In-Situ Assessment Methodology
3.4 Discussion of Key Outcomes and Next Steps
4 Conclusions
References
Climate Protection Versus Building Heritage Preservation - Influence of Renewable Energy Installations on Historical Buildings
1 Introduction
2 Research Methodology
3 Renewable Energy Solutions
3.1 Legal and Political Background in Europe
3.2 Legal and Political Background in Germany
4 Building Heritage Protection Requirements
5 Conflict Between Environmental Interests and Building Heritage Protection
5.1 Court Decisions Regarding Solar Energy
5.2 Court Arguments Regarding Wind Energy Turbines
5.3 Future Development
6 Conclusions
References
Identification of Gediminas Hill Possible Landslides Formations Zones
1 Introduction
2 Landslides History
3 Numerical Model Overview
4 Past Landslides and Numerically Predicted Ones
5 Conclusions
References
Coupled Multi-risk Mitigation in Historical Urban Outdoor Built Environment: Preliminary Strategies Evaluation Through Typological Scenarios
1 Introduction
2 Phases and Methods
2.1 Model Definition and Implementation
2.2 BET Scenarios for Simulations
2.3 Analysis and Comparisons Criteria
3 Results and Discussion
4 Conclusions and Remarks
References
Optimizing Shelters and Evacuation Paths Against Flood in Historic Urban Built Environments
1 Introduction
2 Methodology
2.1 Typological HUBE Definition
2.2 Evacuation Optimization Through Integer Linear Programming
2.3 Selection of the Best Evacuation Solution
3 Results
4 Discussion
5 Conclusions
Appendix A
References
Challenges in the Preventive Maintenance of Early 20th-Century Reinforced Concrete Architectural Sculptures
1 Introduction
2 Concrete Degradation and Other Factors to Ponder in Conservation Interventions in Architectural Sculptures
2.1 The Proposed Intervention Index ITI
2.2 Maintenance Plan Indicators
3 Case Study: The São João National Theatre
3.1 Application of the ITI to São João National Theatre
3.2 Assessment of the Maintenance Plan Indicators
4 Conclusions
References
Vulnerability Assessment: Comparison of Empirical and Analytical Approach – A Case Study in Zagreb, Croatia
1 Introduction
2 Empirical Approach
3 Analytical Approach
4 Discussion and Conclusion
References
Deep Learning Modelling of Earthquake Damage Data for Identification of Patterns of Damage in Heritage Structures
1 Introduction
2 The Data
2.1 The September 2017 Earthquakes
2.2 Observed Earthquake Damage of Historical Churches in Mexico – II-UNAM Database.
2.3 II-UNAM Database
3 Information Types
3.1 Emergency Shoring and Restoration Techniques
4 Objectives
4.1 Benefits Of ML for Earthquake Data Analysis
5 Methodology
5.1 Data Modelling
6 Results and Outcomes
7 Conclusions
References
Seismic Vulnerability Assessment of Churches Through an Expeditive Evaluation Form: Application to a Representative Sample from Central Italy
1 Introduction
2 Structure of the Machro Form
3 Methodology for Large-Scale Vulnerability Assessment
4 Analyzed Sample of Churches
4.1 Anti-Seismic Devices
4.2 Fragility Indicators
4.3 Seismic Vulnerability Assessment: from the Building Scale to the Macro-Regional Scale
5 Conclusions
References
Vulnerability Assessment of Masonry Constructions Towards Rockfall Hazard
1 Introduction
2 Experimental Design
3 Full-Scale Test Results and Discussion
4 Numerical Simulations and Preliminary Validations
4.1 Discrete DEM Approach
4.2 Continuous FEM Approach
4.3 Preliminary Validations and Failure Mode Characterisation
5 Conclusion
References
Simplified Vulnerability Assessment of Masonry Bell Towers
1 Introduction
2 The Vulnerability Assessment Method for Masonry Bell Towers
3 Empirical Fragility Curves
4 Application to Neapolitan Bell Towers
4.1 Description of the Samples
4.2 Construction of the Empirical and Parametric Fragility Curves
5 Conclusions
References
Author Index
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RILEM Bookseries
Yohei Endo Toshikazu Hanazato Editors
Structural Analysis of Historical Constructions SAHC 2023 - Volume 2
Structural Analysis of Historical Constructions
RILEM Bookseries
Volume 46
RILEM, The International Union of Laboratories and Experts in Construction Materials, Systems and Structures, founded in 1947, is a non-governmental scientific association whose goal is to contribute to progress in the construction sciences, techniques and industries, essentially by means of the communication it fosters between research and practice. RILEM’s focus is on construction materials and their use in building and civil engineering structures, covering all phases of the building process from manufacture to use and recycling of materials. More information on RILEM and its previous publications can be found on www.RILEM.net. Indexed in SCOPUS, Google Scholar and SpringerLink.
Yohei Endo · Toshikazu Hanazato Editors
Structural Analysis of Historical Constructions SAHC 2023 - Volume 2
Editors Yohei Endo Department of Architecture Shinshu University Nagano, Japan
Toshikazu Hanazato Department of Architecture Mie University Tsu City, Mie, Japan
ISSN 2211-0844 ISSN 2211-0852 (electronic) RILEM Bookseries ISBN 978-3-031-39449-2 ISBN 978-3-031-39450-8 (eBook) https://doi.org/10.1007/978-3-031-39450-8 © RILEM 2024 Chapters “The Challenges of the Conservation of Earthen Sites in Seismic Areas” and “Performance Evaluation of Patch Repairs on Historic Concrete Structures (PEPS): Preliminary Results from Two English Case Studies” are licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativec ommons.org/licenses/by/4.0/). For further details see license information in the chapters. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Permission for use must always be obtained from the owner of the copyright: RILEM. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
The thirteenth edition of the International Conference on Structural Analysis of Historical Constructions (SAHC) was held in Kyoto, Japan, during 11–15 September 2023. Owing to the success of the past editions including the celebration of the 25th anniversary in Barcelona in 2021, the SAHC conferences have become one of the finest exceptional recurrent events for scientific discussion, communication and professional networking. In recent decades, the conservation and study of historical structures has shown remarkable technological and scientific advances. The conservation of heritage structures is performed on the basis of advanced non-destructive testing techniques, effective monitoring systems, rigorous numerical analysis and comprehensive intervention schemes. Therefore, the study of historical structures requires comprehensive international scientific collaboration as conservation practice faces problems at different scales such as materials, structures and surroundings. The slogan of the SAHC 2023 was “Heritage conservation across boundaries”. This conference aimed to provide opportunities for the better understanding of one another across their cultural boundaries through communication and interaction. For this reason, a variety of thematic sessions were organised including one on the impact of the 2023 Turkey–Syria earthquake sequence on the historic built environment. Participants from diverse backgrounds discussed and shared novel concepts, technologies and practice on the study, conservation and management of historical constructions in this far-east island country. The SAHC 2023 conference owed huge gratitude to the scientific committee and reviewer panel for their enormous contributions throughout the reviewing process. We also would like to acknowledge sponsors, supporting organisations and the advisory committee for their moral and financial supports. Above all, the conference was never possible without the contributions of the authors who submitted exceptionally valuable papers. We also would like to allude to the hard work of the local committee formed by the students of Shinshu University. The success of the conference owed much to their dedication and devotion. The SAHC conferences will continue to serve as a platform for engineers, architects and all professionals to share state-of-the-art knowledge and latest involvement in principles, technologies and practice for heritage conservation across the world. Yohei Endo Conference Chair
Organisation
Organising Committee Yohei Endo Toshikazu Hanazato
Shinshu University Mie University
Advisory Committee Paulo Lourenço Claudio Modena Pere Roca
University of Minho University of Padua Polytechnic University of Catalonia
Scientific Committee Rafael Aguilar Alessandra Aprile Oriol Arnau Görün Arun Hiram Badillo Rita Bento Katrin Beyer Rubén Boroschek Lam Angus Chi Chiu Eva Coïsson Gianfranco de Matteis Matthew DeJong Tasos Drougkas Milos Drdácký Khalid El Harrouni Ahmed Elyamani Antonio Formisano Dora Foti Enrico Garbin Leire Garmendia Arrieta Marcela Hurtado Jason Ingham Wolfram Jager Stephen J. Kelley Debra Laefer
Pontifical Catholic University of Peru University of Ferrara National Autonomous University of Mexico Yildiz Technical University Autonomous University of Zacatecas University of Lisbon Swiss Federal Institute of Technology in Lausanne University of Chile University of Macau University of Parma University of Campania University of California at Berkeley Polytechnic University of Catalonia Institute of Theoretical and Applied Mechanics National School of Architecture, Rabat, Morocco Cairo University University of Naples Federico II University of Bari University of Padua University of the Basque Country Federico Santa María Technical University University of Auckland Technical University Dresden SJK Inc. New York University
viii
Organisation
Sergio Lagomarsino Alessandra Marini Arun Menon Climent Molins Daniel Oliveira Luca Pelà Fernando Peña Andrea Penna Maurizio Piazza Mariapaola Riggio Jan Rots Antonella Saisi Savvas Saloustros Vasilis Sarhosis Cristián Sandoval Nigel Shrive Marek Sklodowski Pierre Smars Luigi Sorrentino Nicola Tarque Daniel Torrealva Maria Rosa Valluzzi Koenraad Van Balen Humberto Varum Els Verstrynge Elizabeth Vintzileou Xuan Wang
University of Genova University of Bergamo Indian Institute of Technology Madras Polytechnic University of Catalonia University of Minho Polytechnic University of Catalonia National Autonomous University of Mexico University of Pavia University of Trento Oregon State University Delft University of Technology Polytechnic University of Milan Federal Institute of Technology in Lausanne University of Leeds Pontifical Catholic University of Chile University of Calgary Institute of Fundamental Technological Research National Yunlin University of Science and Technology Sapienza University of Rome Universidad Politécnica de Madrid, Pontifical Catholic University of Peru Pontifical Catholic University of Peru University of Padua KU Leuven University of Porto KU Leuven National Technical University of Athens Ningbo University
Reviewer Panel Giuliana Cardani Rosario Ceravolo Sara Dimovska Chiara Ferrero Donald Friedman Lluis Gil Belén Jiménez Chandra Kiran Kawan Nuno Mendes Camilla Mileto
Androniki Miltiadou Marius Mosoarca Tom Morrison Bartolomeo Pantò Athanasios Pappas Bora Pulatsu Enrico Quagliarini Luisa Rovero Fernando Vegas
Contents
Protection of Heritage Structures in Japan and Southeast Asia Structural Characteristics of Carian Rock-Cut Tombs: The Effect of Discrepancy Between the Connecting Part and the Back Passage . . . . . . . . . . Akisumi Takeda The Authenticity and Integrity of the Soil and the Foundation of the Heritage Structure of Bayon Temple, Angkor . . . . . . . . . . . . . . . . . . . . . . . Yoshinori Iwasaki, Mitsuharu Fukuda, Mitsumasa Ishizuka, Ichita Shimoda, Robert McCarthy, Vanna Ly, and Takeshi Nakagawa Restoration of Architectural Stone Heritage Damaged by 2011 Great East Japan Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toshikazu Hanazato, Hayato Suzuki, Hideaki Takahashi, Shigenori Kita, and Tomoaki Suzuki
3
12
26
Study on Evaluation Method of Reinforcement Effect of Dry Masonry in Historical Monuments Applying DDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Yamada, R. Hashimoto, T. Koyama, M. Fukuda, and Y. Iwasaki
41
Modern Japanese Pampas Grass Harvest Methods for Thatched Roof Houses Based on Case Studies of Self-procurement of Grasses in Shikoku . . . . Shohei Tsumura, Miyako Kamatoko, and Naoki Kakehashi
51
Estimating the Structural Characteristics of Historic Armenian Church Buildings and Examining Their Strengthening Applications . . . . . . . . . . . . . . . . Atsushi Mutoh, Yasuhito Fujita, Hitoshi Morikawa, Shojiro Motoyui, and Shiro Sasano Vibration Characteristics of Traditional Masonry Buildings in the Kingdom of Bhutan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miyamoto Mitsuhiro, Aoki Takayoshi, Hamaoka Miku, Hayashi Riho, Kunzang Tenzin, Kshitij C. Shrestha, Takahashi Noriyuki, and Zhang Jingyao The Introduction and Disappearance of Mixed-Structure Buildings Made from Brick Walls and RC Slabs Between 1900 to 1926 in Japan . . . . . . . Shigeyasu Ikegami
63
75
83
x
Contents
Snow Load Effect to Vibration Characteristics of Japanese Traditional Wooden Main Temple Building and Three-Story Pagoda Based on Ambient Vibration and Earthquake Observation Records . . . . . . . . . . . . . . . . K. Mitsji, T. Hanazato, and Y. Niitsu Proposal of Strength Estimation Formula of Wall Clays Using Multiple Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kimiko Miyoshi, Yoichi Hayasaki, Naoya Syojo, and Yoshimitsu Ohashi Numerical Investigation of the Properties of Unreinforced and Reinforced Nepalese Historical Brick Masonry Structures . . . . . . . . . . . . . . Chhabi Mishra, Kentaro Yamaguchi, Tingyun Jing, Toshikazu Hanazato, Yohei Endo, and Manjip Shakya
101
112
125
Numerical Modeling and Structural Analysis Impact Loading Analysis of an Earthen Masonry Structure Using Finite Element Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Demiana Tse, João M. Pereira, and Paulo B. Lourenço
143
Reverse Engineering for the Structural Analysis of Heritage Constructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Massafra, D. Prati, and R. Gulli
156
Lateral Capacity Assessment of the Main Pyramid of Huaca de la Luna (Peru) Using 2D Finite Element Macroblock Model . . . . . . . . . . . . . . . . . . . . . . . Cristiana Riccio, Anna Remus, Selman Tezcan, Luis C. Silva, Gabriele Milani, and Renato Perucchio Evaluation of Microscale Behavior and Structural Deformation for Yeonji Wall in Gongsanseong Fortress of the Sixth Century in Korea . . . . . . Jun Hyoung Park, Gwan Su Lee, Seok Tae Park, and Chan Hee Lee Stability Interpretation for the Tomb of King Muryeong and the Royal Tombs in Baekje Kingdom of Ancient Korea Using 3D Deviation Analysis and Microscale Behavior Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . Il Kyu Choi, Hye Ri Yang, and Chan Hee Lee
170
184
195
Structural Analysis of Constructions by Means of Automatic Crack Parameterisation Based on Photographs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Friedrich Romstedt, Sebastian Vetter, and Gunnar Siedler
203
Simplified Assessment of the in-Plane Seismic Response of Old Brick Masonry Building Aggregates Using DE Macro-Crack Networks . . . . . . . . . . . . Zinan Zhang, Lucy Davis, and Daniele Malomo
217
Contents
Accurate and Efficient 2D Modelling of Historical Masonry Buildings Subjected to Settlements in Comparison to 3D Approaches . . . . . . . . . . . . . . . . Alfonso Prosperi, Michele Longo, Paul A. Korswagen, Mandy Korff, and Jan G. Rots
xi
232
Estimation of Load Multipliers in Overturning Mechanisms with Frictional Resistances: Comparison Among Literature Approaches . . . . . . Tatiana Zanni, Luca Sbrogiò, Ylenia Saretta, and Maria Rosa Valluzzi
245
On the Use of Finite Element Method and LEFM to Assess Bearing Capacity of Historic Notched Timber Beams at Arbitrary Location . . . . . . . . . . Jiˇrí Kunecký, Georg Hochreiner, and Martin Hataj
259
Influence of Geometric Ratios on the Structural Behaviour of Historic Timber Roof Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alexandra I. Keller and Marius Mosoarca
268
The Effect of a Top Flexible Restraint on a Two-Bodies Vertical Spanning Wall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Giacomo Destro Bisol, S. Prajapati, L. Sorrentino, and O. AlShawa
278
Investigation of the Structural Performance of Masonry Wharf Cellars in Utrecht Using the Distinct Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yopi Oktiovan, Anjali Mehrotra, Francesco Messali, and Jan Rots
287
Analytical Model of Bracket Set Frame in Traditional Chinese Timber Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qingshan Yang, Ke Liu, and Pan Yu
301
Stability Assessment of an Ancient Roman Heritage Tunnel: The Crypta Neapolitana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emilio Bilotta, Raoul Paolo Conte, Fausto Somma, and Alessandro Flora Contributions of Numerical Modelling to the Stability Analysis of Old Masonry Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . O. Moreno Regan Experimental and Numerical Analysis on the Effect of Joint Deformability and Imperfections on the Response of Masonry Arches Subject to Large Support Displacements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chiara Ferrero, Chiara Calderini, and Pere Roca
312
323
339
xii
Contents
Coupled Deformation and Structural Analysis for the Damage Assessment of Cultural Heritage Buildings: The Case of a Masonry Church Exposed to Slow-Moving Landslides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chiara Ferrero, Giulio Lucio Sergio Sacco, Marco Ferrero, Carlo Battini, and Chiara Calderini
352
3D Non-periodic Masonry Texture Generation of Cultural Heritage Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Pereira, A. M. D’Altri, S. de Miranda, and B. Glisic
366
Stability of Masonry Vaulted Tunnels in Purely Frictional and Cohesive-Frictional Grounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Menil, A.-S. Colas, D. Subrin, and M. Bost
374
Numerical Modelling and Structural Analysis of Armoury Museum at City Palace Udaipur, Rajasthan, India . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Omkar S. Adhikari and João M. Pereira
387
Numerical Modeling of FRP-Strengthened Masonry Structures Using Equivalent Frame Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ivana Božuli´c, Francesco Vanin, and Katrin Beyer
400
The Evaluation of the Wooden Structural System in Hijazi Heritage Building via Heritage BIM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ahmad Baik
407
Modeling of Masonry Bridges in Presence of Damage: The Case Study of San Marcello Pistoiese Bridge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Daniela Addessi, Domenico Liberatore, and Andrea Battisti
421
Macroelement Modelling Based on a Bouc – Wen Formulation with Degradation for the Dynamic Analysis of Masonry Walls . . . . . . . . . . . . . . Domenico Liberatore, Daniela Addessi, and Alessandra Paoloni
433
Structural Analysis of Historic Absorption Building in Turner Valley, Alberta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emina Burzic, George Iskander, Neil A. Duncan, and Nigel G. Shrive
445
Sensibility Analysis of Traditional Span Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . Lawrence Kauffmann, Jean-Luc Coureau, Alain Cointe, and Philippe Galimard
458
Contents
Structural Behaviour Assessment of the Anastylosis Reconstruction of the Ruins of Kfar Synagogue in Bar’am (Israel) . . . . . . . . . . . . . . . . . . . . . . . . Yaacov Schaffer, Raffaele Italia, Aharon Levi, Meir Ronen, Matteo Salvalaggio, Maria Rosa Valluzzi, Marco Mocellini, Sonia Bellin, and Filippo Casarin Discontinuous Dynamics of Santa Maria Annunziata Church Under Seismic Loading: A Non-smooth Contact Dynamics Approach . . . . . . . . . . . . . . Mattia Schiavoni, Gianluca Standoli, Francesca Bianconi, Ersilia Giordano, and Francesco Clementi Dynamic Numerical Study of Traditional Dry-Stone Walls with YADE . . . . . . . Paola Ita, Sandra Santa-Cruz, Dominique Daudon, and Nicola Tarque Material Characterization, Dynamic Identification and Mechanical Modelling of the Fifth Minaret of Herat, Afghanistan . . . . . . . . . . . . . . . . . . . . . . G. Misseri, G. Lacanna, R. Grazzini, F. Fratini, A. Boostani, and L. Rovero FE Model Update of a Historic Masonry Building After Restoration. The Case of the Palacio Pereira in Santiago, Chile . . . . . . . . . . . . . . . . . . . . . . . . María I. Valenzuela, Wilson Torres, Cristián Sandoval, and Diego Lopez-Garcia Preliminary Assessment of the Resistance Characteristics and Dynamic Behavior of the San Francisco of Assis Church in Marcapata, Cusco-Perú . . . . Mijail Montesinos, Julio Rojas-Bravo, Matt Valer, and Susan Choquemaqui Detailed Numerical Micro-modelling of Masonry TRM Reinforcements . . . . . . La Scala Armando, Javier Pereiro-Barceló, Dora Foti, and Salvador Ivorra Parametric Study of In-Plane Collapse Mechanism of Panels with Different Masonry Geometric Bond Patterns . . . . . . . . . . . . . . . . . . . . . . . . . Hoi Lon Wan and Chi Chiu Lam A P-Delta Discrete Macro-Element Model for Rocking Masonry Walls . . . . . . . Valeria Cusmano, Bartolomeo Pantò, Davide Rapicavoli, and Ivo Caliò Numerical Modelling and Structural Health Monitoring for Built Heritage Management: The Case of the Church of Santa Croce in Ravenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Francesca Ferretti, Chiara Monteferrante, and Claudio Mazzotti
xiii
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484
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xiv
Contents
Micro Modeling of Irregular Stone Masonry Walls Using Mathematical Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qianqing Wang, Ketson Roberto Maximiano dos Santos, and Katrin Beyer
591
Simulation of Brittle Collapse Mechanisms in Historical Masonry Using Sequentially Linear Analysis (SLA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manimaran Pari and Jan Rots
603
Numerical Study of Three-Point Bending Fracture Tests for Examination of Wood in Mode II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Václav Sebera and Jiˇrí Kunecký
617
Thrust Layout Optimization for the Analysis of Historic Masonry Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isuru Nanayakkara, Andrew Liew, and Matthew Gilbert
626
Vernacular Constructions: Conservation and Management Double Quincha in Lima, Peru: Innovation, Adaptation and Comfort in the XVII–XIX Centuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Scaletti, T. Montoya, and M. Wieser
641
Exploration on the Original Architecture of a Vernacular Workshop in East Sichuan Basin of China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bowen Qiu, Chi Jin, Lingyan Xu, Yongkang Cao, and Qian Du
655
Management of Urban Areas by Preserving the Historic Roofscapes and Timber Traditional Building Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emanuel I. Tamas and Alexandra I. Keller
669
Construction of Traditional Stepped Wells in Rajasthan (India)Learning from the Past to Conserve for the Future . . . . . . . . . . . . . . . . . . . . . . . . Deepika Ghosh Saxena and Richard Hughes
683
From the Intervention of a Vernacular Heritage Structure in Oña – Ecuador, to the Improvement of the Cultural Landscape . . . . . . . . . . . . M. C. Achig-Balarezo, S. Astudillo Cordero, and G. Barsallo Chávez
698
The Challenges of the Conservation of Earthen Sites in Seismic Areas . . . . . . . Claudia Cancino Post-Earthquake Assessment and Possibilities for Management of Existing Masonry Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Karlo Oži´c, Mislav Stepinac, Luka Luli´c, and Dominik Skokandi´c
709
724
Contents
The Identity Value of Vernacular Productive Architecture Knowledge, Recovery and Enhancement of the Val D’Agri Water Mills . . . . . . . . . . . . . . . . . Antonella Guida, Vito Domenico Porcari, Alessandro Lanzolla, and Giuseppe Andrisani Analysis of Local Mechanical Characteristics and Global Structural Arch Behaviour of Cane (Arundo Donax) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sadhbh Donovan, Elisa Poletti, and Hélder Sousa
xv
736
745
Interdisciplinary Projects and Case Studies Restoration of Cast Iron and Wrought Iron Structures – Case Study: The Restoration of the Orangery at Hof ter Borght in Westmeerbeek (Belgium) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Verreydt, M. de Bouw, B. Dewaele, K. Brosens, and D. Van Gemert
763
Comprehensive Study of Brody Bastion Castle . . . . . . . . . . . . . . . . . . . . . . . . . . . Olha Tikhonova
774
Rehabilitation of Santini Water System in the Plasy Monastery . . . . . . . . . . . . . . ˇ ˇ Jakub Rehák, Eva Burgetová, and Josef Rehák
785
Restoration of the Moorish Pavilion and Architectural Complex of Manguinhos, in Rio de Janeiro, Brazil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benedito Tadeu de Oliveira Accuracy of Past Analysis: The Steel Frame of the Gillender Building . . . . . . . Donald Friedman
799
810
Two Looks Back to Move Forward. Today’s Evaluation of Opposite Approaches of Concrete Repair in Heritage Preservation . . . . . . . . . . . . . . . . . . . Elisabeth Hinz and Andreas W. Putz
824
The Conservation and Rehabilitation of Listed Buildings in Line with the Relevant Regulations and Community Needs . . . . . . . . . . . . . . . . . . . . . A. Mosoarca and I. Onescu
838
Textile-Reinforced Alkali-Activated Mortar for In-Plane Shear Capacity Improvement of Masonry Before and After High Temperature Exposure . . . . . . Andres Arce, Panagiotis Kapsalis, Catherine G. Papanicolaou, and Thanasis C. Triantafillou Dilemmas in Upgrade and Use of Railways Heritage: Approaches and Reflections on Structural Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicholas J. Clarke and Arkadiusz Kwiecie´n
849
858
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FRPU Composite Protection of Masonry with Reversible Mineral Interlayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Arkadiusz Kwiecie´n, Łukasz Hojdys, Piotr Krajewski, and Marcin Tekieli Studies for Sighis, oara Citadel Conservation –Ensemble Listed as World Heritage Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imola Kirizsán and Adrian Tudoreanu-Cris, an Performance Evaluation of Patch Repairs on Historic Concrete Structures (PEPS): Preliminary Results from Two English Case Studies . . . . . . Simeon Wilkie, David Farrell, Nicola Lauder, and Ana Paula Arato Goncalves Base Isolation Technology for Rocking Statues: A Simplified Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Giacomo Destro Bisol, M. DeJong, D. Liberatore, and L. Sorrentino Tool – Object – Fragment: The Afterlife of Physical Measurement Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benjamin Schmid, Christiane Weber, Baris Wenzel, and Eberhard Möller Experimental Activities and Structural Analyses for the Restoration and Re-use of the Lazzaretto Vecchio Island in Venice . . . . . . . . . . . . . . . . . . . . . Giulia Passante, Andrea Bondi, Leonardo Cappi, and Filippo Casarin Cosmic Rays Pavilion: Candela’s First Experimental Hypars - Analysis of Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Muciño-Vélez, C. Guillén-Guillén, A. Tahuiton-Mora, and J. Del Cueto-Ruíz Funes Interventions on Roof Structures as Part of Conservation of Historic Buildings with Local Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adrian Tudoreanu-Cris, an and Imola Kirizsán Is Holism Needed in the Diagnosis of Historical Structures? . . . . . . . . . . . . . . . . Tomasz Szkuta Exploring AI and Related Technologies in Understanding Cultural Heritage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prathyusha Dokku and Vrushali Kamalakar
873
884
899
913
924
935
950
959
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985
Contents
Application of the Electrical Resistivity Tomography Technique in the Assessment of Historical Buildings in the State of Aguascalientes, Mexico . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Raudel Padilla-Ceniceros, Edith Estefanía Orenday-Tapia, Jesús Pacheco-Martínez, José Luis García-Rubalcava, and William Herbe Herrera-León
xvii
996
Impact of Environmental Conditions on Rammed Earth Heritage Buildings Seismic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009 J. Villacreses, B. Caicedo, and F. Yépez Conservation of Modernism Movement Concrete: Tackling the Compatibility Issue of Retrofit Solutions with the Degraded Substrate . . . . 1021 Travasso Jocelyn, Loic Gatti, and Tsangouri Eleni Flat Roofs Characterization in Barcelona’s Historic Center . . . . . . . . . . . . . . . . . 1031 Còssima Cornadó, Ainhoa Varela, Sara Vima-Grau, Marta Domenech, and Pere-Joan Ravetllat Test of Authenticity in the Evaluation of Historic Structures. Theory vs Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1042 Katarina Terao Voskova and Andrea Urland Vulnerability and Risk Assessment in Natural Hazards and Climate Change Temporal Variation of Charring Depth of the Wood-Frame Walls in Fire . . . . . . 1059 Shu-Fen Tung, Hung-Chi Su, C. T. Tzeng, Yi-Pin Lin, and Chi-Ming Lai Flood Risk Assessment of Traditional Adobe Buildings: Analysis of Case Studies in the River Ebro Basin, Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067 Francesca Trizio, F. Javier Torrijo Echarri, Camilla Mileto, and Fernando Vegas The DALIH Database for Recording Disaster Damage and Loss Data in Cultural Heritage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1080 Xavier Romão, Esmeralda Paupério, and Olha Tikhonova Vulnerability Assessment of Historic Areas to Heat Waves. The Case Study of Bilbao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093 Laura Quesada-Ganuza, Leire Garmendia, Ane Villaverde, Ziortza Egiluz, Eduardo Roji, and Ignacio Piñero
xviii
Contents
Development of Refined Data-Driven Stochastic Subspace System Identification for Buildings and Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106 Chia-Ming Chang and Yi-Ji Chuang A Hybrid Approach for the Assessment of Flood Vulnerability of Historic Constructions and Their Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117 L. Gerardo F. Salazar, Xavier Romão, and Rui Figueiredo Uplift Vulnerability Analysis of Roofing Tiles for Traditional Chinese Timber Buildings Under Strong Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1134 Yidan Han, Qing Chun, and Xiaoyue Gao Vulnerability Assessment of Historical Churches in Banat Seismic Region, Romania . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146 Iasmina Onescu, Anna Lo Monaco, Mihai Fofiu, Nicola Grillanda, Marius Mosoarca, Michele D’Amato, and Antonio Formisano Monitoring the Combined Effects of Induced Earthquakes and Climate Change on a Heritage Building in Groningen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1159 Eleni Smyrou, Katerina Paxinou, and Ihsan E. Bal GIS Methodologies for the Management of Seismic Risk and the Damage Prevention on Masonry-Built Heritage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1169 Eva Coïsson, Daniele Ferretti, Erica Lenticchia, and Elena Zanazzi Towards a Vulnerability Assessment of Historic Timber Barns in the U.S. Midwest Under Severe Windstorms . . . . . . . . . . . . . . . . . . . . . . . . . . . 1181 Moriah G. Hughes and Branko Gliši´c Climate Protection Versus Building Heritage Preservation - Influence of Renewable Energy Installations on Historical Buildings . . . . . . . . . . . . . . . . . 1192 Ulrike Quapp and Klaus Holschemacher Identification of Gediminas Hill Possible Landslides Formations Zones . . . . . . 1204 Šar¯unas Skuodis, Mykolas Daugeviˇcius, Jurgis Medzvieckas, Arnoldas Šneideris, Aidas Jok¯ubaitis, Justinas Rastenis, and Juozas Valivonis Coupled Multi-risk Mitigation in Historical Urban Outdoor Built Environment: Preliminary Strategies Evaluation Through Typological Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1212 Gabriele Bernardini, Marco D’Orazio, and Enrico Quagliarini
Contents
xix
Optimizing Shelters and Evacuation Paths Against Flood in Historic Urban Built Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227 Guido Romano, Fabrizio Marinelli, Gabriele Bernardini, and Enrico Quagliarini Challenges in the Preventive Maintenance of Early 20th-Century Reinforced Concrete Architectural Sculptures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1242 Esmeralda Paupério, Xavier Romão, Rui Silva, and Susana Moreira Vulnerability Assessment: Comparison of Empirical and Analytical Approach – A Case Study in Zagreb, Croatia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256 Antonela Moreti´c, Mislav Stepinac, Nicola Chieffo, and Paulo B. Lourenço Deep Learning Modelling of Earthquake Damage Data for Identification of Patterns of Damage in Heritage Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1268 Satwant Rihal, Hisham Assal, and Fernando Peña Seismic Vulnerability Assessment of Churches Through an Expeditive Evaluation Form: Application to a Representative Sample from Central Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1280 Giorgia Cianchino, Maria Giovanna Masciotta, and Giuseppe Brando Vulnerability Assessment of Masonry Constructions Towards Rockfall Hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293 Anne-Sophie Colas, Marion Bost, Franck Bourrier, and Isabelle Ousset Simplified Vulnerability Assessment of Masonry Bell Towers . . . . . . . . . . . . . . . 1303 Corrado Chisari, Mattia Zizi, Francesco Roselli, and Gianfranco De Matteis Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1313
RILEM Publications
The following list is presenting the global offer of RILEM Publications, sorted by series. Each publication is available in printed version and/or in online version.
RILEM Proceedings (PRO) PRO 1: Durability of High Performance Concrete (ISBN: 2-912143-03-9; e-ISBN: 2-351580-12-5; e-ISBN: 2351580125); Ed. H. Sommer PRO 2: Chloride Penetration into Concrete (ISBN: 2-912143-00-04; e-ISBN: 2912143454); Eds. L.-O. Nilsson and J.-P. Ollivier PRO 3: Evaluation and Strengthening of Existing Masonry Structures (ISBN: 2-91214302-0; e-ISBN: 2351580141); Eds. L. Binda and C. Modena PRO 4: Concrete: From Material to Structure (ISBN: 2-912143-04-7; e-ISBN: 2351580206); Eds. J.-P. Bournazel and Y. Malier PRO 5: The Role of Admixtures in High Performance Concrete (ISBN: 2-912143-05-5; e-ISBN: 2351580214); Eds. J. G. Cabrera and R. Rivera-Villarreal PRO 6: High Performance Fiber Reinforced Cement Composites - HPFRCC 3 (ISBN: 2-912143-06-3; e-ISBN: 2351580222); Eds. H. W. Reinhardt and A. E. Naaman PRO 7: 1st International RILEM Symposium on Self-Compacting Concrete (ISBN: 2-912143-09-8; e-ISBN: 2912143721); Eds. Å. Skarendahl and Ö. Petersson PRO 8: International RILEM Symposium on Timber Engineering (ISBN: 2-91214310-1; e-ISBN: 2351580230); Ed. L. Boström PRO 9: 2nd International RILEM Symposium on Adhesion between Polymers and Concrete ISAP ’99 (ISBN: 2-912143-11-X; e-ISBN: 2351580249); Eds. Y. Ohama and M. Puterman PRO 10: 3rd International RILEM Symposium on Durability of Building and Construction Sealants (ISBN: 2-912143-13-6; e-ISBN: 2351580257); Ed. A. T. Wolf PRO 11: 4th International RILEM Conference on Reflective Cracking in Pavements (ISBN: 2-912143-14-4; e-ISBN: 2351580265); Eds. A. O. Abd El Halim, D. A. Taylor and El H. H. Mohamed PRO 12: International RILEM Workshop on Historic Mortars: Characteristics and Tests (ISBN: 2-912143-15-2; e-ISBN: 2351580273); Eds. P. Bartos, C. Groot and J. J. Hughes PRO 13: 2nd International RILEM Symposium on Hydration and Setting (ISBN: 2-912143-16-0; e-ISBN: 2351580281); Ed. A. Nonat
xxii
RILEM Publications
PRO 14: Integrated Life-Cycle Design of Materials and Structures - ILCDES 2000 (ISBN: 951-758-408-3; e-ISBN: 235158029X); (ISSN: 0356-9403); Ed. S. Sarja PRO 15: Fifth RILEM Symposium on Fibre-Reinforced Concretes (FRC) - BEFIB’2000 (ISBN: 2-912143-18-7; e-ISBN: 291214373X); Eds. P. Rossi and G. Chanvillard PRO 16: Life Prediction and Management of Concrete Structures (ISBN: 2-912143-195; e-ISBN: 2351580303); Ed. D. Naus PRO 17: Shrinkage of Concrete – Shrinkage 2000 (ISBN: 2-912143-20-9; e-ISBN: 2351580311); Eds. V. Baroghel-Bouny and P.-C. Aïtcin PRO 18: Measurement and Interpretation of the On-Site Corrosion Rate (ISBN: 2-912143-21-7; e-ISBN: 235158032X); Eds. C. Andrade, C. Alonso, J. Fullea, J. Polimon and J. Rodriguez PRO 19: Testing and Modelling the Chloride Ingress into Concrete (ISBN: 2-91214322-5; e-ISBN: 2351580338); Eds. C. Andrade and J. Kropp PRO 20: 1st International RILEM Workshop on Microbial Impacts on Building Materials (CD 02) (e-ISBN 978-2-35158-013-4); Ed. M. Ribas Silva PRO 21: International RILEM Symposium on Connections between Steel and Concrete (ISBN: 2-912143-25-X; e-ISBN: 2351580346); Ed. R. Eligehausen PRO 22: International RILEM Symposium on Joints in Timber Structures (ISBN: 2-912143-28-4; e-ISBN: 2351580354); Eds. S. Aicher and H.-W. Reinhardt PRO 23: International RILEM Conference on Early Age Cracking in Cementitious Systems (ISBN: 2-912143-29-2; e-ISBN: 2351580362); Eds. K. Kovler and A. Bentur PRO 24: 2nd International RILEM Workshop on Frost Resistance of Concrete (ISBN: 2-912143-30-6; e-ISBN: 2351580370); Eds. M. J. Setzer, R. Auberg and H.-J. Keck PRO 25: International RILEM Workshop on Frost Damage in Concrete (ISBN: 2-912143-31-4; e-ISBN: 2351580389); Eds. D. J. Janssen, M. J. Setzer and M. B. Snyder PRO 26: International RILEM Workshop on On-Site Control and Evaluation of Masonry Structures (ISBN: 2-912143-34-9; e-ISBN: 2351580141); Eds. L. Binda and R. C. de Vekey PRO 27: International RILEM Symposium on Building Joint Sealants (CD03; e-ISBN: 235158015X); Ed. A. T. Wolf PRO 28: 6th International RILEM Symposium on Performance Testing and Evaluation of Bituminous Materials - PTEBM’03 (ISBN: 2-912143-35-7; e-ISBN: 978-2-91214377-8); Ed. M. N. Partl PRO 29: 2nd International RILEM Workshop on Life Prediction and Ageing Management of Concrete Structures (ISBN: 2-912143-36-5; e-ISBN: 2912143780); Ed. D. J. Naus
RILEM Publications
xxiii
PRO 30: 4th International RILEM Workshop on High Performance Fiber Reinforced Cement Composites - HPFRCC 4 (ISBN: 2-912143-37-3; e-ISBN: 2912143799); Eds. A. E. Naaman and H. W. Reinhardt PRO 31: International RILEM Workshop on Test and Design Methods for Steel Fibre Reinforced Concrete: Background and Experiences (ISBN: 2-912143-38-1; e-ISBN: 2351580168); Eds. B. Schnütgen and L. Vandewalle PRO 32: International Conference on Advances in Concrete and Structures 2 vol. (ISBN (set): 2-912143-41-1; e-ISBN: 2351580176); Eds. Ying-shu Yuan, Surendra P. Shah and Heng-lin Lü PRO 33: 3rd International Symposium on Self-Compacting Concrete (ISBN: 2-91214342-X; e-ISBN: 2912143713); Eds. Ó. Wallevik and I. Níelsson PRO 34: International RILEM Conference on Microbial Impact on Building Materials (ISBN: 2-912143-43-8; e-ISBN: 2351580184); Ed. M. Ribas Silva PRO 35: International RILEM TC 186-ISA on Internal Sulfate Attack and Delayed Ettringite Formation (ISBN: 2-912143-44-6; e-ISBN: 2912143802); Eds. K. Scrivener and J. Skalny PRO 36: International RILEM Symposium on Concrete Science and Engineering – A Tribute to Arnon Bentur (ISBN: 2-912143-46-2; e-ISBN: 2912143586); Eds. K. Kovler, J. Marchand, S. Mindess and J. Weiss PRO 37: 5th International RILEM Conference on Cracking in Pavements – Mitigation, Risk Assessment and Prevention (ISBN: 2-912143-47-0; e-ISBN: 2912143764); Eds. C. Petit, I. Al-Qadi and A. Millien PRO 38: 3rd International RILEM Workshop on Testing and Modelling the Chloride Ingress into Concrete (ISBN: 2-912143-48-9; e-ISBN: 2912143578); Eds. C. Andrade and J. Kropp PRO 39: 6th International RILEM Symposium on Fibre-Reinforced Concretes - BEFIB 2004 (ISBN: 2-912143-51-9; e-ISBN: 2912143748); Eds. M. Di Prisco, R. Felicetti and G. A. Plizzari PRO 40: International RILEM Conference on the Use of Recycled Materials in Buildings and Structures (ISBN: 2-912143-52-7; e-ISBN: 2912143756); Eds. E. Vázquez, Ch. F. Hendriks and G. M. T. Janssen PRO 41: RILEM International Symposium on Environment-Conscious Materials and Systems for Sustainable Development (ISBN: 2-912143-55-1; e-ISBN: 2912143640); Eds. N. Kashino and Y. Ohama PRO 42: SCC’2005 - China: 1st International Symposium on Design, Performance and Use of Self-Consolidating Concrete (ISBN: 2-912143-61-6; e-ISBN: 2912143624); Eds. Zhiwu Yu, Caijun Shi, Kamal Henri Khayat and Youjun Xie PRO 43: International RILEM Workshop on Bonded Concrete Overlays (e-ISBN: 2-912143-83-7); Eds. J. L. Granju and J. Silfwerbrand
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RILEM Publications
PRO 44: 2nd International RILEM Workshop on Microbial Impacts on Building Materials (CD11) (e-ISBN: 2-912143-84-5); Ed. M. Ribas Silva PRO 45: 2nd International Symposium on Nanotechnology in Construction, Bilbao (ISBN: 2-912143-87-X; e-ISBN: 2912143888); Eds. Peter J. M. Bartos, Yolanda de Miguel and Antonio Porro PRO 46: ConcreteLife’06 - International RILEM-JCI Seminar on Concrete Durability and Service Life Planning: Curing, Crack Control, Performance in Harsh Environments (ISBN: 2-912143-89-6; e-ISBN: 291214390X); Ed. K. Kovler PRO 47: International RILEM Workshop on Performance Based Evaluation and Indicators for Concrete Durability (ISBN: 978-2-912143-95-2; e-ISBN: 9782912143969); Eds. V. Baroghel-Bouny, C. Andrade, R. Torrent and K. Scrivener PRO 48: 1st International RILEM Symposium on Advances in Concrete through Science and Engineering (e-ISBN: 2-912143-92-6); Eds. J. Weiss, K. Kovler, J. Marchand and S. Mindess PRO 49: International RILEM Workshop on High Performance Fiber Reinforced Cementitious Composites in Structural Applications (ISBN: 2-912143-93-4; e-ISBN: 2912143942); Eds. G. Fischer and V. C. Li PRO 50: 1st International RILEM Symposium on Textile Reinforced Concrete (ISBN: 2-912143-97-7; e-ISBN: 2351580087); Eds. Josef Hegger, Wolfgang Brameshuber and Norbert Will PRO 51: 2nd International Symposium on Advances in Concrete through Science and Engineering (ISBN: 2-35158-003-6; e-ISBN: 2-35158-002-8); Eds. J. Marchand, B. Bissonnette, R. Gagné, M. Jolin and F. Paradis PRO 52: Volume Changes of Hardening Concrete: Testing and Mitigation (ISBN: 2-35158-004-4; e-ISBN: 2-35158-005-2); Eds. O. M. Jensen, P. Lura and K. Kovler PRO 53: High Performance Fiber Reinforced Cement Composites - HPFRCC5 (ISBN: 978-2-35158-046-2; e-ISBN: 978-2-35158-089-9); Eds. H. W. Reinhardt and A. E. Naaman PRO 54: 5th International RILEM Symposium on Self-Compacting Concrete (ISBN: 978-2-35158-047-9; e-ISBN: 978-2-35158-088-2); Eds. G. De Schutter and V. Boel PRO 55: International RILEM Symposium Photocatalysis, Environment and Construction Materials (ISBN: 978-2-35158-056-1; e-ISBN: 978-2-35158-057-8); Eds. P. Baglioni and L. Cassar PRO 56: International RILEM Workshop on Integral Service Life Modelling of Concrete Structures (ISBN 978-2-35158-058-5; e-ISBN: 978-2-35158-090-5); Eds. R. M. Ferreira, J. Gulikers and C. Andrade PRO 57: RILEM Workshop on Performance of cement-based materials in aggressive aqueous environments (e-ISBN: 978-2-35158-059-2); Ed. N. De Belie
RILEM Publications
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PRO 58: International RILEM Symposium on Concrete Modelling - CONMOD’08 (ISBN: 978-2-35158-060-8; e-ISBN: 978-2-35158-076-9); Eds. E. Schlangen and G. De Schutter PRO 59: International RILEM Conference on On Site Assessment of Concrete, Masonry and Timber Structures - SACoMaTiS 2008 (ISBN set: 978-2-35158-061-5; e-ISBN: 978-2-35158-075-2); Eds. L. Binda, M. di Prisco and R. Felicetti PRO 60: Seventh RILEM International Symposium on Fibre Reinforced Concrete: Design and Applications - BEFIB 2008 (ISBN: 978-2-35158-064-6; e-ISBN: 978-235158-086-8); Ed. R. Gettu PRO 61: 1st International Conference on Microstructure Related Durability of Cementitious Composites 2 vol., (ISBN: 978-2-35158-065-3; e-ISBN: 978-2-35158-084-4); Eds. W. Sun, K. van Breugel, C. Miao, G. Ye and H. Chen PRO 62: NSF/ RILEM Workshop: In-situ Evaluation of Historic Wood and Masonry Structures (e-ISBN: 978-2-35158-068-4); Eds. B. Kasal, R. Anthony and M. Drdácký PRO 63: Concrete in Aggressive Aqueous Environments: Performance, Testing and Modelling, 2 vol., (ISBN: 978-2-35158-071-4; e-ISBN: 978-2-35158-082-0); Eds. M. G. Alexander and A. Bertron PRO 64: Long Term Performance of Cementitious Barriers and Re inforced Concrete in Nuclear Power Plants and Waste Management - NUCPERF 2009 (ISBN: 978-2-35158-072-1; e-ISBN: 978-2-35158-087-5); Eds. V. L’Hostis, R. Gens, and C. Gallé PRO 65: Design Performance and Use of Self-consolidating Concrete - SCC’2009 (ISBN: 978-2-35158-073-8; e-ISBN: 978-2-35158-093-6); Eds. C. Shi, Z. Yu, K. H. Khayat and P. Yan PRO 66: 2nd International RILEM Workshop on Concrete Durability and Service Life Planning - ConcreteLife’09 (ISBN: 978-2-35158-074-5; ISBN: 978-2-35158-074-5); Ed. K. Kovler PRO 67: Repairs Mortars for Historic Masonry (e-ISBN: 978-2-35158-083-7); Ed. C. Groot PRO 68: Proceedings of the 3rd International RILEM Symposium on ‘Rheology of Cement Suspensions such as Fresh Concrete (ISBN 978-2-35158-091-2; e-ISBN: 978-2-35158-092-9); Eds. O. H. Wallevik, S. Kubens and S. Oesterheld PRO 69: 3rd International PhD Student Workshop on ‘Modelling the Durability of Reinforced Concrete (ISBN: 978-2-35158-095-0); Eds. R. M. Ferreira, J. Gulikers and C. Andrade PRO 70: 2nd International Conference on ‘Service Life Design for Infrastructure’ (ISBN set: 978-2-35158-096-7, e-ISBN: 978-2-35158-097-4); Eds. K. van Breugel, G. Ye and Y. Yuan
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RILEM Publications
PRO 71: Advances in Civil Engineering Materials - The 50-year Teaching Anniversary of Prof. Sun Wei’ (ISBN: 978-2-35158-098-1; e-ISBN: 978-2-35158-099-8); Eds. C. Miao, G. Ye and H. Chen PRO 72: First International Conference on ‘Advances in Chemically-Activated Materials – CAM’2010’ (2010), 264 pp, ISBN: 978-2-35158-101-8; e-ISBN: 978-2-35158115-5, Eds. Caijun Shi and Xiaodong Shen PRO 73: 2nd International Conference on ‘Waste Engineering and Management ICWEM 2010’ (2010), 894 pp, ISBN: 978-2-35158-102-5; e-ISBN: 978-2-35158-103-2, Eds. J. Zh. Xiao, Y. Zhang, M. S. Cheung and R. Chu PRO 74: International RILEM Conference on ‘Use of Superabsorbent Polymers and Other New Addditives in Concrete’ (2010) 374 pp., ISBN: 978-2-35158-104-9; e-ISBN: 978-2-35158-105-6; Eds. O. M. Jensen, M. T. Hasholt and S. Laustsen PRO 75: International Conference on ‘Material Science - 2nd ICTRC - Textile Reinforced Concrete - Theme 1’ (2010) 436 pp., ISBN: 978-2-35158-106-3; e-ISBN: 978-2-35158-107-0; Ed. W. Brameshuber PRO 76: International Conference on ‘Material Science - HetMat - Modelling of Heterogeneous Materials - Theme 2’ (2010) 255 pp., ISBN: 978-2-35158-108-7; e-ISBN: 978-2-35158-109-4; Ed. W. Brameshuber PRO 77: International Conference on ‘Material Science - AdIPoC - Additions Improving Properties of Concrete - Theme 3’ (2010) 459 pp., ISBN: 978-2-35158-110-0; e-ISBN: 978-2-35158-111-7; Ed. W. Brameshuber PRO 78: 2nd Historic Mortars Conference and RILEM TC 203-RHM Final Workshop – HMC2010 (2010) 1416 pp., e-ISBN: 978-2-35158-112-4; Eds. J. Válek, C. Groot and J. J. Hughes PRO 79: International RILEM Conference on Advances in Construction Materials Through Science and Engineering (2011) 213 pp., ISBN: 978-2-35158-116-2, e-ISBN: 978-2-35158-117-9; Eds. Christopher Leung and K. T. Wan PRO 80: 2nd International RILEM Conference on Concrete Spalling due to Fire Exposure (2011) 453 pp., ISBN: 978-2-35158-118-6, e-ISBN: 978-2-35158-119-3; Eds. E. A. B. Koenders and F. Dehn PRO 81: 2nd International RILEM Conference on Strain Hardening Cementitious Composites (SHCC2-Rio) (2011) 451 pp., ISBN: 978-2-35158-120-9, e-ISBN: 9782-35158-121-6; Eds. R. D. Toledo Filho, F. A. Silva, E. A. B. Koenders and E. M. R. Fairbairn PRO 82: 2nd International RILEM Conference on Progress of Recycling in the Built Environment (2011) 507 pp., e-ISBN: 978-2-35158-122-3; Eds. V. M. John, E. Vazquez, S. C. Angulo and C. Ulsen
RILEM Publications
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PRO 83: 2nd International Conference on Microstructural-related Durability of Cementitious Composites (2012) 250 pp., ISBN: 978-2-35158-129-2; e-ISBN: 978-2-35158123-0; Eds. G. Ye, K. van Breugel, W. Sun and C. Miao PRO 84: CONSEC13 - Seventh International Conference on Concrete under Severe Conditions – Environment and Loading (2013) 1930 pp., ISBN: 978-2-35158-124-7; e-ISBN: 978-2-35158-134-6; Eds. Z. J. Li, W. Sun, C. W. Miao, K. Sakai, O. E. Gjorv and N. Banthia PRO 85: RILEM-JCI International Workshop on Crack Control of Mass Concrete and Related issues concerning Early-Age of Concrete Structures – ConCrack 3 – Control of Cracking in Concrete Structures 3 (2012) 237 pp., ISBN: 978-2-35158-125-4; e-ISBN: 978-2-35158-126-1; Eds. F. Toutlemonde and J.-M. Torrenti PRO 86: International Symposium on Life Cycle Assessment and Construction (2012) 414 pp., ISBN: 978-2-35158-127-8, e-ISBN: 978-2-35158-128-5; Eds. A. Ventura and C. de la Roche PRO 87: UHPFRC 2013 – RILEM-fib-AFGC International Symposium on Ultra-High Performance Fibre-Reinforced Concrete (2013), ISBN: 978-2-35158-130-8, e-ISBN: 978-2-35158-131-5; Eds. F. Toutlemonde PRO 88: 8th RILEM International Symposium on Fibre Reinforced Concrete (2012) 344 pp., ISBN: 978-2-35158-132-2, e-ISBN: 978-2-35158-133-9; Eds. Joaquim A. O. Barros PRO 89: RILEM International workshop on performance-based specification and control of concrete durability (2014) 678 pp, ISBN: 978-2-35158-135-3, e-ISBN: 978-2-35158-136-0; Eds. D. Bjegovi´c, H. Beushausen and M. Serdar PRO 90: 7th RILEM International Conference on Self-Compacting Concrete and of the 1st RILEM International Conference on Rheology and Processing of Construction Materials (2013) 396 pp, ISBN: 978-2-35158-137-7, e-ISBN: 978-2-35158-138-4; Eds. Nicolas Roussel and Hela Bessaies-Bey PRO 91: CONMOD 2014 - RILEM International Symposium on Concrete Modelling (2014), ISBN: 978-2-35158-139-1; e-ISBN: 978-2-35158-140-7; Eds. Kefei Li, Peiyu Yan and Rongwei Yang PRO 92: CAM 2014 - 2nd International Conference on advances in chemically-activated materials (2014) 392 pp., ISBN: 978-2-35158-141-4; e-ISBN: 978-2-35158-142-1; Eds. Caijun Shi and Xiadong Shen PRO 93: SCC 2014 - 3rd International Symposium on Design, Performance and Use of Self-Consolidating Concrete (2014) 438 pp., ISBN: 978-2-35158-143-8; e-ISBN: 978-2-35158-144-5; Eds. Caijun Shi, Zhihua Ou and Kamal H. Khayat PRO 94 (online version): HPFRCC-7 - 7th RILEM conference on High performance fiber reinforced cement composites (2015), e-ISBN: 978-2-35158-146-9; Eds. H. W. Reinhardt, G. J. Parra-Montesinos and H. Garrecht
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RILEM Publications
PRO 95: International RILEM Conference on Application of superabsorbent polymers and other new admixtures in concrete construction (2014), ISBN: 978-2-35158-147-6; e-ISBN: 978-2-35158-148-3; Eds. Viktor Mechtcherine and Christof Schroefl PRO 96 (online version): XIII DBMC: XIII International Conference on Durability of Building Materials and Components (2015), e-ISBN: 978-2-35158-149-0; Eds. M. Quattrone and V. M. John PRO 97: SHCC3 – 3rd International RILEM Conference on Strain Hardening Cementitious Composites (2014), ISBN: 978-2-35158-150-6; e-ISBN: 978-2-35158-151-3; Eds. E. Schlangen, M. G. Sierra Beltran, M. Lukovic and G. Ye PRO 98: FERRO-11 – 11th International Symposium on Ferrocement and 3rd ICTRC - International Conference on Textile Reinforced Concrete (2015), ISBN: 978-2-35158152-0; e-ISBN: 978-2-35158-153-7; Ed. W. Brameshuber PRO 99 (online version): ICBBM 2015 - 1st International Conference on Bio-Based Building Materials (2015), e-ISBN: 978-2-35158-154-4; Eds. S. Amziane and M. Sonebi PRO 100: SCC16 - RILEM Self-Consolidating Concrete Conference (2016), ISBN: 978-2-35158-156-8; e-ISBN: 978-2-35158-157-5; Ed. Kamal H. Kayat PRO 101 (online version): III Progress of Recycling in the Built Environment (2015), e-ISBN: 978-2-35158-158-2; Eds. I. Martins, C. Ulsen and S. C. Angulo PRO 102 (online version): RILEM Conference on Microorganisms-Cementitious Materials Interactions (2016), e-ISBN: 978-2-35158-160-5; Eds. Alexandra Bertron, Henk Jonkers and Virginie Wiktor PRO 103 (online version): ACESC’16 - Advances in Civil Engineering and Sustainable Construction (2016), e-ISBN: 978-2-35158-161-2; Eds. T. Ch. Madhavi, G. Prabhakar, Santhosh Ram and P. M. Rameshwaran PRO 104 (online version): SSCS’2015 - Numerical Modeling - Strategies for Sustainable Concrete Structures (2015), e-ISBN: 978-2-35158-162-9 PRO 105: 1st International Conference on UHPC Materials and Structures (2016), ISBN: 978-2-35158-164-3, e-ISBN: 978-2-35158-165-0 PRO 106: AFGC-ACI-fib-RILEM International Conference on UltraHigh-Performance Fibre-Reinforced Concrete – UHPFRC 2017 (2017), ISBN: 9782-35158-166-7, e-ISBN: 978-2-35158-167-4; Eds. François Toutlemonde and Jacques Resplendino PRO 107 (online version): XIV DBMC – 14th International Conference on Durability of Building Materials and Components (2017), e-ISBN: 978-2-35158-159-9; Eds. Geert De Schutter, Nele De Belie, Arnold Janssens and Nathan Van Den Bossche PRO 108: MSSCE 2016 - Innovation of Teaching in Materials and Structures (2016), ISBN: 978-2-35158-178-0, e-ISBN: 978-2-35158-179-7; Ed. Per Goltermann
RILEM Publications
xxix
PRO 109 (2 volumes): MSSCE 2016 - Service Life of Cement-Based Materials and Structures (2016), ISBN Vol. 1: 978-2-35158-170-4, Vol. 2: 978-2-35158-171-4, Set Vol. 1&2: 978-2-35158-172-8, e-ISBN : 978-2-35158-173-5; Eds. Miguel Azenha, Ivan Gabrijel, Dirk Schlicke, Terje Kanstad and Ole Mejlhede Jensen PRO 110: MSSCE 2016 - Historical Masonry (2016), ISBN: 978-2-35158-178-0, eISBN: 978-2-35158-179-7; Eds. Inge Rörig-Dalgaard and Ioannis Ioannou PRO 111: MSSCE 2016 - Electrochemistry in Civil Engineering (2016), ISBN: 978-235158-176-6, e-ISBN: 978-2-35158-177-3; Ed. Lisbeth M. Ottosen PRO 112: MSSCE 2016 - Moisture in Materials and Structures (2016), ISBN: 978-235158-178-0, e-ISBN: 978-2-35158-179-7; Eds. Kurt Kielsgaard Hansen, Carsten Rode and Lars-Olof Nilsson PRO 113: MSSCE 2016 - Concrete with Supplementary Cementitious Materials (2016), ISBN: 978-2-35158-178-0, e-ISBN: 978-2-35158-179-7; Eds. Ole Mejlhede Jensen, Konstantin Kovler and Nele De Belie PRO 114: MSSCE 2016 - Frost Action in Concrete (2016), ISBN: 978-2-35158-182-7, e-ISBN: 978-2-35158-183-4; Eds. Marianne Tange Hasholt, Katja Fridh and R. Doug Hooton PRO 115: MSSCE 2016 - Fresh Concrete (2016), ISBN: 978-2-35158-184-1, e-ISBN: 978-2-35158-185-8; Eds. Lars N. Thrane, Claus Pade, Oldrich Svec and Nicolas Roussel PRO 116: BEFIB 2016 – 9th RILEM International Symposium on Fiber Reinforced Concrete (2016), ISBN: 978-2-35158-187-2, e-ISBN: 978-2-35158-186-5; Eds. N. Banthia, M. di Prisco and S. Soleimani-Dashtaki PRO 117: 3rd International RILEM Conference on Microstructure Related Durability of Cementitious Composites (2016), ISBN: 978-2-35158-188-9, e-ISBN: 978-2-35158189-6; Eds. Changwen Miao, Wei Sun, Jiaping Liu, Huisu Chen, Guang Ye and Klaas van Breugel PRO 118 (4 volumes): International Conference on Advances in Construction Materials and Systems (2017), ISBN Set: 978-2-35158-190-2, Vol. 1: 978-2-35158-193-3, Vol. 2: 978-2-35158-194-0, Vol. 3: ISBN:978-2-35158-195-7, Vol. 4: ISBN:978-2-35158-1964, e-ISBN: 978-2-35158-191-9; Eds. Manu Santhanam, Ravindra Gettu, Radhakrishna G. Pillai and Sunitha K. Nayar PRO 119 (online version): ICBBM 2017 - Second International RILEM Conference on Bio-based Building Materials, (2017), e-ISBN: 978-2-35158-192-6; Eds. Sofiane Amziane PRO 120 (2 volumes): EAC-02 - 2nd International RILEM/COST Conference on Early Age Cracking and Serviceability in Cement-based Materials and Structures, (2017), Vol. 1: 978-2-35158-199-5, Vol. 2: 978-2-35158-200-8, Set: 978-2-35158-197-1, e-ISBN: 978-2-35158-198-8; Eds. Stéphanie Staquet and Dimitrios Aggelis
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RILEM Publications
PRO 121 (2 volumes): SynerCrete18: Interdisciplinary Approaches for Cement-based Materials and Structural Concrete: Synergizing Expertise and Bridging Scales of Space and Time, (2018), Set: 978-2-35158-202-2, Vol.1: 978-2-35158-211-4, Vol. 2: 978-235158-212-1, e-ISBN: 978-2-35158-203-9; Eds. Miguel Azenha, Dirk Schlicke, Farid Benboudjema and Agnieszka Knoppik PRO 122: SCC’2018 China - Fourth International Symposium on Design, Performance and Use of Self-Consolidating Concrete, (2018), ISBN: 978-2-35158-204-6, e-ISBN: 978-2-35158-205-3; Eds. C. Shi, Z. Zhang and K. H. Khayat PRO 123: Final Conference of RILEM TC 253-MCI: Microorganisms-Cementitious Materials Interactions (2018), Set: 978-2-35158-207-7, Vol.1: 978-2-35158-209-1, Vol.2: 978-2-35158-210-7, e-ISBN: 978-2-35158-206-0; Ed. Alexandra Bertron PRO 124 (online version): Fourth International Conference Progress of Recycling in the Built Environment (2018), e-ISBN: 978-2-35158-208-4; Eds. Isabel M. Martins, Carina Ulsen and Yury Villagran PRO 125 (online version): SLD4 - 4th International Conference on Service Life Design for Infrastructures (2018), e-ISBN: 978-2-35158-213-8; Eds. Guang Ye, Yong Yuan, Claudia Romero Rodriguez, Hongzhi Zhang and Branko Savija PRO 126: Workshop on Concrete Modelling and Material Behaviour in honor of Professor Klaas van Breugel (2018), ISBN: 978-2-35158-214-5, e-ISBN: 978-2-35158-215-2; Ed. Guang Ye PRO 127 (online version): CONMOD2018 - Symposium on Concrete Modelling (2018), e-ISBN: 978-2-35158-216-9; Eds. Erik Schlangen, Geert de Schutter, Branko Savija, Hongzhi Zhang and Claudia Romero Rodriguez PRO 128: SMSS2019 - International Conference on Sustainable Materials, Systems and Structures (2019), ISBN: 978-2-35158-217-6, e-ISBN: 978-2-35158-218-3 PRO 129: 2nd International Conference on UHPC Materials and Structures (UHPC2018-China), ISBN: 978-2-35158-219-0, e-ISBN: 978-2-35158-220-6; PRO 130: 5th Historic Mortars Conference (2019), ISBN: 978-2-35158-221-3, e-ISBN: 978-2-35158-222-0; Eds. José Ignacio Álvarez, José María Fernández, Íñigo Navarro, Adrián Durán and Rafael Sirera PRO 131 (online version): 3rd International Conference on Bio-Based Building Materials (ICBBM2019), e-ISBN: 978-2-35158-229-9; Eds. Mohammed Sonebi, Sofiane Amziane and Jonathan Page PRO 132: IRWRMC’18 - International RILEM Workshop on Rheological Measurements of Cement-based Materials (2018), ISBN: 978-2-35158-230-5, e-ISBN: 978-2-35158-231-2; Eds. Chafika Djelal and Yannick Vanhove PRO 133 (online version): CO2STO2019 - International Workshop CO2 Storage in Concrete (2019), e-ISBN: 978-2-35158-232-9; Eds. Assia Djerbi, Othman OmikrineMetalssi and Teddy Fen-Chong
RILEM Publications
xxxi
PRO 134: 3rd ACF/HNU International Conference on UHPC Materials and Structures UHPC’2020, ISBN: 978-2-35158-233-6, e-ISBN: 978-2-35158-234-3; Eds. Caijun Shi and Jiaping Liu PRO 135: Fourth International Conference on Chemically Activated Materials (CAM2021), ISBN: 978-2-35158-235-0, e-ISBN: 978-2-35158-236-7; Eds. Caijun Shi and Xiang Hu
RILEM Reports (REP) Report 19: Considerations for Use in Managing the Aging of Nuclear Power Plant Concrete Structures (ISBN: 2-912143-07-1); Ed. D. J. Naus Report 20: Engineering and Transport Properties of the Interfacial Transition Zone in Cementitious Composites (ISBN: 2-912143-08-X); Eds. M. G. Alexander, G. Arliguie, G. Ballivy, A. Bentur and J. Marchand Report 21: Durability of Building Sealants (ISBN: 2-912143-12-8); Ed. A. T. Wolf Report 22: Sustainable Raw Materials - Construction and Demolition Waste (ISBN: 2-912143-17-9); Eds. C. F. Hendriks and H. S. Pietersen Report 23: Self-Compacting Concrete state-of-the-art report (ISBN: 2-912143-23-3); Eds. Å. Skarendahl and Ö. Petersson Report 24: Workability and Rheology of Fresh Concrete: Compendium of Tests (ISBN: 2-912143-32-2); Eds. P. J. M. Bartos, M. Sonebi and A. K. Tamimi Report 25: Early Age Cracking in Cementitious Systems (ISBN: 2-912143-33-0); Ed. A. Bentur Report 26: Towards Sustainable Roofing (Joint Committee CIB/RILEM) (CD 07) (eISBN 978-2-912143-65-5); Eds. Thomas W. Hutchinson and Keith Roberts Report 27: Condition Assessment of Roofs (Joint Committee CIB/RILEM) (CD 08) (e-ISBN 978-2-912143-66-2); Ed. CIB W 83/RILEM TC166-RMS Report 28: Final report of RILEM TC 167-COM ‘Characterisation of Old Mortars with Respect to Their Repair (ISBN: 978-2-912143-56-3); Eds. C. Groot, G. Ashall and J. Hughes Report 29: Pavement Performance Prediction and Evaluation (PPPE): Interlaboratory Tests (e-ISBN: 2-912143-68-3); Eds. M. Partl and H. Piber Report 30: Final Report of RILEM TC 198-URM ‘Use of Recycled Materials’ (ISBN: 2-912143-82-9; e-ISBN: 2-912143-69-1); Eds. Ch. F. Hendriks, G. M. T. Janssen and E. Vázquez Report 31: Final Report of RILEM TC 185-ATC ‘Advanced testing of cement-based materials during setting and hardening’ (ISBN: 2-912143-81-0; e-ISBN: 2-912143-705); Eds. H. W. Reinhardt and C. U. Grosse
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Report 32: Probabilistic Assessment of Existing Structures. A JCSS publication (ISBN 2-912143-24-1); Ed. D. Diamantidis Report 33: State-of-the-Art Report of RILEM Technical Committee TC 184-IFE ‘Industrial Floors’ (ISBN 2-35158-006-0); Ed. P. Seidler Report 34: Report of RILEM Technical Committee TC 147-FMB ‘Fracture mechanics applications to anchorage and bond’ Tension of Reinforced Concrete Prisms – Round Robin Analysis and Tests on Bond (e-ISBN 2-912143-91-8); Eds. L. Elfgren and K. Noghabai Report 35: Final Report of RILEM Technical Committee TC 188-CSC ‘Casting of Self Compacting Concrete’ (ISBN 2-35158-001-X; e-ISBN: 2-912143-98-5); Eds. Å. Skarendahl and P. Billberg Report 36: State-of-the-Art Report of RILEM Technical Committee TC 201-TRC ‘Textile Reinforced Concrete’ (ISBN 2-912143-99-3); Ed. W. Brameshuber Report 37: State-of-the-Art Report of RILEM Technical Committee TC 192-ECM ‘Environment-conscious construction materials and systems’ (ISBN: 978-2-35158-0530); Eds. N. Kashino, D. Van Gemert and K. Imamoto Report 38: State-of-the-Art Report of RILEM Technical Committee TC 205-DSC ‘Durability of Self-Compacting Concrete’ (ISBN: 978-2-35158-048-6); Eds. G. De Schutter and K. Audenaert Report 39: Final Report of RILEM Technical Committee TC 187-SOC ‘Experimental determination of the stress-crack opening curve for concrete in tension’ (ISBN 978-235158-049-3); Ed. J. Planas Report 40: State-of-the-Art Report of RILEM Technical Committee TC 189-NEC ‘NonDestructive Evaluation of the Penetrability and Thickness of the Concrete Cover’ (ISBN 978-2-35158-054-7); Eds. R. Torrent and L. Fernández Luco Report 41: State-of-the-Art Report of RILEM Technical Committee TC 196-ICC ‘Internal Curing of Concrete’ (ISBN 978-2-35158-009-7); Eds. K. Kovler and O. M. Jensen Report 42: ‘Acoustic Emission and Related Non-destructive Evaluation Techniques for Crack Detection and Damage Evaluation in Concrete’ - Final Report of RILEM Technical Committee 212-ACD (e-ISBN: 978-2-35158-100-1); Ed. M. Ohtsu Report 45: Repair Mortars for Historic Masonry - State-of-the-Art Report of RILEM Technical Committee TC 203-RHM (e-ISBN: 978-2-35158-163-6); Eds. Paul Maurenbrecher and Caspar Groot Report 46: Surface delamination of concrete industrial floors and other durability related aspects guide - Report of RILEM Technical Committee TC 268-SIF (e-ISBN: 978-235158-201-5); Ed. Valerie Pollet
Protection of Heritage Structures in Japan and Southeast Asia
Structural Characteristics of Carian Rock-Cut Tombs: The Effect of Discrepancy Between the Connecting Part and the Back Passage Akisumi Takeda(B) Architecture and Building Engineering Research Unit, College of Design and Manufacturing Technology, Muroran Institute of Technology, Mizumoto 27-1, Muroran 050-8585, Japan [email protected]
Abstract. Studies of the history of ancient Greek architecture have primarily covered public architecture such as temples and stoa, which had similar architectural forms and structures. Consequently, many studies have been conducted from a formalistic perspective or have focused on design related aspects, and ancient Greek architects’ conception of the structure have hardly been elucidated. Analyzing tombs of the Hellenistic age which have diverse architectural forms and structures is considered to shed light on how ancient Greek architects conceived the relation between structure and design. Against the backdrop described above, with the elucidation of ancient architectural engineers’ conception of structure and design as the ultimate goal, this paper analyzes the impact on the structural characteristics of rock-cut tombs by the ‘position of the connecting part’ and the ‘height of the back passage of a rock-cut tomb’ by performing structural analysis using a three-dimensional FEM analysis program. As a result, above all, it was revealed that the maximum principal stress could be minimized by balancing the position of the connecting part and the height of the back passage of a rock-cut tomb. Keywords: Ancient Greece · Caria · Rock-cut tomb · Structural properties · Three-dimensional FEM analysis
1 The Background of This Study Ancient Greek architecture has traditionally been said to be mainly characterized by uniformity, with each type of structure mostly having a definite corresponding architectural form, as seen in structures such as temples and stoa. Tombs of the Hellenistic age in the Mediterranean world have such multifarious architectural forms that there are said to be no two tombs that are exactly alike [1]. It is not difficult to imagine that these multifarious architectural forms developed for tombs of the Hellenistic age and a new sense of value approving them greatly contributed to later Roman architecture, for instance, by providing multifarious architectural languages and universalizing the freedom of choosing any of those languages. I have been working on tombs of the Hellenistic age for the major purpose of systematizing Hellenistic tombs and situating them © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 3–11, 2024. https://doi.org/10.1007/978-3-031-39450-8_1
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in the history of architecture in light of the ‘peculiarity of Hellenistic tombs as ancient Greek architecture’ and a ‘possibility of their contribution to Roman architecture’ [2]. In the course of conducting this research on Hellenistic tombs, tombs were found that had diverse structures not found in other types of Greek architecture than tombs. Examples include Grave Monument III in Messene, which has a concave conical roof, and rock-cut tombs [3] in Caria [4] made by excavating a rock cliff (Fig. 1). Studies of the history of ancient Greek architecture have primarily covered public architecture such as temples and stoa, with numerous studies conducted from a formalistic perspective or on design methods by focusing on design related aspects. Consequently, no light has been shed on how ancient Greek architects conceived the relation between structure and design and embodied their conception in their design. Analyzing the relationship between the design method and structural characteristics of tombs of the Hellenistic age with diverse architectural forms and structures is considered to contribute to elucidating ancient Greek architects’ conception of design and structure.
Fig. 1. An example of Hellenistic tombs (Left: Grave Monument III (Elevation, Section), Right: Rock-cut tombs in Caunus). Source: Left: Akisumi, T., RESTORATION OF THE GRAVE MONUMENT III: Architectural survey of ancient city of Messene in Greece (2), Journal of the Architectural Institute of Japan, Planning systems, No. 549, p. 288, (2001.11). Right: Hengirmen M., KAUNOS, p. 35, Baskent Repro, Ankara (1997).
Based on the above backdrop, this study is intended to shed light on the influence of differences in the ‘position of the connecting part’ and the ‘height of the back passage’ (Fig. 2) on the structural characteristics of a rock-cut tomb by focusing on rock-cut tombs in Caria with a view to elucidating ancient Greek architects’ conception of design and structure.
2 Method The effects of differences in the ‘position of the connecting part’ and the ‘height of the back passage’ on the structural characteristics of a rock-cut tomb are examined on the basis of the result of static-elastic stress analysis with three-dimensional solid models using the three-dimensional analysis program FEMLEEG (made by FORUM8). Note that it was decided to choose an analysis method using the linear finite element method based on the consideration that an exact analysis is not required since the purpose of
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Position of the connecting part Height of the back passage
Sepulcher
Fig. 2. A schematic diagram of the cross-section of a rock-cut tomb. Source: Created by the Author.
this study is to shed light on the relative impact of differences in architectural form on structural characteristics. In order to make it easier to find the effects on the structural characteristics of a rock-cut tomb, an analytical model is used which is uniform except for properties under examination (hereinafter referred to as the “standard model”). In creating the standard model, information on rock-cut tombs is obtained from the survey by Paavo Roos [5]. 2.1 Outline of the Analytical Model In light of the intended future evaluation of the structural reasonability of real rock-cut tombs using the result of the analysis in this study, it can be said to be desirable that the standard model have a shape similar to those of many rock-cut tombs. In order thus to find the universal shape of a rock-cut tomb, five tombs are selected each whose values of their “total width,” “total height,” and “total depth” lie near the median. Among those five tombs, Tomb C2 of Caunos (Fig. 3), which has been best preserved and does not have a peculiar shape, was chosen as the prototype for the standard model. Taking it into consideration that a rock-cut tomb is affected by the ground pressure of rock walls surrounding it, the analytical model was determined to include rock walls around a rockcut tomb. Since, however, a rock-cut tomb is symmetrical, the model was halved to reduce the analysis load. The size of the entire model was determined as shown in Fig. 4 in order to prevent the analysis load from getting excessive and stabilize the stress distribution. The fine decoration on the tomb’s facade was omitted in modeling as it is considered to have a small effect on structural characteristics. In addition, since hexahedral elements are used in the analysis in this study, circular columns were replaced by square columns in order to stabilize the result of the analysis. Likewise, in order to stabilize the result of the analysis, a uniform mesh size was used by adjusting the dimensions of each part by 5% at maximum. Since the above three changes are similarly made in all modeling studies, they are not considered to have a significant impact on the analysis of the structural characteristics of a rock-cut tomb.
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Fig. 3. Tomb C2 of Caunus (Left: Elevation, Center: Plan, Right: Cross-section). Source: Roos op. Cit. 1972, Pl.34.
16m
16m
16m
Fig. 4. A schematic diagram of the analytical model. Source: Created by the Author.
2.2 Physical Property Values and Boundary Conditions As rock-cut tombs in Caria are built into a limestone rock wall, the physical property values of limestone are used, setting Young’s modulus to 3.5 × 1010 [Pa], mass density to 2,700 [Kg/m3 ], and Poisson’s ratio to 0.25. Based on the photographic measurement, there is a rock wall approximately 14 m high above Tomb C2. Still, it is difficult to replicate the weight of this rock wall itself only by the magnitude of the model due to the limit of analytical capacity. A uniformly distributed load of 1.59 × 105 [N/m2 ] is thus applied on the top surface of the model in this study. Besides the ground pressure from the upper part, the ground pressure from the sides and the bottom is considered to act on a model of a part of a rock wall such as the analytical model in this study. In order to replicate the ground pressure from surrounding rock walls, movable supports are used except for the top and the front, and a force having the same value as the side pressure is generated as a reaction force.
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2.3 Examination of Analysis Patterns Measured by its proportion in the ‘total depth of the tomb,’ the ‘position of the connecting part’ of an actual rock-cut tomb is mostly 10% or less from the front and about 30% at maximum. Therefore, the ‘position of the connecting part’ in the model is varied by an increment of ‘1 mesh (0.2 m)’ from 0 m to 1.4 m, which corresponds to a position slightly behind one that is 30% from the front. On the other hand, the ‘height of the floor of the back passage” varies, depending on whether the passage is carved without digging at all or by digging to the same level as the sepulcher floor or halfway. Therefore, the analysis pattern is varied by varying the back passage floor level by 1 mesh from ‘0 m,’ which corresponds to cases without digging, to ‘3.6 m,’ which corresponds to cases where the passage was carved out by digging to the same level as the sepulcher floor.
3 Results and Discussion Figure 5 shows a graph indicating the maximum value of the maximum principal stress. As indicated in this graph, regardless of the position of the connecting part, the maximum value of the maximum principal stress increases slightly as the back passage is lowered and then turns to decrease, turning to increase again after reaching its minimum value. Note that the location where the maximum principal stress occurs is the roof over the front side of the connecting part (Fig. 5-A) before the maximum principal stress reaches the minimum value and the roof over its rear side (Fig. 5-B) after the maximum principal stress reaches the minimum value. The following reason is conceivable for the above change in the maximum value and the location where the maximum principal stress occurs.
B A
Fig. 5. The maximum value of the maximum principal stress and Location of the maximum value of the maximum principal stress. Source: Created by the Author.
According to the deformation diagram of the rock-cut tomb, before the floor of the back passage is lowered, the connecting part is tilted in such a manner that its lower end is pulled toward the rear of the rock-cut tomb (Fig. 6-A). As the floor of the back passage is lowered, the tilt decreases, and the connecting part becomes vertical (Fig. 6-B). When
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Fig. 6. A schematic diagram of deformation patterns of the connecting part. Source: Created by the Author.
the back passage is lowered further, the connecting part becomes tilted in such a manner that its lower end is pulled toward the front of the rock-cut tomb (Fig. 6-C). In light of this, whereas the load P1 (Fig. 7) is applied to the rock-cut tomb from the rock wall over its upper part via the connecting part, since this load is displaced from the center of gravity of the rock-cut tomb (Fig. 7-X1 ), the overturning moment M1 (=P1 × X1 ) (Fig. 7) is generated on the rock-cut tomb. On the other hand, a load from a rock wall behind the rock-cut tomb (Fig. 7-A) generates the diagonal load P2 (Fig. 7) to the rear of the back wall of the rock-cut tomb via the floor of the back passage. P3 (Fig. 7), the horizontal component of the load P2 , generates the counterclockwise overturning moment M2 (=P3 × X2 ) (Fig. 7), and P4 (Fig. 7), its vertical component, generates M3 (=P4 × X3 ) (Fig. 7). If the floor level of the back passage is “0 m”, the rock-cut tomb is caused to rotate backward since “M2 + M3 ” is greater than M1 . Therefore, the lower end of the connecting part is pulled backward as shown in Fig. 6-A, and an enormous maximum principal stress is generated on the roof surface anterior to the connecting part. If the floor of the back passage is lowered, as the volume of the rock wall above the floor of the back passage (Fig. 7-B) then increases, P3 and P4 increase, making “M2 + M3 ” more excellent. Therefore, the tilt of the connecting part increases, and the maximum principal stress generated in locations anterior to the connecting part becomes even greater. If the floor of the back passage is lowered further, the difference between M1 and “M2 + M3 ” becomes smaller since X2 becomes shorter even though P3 and P4 increase. Therefore, the rotational force toward the rear of the rock-cut tomb decreases, and the connecting part changes its direction toward the vertical direction, causing the maximum principal stress to be distributed to the roof surfaces anterior and posterior to the connecting part to reduce the maximum value of the maximum principal stress. If the floor level of the back passage falls below the center of gravity of the rock-cut tomb, as P3 turns into a counterclockwise overturning moment, the tilt of the connecting part, in turn, comes to be determined by the balance between “M1 + M2 ” and M3 : if these two values become equal, the connecting part becomes completely vertical as shown in Fig. 6-B. As a result, the maximum principal stress comes to be equally distributed between the roof surfaces anterior and posterior to the connecting part, minimizing the maximum value of the maximum principal stress. Subsequently, the rock-cut tomb is caused to rotate forward as “M1 + M2 ” becomes greater than M3 . Therefore, the lower end of the connecting part is pulled forward as shown in Fig. 6-C to cause the maximum
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value of the maximum principal stress to occur on the roof posterior to the connecting part: the maximum principal stress then increases as its tilt grows greater.
Center of gravity
Fig. 7. A schematic diagram of the cross-section of a rock-cut tomb. Source: Created by the Author.
Incidentally, the further backwards the position of the connecting part is, the lower the floor level of the back passage is when the maximum value of the maximum principal stress is minimized (Fig. 8). This is because a larger value of M2 , hence a larger value of X2 , is required to obtain “M1 + M2 = M3 ” since M1 becomes smaller if X1 becomes smaller.
Fig. 8. Different positions at which the maximum principal stress becomes minimum. Source: Created by the Author.
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4 Conclusion The conclusion obtained by this study is summarized below. 1) As the floor level of the back passage is lowered, the maximum value of the maximum principal stress initially occurs on the roof surface over the front side of the connecting part, increases slightly, and then turns to decrease. After the maximum value of the maximum principal stress reaches its minimum value, the location where the maximum value of the maximum principal stress occurs changes to the back side, and the maximum value of the maximum principal stress starts to increase. 2) The further backward the position of the connecting part is moved, the lower the floor level of the back passage is when the maximum value of the maximum principal stress becomes minimal. In the future, it is intended to analyze, among others, the influence of differences in aspects of a rock-cut tomb other than its connecting part and back passage, for instance, differences in the shape of its roof and its side passage, on its structural characteristics. It is intended to evaluate the structural reasonability of actual rock-cut tombs at the stage where the influences of differences in each part of a rock-cut tomb on its structural characteristics are grasped.
Reference and Notes 1. Fedak, J.: Momumental Tombs of the Hellenistic Age, p.3, Toronto (1990). In this book, Fedak summarizes information on tombs of the Hellenistic age hitherto reported and describes their characteristics. Fedak therein cites the possession of multifarious architectural forms as one of the characteristics of tombs of the Hellenistic age 2. Akisumi, T.: A study of the regional and historical trait of built tombs from the view point of use of the column: A study of the regional and historical trait of Hellenistic tombs (1), Journal of the Architectural Institute of Japan, Planning systems, No. 597, pp. 189–195 (2005). Akisumi, T.: A study of the regional and historical trait of built tombs from the view point of the burial position and use of the podium: A study of the regional and historical trait of Hellenistic tombs (2), Journal of the Architectural Institute of Japan, Planning systems, No. 611, pp. 219–224 (2007). Akisumi, T.: Design method of the lion tomb at amphipolis: Design methods of Hellenistic tombs (1), Journal of the Architectural Institute of Japan, Planning systems, No. 613, pp. 235– 241 (2007). Akisumi, T.: Planning method of the nereid monument at xanthos: design methods of Hellenistic tombs (2), Journal of the Architectural Institute of Japan, Planning systems, No. 627, pp. 1105–1112 (2008). Akisumi, T., The Architectural Elevation Planning Method of the Nereid Monument at Xanthos Design methods of Hellenistic tombs (3), Journal of the Architectural Institute of Japan, Planning systems, No. 658, pp. 2961–2967 (2010). Akisumi, T., Characteristics of the Facades of Rock-Cut Tombs in Southeast Caria that Imitate Ancient Greek Temples, Journal of the Architectural Institute of Japan, Planning systems, No. 695, pp. 217–226 (2014) 3. It is one of morphological categories of toms of the Hellenistic age and refers to tombs built by excavating rock walls. There are two types of rock-cut tombs: tombs of the stand-alone type built by separating them from surrounding rock walls and tombs of the facade type built by directly constructing the facade of a tomb without separating it from rock walls
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4. Caria is an area in the present southwestern part of Turkey. Caunus is one of ancient cities located in Caria 5. Roos, P.: Survey of Rock Chamber-Tombs in Caria, Part 2 Central Caria, Goteborg (2006). Roos, P.: Survey of Rock Chamber-Tombs in Caria, Part 1 South-Eastern Caria and the LycoCarian Borderland, Goteborg (1985). Roos, P.: The Rock Tombs of Caunus, Goteborg (1972)
The Authenticity and Integrity of the Soil and the Foundation of the Heritage Structure of Bayon Temple, Angkor Yoshinori Iwasaki1(B) , Mitsuharu Fukuda2 , Mitsumasa Ishizuka3 , Ichita Shimoda4 , Robert McCarthy3 , Vanna Ly5 , and Takeshi Nakagawa6 1 Geo Research Institute, Kobe 658-0064, Japan
[email protected]
2 Kumamoto Geoinformation Institute, Kumamoto, Japan 3 JASA, SiemReap, Cambodia 4 Tsukuba University, Tsukuba, Japan 5 National Committee for World Heritage, Phnon Penh, Cambodia 6 Waseda University, Tokyo, Japan
Abstract. Soils and foundation of Bayon temple of Angkor Thom has been studied since 1994 by Japanese Government Team for Safeguarding Angkor (JSA). The main tower of Bayon of 32 m in height from the base foundation mound which consists manmade fill of 14 m in thickness. The foundation was studied and found as a simple shallow direct foundation. This is just like a10 story RC building standing upon thick manmade sand fill without such a deep foundation with piling. At present, such a structure based upon thick sandy fill will lose the foundation stability in rainy season under monsoon climate of South-eastern Asia. The amazing mechanism attributed to the monument the standing for 700 years has been revealed as the unsaturated characteristics of well compacted silty sand. Keywords: Bayon temple · foundation mound · direct foundation · Kaolin sand · Angkor
1 Bayon Temple, Angkor The Bayon temple, the Cambodian Buddhist pyramid temple at the center of the heart of the ancient city of Angkor Thom, is the symbolic center of the Khmer empire of the late 12th early 13th century. The Bayon temple was constructed by King Jayavarman VII (1181–1220). In addition to the Central Tower, 54 towers with faces at each four sides are located on a man-made soil mound with three stepped terraces as a trenched foundation. [1] In 1994, Japanese Government Team for Safeguarding Angkor (JSA) started the study of Bayon temple in various field including geotechnical engineering (Fig. 1).
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 12–25, 2024. https://doi.org/10.1007/978-3-031-39450-8_2
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Fig. 1. Bayon temple
2 Foundation System and Ground Conditions 2.1 Trenched Foundation and Ground Condition Archaeological team of JSA studied the underground structure of the northern side of the first terrace extending to outside of the temple as shown a long trench of N2-N3 in Fig. 2. The result of the trench is shown in Fig. 3. The original ground surface was excavated 2–3 m not only the inside of the temple but also the outside ground of about 10 m from the outer gallery and backfilled with compacted sand. After the backfilling, further additional filling was made to construct the first terrace of the mound. The section view of the Bayon temple is shown in Fig. 3, which show three stepped terraces with height of +2.5 m, +6.0 m, and 12.4 m. The main tower of Bayon stands upon the top of the mound of +13. 8m which is 42.2 in height.
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JSA performed a geotechnical boring to about 100 m at northern yard outside of the temple. The ground consists of sandy soils down to around GL-35 m with several silty layers followed by weathered tuff layers as shown in Fig. 4. SPT, N-values increases with depth from N = 0 to 50. Underground water levels show seasonal change from the top of the ground surface at the end of rainy season to the lowest level of GL-5.0 m at the end of the dry season. SPT-N-values increases during the dry season as shown in Fig. 4.
Fig. 2. Plan of Bayon temple with position of the long trench
Fig. 3. Archaeological section of the long trench at the north side of Bayon temple
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Fig. 4. .
2.2 Direct Shallow Foundation JSA conducted archaeological trench excavation along the inside of the base stone and geotechnical hand auger sounding beneath the stone to determine if any special base structure was installed to support the heavy central tower masonry structure. Horizontal hand auger tests were carried out at 5 points as shown in Fig. 5 and has resulted in finding no supporting stones, but only very dense sandy fill beneath the base stone support. [2] The direct shallow foundation was confirmed as the foundation type of the main tower of the Bayon.
Fig. 5. Archaeological excavation of the base foundation
Fig. 6. Direct Shallow foundation
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2.3 Foundation Mound with Vertical Shaft at the Center EFEO, a France sponsored organization, in 1933 dug out the center of the base of the main central tower below the pavement and found a fragmented Buddha statue. It was recorded that the vertical shaft had been backfilled. Geotechnical boring was performed at the backfilled vertical shaft and at the top terrace of the original manmade filled mound as shown in Fig. 7. The backfilled soil for BY09 was found in a very loose state of SPT, N-values N < 4 of BYV2009. Another boring of BYV2010 at the top terrace shows the sandy fill lower than GL-6m of N = 100–150, which is a very large value compared to the expected values of 20–40 for common filled sandy soil [3, 4].
Fig. 7. Borings at the vertical shaft and at top terrace
3 Characteristics of Sandy Soil of the Foundation Mound 3.1 Grainsize Distribution of the Filled Soil The grain size distributions of the sampled soil by the boring of BYV2010 and BYH201030 as well as other sites are shown in red and blue colour for sand and clay soils respectively in Fig. 8. The sandy soil is filled soil and the entire samples of the filled soil show the same distribution, which implies very uniform fill material. The silty/clayey fill was found at the boundary of such zone to prevent seepage as laterite blocks retain the sandy fill mound. The ancient Khmer engineers in clearly identify these two types of clayey fill and sandy fill.
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3.2 Weakening Strength with Water Contents The obtained SPT, N-values are plotted against water contents of the sampled soils for both borings and is shown in Fig. 9 No relationship is found for BV09 of the backfilled soil; however, the decrease of water is found to result in the increase of the SPT, N-values for boring BV10.Sampled soil of very high SPT-N-value for boring BYV2010 looks like soft sandstone as shown at the upper left position of Fig. 10. When the sampled soil was put into water, it sucked water, and finally collapsed within 10 min as shown in Fig. 10. A series of laboratory tests were performed to see how much strength changes due to the decrease of the moisture contents. More than 25 samples in containers were prepared with water content of 15%, which almost creates a 100% saturated condition. The samples were placed outside of the test room and the water evaporated from the sample and the water content decreased day by day. Yamanaka cone penetration tester was used to evaluate the bearing strength of the soils as shown in Fig. 11. The results are shown in Fig. 12 and It shows clearly an increase of strength more than 50 times due to the decrease of the water content.
Fig. 8. Grainsize distribution.
3.3 Mineral Components of the Filled Sand Micrograph of the section of the sample is shown in Fig. 13, where the round shape of sand is seen filled with clay material. X-ray diffraction analysis was applied to the fine particle of the foundation sand is shown in Fig. 14. In addition to quartz, halloysite (Kaolinite group) was detected as the clay component. Compared to other clay minerals, the power to absorb water is very small and does not swell and the volumetric change is very small and stable compared to montmorillonite.
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Fig. 9. SPT-N values vs. water contents
Fig. 10. Collapse of stiff filled sand in water condition
Fig. 11. Yamanaka Cone test
Fig. 12. Strength increase with decrease of water
Fig. 13. Micrograph of sampled soil
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Fig. 14. X-ray diffraction analysis for the filled soil
3.4 Expected Mechanism of Dramatic Change of the Strength and Water Contents A possible mechanism of the increase of the strength with the decrease of the water is the effects of the meniscus of the water film created between nearby particles to make bridging the particles as shown in Fig. 12. The vacuum suction pressure of the water inside the meniscus is increased with the decrease of the radius of the meniscus. The increased vacuum suction pressure attracts soil particles that creates the very large strength as shown the extra-large SPT, N-values of N = 100–200 as shown in Fig. 3. However, when the soil is submerged in water, the water meniscus disappears, and the suction pressure diminishes resulting in the minimum level of the cohesion strength by kaolin clay. The sudden decrease of the strength with collapse as shown in Fig. 6 is possible under free boundary conditions. In the field, the densely compacted soil with some confinements keeps its stability with the large frictional angle.
Fig. 15. Vacuum suction of water within meniscus (a) small attraction (b) large attraction
3.5 Field Monitoring of Water Contents by Rain When rain falls and infiltrates into the mound, the water content within the mound will be increased. Monitoring the change of the moisture in the soil mound was performed in
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the platform mound at Bayon temple [5]. Moisture sensors (Fig. 16) had been installed at several depths at GL-0.5, -0.75, and -1.0 m and the monitored results are shown in Fig. 17 with rain fall results. As expected, the volumetric water contents increases when the rain falls. In Fig. 17, the monitored results at S-point of two cases of rain events are shown. The earlier case shows the increase of the volume water content are found at the upper two depth points. The deepest point at GL-1.5 m, the volume water content keeps the constant value, which means the infiltrated rainwater reached to the upper two sensors but did not reach the bottom one. The amount of the rain was too small to provide enough rainwater in the earlier case. In the latter case, the sensor at the bottom of GL-1.5 m increases with a time delay of about 1.5 h compared to the top sensor at the GL-0.5 m. The infiltration rate is about 1.0 m/1.5h. When the heavy rain stops the volume water content begins to decrease due to evaporation, and to some extent drainage. The present rain style is “Squall” which begins suddenly and continues for a few hours in heavy intensity and stops. In the squall type rain, rainwater penetrates from the surface to only a few meters, and did not cause fatal failure.
Fig. 16. Monitoring points and sensor
Fig. 17. Monitored results of water in the filled mound
4 The Authenticity of the Foundation of Main Tower of Bayon As discussed in the previous sections, the shallow direct foundation of Bayon has been standing for about 700 years because of the special character of sandy filled mound. Figures 18 and 19 compares the stability of foundation in common sand fill and that of Bayon temple. In common sand fill, RC10 story building as well as the main tower of Bayon with shallow direct foundation will collapse. Pile foundation is the common design procedure at present. Sand filled mound of Bayon temple shows extraordinarily large strength in dry, but weakened in wet and saturated conditions. Main tower of Bayon has been supported safely with direct foundation in the sand filled mound of Bayon temple in monsoon climate with “squall type rain.”
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Fig. 18. Common sand filled mound
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Fig. 19. Sand filled mound of Bayon temple
The character defining elements of the foundation system of Bayon temple consist of several factors as follows: 1. 2. 3. 4. 5.
Trenched foundation extending to outside of the temple Three stepped mound is constructed by compacted uniform sandy soil Uniform grain-size distribution of sand with 10–20% of fine grain contents Very large strength of the sandy fill in dry but weakened under water Thick laterite block surrounding the base of the foundation of main tower from the 2nd step
5 Proactive Countermeasures Against the Risk Inherent with Global Warming 5.1 Anticipated Risk to the Heritage Structure with Global Warming In the coming climate warming period, the rain type of “squall” at present is anticipated to change to “long and heavy” rain. This change of climate could result in the deeper penetration of rainwater into the sandy filled mound and weaken the foundation mound. As noted in Fig. 7, the vertical shaft with backfilled soil in very loose state could cause inwards displacement and finally failure of the shaft resulting the collapse of the main tower of Bayon. Based upon a serious of borings at the mound, the basic structure of the foundation is found as the shallow direct foundation on sandy soil which is surrounded by a thick laterite blocks of 6 m in thickness as shown in Fig. 20. The mechanical strength of soil is generally expressed frictional resistance angle and cohesion. The very dense compacted sand is assumed to have a constant value of the shear resistance internal frictional angle as φ = 40°. The cohesion may be assumed as the highest uniaxial compression strength value of Qu = 1000 (kN/m2 ) in dry state and the lower one of Qu = 5 (kN/m2 ). A 3D FEM model of the foundation was created to simulate the mechanical behavior by weakened sandy filled mound as shown in Figs. 21 and 22. Plastic failure points are concentrated into just beneath the Central Tower and the outer edge of the surrounding foundation step. zones. Direction of the displacements beneath the foundation is not
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only downwards but also inwards which is caused by the very loose state of the sand. Direction of the displacement at the outer edge of the foundation mound is a horizontal outwards direction. It is shown that the effects of the weakened filled soil by the long and heavy rain will cause plastic zones in the foundation and deformation of the inwards and outwards directions at the inside of the shaft and at the outer edge of the mound, respectively (Table 1).
Fig. 20. Foundation of main tower of Bayon
Fig. 21. Strength of sandy fill at present
Fig. 22. Weakened sandy fill beneath the main tower
5.2 Proactive Counter Measures Against the Risk of Global Warning to Central Tower of Bayon The plastic zone near the vertical shaft is found to concentrate just beneath the base stone of the central tower within about three meters. Inwards horizontal displacements
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Table 1. Load to direct foundation unit
Central Tower
A sub-tower
Unit mass
kN/m3
23
23
Vol
m3
967
156
mass
kN
22,240
3,588
area
m2
15
7.64
load
kPa
1,482
470
Central tower section is colored in red and sub-tower in blue in the Fig. 23 below.
Fig. 23. Sections of the main tower and a sub-tower
Fig. 24. Plastic yield zone
Fig. 25. Displacement vector
also appear associated with the plastic zone beneath the base stone within three meters. Another plastic zone is recognized around the edge of the foundation mound with outwards displacements. The simplest measure to keep the integrity of the characteristics of the sandy fill in Bayon temple is to provide impervious layers beneath the surface stones. Among several methods of interventions available, three basic principles of conservation of cultural heritage, ie.1. minimum level intervention, 2. incremental approach, and 3. Removable/reversible measures are to be considered.
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The proposed method at present consists of the following four methods to prevent the rainfall penetration into foundation mound and strengthening the upper portion of the vertical shaft from the top to about 5 m in depth as shown in Fig. 26. A. To close openings at the top of main and sub-towers to prevent rainwater infiltration. B. To replace soils under stepped stone with lime mixed sand to stop infiltration of rainwater. C. To shield the gaps between paving stone. D. To strengthen the upper part of the vertical shaft at the central base of the main tower. In addition to the above-mentioned prevention of rainwater penetration into the foundation mound, the present surface drainage system should be studied. If the capacity of drainage is smaller than the anticipated rainfall under the warm climate, necessary modification should be arranged. 5.3 Monitoring the Moisture Change During Rain Monitoring system of rainfall at the Bayon and moisture contents in the filled mound should be established. There are two methods available to monitor the change of the water contents of the filled mound. The direct method is to install moisture sensors at several depths as shown in Fig. 16. Another method utilizing a geophysical method such as electric survey, which utilizes the change of electric resistance of the ground with water contents However, this method does not give precise changes of moisture at points, but rather evaluates the moisture condition by the change of electric resistivity at different time of surveys. The combination of these methods is expected to provide overall better understanding of the field situation and are recommended to be adapted.
Fig. 26. Countermeasures against water penetration to the foundation mound
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6 Conclusions The filled sandy soil of the foundation mound for Bayon temple was identified as kaolin sand very stiff in unsaturated dry condition, but easily collapsed under submerged conditions. In the past and present, the rain type has been “squall type” of very heavy rain fall but rather in short duration and resulted in a cyclic process of infiltration of rainwater and evaporation with no damage within the foundation mound. However, in the coming warm climate, the rain is anticipated to be not only heavy, but also continuous in duration which may bring deep infiltration of water into the foundation mound resulting in the collapse of the main tower. Against the anticipated failure caused by global warming events, a proactive method is proposed as the minimum counter measure to keep the integrity of the character defining elements of the authenticity and protect the Bayon tower.
References 1. Narita, T., Nishimoto, S., Shimizu N., Akazawa Y.: Trench Excavation of Outer Gallery, Bayon, Annual Report on the Technical Survey of Angkor Monument 2000, pp. 3–18, 317 (2001) 2. Shimoda, I., Yamamoto, N., Iwasaki, Y., Fukuda, M.: Excavation Survey of the Central Tower Chamber. Annual Technical Report on the Survey of Angkor Monument 2008, JASA, Tokyo, pp. 67–88 (2009) 3. Iwasaki, Y., Fukuda, M.: FY2009 Report-Geoengineering/Environment Unit. Annual Technical Report on the Survey of Angkor Monument 2008, JASA, Tokyo, pp. 323–356 (2009) 4. A Iwasaki, Y., Fukuda, M., Haraguchu,T., Kitamura, A., Ide, Y., Tokunaga, T., Mogi, K.: Structural of Platform Mound of Central Tower Based upon Boring Information. Annual Technical Report on the Survey of Angkor Monument 2012–2013, JASA, Tokyo, pp. 93–113 (2014) 5. Koyama, T., Yamada, S., Iwasaki, Y., Fukuda, M., Shimoda,I., Ishizuka, M.: Installation of Moisture Sensor. Annual Technical Report on the Survey of Angkor Monument 2014–2015, JASA, Tokyo, pp. 132–137 (2016)
Restoration of Architectural Stone Heritage Damaged by 2011 Great East Japan Earthquake Toshikazu Hanazato1(B) , Hayato Suzuki2 , Hideaki Takahashi2 , Shigenori Kita3 , and Tomoaki Suzuki4 1 Kanagawa University, Yokohama 221-8686, Japan
[email protected]
2 Borderless Architect Ltd., Fukushima-shi 960-8204, Japan 3 Kita Shigenori Structural Design Office Co., Ltd., Tokyo 175-83, Japan 4 ARK Information Systems, Inc., Tokyo 102-0076, Japan
Abstract. The Great East Japan Earthquake of 2011 caused serious damage to a number of architectural heritages. Fukushima Photo Museum (Former Laboratory of Electrics Ministry of Communications), constructed in 1922 and designated as the local governmental important cultural property, was damaged. This heritage structure was categorized into an unreinforced stone structure with local tuff stones. The strong ground motion caused cracks in the stone walls, tilting of the pediment, and falling of the stucco ceiling in the rooms. The multi-disciplinary expert committee for the restoration project was established. In order to discuss the seismic reinforcement of this damaged stone building, structural survey was performed at the first stage of the restoration project. The construction material was the local tuff stone characterized by its rather low specific gravity of 1.2. While the joints were made of cement with insufficient bonding strength, the friction coefficient of the joints was evaluated to be as high as 1.5. Finally, the committee proposed the seismic reinforcement by employing prestressing technique utilizing vertical high-strength steel-bars. The girders on the stone walls were placed by utilizing laminated wood panel of the local products. 3-D finite element model was made to detarmine the prestressing force induced. Furthermore, seisimc safety of the structure was ensured by the static structural caluclation acccording to the Japanese Seismic Evaluation Standard of exsisting RCC building. The microtremore measurement was performed before and after the structural restoration. After completion, the long-term monitoring of stress of the prestressig force induced at the steel-bars has been conducted to check the relaxation of the induced stress to the steel-bars. Keywords: Earthquake damage · Seismic reinforcement · Stone heritage · Prestressing technique · Monitoring
1 Introduction The Great East Japan Earthquake of 2011 caused serious damage to a number of architectural heritages. Except for the catastrophic damage caused by the devastating Tsunami, it should be emphasized that the predominant short period of the strong ground motions © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 26–40, 2024. https://doi.org/10.1007/978-3-031-39450-8_3
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gave severe impact to masonry heritage structures. In Fukushima City, Fukushima City Museum of Photography (Fig. 1), constructed in 1922 and designated as a local governmental cultural property, was damaged and had been closed for public. Because of the economic reason affected by the severe accident of the Nuclear Power Plant, Fukushima City, the owner of this architectural heritage, considered dismantlement and removal of this damaged architectural heritage just after the earthquake. However, the volunteers and the experts who understood its historical and cultural values appealed the local government not to be demolished and to be restored for opening again. One of the authors wrote the letter to the local Government to express it would be able to be restored from a structural engineering point of view and should not be removed as a cultural property. The Government finally decided that this architectural heritage would be restored, having established the multi-disciplinary expert committee for restoration. The present case study introduces, as the 10 years story of restoration project from the crisis of demolition to restoration and opening for public, the seismic reinforcement employed by prestressed technique utilizing high-strength steel bars. This architectural heritage was categorised into non-reinforcement structure from a structural engineering point of view. In consideration of the light tuff stone and rather high friction coefficient of the joints, the committee proposed the seismic reinforcement by employing prestressing technique utilizing vertical high-strength steel bars. Furthermore, the girders for structural confinement on the stone walls and the diagonal struts for enduring horizontal stiffness were placed by utilizing laminated wood panel of the local products. Before and after the restration, microtremore meassuments were performed to investigate the fundamental dynamic characteristics. After the structural restoration was completed, the long-term monitoring of the induced tension stress of the high-strength steel bar installed in the stone walls has been conducted for maintemance, as the wooden materials that would be affected by creep phenomenon was utilized for the girder on the stone walls.
Fig. 1. Appearance of building in 1930’s
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2 Overview of Earthquake and Damage of 2011 Great East Japan Earthquake 2.1 Outlines of Earthquake On 11th March, 2011, a devastating earthquake of the moment magnitude 9.0(Mw ) struck with an epicenter off the Pacific Ocean of Japan from the Tohoku to the Kanto region [1]. This 2011 Tohoku Area Pacific Offshore Earthquake was the largest earthquake to have hit Japan since records began. The huge fault caused the main shock was a low angle reverse fault and was estimated to be approximately 450 km long, approximately 200 km wide with the maximum strike slip of 20 to 30 m [1]. Furthermore, dividing the main rapture area was dividing into three, it was estimated that the depth of the epicenter was 24 km, and the duration of rapture was approximately 3 min [1]. There have been 500 aftershocks exceeding magnitude 5.0 [2]. The seafloor movement of the mainshock generated the devastating huge tsunami, and caused a large number of human loses and missing. Since 1996, the Japan Meteorological Agency has conducted the mechanical measurement of seismic intensity and announced the instrumental seismic intensity. Based on this, regions where the seismic intensity of the mainshock was X or exceeded X under the modified Mercalli Intensity Scale (6 or more under the JMA intensity Scale) were widely distributed from Iwate Prefecture to the Pacific coast of northern Ibaragi Prefecture. According to the seismic records collected by KNET strong motion seismogram network system provided by the National Research Institute for Earth Science and Disaster Prevention, there were approximately 20 stations with peak acceleration exceeding 1.0G. However, those records showed that the short period components was large, and it was reported that the predominant frequency was higher than 5 Hz [2]. In Fukushima City, the strong ground motions at the level of 0.3G, corresponding to seismic intensity 6 (JMA Scale), were recorded by KNET system. 2.2 Damage to Cultural Properties The human damage caused by the 2011 Great East Japan Earthquake as of September 16th , 2011, was approximately 16,000 dead, 4000 missing and 5,500 injured [2]. According to the Preliminary Reconnaissance Report of the 2011 Tohoku-Chiho Taiheiyo-oki Earthquake published by the Architectural Institute of Japan, approximately 105,000 houses were completely destroyed and 107,000 were partially destroyed. Most of this human and residential damage were caused by the Tsunami. As for the cultural properties, more than 700 damage cases relating to nationally-designated or registered cultural properties were reported as of August 3rd . It was believed that a total number of cultural properties damaged by the earthquake exceeded 1,000. The earthquake damage was caused the tangible cultural properties, intangible ones, fork ones, monuments, cultural landscapes, and groups of traditional buildings. In particular, the earthquake ground motions with short predominant period affected the masonry heritage structures more than wooden buildings.
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3 Description of Fukushima City Museum of Photography 3.1 Building Description Fukushima City Museum of Photography is a 2 stored stone building with eave height of 9.2 m, having been a city-designated cultural property. The stone buildings was constructed in 1922, as Laboratory of Electrics Ministry of Communications. The building has a plan of 25.5 m and 12.7 m in longitudinal and width direction, respectively (See Fig. 2). The stones used for the construction was called Kunimi-stone, a type of volcanic tuff stone. The typical dimension of a stone block is about 55 cm in height, 85 cm in length, 35 cm in depth. The mechanical properties of this tuff stone are introduced in the next section. A cementitious materials were used for the joints of about 5mm thickness. It was not certain whether some kind of connector was used for the joinery, but at least, metal was not used for strengthening. The framework of roof truss was made of wood. The foundation was of reinforced concrete with bricks. 3.2 Earthquake Damage and Process for Restoration Major damage found after the earthquake included the tilting and the cracks in the decorative pediment above the entrance (See Fig. 2(a) (b)) To support the pediment, the temporary scaffolds were erected as an emergency countermeasure, shown in Fig. 2(a). In addition, visible cracks and the slight movement were found near the southwest corner (See Fig. 2(c)). Inside of the building, there were cracks at the corner of the openings, Some plastering of interior walls fell as well, shown in Fig. 2(d). For safety reason, the museum had been closed since the earthquake occurred. In April 2011, an investigation was conducted by the Architectural Institute of Japan. In November of the same year, Cultural Properties Doctor Dispatch also surveyed the building. In September 2014, Fukushima City, the owner of the building, decided to restore the building to use as a regional cultural asset.
4 Survey for Structural Restoration 4.1 Material Properties Tests For seismic diagnosis and seismic retrofit studies, mechanical tests of the building materials were performed. This heritage structure composed mainly of local volcanic tuff stone “Kunimi-stone” that was used to construct the structural walls. This stone was characterized by rather low specific gravity of 1.2 with compressive strength of 4.1 (N/mm2 ), Young’th modulus of 1.4 (N/mm2 ), and tensile strength of 0.37(N/mm2 ). In the base and the foundation, another rigid stone and concrete were used, of which compressive strength of 14.9(N/mm2 ) and 13.8 (N/mm2 ), respectively. In addition, bricks were utilized at some parts of the building. It should be emphasized that seismic performance was significantly affected by the joints between stones of the walls. In the present study, laboratory shear test was performed by using the specimens sampled by the core boring from the walls. As the shear strength was affected by the normal stress caused by the dead weight, Fig. 3 shows relation of strength and normal stress. Portland
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(a)
(b)
(c)
(d)
Fig. 2. (a) Appearance after earthquake (b) Tilting of pediment (c) Cracks at SW corner (d) Falling of plaster finishing
cement was already used widely in Japan during this period of the construction, it was believed that the cement was used for the joint materials. However, the bonding effect of the joints was too small to evaluate the strength, as shown in Fig. 3. On the other hand, the friction coefficient was evaluated to be approximately 1.5, because the surface of the stone that touched the joints was rather rough. Shear stress (N/mm2)
Normal stress (N/mm Fig. 3. Shear tests of joint
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4.2 Microtremore and Earthquake Monitoring Before the restoration operation of this damaged architectural heritage started, microtremore measurement was performed by utilizing 12 velocity sensors. The natural frequency was evaluated to be 4.6 Hz in EW direction. On the other hand, in NS direction, it was evaluated to be 3.5 Hz and 4.5 Hz in the east wall and the west wall, respectively. It was considered that this difference was caused by the structural condition that the east side wall had much more openings than the west side. These fundamental dynamic characteristics were compared with those measured after the seismic reinforcement, shown in Sect. 6. Earthquake monitoring utilizing 3 MEMS accelerometers (3 components sensors) was also performed for 6 months during May 16, 2017 and December 8. During this period, a total of 16 earthquake records were obtained. Those earthquake records were compared with the dynamic structural analysis utilizing simplified SR model (Fig. 4).
Fig. 4. Plan (upper: 1st Floor, lower: Ground) floor)
5 Seismic Reinforcement 5.1 Seismic Loads for Designing Reinforcement After the structural restoration was completed, a major aftershock that occurred on Feb. 13, 2021 with magnitude of 7.3(Mj ) struck this building. Table 1 shows the outline of the mainshock and this aftershock, related to the present study. Magnitude, peak acceleration and intensity scale (Japan Meteorological Agency Scale) recorded in Fukushima City are compared in this table. In addition, the simulated ground motions compatible with the strongest earthquake provided by Japan Building Code were also utilized in the present study. As the spectrum was given at the engineering bedrock, surface soil response should be taken into account. The amplification due to soil response, corresponding to Type 2, was accounted. Figure 5 shows the acceleration response spectra of those ground motions with damping factor of 5%. It can be noticed that the predominant period of the recorded motions were around 0.1–0.3 s, being very short one, in addition, there finds another peaks around 1.0 s. As masonry structures are, in general, short period structure, the earthquake ground motions generated by 2011 East Japan Great Earthquake might affect structurally masonry buildings. Furthermore, it can be recognized that the intensity of the recorded ground motions was lower than that of the strongest earthquake by Japan Building Code. The intensity and frequency characteristics of one of the most severe aftershock of Feb. 13, 2021 was similar to the ground motions of the mainshock.
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For structural designing of reinforcement, both dynamic 3-D FEM analysis and static calculation method defined by Japan Standard for Seismic Evaluation of existing reinforced concrete buildings3) . The present building was of brick masonry, however, we applied mutatis mutandis of the standard for existing reinforced concrete structure. To conduct dynamic FEM analysis, the following input ground motions were adopted as, 1) Simulated ground motion at the site when 2011 Great East Japan Earthquake (mainshock) occurred. In order to simulate the ground motions, the strong motion records in Fukushima City was utilized, shown in Table 1. Non-linear soil response of the surface layer was taken into account by employing equivalent linearization method where strain-dependent characteristics of soil stiffness and damping factor was considered. 2) According to Japan Building Code, the ground motion that conformed to the response spectra of strongest earthquake motion at the engineering bedrock was synthesized. Non-linear soil response of surface layer was also taken into account. On the other hand, for the latter static calculation used for seismic diagnosis, seismic index of structure Is, representing the seismic performance, was introduced for in-plane direction. Here, seismic safety evaluation for out-of-plane direction was performed by the dynamic 3-D FEM analysis, as the prestressing technique was introduced in the present case study. Table 1. Outline of earthquakes Occurence date
Main shock
After shock
March 11, 2011
Feb. 13, 2021
Magnitude
9.0(Mw)
7.3(Mj)
Intensity in Fukushima
5.3
5.2
PGA (EW)
0.30G
0.27G
PGA (NS)
0.33G
0.21G
PGA (UD)
0.15G
0.20G
Sa(cm/s2) EW Mainshock 11 March 2011 NS Mainshock 11 March 2011 EW Aftershock 13 Feb. 2022 NS Aftershock 13 Feb. 2022 Building Code (Engineering bedrock) Building Code (Surface)
Fig. 5. Response spectra of input ground motions (h = 5%)
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5.2 Reinforcement Concept and Decision Making In order to ensure the seismic safety of this damaged unreinforced stone heritage architecture of stone, the following issues should be solved from an earthquake point of view as (Fig. 6), 1) Stone walls should be reinforced. The strength of joint mortar was insufficient against seismic loads. In particular, reinforcement to ensure safety in out-of-plane direction should be done. 2) In order to connect between the walls, the girder (kerb) should be installed. 3) Horizontal stiffness at the 1st floor and the roof should be endured to transmit the seismic loads to the baring walls. 4) The pediment should be reinforced so that it would not fall.
Fig. 6. 3-D finite element model
As shown in Fig. 1, the friction coefficient of the joints was as large as 1.5, while the bonding strength was negligibly small. Furthermore, the specific gravity was as low as 1.5. These mechanical condition at the joint suggested that prestressed technique was the most appropriate method to reinforce the stone walls. The expert committee for restoration finally decided to employ the prestress technique for seismic reinforcement. The tensile loading to be induced would be determined by dynamic linear FEM analysis. Figure 7 shows the 3-D analysis model in the present study. The stone walls were modeled by 3-D solid elements. Note that FEM analysis was employed to evaluate the tensile force induced for the prestress technique. In the present study, the elements used were solid elements, which were divided into 6 elements in the cross-sectional direction so that variation in cross-sectional stress could be evaluated more accurately. The boundary condition of the FE model at the base was fixed. The eigenvalue analysis of unreinforced structural model resulted in the natural frequencies were 3.8 Hz and 4.7 Hz in NS direction and EW direction, respectively. First, the dynamic response analysis was performed for the case of the ground vibrations due to the Great East Japan Earthquake of 2011. Figure 7 shows the peak normal stress (tensile stress) of the south wall. It can be found in this figure that higher tensile stress was generated at the base stone as high as 600 kN/m2 , which is lower than the
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(b)
(c)
Fig. 7. (a) Peak normal stress induced by simulated ground motions of Great East Japan Earthquake at the site (before reinforcement) (b) Peak shear stress induced by simulated ground motions of Great East Japan Earthquake at the site (before reinforcement) (c) Peak normal stress induced by simulated ground motions of Great East Japan Earthquake at the site (after reinforcement)
tensile strength of the base stone, 1,400 kN/m2 evaluated from the mechanical material tests (See Sect. 4.1). Furthermore, the tensile stress was generated around the openings, in particular, rather high tensile strength was shown at the lintels. However, as the mean stress was less than 300 kN/m2 , it would not be anticipated that the structure would collapse by the failure of the wall stone. The lintels had enough strength because they were of reinforced concrete. Figure 7 shows the in-plane peak shear stress of the south wall before the reinforcement. The analysis indicated that the shear stress would exceed locally the shear strength, however, it would be caused just in a small area. The stone wall was damaged at the small area near the SE corner (See Fig. 2) by that devastating earthquake, but was not destroyed. The analysis was consistent with the actual damage. 5.3 Implementation of Reinforcement Utilizing Prestressing Technique A total of 46 high tensile steel bars (ϕ23 mm in diameter) were placed into the holes after the core boring (ϕ50 mm). The specification showed that yielding and ultimate strength of the steel bar was 397 kN, 449 kN, respectively. Those bars were modeled by using spring elements, shown in Fig. 8. Described in Fig. 8, the beam elements were utilized to show not only vertical high strength steel-bar but also the steel braces to ensure the horizontal stiffness at the 1st floor, and the wooden horizontal angle brace at the corner to improve the horizontal stiffness at the girder (kerb) level on the walls. Figure 9 shows the elevation in which the high strength steel bars were inserted and tensile force was applied. Un-bond space existed between the hole and the steel bars. At the lower and the upper ends of the bars were fixed with steel plates (See Fig. 8).
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wooden gird-
Fixed anchor
(a)
Steel bar
(b)
Fig. 8. (a) 3-D Arrangement of reinforce elements (b) Reinforcement of front wall
Fig. 9. Peak normal stress after reinforcement induced by strongest earthquake given by Japan Building Code
Fig. 10. Section where peak normal stress shown in Fig. 11
Prestressing force was applied with a jack (See Fig. 7) The force was determined from the seismic response analysis utilizing FEM. In the response analysis, the strongest earthquake ground motions defined by Japan Building Code was used as the input motions. The acceleration response spectrum at the engineering bedrock and the ground surface are shown in Fig. 2. The ground motions compatible to those spectra was simulated. In Japan, even cultural heritage, it is normally applied the seismic safety that is required by the National Building Code. For designing seismic reinforcement employing prestressing technique, the ground motion level was the same one as the National Building Code.
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As analysis results, we determined that the prestressing tensile force should be 50kN for each steel bar. After reinforcement with applying prescribed high tensile force to the steel bars, the dynamic response analysis was conducted by utilizing FEM. Figure 9 shows the peak normal stress induced by the strongest ground motion given by the Japan Building Code. The analysis showed that the peak stress approximately 600 kN/m2 was generated at the base stone, which was enough smaller than the tensile strength 1340 kN/m2 . On the other hand, the peak tensile stress generated in the lintel of the opening was larger than the tensile strength of the local tuff stone of 370 kN/m2 , however, the lintel was of RCC, therefore, it would be judged to be safe. In order to verify the effectiveness of the prestressing force, the normal stress induced at the section of the walls was described. Figure 10 shows the section level where the peak stress is compared between before and after the reinforcement. The peak normal stress generated by the strongest earthquake ground motion by Japan Building Code is presented in Fig. 11 comparing before and after the reinforcement. It can be recognized in this figure that the reinforcement employing prestressing method is effective in reducing the tensile stress generated during the most severe earthquake. The peak tensile stress induced during the strongest ground motion was evaluated to be 155 N/mm2 , which was enough smaller than the tensile strength of the high strength steel bar of 1080 kN/mm2 .
(a)
(b)
Fig. 11. Normal stress generated at 99.19 s for the case of the strongest ground motion by Japan Building Code (a) induced tensile stress exceeded tensile strength of joint (b) induced tensile stress was lower than tensile strength of joint
5.4 Strengthening for Structural Connection Another important reinforcement was confinement of stone walls, i.e. connection at top (girder) of the walls. In this restoration project, wooden material was used for reinforcement. It was reported that reinforcement using RCC structure might cause the severe damage to the historical stone heritages by the recent devastating earthquake in Italy. Endo. Y [3] indicated the difference in rigidity between the stone masonry and the concrete might cause the collapse of the historical stone church in L’Aquila when 2009 earthquake occurred. In the present restoration project, therefore, wooden material was used in place of reinforced concrete members for strengthening. Laminated woods of local products (Section 500 mm × 200 mm) were utilized here (See Fig. 12) to connect horizontally at the top of the stone walls. Furthermore, the horizontal connection at the
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level of 1st floor was endured by steel beam. On the other hand, the horizontal stiffness at the level of the tops of the walls were endured by angle brace of wood. Steel members were utilized to endure the horizontal stiffness of the present stone structure. 5.5 Calculation of Ultimate Lateral Strength As for the ultimate lateral strength of the structure, the Seismic Index of Is, the index for seismic diagnosis of existing reinforced concrete structure in Japan [4], was modified for masonry structures and employed [5] (See Appendix). Table 2 shows the seismic index of Is, which compares before and after the reinforcement. For the diagnosis of existing reinforced concrete buildings, the safety limit of Is = 0.6 is recommended for the criteria for judgement. Is = 0.6 was evaluated from experience of the earthquake damage and collapse of the reinforced concrete buildings due to past earthquakes in Japan. This table indicates the effectiveness of the reinforcement employed in this practical project. Table 2. Ultimate lateral capacity represented by seismic index of structure Is Before Reinforcement
After reinforcement
Ground floor
1st Floor
Ground floor
1st Floor
Longitudinal (EW)
0.32
0.31
2.63
1.06
Transverse (NS)
0.36
0.35
1.88
0.86
(a)
(b)
(c)
Fig. 12. (a) Placement of girder of laminated wood (b) Prestressing work (c) Reinforcement of foundation and anchor of prestressing bar
5.6 Another Reinforcement As shown in Fig. 2, the pediment just above the entrance was damaged and tilted. It was needed to restore and strengthen it. Reinforcement was done by employing steel frame (See Fig. 13).
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Fig. 13. Reinforcement of pediment by steel frame
6 Microtremore Measurement to Verify Reinforcement Implementation In the present case study, microtremore measurement was done to verify the effectiveness of the seismic reinforcement. Figure 14 compares the transfer function (amplification) direction in EW (out-of plane) direction from the base to the top of the east wall, pointed in Fig. 2, before and after the reinforcement. Shown in Fig. 14, the reinforcement rose the natural frequency and reduced the peak amplitude. This figure demonstrated that the reinforcement increased the rigidity of the structure and would reduce the seismic response. The same effectiveness in dynamic response was found in the other measuring points, a total of 9 points.
Before reinforcement After reinforcement
Fig. 14. Transfer function before and after reinforcement
7 Monitoring of Prestressing Force As described in Sect. 5.4, wooden materials were introduced for the connection of the structure as the girders placed at the top of the stone walls. There is a creep phenomenon in the properties of wood. Also, there is a possibility of such tuff stone. Therefore, the long term monitoring of prestressing force has been conducted to investigate the effect of relaxation of the prestressing force due to creep phenomenon. Shown in Fig. 15, a total
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of 4 strain gages to measure the variation of the prestressing force were installed at 2 steel bars. Since material’s strain is affected by temperature, the temperature at the holes where the steel bars were inserted has been also monitored as well. The monitoring started at the same time when the prestressing force was induced on April 2, 2020. Figure 15 describes the temperature and the tensile force calculated from the measured strain, respectively. Figure 15 shows that, although the prestressing force was reduced just after the loading and affected by the temperature, it varied with in allowable criteria shown in the prestressed concrete structure standard in Japan. The monitoring has been ongoing to endure the prestressing force.
8 Concluding Remarks Prestressing method was introduced to the heritage stone structure that was damaged by the 2011 Great East Japan Earthquake, and it was reinforced using wooden girders to endure the structural connection. Microtremor measurement and monitoring of prestressing force were performed to check the effect of reinforcement. This architectural heritage was opened for public in April 2011, 10 year’s anniversary. As commemoration of the recovery from the earthquake, the use of local people had begun. No structural damage was caused by the major aftershock of Feb. 13, 2021, described in Table 1, which would demonstrate that the seismic reinforcement introduced in this case study was appropriate.
(a)
(b)
Gage
Stone wall
High strength steel bar
(c)
Fig. 15. (a) Strain gage installation (b) Temperature (c) Prestressing force
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Appendix Seismic Index of Structure Is. On the basis of the Japanese Seismic Evaluation Standard of existing RCC building was modified for brick masonry for each story Is is calculated by the following equation (Hokkaido Building Engineering Association [5]). Qu · F · T · SD Is = (Wi · Ai · Z · Rt ) Here, Qu : Ultimate lateral load carrying capacity F: Ductility index (F = 0.6 recommended for brick masonry) T: Time index (T express effects of structural defects) SD : Irregularity index (Sd = 1.0 for regular shape) Wi : Wight of each story Ai : value representing a vertical distribution of seismic shear coefficient Z: Value representing regional seismic activity (Z = 1.0 for Fukushima) Rt : Value representing vibration characteristics evaluated from structural natural period and soil conditions The denominator Wi Ai Z Rt is lateral shear resistance required by Japan Building Code for designing new buildings.
References 1. 25th March, 2011(5:30 pm) press release by the Japan Meteorological Agency: Re: The 2011 Tohoku Area Pacific Offshore Earthquake (28). http://ww.jma.go.jp/jma/press/1103/25b/kai setsu201103251730 2. Architectural Institute of Japan: Preliminary Reconnaissance Report on the 2011 Tohoku-Chiho Taiheiyo-oki Earthquake 3. Endo, Y.: Comparison of seismic analysis methods applied to a historical church struck by 2009 L’Aquila earthquake. Bull Earthquake Eng. 13, 3749–3778 (2015). https://doi.org/10. 1007/s10518-015-9796-0 4. The Japan Building Disaster Prevention Association: Standard for Seismic Evaluation of Existing Reinforced Concrete Buildings, 2001 5. Hokkaido Building Engineering Association. https://hobea.or.jp/wp-content/uploads/2016/07/ renga_kijyun_ver2.pdf
Study on Evaluation Method of Reinforcement Effect of Dry Masonry in Historical Monuments Applying DDA S. Yamada1(B) , R. Hashimoto2 , T. Koyama3 , M. Fukuda4 , and Y. Iwasaki5 1 Yasuda Women’s University, Yasuhigashi 6-13-1, Hiroshima 731-0153, Japan
[email protected]
2 Kyoto University, Katsura Campus, Nishikyo-ku, Kyoto 615-8540, Japan
[email protected]
3 Kansai University, Hakubaichou 1-3-2, Osaka 569-1098, Japan
[email protected]
4 Kumamoto Geo-info Evaluation, Suizenji 1-1-9, Chuo-ku, Kumamoto 862-0951, Japan
[email protected]
5 Geo-Research Institute, Otemae 2-1-2, Chuo-ku, Osaka 540-0008, Japan
[email protected]
Abstract. In this paper, we propose a method for an evaluation method of reinforcement effect of dry masonry in historical monuments applying DDA, which is one of the discrete mechanics methods, to evaluate structural performance and to design effective countermeasures. In DDA analysis methods, we developed a method to evaluate the capacity load after reinforcement of dry masonry by incorporating a spring of the reinforcement member, and verified the reinforcement effect using this method. From the numerical analysis, it was confirmed that the results differ depending on the installation location, and these parameters affect the performance. It is important that the masonry construction of dry masonry has an influence on the collapsing mode and capacity load, and it is thought that the non-linear collapsing phenomenon is well simulated by our proposed method. As the result, we tried to propose an evaluation function to verify the reinforcement effect due to the difference in the reinforcement method. Keywords: DDA · Dry masonry · Wind pressure · Angkor monument · Cambodia
1 Introduction 1.1 Outline of Bayon Temple In this paper, we propose a method for an evaluation method of reinforcement effect of dry masonry in historical monuments applying DDA, which is one of the discrete mechanics methods, to evaluate structural performance and to design effective countermeasures. And the object of this paper is the Bayon Temple of Angkor Thom in Cambodia, which © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 41–50, 2024. https://doi.org/10.1007/978-3-031-39450-8_4
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was built in the 12th century [1]. It is composed of masonry towers, and they were constructed by dry masonry of sandstone. The main tower of it is about 40 m high from the ground. The shape of the upper area of the main tower is now complicated because of its partial collapse in the past. Around 1930, EFEO carried out reloading, repair with concrete, and reinforcement with iron hose, but due to their deterioration, new reinforcement and repair measures are required (Fig. 1).
Fig. 1. View of Bayon temple and location of the analysis
There are multiple structural cracks in the middle part of the Bayon main tower, and there is concern that the masonry may partially collapse due to these structural cracks. At this location, strong wind is suggested as an external factor that causes the masonry to collapse. The authors have so far conducted and analyzed long-term environmental measurements at the site and monitoring of crack deformation [2]. In addition, we have also conducted research such as wind pressure evaluation using wind tunnel tests at the site, which has a complicated shape [3].
2 Overview of Analysis Using DDA 2.1 Previous Studies Using DDA Discontinuous deformation analysis (DDA) is originally proposed by Shi and Goodman [4]. In DDA, jointed rock masses are modeled as an assembly of arbitrary polygonal elastic blocks, and the dynamic and quasi-static behaviors of the blocky system are analyzed considering the contact, slippage, and separation between the blocks. In relation to DDA, we have been conducting research related to the method of calculating the horizontal strength of dry masonry related to this paper. Previously, using analysis by NMM-DDA, a discrete body analysis method developed from DDA, we also verified the decrease in horizontal bearing strength caused by structural cracks and the reinforcement method [5]. However, while the analysis method by NMM-DDA can evaluate the stress in the element in more detail, it was evaluated by modeling with the reinforced point as the fulcrum. In this paper, we focus on the reinforcement design using DDA. And, we evaluate the horizontal bearing capacity by reinforcement, analyze the stress of the reinforcement member, and report a new method to verify the reinforcement effect.
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2.2 Outline of DDA Theory An outline of DDA theory is described below. In ordinary DDA, the potential energy of the entire element is obtained, and the equilibrium equation is derived using the energy minimization principle. The equilibrium state of displacement, moment and stress acting on one element in the X and Y directions can be obtained by minimizing the potential energy of each element. Based on Hamilton’s principle, the equation of motion is obtained by the energy minimization principle and the equilibrium equation is formulated. In this paper, the full implicit DDA is used. It is developed by introducing an implicit updating method of the friction law, the so-called return mapping algorithm, and the Newton–Raphson method to solve the nonlinear equilibrium equation. In addition, to reproduce the shear-strength reduction of the joint after sliding, a simple transition algorithm from the static friction to the residual friction is presented within the framework of the return mapping method [6] (Fig. 2).
Fig. 2. Flowchart of the full implicit DDA [6]
2.3 Quasi-static Analysis of DDA In this paper, the verification by quasi-static analysis was carried out for the analysis of horizontal force loading assuming the strong wind on the dry masonry structure. In the
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quasi-static analysis of DDA, the static stable state is analyzed by solving the equation of motion with the velocity of the previous step as 0. When horizontal force is applied to the dry masonry structure treated in this paper, the amount of loading time depends on the amount of large deformation after collapse. In order to obtain such a large amount of deformation appropriately, it is necessary to solve it in the condition of dynamic analysis instead of quasi-static analysis. In this paper, we mainly focus on evaluating the horizontal strength of the masonry before it collapses, the stress acting on the reinforcing material, and the stress of the stone, so we decided that the DDA quasi-static analysis method is appropriate. In addition, as one of the features of this paper, the reinforcing member is modeled as a connecting spring element that connects the elements. This connecting spring element is analyzed by incorporating it into the formulation of the entire element. 2.4 Numerical Analysis Model of DDA In this paper, we used the DDA method to verify the retained horizontal capacity and the reinforcement effect when horizontal load was applied to the models of the locations shown in Chapter 1, depending on the difference in the reinforcement locations. Figure 3 shows the analysis model and the reinforcement points, and Table 1 shows the analysis conditions. The analysis model is an area with a height of 6.2 m. Using DDA, the masonry of dry masonry is modeled as a discrete body of elastic blocks for each element, and the analysis is performed by gradually increasing the horizontal load which is a uniform load on one side of masonry assuming wind load during strong winds. Model_0 is an analytical model showing the current situation without reinforcement. Model_3_1, Model_3_2, and Model_3_3 all have three reinforced points, each with different reinforced points. About this reinforcement, we assume iron clamps and rock bolts, and model it as a connecting spring that connects discrete elements in DDA. Observation points A, B, and C were set as points to observe stress and displacement to verify the reinforcement effect due to the difference in reinforcement points. Table 1. Analysis conditions Elastic modulus [kN/m2 ]
1.7 × 107
Poisson’s ratio
0
Friction angle [degree]
35.8
Penalty normal spring stiffness [kN/m]
1.7 × 107
Penalty shear spring stiffness [kN/m]
1.7 × 105
Elastic modulus of reinforcement spring [kN/m2 ]
2.0 × 108
Member section of reinforcement spring [m2 ]
0.001
Maximum horizontal load [kN/m2 ]
6.0
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Fig. 3. Figure of each model (point: observation point of stress and displacement, (Num): location of reinforcement)
2.5 Calculation Results This section describes the analysis results. Figure 4 shows the displacement diagram and Fig. 5 shows the shear stress diagram of each model after the final loading. Model_0, which has no reinforcement, shows the deformation that the whole collapses, and high stress is generated in the lower stone materials. In Model_3_1, Model_3_2, and Model_3_3, which are assumed to be reinforced, deformation like Model_0 where the whole collapses is suppressed. Model_3_1, Model_3_2, and Model_3_3 show different deformation modes and stress distributions due to differences in the reinforcement locations. It is also important to point out that reinforcement does not reduce the stress of all stones, and that some stones have increased stress. Figure 6 and Fig. 7 show the comparison of horizontal load vs. displacement and horizontal load vs. shear stress at each observation point for each model. And, Fig. 8 shows the horizontal load vs. axial force of each reinforcement of each model.
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Fig. 4. Displacement mode diagram of each model (Drawn with the displacement amount at the final load multiplied by 3000)
Fig. 5. Shear stress diagram of each model (Shear stress at final load [kpa])
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Fig. 6. Comparison of the load vs. displacement relationship at each observation point for each model (vertical axis: horizontal load [kN/m2 ], horizontal axis: displacement [m])
Fig. 7. Comparison of load vs. shear stress at each observation point for each model (vertical axis: horizontal load [kN/m2 ], horizontal axis: shear stress [kpa])
Fig. 8. Horizontal load vs. axial force of each reinforcement of each model. (vertical axis: horizontal load [kN/m2 ], horizontal axis: axial force [kN])
2.6 Discussion of Evaluation Methods for Analysis Results In complex masonry, the stress distribution and deformation are non-uniform and complex due to masonry configuration. In masonry reinforcement design, which has cultural property value, the main purpose is often different, such as preventing the destruction of the stone material in the relief, suppressing the overall deformation, and suppressing the stress of the reinforcing material. In this way, there are many cases where composite evaluation, such as structural evaluation and cultural property evaluation, is required. In this paper, even if three reinforcements are assumed in the same way, such as model_3_1, model_3_2, and model_3_3, the deformation performance and stress distribution differ depending on the reinforcement locations. In discussing the differences between these reinforcement methods, this paper attempts to use the evaluation function shown in Eq. (1). The outline of Eq. (1) is obtained by weighted average with a, ß, and ? as the coefficients of each parameter, using displacements, stresses, and stresses of
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reinforcing members set at multiple locations as parameters. 1 1 n1 Dxi 1 n2 τ xyi 1 n3 Nt i X= α· +β · +γ · · · · i=1 ADx i=1 fs i=1 Ft α+β +γ n1 n2 n3 (1) Dxi : X direction displacement, ADx: Allowable X direction displacement, τ xyi : xy direction shear stress, fs: Allowable shear stress, Nt i : Axial force of reinforcement, Ft: Allowable axial force of reinforcement. In the analysis model of this paper, three observation points are set and each model is compared. These evaluation results are shown in Fig. 9 and Table 2. The parameters of the evaluation functions X1, X2, X3, and X4 obtained by changing the a, ß, and ? parameters are shown in the left column of Table 2. In the final state of horizontal loading, Model_3_3 shows the best results in evaluation functions X1, X2, X3 and X4. In Model_3_1 and Model_3_2, different results were obtained depending on the evaluation function. This indicates that the best solution differs depending on which of the deformation amount, the stress level of the stone material, and the axial stress of the reinforcing member is emphasized in the evaluation.
Fig. 9. Comparison of evaluation functions X1, X2, X3, and X4 for each model (Vertical axis: horizontal load [kN/m2 ], horizontal axis: evaluation function)
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Table 2. Calculation results for each evaluation function for each model (at final load)
X1
X2
X3
X4
a
1
ß
1
?
1
a
10
ß
1
?
1
a
1
ß
10
?
1
a
1
ß
1
?
10
Model_3_1
Model_3_2
Model_3_3
0.135
0.103
0.055
0.168
0.111
0.085
0.116
0.173
0.066
0.119
0.026
0.014
* : Ranking within each evaluation function
3 Conclusions In this paper, we showed the method of analysis using DDA under the condition that horizontal force was applied assuming a strong wind on the dry masonry structure. Next, we performed an analysis assuming reinforcement and showed a method for evaluating the deformation mode and stress distribution depending on the difference in the reinforcement location. As a result, we tried to propose an evaluation function to verify the reinforcement effect due to the difference in the reinforcement points. The evaluation function is not an absolute evaluation function for verifying the reinforcement effect because it has a structure in which the coefficient is set arbitrarily by the evaluator or designer. However, in historical buildings such as the case of this paper, we have experienced that situations such as which of the amount of deformation, the degree of stress of stone materials, and the axial stress of reinforcing materials should be emphasized in the evaluation are often different. In such a situation, the evaluation function proposed in this paper is considered to have some significance.
References 1. Nakagawa, T., et al.: The Master Plan for the Conservation & Restoration of the Bayon Complex. JASA (2005) 2. Koyama, T., Yamada, S.: Chapter 5. 5.9 Joint Opening Monitoring, Technical Report on the Survey of Angkor Monument 2016–2021, Safegurding of Bayon temple of Angkor Thom, JASA Japan+APSARA Authority, pp. 200–208 (2022) 3. Yamada, S., Araya, M., Yoshida, A., Ohishi, T.: Structural stability evaluation study applying a wind tunnel test and monitoring of bayon main tower, angkor thom Cambodia. WIT Trans. Built Environ. 171, 287–296 (2017)
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4. Shi, G.H., Goodman, R.E.: Generalization of two-dimensional discontinuous deformation analysis for forward modelling. Int. J. Numer. Anal. Methods Geomech. 13, 359–380 (1989) 5. Hayashi, M.,Yamada, S., Araya, M., Koyama, T., Iwasaki, Y.: Study for reinforcement planning of masonry structure with cracks at Bayon main tower, Angkor. In: Advances in Discontinuous Numerical Methods and Applications in Geo-mechanics and Geoengineering, pp. 247–252. Taylor & Francis Group, London (2014) 6. Hashimoto, R., Sueoka, T., Koyama, T., Kikumoto, M.: Improvement of discontinuous deformation analysis incorporating implicit updating scheme of friction and joint strength degradation. Rock Mech. Rock Eng. 54, 4239–4263 (2021)
Modern Japanese Pampas Grass Harvest Methods for Thatched Roof Houses Based on Case Studies of Self-procurement of Grasses in Shikoku Shohei Tsumura1(B) , Miyako Kamatoko2 , and Naoki Kakehashi2 1 Kyoto Institute of Technology, Matsugasaki Hashikamicho, Kyoto 606-7014, Japan
[email protected] 2 Kagawa University, Hayashicho 2217-20, Kagawa 761-0396, Japan
Abstract. Thatch fields (grasslands where the thatch for thatched roofs is harvested) and thatched roofs are dwindling due to the decline of mutual aid, lifestyle changes, and modernization of agriculture. In recent years, there has been a shortage of thatch needed to replace even cultural heritage thatched roofs, making the maintenance of ordinary thatched buildings more impractical. This study aimed to identify modern maintenance and management methods of thatch fields in Shikoku based on case studies of self-procurement of Japanese pampas grasses in Shikoku. We surveyed seven fields that had harvested grasses as a material for thatched roofs within the past five years. We interviewed managers and harvesters of those fields regarding the harvesting process from November 2021 to February 2022. Results showed that the harvesting process depended on the availability of snowfall and storage warehouses. In conclusion, there were both technical issues in making “Kuro” and facility issues in storing grasses to sustain thatched roofs. Keywords: thatch field · thatched roof · Japanese pampas grass · sustainable material · Shikoku
1 Introduction Thatch fields (grasslands where the thatch for thatched roofs is harvested) have been decreasing along with thatched roofs due to the decline of mutual aid, lifestyle changes, and modernization of agriculture. In recent years, there has been a shortage of thatch needed to replace even cultural heritage thatched roofs, making the maintenance of ordinary thatched buildings more impractical. Although a significant number of people wish to see thatching continue due to a return to rural areas, environmental consciousness, and a growing appreciation of thatched roofs as a resource for tourism and historical culture; it is often abandoned, in part, because thatch cannot be easily procured. However, compared to other traditional building materials, thatch (e.g., Japanese pampas grass and reeds) is a building material that can be procured even today. Ordinary thatched houses, other than cultural property buildings using thatch purchased from producers, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 51–62, 2024. https://doi.org/10.1007/978-3-031-39450-8_5
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are not financially sustainable, and their future survival will likely depend on whether the prospect of self-procurement of thatch, which is feasible even today, can be demonstrated in concrete terms. However, previous studies on thatch collection (comprehensive thatch material production activities such as thatch harvesting, transportation, storage, and maintenance of thatch fields) have been limited to those aimed at implementation in modern society. Previous research on thatch field has been limited to traditional techniques and regions, and there has been limited research on modern practical thatch field techniques [1–4]. Therefore, this study aimed to construct a versatile method of thatch collection that is feasible even today, and to generalize the method and technique through a comprehensive survey of currently practiced cases of self-procurement. The selected study site is in Shikoku, one of the places where thatched buildings are on the verge of extinction, especially due to the ongoing shortage of craftsmen and thatched buildings. (Fig. 1) We also noted that the number of thatch fields in Shikoku has been decreasing over the past few years, and that the record of the highly-localized method of thatch collection itself would be important. Studies on thatch collection in Shikoku include a survey of traditional thatch collection [5], a survey of a thatch field in Toyo, Ehime Prefecture [6], and a study that proposes a support system model for supplying materials for thatched houses in Higashiiya Ochiai [7]. However, all of these studies documented traditional techniques and were limited to a select few districts. This research was conducted to construct a versatile method of thatch collection that could be practiced in modern times by comprehensively surveying cases of thatch self-procurement in various parts of Shikoku.
Fig. 1. A thatched building in Shikoku
2 Research Methodology The survey method was to comprehensively investigate the cases of thatch collection currently being conducted and to derive a general methodology. Two specific surveys were conducted: (1) examining the actual conditions of thatch collection, and (2) taking actual measurements of thatch fields and thatch. Survey 1 interviewed each subject and
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observed their participation in thatch collection. Survey 2 was an attempt to quantitatively evaluate the entire survey area by measuring the actual condition of the thatch and thatch field collected at each survey site in survey 1. This was done, efficiently collect highquality thatch, as it was considered necessary to quantitatively indicate the thatch field and thatch material. First, the subjects of survey 1 cases in Shikoku where thatch collection for roofs is regularly conducted. In addition to previous studies [8], information was requested from a craftsman, local government officials who own thatched buildings, architects, and others, and all identified cases were surveyed. Figure 2 gives a summary of the survey fields. Five cases in four prefectures in Shikoku were found to be engaged in thatch collection, and all of them were collecting Japanese pampas grass. In two cases, the residents of the thatched houses themselves collected thatch, and in another two cases, local residents jointly collected it to maintain local thatched buildings. In the last case, craftsmen collected it for use in their work. Notably, the village and thatch fields in Miyoshi City, Tokushima Prefecture (Case 3) are cultural properties, while the other cases are villages and thatch fields that are not cultural properties.
Fig. 2. A summary of the survey fields
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In the course of researching the five cases, we also conducted a detailed record survey on the production of the traditional thatch-drying craft called “Kuro” (Fig. 3), as it was a technical challenge in practice. The “Kuro” was known to exist through previous studies [1, 6, 9, 10], but the details of its working had not been clarified. For the “Kuro” survey, we investigated all cases with an experienced person and requested demonstrations in three locations: Kuma Kogen, Ehime Prefecture (Case 1), Miyoshi City, Tokushima Prefecture (Case 3), and Yusuhara Town, Kochi Prefecture (Case 5), documented by video recording and actual measurements. Next, in survey 2, a total of seven locations were surveyed, as two of the five cases had two thatch fields each. Figure 4 shows the locations of the surveyed thatch fields. Six out of those seven fields, excluding the Katsura field (where no thatch harvesting was conducted during the survey period) were used as subject fields for quantitative evaluation. For comparison, the same items were also examined at the Genjigadaba field in Seiyo City, Ehime Prefecture, where thatch was being produced for sale. Furthermore, there was no example of stubble burning in the thatch fields where the survey was conducted; thus, the same items were surveyed on the Ehime Prefecture and Tokushima Prefecture sides of the Shioduka Kogen, which straddles Shikokuchuo City, Ehime Prefecture and Miyoshi City, Tokushima Prefecture, where areas of Japanese pampas grass is burned as a reference. Consequently, a total of nine sites were surveyed for quantitative evaluation. Figure 5 gives the specific measurement items at those nine sites. First, we set up three 2 m × 2 m quadrates in each location, photographed the thatch in the quadrates, measured the number of plants and the slope angle of the ground surface, and harvested the thatch using sickles and measured five items as follows: the number of thatch, longest length, shortest length, longest length diameter, and shortest length diameter. Subsequently, the two longest and shortest thatches per quadrate were
Fig. 3. “Kuro”
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selected, and from these, the average length and average diameter of the thatches were calculated. In addition, the following four basic survey items were measured for the soil in the quadrates: soil hardness, soil temperature, EC, and pH. For these four items, measurements were taken at three locations per quadrate, and the average was calculated. All of the above field surveys were conducted between November 2021 and December 2021. This paper derives a general methodology from examples of thatch collection practices in Sect. 3, details the production method of “Kuro” in Sect. 4, presents quantitative data on thatch fields and thatch in Sect. 5, and discusses issues and possibilities for future practice and development of thatch collection in Shikoku in Sect. 6.
Fig. 4. The locations of the surveyed thatch fields
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Fig. 5. The specific measurement items at those nine sites
3 Maintenance and Management of Thatch Fields Figure 6 shows photographs and overviews of each thatch field. Figures 7 and 8 show the process of thatch collection for each thatch field and how the process of thatch collection is determined, respectively. The most important factor in determining when to harvest thatch was the availability of snow cover. In thatch fields with snow cover, thatch was harvested in November–December, before snowfall; in thatch fields without snow cover, thatch was harvested in February–April. This is because thatch bends under the weight of the accumulating snow, making it unsuitable for roofing materials. For the maximum reduction of water content in thatch, it should be harvested as late as possible just before the snow falls in thatch fields with snowfall, and around February before the thatch decays, in thatch fields without snowfall. In the Higashiiya Ochiai field and M house field, where thatch harvesting is done in November due to snow cover, an ingenious way is employed to dry the thatch by making “Kuro” during the winter months. At the Kyobashira Pass field, which also had snowfall and a simple warehouse next to the thatch field, thatch was dried in the warehouse and transported to a warehouse dedicated to thatch in Ochiai village. To improve transportation efficiency by reducing its weight, the thatch is dried by “Kuro” before getting transported to the warehouse. However, when there is a distance between the thatch field and the warehouse, and manpower is scarce, as in the case of the Jiyoshi Pass field, the thatch is sometimes transported to the warehouse immediately after harvesting.
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Fig. 6. Photographs and overviews of each thatch field
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Fig. 7. The process of thatch collection for each thatch field
4 Skills Required for “Kuro” Figure 9 lists the procedure for making the three “Kuro” at Kumakogen Town, Ehime Prefecture, Miyoshi City, Tokushima Prefecture, and Yusuhara Town, Kochi Prefecture. Kumakogen Town, Ehime Prefecture: The basic type is 3 × 3 bundles per 1 “Kuro,” as three small bundles are combined into one bundle when stored in the attic of the home. Resident M’s parent and child cultivated rice, which was characterized by the use of rice straw to bind bundles and “Kuro.” The tying method at each location includes twisting and securing; although they may loosen or topple over in strong winds during overwintering, they are close to home and can be maintained on a case-by-case basis.
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Fig. 8. A diagram showing how collection was determined
Miyoshi City, Tokushima Prefecture: In the past, large “Kuro” were made in thatch fields in the mountains, but here, “Kuro” are made based on the “Koeguro” produced in the village fields. “Kuwanoko” is often the most-favored tying method, allowing the “Kuro” to be tied strongly. The method of temporarily securing the bundles tightly with ropes and tying them together with PP ropes was fashioned out of the improvement of harvesters. Yusuhara Town, Kochi Prefecture: This location is windy and snowy in the winter months, requiring techniques to create strong “Kuro.” It is the only one of the three “Kuro” that utilizes pickets, and the same tying methods used are also used for thatched roofs. In addition, “Tasukigake” is used, which can cover the entire “Kuro”.
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Fig. 9. The procedure for making the three “Kuro”
5 Quantitative Evaluation of Thatch Fields and Thatch Figure 10 gives the measurement results for the thatch fields and thatch. These indicated that soil conditions were not affecting the growth of thatch. However, it was found that thatch fields, which were harvested the previous year, grew longer thatch on average. The importance of continued harvesting was thus confirmed. This section estimates the thatch field area required to rethatch one thatched house. Referring to the survey of the actual condition of thatched houses [11], we assume that the roof area of a typical thatched house is 130 m2 and that the number of thatch bundles required per house is 870 bundles (circumference approx. 150 cm), using the financial data. Based on the measurement results, the average number of thatch per 4 m2 was 476. One bundle harvested in Higashiiya Ochiai contained approximately 1,500 thatch; thus, the thatch field area required to make one bundle was 12.6 m2 . This means that a thatch field of 1.1 ha is needed to roof one building. Assuming that the thatch on the roof will be replaced in a 20-year cycle, 0.055 ha of thatch field should be harvested per year. This is equivalent to about two tennis courts.
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Fig. 10. The measurement results for thatch fields and thatch
6 Conclusions On the one hand, the need for warehouses and other facilities to store thatch became apparent as thatch harvesting was no longer done through mutual aid, and making “Kuro” in thatch fields was no longer necessary due to the widespread use of trucks and other equipment. On the other hand, the creation of “Kuro” would allow temporary storage of thatch without equipment. “Kuro” was found to be a technique whose production method varied depending on the climate of the thatch field, its historical background, and its distance from the settlement (home). The case of Miyoshi City, where the government is involved in the operation of thatch fields, thereby creating employment and contributing to maintaining thatched roofs with locally-sourced thatch, is an effective model for preserving and utilizing local thatchroofs in the future. Acknowledgements. This study was supported by JSPS Grant-in-Aid for Scientific Research JP19K12460 and the Nippon Life Foundation. We would like to thank the owners of thatched houses, Yusuhara thatchers, residents of Iya, Onogahara, and Katura, and the boards of education of Miyoshi City and Seiyo City for their generous cooperation in conducting this survey.
References 1. Ando, K.: Kayabuki no minzokugaku-Folklore of the Thatch-. Haru Shobo (1983) 2. Ando, K., Inui, N., Yamashita, K.: Sumai no dentogijyutsu. Kenchiku Shiryo Kenkyusha (1995) 3. Wada, N., Suzuki, M., Yokohari, M.: A study on the Maintenance System of Thatched Roofs in Gokayama Aikura Village, Japan. LRJ 70(5), 689–694 (2007) 4. Maeda, N., Goto, H., Yamazaki, Y.: Making the sustainable model of thatching from views of labor expenditure-from the comparison of the past and present in Oginoshima-area, Takayanagi-cho and Tamugi-area, Oshima-mura, Niigata prefecture-. J. Archit. Plan. (Trans. AIJ) (571), 77–84 (2003)
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5. Kamatoko, M.: Traditional methods of harvesting, drying, and storage of Kaya-Shikoku district-. Summaries of technical papers of annual meeting (AIJ), pp. 175–176 (2020) 6. Sasaki, A., Tsurumi, T., Murayama, T., Miyamoto, M.: Study on the traditional cooperative system of keeping silver grass field as inherited culture and thatched roof village communityabout preservation of traditional grass field in IUCHI and survey on restoration of local residential environment. J. Housing Res. Found. “Jusoken” (41), 229–240 (2014) 7. Tsuji, M., Otomi, A., Masui, M.: The support system of landscape preservation in traditional villages-a case study on the traditional structures of the mountain village in Higashiiya of Miyoshi city, Tokushima prefecture. J. Archit. Plan. (Trans. AIJ) 74(635), 91–97 (2009) 8. Japan Thatching Cultural Association: Survey of records related to thatch collection and thatch field. Japan Thatching Cultural Association, pp. 64–87 (2020) 9. Ishida, J.: Yane no hanashi-Monogatari Mono no Kenchikushi-. Kajima Shuppankai (1990) 10. Kawashima, T.: Horobiyuku minka-Yane, Gaikan-. Shufu to Seikatsusha (1979) 11. Awa no machinami kennkyukai: Survey of thatched houses. Awa no machinami kennkyukai (2002–2015)
Estimating the Structural Characteristics of Historic Armenian Church Buildings and Examining Their Strengthening Applications Atsushi Mutoh1(B) , Yasuhito Fujita2 , Hitoshi Morikawa2 , Shojiro Motoyui2 , and Shiro Sasano2 1 Department of Architecture, Faculty of Science and Technology, Meijo University,
Shiogamaguchi 1-chome, Tempaku-ku, Nagoya 468-8502, Japan [email protected] 2 Department of Architecture and Building Engineering, School of Environment and Society, Tokyo Institute of Technology, 4259, Nagatsuda-cho, Midori-ku, Yokohama 226-8503, Japan
Abstract. In Armenia, the rubble core method was used to build numerous extant churches, several of which are used daily. However, the country has a high risk of earthquakes, and some buildings are significantly likely to collapse owing to structural damage, including deterioration over time. In this study, detailed structural assessments of the deterioration of two typical churches were conducted. First, we discuss the on-site vibration measured and the vibration characteristics identified using a detailed three-dimensional structural analysis of the church of St. Hripsime. [1] The St. Hripsime church has large cracks inside and deterioration caused by water leaking from the inside due to the partial peeling of the south side wall surface. We infer that the vertical cracks observed in the niche may have been caused by previous small and medium-sized earthquakes. An analysis considering damage and deterioration quantitatively estimated a decrease in ultimate strength. Next, the vibration characteristics of Etchmiadzin Cathedral are presented, and the findings of a detailed structural characteristics analysis assuming damage and deterioration are described. The drums and domes of Etchmiadzin Cathedral are elongated compared to the substructure and have four independent pillars in the center. Finally, we discuss the results of an investigation of reinforcement plans focusing on the earthquake damage to the dome and the drum components of these churches. Keywords: Armenian Church · St. Hripsime · Etchmiadzin Cathedral · Structural Properties · Damage and Deterioration
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 63–74, 2024. https://doi.org/10.1007/978-3-031-39450-8_6
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1 Structural Behavior of St. Hripsime Church 1.1 Analysis Model The configurations of St. Hripsime Church are shown in Fig. 1. To maintain the accuracy of expression of axial and flexural rigidities, a fine element subdivision was required (4noded brick element). In the computation, a total of 1,765,000 elements and 355,000 nodes with 1,065,000 d.o.f. were used for the full 3-D simulation model shown in Fig. 2 [2–6].
Fig. 1. Configurations of St. Hripsime Church.
(a)
(b)
Fig. 2. FE mesh for the simulation of St. Hripsime Church: (a) outline of appearance, (b) outline of inner view
In this research, the material characteristics of the structure with a rubble core were assumed to be homogeneous slaked lime mortar as the first step of the examination. In addition, tensile strength was assumed to be 1/10 of the compressive strength. The assumed material properties in the computation are shown in Table 1. 1.2 Analysis Results Identification of Eigenmode. By the eigenvalue analysis, calculated eigenmodes and natural periods corresponding to the first, second, and third modes are shown in Fig. 3 and
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Table 1. Assumed mechanical properties in the analysis. Young’s modulus
4.91 × 102 (N/mm2 )
Poisson’s ratio
0.167
Mass density
1.08 × 103 (kg/m3 )
Compressive strength (criterion; Drucker Prager)
2.1 (N/mm2 )
Tensile strength (smeared crack model)
2.1 × 10–1 (N/mm2 )
Table 2, respectively. By the on-site vibration measurement result using the microtremor survey [7] and the numerical analysis result, the first and second vibration modes were identified successfully. Table 2. Eigen frequencies Estimated by the Measurement
Eigen Value Analysis
1st
2.9 (Hz)
3.116 (Hz)
2nd
3.7 (Hz)
3.653 (Hz)
3rd
4.8 (Hz)
4.647 (Hz)
(a)
(b)
(c)
Fig. 3. Eigenmode of St. Hripsime Church: (a) First mode; translational, N–S direction, (b) Second mode; translational, E–W direction, (c) third mode; torsional
Structural Performance under Vertical and Horizontal Loads. At first, the action of the self-weight type load was evaluated by elastoplastic analysis (Mutoh, 2010). The relationships between the factor for self-weight type load and displacements at the
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principal locations of the structure are shown in Fig. 4, along with the deformed shape. From the obtained result, it may be seen that there are about five times as many ultimate load margins as the self-weight type load and that the drum portion is the first weak point of the structure.
(a)
(b)
Fig. 4. Load-displacement relationships and deformed shape to self-weight type load: (a) loaddisplacement, (b) deformed shape, 1.0 times self-weight (deformation is enlarged 50 times)
Next, to estimate the outline of the earthquake-resistance performance, the characteristics under lateral load are examined. The relationships between the factor for the mass proportional uniform lateral load and displacements at the principal locations of the structure are shown in Fig. 5. From the result obtained, it may be seen that there are about 0.4–0.5 times as many ultimate load margins as the uniform lateral self-weight type load (after the preceding vertical self-weight loading).
Fig. 5. Load-displacement relationships and deformed shape to self-weight type load
Estimated crack patterns around the ultimate strength for Y-dir. are shown with incremental crack strains in Fig. 6.
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Fig. 6. Crack patterns due to the uniform lateral loads (1.0 times self-weight + C0 = 0.4–0.42 uniform lateral load), crack incremental (max. crack strain = 50000 µ)
Trial to Identify the Observed Structural Damage. Concerning St. Hripsime Church, a clear and wide-band vertical crack is observed in the wall between the niche and room located in a corner. We tried to identify the structural cracks and found that the simulated cracks, due to 1.0 times self-weight + uniform lateral load (Co = 0.2, Y -dir.) show good agreement with the observed cracks (Fig. 7). According to the analysis result, it is presumed that the penetrated vertical crack, which is observed may have been generated resulting from the middle-scale earthquakes experienced in the past. Although the influence this damage has on the drop in ultimate strength is not judged to be urgent, future detailed analysis is desired with continuous observation.
Fig. 7. Correspondence of the observed structural cracks and the simulated crack pattern
1.3 Investigation of the Appearance In the outer wall of the southeastern corner, color changes presumed to be based on the localized accumulation of moisture and exfoliation of an outer wall stone are seen and presumed to have advanced in a comparatively short time (Fig. 8). It is judged that the
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portion concerned is clear also in the history of repair, and the specification and measures to deal with the cause that is presumed to be the elution of internal mortar are required.
Fig. 8. Degradation of the outer wall in the southeastern corner
The implementation of a detailed evaluation of damage and degradation is desired based on the internal investigation by non-destructive testing.
2 Structural Behavior of Etchimiadzin Cathedral 2.1 Analysis Model The configurations of Etchimiadzin Cathedral are shown in Fig. 9 To maintain the accuracy of expression of axial and flexural rigidities, a fine element subdivision was required. In the computation, a total of 1,045,000 elements and 218,000 nodes with 654,000 d.o.f. were used for the full 3-D simulation model shown in Fig. 10.
(a)
(b)
(c)
Fig. 9. Configurations of Etchimiadzin Cathedral: (a) South Elevation, (b) Plan, (c) North-South Section
The material properties in the computation are assumed to be identical to those used for the simulations of St. Hripsime Church as shown in Table 1. 2.2 Analysis Results Identification of Eigenmode. By the eigenvalue analysis, calculated eigenmodes and natural periods corresponding to the total five modes are shown in Fig. 11 and Table 3,
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(a)
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(b)
Fig. 10. FE mesh for the simulation of Etchimiadzin Cathedral: (a) outline of appearance, (b) outline of inner view
respectively. At present, the identification of the eigenmode using the data measured by the microtremor survey (Morikawa, 2013) is under analysis. In Table 3, index “A” denotes the E–W direction and index “B” denotes the N–S direction, caused by the asymmetry in the plan. Table 3. Eigen frequencies mode
Period (Eigen Frequencies)
1
0.488 s (2.051 Hz)
1-A
2
0.487 s (2.052 Hz)
1-B
3
0.305 s (3.277 Hz)
2-A
4
0.280 s (3.573 Hz)
2-B
5
0.218 s (4.587 Hz)
3
Structural Performance under Vertical and Horizontal Loads. At first, the action of the self-weight type load was evaluated by elastoplastic analysis (Mutoh, 2010). The relationships between the factor for self-weight-type load and displacements at the principal locations of the structure are shown in Fig. 12 along with the deformed shape. From the result obtained, it may be seen that there are about 5.5 times as many ultimate load margins as the self-weight type load and that the drum portion is the first weak point of the structure. Next, to estimate the outline of the earthquake-resistance performance, the characteristics under lateral load are examined. The relationships between the factor for the mass proportional uniform lateral load and displacements at the principal locations of the structure are shown in Fig. 13. From the result obtained, it may be seen that there are about 0.35 times as many ultimate load margins to the uniform lateral self-weight type load (after the preceding vertical self-weight loading).
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(a)
(b)
(c)
Fig. 11. Eigenmode of Etchimiadzin Cathedral: (a) mode 1A; first, E–W direction, translational, (b) mode 2A; second, E–W direction, translational, (c) mode 3; drum torsional
㻼㻝
㻼㻞 㻼㻟
㼆
㻼㻠
㼅 㼄
(a)
(b)
Fig. 12. Load-displacement Relationships and Deformed Shape to Self-Weight-Type Load: (a) load-displacement, (b) deformed shape, 1.0 times self-weight (deformation is enlarged 50 times)
Fig. 13. Load-displacement relationships and deformed shape to self-weight-type load
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2.3 Investigation of the Appearance In this church, the whole interior surface is covered by ornamentation so the inside is in the situation of being hard to check for damage to the structure owing to the presence of four independent pillars, and this feature is shown in Fig. 14.
Fig. 14. Inside views and an estimated stress concentration for pillars (von Mises stress for D.L.)
The long-term axial force of the four columns is relatively large, and this serves as a point of evaluation of these structural properties. An examination of the influence of long-term creep and the influence of different subsidence are indispensable. When a pillar becomes a point of reinforcement on future examination, the method by the addition of the reinforcing member and/or confinement by a steel plate, a carbon fiber, etc. will also be assumed. In the case of examination, a prior structural analysis will be directly effective. The comparatively high dome and drum serve as key points for the vibration characteristics. Although based on the magnitude of the earthquake assumed, generation of damage in a dome and a drum portion is expected as is the evaluation of the behavior, including underground reinforced concrete structure and evaluation of the connection between the dome-drum portion and the substructure. 2.4 Examination of the Reinforcement Plan In this type of church, there are many cases of damage to the dome and drum parts as shown in Fig. 15, so we will examine the reinforcement plan for this part. Figure 16 shows the analysis model. The analysis model was modeled using shell elements, and to conduct a detailed analysis, different thicknesses were set for each part in consideration of irregularities such as decorations. As for the physical property values, the values in Table 1 used in the analysis of the overall model were used. Figure 17 shows the natural vibration modes. The natural vibration mode was the first translational mode in the direction orthogonal to each of the first and second modes, and the third mode was the torsional mode. Since the damage around the opening of the drum part is considered to be sizable, a continuous reinforcement plan was drawn up by closing the opening shown in Fig. 18, and the reinforcement method was evaluated by numerical analysis. Reinforcement Plan
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First (2.79 Hz) Fig. 15. Dome and drum
Fig. 16. Analysis model
Second (5.31 Hz)
Fig. 17. Eigenmodes of the dome and drum Part
A reinforces the inside of the opening with steel materials, and reinforcement plan B uses the opening with a grid-like frame and window glass. The reinforcement effect is evaluated by response analysis. As an input waveform, a .0 Hz sinusoidal acceleration was gradually increased and input. Table 4 shows the maximum input acceleration, and Fig. 19 shows the deformation and cracks. Reinforcement plan A collapsed with an input less than the maximum input acceleration, but reinforcement plan B was able to withstand up to about twice the input before reinforcement. From the deformation and cracks, it was confirmed that deformation and damage to the opening were not suppressed in reinforcement plan A, but deformation and damage to the opening were suppressed in reinforcement plan B. In this report, a proposal for the reinforcement of the dome and drum was proposed and evaluated by numerical analysis. It was confirmed that the lattice-like frame and window glass reinforcement at the opening have continuity and are effective.
window frame (30020)
(a)
(b)
window frame (505)
(c)
Fig. 18. Reinforcement plans: (a) before reinforcement, (b) Plan A, (c) Plan B
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(a)
(b)
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(c)
Fig. 19. Deformation and cracks: (a) before, (b) Plan A (c) Plan B
Table 4. Maximum input accelerations before reinforcement
98 (cm/s2 )
Plan A
72 (cm/s2 )
Plan B
225 (cm/s2 )
3 Conclusion In this study, St. Hripsime Church and Etchimiadzin Cathedral were evaluated from the viewpoints of the estimation of vibration characteristics, and current damage and load capacity by numerical simulations using full 3-D FE analyses. The results obtained for the two churches are as follows: St. Hripsime Church: 1) Simulated eigenmodes (first and second for translational modes) were identified by the measured data successfully, then the fundamental vibrational characteristics of the structure were verified and the foundation of the future numerical analysis model has been prepared. 2) It may be shown that there are about 0.4–0.5 times as many ultimate load margins as the uniform lateral self-weight type load. 3) It is presumed that the penetrated vertical crack, which is observed, may have been generated according to those middle-scale earthquakes experienced in the past. Although the influence that this damage has on the drop in ultimate strength is not judged to be urgent, future detailed analysis is desired with continuous observation. Etchimiadzin Cathedral: 1) By the eigenvalue analysis, calculated eigenmodes and natural periods corresponding to the total five modes are estimated and now identified using the measured data. 2) It can be seen that there are about 5.5 times as many ultimate load margins of the self-weight-type load and that a drum portion is the first weak point of the structure. 3) It can be seen that there are about 0.35 times as many ultimate load margins as the uniform lateral self-weight-type load. 4) The long-term axial force of the four columns is relatively large, and this serves as a point of evaluation of these structural properties. An examination of the influence of
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long-term creep and the influence of different subsidence are indispensable. When a pillar becomes a point of reinforcement by future examination, the method by the addition of the reinforcing member and/or confinement by a steel plate, a carbon fiber, etc. will also be assumed. In the case of examination, a prior structural analysis will be directly effective. The comparatively high dome and drum serve as key points for the vibration characteristics. Here, we proposed a reinforcement plan based on vibration characteristics while minimizing changes to the interior and exterior of the dome and drum. The exfoliation of the internal mortar from the joint by aged deterioration is seen everywhere, and even if the scale of the fall itself is small, it will be thought from now on that examination of the influence it has on structural performance is indispensable. The implementation of a detailed evaluation of damage and degradation is desired based on the internal investigation by a non-destructive test. Acknowledgments. I would like to express my gratitude to Mr. A. Masuda. This study is part of the research program at Meijo University, funded by ‘NDRR.’
References 1. Motoyui, S.: Structural characteristics of S. Hripsime. In: Sasano, S. (ed.) The Armenian Architecure in the Transitional Period, pp. 185–191 (2011) 2. Bull, J.W. (ed.): Computational Modelling of Masonry, Brickwork and Blockwork Structures. Saxe-Coburg (2001) 3. Lourenzo, P.B.: Guidelines for the analysis of historical masonry structures. Finite Elements in Civil Engineering Applications, pp. 241–247 (2002) 4. Mark, A.: Experiments in Gothic Structure. MIT Press, Cambridge (1982) 5. Mutoh, A.: Users Manual & Examples for SS-DNA (V5). Structural Engieering Labo., MeijoUniv. (2005). (in Japanese) 6. Mutoh, A.: Evaluation of nonlinear behavior of historical masonry structures subjected to wind load by FE analysis. In: The 10th International Conference on Computational Structures Technology, pp. 1–8. Civil-Comp Press (UK) (2010). (CD-ROM) 7. Morikawa, H., et al.: Estimation of dynamic behavior of historical church in armenia using microtremor survey. In: International Conference on Urban Earthquake Engineering (2013)
Vibration Characteristics of Traditional Masonry Buildings in the Kingdom of Bhutan Miyamoto Mitsuhiro1(B) , Aoki Takayoshi2 , Hamaoka Miku3 , Hayashi Riho4 , Kunzang Tenzin5 , Kshitij C. Shrestha6 , Takahashi Noriyuki7 , and Zhang Jingyao8 1 Faculty of Engineering and Design, Kagawa University, Kagawa, Japan
[email protected]
2 Graduate School of Design and Architecture, Nagoya City University, Nagoya, Japan
[email protected]
3 Graduate School of Science for Creative Emergence, Kagawa University, Kagawa, Japan
[email protected]
4 Graduate School of Engineering, Kagawa University, Kagawa, Japan
[email protected]
5 Department of Culture, MoHCA, Thimphu, Bhutan
[email protected]
6 Department of Civil Engineering, Pulchowk Campus, IOE, Tribhuvan University, Lalitpur,
Nepal [email protected] 7 Graduate School of Engineering, Tohoku University, Miyagi, Japan [email protected] 8 Graduate School of Engineering, Kyoto University, Kyoto, Japan [email protected]
Abstract. Ensuring the seismic resilience of traditional rammed earth and stone masonry buildings in the Kingdom of Bhutan is essential for their preservation. This study aims to clarify the vibration characteristics of traditional masonry buildings during an earthquake, based on shaking table tests and seismic response analyses. Shaking table tests were conducted on four 1/6 scaled specimens of the same design and geometry as the full-scale specimens in previous studies. The test results clarified the relationship between the nominal PGA and acceleration response factor and the change in the vibration characteristics due to damage. For the numerical modelling, two-mass system models for each specimen were constructed based on the microtremor measurements conducted for each specimen before the shaking table tests and static full-scale lateral loading tests. Seismic response analysis, using two-mass system models, was conducted to simulate the dynamic behavior observed and recorded during the shaking table tests. The results showed that the numerical analysis produced a similar output trend until rocking or large horizontal cracks occurred. Keywords: Composite masonry building · Shaking table test · Seismic response analyses
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 75–82, 2024. https://doi.org/10.1007/978-3-031-39450-8_7
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1 Introduction In the Kingdom of Bhutan, 66% of households, mostly in rural areas, live in traditional rammed earth and stone masonry buildings. These traditional buildings are particularly vulnerable to earthquakes, as evident after the earthquakes in the eastern region of Bhutan (September 21, 2009, M6.1) and the India-Nepal border (September 18, 2011, M6.9). Therefore, ensuring the seismic resilience of traditional buildings is essential for their preservation. In our previous studies, static loading tests were conducted on full-scale specimens with the same design and geometry as typical two-story traditional rammed earth and stone masonry buildings [1, 2]. In these studies, we examined the seismic performance of traditional masonry buildings and proposed a seismic retrofitting solution. However, studies that consider the vibration characteristics of traditional masonry buildings are scarce. Therefore, the present study aims to clarify the vibration characteristics of traditional masonry buildings during an earthquake, based on shaking table tests and seismic response analyses. The shaking table tests were conducted on four 1/6 scaled specimens of the same design and geometry as the full-scale specimens in our previous studies. In addition to unreinforced rammed earth and stone masonry structures, reduced-scale mesh-wrap retrofitted specimens of these structures were also investigated because of their effectiveness, as shown in our previous studies. For numerical modelling, two-mass system models for each specimen were constructed based on the microtremor measurements conducted for each specimen before the shaking table tests and static full-scale lateral loading tests. Seismic response analysis, using two-mass system models, was conducted to simulate the dynamic behavior observed and recorded during the shaking table tests. From the test results, the changes in vibration characteristics were clarified.
2 Shaking Table Tests 2.1 Specimen Configuration The specimens were a reduced-scale prototype of a traditional Bhutanese masonry building, considering the limitation of the shaking table capacity. Eight specimens were constructed: four rammed earth and four stone masonry specimens, and two of each specimen were retrofitted. That is, there were two identical specimens, each with a different excitation direction in the short and long directions. The same materials were used in both the prototype and the models. The specimens were constructed by local craft men following the standard construction procedures in the Kingdom of Bhutan. All specimens were built on a steel base plate with a thickness of 10 mm and later fixed on a shaking table using bolts. The specimens were cured for 30 days after the construction was completed in the open air. The specimens were geometrically reduced to a scale of 1:6. As shown in Fig. 1, the two-storied prototype building had a floor area of 1350 mm × 900 mm, with a height of 580 mm for each floor. The wall thickness was 100 mm. After completing the construction, two of each specimen types were retrofitted with a mesh wrapping technique same as in the previous studies [1, 2]. As shown in Fig. 2, a hexagonal shaped chicken wire mesh having 0.4 mm diameter was used as the main material for retrofitting
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and anchored using nails. 10 mm thick cement plasters with a 1:3 cement–sand ratio were used to provide better bonding between the walls, mesh, and plasters.
(GL)
Acceleration sensor Microtremor sensor
Fig. 1. Plan of specimen.
(GL)
Fig. 2. Reinforcement with wire mesh.
2.2 Outline of Shaking Table Tests The shaking table tests were performed on two specimens at the same time: one was unreinforced, and the other was retrofitted. Comparisons were made on the spot, as shown in Fig. 3. The response of the structure was measured using an accelerometer (STP-300S), and data logging was conducted using the National Instrument System (Signal Express). A total of 16 accelerometers were used to measure the response of the two specimens: eight on the unreinforced specimen and eight on the retrofitted specimen. For each specimen, one sensor was installed at the base, four at the second-floor level, and three at the roof level, as shown in Fig. 1. The sampling frequency was set to 200 Hz. The test was performed only in one direction of the specimens and was subjected to two types of dynamic excitations: sweep sine waves and real earthquake inputs. A sweep test was carried out with a low intensity (0.03 g by gradually increasing the frequency from 1 Hz to 25 Hz to obtain the vibration characteristics of a model in the elastic range. Following the sweep test, a series of earthquake motions with increasing intensities were used for testing in the nonlinear range. The earthquake ground motion recorded in Thimphu, Bhutan, on September 12, 2018, was used as the input motion. The original wave was scaled following the similitude rule to suit the reduced-scale specimen [3], that is, the time axis of the original wave was reduced by a factor of 6–3/4 times. The test was performed with increasing the maximum acceleration of a ground motion from 0.2 g to1.4 g in 0.2 g increments. When the specimen was about to collapse, the test was stopped halfway through. Figure 4 and Fig. 5 show the time history and acceleration response spectra of the input wave of 0.2 g. 2.3 Results and Discussion The acceleration response factors at the floor and roof levels, crack patterns after tests in the short and long directions, and changes in natural frequencies are shown in Fig. 6, 7, 8 and 9, respectively. The acceleration response factors were obtained from the average absolute peak acceleration response at each level by the absolute peak acceleration at
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Fig. 3. Installation of specimen.
Acceleration Response[g]
Acceleration[g]
0.8
0.2 0.0 -0.2 0
5
10
15 20 Time[s]
25
Fig. 4. Example of time history.
30
35
0.6 0.4 0.2 0.0 0.01
0.1 Period[s]
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Fig. 5. Example of acceleration spectrum.
the shaking table level. The measured values were used for the analysis after baseline correction and filtering using the band-pass filtering technique with cut-off frequencies of 1–50 Hz. Microtremor measurements of the specimens were performed before and after each test to understand the change in the vibration characteristics. The data loggers and sensors used for the measurement were GEODAS 15 h and CR 4.5-2S velocity sensors, respectively. Microtremor waves were measured over 3 min by setting four sensors at each level in both directions, as shown in Fig. 1, at a sampling frequency of 200 Hz. Subsequently, the measured values were divided by 20.48 s after filtering using the band-pass filtering technique with cut-off frequencies of 1–50 Hz. Those portions with less noise, such as those caused by traffic vibrations, were subjected to ensemble averaging and smoothing (Hanning Window:30). The obtained records were Fouriertransformed and the natural frequency of the specimen was estimated from the ratio of the Fourier spectra at each measurement point to that at the roof level. The test results for the short direction are as follows: After a nominal PGA of 0.8 g for an unreinforced rammed earth specimen (URE), the acceleration factor became almost the constant between the floor and roof level, and the natural frequency drastically dropped because of the occurrence of large horizontal cracks at the floor level and huge vertical cracks in the middle of the back wall (Fig. 7a). In a retrofitted rammed earth specimen (RRE), the acceleration factors gradually decreased at both the floor and roof levels and approached 1.0, owing to the effect of rocking. However, the natural frequency was almost constant, and there were few cracks although the nominal PGA increased in steps (Fig. 7b). In an unreinforced stone masonry specimen (USM), the acceleration factor was close to 1.0, at the roof level from the beginning owing to initial cracks, and the natural frequency was almost constant despite the gradual increase in the number of cracks. After a nominal PGA of 0.8 g, the natural frequency drastically decreased because of the occurrence of large horizontal cracks on both sides at the floor level (Fig. 7c). In a retrofitted stone masonry specimen (RSM), the acceleration factors at the roof level and the natural frequency gradually decreased, although almost no cracks appeared on the surface of the exterior walls. (Fig. 7d). The test results for the long direction are as follows: In an unreinforced rammed earth specimen (URE), the acceleration factors at both the floor and roof levels were almost constant, and almost no cracks appeared on the surface of the exterior walls (Fig. 8a), although the natural frequency gradually decreased. In a retrofitted rammed earth specimen (RRE), the acceleration factors gradually decreased at the roof level owing to the effect of rocking, especially after a nominal PGA of 1.0 g. On the other
Vibration Characteristics of Traditional Masonry Buildings RRE (2FL)
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RRE (RFL)
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Fig. 6. Acceleration response factor.
hand, the natural frequency was almost constant, and there were few cracks on the surface of the exterior walls (Fig. 8b). In an unreinforced stone masonry specimen (USM), the acceleration factors at the roof level and the natural frequency gradually decreased until a nominal PGA of 0.6 g. However, after a nominal PGA of 0.8 g, these values began to increase owing to the prominence of wall vibration in the out-of-plane direction at the first floor (Fig. 8c). In a retrofitted stone masonry specimen (RSM), the natural frequency gradually decreased and there were few cracks on the surface of the exterior walls, even though the nominal PGA increased in steps (Fig. 8d).
(a)
URE
(b)
RRE
(c)
USM
(d)
RSM
Fig. 7. Crack patterns after tests (Short direction).
(a)
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(b)
RRE
(c)
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Fig. 8. Crack patterns after tests (Long direction).
(d)
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(b)
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(c)
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(d)
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Fig. 9. Change of natural frequencies.
3 Seismic Response Analyses 3.1 Analysis Model In this study, a simple numerical analysis was performed using a two-mass system model to simulate the behavior during the shaking table tests. For each specimen, an analysis model was constructed based on the results of the microtremor measurements for each specimen before the shaking table tests and static full-scale lateral loading tests [1, 2]. For the mass values m1 and m2 , unit weights of 1700 kg/m3 and 2600 kg/m3 were assumed for the rammed earth and stone masonry walls, respectively. The values of stiffness k 1 and k 2 were calculated based on the natural frequencies of the reduced-scale specimens immediately before the shaking table tests. The stiffness ratios k 1 and k 2 were assumed to be k 2 = 1/2k 1 and k 2 = 1/3k 1 in the short and long directions, respectively, based on the length of the in-plane walls. Rayleigh damping was applied with the first and second damping ratios assumed to be 0.02. The damping value was determined from the results of microtremor measurements before the shaking table tests based on the random decrement technique [4]. The skeletal curves for the rammed earth and stone masonry specimens, both unreinforced and retrofitted in the short and long directions, were assumed to be perfect elastic-plasticity models. Based on the results of static full-scale lateral loading tests [1, 2], the maximum story shear coefficient was used as the yield shear coefficient of a perfect elastic-plasticity model. To perform the analysis on the reduced-scale specimen, the yield shear coefficients of the full-scale tests were transformed to obtain corresponding values [3], that is, the maximum story shear coefficient of the full-scale specimen was multiplied six times. Because there is no common hysteresis model for nonlinear analysis of composite masonry structures, the Takeda model was used for this analysis. 3.2 Analysis Method In this study, the ground motion from shaking table tests was used as an input earthquake. All input ground motions were simultaneously used in this analysis to consider the effects of residual deformation. Five nonlinear models were subjected to time history analysis, except for the unreinforced stone masonry specimens in the short direction and unreinforced and reinforced stone masonry specimens in the long directions without the results of full-scale static loading tests. The Newmark-β method was used to compute
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the acceleration responses, and the maximum response acceleration for each test case was calculated. 3.3 Results and Discussion The experimental results were compared with the numerical analysis results for the acceleration response at each floor level. The maximum acceleration response of the experimental result is the average absolute maximum acceleration accounting response of all sensors on each floor. Furthermore, the numerical results were correlated with the damage occurrence on the specimens during the experiment. The comparison results for each input of the nominal PGA for each specimen are shown in Fig. 10. The comparison results for the short direction are as follows: At nominal PGA from 0.2 g to 0.8 g for the unreinforced rammed earth specimen (URE), all the acceleration response is in a close range and during the experiment there was no significant damage detected. From the experiment, at a nominal PGA of 0.8 g, large horizontal cracks developed at the floor level, and the analysis results were smaller than the experimental results at the floor level. At nominal PGA from 0.2 g to 0.8 g for the reinforced rammed earth specimen (RRE), all the acceleration response is in a close range. However, for a nominal PGA of 0.8 g, the analysis results are larger than the experimental results at the floor level owing to the effect of rocking. At each nominal PGA for the reinforced stone masonry specimen (RSM), the analysis results were smaller than the experimental results at the roof level, even though almost no cracks appeared on the surface of the exterior walls. It is possible that the initial cracks inside the wall were affected. Experiment (2FL)
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The comparison results for the long direction are as follows: At each nominal PGA for the unreinforced rammed earth specimen (URE), the analysis results were larger than the experimental results at the roof level, although almost no cracks appeared on the surface of the exterior walls. There is a possibility that the prominence of the wall vibration in the out-of-plane direction on the first floor is affected. At low nominal PGA from 0.2 g to 0.6 g for the reinforced rammed earth specimen (RRE), all the acceleration response is in a close range. However, as the nominal PGA increased, the difference between the experimental and analytical results increased at each level owing to the rocking effect.
4 Conclusions To understand the behavior of structures during earthquakes, this study aimed to study the dynamic characteristics of composite masonry buildings through shaking table tests and numerical analysis. The natural frequency of the specimen showed a decreasing trend with an increase in the nominal PGA, reflecting the degradation of the stiffness due to damage. The acceleration factor also reflected damage propagation, where a decrease in factors occurred when the damage was significant. However, there is no clear tendency of the relationship between the nominal PGA and acceleration response factor owing to the variation in measurement results or the effect of rocking. A comparative analysis was performed between the numerical analysis and the experiments in terms of the maximum acceleration response at each floor level relative to the nominal PGA. The results showed that the numerical analysis produced a similar output trend until rocking or large horizontal cracks occurred. Acknowledgement. This research was supported by the JST/JICA, SATREPS (Science and Technology Research Partnership for Sustainable Development) project. We would also like to acknowledge the support of the Department of Culture, Ministry of Home and Cultural Affairs, and the Royal Government of Bhutan.
References 1. Wangmo, P., et al.: Study on earthquake resistance technology of composite masonry buildings in Bhutan Part 13: Full scale tests on composite masonry buildings: unreinforced and meshwrapped rammed earth construction. Summaries of Technical Papers of Annual Meeting, AIJ, Structures-IV, pp. 861–862 (2019) 2. Shrestha, K.C., et al.: Study on earthquake resistance technology of composite masonry buildings in Bhutan Part 14: Full scale tests on composite masonry buildings: Mesh-wrapped stone masonry with mud mortar construction. Summaries of Technical Papers of Annual Meeting, AIJ, Structures-IV, pp. 863–864 (2019) 3. Kagawa, T.: On the similitude in model vibration tests of earth-structures. Proceedings of the Japan Society of Civil Engineers, No. 275, pp. 69–77 (1977) 4. Tamura, Y., Sasaki, A., Tsukagoshi, H.: Evaluation of damping ratios of randomly excited buildings using the random decrement technique. J. Struct. Constr. Eng. Trans. AIJ (454), 29–38 (1993)
The Introduction and Disappearance of Mixed-Structure Buildings Made from Brick Walls and RC Slabs Between 1900 to 1926 in Japan Shigeyasu Ikegami(B) Graduate School of Engineering, Hokkaido University, N13 W8 Kita-ku, Sapporo 0608628, Hokkaido, Japan [email protected]
Abstract. After the Meiji Restoration in 1868, masonry techniques were introduced to Japan by the West, and Japanese architectural engineers were taught new techniques in construction. However, Japan is an earthquake-prone country and the Great Kanto Earthquake that occurred on September 1, 1923, in particular, caused devastating damage from Tokyo to Kanagawa. Consequently, masonry structures were deemed unsuitable in Japan, and reinforced concrete (RC)—which was introduced from around 1900—moved into mainstream fire-resistant construction. In the first quarter of the twentieth century, when the architectural structure was in a state of transition, a mixed structure that comprised brick walls and RC slabs was attempted, but the full picture was not clarified. Through an analysis of articles that were published by the Journal of Architectural Institute of Japan and drawings of mixed-structure buildings, this study examines the characteristics and changes of the mixed structure. Until 1910, concrete that was poured over shallow vaulted brick or corrugated iron plates that were combined with steel beams were widely used in the construction of fire-resistant floors. Simultaneously, there were examples of RC structures that were used in the construction of stair landings and entire staircases. After 1910, fireproof floors that were built with RC slabs on steel beams made way for RC slabs that used both small and large beams and haunching beams. Keywords: Fireproof Floor · Taisho Period · Journal of Architectural Institute of Japan · Building Division of Government Offices · Head Office of Takaoka Kyoritsu Bank · Sapporo Court of Appeal
1 Introduction After the Meiji Restoration in 1868, masonry techniques were introduced to Japan by the West, and they were taught to eager Japanese architectural engineers who were keen to learn new architectural methods. However, Japan is an earthquake-prone country and despite the progress of modernization, it continues to suffer from frequent earthquakes. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 83–100, 2024. https://doi.org/10.1007/978-3-031-39450-8_8
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One of these, the Great Kanto Earthquake that occurred on September 1, 1923, devastated the entire area from Tokyo to Kanagawa, and reduced the city into a mountain of rubble. Consequently, masonry structures were considered unsuitable for Japan due to the frequent occurrence of huge earthquakes. Hence, the use of reinforced concrete (RC)—which was introduced toward the end of the Meiji era around 1900—became the mainstream method in fire-resistant construction [1]. During the Taisho period from 1912 to 1926, an attempt was made to build a mixed structure from the use of masonry structure for walls and RC for the stairs and slabs. Although the fact that the building division of the government offices had adopted this construction technique was established after restoration work was performed on cultural property buildings, however, the information is fragmented and the full picture of this mixed structure has not been elucidated. In this study, based on the construction reports that were published in the Journal of Architectural Institute of Japan and drawings of eleven mixed-structure buildings—which were courthouses and university buildings designed by architectural engineers from the Ministry of Justice and the Ministry of Education—I examined the transitional process of joining methods for the RC slab with the brick wall.
2 Early History of Mixed-Structure Buildings and Fireproof Floor Takeyoshi Hori describes the structure of Japanese architecture in the late Meiji era as follow: “After 1897, American-style steel structures began to appear. This structure was often used when the Meiji era changed to the Taisho era. Many large buildings and multistory buildings rely on their construction. Later, around 1907, RC began to become popular, and in 1911, four-story office buildings appeared. It was during the Taisho period that such structures began to be widely used.” [2] Based on his description, the steel structure was introduced prior to the use of RC, and it was highly developed by the Taisho period. Here, I focus on the construction of Maruzen Co., Ltd. Building in the Nihonbashi district of Tokyo that was begun in August 1907 and completed in December 1909. During its construction, RC slabs were used by Hori who was also responsible for the building of other steel-framed buildings in the Meiji period. The Maruzen Building was designed by Toshikata Sano, who was a master of steel and RC in Japan. Unfortunately, since drawings of the joints between the steel frame structure and RC slabs lacked details, the reinforcement method could not be determined. Hori summarized the structure of the masonry fireproof floor as follow: “Brick buildings are basically made by inserting joists into brick walls and laying floorboards to create wooden floors. Because the roof truss is also placed on the brick wall, the floor load and roof load are basically supported by the brick wall. This support relationship does not change even if the floor trusses and roof trusses are replaced with steel frames. Therefore, the steel floor trusses and steel roof trusses themselves are not involved in the structural concept of the main structure as long as they are supported by brick walls. Therefore, for the time being, fire floors in which brick vaults or corrugated iron plates are laid between steel beams and lightweight concrete are placed, and RC slabs can be dealt with only for a matter of floor structures.” [2] He particularly pointed out the potential of using RC slabs as fireproof floors for brick buildings. In the instances of fireproof floors in the
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Meiji era that he cited after this description, although the use of some RC slabs were reported, however, actual examples were not shown. The landing of the staircase in the Yokohama Bank Meeting Hall—a two-storied brick building with a basement that was designed by Oto Endo and completed in 1905—was made from RC. Although the floor structure of the Yokohama Shinko Wharf brick warehouses—which were designed by the Temporary Construction Department of the Ministry of Finance and completed in 1913—was made from RC, however, the steel floor framing was still used. Furthermore, he stated that the Kyoto Commodity Exhibition Hall—which was designed by Goichi Takeda and completed in 1909 using brick construction—used RC beams and vaulted floors. Although the advent of RC fireproof floors were recognized by the Meiji period, however, it was thought that the construction of mixed-structure buildings did not occur in the Taisho period even though they had been widely developed by then.
3 Articles on Mixed-Structure Buildings in the Journal of Architectural Institute of Japan Between the late Meiji period to the early Taisho period, the latest information on RC was frequently published in the Journal of Architectural Institute of Japan. Properties that were newly built were introduced by articles that were included at the end of every issue in the journal, and many buildings with brick walls and fireproof floor structures were shown. By focusing on floor structures, Table 1 shows the trends that occurred in mixed-structure buildings from 1907—when Sano designed the Maruzen Building—to 1921, when their occurrences could no longer be confirmed. Prior to 1910, buildings with so-called “fire floors” were constructed with either corrugated iron plates or brick vaults that spanned I-beams, and concrete was poured over them. Since the branch building of the Mitsubishi Joint Stock Company in Osaka used triangular mesh steel wire reinforcement for part of its concrete floor, it should be called wire mesh concrete rather than RC. However, it can at least be described as a structure that is clearly different from the conventional “fire floor.” After 1910, the construction of floors of buildings that had commenced by the end of the Meiji era and designed by Yorinaka Tsumaki and Kingo Tatsuno were assessed as “fire floors.” Nevertheless, an increasing number of buildings that were completed in the Taisho era were found to have RC slabs that spanned steel beams. Since this was only textual information, it was possible that concrete may have been poured on the so-called “fire floor” and rebars were inserted. Incidentally, although the Morimura Bank building in the Nihonbashi district in Tokyo—which was built by Shimizu Gumi Design and Construction in 1911 and completed in 1914—was made from RC, however, the floor structure was “reinforced concrete placed over steel beams.” [3].
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Table 1. List of mixed-structure buildings that were published in the Journal of Architectural Institute of Japan from 1907 to 1921 Building name
Location
Completion date
Wall structure
Floor structure
Architect/firm
Publication date
Tanaka Photo Plate Factory
Tokyo
Undescribed
B
Steel beams and concrete floor
Tatsuno Kasai Office
Oct. 1907
Naval Museum
Tokyo
Apr. 1908
SB
Concrete was Undescribed poured into corrugated iron plates that spanned I-beams
Sep. 1908
Marquis Maeda Residence
Tokyo
May 1907
B
Concrete was Undescribed poured into arc-shaped iron plates that spanned steel beams
Nov. 1908
Yokohama City Hall
Yokohama
Jul. 1911
RB
Concrete with Minoru Ikeda, an average Kyukichi thickness of Adachi 30 cm was poured into corrugated iron plates that spanned I-beams
May 1909
Kobe City Hall
Kobe
Dec. 1909
S
Fire-resistant construction with brick vaults that spanned 60-pound rail beams
Kintoku Akiyoshi
Aug. 1910
Sep. 1910
B
The floor beams were I-beams, and the bearing columns were bricks that were covered with concrete
Shigenori Yoshii, Shiro Uchida, Yoshihiro Kitabatake
Dec. 1910
Tokyo Central Tokyo Telephone Office (Kyobashi Branch Office)
(continued)
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Table 1. (continued) Building name
Location
Completion date
Wall structure
Floor structure
Architect/firm
Publication date
Mitsubishi Joint Stock Company (Osaka Branch)
Osaka
Dec. 1907
SB
Using I-beams, Tatsuzo Sone, concrete that Katsuya measured 5 Yasuoka inches in thickness was poured over 2 mm-thick corrugated iron plates across the beams, and steel RC that measured 5 inches in thickness was poured over steel beams by using triangular mesh steel wire reinforcement
Feb. 1911
Shueisha Head Office
Tokyo
Nov. 1911
B
Fireproof floors were constructed from steel frame concrete
Kuichi Kitada
Apr. 1912
The Jugo Bank (Nihonbashi Branch)
Tokyo
Mar. 1909
B
Arc-shaped corrugated plates were inserted between the I-beams, and coal ash concrete was poured
Yorinaka Tsumaki, Kimpei Kobayashi
Sep. 1912
Life Insurance Tokyo Companies Association
Nov. 1912
B
Fireproof floors were constructed from steel beams and concrete
Kingo Tatsuno, Manji Kasai, Yasushi Kataoka
Aug. 1913
(continued)
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Building name
Location
Completion date
Wall structure
Floor structure
Architect/firm
Publication date
Port Opening Memorial Yokohama Hall
Yokohama
Jul. 1917
SB
Steel beams and RC
Yoshitoki Nishimura
Dec. 1913
Takada Shokai Head Office
Tokyo
Mar. 1914
B
Steel beams George de were used and Lalande concrete was poured over flat vaulted bricks
Jul. 1014
Nakai Bank (Urawa Branch)
Urawa
May 1914
B
Floor beams were made from RC and wood
Katsuya Yasuoka
Sep. 1914
Nippon Life Insurance (Nagoya Branch)
Nagoya
Apr. 1910
SB
Steel beams and concrete
Kingo Tasuno, Oct. 1914 Yasushi Kataoka
Osaka Ceramics
Osaka
Oct. 1913
SB
Steel beams Undescribed were spanned, and the floor was made from RC
Nov. 1914
Yasuda Corporation (Osaka Branch)
Osaka
Jan. 1913
SB
RC with steel beams
Kingo Tatsuno, Yasushi Kataoka
Nov. 1914
Nippon Life Insurance (Kyoto Branch)
Kyoto
Jun. 1914
SB
Steel beams and RC
Kingo Tatsuno, Yasushi Kataoka
Mar. 1915
Osaka Court of Appeal
Osaka
May 1916
B
Steel beams and RC
Keijiro Yamashita, Tsutomu Yokohama, Moritato Kanesashi
Jul. 1916
(continued)
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Table 1. (continued) Building name
Location
Completion date
Wall structure
Floor structure
Architect/firm
Publication date
Mr. Iwamoto’s main residence
Muko, Hyogo
Dec. 1914
B
RC fireproof floor
Undescribed
Aug. 1916
Mitsui Bank (Osaka West Branch)
Osaka
Jun. 1916
B
RC construction
Kantaro Matsui
Aug. 1916
Takaoka Takaoka Kyoritsu Bank (Head Office)
Dec. 1914
SB
RC construction
Junkichi Tanabe
Sep. 1916
Tanaka Bank
Tokyo
Aug. 1916
SB
RC construction
Fukuzo Watanabe
Nov. 1916
Tokyo Bank meeting place
Tokyo
Sep. 1916
B
Steel beams spanned the brick wall and the floors were made from RC
Kantaro Matsui
Jan. 1917
Mitsui Bank (Kobe Branch)
Kobe
Nov. 1916
B
RC construction
Uheiji Nagano Feb. 1917
Meiji Fire Insurance (Kobe Branch)
Kobe
Jan. 1917
B
RC construction
Yokokawa Construction
Apr. 1917
Kagisan Bank Niigata
Feb. 1917
B
RC construction
Minoru Tanaka
May 1917
Sumitomo Bank (Tokyo Branch)
Tokyo
Sep. 1917
SB
RC construction with steel beams
Magoichi Oct. 1917 Noguchi, Yutaka Hidaka
Nakai Bank
Tokyo
Oct. 1917
SB
RC construction
Katsuya Yasuoka
Oct. 1917
(continued)
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Building name
Location
Completion date
Wall structure
Floor structure
Architect/firm
Publication date
Teiyu Bank (Head Office)
Tokyo
Nov. 1916
B
Inland steel beams were spanned and US-made high-rib metal laths were placed between nearly every beam. Reinforcement was made by inserting rib bars into key points and pouring concrete
Yorinaka Tsumaki, Kenkichi Yabashi, Kimpei Kobayashi
Jan. 1918
Temporary Mitsubishi headquarters
Tokyo
Apr. 1918
SB
RC construction
Mitsubishi Joint Stock Estate
Apr. 1918
Yokohama Specie Bank (Kobe Branch)
Kobe
Jul. 1919
B
RC construction
Uheiji Nagano Oct. 1919
Daiichi Bank (Kumamoto Branch)
Kumamoto
May 1919
B
RC construction
Yoshitoki Nishimura
Yokohama Specie Bank (Shimonoseki Branch)
Shimonoseki
Jan. 1920
B
RC construction
Uheiji Nagano Oct. 1920
Mar. 1920
S
RC construction
Uheiji Nagano Oct. 1920
Industrial Osaka Bank of Japan (Osaka Branch)
Feb. 1920
Notes. B: Brick Masonry, SB: Steel-framed Brick Masonry, RB: Reinforced Brick Masonry, RC: Reinforced Concrete, S: Stone Masonry
During the transitional period from the Meiji era to the Taisho era, the method of floor construction in mixed and RC structures was developed through a process of trial and error. The floor structure in the head office of Takaoka Kyoritsu Bank was simply described as “reinforced concrete construction.” A nondestructive inspection of this existing building had confirmed the placement of the rebar and the use of RC slabs, albeit only on a part of the second floor. In Fig. 1, the drawing shows that the I-beams were placed inside the girder which can be attributed to the steel-framed brick masonry structure of the building. [4] I would like to emphasize that the head office of Takaoka
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Kyoritsu Bank was the first mixed-structure building in Japan that used RC slabs for its floor in 1913. Hence, the practice of laying RC slabs—instead of steel beams—on brick walls in mixed-structure buildings was introduced and promoted in the Taisho period (1912–1926).
Fig. 1. A cross-sectional drawing of the head office of Takaoka Kyoritsu Bank.
4 Mixed-Structure Buildings Constructed by the Ministry of Justice Building Division The Supreme Court building—which was designed by the German architects Hermann Ende and Wilhelm Böckmann—was launched in 1887 and completed in 1896. It was claimed as the first mixed-structure building that was supervised by the Ministry of Justice Building Division. [5] However, it was difficult to imagine that RC slabs were used in its construction since the floor of the main building of the Ministry of Justice— which is an important cultural property that was also designed by both German architects and completed in 1895—had a “fire floor” which was made from a vaulted brick ceiling that spanned steel beams. The floor specifications of the Osaka Court of Appeal building—which was designed by Kozo Kawai and completed in 1900—stated that “the ceiling is covered with iron plates,” and it was possible that the building had a “fire floor” that was made of vaultshaped corrugated iron plates that spanned I-beams. [6] Although the Kobe District Court building—also designed by Kozo Kawai and completed in 1904—was demolished, however, its outer walls have been retained. According to a drawing of its floor specifications that are shown in Fig. 2, the second floor was a wooden structure with cross-bridging while the first floor, which had a semi-basement, was a brick-vaulted “fire floor.” [7] The buildings of the Osaka Court of Appeal—which was designed by Keijiro
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Yamashita et al. and completed in 1916—, the Miyagi Court of Appeal (completed in 1925), the Nagoya Court of Appeal and the Kyoto District Court (both were completed in 1926), and the Sapporo Court of Appeal (completed in 1926) are examples of mixedstructure construction. The courthouses in Osaka, Kyoto, and Sendai, however, have been demolished. The courthouses in Nagoya and Sapporo are discussed later in this paper. Since the Osaka Court of Appeal building was featured by a magazine, I would like to further its discussion. The construction of the Osaka Court of Appeal building began in April 1910 and was expected to last five years. Due to the outbreak of World War I, it was eventually completed in May 1916. Architectural engineers such as Keijiro Yamashita, Tsutomu Yokohama, and Moritaro Kanasashi were tasked to supervise its design. The floor specification of the building was as follow: “The structure of the first floor is made by pouring concrete and laying stones or paving asphalt. The structures of the second and third floors were RC with steel beams.” Since steel beams were used in its construction, it is presumed to have the same specifications as the Yokohama Shinko Wharf warehouses that were mentioned earlier [8]. The Tokyo Ward Court building—which was completed in 1920—was made entirely from concrete. Although its walls were made of plain concrete [9], however, the slab structure stood out. The floor specification was as follow: “Above the attic conference room is a slab with partial lattice beams; corridors are made of flat slabs; the first, second, and attic floors are beamed slabs; the outer corridors are cantilever slabs; the outside platform of the driveway is dome-shaped; the audience seats in the Grand Court is stepped; every floor is made of RC.” [10] The ceiling specifications were as follow: “The upper part of the hall is hemispherical with a circular light window in the middle; finish the RC with plaster about 15-cm thick; the ceiling of the Grand Court and the entrance hall are made of RC.” [10] Since there were no drawings, the details were not known. However, it was assumed that the specification of the RC floor slab was established as a technology after various attempts were made. The floor and staircase specifications of the Nagoya Court of Appeal building, which were written in 1918 and owned by the Nagoya Municipal Archives, included the following statements: “The floor shall be RC (partially or entirely) on both the second and third floors, and reinforcing steel shall be selected according to the location, and auxiliary steel wire shall be fully constructed with annealing wire.” “Each staircase shall be constructed with I-beams of appropriate cross-section according to the location, completely installed with attached ironwork, etc., and constructed carefully so as not to pose a danger.” There are eight drawings—four on detailed cross-sections, two on beam plans, and two on reinforcement plans—which are also owned by Nagoya City Municipal Archives, and they illustrate how the RC slabs and stairs are attached to the brick walls. Although there was a description of “steel beams” in the staircase specifications, however, this claim was not confirmed by the reinforcement diagram of the stairs. Since these rebar plans were not intended for the central grand staircase, it was not known whether I-beams were used. However, it can be surmised that there was an intention to use steel beams
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for added reinforcement since there was unease over the structural soundness of the RC structure. According to the detailed cross-sectional drawings, the thickness of the RC slab was 12 cm and appropriate adjustments were made to the width and length of the beams according to the location. A total of 18 beam shapes were confirmed, including the difference in the number of reinforcements at the bottom (Fig. 3). As for the installation of the RC slab on the brick wall, the actual measurement from the drawing showed that the slab penetrated the brick wall by approximately 9 cm, and the brick that supported the slab overhung by approximately 9 cm (Fig. 4).
Fig. 2. A detailed drawing showing the RC floor of the Kobe District Court building.
The specifications of the construction of the Sapporo Court of Appeal building— which are owned by the Sapporo City Archives—included 15 documents and over 100 drawings. There were ten drawings—four on detailed cross-sections, four on reinforcement plans, and two on beam plans—which showed the specifications to join brick walls to RC slabs and stairs. The thickness of the RC slab was mainly 12 cm; in some short spans, it was 9 cm (Fig. 5). The specification of the RC slab that penetrated the brick wall differed greatly from the courthouse of Nagoya. At Nagoya, the joint basement had brick overhangs, whereas at Sapporo, haunching beams were attached to the ends of the slabs. Although the dimension of the penetration varied depending on the location, however, there were places where either the RC slab penetrated into half of the wall thickness or it was designed to divide the brick walls vertically, such as the circumferential girder (Fig. 6). Although it was a simple wall-to-slab joint in the case of Nagoya, however, in
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Fig. 3. A detailed drawing showing the RC floor of the Nagoya Court of Appeal building.
Fig. 4. A detailed cross-sectional drawing of the Nagoya Court of Appeal building
the case of Sapporo, it may be perceived as the use of a combination of RC and bricks in order to reinforce the structure.
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Fig. 5. A detailed drawing showing the floor and column reinforcement arrangements of the Sapporo Court of Appeal building.
Fig. 6. A detailed drawing showing the floor reinforcement arrangement of the Sapporo Court of Appeal building.
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5 Mixed-Structure Buildings Constructed by the Ministry of Education Building Division At Kyoto Imperial University, mixed-structure buildings were confirmed from the drawings of the Law School (completed in 1915), the Metallography Research Institute (completed in 1918), and the schools of Geology and Mineralogy (completed in 1920), Biological Science (completed in 1922), and Physics (completed in 1922; upper-floor extension) in the Faculty of Science. [11] The Law School building used a simple RC slab that was similar to the Nagoya Court of Appeals building. In the Metallography Research Institute building, haunching beams were attached to RC slabs and they were connected to each other upon the columns to form a circumferential girder (Fig. 7). Large and small beams were used in the buildings of Geology and Mineralogy and Biological Science to accommodate large spans (Fig. 8). Consequently, over a short period of just seven years, a simple slab was developed into a beamed slab a beamed slab that incorporated the full attributes of RC. All the buildings were designed by Kyozo Nagase, an architectural engineer who was based at Kyoto Imperial University and provided a valuable example of how an architect from an organization made the transition from masonry structures to RC structures through a process of trial and error. As a side note, the building of the Department of Architecture—which was designed by Goichi Takeda and completed in 1922—was made from RC, which verified a move that was made by the Ministry of Education Building Division to use RC before the Great Kanto Earthquake occurred. At Tohoku Imperial University, the main building of the Metals Institute (completed in 1921) was designed by Senjiro Nakajima who was an architectural engineer with the university, and it featured a secession-style façade design that was preferred by him. The second and third floor slabs, roof slabs, and stairs were made from RC. [12] Although the drawing that showed the bar arrangement had been lost, however, the joints between the brick wall and the RC slab were the same as those in the Sapporo Court of Appeal building (Fig. 9). At Kyushu Imperial University, the buildings of the Department of Naval Architecture (completed in 1921) and its extension (completed in 1922) and the temporary laboratory of the Faculty of Engineering were designed by Ken Kurata, an architectural engineer who was based at the university. [13] In December 1923, the main building of the Faculty of Engineering (completed in 1914) was destroyed by a fire. At the strong request of Toranosuke Furukawa who also donated to its rebuilding, a temporary laboratory was built in 1925 that reused the brick walls of the burn-out main building. In the building of the Department of Naval Architecture, only the stairs—not the floors—were made from RC, and the connection with the brick wall was the same as the building of the Metals Institute at Tohoku Imperial University, which was completed in the same year. The slabs that were used to construct the extension of the Department of Naval Architecture were also made from RC, and the joints with the walls were the same as the Nagoya Court of Appeals building (Fig. 10). Although the construction of the temporary laboratory was premised on the reuse of old brick walls, however, the building of the Sapporo Court of Appeal had demonstrated that the vertical division of brick walls were based on the specifications of RC slabs (Fig. 11).
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Fig. 7. A cross-sectional drawing of the Metallographic Research Institute building at Kyoto Imperial University.
Fig. 8. A detailed drawing showing the RC floor and second floor beam of the Geological and Mineralogy building at Kyoto Imperial University.
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Fig. 9. A detailed cross-sectional drawing of the Metals Instal University.
Fig. 10. A cross-sectional drawing showing the extension of the Department of Naval Architecture building at Kyushu Imperial University.
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Fig. 11. A cross-sectional drawing of the temporary laboratory of the Faculty of Engineering at Kyushu Imperial University.
6 Conclusion Prior to the first decade of the twentieth century, fireproof floors that were made from concrete that was poured over shallow vaulted bricks or corrugated iron plates which spanned steel beams were widely used, and RC was occasionally used to build stair landings and staircases. After 1910, the practice of using RC slabs with steel beams to construct fireproof floors was introduced. Subsequently, the steel beams were replaced by using both small and large beams and haunching beams with RC slabs. The mixed-structure building was likely a result of a partial incorporation of the merits of RC, which was introduced in the first two decades of the twentieth century. This study has demonstrated that the construction of mixed-structure buildings in Japan was introduced through the building of the head office of Takaoka Kyoritsu Bank, which was completed in 1914 and has a steel-framed brick masonry wall structure. The construction of mixed-structure buildings disappeared after the Sapporo Court of Appeal building was completed in 1926. All walls in mixed-structure buildings examined in this study were constructed with unreinforced brick, with the exception of the Takaoka Kyoritsu Bank head office. Due to variations in site conditions, a standardized numerical value for wall thickness cannot be determined. Before the Great Kanto Earthquake, however, mainstream fireresistant construction had switched to the use of RC to build small- and medium-sized buildings. The Great Kanto Earthquake did not eliminate the possibility of constructing masonry buildings, and only remnants of mixed-structure construction are seen in largescale buildings. Depending on how one looks at it, the damage to masonry buildings that was caused by the Great Kanto Earthquake can be described as the final blow that caused the demise of masonry buildings in Japan. It will be interesting to examine whether a similar phenomenon is also observed with mixed-structure buildings in other countries over the same period.
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Acknowledgements. This work was supported by Matsui Kakuhei Memorial Foundation Research Grants in 2018 and 2019.
References 1. Muramatsu, T.: Nihon Kindai Kenchiku Gijutsu-Shi [History of Architectural Techniques in Modern Japan], Shokokusha (1976) 2. Hori, T.: Nihon ni-okeru Tekkin Konkurito Kenchiku Seiritsu Katei no Kouzou Gijutsu-shiteki Kenkyu [A Historical Study of Structural Technology on the Establishment Process of RCBuildings in Japan], Dissertation, private edition (1981) 3. Morimura Bank Building New Construction Completed. J. Archit. Inst. Japan 28(11), 36–38 (1914) 4. Owned by Takaoka City Board of Education 5. Accounting Division, Minister of Justice. Shiho-sho oyobi Saiban-sho Chosha Shasin-cho [Photo Album of the Ministry of Justice and Court Buildings], Accounting Division, Minister of Justice (1939) 6. Construction of the Osaka Court of Appeal and Osaka District Court buildings. J. Archit. Inst. Japan 12(6), 217 (1898) 7. Association for Considering Architecture in Kobe: Kobe Chiho Saiban-sho Hozon he-no Michi[The Road to Kobe District Court Building Preservation] (1987) 8. Overview of Osaka Court of Appeal, District Court, Ward Court, Merged Office Building. J. Archit. Inst. Japan 30(7), 54–55 (1916) 9. Round-table: Talking about Architecture in the Taisho Period. J. Archit. Inst. Japan 84(1), 529–537 (1970) 10. Overview of Tokyo Ward Court Building Construction. J. Archit. Inst. Japan 34(9), 30–32 (1920) 11. Owned bythe Facilities Department of Kyoto University 12. Owned bythe Department of Civil Engineering and Architecture of Tohoku University 13. These drawings are owned by Kyushu University Archives
Snow Load Effect to Vibration Characteristics of Japanese Traditional Wooden Main Temple Building and Three-Story Pagoda Based on Ambient Vibration and Earthquake Observation Records K. Mitsji1(B) , T. Hanazato2 , and Y. Niitsu3 1 Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata, Japan
[email protected]
2 Kanagawa University, 3-27-1 Rokkakubashi, Kanagawa-ku, Yokohama, Japan 3 Tokyo Denki University, 5 Senju Asahi-cho, Adachi-ku, Tokyo 120-8551, Japan
Abstract. Snow load effect to vibration characteristics of Japanese traditional wooden main temple building and three-story pagoda of “Jion-ji”, Japan is studied using ambient vibration measurement and earthquake observation data. The 1st natural frequency of the main temple building ranged from 1.07 to 1.73 Hz in EW and 0.98 to 1.88 Hz in NS. The 1st natural frequency of the pagoda ranged from 1.23 to 1.66 Hz in EW and 1.20 to 1.49 Hz in NS. As a result, vibration characteristics of those heritage structures were affected by snow load distribution on the roof and amplitude of earthquake. In winter, thickly accumulated snow leads to the additional load, having caused the significant change of the vibration characteristics of the structure. The snow load on the natural frequency was as effective as small earthquakes. Large amplitude of strong earthquake is more effective to vibration characteristics of those buildings and decrease the natural frequency. From an earthquake engineering point of view, the equivalent mass of the structure with the snow load in winter was 1.9 times as heavy as that in summer, which indicated seismic safety of the structure would be affected by the snow load in snow area. Keywords: Snow Load · Temple · Pagoda · Ambient Vibration · Earthquake Observation
1 Introduction Multi-story pagoda is well known to be excellent earthquake resistance from the ancient period in Japan. Ohmori [1] studied the vibration characteristics of six five-story pagoda by ambient vibration and free vibration measurement. Sezawa and Kanai [2, 3] discussed the dissipation of the vibrational energy of five-story pagoda by numerical calculation. Yamabe and Kanai [4] pointed out that the principal axis of pagoda tends to have diagonal direction based on ambient vibration and free vibration measurement and earthquake © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 101–111, 2024. https://doi.org/10.1007/978-3-031-39450-8_9
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observation. Hanazato et al. [5] developed the structural model of pagoda and discussed the structural safety in design. Ohba and Kinoshita [6] formulated the prediction relation of the 1st and 2nd natural frequency of pagoda to the height based on ambient vibration and free vibration measurement. Chiba et al. discussed the vibration characteristics of 1/5 scale model of pagoda by shaking table test [7]. Nakahara et al. [8] studied earthquake resistance and vibration characteristics of “Horyu-ji” temple in Japan by microtremor data and numerical analysis. Thus, Vibration characteristics and earthquake resistance of pagoda have been studied by many researchers and basic characteristics are becoming clear. However, snow load effect to vibration characteristics of pagoda is not clearly understood in heavy snowfall area. Recently snowfall is locally getting heavier in short period that is alleged to global warming. Considering snow effect to structural design of building may become more important in the near future. Therefore, it is important to quantitatively investigate snow load effect to vibration characteristics of pagoda and other traditional wooden building. The author studied seasonal variation of vibration characteristics of multi-layered wooden building by ambient vibration measurement and earthquake observation, and pointed out that the effect of snow load is quantitatively same as small earthquake, but the effect of large earthquake tends to decrease the natural frequency of the building [9]. The authors conducted ambient vibration measurement and earthquake observation at the Japanese traditional wooden structures of the main temple building and the threestory pagoda, having discussed the effect of the snow load to the vibration characteristics of those structures. Both structures belong to the “Jion-ji” temple of Yamagata where is well known heavy snow region of the north Japan. Two types of measurement systems were installed for this study. One is the measurement of ambient vibration by utilizing velocity sensors, and the other is the long-term monitoring measurement system by MEMS accelerometers being measurable for wide range of amplitude from ambient vibration to strong motions due to earthquakes. We discuss the snow load and earthquake effect to vibration characteristics of the main temple building and the three-story pagoda of “Jion-ji” in the followings. Investigation of vibration characteristics of pagoda and main temple building can be applied to structural design of mid-rise wooden buildings and wooden space structure. Providing basic information for structural design of modern wooden buildings and structures is expected.
2 Outline of the Investigated Buildings: Main Temple Building and Three-Story Pagoda The temple of “Jion-ji” exists in Yamagata of northern east of Japan. The temple is the religious complex consisting of three temples and 17 monk’s residences. The main temple building was constructed in 1618 and designated as the national important cultural property in 1950. According to the investigation report of “Jion-ji” temple, the height of the main temple building is 15.06 m and eave height is 5.34 m. It is one-story wooden structure with seven spans in girder direction (EW) and five spans in the direction perpendicular to the girder (NS). The rood structure is gabled type called “Irimoyadukuri” with the thatched roof.
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The original three-story pagoda was burn down in 1823 and rebuilt in 1830. The three-story pagoda was registered tangible cultural property of Yamagata Prefecture in1955. The total height including the top called “Sorin” made of metal is 23.92 m, and the height of the tower is 14.61 m. It is a traditional Japanese-style pagoda with copper plate tiled roofing. Photos in Fig. 1 are the main temple building and the three-story pagoda in summer and winter, respectively. In winter season of 2020–2021 and 2021–2022, snow was thickly accumulated on the roof of the main temple building. However, the three-story pagoda stands without snow on its roof because snow on the copper plate tiled roof tends to slide down without accumulation.
Fig. 1. Photo of the main temple building and the three-story pagoda (left: 26 May of 2022, right: 22 Dec. of 2020 with snow)
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3 Ambient Vibration Measurement and Earthquake Observation of the Main Temple Building Two types of measurement systems were installed for this study. One is the measurement of ambient vibration by utilizing velocity-meters, and the other is the long-term monitoring measurement system by MEMS accelerometers being measurable for wide range of amplitude from ambient vibration to strong motions due to earthquakes. In the followings, vibration characteristics of the main temple building, and the three-story pagoda are studied based on the results of the ambient vibration measurement and earthquake observation. In case of the main temple building, sensors were placed on the girders and on the foundation to understand the basic vibration characteristics of the building. Sensor location is illustrated in Fig. 2. Blue squares of #1 to #9 are the positions of the velocitymeters and orange stars are the positions of the MEMS accelerometers of com5, com6, com7 and com10. The ambient vibration measurement lasts 10 min. The window is applied to all the duration and divided into the 40.96 s small data. Shifting by the half of the window width, and applying FFT to the 40.96 s small data, and average characteristics of the 10 min data of each velocity-meter are obtained. N #1(EW)→ MEMS_com6 #2(EW) →
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Fig. 2. Section [10] and schematic plan of the main temple building with sensor location
Ambient vibration measurements were carried out several times both in summer and winter after 2019 to discuss the snow load effect on the natural frequency of 1st mode. Amplitude ratios of #3/#8 in EW direction and #4/#9 in NS direction are shown in Fig. 3 on behalf of all the velocity-meters. The 1st natural frequency is estimated 1.61 Hz in EW and 1.86 Hz in NS at the corner of the building on 2019/09/08. All the natural frequencies of the 1st mode of the main temple building estimated by amplitude ratios of #1 to #7 compared to #8 and #9 are summarized in Table 1.
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Fig. 3. Amplitude ratio of the main temple building by velocity-meters Table 1. The 1st natural frequency of the main temple building (unit: Hz) #1(EW)
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Seasonal variation of the 1st natural frequency of the main temple building by velocity-meters is shown in Fig. 4. The 1st natural frequency tends to be slightly higher at the corner of #1 in EW and #4 in NS than other positions. Based on the results of #2 and #3 in EW and #5, #6 and #7 in NS, the 1st natural frequency tends to be higher in NS than in EW. It can be considered because there are more structural walls installed in NS than in EW. Results from the measurements in winter (2021/1/23, 2021/2/06, 2022/2/22, 2022/2/3) show the 1st natural frequency becomes lower than in summer. The variation was caused by snow load thickly accumulated on the thatched roof of which thickness was estimated about 1m at deepest. Damping factors of the main temple building estimated by free vibration test on 2019/09/08 were also about 1.9% in EW and 2.3% in NS.
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Fig. 4. Seasonal variation of the 1st natural frequency of the main temple building by velocitymeters
MEMS accelerometer can record vibration data from low amplitude as 0.1gal to large amplitude as strong earthquake in tri-axis. Ambient vibration measurement started on 2019/09/08 and currently continues at the time of Feb. 2023. Four sets of sensors were placed into the main temple building of com5, com6, com7, and com10 (on the foundation) shown in Fig. 2. Amplitude ratios of com5 to com10 estimated by MEMS accelerometers are shown in Fig. 5. Ambient vibration data recorded by MEMS accelerometers are not good enough S/N ratio in resting state for the signal analysis to obtain vibration characteristics of the building. Some effort was necessary to find appropriate data having good S/N ratio. However, amplitude ratio can be derived from the recorded data including small earthquake, and ambient vibration with large amplitude generated by human activity.
Fig. 5. Amplitude ratio of the main temple building by MEMS accelerometers (com5/com10)
In Fig. 5, amplitude ratios of 2019/09/16 and 2011/12/30 are estimated by the data including large amplitude ambient vibration generated by human walking. Case of 2019/09/16 is without snow on the roof, and case of 2021/12/30 is thickly accumulated snow on the roof. Amplitude ratio of 2022/03/16 is including earthquake that is the largest (max. acc. is 135gal in NS) during the observation period. It can be found that the 1st natural frequency in large earthquake (2022/03/16) is lowest during the observation period. The 1st natural frequency with snow on the roof is lower than without snow. Variation of the natural frequency depends on the amplitude of vibration and weight of the roof. Analyzing other data and obtaining amplitude ratio of different observation period, seasonal variation of the 1st natural frequency of the main temple building by MEMS accelerometers (com5/com10) is shown in Fig. 6. Blue dotted line is the accumulated snow depth observed in Yamagata city about 20 km south from the site of “Jion-ji”. As suggesting from the results of Fig. 5, the 1st natural frequency tends to be lower in
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earthquake. When snow is on the roof, the natural frequency is also shifting to lower range of frequency but stay in the middle of earthquake and ambient vibration without snow. The highest of the 1st natural frequency is 1.73 Hz in EW and 1.88 Hz in NS, and the lowest is 1.07 Hz in EW and 0.98 Hz in NS. The ratio of the highest to the lowest is 1.62 in EW and 1.92 in NS. Difference in EW and NS can be considered because snow on the roof may not have been uniformly distributed, and the directivity of earthquake.
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Displacement time history of com 5 and com10 and displacement orbit in EW and NS plane are shown in Fig. 7. Displacement is derived by applying numerical integration twice to the recorded acceleration data. To avoid long period component, band pass filter of 1 to 2 Hz including the 1st natural frequency is applied. Comparing displacements of com5 to com10, the roof of the main temple building behaves in phase with the foundation in almost all the duration, especially before the large amplitude. However, after large amplitude, displacement of the roof tends to be out of phase with the foundation. Displacement orbit also indicates interesting result. While displacement orbit of the foundation (com10) shapes almost the round, the roof (com5) looks like moving in the shape of ellipse with gradient axis. It can be said because snow on the roof may not have been uniformly distributed, as well as the 1st natural frequency variation. 1.0
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Fig. 7. Displacement time history of com 5 and com10 and displacement orbit in EW and NS plane.
4 Ambient Vibration Measurement and Earthquake Observation of the Three-Story Pagod Ambient vibration measurement was conducted on 2019/09/08 for the three-story pagoda by velocity-meters. Four sets of velocity-meters were installed into the pagoda. As well as the main temple building, MEMS accelerometers were installed into the pagoda for
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the long-term monitoring. Three sets of sensors were installed at the top, the middle layer, and entrance of the three-story pagoda. Sensor location is shown in Fig. 8 with the façade and schematic plan of the pagoda. According to the amplitude ratio of RF/1F measured on 2019/09/08, the 1st natural frequency of the three-story pagoda was estimated 1.45 Hz in EW and 1.36 Hz in NS. Clear small peaks indicating torsional motion at around 2.0 Hz, and the second mode at around 3.5 Hz are found in both directions.
RF: #1 (EW)→ #2 (NS) ↑ 3F:MEMS_com11
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Fig. 8. Façade [10] and schematic plan of the three-story pagoda with sensor location (left and center); Amplitude ratio estimated on 2019/09/08 (right)
Amplitude ratios of 3F/1F of the three-story pagoda estimated by MEMS accelerometers are shown in Fig. 9. Ambient vibration measurement started on 2019/09/08 at the same time as the main temple building. Three sets of sensors were placed into the pagoda of com9, com11, and com12 shown in Fig. 8. Amplitude ratios of com11 (3F) to com9 (1F) estimated by one-hour records of MEMS accelerometers are shown in Fig. 9. As well as the main temple building, ambient vibration data recorded by MEMS accelerometers are not so good S/N ratio that data including earthquake and large amplitude of ambient vibration are adopted for the analysis. In Fig. 9, amplitude ratios of 3F/1F of 2020/01/03 include small earthquake without snow even in winter season. Amplitude ratio of 2021/02/13 are affected by large amplitude of earthquake (max. acc. is 49gal in EW). Amplitude ratio of 2021/02/19 are ambient vibration in snow season. It is clearly understood that the 1st natural frequency under the earthquake of 2021/02/13 is 1.36 Hz in EW and 1.33 Hz in NS that is the lowest. On the other hand, the 1st natural frequency under the small earthquake of 2020/01/03 is 1.51 Hz in EW and 1.42 Hz in NS that is almost the same as that of ambient vibration with snow of 2021/02/19. Amplitude at the 1st natural frequency becomes larger under earthquake than ambient vibration. Moreover, Peak shape at the 1st natural frequency of amplitude ratio of 2021/02/13 is spread wider than small earthquake of 2020/01/03. That indicates that the pagoda has potential of a high damping factor and much energy consumption under large earthquake. Figure 10 shows seasonal variation of the 1st natural frequency of the three-story pagoda by MEMS accelerometer (com11/com9). Likewise in Fig. 5, blue dotted line
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Fig. 9. Amplitude ratio of 3F/1F of pagoda by MEMS accelerometers
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is the accumulated snow depth observed in Yamagata city. Although decrease of the 1st natural frequency can be seen in the pagoda, the effect of earthquake and snow is relatively small compares to the main temple building. The highest of the 1st natural frequency is 1.66 Hz in EW and 1.49 Hz in NS, and the lowest is 1.23 Hz in EW and 1.20 Hz in NS. The ratios of the highest to the lowest are 1.35 in EW and 1.24 in NS that are smaller than the main temple building. Snow was rarely accumulated on the roof of the pagoda because of the copper plate tiled roofing, so difference in EW and NS can be considered because of the amplitude of earthquake. Damping factors measured in summer were 3.2% in EW and 3.1% in NS for the pagoda based on the results of free vibration measurement.
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Displacement time history in EW and displacement orbit in EW and NS plane of com 9 (1F), com12 (2F) and com11 (3F) are shown in Fig. 11. As well as the main temple building, displacement is derived by applying numerical integration twice to the recorded acceleration data. To avoid long period component, band pass filter of 1 to 2 Hz including the 1st natural frequency is applied. Comparing displacements of 1F to 3F, all the floors behave in phase in almost all the duration, especially 2F and 3F. However, displacement of 1F tends to be out of phase with 2F and 3F after large amplitude. Displacement orbit shows the behavior of
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the pagoda is complicated as sometimes like an ellipse flat in EW and sometimes with gradient axis in NW-SE direction.
Fig. 11. Displacement wave forms and particle orbit in EW and NS
5 Conclusions Vibration characteristics of the main temple building and the three-story pagoda in heavy snowfall area in the northern Japan were investigated using ambient vibration measurement and earthquake observation. The effects of snow on the roof and earthquake were discussed. Findings in this study are described below. 1) The 1st natural frequency of the main temple building is estimated 1.61 Hz in EW and 1.86 Hz in NS at the corner of the building by velocity-meters on 2019/09/08 and tends to be higher in NS than in EW. It can be considered because there are more structural walls installed in NS than in EW. Results from the measurements in winter indicate that the 1st natural frequency becomes lower than in summer. The variation was caused by snow load thickly accumulated on the thatched roof. 2) According to the results of MEMS accelerometers of the main temple building, the highest of the 1st natural frequency is 1.73 Hz in EW and 1.88 Hz in NS, and the lowest is 1.07 Hz in EW and 0.98 Hz in NS. Variation in the 1st natural frequency can be considered because of snow on the roof and large amplitude of earthquake. 3) The roof of the main temple building behaves in phase with the foundation, especially before the large amplitude coming. However, after large amplitude, displacement of the roof tends to be out of phase with the foundation. While displacement orbit of the foundation shapes almost the round, the roof behaves in the shape of ellipse with gradient axis. 4) Based on the results of the amplitude ratios of RF/1F of the pagoda measured on 2019/09/08, the 1st natural frequency of the three-story pagoda was estimated 1.45 Hz in EW and 1.36 Hz in NS. Clear small peaks indicating torsional motion at around 2.0 Hz, and the second mode at around 3.5 Hz are found in both directions. 5) Although decrease of the 1st natural frequency can be seen in the three-story pagoda, the effect of earthquake and snow is relatively small compared to the main temple building. The highest of the 1st natural frequency is 1.66 Hz in EW and 1.49 Hz in NS, and the lowest is 1.23 Hz in EW and 1.20 Hz in NS. Variation seen in the pagoda is smaller than the main temple building. Snow was rarely accumulated on the roof of the pagoda because of the copper plate tiled roofing that is effective to decrease the snow load effect.
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6) All the floors of the pagoda behave in phase in almost all the duration, especially 2F and 3F. However, displacement of 1F tends to be out of phase with 2F and 3F after large amplitude coming. Displacement orbit shows the behavior of the pagoda is so complicated that sometimes as an ellipse flat in EW and sometimes with gradient axis in NW-SE direction. As a whole, the snow load effect to vibration characteristics of the main temple building and the three-story pagoda of “Jion-ji” temple is quantitatively same as the case of small earthquake. In case of large earthquake of which maximum acceleration is over 100gal, the effect is larger than snow load. However, if strong earthquake hits the buildings with snow on the roof in winter, damage will be more sever than in other season without snow. The results indicate good agreement with the case of multi-layered wooden building of the author’s previous study. Acknowledgments. The authors are grateful to Mr. Mizuki Aritsuku, Ms. Fuko Togawa, Ms. Chihiro Niizeki, Prof. Yasuo Nagai of Yamagata University, and all concerned of the “Jion-ji” temple for the cooperation of this investigation.
References 1. Ohmori, F.: On the vibration of Gozyunoto (Pagoda). J. Inst. Japan. 414, 219–227 (1921). (in Japanese) 2. Sezawa, K., Kanai, K.: Further study on the seismic vibration of a Gozyunoto (Pagoda). Bull. Earthq. Res. Inst. Tokyo Imperil Univ. 14, 525–533 (1936) 3. Sezawa, K., Kanai, K.: On the seismic vibration of a Gozyunoto (Pagoda). Bull. Earthq. Res. Inst. Tokyo Imperial Univ. 15(1), 33–40 (1937) 4. Yamabe, K., Kanai, K.: Study on the aseismic properties of the Gozyunotos (Pagodas). Journal of the College of the Industrial Technology, Nihon University, Japan, pp. 91–110 (1988). (in Japanese) 5. Hanazato et al.: Structural design of traditional five-storied pagoda. AIJ J. Tech. Design (7), 33–38 (1999). (in Japanese) 6. Ohba, S., Kinoshita, A.: Dynamic characteristics of multi-story wooden pagodas. J. Struct. Constr. Eng. AIJ 559, 47–54 (2002). (in Japanese) 7. Chiba, K., et al.: Fundamental vibration characteristics of traditional five storied pagoda by shaking table tests-Part 1. J. Struct. Constr. Eng. AIJ 614, 69–75 (2007). (in Japanese) 8. Nakahara, K., et al.: Earthquake Response of Ancient Five-story Pagoda Structure of Horyu-ji Temple in Japan, 12th World Conference on Earthquake Engineering, 1229/11/A (2000) 9. Mitsuji, K., Adachi, H.: Variation of dynamic characteristics of multi-layer wooden building based on continuous observed records. In: 17th World Conference on Earthquake Engineering, Paper No.C001887 (2020) 10. Board of Education of Sagae city: Investigation report of Jion-ji temple (2014). (in Japanese)
Proposal of Strength Estimation Formula of Wall Clays Using Multiple Regression Analysis Kimiko Miyoshi1(B) , Yoichi Hayasaki2 , Naoya Syojo3 , and Yoshimitsu Ohashi4 1 Kyushu Sangyo University, 2-3-1, Matsukadai, Higashi-Ku 813-8503, Fukuoka, Japan
[email protected]
2 Testing Center for Construction Materials, Sanyo Onoda, Japan 3 University of Hyogo, Kobe, Japan 4 Tokyo City University, Tokyo, Japan
Abstract. Mud walls, which have been used since ancient times in Japanese timber structures, have the advantages of being harmless to the human body and having a low environmental impact. However, as the quality of the materials is not uniform, it is difficult to clarify the mechanical properties without conducting the strength test. Therefore, in this study, compression and shear tests were performed on the wall clay. Furthermore, authors performed multiple regression analysis to derive the estimation formulas for the wall clay strength using the material properties, e.g., mixing ratio, particle size distribution, and wall clay density. As a result, the soil source, maturity period, and sand volume in the second coating soil affect the wall clay strength. The strength ratios of compression and shear of the wall clay were divided between 57% and 64% of the passing mass percentage of grain size 0.075 mm. The estimation formulas for the compression and shear strengths of the wall clay agreed with the measured values when the soil test data, water content, and density of the wall soil during construction and after drying were combined. Furthermore, shear strength could be estimated using the passing mass percentage of grain size 0.075 mm and average compressive strength. Keywords: Mud wall · Compressive strength · Shear strength · Multiple regression analysis · Particle size distribution
1 Introduction Mud wall is a type of wall in a Japanese timber structure. During the mass housing era (1950–1980), the industrial production method became mainstream, and the use of mud walls decreased. Recently, environmental concerns on residential construction have increased, e.g., the sick house/building syndrome or increased industrial waste. This has led to the re-evaluation of mud walls. Mud walls have low environmental impact, do not emit toxic substances, and allow for easy soil disposal and reuse. However, the quality of materials used for mud walls is not uniform. The physical and mechanical properties of soil, which have the greatest effect on the wall clay strength, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 112–124, 2024. https://doi.org/10.1007/978-3-031-39450-8_10
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differ depending on the region and stratum. Therefore, it is necessary to adjust the wall clay mix every time, and the material and mechanical properties cannot be clarified unless strength tests are performed after drying the wall clay. Yamada et al. [1] derived the optimal mixing ratios for the first coating soil, which integrates the front and back of the wall, and second coating soil, which does not cause cracks, along with the compression characteristics of wall clay. Hirano et al. [2] reported that the compressive strength increased during the Mizuawase period (the period during which wall clay materials are stored in a wet state after mixing) between 11 and 34 weeks. Nakao et al. [3] reported that the compressive strength of reused soil is the highest, and that the strength decreases when new soil, straw, and Mizuawase period are added. Muramoto et al. [4, 5] statistically analyzed the load–deformation angle envelope curves of full-scale mud wall experiments in the literature, and estimated the wall strength ratios and load–deformation angle envelope curves of full-scale mud walls from the compressive strengths of wall clays. However, there are no studies that statistically analyze material properties, such as the mixing ratio, particle size distribution, and wall clay density, and estimate wall clay strength from these factors. Therefore, the authors first researched literature and the empirical know-how of plasterers. Among them, the presence or absence of reused soil, quantity and length of cut straw, Mizuawase period, soil source, and volume of sand in the second coating soil were selected as the factors that are assumed to affect the wall clay strength. Then, wall clay specimens were prepared and uniaxial compression tests and double shear tests were conducted. Furthermore, we statistically analyzed the obtained specification and experimental data by multiple regression analysis. Then, we attempted to derive the estimation formulas (multiple regression equations) for the compressive strength σmax and shear strength τmax of wall clays using material property values, such as the mixing ratio, particle size distribution, and wall clay density. The wall clay strength estimation formulas in this study are limited to the specimen shape and test method.
2 Strength Tests 2.1 Specimens and Test Methods Table 1 shows the specifications and number of specimens. The standard specimens of the first coating soil (mud plaster that is first painted to the wall base) and second coating soil (mud plaster that is painted on top of the first coating soil) of the mud wall are named Arahyo and Nakahyo. The standard specifications are shown in white, whereas comparison litems are in gray. The standard specifications of the first coating soil were 100 of new soil from Kumamoto (Yatsushiro), 4 kg of cut straw (5–6 cm), 30 of water, and Mizuawase period of 7 days. The standard specifications of the second coating soil are 100 of new soil from Kumamoto (Yatsushiro), 3.33 kg of cut straw (mixture of Tsunasusa of approximately 1–2 cm and Hidashisusa of about 1 cm), 35 of water, and blend sand (mixture of river gravel, river sand, and mountain sand) 55.8 . These mixing ratios were judged to be optimal by a first grade plastering technician. For comparison, the mixing ratio of reused soil to new soil in Tsuchimaze was 1:3 (volume ratio). The used soils were new soils from Kumamoto (Yatsushiro, Taragi, Aso, and Amakusa), Saitama, and Kyoto, whereas reused soil was collected from earthen storehouse wall.
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Table 2 shows the mixing ratios of specimens. The numbers in the parentheses indicate the water content ratios of the soil and cut straw. To grasp the grain size characteristics of the wall clays, a soil grain size test (Japanese Industrial Standards JIS A 1204) was conducted after removing the cut straw. Figure 1 shows the particle size accumulation curves of the specimens. As shown in the passing mass percentage of particle size 0.075 mm, soils with 50% or more were classified as fine-grained soil, whereas soils with less than 50% were classified as coarse-grained soil. Thus, the Sansai, Nakahyo, Sunata, and Sunasyo specimens resulted in coarse-grained soil, whereas other specimens resulted in fine-grained soil. The mud plasters of specimens were filled in wooden formworks of 450 × 600 × 60 mm using a trowel. After drying them indoors for over a year, the wall soils were cut into 150 × 150 mm (for compression test) and 60 × 180 mm (for shear test) samples using an electric circular saw. The tests include uniaxial compression test and double shear test. Figure 2 shows a schematic diagram of the tests. The compression force was applied at a rate of 1 mm/min. Table 1. Specifications and number of specimens
Proposal of Strength Estimation Formula of Wall Clays Table 2. Mixing ratios of specimens
Fig. 1. Particle size accumulation curve of specimens
Fig. 2. Schematic diagrams of tests (left: compression, right: shear)
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Fig. 3. σ –ε and τ –δ curves
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2.2 Test Results and Discussion Factors affecting the wall clay strength were the presence or absence of reused soil, Mizuawase period, soil source, and volume of blend sand added to the second coating soil. The average compressive stress–strain curves (σ –ε curves) and average shear stress–displacement curves (τ –δ curves) of the specimens are shown in Figs. 3a–d The compression stress σ was calculated by P/(b × t), strain ε by compression displacement δ/h, and shear stress τ by P/(2 × t × h). t is the thickness after drying shrinkage. As shown in Fig. 3a, σmax of the reused soil Tsuchifuru was higher than that of the new soil Arahyo➀. However, σmax and τmax of Tsuchimaze, which is a mixture of the two, hardly increased. As shown in Fig. 3b, σmax and τmax during the Mizuawase period of 90 days Nenaga were 1.2–1.3 times higher than 0 days Nenashi and 7 days Arahyo➁. As shown in Fig. 3c, the effect of the soil source was conspicuous in the Kyoto soil. Additionally, the strength differed among the Kumamoto soils (Yatsushiro, Taragi, Aso, and Amakusa). As shown in Fig. 3d, the Young’s modulus and σmax of the second coating soil were higher than those of the first coating soil, but those decreased when the quantity of sand in the second coating soil increased. τmax of the first and second coating soils hardly
(N/mm2)
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Fig. 4. Relationship between σ max and τ max Table 3. Strength ratio (τ max /σ max ) Classification
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changed. Furthermore, the second coating soil showed brittle fracture behavior, whereas the first coating soil showed high toughness. As shown in Fig. 4, the average compressive strengths σ max of the coarse-grained soil specimens were larger than those of the fine-grained ones. Additionally, strength ratios of τ max /σ max , as shown in Table 3, were 0.6–0.7 for coarse-grained soil specimens and reused soil Tsuchifuru, and 0.8–1.0 for other fine-grained soil specimens. Expressing this result using the passing mass percentage of particle size 0.075 mm in Fig. 1, the strength ratio of the soil of 57% or less was 0.6–0.7, and that of 64% or more was 0.8–1.0.
3 Multiple Regression Analysis In multiple regression analysis, Eq. (1) was obtained by extending the simple regression equation to multiple dimensions. yˆ is called the objective variable (predicted value), x1 to xp are the explanatory variables (p: the number of explanatory variables), β1 to βp are the partial regression coefficients, and β0 is the constant term. In this study, σmax and τmax obtained in the experiment are used as objective variables, and the 27 items in Table 4 are used as explanatory variables. The combinations of specimens used in the analysis are three patterns: (A) all specimens, (B) first coating soil specimens with different source of soils, and (C) specimens (B) + Nakahyo. yˆ = β0 + β1 x1 + β2 x2 + · · · + βp xp
(1)
However, when the correlation relationship between variables used in multiple regression analysis is a nonlinear relationship (relationship distributed on a curve), one or both variables must be converted by natural logarithm and replaced with linear relationship. Furthermore, when the objective variable yˆ was logarithmically transformed, log yˆ must be converted back to yˆ by exponential transformation, as shown in Eq. (2) yˆ = alog(yˆ ) = a(β0 +β1 x1 +β2 x2 +···+βp xp )
(2)
To obtain the multiple regression equation with the smallest residual error e (difference between 2 actual value and predicted value yˆ ) of the specimens, the residual sum of square ei in Eq. (3) was partially differentiated by each unknown of β0 to βp . Additionally, the unknowns β0 to βp were calculated when they were 0. n in Eq. (3) indicates the number of specimens. n n 2 n 2 yi − yˆ i = yi − β0 − β1 x1i − β2 x2i − · · · − βp xpi (3) ei2 = i=1
i=1
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The selection criteria of the explanatory variables were that the unbiased variance ratio F in Eq. (4) using the residual variances Vp−1 and Vp before and after adding the variables was two or more and the maximum value. The residual variance is the value obtained by dividing the residual sum of squares of the measured and predicted values yˆ of the specimens used in the analysis based on the degrees of freedom. The selection method was forward-backward stepwise selection method, and addition and deletion were repeated until the F values of all variables became two or more. The F value of
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Table 4. Explanatory variables list Measurement timing
Explanatory variable name
Mixing
Water (), Blend sand (), and Cut straw (kg) per soil 100 . Cut straw length (cm) Total 4 items
Painting
Matured period (days), Water content ratio of mud plaster (%), Cut straw content ratio (%), Density of mud plaster (g/cm3 ), Absolute dry density (g/cm3 ), and Drying shrinkage ratio (%) Total 6 items
Strength test (Air-dry state) Air dry density (g/cm3 ), Absolute dry density (g/cm3 ), Air dry water content ratio (%), and Cut straw content ratio (%) Total 4 items Soil test
Mass percentage (%) of particle size 0.075 mm or more and each section of particle size 19 mm or less in Figure 1, Liquid limit (%), Plastic limit (%), Plasticity index, Density of soil particles (g/cm3 ), and Apparent voidage (= Soil particle density − Absolute dry density of test specimen) (g/cm3 ) Total 13 items
two or more means that the residual variance reduced by adding the explanatory variable is more than double the residual variance after adding the explanatory variable. F = Vp−1 − Vp /Vp (4) Furthermore, when the correlation coefficient between the selected explanatory variables is high, multicollinearity occur, where the sign of the partial regression coefficient of the partner is reversed. In that case, the correlation coefficients of the explanatory and objective variables were compared, the lower explanatory variable was deleted, and the analysis was repeated. 3.1 Analysis Results Correlation Relationship. The objective variable σmax and explanatory variables with high correlation showed a nonlinear relationship. Therefore, one or both variables were transformed by natural logarithm and replaced by a linear relationship. Thus, the log σmax of the first and second coating soils showed the highest correlation with clay mass percentage. The correlation coefficient was − 0.90. The log σmax showed high correlation coefficients of − 0.89 with log water content at coating, and 0.80 or more with absolute dry density of mud plaster, specimen air-dry/absolute dry density, apparent porosity, log specimen air-dry water content, log liquid limit, and coarse fraction mass percentage. The correlation diagrams are shown in Fig. 5. The objective variable τmax also showed slightly nonlinear relationship with the explanatory variables of high correlation. Therefore, the logarithmic transformation similar to that of σmax was performed. Thus, the log τmax of the first and second coating soils has the highest correlation with log specimen air-dry water content and log plasticity index, and the correlation coefficient was − 0.85. Similarly, log τmax showed high
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Fig. 5. Correlation diagrams of explanatory variables and log compression strengths
correlation coefficients of 0.84 with log σ max and 0.80 with specimen air-dry/absolute dry density. The correlation diagrams are shown in Fig. 6.
Fig. 6. Correlation diagrams of explanatory variables and log shear strength
Estimation Formulas. Even after analyzing the data of the mixing, painting, and strength tests, we could not derive highly accurate estimation formulas for σmax and τmax . However, when the soil test data was added to the analysis, highly accurate estimation formulas for σmax and τmax could be derived. In the case of the σmax estimation formula, Eq. (5) which used the clay and medium gravel mass percentages, provided the value closest to the measured value. However, small amounts of medium gravel are contained only in Taragi (0.7%) and Sansai (1.1%). Therefore, it is desirable to use Eq. (5) after re-verifying experimentally how much this small amount of medium gravel influences σmax . Additionally, Eqs. (6) and (7) were derived as simple estimation formulas that facilitate data collection. Equation (6) uses the water content and density of mud plaster during painting and the fine sand mass percentage. Equation (7) uses the air-dry water content of the first coating soil, coarse fraction mass percentage, and plastic limit. The values in the parentheses shown in the explanation of the symbols of each estimation formula are the input range of the variables. As shown in Fig. 7, when the predicted and measured values are compared, Eq. (5) generally agrees with the measured values, but the predicted values for Aso and Sunata had slight residuals. Equation (6) generally agrees with the measured values except for Sunata, and Eq. (7) generally agreed with only the specimens of the first coating soil. (Soil test) σmax = a(−0.03x1 +0.338x2 −0.252)
(5)
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(Painting) σmax = a(−0.711logx3 +1.07x4 +0.027x6 −0.277) (First coating soil of air − dry state) σmax = a(−0.53logx5 +0.012x7 −0.017x8 −0.39)
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(6) (7)
x 1 : Clay mass percentage (14.9%–46.0%) x 2 : Medium gravel mass percentage (0.0%–1.1%) x 3 : Mud plaster water content (36.4%–103.8%) x 4 : Mud plaster density (1.37–1.75 g/cm3 ). x 5 : Specimen air-dry water content (1.8%–8.0%) x 6 : Fine sand mass percentage (3.1%–24.7%). x 7 : Coarse fraction mass percentage (3.9%–60.7%) x 8 : Plastic limit (16.7%–39.3%).
Fig. 7. Comparison diagrams of predicted and measured values of σmax
The τmax estimation formula was derived using the same explanatory variables and specimens as the σmax estimation formula. However, some explanatory variables were changed to variables that have a higher correlation with τmax , , and variables that caused multicollinearity were deleted. Therefore, Eqs. (8) and (9), which are limited to first coating soil, were derived. Equation (8) uses the mud plaster density during painting, fine sand mass percentage, and plasticity index. Equation (9) uses the water content of air-dry state. From the comparison of predicted and measured values in Eq. 8, the residual errors of the first coating soil in Eq. (8) were large in Amakusa and Tsuchifuru. The first coating soil in Eq. (9) roughly agreed with the measured values.
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(First coating soil during painting)
τmax = a(1.076x4 +0.009x6 −0.479logx9 −1.787) (8)
(First coating soil of air − dry state)
τmax = a(−0.617logx5 −0.631)
(9)
x 4 : Mud plaster density (1.37–1.75 g/cm3 ) x 5 : Specimen air-dry water content (1.51%–8.88%) x 6 : Fine sand mass percentage (3.1%–24.7%) x 9 : Plasticity index (13.9–34.1).
Fig. 8. Comparison diagrams of predicted and measured values of τmax
Additionally, the τ max /σ max strength ratios of the specimens in Table 3 were divided between 57% and 64% passing mass percentage of particle size 0.075 mm. Therefore, two τmax estimation formulas for 57% or less (coarse-grained soil and reused soil) and 64% or more (other fine-grained soil) were derived using σ max . The τmax estimation formulas are shown in Eqs. (10) and (11). Figure 9 shows a comparison of the predicted values obtained using these equations and the measured values. Dotted circles represent coarse-grained soil and reused soil. The predicted values generally agreed with the measured values. (Coarse − grained soil and reused soil) (0.075 mm passage rate ≥57%)
(Other fine − grained soil) (0.075 mm passage rate≥64%)
τmax = 0.459σ max + 0.065
(10)
τmax = 0.827σ max + 0.015 (11)
σ max : Average compressive strength (coarse-grained soil and reused soil are 0.350– 0.741 N/mm2 , other fine-grained soil are 0.163–0.319 N/mm2 ).
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Fig. 9. Comparison diagrams of predicted and measured values of τmax by σ max
4 Conclusions The following items were confirmed by the uniaxial compression and double shear tests of wall clays: • σmax of the reused soil was higher than that of the new soil. However, even if these were mixed, σmax and τmax hardly increased. • σmax and τmax during the Mizuawase period of 90 days were 1.2–1.3 times higher than those of 0–7 days. • The mechanical properties of the wall clays differed based on the soil source. σmax and τmax of the Kyoto soil were the highest. • In the case of Yatsushiro soil, the Young’s modulus and σmax of the second coating soil (coarse-grained soil) was higher than those of the first coating soil (fine-grained soil). However, these values decreased when the volume of sand in the second coating soil increased. Additionally, τmax of the first and second coating soils were almost the same. • The second coating soil, reused soil, and Kyoto soil (first coating soil) showed brittle fracture behavior, but other first coating soils showed high toughness. • σ max of the coarse-grained soil were larger than those of the fine-grained soil. Additionally, the τ max /σ max strength ratios of the coarse-grained soil and reused soil were 0.6–0.7, those of other fine-grained soils were 0.8–1.0. Expressing this result using the passing mass percentage of particle size 0.075 mm, the strength ratio of the soil of 57% or less was 0.6–0.7, and that of 64% or more was 0.8–1.0. The following results were obtained by multiple regression analysis: • Even after analyzing the data obtained from the mixing, painting, and strength tests, the authors could not derive highly accurate estimation formulas for σmax and τmax . However, by adding the soil test data to the analysis, highly accurate estimation formulas could be derived. • As several estimation formulas for σmax and τmax were obtained, the authors selected an explanatory variable estimation formula from which data can be obtained easily.
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The combinations of explanatory variables for the selected estimation formulas are shown below. σmax estimation formulas: (1) water content ratio and density of mud plaster, and fine sand mass percentage, (2) specimen air-dry water content, coarse fraction mass percentage, and plastic limit (total two types). τmax estimation formulas: (1) mud plaster density, fine sand mass percentage, and plasticity index, (2) specimen air-dry water content, (3) passing mass percentage of particle size 0.075 mm, and average compressive strength (total three types). However, these estimation formulas must use the limited specimen shapes, test methods, types of materials, and mixing ratios. Additionally, even for wall clays with almost the same particle size distribution and air-dry density, the wall clay strength differed by the type (source) of soil. Therefore, in the future, the authors plan to further increase the types of soil and investigate the cause and attempt to derive highly versatile multiple regression equations.
References 1. Yamada, M., Koshiishi, N.: Properties of wall clays with straws wall clays for clay wall on bamboo lathing Part 2, J. Struct, Constr. Eng. (Transactions of AIJ) 78(689), 1209–1218 (2013) (in Japanese) 2. Hirano, Y., et al.: Fundamental studies on clay soil wall. -Effect of moisture contents and the period of keeping clay soils with water and straws on compression strength. In: Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, A-1, pp. 333–334 (2002) (in Japanese) 3. Iinuma, K., et al.: A study on structural characteristics of repaired traditional wooden building part1 material testing of reuse clay. In: Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, Structure III, pp. 457–458 (2013) (in Japanese) 4. Muramoto, M., et al.: Statistical study on coefficient of effective wall-length calculated by cyclic loading test of mud walls. J. Struct. Constr. Eng. (Transactions of AIJ) 82(732), 215–225 (2017) (in Japanese) 5. Muramoto, M., et al.: Estimation of the envelope curve calculated by statistical correlation of cyclic loading tests of mud walls, J. Struct. Constr. Eng. (Transactions of AIJ) 82(739), 1391–1401 (2017) (in Japanese)
Numerical Investigation of the Properties of Unreinforced and Reinforced Nepalese Historical Brick Masonry Structures Chhabi Mishra1 , Kentaro Yamaguchi2(B) , Tingyun Jing1 , Toshikazu Hanazato3 , Yohei Endo4 , and Manjip Shakya5 1 Department of Architecture, Graduate School of Human-Environment Studies, Kyushu
University, Fukuoka, Japan [email protected] 2 Department of Architecture and Urban Design, Faculty of Human-Environment Studies, Kyushu University, 744 Motooka , Nishi-u 819-0395, Fukuoka, Japan [email protected] 3 Laboratory for Engineering, Kanagawa University, Yokohama, Japan [email protected] 4 Department of Architecture, Faculty of Engineering, Shinshu University, Nagano, Japan [email protected] 5 Khwopa Engineering College, Purbanchal University, Bhaktapur, Nepal [email protected]
Abstract. Considering the limited strength of traditional masonry structures, retrofitting is essential. The purpose of this study was to discretize a numerical model that can be used to assess the behavior of brick masonry in earth mortar. The behavior of unreinforced brick masonry (URM) and brick masonry reinforced with timber was investigated through numerical simulation. The flexural strength of URM and reinforced masonry prism of size 280 mm x 350 mm x 860 mm (B x D x L) was calculated by three-point bending experiments. For reinforced masonry prism, ladder and diagonal brace reinforcement with timber were studied. From the results, it was observed that the diagonal brace reinforced prism withstood higher flexural tensile stress compared to the URM and ladder reinforced prisms. From the uniaxial compression test conducted on the same size of masonry prism, the elastic modulus (E) calculated was 310 MPa. A homogenous macro model was used in ABAQUS software to reproduce a previously performed three-point bending test of a prism built of brick masonry in earth mortar. Material properties such as density, E, and Poisson’s ratio were input to the software. The displacement value obtained was very low compared to the experimental result when E of 310 MPa determined from the uniaxial compression test was taken. The reason might be due to the involvement of both tensile and compressive forces in the bending test. In this study, the elastic modulus in tension (Et ) was considered 1/5 of that in compression (Ec ) for URM prism. Numerical model for the URM prism gave closer results to experimental value when Ec was 41 MPa, which was 1/8 of E determined from the uniaxial compression test (310 MPa). In uniaxial compression test, the direction of compressive strut formed was 90° to the bed angle. However, in three-point bending test, a compressive strut was formed from © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 125–139, 2024. https://doi.org/10.1007/978-3-031-39450-8_11
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C. Mishra et al. the point of loading to the supports. For URM and diagonal braced specimen compressive strut formed was 56.3° to the bed angle (θstrut ), whereas for ladder reinforced specimen, it was 37.2°. For the ladder and diagonal braced reinforced model, crack was assumed at the tensile side of the masonry. By trial and error, the numerical result was in good agreement with the experimental value for maximum displacement at the mid-point under the condition that the E of 20.5 MPa and 41.0 MPa was taken for the ladder and diagonal brace model, respectively, with a 70 mm crack at the tensile side of masonry. In the analysis, it was observed that for URM and diagonal brace reinforced model, E was greater than for the ladder reinforced model. Namely, with the increase in compressive strut angle (θstrut ), there was an increase in the value of E. Keywords: Historical · Masonry · Numerical modeling · Retrofitting · Sal timber
1 Introduction 1.1 Masonry in Earth Mortar Mechanical Behavior of Masonry in Earth Mortar. There are a large number of nonengineered constructions still exist in many parts of the world which are mostly constructed with locally available materials such as stones, bricks or adobe joined together with mortar [1]. About 30% of the world’s population lives in earth building [2]. These buildings are constructed by local masons based on experience and knowledge and are vulnerable to earthquakes [3]. Earth construction is widely spread and the oldest type of construction. The historical buildings constructed with brick and mud mortar are vulnerable to earthquakes due to the low strength of materials, poor structural detailing, and lack of seismic design and thus require seismic protection [4]. Compressive strength, elastic modulus, and shear modulus are mechanical properties that are required to analyze and design masonry structures. The value of mechanical properties varies widely depending on the quality of materials, size, and workmanship of construction [5]. An experimental investigation is needed for understanding the mechanical behavior of earth building properly [2, 6]. Strengthening of Masonry in Earth Mortar. Retrofitting of unreinforced brick masonry (URM) buildings is important as they are vulnerable to damage against in-plane and out-of-plane failure due to limited shear strength, flexural strength, and deformation capacity [7]. Timber panels are used in masonry structures with earthen mortar to enhance the integrity of the masonry walls [8]. Moreira et al. [9] reported that ductility was increased by retrofitting the masonry wall with a timber frame in their quasi-static monotonic and cyclic pull-out tests. Sustersic and Dujic [10] reported that the strength and ductility of URM were increased by retrofitting with Cross Laminated Timber (CLT) panels. The plywood panels can withstand diagonal tension forces compared to timber frames [11]. Retrofitting with timber strong-back prevents the out-of-plane failure of masonry walls [12].
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1.2 Numerical Analysis of Masonry in Earth Mortar For the reliability and accuracy of the numerical model, the material properties are necessary based on experimental results. Once the model is calibrated, it is possible to vary the desired parameters and verify the effect of each component [13]. The modeling strategies can be classified as detailed micro-modeling, simplified micro-modeling, and macro-modeling [14]. In micro-modeling technique, the units, mortar, and the unitmortar interface are modeled separately. However, in macro modeling, no distinction is made between units and joints, and masonry is modeled as a homogeneous material with equivalent material properties [15]. A macro model which is easy to use for structural design, seismic diagnosis, and retrofitting was used in this study. The purpose of this study was to discretize a numerical model that can be used to assess the behavior of brick masonry in earth mortar. The behavior of URM and brick masonry reinforced with timber was investigated through numerical simulation.
2 Materials and Methods 2.1 Description of the Experiment Uniaxial compression experiments were conducted to clarify the basic mechanical properties of elements of brick walls (unit bricks, mud mortar, and masonry prisms) [16]. The bulk density of the masonry prism was 1566 kg/m3 , which was calculated from the proportion of brick and mud mortar in a prism. To study the flexural behavior of the wall, six prism specimens with dimensions of 280 mm × 350 mm × 860 mm (B × D × L) were constructed by brick and mortar, namely B5U1, B6U2, B1L1, B2L2, B3B1, and B4B2, respectively [6]. In the bending experiment, the B5U1 and B6U2 were unreinforced specimens (Fig. 1a), while the rest of the four specimens were reinforced with timber (Sal wood). The specimens (B1L1 and B2L2) were reinforced with laddertype reinforcement (Fig. 1b), and the other two (B3B1 and B4B2) were reinforced with diagonal type braces (Fig. 1c). The cross-section of the timber plate was 50 × 10 mm2 and was connected by steel bolts of 12 mm diameter. The load of 100 kN was applied manually by a mechanical jack. The jig system and displacement transducers were also used. Three-point bending tests were carried out on prisms that were set vertically and horizontal force was applied at the center of the prism. Supports were fixed at the top and bottom of the prisms. Displacement transducers were set up at the top, middle, and bottom of the prisms. Calculation of Flexural Strength and Deformation Angle. The flexural strength fr was calculated using Eq. (1), Fr =
(1.5Pl) (BD2 )
where, P is the maximum load taken by the specimen, Fr is the flexural strength of the masonry prism, l is the support span of the member;
(1)
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B is the width of the specimen and D is the thickness of the specimen. To estimate the net displacement in the specimen mid-height, the average value of horizontal displacement at the top and bottom of the specimen was removed from the mean value of the displacement measured at the specimen mid-height. From the displacement measured, the deformation angle was calculated.
( a)
(b)
(c)
Fig. 1. Bending test setup (a) URM specimen (b) ladder reinforced specimen and (c) diagonal brace reinforced specimen
2.2 Research Methodology The present research was composed of the following three stages. First, a case study on the results obtained in bending experiments of brick masonry that constitutes historical buildings in Nepal is presented. The three-point loading test on the URM prism and reinforced masonry prism with wood (SAL timber) and bolts was performed. Second, for numerical modeling, elastic regions were determined from a graph of flexural stressdeformation angle. The first crack point was identified from experimental data and was also confirmed by basic mechanics theories. Third, numerical analysis was performed on the bending test models. This stage was articulated in two steps, which included (i) validation of the URM prism, and (ii) validation of the retrofitted masonry prism with timber panels. The numerical models were developed and validated using a macro model elastic analysis. The general-purpose finite element method software ABAQUS was used for the analysis. As the micro model is complicated to be used for historical buildings and requires longer time and effort, this research aims to develop an analysis method that can more easily reflect the behavior of actual structures by using macro modeling. In addition, it is not realistic to design structures that cause large deformations in the case of brittle masonry; hence this study mainly focuses on small deformation regions that can be used for safer structural design. The purpose of this study was to discretize a numerical model that can be used to assess the behavior of brick masonry in earth mortar. The behavior of URM and brick masonry reinforced with timber was investigated through numerical simulation. In general, for macro-modeling same elastic modulus (E) is assumed for compression and tension. In our study, the flexural modulus of elasticity (Eb ) was 14.816 MPa which was
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several times lower than E determined from the uniaxial compression test (310 MPa). When E of 310 MPa was used as input to the software, the displacement value obtained was very low compared to the experimental result. The reason might be due to the involvement of both tensile and compressive forces in the bending test. Kanno et al. [17] reported that for URM, Ec is 5–6 times higher than the (Et ). For URM, Et was assumed as 1/5 of the Ec . By trial and error, the numerical result was matched with the experimental value for maximum displacement at the mid-point. For reinforced masonry, cracks were assumed at the tensile side of the masonry at about a depth of 70mm, 90 mm, and 130 mm. By trial and error, the numerical result was matched with the experimental value for maximum displacement at the mid-point for the crack introduced model. The calibrated value of E for the diagonal brace reinforced model was compared to the ladder reinforced model. The effect of compressive strut angle formed in the specimen was also studied. 2.3 Results and Discussion Figure 2 shows the flexural stress versus deformation angle curve for all specimens. The values in the graph show the maximum flexural stress of each specimen. The flexural strength was increased in reinforced specimens. Failure Modes of URM and Reinforced Prism Specimens. For URM, the specimen starts taking load and suddenly decreases when opening starts due to tensile splitting. However, due to the strut mechanism, the specimen again starts taking load. The flexural strength was increased in reinforced specimens showing the maximum for diagonal braced rein-forced prism, however sudden drop was observed in the graph when maximum load was reached which was also evidenced by the sudden split in the specimen, whereas the failure in ladder reinforced prism was mild and cracks were dispersed all over the specimen. Among ladder reinforced specimens, specimen B1L1 was damaged before loading and as a result, the graph was slightly different from specimen B2L2 which shows a smooth curve.
Fig. 2. Flexural stress versus deformation angle curve for all the specimens
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Calculation of Restoring Force Characteristics. First, the elastic-plastic deformation range was determined. The elastic-plastic range and the deformation angle of each masonry prism for the bending experiment are shown in Table 1. First and second crack points A and B were determined as the intersections of linear regressions as shown in Fig. 3a. The flexural stress versus deformation angle curves of URM, ladder reinforced, and diagonal braced reinforced specimens are shown in Fig. 3b, 3c, and 3d, respectively. The flexural stress versus deformation angle curves for all specimens are shown in Fig. 3e.
Table 1. Deformation range of URM and reinforced specimens Specimens
Elastic deformation (×10–2 rad)
Plastic deformation (×10–2 rad)
URM (B5U1, B6U2)
0–0.10
0.10–1.33
Ladder (B1L1, B2L2)
0–0.95
0.95–2.00
Brace (B3B1, B4B2)
0–0.75
0.75–2.00
Table 2. Calculation of first and second crack points, load, horizontal displacement, and flexural modulus at first crack points Specimens
First crack point
Second crack point
Stiffness in elastic
Stiffness in plastic
Load P at first
Horizontal displacement
Flexural modulus at
Deformation (×10–2 rad)
Stress (N/mm2 )
Deformation (×10–2 rad)
Stress (N/mm2 )
deformation (N/mm2 )
deformation (N/mm2 )
crack (N)
at first crack (mm)
first crack Eb (MPa)
URM
0.095
0.020
1.330
0.032
0.2103
0.0099
618
0.352
14.816
Ladder
0.954
0.211
2.000
0.294
0.2214
0.0788
6520
3.533
15.573
Brace
0.804
0.389
2.026
0.549
0.4839
0.1308
12020
2.978
34.061
The bilinear characteristics of restoring force for URM prism were calculated by the first crack point, the second crack point, the elastic deformation, and the plastic deformation. The first crack point was obtained from experimental data when the deformation increased rapidly compared to flexural stress. The elastic deformation is the range from the beginning of the experiment till the first crack point. The URM prism is elastic for a small deformation. The second crack point was obtained from the experimental data when the ratio of change in deformation was less compared to the increase in flexural stress. The plastic deformation was in the range from the first crack point to the second crack point. The characteristics of restoring force for URM and reinforced masonry specimens were determined as shown in Fig. 4. Deformation, the stress at the first crack point, the stiffness of elastic deformation range, and the stiffness of plastic deformation range are shown in Table 2. The stiffness of the elastic deformation of the ladder and diagonal brace reinforced specimens were 1.05 times and 2.30 times greater than the stiffness of the elastic deformation of URM specimens, respectively. However, the stiffness of the plastic deformation range of the ladder and diagonal brace reinforced specimens were 7.96 times and 13.21 times greater than the stiffness of the plastic deformation of the
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URM specimen. Stiffness reduction from the elastic area to the plastic area of URM, ladder, and diagonal brace reinforced specimen were 0.0471 times, 0.356 times, and 0.270 times, respectively.
( a)
( c)
(b)
(d)
(e)
Fig. 3. Flexural stress versus deformation angle curves of specimens (a) Crack points and elastic-plastic deformations range of URM specimens (b) URM specimens (c) Ladder reinforced specimens (d) Diagonal brace reinforced specimens (e) All prism specimens
Fig. 4. Characteristics of restoring force for URM and reinforced specimens (a) URM specimen (b) Ladder reinforced specimen (c) Diagonal brace reinforced specimen
Load Calculation During Rigid Body Rotation of URM Specimens. The URM prism, subjected to the horizontal load applied from a hydraulic Jack is shown in Fig. 5a. The load was calculated from Eqs. (2) and (3) when the masonry prism began to rigid body rotation [18].
MB = Q ×
D L −W × 2 2
Fx = P − Q − Q = 0
(2) (3)
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where, Q is the reaction force at the top and bottom supports, W is the self-weight of half of the masonry prism, P is the horizontal force from the hydraulic jack, D is the depth of the masonry prism, and L is the height of the masonry prism. The calculated value of horizontal force (P) when rigid body rotation occurred was 609 N. At a stress of 0.019 N/mm2 , the URM specimen started rigid body rotation which was close to the stress in the first crack point of URM specimen (Fig. 4a). Figure 5b shows the load at rigid body rotation and load at the first crack point.
Fig. 5. (a) Horizontal and reaction force of bending experiment (b) Load at rigid body rotation and load at first crack point
Flexural Modulus for Bending Test. Flexural modulus (Eb ) for Bending test specimens was determined as follows. Eb =
P l3 × 3 4BD δ
(4)
where, D is the depth of the masonry prism, B is the width of the cross-section, l is the span of the masonry prism, P/δ is the ratio of the elastic range of load and deflection. The load, deflection, and flexural modulus at the first crack point of all masonry prisms are shown in Table 2. Flexural modulus (Eb ) of masonry prisms calculated from Eq. (4) was less than E determined from uniaxial compression experiment (310 MPa) due to anisotropic behavior of brick masonry with low strength mortar. Determination of Poisson’s Ratio. Figure 6a shows the shear stress versus tensile/compressive strain of the diagonal compression experiment for D2 and D6 Specimens. Poisson’s ratio was calculated as the ratio of strain in the tensile direction to the compressive direction as the difference in tensile and compressive strain were large in the diagonal experiment (Fig. 6a). Tensile strain is the elongation in the tensile diagonal direction measured by displacement transducer L2 (Fig. 6b). Similarly, compressive strain is the shortening in the compressive diagonal direction measured by displacement transducer L1 (Fig. 6b). Poisson’s ratio was calculated by taking linear regression of data up to 33% of maximum load (Fig. 6c). The Poisson’s ratio of D2 and D6 specimens were 0.0705 and 0.0260, respectively. The average Poisson’s ratio was 0.0483.
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(c)
Fig. 6. Diagonal compression experiment (a) Shear stress versus compressive/tensile strain (b) Schematic diagram of specimen in diagonal compression experiment (c) Tensile strain versus compressive strain for D2 and D6 specimen
3 Numerical Modeling of URM and Reinforced Masonry Prisms 3.1 Numerical Modeling of Masonry Prism A numerical model of a masonry prism was created using a three-dimensional solid (or continuum) element in ABAQUS finite element software. C3D8R is a hexahedral 8-node linear brick element with reduced integration (one integration point). The integration point of the C3D8R element is located in the middle of the element. C3D8R was selected for mesh generation as it is cost-effective and has enhanced convergence compared to full integration [14]. A mesh size of 30 mm was used. The size of URM, ladder reinforced, and diagonal brace reinforced model was 350 mm × 280 mm × 860 mm. Masonry was modeled as an isotropic and homogeneous material. The sizes of steel plates used at the top, bottom, and base supports were 280 mm × 20 mm × 100 mm, and a friction coefficient of 0.30 was taken for the interface between masonry and steel plates [14]. In ladder and diagonal brace models, brick masonry prisms were reinforced with timber of cross-section 50 mm × 10 mm. The timber reinforcement was connected to a brick masonry prism with 12 mm bolts by multi-point constraints (MPC). MPC is used to connect the elements between them and to impose constraints between different degrees of freedom of the model. The MPC is a rigid body between two nodes to constrain the displacement and rotation at the first node to the displacement and rotation at the second node. The bolt was considered a one-dimensional element and timber plate and brick masonry were considered as three-dimensional elements. There were three boundary conditions (BC), namely top BC, bottom BC, and base BC in the modeling to replicate the experimental condition (Fig. 7a). For URM, ladder reinforced and diagonal brace reinforced specimens load was applied in terms of pressure 0.02207 N/mm2 , 0.2329 N/mm2 and, 0.2329 N/mm2 , respectively. The timber material properties were taken as input to the software (Table 3) [19]. Poisson’s ratio and density were also taken as input to the software. Elastic modulus (E) from the prism compression experiment was taken as the E initial for the first iteration. The trials for different values of E during modeling were done until the numerical result was in good agreement with the experimental value for maximum displacement at the mid-point.
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Materials
Elastic modulus E (MPa)
Poisson’s ratio
Density (kg/mm3 )
Masonry
23
0.0483
1.57 × 10–6
Steel
205000
0.30
7.85 × 10–6
Timber (SAL)
20500
0.40
8.86 × 10–7
3.2 Output of URM Model The 3D model, tensile principal stress, and compressive principal stress contour for the URM model are shown in Fig. 7a-c, respectively. The stress contours show the part under load was in compression, and the part away from the load was in tension, which was in good agreement with the experimental result. The numerical result was in good agreement with the experimental value for maximum displacement (0.352 mm) at the mid-point when E (23 MPa) was taken (Table 4). 3.3 Output of Ladder Reinforced Model The 3D model, tensile principal stress, and compressive principal stress contour for ladder reinforced model are shown in Fig. 8a-c respectively. The compressive strut in masonry is formed in the ladder reinforced model as shown in Fig. 8c. The numerical result was in good agreement with the experimental value for maximum displacement (3.533 mm) at the mid-point when E (16.45 MPa) was taken (Table 4). 3.4 Output of Diagonal Brace Reinforced Model The 3D model, tensile principal stress, and compressive principal stress contour for the diagonal brace reinforced model are shown in Fig. 9a-c respectively. The numerical result was in good agreement with the experimental value for maximum displacement (1.615 mm) at the mid-point when E (38 MPa) was taken (Table 4). In the ladder reinforced model, E (16.45 MPa) used for best fit was smaller compared to E (24 MPa) for the URM model and E (38 MPa) for the diagonal brace reinforced model.
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3.5 Effect of Strut Angle on the Elastic Modulus for Reinforced Masonry Model In a ladder type, the compressive/strut mechanism is formed due to a ladder-type truss, similar to a reinforced concrete beam. The compressive force in a diagonal direction is the compressive force of masonry, which is the shear resistance mechanism in a beam. Similarly, in the diagonal brace type, the tensile force in diagonal timber members is effective to resist the compressive force of masonry. Due to the formation of truss mechanism in the ladder reinforced model, the strut angle (θstrut ) of ladder reinforced model was smaller compared to the diagonal brace reinforced model. For URM and diagonal braced specimen compressive strut formed was 56.3° to the bed angle (θstrut ), whereas for ladder reinforced specimen, it was 37.2°. The ladder and diagonal brace reinforced specimens take higher loads even after the crack is developed in the masonry. Hence, the tensile cracks were assumed at the tensile side of masonry in reinforced specimens at about a depth of 70 mm, 90 mm, and 130 mm (Fig. 10b-c). The numerical and experimental results by assuming a crack in the tensile side of masonry of the reinforced model is shown in Table 5. In the ladder reinforced model, after the introduction of a crack of 70 mm, 90 mm, and 130 mm at the tensile side of the masonry, the numerical result was in good agreement with the experimental value for maximum displacement (3.533 mm) at the mid-point when E of 20.5 MPa, 22.5 MPa, and 27 MPa was taken, respectively. Similarly, in the diagonal brace reinforced model, after the introduction of a crack of 70mm, 90 mm, and 130 mm at the tensile side of the masonry, the numerical result was in good agreement with the experimental value for maximum displacement (1.615 mm) at the mid-point when E of 41 MPa, 43 MPa, and 47 MPa were taken, respectively. The numerical result matched the experimental value with an increased value of E for both the ladder and diagonal braced reinforced models compared to the model without cracks. The calibrated value of E for the diagonal brace reinforced model was greater compared to the ladder reinforced model. This might be due to the larger strut angle in the diagonal brace reinforcement model compared to the ladder reinforcement model. Nowak et al. [20] also reported that with the increase in the angle formed between the compressive strut developed in the model and the bed angle, there is an increase in the value of E.
(a)
(b)
(c)
Fig. 7. (a) URM model (b) Tensile principal stress of URM model (c) Compressive principal stress of URM model
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3.6 Effect of Elastic Modulus in Compression and Tension in URM Model Kanno et al. (2001) reported that the elastic modulus in tension (Et ) for URM is in the range of 1/5–1/6 of that in compression (Ec ) as E in tension and compression sides differ greatly. Therefore, in this study, E on the tension side of URM model was taken as 1/5 of E on the compression side. The tensile zone in the URM model in this study was chosen in such a way that the compressive strut formation still occurs between the supports and the loading point. By trial and error, the numerical result was in good agreement with the experimental value for maximum displacement (0.352 mm) at the mid-point for the T-shaped area on the tensile side with a lower value of elastic modulus (Et = 1/5 of Ec ) (Fig. 10a). Numerical result matched the experimental value when the Ec was 41 MPa and Et was 8.2 MPa for URM model (Fig. 10a) (Table 6). Similarly, for the diagonal braced reinforced model with tensile crack, the numerical result showed the maximum displacement (1.615 mm) when E of 41 MPa was taken (Table 5). This might be due to the angle of the compressive strut formed with the bed angle (56.3°) being equal for both models [20]. Table 4. Numerical and experimental results of displacement at the mid-point of three models Specimens
Load P (N)
E (MPa)
θstrut (°)
Num. disp. (mm)
Exp. disp. (mm)
URM model
618
23.00
56.30
0.352
0.352
Ladder model
6520
16.45
37.20
3.533
3.533
Brace model
6520
38.00
56.30
1.615
1.615
Where, E is elastic modulus of brick masonry, θstrut is the strut angle, Num. disp. is numerical displacement, and Exp. disp. is experimental displacement
Table 5. Numerical and experimental results assuming a crack in the tension side of masonry in reinforced model Specimens
Load P (N)
E (MPa) with crack (70 mm)
E (MPa) with crack (90 mm)
E (MPa) with crack (130 mm)
θstrut (°)
Num. disp. (mm)
Exp. disp. (mm)
Ladder model
6520
20.5
22.5
27.0
37.2
3.533
3.533
Brace model
6520
41.0
43.0
47.0
56.3
1.615
1.615
Where, E is the elastic modulus of brick masonry, θstrut is strut angle, Num. disp. is numerical displacement, and Exp. disp. is experimental displacement
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(a)
(b)
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(c)
Fig. 8. (a) Ladder reinforced model (b) Tensile principal stress for ladder reinforced model (c) Compressive principal stress for ladder reinforced model
(a)
(b)
(c)
Fig. 9. (a) Diagonal brace reinforced model (b) Tensile principal stress for diagonal brace reinforced model (c) Compressive principal stress for diagonal brace reinforced model
(Et=1/5*Ec)
Cracks assumed at tension side
Cracks assumed at tension side
strut
strut
strut
Ec (a)
(b)
(c)
Fig. 10. Model for (a) URM specimen with different elastic modulus in compression and tension side (b) ladder reinforced specimen with cracks in the tension side of masonry (c) diagonal brace reinforced specimen with cracks in the tension side of masonry
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Table 6. Numerical and experimental results of the URM model by considering Et = 1/5 of Ec Specimens
Load P (N)
Elastic modulus in Compression (Ec ) (MPa)
Elastic modulus in Tension (Et ) (MPa)
θstrut (°)
Num. disp. (mm)
Exp. disp. (mm)
URM model
618
41.0
8.20
56.3
0.352
0.352
Where, θstrut is strut angle, Num. disp. is numerical displacement, and Exp. disp. is experimental displacement
4 Conclusions 1. A homogenous macro model was used to reproduce a previously performed threepoint bending test of a prism built of brick masonry in earth mortar. In this study, the elastic modulus in tension (Et ) was considered 1/5 of that in compression (Ec ) for unreinforced brick masonry (URM) prism. 2. Numerical model for the URM prism gave closer results to experimental value when Ec was 41 MPa which was 1/8 of E calculated from the uniaxial compression experiment (310 MPa). 3. In uniaxial compression test, the direction of compressive strut formed was 90° to the bed angle, and E determined was 310 MPa. However, in three-point bending test, compressive strut was formed from the point of loading to the supports. For URM and diagonal braced specimens, the compressive strut formed was 56.3° to the bed angle (θstrut ) whereas for ladder reinforced specimens, it was 37.2°. 4. For the ladder and diagonal braced reinforced model, crack was assumed at the tensile side of the masonry. By trial and error, the numerical result was in good agreement with the experimental value for maximum displacement at the mid-point under the condition that the E of 20.5 MPa and 41.0 MPa was taken for the ladder and diagonal brace model, respectively, with a 70 mm crack at the tensile side of masonry. 5. In the analysis, it was observed that for URM and diagonal brace reinforced model, E was greater compared to ladder reinforced model. Namely, with the increase in compressive strut angle (θstrut ), there was an increase in the value of E. This numerical result tends to coincide with the findings of Nowak et al. [20] Acknowledgement. The experiment in this study was supported by JSPS KAKENHI Grant Number JP16H01825 and the analysis was supported by JSPS KAKENHI Grant Number JP22K04411.
References 1. Ravichandran, N., Losanno, D., Parisi, F.: Comparative assessment of finite element macromodelling approaches for seismic analysis of non-engineered masonry constructions. Bull. Earthq. Eng. 19(13), 5565–5607 (2021). https://doi.org/10.1007/s10518-021-01180-3
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2. Varum, H., et al.: Structural behaviour and retrofitting of adobe masonry buildings. In: Costa, A., Guedes, J.M., Varum, H. (eds.) Structural Rehabilitation of Old Buildings, pp. 37–75 (2004) 3. Parisi, F., Iovinella, I., Balsamo, A., Augenti, N., Prota, A.: In-plane behaviour of tuff masonry strengthened with inorganic matrix–grid composites. Compos. B Eng. 45(1), 1657–1666 (2013) 4. Arya, A.S., Boen, T., Ishiyama. Y.: Guidelines for Earthquake Resistant Non-Engineered Construction. UNESCO (2014) 5. Phaiju, S., Pradhan. P.M.: Experimental work for mechanical properties of brick and masonry panel (2018) 6. Endo, Y., Yamaguchi, K., Hanazato, T., Mishra, C.: Characterisation of mechanical behaviour of masonry composed of fired bricks and earthen mortar. Eng. Fail. Anal. 109, 104280 (2020) 7. Shrestha, H. D., Subedi, J., Rajbhandari, M.: Seismic retrofitting guidelines of buildings in Nepal. Kathmandu, Nepal: Government of Nepal, Ministry of Urban Development, Department of Urban Development and Building Construction (2016) 8. Langenbach, R.: Bricks, mortar and earthquakes. APT Bull. 31(3–4), 31–43 (1989) 9. Moreira, S., Ramos, L.F., Oliveira, D.V., Lourenço, P.B.: Experimental behavior of masonry wall-to-timber elements connections strengthened with injection anchors. Eng. Struct. 81, 98–109 (2014) 10. Sustersic, I., Dujic, B.: Seismic strengthening of existing concrete and masonry buildings with crosslam timber panels. In: Materials and Joints in Timber Structures: Recent developments of Technology, pp. 713–723. Springer Netherlands (2014) 11. Maduh, U.J., Shedde, D., Ingham, J., Dizhur, D.: In-plane testing of URM Wall panels retrofitted using timber strong-backs In: Proceedings of the Australian Earthquake Engineering Society 2019 Conference, Newcastle, Australia, vol. 29 (2019)\ 12. Dizhur, D.Y., Giaretton, M., Giongo, I., Ingham, J.M.: Seismic retrofit of masonry walls using timber strong-backs. SESOC J. 30(2), 30–44 (2017) 13. Oliveira, L M.F.D.: Theoretical and experimental study of the behavior of vertical interfaces of interconnected structural masonry walls” (Doctoral dissertation, Universidade de São Paulo) (2014) 14. Dauda, J.A., Silva, L.C., Lourenço, P.B., Iuorio, O.: Out-of-plane loaded masonry walls retrofitted with oriented strand boards: numerical analysis and influencing parameters. Eng. Struct. 243, 112683 (2021) 15. Parisi, F., Balestrieri, C., Varum, H.: Nonlinear finite element model for traditional adobe masonry. Constr. Build. Mater. 223, 450–462 (2019) 16. Mishra, C., Yamaguchi, K., Endo, Y., Hanazato. T.: mechanical properties of components of nepalese historical masonry buildings (2018): In: Proceedings of International Exchange and Innovation Conference on Engineering and Sciences, vol. 4, No. 1, pp. 118–123 17. Kanno, T., Kino, J., Furuya. T.: Applicability of concrete structural analysis method to brick structure. In: 56th Annual Conference of the Japan Society of Civil Engineers (October 2001). vol. 110, pp. 220–221 (2 pages) (Japanese) 18. Mishra, C., Yamaguch, K., Araki, K., Ninakawa, T., Hanazato, T.: Structural behavior of brick wall specimens reinforced on the surface with RC walls under horizontal loading. J. Adv. Concr. Technol. 19(6), 593–613 (2021) 19. Kim, S., Fujita, K., Hanazato. T.: Restoration of seismically-vulnerable historical masonry structures struck by an earthquake Part 3 Micro tremor measurement and damage of multistoried pagodas by 2015 Nepal Gorkha earthquake. In: 2017 AIJ Conference 31–3 September (2017), Hiroshima, Japan (2 pages) (Japanese) 20. Nowak, R., et al.: Strength parameters of clay brick walls with various directions of force. Materials 14(21), 6461 (2021)
Numerical Modeling and Structural Analysis
Impact Loading Analysis of an Earthen Masonry Structure Using Finite Element Methods Demiana Tse1(B) , João M. Pereira2 , and Paulo B. Lourenço2 1 Wiss, Janney, Elstner Associates, Inc., 50 Congress Street, Suite 430, Boston, MA 02109, USA
[email protected] 2 ISISE, Department of Civil Engineering, University of Minho, 4800-058 Guimarães, Portugal
Abstract. Throughout the years, historical monuments have been at risk from natural and man-made causes. Impact loading analysis plays an important role in structural engineering and is one of the risks to existing construction, whether being through partial collapses, vehicle crashes, or historical or modern-day warfare. This case study analyses the local response of a wall portion of the Torre de la Vela, a rammed earth tower within the UNESCO World Heritage Site of the Alhambra, Grenada, under impact loading. For this case study, the wall section of the tower was modelled with finite element methods (FEM) using different modelling approaches: using a continuum model, using a continuum model with removal of damaged elements, and using a contact element model. The Concrete Damage Plasticity (CDP) material model was adopted for the rammed earth structure. Different impactors were considered, including a cannonball with properties from the 16th and 17th centuries. The effect of impulsive loading on the material properties was accounted for using existing dynamic increase factors. The problem was solved using the explicit dynamic analysis available in Abaqus/Explicit. The different modelling strategies were compared and discussions on the use of different approaches were raised. Keywords: Rammed earth · Finite element modelling · Impact analysis · Dynamic increase factors
1 Introduction Impact loading analysis plays an important role in structural engineering, both within the modern-day context and historical contexts. Depending on the type of impactor itself, the structure may exhibit either a local response, such as a dent/hole in a section, or a global response, such as a progressive collapse. In this paper, a portion of the Torre de la Vela, a tower in the Alhambra in Grenada, Spain, was studied under impact loading using Finite Element Methods (FEM). The local response of the building in the region of impact of a historical cannon ball and a hypothetical impactor was investigated. Models using continuum elements with and without the removal of damaged elements, and a model using contact elements were compared to assess the damage from the impactor.
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 143–155, 2024. https://doi.org/10.1007/978-3-031-39450-8_12
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2 Materials and Models Impact loading is categorized as an “impulsive load”. Upon impact of an object on a structure, the structural response will depend on the velocity and the material properties of the object in motion, and of the structure itself. Consequently, if a minor object hits a structure at a high velocity, local damage around the impact zone will develop faster than the global deformation of the structure being struck. Furthermore, the stresses in both the object and the structure will depend on their respective material properties [1]. Under concentrated loading, the structural component can demonstrate both a local and a global failure response (Fig. 1).
(a)
(b)
Fig. 1. Concrete beams subjected to impact loading: (a) local response; (b) global response (adapted from [2]).
Impact loads can be classified either by their intensity and duration, or by the dissipative mechanism. – Intensity and Duration. Loads classified by intensity and duration can be further classified in three sub-categories: particle impact, rigid body impact, and transverse impact on flexible bodies [3]. • Particle Impact is an analytical approximation where only the normal component of the impact force is taken into consideration. This type of classification is for large forces of negligible duration; it provides a simple solution when only the impacts of kinematics are considered, and the structural vibration is negligible. • Rigid Body Impact is the classification used when the contact area between two compact bodies is small relative to its overall dimensions. The stress created in the contact area decreases significantly as the radial distance from the contact region increases. Various contact laws can be used to obtain the time-history of the impact force. This classification of impact can be modelled using the massive beam and the effective mass models. • Transverse impact on flexible bodies occurs when one of the bodies displaces in bending from the impact force, resulting in a lower impact force from the reduction in stiffness.
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– Dissipative Mechanism. Loads classified by their dissipative mechanism can be classified in two ways: soft impact and hard impact [4]. • Soft impact mechanisms occur between two rigid bodies. Here, most of the kinetic energy is dissipated by the impacted structure. • Hard impact mechanisms occur between two objects with deformable components. In this mechanism, the initial kinetic energy is dissipated by the impactor. Two simplified approaches can be used to understand the structural response of a subject to soft and hard impacts [4]. A single degree of freedom problem can be used to understand the global effect of soft impacts (Fig. 2a), whereas a two degree-of-freedom problem is used for hard impacts (Fig. 2b). In the soft impact model, a distributed impact load, p(t), acts on the partial mass of the structure, M1 . The impact load can then be idealized with a point-mass connected to a spring element, representing the global stiffness of the member under an equal concentrated dynamic load. In the hard impact model, the impactor is modelled as a mass and not as a distributed load. The idealized system is then represented as two lumped masses, M1 and M2 , connected by a spring.
Fig. 2. Simplified models recommended by Eurocode for structures under impact loads (adapted from [4]).
Numerical simulation can be used to analyze structures under impact loading. Materials subjected to different impact speeds will have different strength properties, which in turn modifies the material’s resistance to penetration. Methods of identification can be used to describe the material properties of a structure subjected to impactors at different velocities. Amongst the material models available, those often used for numerical modelling of solid penetration through the structure include: the Mohr-Coulomb model, the Johnson-Cook mode, the Zerilli-Armstrong model, and the thermos-mechanical material model [5]. Impact loads can produce very high strain rates in the range of 100 to 102 s−1 , which alters the dynamic mechanical properties of the structure being impacted [6]. As the dynamic mechanical properties are greater in strength than the static properties, dynamic increase factors (DIFs) can be used to account for the difference in properties. The DIFs for Young’s Modulus, E, and the compressive strength of rammed earth were calculated using a strain rate of 100 s−1 using equations determined in previous work by Pereira [7]. As the DIFs for tensile strength of the rammed earth was unavailable, these DIFs were assumed to be the same as the compressive strength. The DIFs used in this research can be seen in Table 1, and the material properties with and without accounting
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for the dynamic increase factors can be seen in Table 2, in line with previous work by the authors [8]. Table 1. Dynamic increase factors for the brick masonry under impact loading. Material Property
DIF (Rammed Earth)
E
2.65
σc
1.76
σt
1.76
Table 2. Material properties for rammed earth in the Torre de la Vela, before and after being updated using the DIFs. Material Property
Original Value
Value with DIF
E [kN/m2 ]
1.60 × 106
4.25 × 106
ν [−]
0.25
0.25
ρ [T/m3 ]
1.60
1.60
σ c [kN/m2 ]
4000
7020
Gf c [kN/m]
6.40
11.24
σ t [kN/m2 ]
200
351
Gf t [kN/m]
0.013
0.019
Ballistic impact can be simulated using Abaqus/Explicit. The explicit dynamic analysis procedure in Abaqus/Explicit implements an explicit integration rule combined with diagonal or “lumped” element matrices [5]. The calculation of the nodal accelerations at ¨ any point in time, u(t), can be calculated using the lumped mass matrix, M, the internal and external forces, F(t)int and F(t)ext , respectively, using Eq. 1. ¨ = M −1 • F(t)ext − F(t)int u(t)
(1)
Masonry structures can be numerically represented using several approaches, including macro-modelling, detailed micro-modelling, and simplified micro-modeling [9]. In the simplified facade model of the Torre de la Vela, a combination of macro-modeling and simplified micro-modeling approaches were used. Previous authors have used to Concrete Damaged Plasticity (CDP) model for masonry buildings under high strain rates from blast loading [10, 11], concrete members subjected to high strain rates [12], and rammed earth constructions under seismic events [13]. The CDP model, a modification of the Drucker-Prager model [14, 15], was the constitutive model adopted in Abaqus for this work. The CDP material model uses the concepts of isotropic damage evolution, and isotropic tensile and compressive plasticity to represent the behaviour of the material in the inelastic or fracture ranges. This model
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also allows the strain softening in tension and strain hardening in compression to be defined, as it assumes that damage plasticity characterizes the failure in tension and compression. The values for the dilation angle, flow potential eccentricity, ratio of initial equibiaxial compressive yield stress to the initial uniaxial compressive yield stress, and viscosity parameter were defined according to work by Mohamad and Chen [16]. The parabolic stress-strain law and the exponential stress-strain law were selected for the compressive and tensile behaviour of the rammed earth, respectively. A damage parameter of 0.95 was assigned to the maximum tensile strain of the rammed earth as the damage criterion. For the micro-modelling approach, the Mohr-Coulomb model was selected to represent the sliding failure of the frictional interfaces between the contact elements. The model assumes non-associative flow and the dilatancy angle in the model was assigned a value of zero, as this interaction does not work within the plasticity framework [17, 18]. The use of a dilation angle of zero produces more conservative results, since the strength of the material increases with the dilation angle [19]. Since the Mohr-Coulomb failure criterion cannot be modeled in Abaqus, the cohesion was considered as negligible in this analysis. The normal and tangent stiffness of the rammed earth blocks were based on previous literature [17]. When modelling contact elements (or discrete elements), the joint stiffness must be taken into consideration to ensure the same wall stiffness as with continuum elements. As such, the Young’s Modulus of the contact elements could be recalculated based on Lourenço et al. to account for the joint stiffness [20]. The friction coefficient was taken as the average value from literature [17, 21–23]. A summary of the interaction properties used for the micro-modelling approach can be seen in Table 3. Table 3. Interaction properties Normal Stiffness, Kn,joint
Tangent Stiffness, Ks,joint
Young’s Modulus (Contact Elements)
Friction Coefficient
1.50 × 108 kN/m3
7.50 × 107 kN/m3
1.12 × 109 kN/m2
0.73
The use of the “removal of damaged elements” feature in Abaqus allows to better understand the failure occurring when a model is subjected high levels of damage [24]. Using this feature, elements which reach a maximum level of degradation are removed from the model during analysis. In Abaqus/Explicit, this occurs when the maximum degradation point occurs at a single integration point in the element. The advantage of using this feature is that highly distorted elements are removed from the analysis. However, in case of substantial damage, the accuracy of simulation will decrease as the deletion of damaged elements also removes mass and energy from the system.
3 Impact Loading on the Torre de la Vela The first known examples of cannons date from the Song dynasty in China, around the 12th century [25]. Evidence of cannons in the Middle East appeared in the 14th century, and cannons were used soon after in Europe. By the end of the 14th century,
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cannons were widespread in Europe [26]. Cannons were particularly important during the Grenada War, fought between the Catholic Monarchs and the Nasrid Dynasty’s Emirate of Granada. The diameter, weight, and velocities of the impactor in this work was selected based on the properties of 17th century Spanish cannons [27–30]. Two loading scenarios were studied in this analysis, corresponding to a 16th century cannon ball, and a larger hypothetical cannon ball. The properties of both impactors can be seen in Table 4. The fourth floor of the Torre de la Vela was selected as the location of the impact. As the size of the impactors were negligible compared to the size of the walls, a local response was expected and only the upper portion of the tower was modelled. Table 4. Properties of the historical and hypothetical impactors.
Historical Hypothetical
Diameter
Density
Velocity
Young’s Modulus
Poisson’s ratio
13 cm
6.31 T/m3
408 m/s2
165 × 106 kN/m2
0.27
50 cm
6.31 T/m3
600 m/s2
165 × 106 kN/m2
0.27
3.1 Effects of 16th Century Cannonballs Three different models were created to assess the effect of 16th century cannonballs on the Torre de la Vela: a continuum model with the removal of damaged elements, a continuum model without the removal of damaged elements (Fig. 3a), and a contact model (Fig. 3b). General purpose tetrahedron pyramid elements (C3D10) were used, with varying mesh sizes such that a finer mesh was used around the location of impact. The cannon ball was modelled as a soft-body impactor, at an initial distance of 0.02 m from the wall which reduced the computational time of the analysis (Fig. 3c). The interaction between the impactor and the structure wall was defined by general contact. Hard contact was used as the normal behaviour of the contact property, with separation allowed after contact. In the continuum element model, the mesh was refined around the impact location.
( a)
(b)
(c)
Fig. 3. Loading definition: (a) continuum model; (b) contact element model; (c) impactor.
Negligible damage occurred in both the continuum models with and without the removal of damaged elements, and the stress distributions for both continuum models were identical. Consequently, the results from the continuum model with removable damaged elements will not be presented. The time history of the compressive stresses
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in the wall at and after impact can be seen in Fig. 4, with the time normalized such that the impact occurs at 0.0 s. The lower bound of the compressive stress is plotted at 100 kN/m2 , which is significantly lower than the actual compressive strength of the rammed earth of 4390 kN/m2 . The contact model dissipates energy faster than in the continuum model, as there is a higher concentration of compression stresses found at the location of impact in the continuum model but not in the contact model at 0.006 s (Fig. 4). In the contact element model, the compressive stresses are mostly confined to the contact block when the projectile impacts the wall. As the energy dissipates, the contact block impacted applies compressive stresses on the blocks horizontally adjacent to the initial block. Additionally, the stresses in the continuum model are transferred from the front to the back of the wall, which does not occur in the contact element model (Fig. 5). 0.000 s
0.002 s
0.004 s
0.006 s
(a)
(b)
Fig. 4. Time history of compression stresses immediately after impact on the front of the wall: (a) continuum model; (b) contact model
(a)
(b)
Fig. 5. Compression stresses in the back of the models after impact: (a) continuum model; (b) contact element model.
The time history of the tensile stresses in the wall at and after impact can be seen in Fig. 6, with the time normalized to the impact occurring at 0.0 s. The upper bound of the tensile stresses is plotted at 100 kN/m2 , which is significantly lower than the tensile
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strength of the rammed earth of 527 kN/m2 . At the moment of impact, the tensile stresses are much lower in the continuum model than in the contact model. No tensile stresses are present where the impact strikes the wall in the contact model, which is likely due to the compressive stresses at that location. Nonetheless, there is still a large concentration of tensile stresses at the location of impact in the continuum model, likely caused by the extrapolation of the tensile stresses to the nodes in that region. The tensile stresses dissipate much faster in the contact model than in the continuum model, which is similar to the previously mentioned compressive stresses. The distribution of the tensile stresses in both the continuum and the contact models differ as well. In the continuum model, the tensile stress is concentrated at the point of impact and expands radially from its center. In the contact model, only the element struck by impact have tensile stresses, with those stresses being confined to that block element in both horizontal and vertical directions. As with the compressive stresses, a tensile stress concentration is visible at the back of the wall for the continuum model, but not in the contact model. 0.000 s
0.002 s
0.004 s
0.006 s
(a)
(b)
Fig. 6. Time history of tensile stresses immediately after impact on the front of the wall: (a) continuum model; (b) contact model.
3.2 Effects of a Hypothetical Impactor Since the 16th century cannonball did not cause any damage to the model, a hypothetical impactor was modelled to analyse the effect of impact loading using the removal of damaged elements feature in Abaqus. The diameter and initial velocity of the cannonball were updated for this analysis (see Table 4), but the remaining properties of the impactor and the continuum model remain the same. Minor damage to the surface of the wall was observed, characterized by the removed elements at the surface of the model (Fig. 7). As with the previous impactor, the lower bound of the compressive stress is plotted at 100 kN/m2 , which is significantly lower than the compressive stress of the rammed earth of 4390 kN/m2 . The damage in the wall
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increases significantly between 0.0 s and 0.4 s, but the change in damage is minimal between 0.4 s and 0.6 s. Likewise, the stress distribution at the location of impact does not change significantly between 0.4 s and 0.6 s. The stress distribution in the wall is localized in the area surrounding the damage caused by the impactor. The higher values of compressive stress are located inside the hole caused by the impactor, with little stress at the perimeter of the hole. Although several elements have been removed, the compressive stresses in the wall are still well below the compressive strength of the rammed earth masonry for the remaining elements. As with the compressive stresses, the tensile stresses are mostly located around the damaged area of the wall (Fig. 8). In Fig. 8, the upper bound of the tensile stresses is plotted at 200 kN/m2 , which is lower than the tensile strength of the rammed earth of 527 kN/m2 . The higher values of tensile stress are in the regions surrounding the hole caused by the impactor, but not inside the hole itself. 0.0 s
0.2 s
0.4 s
0.6 s
Fig. 7. Time history of compression stresses in the wall caused by the hypothetical impactor. 0.0 s
0.2 s
0.4 s
0.6 s
Fig. 8. Time history of tensile stresses in the wall caused by the hypothetical impactor.
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4 Discussion When looking at the results from the 16th -century cannonball, both models show similar displacement trends after impact, as seen in the plot of the displacement at the impacted node over time (Fig. 9a). Through the displacement from the continuum model is greater than the contact model, both displacements can be considered as negligible. This difference in displacement is likely caused by a difference in energy that remains in the system after the impact (Fig. 9b). After impact, the energy in the continuum model remains constant, whereas the energy in the contact model increases and decreases sharply before remaining constant.
Fig. 9. (a) Displacement at the impacted node in the direction of the load; (b) total energy of the output set.
The diameter of hole caused by the impactor over time followed a logarithmic trend (Fig. 10). At the end of the analysis, the diameter of the hole remained constant, with a maximum diameter of 53 cm. This maximum diameter is slightly larger than the diameter of the impactor (50 cm), indicating the maximum size of the possible damage is approximately the same size as the impactor. The depth of the hole caused by the impactor was approximately 6.2 cm and was constant over the depth damaged area. An inspection of the mesh showed that the depth of the damage corresponds to the depth of a single layers of elements in that location. Since the damaged elements in Abaqus are removed when a single integration point in the element reaches the damage threshold, the depth of the damage caused by the impactor is mesh dependent. Consequently, the mesh would need to be refined further in the area of the impact to understand the true effects of the hole caused by an impactor.
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Fig. 10. Time history of the diameter of the hole caused by the hypothetical spherical impactor.
5 Conclusions When assessing the effect of a 16th century cannonball on a wall in the Torre de la Vela, three models of a wall section of the tower were created: a continuum model, a continuum model with removal of damaged elements, and a contact model. In all three models, the 16th century cannonball would not cause any damage to the Torre de la Vela. Some differences in displacement occurred between the continuum model and the contact element model, as a result of the energy dissipation in the structure following impact. A hypothetical spherical impactor was modelled to better understand the damage caused by an impactor in the continuum model. This second impactor caused localized damage on the surface of the wall, where the diameter of damage was slightly larger than the diameter of the impactor. The depth of the damage also corresponded to the size of the mesh elements in the region of impact. Future work should consider the use of a more refined mesh in the region of impact to better replicate the potential damage of an impactor on the surface of the rammed earth masonry walls.
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Reverse Engineering for the Structural Analysis of Heritage Constructions A. Massafra1(B)
, D. Prati2
, and R. Gulli1
1 Department of Architecture, Alma Mater Studiorum University of Bologna, 40100 Bologna,
Italy [email protected] 2 Department of Engineering and Applied Science, Università Degli Studi di Bergamo, 24100 Bergamo, Italy
Abstract. Reverse engineering is a process in which an existing object is studied to understand how it works and potentially improve it. In the Cultural Heritage (CH) sector, 3D scanning and parametric modeling tools have made reverse engineering a viable approach for studying and understanding historical buildings. This paper presents a method for studying the displacements and deformations in historical masonry buildings over time using reverse engineering techniques, such as Terrestrial Laser Scanning (TLS) and parametric 3D modeling. The proposed workflow is divided into three phases. First, a digital survey is conducted to create a 3D point cloud that accurately represents the current condition of the building’s structural elements. This point cloud is called the Basic 3D Model (B3M). Next, the point cloud is reconstructed as a 3D NURBS topological model, and specific visual programming algorithms are used to cancel out the hypothetical deformations that have occurred over time. This model is called the Ideal 3D Model (I3M) because it represents the theoretical, undeformed configuration of the structures. Finally, the I3M is compared to the B3M to identify the deviation between the deformed and undeformed configurations. This comparison allows for determining the structural behaviour of the building’s parts and evaluating the overall condition of the building to guide interventions for structural improvement. The method has been applied to several case studies in Italy, including masonry columns, façades, and timber trusses. Keywords: Reverse engineering · Cultural Heritage (CH) · Terrestrial Laser Scanning (TLS) · Parametric modeling · generative algorithms · Structural analysis
1 Introduction Preserving masonry heritage is crucial as many historical buildings were constructed using this technique worldwide. To ensure these structures’ longevity, effective conservation methods must be developed based on an understanding of their structural systems. When working on protected buildings, minimally invasive approaches are needed, as they © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 156–169, 2024. https://doi.org/10.1007/978-3-031-39450-8_13
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allow for improving buildings’ knowledge without causing damage. In the Cultural Heritage (CH) field, digital technologies, such as 3D scanning and computational modeling, have transformed the practice of researching and comprehending historical structures. In particular, reverse engineering has risen as a non-invasive approach for analyzing how existing buildings work and identifying areas where they could be improved. Using reverse engineering techniques, such as Terrestrial Laser Scanning (TLS) and parametric 3D modeling, this paper outlines a process for studying displacements and deformations that occur in some structural elements typical of historical masonry buildings throughout their life cycle. This strategy, originally developed for analyzing timber trusses, has been implemented for several types of structural elements belonging to various case study buildings in Italy, such as masonry columns and masonry facades. In this study, findings from previous research are organized to structure the method comprehensively, demonstrating how researchers and professionals could take advantage of this approach. In particular, in the following sections, the application of the assessing method is described on two case study heritage buildings: the Basilica of San Domenico in Siena and the Teatro Comunale in Bologna. The suggested workflow is broken up into three distinct stages. In the first place, a digital survey is carried out to generate a 3D point cloud that faithfully depicts the building’s structural components in their current state. This point cloud, which discretizes the geometry of surveyed building parts, is also called the “Basic 3D Model” (B3M). After that, during the second step of the method, the point cloud is reconstructed as a three-dimensional NURBS topological model, and then visual programming (VP) algorithms are used to remove the possible deformations that have taken place over time on the scanned structural components. The output model of this stage is named the “Ideal 3D Model” (I3M), as it represents the unaltered theoretical configuration of the structural elements, as the architects and the master carpenters conceived it at the time of construction. In the final step, the I3M is compared to the B3M to determine the geometrical deviation between the deformed (current) and undeformed (theoretical) states. This comparison enables the understanding of the structural behaviour of the analyzed building’s parts and the formulation of coherent hypotheses about the overall condition of the building, which can then guide interventions for its structural improvement. The paper is organized as follows. Section 2 provides the background of the research, including the tools, technologies, and approaches used. Section 3 offers a conceptual overview of the methods employed, delving deeper into each stage of the process. Section 4 presents a case study demonstrating how the method can be applied to different types of construction while maintaining a consistent approach. Finally, in Sect. 5, we highlight the most intriguing results of our analysis, including the facades and columns of the Basilica of San Domenico and the timber trusses of the Teatro Comunale.
2 Background 2.1 Terrestrial Laser Scanning In recent decades, the digitization of the existing building stock has become increasingly commonplace, particularly with regard to preservation and management. In this context, laser scanner surveying has emerged as a fundamental tool for quickly and accurately
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collecting and representing geometric and dimensional information in the form of threedimensional point clouds. Nowadays, 3D scanners can automatically, systematically, and rapidly acquire an object’s spatial coordinates or surface. The basic principle upon which different types of laser scanners operate is the emission of a beam, light field, or pattern onto the object, followed by the analysis of the returned signal. For this reason, laser scanners are classified as active optical sensors, as they emit energy in the form of light. For instance, TLS technology is based on the emission and reception of a beam, light field, or light pattern. It differs from photogrammetry, which does not involve the active emission of light. Overall, laser scanners are a valuable tool for efficiently and accurately capturing and representing the geometry of an object or environment in a digital format. During the scanning process, the device records angular data, distance, and reflectance related to the material properties of the scanned surface. The laser projects a beam onto the surface of the surveyed object, and a sensor measures the time of flight (TOF) or phase shift (PS) of the returned beam and calculates the distance between the device and the object. By performing and aligning multiple scans, the complete geometry of the object can be determined. Laser scanners usually capture the surrounding reality as a series of points in three-dimensional space, known as a point cloud. This point cloud is structured, with each point associated with a group of neighbouring points. 2.2 Parametric 3D Modeling Parametric modeling is a digital modeling technique that has garnered significant attention within the fields of architecture and construction in recent years. It is often referred to as “feature-based modeling” due to the fact that objects are created through a series of processes or “features” with specific attributes that are controlled by parameters. This approach enables constant control over the geometry and underlying mathematical rules of a model. It involves a separation from traditional Computer-Aided Design (CAD) techniques and has been embraced by many professionals due to its flexibility and innovation. Three primary techniques for parameterizing geometries are available: geometric constraint solving, textual scripting, and nodal (or visual) scripting. Geometric constraint solving involves connecting different parts of a model through dimensional and geometric constraints. For example, this technology is used to directly model parametric BIM object families. Textual scripting utilizes text-based programming languages (e.g., C#, Python, etc.) to execute programs. It allows for maximum versatility and accessibility to computer system resources but requires a high level of computer knowledge. On the other hand, nodal programming utilizes visual and non-textual objects and does not require programming knowledge. It uses a graphical interface with two screens: one for drawing the node diagram and the other for visualizing the generated geometries. By relying on graphs and flowcharts, visual programming (VP) makes parametric modeling more accessible to non-computer operators who lack textual programming skills. This way, complex modeling systems can be created by appropriately connecting nodes and arrows in sequence. VP languages are commonly employed in Cultural Heritage (CH) due to their ability to create complex data processing systems without high programming expertise. As the
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adoption of parametric modeling continues to grow, many professionals have started utilising these techniques in their work. 2.3 Reverse Engineering for Improved Built Heritage Structural Knowledge Historical buildings’ structures often exhibit a high degree of complexity in their geometric, construction, and technological characteristics. For instance, timber roofs often have various structural patterns, methods of cutting and assembling elements, metal connections, and elements with variable or irregular cross-sections. At the same time, masonry façades often show numerous architectural details on their surface, such as half pilasters, buttresses, protrusions, and recesses. The digital interpretation of these complexities needs precise and accurate surveying tools, as well as advanced 3D modeling techniques, able to capture the unique features of each structural category while adhering to their specific semantic rules. As anticipated, digital tools for surveying existing buildings have gained widespread adoption among professionals due to their ability to quickly and accurately acquire data at a reasonable cost. LIDAR (Laser Imaging Detection and Ranging) and TLS techniques have become prevalent. Moreover, there are numerous methods for generating 3D models in various formats from scanned point clouds, including the interpolation of surveyed points using meshes or 3D reconstructions based on NURBS surfaces. However, the application of raw survey data to create 3D models for understanding the structural behaviour of heritage buildings is still in its early stages. While there have been some notable efforts in this direction in recent years, they have been mainly geared towards research rather than practical-professional purposes. For instance, Bertolini et al. [1] utilized TLS point cloud data to manually render a finite element model (FEM) for analyzing the state of the roof at the Castello del Valentino. Andriasyan et al. [2] employed TLS or Structure From Motion (SFM) data to reconstruct the geometry of elements within historic buildings into information models using parametric algorithmic modeling techniques. Santos et al. [3] developed a method for analyzing the structural health of historical timber structures with irregular sections by combining LIDAR data with data from non-destructive tests and storing them in a Heritage Building Information Model (HBIM) for numerical analysis using FEM. Youn et al. [4] applied a similar approach to analyze the structural behaviour of a Korean historic building before and after a restoration project. Among other examples, Moyano et al. [5] used TLS tools to acquire accurate geometric data of a historic portico in Spain. In their investigation, the cloud of survey points was converted to 3D models and then compared with them through VP algorithms to detect hypothetical structural deformations of the columns. Instead, Wang et al. [6] have developed a fully automatic method for generating the axes of some masonry columns from the output data of a TLS survey to transform the clouds into FEM models and perform numerical calculations.
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3 Method 3.1 Methodological Approach The experimental methodology described in this study aims to understand, evaluate, and interpret the behaviour of some heritage building components by analyzing the hypothetical displacements and deformations that they have gone through over time. This method considers the geometric and typological properties of these building parts and their evolution over the years. It has been tested and applied in various case studies and refined through years of research. As a result, some tools and procedures have been developed. These latter can be generalized to different kinds of construction elements, including linear features such as beams and columns, surface features such as façades and slabs, and more complex systems such as timber trusses. The main premise of the method is to take advantage of the vast amount of spatial information that can be obtained from a survey conducted using digital instruments such as the TLS. This instrumentation allows for the detailed examination of parts of the building which are difficult to access or observe using traditional (manual) tools due to their inaccessibility, height, or obstruction generated by other elements commonly found in such places. These highly accurate geometric data are first used to analyze the geometry of the structural elements in detail. Afterwards, these data are processed to draw conclusions about the deformational state of the surveyed building parts and, therefore, of their state of preservation. In addition, the integration of geometric data with information from historical-archival research enables the construction of solid hypotheses about the actual behaviour of the whole surveyed building, aiding in the structural understanding of these constructions for conservation designers. 3.2 Method Articulation In summary, the 3D points related to every single structural element are extracted from the point cloud of the entire building, got through laser scanning, and the section curves of the component are vectorized using parametric modeling software. By extruding these curves into space, two three-dimensional models are obtained; they are defined as the Basic 3D Model (B3M) and the Ideal 3D Model (I3M). The B3M represents the current state of the structural elements, while the I3M recreates their hypothetical original condition based on solid and reasoned assumptions. The comparison of these models with the point cloud allows for the detailed analysis of the hypothetical displacements of the elements, the deduction of punctual and comparative information on their behaviour, and the development of global considerations on the health of the structure. This information can be used to plan monitoring and maintenance cycles or, if necessary, to support structural renovation or reinforcement interventions. The investigation method consists of four main steps: data collection, data modeling, data analysis, and critical interpretation of the results. A fifth monitoring phase can also be added to these steps (Fig. 1). In the first phase of the experimental methodology, the elements to be analyzed are identified, and a preliminary survey is conducted to acquire relevant spatial data using laser scanning techniques. After the survey, the various TLS scans are aligned using
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Fig. 1. The investigation method workflow.
dedicated programs to create a point cloud, which accurately represents the current state of the structural elements. The point cloud is then edited to remove unwanted objects, such as furniture, pipes, ducts, and scaffolding. In parallel with the registration of the scans, historical-archival research is conducted on the building’s records to identify the main evolutionary stages of the structural system that have occurred over time. In the data modeling phase, the point cloud is transformed into semantically defined three-dimensional parametric models using generative algorithms. These models are then compared with the original point cloud to highlight deviations between the models and the actual geometry from which they are defined. This data collection is summarised in tables, graphs or reports, providing a knowledge base for assessing the hypothetical deformation state of each element. The displacement analysis phase involves the interpretation of the displacements of every single structural element to formulate hypotheses about the overall behaviour of the building system and to identify the criticality of the connected structural parts. The interpretation of all the acquired and processed information represents the first critical step in order to figure out the surveyed building components’ behaviour and serves as the starting knowledge base for planning any maintenance or structural improvement interventions. The process can be repeated periodically or after unpredictable catastrophic events, such as fires, storms, or earthquakes, to monitor the building elements’ displacement and deterioration trends, assess the building’s health, and retrieve further data. This can be defined as the monitoring phase.
4 Case Studies The presented paper describes the application of the assessing method on two case study heritage buildings in Italy: the Basilica of San Domenico in Siena and the Teatro Comunale in Bologna. The method has been previously tested on several other historic masonry buildings, but this is the first time it has been applied systematically to identify the specific vulnerabilities of specific building elements. In particular, it has been tried out the masonry façades and columns in the Basilica of San Domenico and timber trusses in the Teatro Comunale. While previous works [7, 8] have helped assess specific vulnerabilities in these and other buildings [9–12], this study, for the first time, represents the approach comprehensively, showing how the authors took advantage of the previous analyses to systematize the method.
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4.1 Façade Modeling Linear kinematic analysis, which decomposes masonry structures into macro-elements, is commonly used to assess out-of-plane mechanisms (1st mode) in historic masonry buildings. This kind of assessment is feasible because studies on buildings that have experienced earthquake damage have shown that their seismic behaviour is characterized by the autonomous structural response of the macro-elements rather than the structure as a whole. This expected behaviour is often due to disconnections between construction elements in historic masonry buildings, which can be exacerbated by earthquake action and do not provide structural continuity. Although standard qualitative assessment methods are widespread and used for understanding masonry building construction and cracking framework while aiding numerical assessments, they depend heavily on the technician’s judgment and interpretation of the activated kinematic chains. For this reason, it was decided to use the point cloud data collected through TLS and process them through parametric modeling to improve and support evaluations and turn them into more objective results. The modeling process applied on masonry façades consists in transforming the surveyed point cloud, namely the façade’s B3M model, into the façade’s I3M one, using generative algorithms (Fig. 2). In this case, the I3M represents the hypothetical undeformed configuration of the wall in which all out-of-plane deformations are removed. In other words, the façade’s I3M coincides with the average “plane” of the façade, also definable as the “Ideal Plane” representing the ideal condition of a perfectly vertical wall. The wall point cloud is first cleaned and divided into inner and outer surfaces to generate this Ideal Plane. Then, a Grasshopper© algorithm vectorizes the horizontal cross-sections of the wall and selects the portion that best represents the planar condition of the facade, removing any protrusions or recesses. A linear regression plane is computed starting from the cross-sections to determine the I3M, representing the ideal condition of the wall, namely the Ideal Plane. The I3M serves as an excellent approximation for evaluating out-of-plane deformation. By comparing it to the B3M, it is possible to identify the areas of the façade that most deviate from the average vertical mean plane. This information, obtained by the I3M and B3M comparison, can be used to assess the current condition of the façade, interpreting its behaviour through the identification of the areas that may require more attention or repairs. 4.2 Column Modeling Masonry columns are frequently found in traditional Italian buildings in many places, including porticoes and church naves. They are intended to transfer the structural loads of horizontal elements, like vaults and arches, to the ground or underlying structures. To properly preserve vaulted structures, it is necessary to thoroughly understand their various characteristics, including form, construction, static and seismic behaviour, and many other relevant factors. Therefore, examining those structures that support masonry vaults, such as columns, can be essential for understanding their behaviour and ensuring long-term preservation. In fact, in many cases, irregularity in column displacements can
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Fig. 2. Facades. Basic 3D Model (B3M), Ideal 3D Model (I3M) and Displacement Model (DM).
be linked to specific crack patterns in the above vaults, allowing for a better understanding of the operational state of the structures and guiding structural intervention efforts. The TLS point cloud of each masonry column, representing its current condition (B3M), is transformed into a parametric 3D model (I3M) using a VP algorithm. The I3M represents the hypothetical initial condition of the structure, generated considering the absence of transverse deformations. These transverse deformations may be caused by the horizontal thrust of arches and vaults resting on the columns, as shown in the case study presented in this paper. Axial deformations are disregarded when modeling the I3M since these may be deemed negligible compared to transverse deformations, which are often present in this kind of construction element. A second fundamental assumption for the model generation is the null displacements at the base of the column. From the computational point of view, the algorithm takes as input the point cloud data of each column. It then selects horizontal bands of 3D points, vectorizes the transverse cross-sections of the column, determines their centroids, and projects the centroids and respective section curves onto a vertical axis passing through the centroid of the lowest elevation section, which represents the base of the column. The I3M model is then created from the projected curves using a loft function, generating a perfect vertical column (Fig. 3). By comparing the I3M to the original point cloud data, deviations between the deformed and undeformed columns can be identified as long as potential safety issues with the structures above, such as arches and vaults, can be highlighted. 4.3 Timber Truss Modeling In the field of Construction History, timber trusses were often used in Italy as covering systems for large spaces, such as churches and theatres. Trusses may be susceptible to material degradation or structural vulnerabilities, proper of past construction techniques; therefore, it is essential to evaluate them critically to preserve their authenticity while ensuring structural safety.
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Fig. 3. Columns. Basic 3D Model (B3M), Ideal 3D Model (I3M) and Displacement Model (DM).
Gathering information about these structural systems is vital for three main reasons: understanding their history and the changes they have undergone over time is necessary for appreciating their material culture and preserving their historical value; knowing their current state is crucial for developing a conscious conservation design, planning maintenance, and allowing for the daily use of the buildings they cover; investigating and monitoring their conservation state can provide valuable information about the overall health of the heritage buildings in which they are located. In order to gather this information, TLS point cloud data and historical data from archival research are collected and modelled to improve the understanding of such timber frame systems. The point cloud data of each timber truss, the B3M, is transformed into a 3D model, the I3M, using generative algorithms in the Grasshopper© software. As for facades and columns, the B3M represents the current condition of the truss, while the I3M depicts the hypothetical initial state of the timber structure. To create the I3M, in-plane and out-of-plane displacements of the truss are removed based on specific theoretical assumptions formulated in previous research by examining the in situ behaviour of timber trusses. These assumptions include the lateral bearings remaining in their original position, the projection of each member’s centroidal axes onto the vertical plane of the truss, slight bending deformations in the tie-beams, inward translation and lowering of lateral rafter-post joints, rotation of bottom rafters around the virtual centre of lateral bearings, and the absence of beam axial deformations. Therefore, the I3M parametric model is compared to the original TLS point cloud to assess displacements and deformation states, producing the so-called Displacement Model (DM). The comparison between the point cloud and the 3D model reveals the differences between the current condition of the truss and its original undeformed state. The geometrical deviations identified between the B3M and the I3M are considered the possible deformations that the timber elements have undergone over time and are represented in the DM using a chromatic scale (Fig. 4). The prime deformations examined are the lowering and rotation of the joints between posts and rafters and the bending deformations of the tie beams.
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Fig. 4. Timber trusses. Basic 3D Model (B3M), Ideal 3D Model (I3M) and Displacement Model (DM).
5 Results The chromatic scale in the following figures highlights deviation trends for some investigated heritage structures. Moreover, the tags in the images report the numerical values of the most significative displacements detected for these structural elements. 5.1 Façade Displacements The combination of displacement analysis with analysis of crack patterns, as well as historical research and in-situ inspections, allowed for the confirmation of hypotheses about the behaviour of the facades of the Basilica of San Domenico, leading to interesting and consistent results. This study shows the analysis performed on the exterior surface of a transept’s façade to understand its behaviour and any potential issues. Following the proposed method, by dividing the façade into its lower and upper parts, the algorithms identified the deviation trends between the B3M and the I3M illustrated in Fig. 5. The lower part of the façade exhibited a relative offset of approximately 9 cm between its base and top, with the top projecting outward from the building (rotation about the x-axis). The upper part of the façade displayed similar displacements. It was also rotated in the horizontal plane with respect to its ideal plane (rotation about the z-axis), with the side of the facade adjacent to the bell tower projected outward from the building. Based on the combined results of these analyses, it appears that the façade has undergone a simple tilting. This hypothetical movement seems to be related to the movements of the bell tower, although further research is needed to confirm this hypothesis. 5.2 Column Displacements In the case of the columns inside the transept of the Basilica of San Domenico, the integration of displacement analysis with crack pattern analysis and the incorporation of historical research and in-situ inspections resulted in coherent findings about their behaviour. Similarly, this combination of approaches also provided insight into the behaviour of the vaults in the basilica’s crypt.
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Fig. 5. Displacement analysis of a transept façade of the Basilica of San Domenico in Siena, Italy. Green points lie on the façade mean plane, red points deviate from the mean plane towards the outside of the building, and blue ones towards the inside. The deviation values are magnified by 100 for improved readability in the sections.
As shown in Fig. 6, qualitatively symmetrical displacements were observed for the two central columns. However, the right central column exhibits higher quantitive deviations compared to the left central column, with a relative offset of approximately 7 cm over a length of 580 cm. The overall displacements of the columns in the crypt underline a deformation mechanism caused by the thrusts of the overhead central vault, which is more significant than the lateral ones. The deformation mechanism is highlighted by a large crack located in the centre of the vault, highlighted in red in Fig. 6. The results of this analysis suggest the need for interventions in the crypt to limit this phenomenon and prevent structural collapses. For example, metal chains could help absorb the thrusts of the vault on the column heads.
Fig. 6. Displacement analysis of some of San Domenico’s crypt columns. Green points lie on the I3M, representing null deviations. Red points deviate from the I3M outside, while blue ones are inside. The deviation values are magnified by 100 for improved readability in the sections.
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5.3 Timber Truss Displacements Applying the method to the timber trusses of the Teatro Comunale provided valuable information on the conservation state of the building’s roof system. Comparisons of the I3M and B3M, such as the one shown in Fig. 7, allow for the development of general evaluations about the current deformation states of the roof trusses. In this case, only the displacement analysis in the vertical plane of the trusses is presented, as it is more significant than the out-of-plane analysis. The Theater’s analyzed trusses exhibit similar behaviour in their plane to that identified for the truss in Fig. 7. According to the results, the behaviour of this truss is slightly asymmetrical in its plane with regard to the lowering of the post-rafter joints. In particular, modest lowering values of about 3 cm are detected for the right post-strut joint, and the lower values of the left post-rafter joint and the ridge joint are negligible. In addition, clockwise rotation is observed for the right queen post and counterclockwise rotation for the left queen post. The right queen post exhibits higher rotation compared to the one on the left, being this imbalance reflected in the king post, for which a slighter clockwise rotation is detected. The rotation values are closely related to the displacement values of the joints: the greater the lowering, the greater the rotation of the joint. When related to the span of the trusses (about 25 m), the lowering values indicate that the covering system suffered only a slight deformation and, therefore, is in good condition. The same can be said for the tie beam, which presents minimal bending displacements.
Fig. 7. Displacement analysis of a timber truss located in the Teatro Comunale of Bologna, Italy. Green points lie on the I3M, representing null deviations. Red points deviate from the I3M outside and blue ones inside.
6 Conclusion The parametric 3D modeling method, which is used to evaluate and interpret the deformation states of some construction elements found in traditional Italian architectures, such as masonry facades, columns, and timber trusses, has proved to be reliable and valuable for examining heritage buildings from the structural point of view. The use of TLS tools and visual programming algorithms on historical structures has demonstrated how crucial integration between digital technologies and building
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restoration practices is. Additionally, applying this research method provides information that is often difficult to obtain through traditional methods. The displacement analysis that was applied to two case study buildings – the Basilica of San Domenico in Siena and the Teatro Comunale in Bologna – has proven to be a valid interpretation method for understanding the structural behaviour of the investigated elements, as well as providing insight into the overall behaviour of the buildings. Although the detected movements do not currently threaten the case study buildings, they highlighted the need for long-term monitoring. The results of the analyses also helped identify anomalies in the behaviour of certain elements, such as the cracked masonry vaults in San Domenico’s crypt. They can become the starting point for future research and potential intervention strategies on these historical buildings. Finally, applying the method to a variety of element types has contributed to the reliability of the process, which was initially developed only for timber trusses. The analyses conducted in this study have allowed for testing different workflows and clarifying definitions using a consistent methodological approach, which helps make typological comparisons between similar construction systems and for understanding many other elements within a building in a more global and comprehensive approach.
References 1. Bertolini-Cestari, C., Invernizzi, S., Marzi, T., Spanò, A.T.: Numerical survey, analysis and assessment of past interventions on historical timber structures: the roof of Valentino Castle. J. Herit. Conserv. 45, 87–97 (2016). https://doi.org/10.17425/WK45VALENTINO 2. Andriasyan, M., Moyano, J., Nieto-Julián, J.E., Antón, D.: From point cloud data to building information modelling: an automatic parametric workflow for heritage. Remote Sens. 12(7), 1094 (2020). https://doi.org/10.3390/rs12071094 3. Santos, D., Cabaleiro, M., Sousa, H.S., Branco, J.M.: Apparent and resistant section parametric modelling of timber structures in HBIM. J, Build. Eng. 49, 103990 (2022). https://doi. org/10.1016/j.jobe.2022.103990 4. Youn, H.C., Yoon, J.S., Ryoo, S.L.: HBIM for the characteristics of Korean traditional wooden architecture: bracket set modelling based on 3D scanning. Buildings 11(11), 506 (2021). https://doi.org/10.3390/buildings11110506 5. Moyano, J., Gil-Arizón, I., Nieto-Julián, J.E., Marín-García, D.: Analysis and management of structural deformations through parametric models and HBIM workflow in architectural heritage. J. Build. Eng. 45, 103274 (2022). https://doi.org/10.1016/j.jobe.2021.103274 6. Wang, X., Wu, C., Bai, C.: Generating the regular axis from irregular column grids through genetic algorithm. Appl. Sci. 12(4), 2109 (2022). https://doi.org/10.3390/app12042109 7. Massafra, A., Prati, D., Predari, G., Gulli, R.: Wooden truss analysis, preservation strategies, and digital documentation through parametric 3D modeling and HBIM workflow. Sustainability 12(12), 4975 (2020). https://doi.org/10.3390/su12124975 8. Massafra, A., Costantino, C., Prati, D., Predari, G., Gulli, R.: Digital survey and parametric 3D modelling for the vulnerability assessment of masonry heritage. The Basilica of San Domenico in Siena, Italy. In: 17th International Conference on Structural Repairs and Maintenance of Heritage Architecture, pp. 173–184. WIT Press, Southampton, UK (2021). https://doi.org/ 10.2495/STR210151 9. Massafra, A., Prati, D., Predari, G.: Computational 3D modeling supporting the preservation of historic timber roofs: the case of San Pietro’s Cathedral in Bologna. In: 10th ReUSO Documentation, Restoration and Reuse of Heritage, pp. 743–754. Porto (2022)
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10. [Massafra, A., Prati, D., Predari, G.: Displacement analysis of wooden trusses through digital survey and visual programming tools. The Basilica of San Petronio in Bologna. In: Rehabend 2022 - Construction Pathology, Rehabilitation Technology And Heritage Management, pp. 854–863. Círculo Rojo, Almería, Spain (2022) 11. Prati, D., Guardigli, L., Mochi, G.: Displacement and deformation assessment of timber roof trusses through parametric modelling. The case of San Salvatore’s church in Bologna. Tema 7(1), 21–31 (2021). https://doi.org/10.30682/tema0701c 12. Prati, D., Zuppella, G., Mochi, G., Guardigli, L., Gulli, R.: Wooden trusses reconstruction and analysis through parametric 3D modeling. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. XLII-2(W9), 623–629 (2019) https://doi.org/10.5194/isprs-archives-XLII-2-W9623-2019
Lateral Capacity Assessment of the Main Pyramid of Huaca de la Luna (Peru) Using 2D Finite Element Macroblock Model Cristiana Riccio1 , Anna Remus2 , Selman Tezcan2 , Luis C. Silva1 , Gabriele Milani1 , and Renato Perucchio2(B) 1 Department of Architecture, Built Environment and Construction Engineering, Politecnico di
Milano, Campus Leonardo – Piazza 32, 20133 Leonardo Da Vinci, Italy [email protected], {luiscarlos.martinsdasilva, gabriele.milani}@polimi.it 2 Department of Mechanical Engineering, Hajim School of Engineering and Applied Sciences, University of Rochester, Rochester, NY 14627, USA [email protected], [email protected], [email protected]
Abstract. This study contributes to the structural assessment of the main pyramid in the archaeological complex of Huaca de la Luna, Peru. Built with millions of adobe bricks by the Moche civilization (200–850 A.D.), the monument is one of the largest adobe structures in the world. Located in a seismically active area, the monument shows signs of severe natural and anthropogenic damage. The pyramid was built as a succession of taller and larger platforms, each formed by erecting adjacent but disconnected vertical piers made of adobe masonry. A multiscale 2D nonlinear FE model is introduced for assessing the contribution of this pier architecture to the dynamic response of the pyramid. A representative cross-section of the pyramid is analyzed under plane strain conditions. Critical regions are modelled with individual piers represented by macroblocks separated by frictional interfaces, while a continuous description is adopted for the remaining part of the model. The analysis is performed in Abaqus/CAE Explicit using concretedamaged plasticity and Mohr-Coulomb formulation for adobe construction and soft soils, respectively. The time-evolution of elastic strain and dissipative plastic energy is used to follow the development of local damage conditions up to structural collapse. The structural assessment includes (i) a quasi-static analysis aiming to predict the stress state due to gravitational loads, and (ii) dynamic analysis to identify lateral capacity and failure mechanisms triggered by monotonically increasing ground acceleration. Sensitivity analyses was conducted to evaluate the effect of the contact friction coefficient and the number of macro-blocks used to discretize the critical area. Keywords: Adobe Masonry · Huaca de la Luna · Concrete Damaged Plasticity · Discretization · Finite Element Method · Plane Strain conditions
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 170–183, 2024. https://doi.org/10.1007/978-3-031-39450-8_14
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1 Introduction The present study contributes to the structural assessment of the main pyramid of Huaca de la Luna. This impressive archaeologic complex is one of the most representative sites of the pre-Columbian Moche society in Peru [1]. It dates to the period 200 A.D. to 850 A.D. and provides a testimony of massive earthen architecture and structural techniques, being classified as a world heritage monument by the World Monuments Fund [2]. Built with adobe bricks in a seismically active area and exposed to extensive looting in colonial times, the monument shows signs of severe natural and anthropogenic damage. A comprehensive structural assessment is an essential requirement for the selection of appropriate preservation and intervention strategies. The structural assessment of heritage buildings is generally challenging [3]. A sound knowledge over the structural and material features lacks in most of the cases [4] and the mechanical response of masonry is rather complex [5], with a generally relevant uncertainty associated with the loading paths. In the evaluation of the structural safety, numerical modelling has made valuable contribution to assess the structural response of historical buildings. Several methodologies have been developed and successfully applied to a wide range of problems. The limit analysis is useful to estimate structural load capacity, yet it still requires an expert-based decision approach to ascertain the potential collapse mechanisms [5–8]. More advanced modelling techniques, such as the Finite Element Method (FE) [9, 10] and the Discrete Element Method (DEM) [11–13] are widely used. DEM is suited for masonries with both dry- and mortared joints but requires a full representation of the masonry unit arrangement. FE models generally rely either on a micro- or macro-modelling approach. In the former, the masonry components are discretized individually, hence leading to higher processing times [14]. In the latter, the masonry is modelled as a continuum and assuming an homogeneous material that can be isotropic or anisotropic [15, 16]. This modelling approach is generally preferred in the analysis of large structures [17, 18]. Finally, the mechanical deformation and failure of masonry is inherently a multi-scale phenomenon, for which the observed macroscopic behavior of the material is governed by processes that occur at finer scales. The coupling between different length scales is well demonstrated but representing masonry at finer levels (micro or meso) may be computationally restricted and devoid of practical sense. Examples of so-called multi-scale or coupled methods recently employed to the analysis of masonry structures are given in [19–21]. The Huaca de la Luna pyramid is the result of a succession of construction stages, each consisting in a taller and larger platform erected on top of the previous one. Each new structure encapsulates in its interior all preceding constructions. In turn, each platform was formed by erecting adjacent but disconnected vertical piers made of well textured adobe masonry. In the present study, a multiscale 2D macro-FE model is introduced for assessing the contribution of this pier architecture to the static and dynamic response of the entire pyramid. Critical regions are modelled with individual piers explicitly represented by macroblocks separated by frictional interfaces, while a continuous description is adopted for the remaining part of the model. The same material macro-modeling approach is used to represent adobe in the macroblocks and the continuous part. An energy-based approach is used to determine collapse conditions when performing nonlinear static or dynamic analysis. Similar approaches have been explored to identify the
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sequential failure of macro-elements of structures [22], or to track the existence of fracture in masonry structures related to localized cracking [23]. This initial study intends to provide an important contribution for the accurate structural assessment of the pyramid at Huaca de la Luna as well as other similar monuments built by the Moche along the Peruvian coast.
2 Huaca de la Luna The monumental complex of Huaca de la Luna is part of the Huacas de Moche archaeological site located near the modern city of Trujillo in north coastal Peru. Huaca de la Luna was erected on the lower slopes of the Cerro Blanco – Fig. 1(a) – as part of a sprawling urban center considered to be the capital of the Moche state. The complex has a surface area that covers approximately 30,000 square meters and reaches a height of 30 m, making it one of the largest adobe structures in the world. After extinction of the Moche culture, circa 850 A.D., the complex was naturally buried under eolian sand deposits, which reduced exposure to seismic loading demands during possible historical earthquakes in that region of Peru. The archaeological work that started in the beginning of the 90s has systematically unearthed and exposed the entire Huaca de la Luna complex [2].
(a)
(b)
Fig. 1. Huaca de la Luna: (a) 3D CAD reconstruction [2], and (b) laser scanning of main pyramid north façade [24].
It is estimated that more than 50 million adobe bricks were used for its construction with material taken from different sources, i.e. some adobes are of granular yellow sediments from local soft soil and some contain organic matter [25]. The pier structure constitutes a particular construction feature of the Huaca. Piers are thick brick columns of non-uniform height, width, and depth, arranged side-by-side to form thick platforms and walls, Fig. 2 and 3. The discontinuities between adjacent piers are clearly visible in Fig. 2. This unique construction feature appears throughout the monument and is coupled with the presence of makers’ marks unique to certain piers. This suggests that coordinated but separate labor groups worked together to construct the monument [26]. This study focuses on the main stepped pyramid at the center of the complex. Built on the slopes of the Cerro Blanco Mountain, the pyramid is supported on the East side
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on sloping bedrock while it is built directly on layers of soft soil on the West side. The pyramid shows signs of extensive anthropogenic and natural damage, primarily in the northwest corner north and west façade – Fig. 1(b). A large excavation, attributed to treasure hunting during colonial time, cuts deeply in the north façade. Structural damage is mainly present in the NW sector of the pyramid including the substantial collapse of the NW corner and large cracks in the upper areas which penetrate deeply in the structural system, Fig. 3. The pyramid is the long-term objective of a multidisciplinary study focused on determining the structural behavior of its massive core as well as the built-up areas on the top of the pyramid under static and dynamic conditions. This includes laser-scan survey and 3D reconstruction of the pyramid [24, 27], mechanical characterization of adobe brick and mud mortar [28] and geotechnical and geophysical exploration of the foundation soils along the northern façade [29]. Initial structural research investigated the relationship between the observed damage and the soft soil support under static conditions using a simplified 2D FE plane strain nonlinear model derived from the geometry and the ground level of the north façade [30]. Subsequent research focused on the west side of the pyramid to capture the effect of the original ground level – located 5.5 m below the north side – to the dynamic response, [31]. Most recently, a sensitivity analysis of the static and dynamic response to (a) variations in the pyramid stepped west side profile, (b) underlying soft soil and bedrock configuration, and (c) adobe material tensile strength was performed on 2- and 3D nonlinear FE models [32]. In each case analyzed in [31, 32], the dynamic response was evaluated by applying lateral ground accelerations leading to the structural collapse of the stepped (west) side of 2D models and of the NW corner of 3D models. Based on a continuous description of the adobe masonry using a material macro-model, these studies demonstrated the seismic fragility of the northwest corner. Lateral capacity for 2D models was found to range between 0.135 g and 0.340 g, with the combination of steeper bedrock angle and lowest adobe tensile strength yielding critical conditions. Results from [32] suggested the need of a refined model, which may account of the discontinuities in the adobe structure introduced by the piers and the role played by contact friction interaction between piers.
Fig. 2. Main pyramid: divisions between “piers” of adobe bricks during site inspection.
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Fig. 3. Significant damage found during the in-situ inspection: North façade (left) and partial collapse of the Northwest corner (right).
3 Numerical Finite Element (FE) Model 3.1 Geometry and Macroblocks A typical mid EW cross section based on previous studies of Huaca de la Luna’s main pyramid [31, 32] is adapted for 2D plane strain nonlinear FE analysis of the pier construction present in the monument. The chosen cross-section has a total length of 122.80 m, where 82.80 m correspond to the width of the pyramid itself and 40 m correspond to the width of the adjacent Plaza 2b – Fig. 4(a). At its greatest height, the monument reaches 28.6 m from west ground level. This section was selected from a sensitivity analysis of potential foundation conditions and west façade configurations as an intermediate version appropriate for preliminary investigation of macroblocks. While previous models use a macro-modelling approach to treat the entire adobe brick structure of the pyramid as a single continuum [31, 32], the present work adopts a multi-scale approach by introducing discrete macroblocks in critical areas of the continuum. Each macroblock represents a pier of adobe bricks. The same macro-modelling approach adopted in [31, 32] for the continuum is used to represent the adobe material within each macroblock/pier. To avoid unnecessary complexities in this preliminary attempt to modeling piers, the geometry of the pier structure is simplified. Each of the nine steps of the west façade is assumed to correspond to one single layer of identical rectangular macroblocks. Thus, the height of the pier ranges between 2.75 m at the bottom layer and 3.16 m at the top. The width of the pier varies according to the layer with 4.3 m at the bottom layer and 3.5 m at the top. The systematic 2D static and dynamic modelling in [31, 32] has identified critical damage development in the western portion of the cross section culminating with partial or total collapse of the stepped façade. Thus, to effectively model how piers affect damage development and collapse mechanism, macroblocks are distributed from the west façade to the interior of the cross section. Five cross sectional configurations of increasing macroblock distribution are considered, with the total number of macroblocks ranging from 37–103 – Fig. 4(b–f). The remainder of the cross section, shown in gray, is modelled as a single continuum. To reproduce the soil-structure interaction, the foundation soil is also modelled. A single, homogeneous layer of soft soil starts from the assumed angle of the bedrock and continues westward, Fig. 4(a). To avoid a possible correlation between the results and
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(a) geometry of the selected east -west cross-section
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(c) model 1: N=37
(e)
(d) model 2: N=47
model 3 (reference): N=70
(f) model 4: N=90
model 5: N=103
Fig. 4. Mid EW cross-section: geometry – dimension in meters (a), and configurations of macroblocks distributions with soil omitted for clarity (b–f).
the boundary condition at the western edge of the soil, the soil extends 100 m west of the base of the pyramid, Fig. 5. The properties for the adobe macro-model and the soil are described in Sect. 3.3 below. 3.2 Finite Element (FE) Mesh The cross-sectional geometry given above forms the basis of five 2D plane strain FE models each representing a specific macroblocks configuration. FE models were created in Abaqus/CAE Explicit [33]. Quadrilateral elements (CPE4R) dominate the mesh, but some triangular elements (CPE3) are found in corner regions. Mesh refinement was increased in the vicinity of the active region and the pyramid-soil interface. The characteristic length of elements varies as given in Fig. 5. The elements within macroblocks have an approximate size of 0.75 m, while the continuum part of the pyramid is defined by a coarse mesh characterized by 1.5 m elements. The soil immediately under the active region starts with a characteristic length of 0.75 m at the eastern corner and progressively increases to 1.5 m at the westernmost edge. The final numerical model has 5,416 CPE4R and 118 CPE3 FEs, leading to 12,898 degrees of freedom. The boundary conditions applied to the model are illustrated in Fig. 7. Pinned supports at the base assume the sand layer is fixed along the bedrock. At the westernmost (right) side of the model, rollers restrain horizontal (x-direction) motion of the foundation soil to simulate soil beyond the scope of the model. This support is maintained under gravitational loading. When the lateral load is applied, the roller is removed and replaced with horizontal acceleration (Fig. 7, bottom).
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Fig. 5. FE mesh for the cross-section with model 3 macroblock configuration.
Fig. 6. Constitutive laws adopted for the adobe masonry [30, 31].
3.3 Material and Interface Contact Properties The assumptions regarding material properties for both adobe masonry and the foundation soil are predicated on existing mechanical characterization tests [28, 30]. Adobe masonry is modelled as a homogeneous and isotropic nonlinear continuum, defined according to the concrete-damaged plasticity (CDP) constitutive model available in Abaqus/CAE Explicit. The CDP model derived in [34, 35] is suitable for quasi-brittle materials in general, and the results indicate that it offers a good compromise between computational time and accuracy, see for example [36, 37] (Table 1). Table 1. Plastic properties for concrete-damaged plasticity modeling of adobe material. Young’s Modulus
Poisson’s ratio
Density
Dilation Angle
Eccentricity
fb 0/fc 0
K
Viscosity Parameter
123MPa
0.2
1735 kg/m3
18°
0.1
1.16
0.67
1E-8
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Table 2. Material parameters adopted for the foundation soil assuming a Mohr-Coulomb formulation. Young’s Modulus
Poisson’s ratio
Density
Friction Angle φ
Cohesion
57 MPa
0.42
2000 kg/m3
43°
1 kPa
The quasi-brittle nature of adobe masonry is represented by an exponential softening in tension. In compression, a parabolic-type hardening exists, followed by a softening regime. The post-peak responses that serve as input for the CDP model shown in Fig. 6 are derived from [30, 31]. The Drucker-Prager hyperbolic function used to define a non-associated flow rule for CDP requires the definition of several physically based parameters. The assumed input for these parameters is described in Fig. 6. The behaviour of the soil foundation was simulated with a Mohr-Coulomb formulation. Soil properties are averaged from data produced via cone penetration tests (CPT) performed at the perimeter of the monument [29, 30]. The stratification of soil in the vicinity of the structure was approximated as a single layer. Properties are given in Table 2. The interactions between macro-blocks were idealized through Abaqus/CAE Explicit general contact formulation, for which both shear and normal behaviour are defined through a penalty approach. For the shear (tangential) response, the contact is defined by a Coulomb friction model with a friction coefficient, μ, whose value ranges from 0.1 to 0.5. For the normal response, a hard contact has been adopted and the interpenetration between blocks under compression is precluded. Blocks are permitted to detach in pure tension.
4 Numerical Structural Assessment 4.1 Sequential Structural Analysis Each model described above undergoes an assessment composed of two analysis steps: (1) the application of self-weight, and (2) the application of a monotonically increasing lateral acceleration. The outputs of these steps illustrate the behaviour and potential failure mechanisms of the structure under load, as well as a maximum lateral load capacity for each configuration. The first stage of analysis considers the application of self-weight over the entire numerical model as a body force, linearly applied over an interval of 5 s. This allows a slow deformation rate producing quasi-static analysis conditions. The validity of such a strategy is confirmed by monitoring the development of kinetic energy which remains negligible throughout the gravitational loading. After gravitational loading, a lateral acceleration is applied directly to the base of the foundation soil. The loading protocol follows a linear ramped acceleration which results in fully dynamic conditions. This nonlinear dynamic analysis based on ground applied acceleration is preferred to a pushover analysis because it more accurately represents the effect of a seismic peak ground acceleration. The two sequential states are illustrated in Fig. 7.
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Fig. 7. Two loading stages applied considered in the sequential analysis: (top) self-weight, and (bottom) lateral acceleration
4.2 Energy-Based Approach for Lateral Capacity Estimation In order to determine the formation of local damage and its evolution into structural failure in the cross-sectional model under static and dynamic conditions, we apply the energy-based approach previously developed for the failure analysis of other CDP plasticity models representing historical structures [31, 38–41]. As explained therein, under purely static loading, structural failure is associated with the transition from static to dynamic equilibrium. This transition can be identified by the sudden decrease in support reactions, the asymptotic growth of kinetic energy, or, in the case of nonlinear FE analysis with CDP models, by the accompanying asymptotic growth of plastic dissipation energy. Under dynamic conditions produced by ground acceleration, the variation of kinetic energy at failure may not be easily distinguished within the high level of kinetic energy already present in the structure due to ground acceleration. Under these circumstances, the failure transition of a nonlinear FE model with CDP material can best be detected by either change in support reactions or asymptotic growth of dissipative energy This situation is illustrated with a simple example shown in Fig. 8. The energy outputs and support reactions of a small model are used to show that the intersection of plastic dissipation (PD) and elastic strain energy (SE) corresponds to the sharp drop in support reactions
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Fig. 8. Propagation of cracks (shown with maximum plastic strains, PE) for a 4-macroblock model (2 m × 2 m) accelerated to the right. Energy and reaction forces plots verify that the PD-SE intersection occurs at the failure time identified by reactions
(b)
(a) = 0.1 and a= 0.11g
(c)
= 0.2 and a= 0.11g
(d) = 0.3 and a= 0.11g
= 0.4 and a= 0.11g
(e) = 0.5 and a= 0.11g
Fig. 9. Effect of the friction coefficient of the interface contact between blocks (configuration 3 with N = 70 blocks).
at failure. The PD/SE intersection provides a practical way for detecting the asymptotic growth of dissipative energy [31, 38–40]. The correlation between PD asymptotic growth and failure can be further explained considering the CDP material formulation. Under the effect of increasing inertial forces fractures must propagate for failure to take place. Because the CDP formulation models fracture opening in the continuum as plastic strains, fracture growth is actually a zone of plastic strains development which in turn produces plastic dissipation energy. In the limit, for a portion of the continuum to separate and move independently, plastic strains – and with them plastic dissipation energy – must grow asymptotically. In contrast, elastic strain energy does not experience the same growth rate since elastic strains will actually decrease during fracture growth. Thus, PD asymptotic growth will be correlated with the PD/PE intersection and this condition can be taken to signal structural failure. 4.3 Sensitivity Analysis: Influence of Friction Coefficient and Number of Macroblocks on Lateral Capacity A total of 25 models are analysed for a sensitivity analysis that examines the effect of the number of macroblocks and friction coefficient of contact between them. Friction
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coefficients range from μ = 0.1 to μ = 0.5, while, as shown in Fig. 4, the number of macroblocks is 37, 47, 70, 90, and 103 in configuration 1 through 5, respectively. Hereafter, each individual model is denoted by the label N-µ.
Fig. 10. Energy plot for model 70–0,3 (a), and lateral capacity expressed in g for all models analysed (b).
Figure 9 illustrates five models, all configuration 3 (70 macroblocks), but each characterized with a different coefficient of friction. All models are shown at the lateral acceleration a = 0.11 g. This is the maximum lateral capacity for model 70–0,1 – Fig. 9(a). However, all other models with 70 macroblocks – Fig. 9(b–e) – have higher lateral capacities, as indicated by their considerably more limited plastic strain zones at a = 0.11 g. For example, the 70–0,5 model sustains more than double the load shown, with a lateral capacity of 0.24 g, Fig. 10(a). The lateral capacities for all 25 models are summarized in Fig. 10(b). Results clearly show the dominant effect of the frictional coefficient on lateral capacity, and the limited effect of number of macroblocks for each μ set. The lower bound for lateral capacity is 0.1 g, corresponding to models 37–0,1 and 47–0,1. The model 103–0,5 yields the maximum lateral capacity of 0.25 g.
5 Conclusion The present model was developed to explore how the Moche pier construction process used at Huaca de la Luna might affect the static and dynamic response to gravitational and lateral acceleration loading. This preliminary study addresses the feasibility of implementing a multi-scale model where, within a macro-modelling approach to represent adobe bricks, a previously defined “active” region is discretized into macroblocks and the remaining portion is modelled as a continuum. The set of 25 models studied yield lateral capacities that vary from 0.1 g–0.25 g. This finding fits with the earlier finding of 0,135 g–0,34 g capacity, as yielded by the set of 2D plane strain continuum models studied in [31, 32]. A qualitative survey of results shows consistency with extant damage and earlier 2D models with localized plastic strains (fracture) at the west façade and on the top of the pyramid. Future research will investigate the effect of macroblock discretization with variably sized macroblocks and irregular configurations, which more closely
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reflect the archaeological finding on the internal layered structure. Following the work in [32], the modelling will then be extended from 2D to 3D, to more closely represent the complex structural behavior the actual pyramid. This work also confirms the utility of an energy-based failure criterion for the assessment of the lateral capacity of structures modelled with CDP formulation. Finally, the multi-scale approach introduced here may find application to a class of similarly built Moche earthen structures in northern Peru.
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31. S. Tezcan, M.A. Pando, R. Aguilar, B. Castañeda, C. Rojas, R. Perucchio, Preliminary nonlinear static and dynamic analysis of the main pyramid of Huaca de la Luna, Peru, COMPDYN Proc. 2021-June (2021). https://doi.org/10.7712/120121.8478.18791 32. Tezcan, S., Pando, M.A., Aguilar, R., Perucchio, R.: Nonlinear 2D and 3D finite element static and dynamic analysis of the main pyramid of Huaca de la Luna, Peru. In: Endo, Y., Hanazato, T. (eds.) 13th International Conference on Structural Analysis of Historical Constructions (SAHC 2023), Kyoto, Japan (2023) 33. Dassault System Simulia - Abaqus, (2020) 34. Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. Int. J. Solids Struct. 25, 299–326 (1989). https://doi.org/10.1016/0020-7683(89)90050-4 35. Lee, J., Fenves, G.L.: Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124, 892–900 (1998). https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892) 36. Lourenço, P.B., Silva, L.C.: Computational applications in masonry structures: from the Mesoscale to the super-large/super-complex. Int. J. Multiscale Comput. Eng. 18, 1–30 (2020). https://doi.org/10.1615/IntJMultCompEng.2020030889 37. da Silva, L.C.M., Milani, G.: A FE-based macro-element for the assessment of masonry structures: linear static, vibration, and non-linear cyclic analyses, Appl. Sci. 12 (2022). https:// doi.org/10.3390/app12031248 38. Tezcan, S., Tambe, N., Muir, C., Aguilar, R., Perucchio, R.: Nonlinear FE analysis of the response to lateral accelerations of the triumphal arch of the church of Andahuaylillas, Peru. In: Aguilar, R., Torrealva, D., Moreira, S., Pando, M.A., Ramos, L.F. (eds.) Structural Analysis of Historical Constructions. RB, vol. 18, pp. 1301–1309. Springer, Cham (2019). https://doi. org/10.1007/978-3-319-99441-3_139 39. Sun, J., Tezcan, S., Perucchio, R.: The structural function of the Dutch buttressing of the east curtain wall of Elmina Castle, Elmina, Ghana. In: Roca, P., Pelà, L., Molins, C. (eds.) Proceedings of 12th International Conference on Structural Analysis of Historical Construction, SAHC 2021, pp. 457–468 (2021) 40. Faleri, F., Grillanda, N., Tezcan, S., Perucchio, R., Milani, G.: Role of repeted seismic events on the collapse of two calidaria in Rome dating back to Imperial age. In: COMPDYN Proceedings 2021-June, pp. 406–414 (2021) 41. Remus, A., Yılmaz, L., Tezcan, S., Perucchio, R.: Effect of eastern architecture and sloping foundation conditions on the structural response of the adobe pyramid Huaca de la Luna (Perú). In: Endo, Y., Hanazato, T. (eds.) 13th International Conference on Structural Analysis of Historical Constructions (SAHC 2023), Kyoto, Japan (2023)
Evaluation of Microscale Behavior and Structural Deformation for Yeonji Wall in Gongsanseong Fortress of the Sixth Century in Korea Jun Hyoung Park1
, Gwan Su Lee2
, Seok Tae Park3
, and Chan Hee Lee3(B)
1 Corporate Research Institute of Creation, Radpion Inc., Daejeon 34014, Republic of Korea
[email protected]
2 Cultural Heritage Management Department, Chungnam Institute of History and Culture,
Gongju 32589, Republic of Korea 3 Department of Cultural Heritage Conservation Sciences, Kongju National University,
Gongju 32588, Republic of Korea [email protected]
Abstract. The Gongsanseong Fortress is a fortress built to defend the capital of Baekje Kingdom, and has been inscribed on the World Cultural Heritage for its outstanding historical value as a cultural site that allows one to see Baekje culture and construction techniques. In 2013, part of the rampart collapsed due to localized heavy rainfall, and since then, scientific and engineering studies have been conducted for its stable conservation. Based on these studies, a maintenance system has been established, and is still in operation currently. Automatic measurement equipment was installed on structurally unstable ramparts to measure the microscopic movements, and it was found that the walls in the pond site (Yeonji) on the north side of the Gongsanseong Fortress moved the fastest. The movement of the wall is concentrated from winter to thawing season, and it is repeated every year. It was interpreted that the movement is caused by the freeze-thaw action of water. To visually confirm these movements, we compared 3D scan data taken in 2014 and 2021. From the analysis, the largest deformation occurred in the central part of the wall in the horizontal direction of the wall, while in the vertical direction, the deformation was more concentrated in the lower part of the wall than in the upper part. Deformation outside the tolerance range was observed in more than 70% of the ramparts, where the walls were pushed and protruded towards the frontal direction. The movement of the wall, as measured by some measurement sensors, takes the form of a reversible deformation that returns to the original movement after structural deformation. However, the 3D scan data shows that this movement is irreversible, which is different data from the measurement sensors. These results indicate that the application of a two-dimensional measurement technique to capture the spatial movement in a 3D space may distort the reflection of an actual movement, so the possibility of such distortion must be considered in the interpretation of the two-dimensional measurement results. Keywords: Baekje Kingdom · Gongsanseong fortress · Monitoring · Behavior measurement · 3D deviation analysis
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 184–194, 2024. https://doi.org/10.1007/978-3-031-39450-8_15
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1 Introduction 1.1 Background and Purpose Baekje Kingdom was an ancient nation located in the southwestern part of the Korean Peninsula from the 1st century BC to the 7th century AD, and is divided into periods based on the location of its capital. The country was first founded in the area around Seoul, and the period from 476 to 538 AD, when the capital was moved to Gongju, is known as the Woongjin Baekje period. The representative remains from the Woongjin Baekje period include Gongsanseong Fortress, the Tomb of King Muryeong and the Royal Tombs. They were inscribed on the World Cultural Heritage in recognition of their outstanding value as valuable monuments that showcase the construction, culture and social aspects of the Baekje. The Gongsanseong Fortress, is a military installation built for the defense of the capital, and is a mountain fortress with the length of 2.6 km. Most of the ramparts are made of stone (Fig. 1A), but a portion in the southeast part is made of soil. There are many references in the historical records for the repairs made to the rampart of the Gongsanseong Fortress after collapse, and the overall major maintenance in the 1970s gave the fortress its current appearance. In September 2013, heavy rainfalls caused a section of the rampart to collapse on the north side of the Gongsanseong Fortress, and scientific and engineering studies were conducted to ensure stable conservation of the rampart. In particular, behavior measurement sensors were installed on the rampart to measure microscopic movement of the wall where structural deformation occurred, and 3D scanning was performed on major deformation sections to obtain point cloud data. In addition, a monitoring system has been established to check the condition of the ramparts through measuring the separation distance using light wave and periodic visual surveys, and a stable maintenance system has been managed to date. Among these monitoring techniques, the monitoring data of the rampart using behavior measurement sensors measuring the changes in the tilt or separation distance of the fortress wall every 10 to 30 min, and is used as a basis for maintenance by checking for sudden structural deformation or irreversible movement [1]. In total, there are more than 20 sensors measuring the movement of the ramparts at Gongsanseong Fortress, with the most significant changes detected on the southern wall of the pond site (Yeonji). In 2014, a detailed investigation confirmed that the pressure of groundwater was acting on the walls due to the site’s close location to the catchment area below the valley (Fig. 1B) [2]. The wall of the Yeonji protrudes heavily towards the front, even noticeable to the naked eye, and the fence, which was placed in parallel to the wall at the upper part, is pushed together to form a curve (Fig. 1C). Two tiltmeter sensors mounted on the walls of the Yeonji repeatedly detected tilt changes of 0.3° or more per year, indicating a steady increase in the structural instability. Based on the monitoring data, it was determined that the irreversible deformation of the Yeonji wall required action, and the protruded walls were returned to a flat position in 2021 during the maintenance carried out with dissolution of the Yeonji. In this study, we analyzed the micro-behavior data of the Yeonji wall collected over a period of about 7 years and examined the factors that affect the movement of the wall compared to environmental data such as temperature and precipitation. In addition,
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Fig. 1. Status of the Gongsanseong Fortress: (A) West-gate (Geumseoru) and ramparts, (B) Plane view of the pond site (Yeonji), and (C) Deformed southern wall of Yeonji.
the deformation of the wall was visualized through the deviation analysis between the 3D scanning data acquired just before the dismantling and the 2014 scanning data, and the characteristics of the behavior change were identified with respect to the position along the wall. Finally, through a comparative analysis of the measuring data and the 3D scanning data, we analyzed the difference between the amount of change measured by the sensor and the actual movement of the wall, and examined the factors that distort the interpretation of the measured data. 1.2 Subject and Methods Measurement sensors are installed in various cultural heritage sites to detect changes in structural stability [3]. In this study, two tiltmeter sensors, labeled as T10 and T11, are attached to measure microscopic behaviors of the Yeonji wall. The attached T10 and T11 sensors are closely spaced, with T10 at the center of the wall and T11 at the end (Fig. 2). The tiltmeter sensor used a durable and highly resolvable conductive liquid tiltmeter that measures the change in the tilt angles in two dimensions, with the X and Y axes centered at the horizontal direction of the wall. These sensors can detect very small changes in the tilt angle, providing high-accuracy measurements. A conductive liquid tiltmeter is also known for its long-term stability, which is demanded for continuous or long-term monitoring. The tiltmeter sensor is the 904-T high-gain version from Jewell, which has a spatial resolution of 0.005° and repeatability of 0.02°. The frequency of measurements was set to every 10 min to account for aliasing of the daily temperature difference, and the power source was a solar cell and storage battery. The sensor was installed on a bracket that was closely attached to the surface of the Yeonji wall. The temperature and electrical-signal changes were measured along the X and Y axes. All buildings expand or contract as the temperature changes. The measured size of an object therefore depends on the thermal expansion coefficient of the object. Although thermal effects can be compensated using the temperature measured by a sensor, they cannot be accurately evaluated for masonry structures. Therefore, the errors introduced by thermal effects should be considered when interpreting short-term measurement results. In this study, we analyzed the data measured over seven years and compared the sizes of expansion and contraction due to thermal expansion and the
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change in slope. We confirmed that the movement exceeded the movement induced by thermal effects, indicating that no separate compensation was required. Changes in environmental factors cause minute movements of buildings and affect structural stability. The environmental instrumentation was installed on a large flat area outside the walls, unaffected by ramparts or trees, and measured temperature, humidity, precipitation, wind direction, and wind speed using the Onset’s HOBOware. Measurements were stored on a CR-1000 data logger unit from Campbell scientific, and transferred to a server computer in the lab using a CDMA modem. The measurements were transformed and processed in the lab to analyze the microscopic behavior of the wall over time. Research is conducted using 3D scanners in various academic fields, and they are used for 3D documentation or structural analysis of cultural heritage [4–6]. To acquire the 3D geometry of the Yeonji wall, we used the Scanstation C10 model, a broadband laser scanner from Leica. The scanner is a time-of-flight method that measures time by irradiating a laser and collects about over 50,000 points per second. It can scan up to 300 m away, and has a positioning accuracy of 6 mm, a distance accuracy of 4 mm, an angular accuracy of 60 µrad, and a surface accuracy of 2 mm. The 3D scanning data was acquired in April 2014 and May 2021, and the geometry information was established based on the results of scanning 7 points in 2014 and 9 points in 2021.
Fig. 2. 3D image showing the shape of the Yeonji wall, sensor positions, and axial setup.
The scanning data were registered, merged and filtered into one object using Leica’s Cyclone software, and deviation analysis was performed using Cloud compare, an open source program. Deviation analysis of point cloud data is a method of calculating the distance between a reference object and a comparison object, which is usually obtained by calculating the distance of the closest points among the points of the two objects. However, these methods have a lot of errors when the density of points is low or the surface condition of the target is poor. In this study, an algorithm using Delaunay Triangulation was applied. This algorithm divides a triangulated irregular network formed by connecting three points, and computes an absolute value of the distance between the network plane and a point. After matching the coordinate system of the geometry
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information from the 2014 with the one from 2021, the deviation in the two data was collected, and was visually analyzed for the actual movement of the wall.
2 Behavior Monitoring 2.1 Annual Micro-behavior Looking at the behavior of the T10 sensor over a time series, we see that there is no change in the tilt angle from April to November every year, but a large change in the tilt angle, more than 0.3°, is detected from December to March (Fig. 3). Characteristically, there is no difference before and after the tilt angle changes, with a sharp change at the beginning and end of the winter season. Unlike the T10 sensor, which recovers to the original position after a change in the tilt angle, the T11 sensor experiences a continuous irreversible change in the tilt angle. From April to November, there is no change in tilt angle, but from December to March, the tilt angle increases by more than 0.3° in the outward direction of the wall. It then resumes its stable behavior and repeats this pattern year after year. The two tiltmeter sensors were installed on a continuous wall but exhibited different micro-behaviors. The movement detected by the T10 sensor was reversible, indicating structural recovery at the sensor-attachment point, whereas the T11 sensor detected an irreversible slope increase. However, the Yeonji wall displayed structural deformation that contradicted the measurements of T10, suggesting that the measurement data are influenced not only the object’s movement, but also by external factors. Both sensors registered a sharp change in tilt angle during the winter months, suggesting that movement of the Yeonji wall depends on environmental changes during the winter months. However, no changes were observed in January of 2020, implying different environmental factors in January 2020 than in other years. This possibility warrants further investigation. 2.2 Environmental Effects There are five elements of micro-meteorological monitoring data of temperature, humidity, precipitation, wind direction and wind speed. Of these, humidity has little effect on the direct behavior of the ramparts, and the maximum wind speed is 8.3 m/s, which is unlikely to directly affect the structural stability of the ramparts based on the Beaufort wind classification. Therefore, we examined the effects of temperature and precipitation on the ramparts. During the measurement period, the lowest temperature was −21.4 °C and the highest was 38.2 °C, with an annual difference of more than 50.0 °C, and the highest precipitation was 57.5 mm per hour. To get an idea of the overall monthly climate, we calculated and plotted the average monthly temperatures and found that while the average winter temperatures dropped below freezing every year, January 2020 did not drop below freezing and stayed in the ambient temperatures.
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Fig. 3. Graphs showing the microscopic behavior affected on environmental elements in the Yeonji wall with two tiltmeter sensor of T10 and T11.
Comparing the behavioral data of the Yeonji wall with the environmental data, the anomalous behavior coincided with the time when the temperature dropped below freezing (Fig. 3). This is because the water inside the wall freezes in sub-zero temperatures and expands in volume, causing structural deformation. This is especially true in January 2020, when the average temperature remained above zero and no structural deformation was detected. It was not possible to directly identify the effects of precipitation, and even if there were effects on the wall, they are considered to be too small to be discernible compared to the structural deformation caused by freeze-thaw action.
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3 3D Image Analysis 3.1 Modeling and Aligning Coordinate Systems To perform a deviation analysis, a baseline model was created using the 3D scanning data collected in 2014 and 2021. In order to compare the two modeling results, they must be projected onto the same coordinate system. Since the 2014 scanning data did not have the ground control point surveyed, the geospatial information could not be obtained objectively. Therefore, we matched the relative coordinates based on the Manharu pavilion building, which is located outside of the Yeonji, and manually reset the location to the same virtual space (Fig. 4). To continuously acquire the quantitative coordinates and detect structural deformations, the reference coordinates must be measured at a fixed ground-reference point, which must first be installed. To optimize the data with the matching coordinate system, data on all parts of the Yeonji other than the data on wall of the pond were removed, and plants that grew in the gaps of the wall were removed through an artificial filtering process. In addition, the texture was mapped based on the color information of the photograph and the point cloud data obtained during the 3D scanning process. The created 3D point cloud data can be converted into a polygon model, but additional errors can be introduced through the conversion process. Therefore, we employed the original point cloud data in the present study.
Fig. 4. Results of aligning coordinate system with 3D data measured at April in 2014 and May in 2021.
3.2 Deviation Analysis Based on the 3D scanning data collected in 2014, a deviation analysis was performed, and it was found that the central part protruded up to 130 mm towards the front in the horizontal direction (Fig. 5). The magnitude of the deviation decreases from the central part to the sides with little to no deviation at either end, or decreased or increased a little within tolerance range. Looking at the vertical direction of the wall, the deviation is larger in the lower part of the wall than in the upper part. In the center, the upper and lower parts is different by more than 2 times. The same trend is seen in the fence
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installed on top of the Yeonji wall, which appears to have been pushed along with the soil that was filling the back of the wall. The T10 tiltmeter sensor detected larger micro-behavior on the Yeonji wall than the T11 sensor, which detected relatively small deviations. However, the T11 sensor exhibited a larger slope change during the seven years than the T10 sensor. In particular, the location of the T10 sensor showed signs of structural recovery, indicating that the data of sensors designed for 2D space may be distorted when converted to motion in 3D space. Further interpretation on the discrepancy between 3D motion and sensor measurement is presented in detail in the discussion. The difference in the amount of deformation depending on the location in the Yeonji wall can be explained by two main reasons. The first is that as the Yeonji was constructed in a rectangular shape, the wall extending perpendicular to the side of the south wall acted as a resistive force against the lateral pressure that was pushing the wall out. Thus, the resistive forces acting on the corners controlled the bulging of the wall on either sides, with the central part of the wall, where the resistive forces were absent, experiencing relatively greater displacement. Secondly, the effect of the rising and falling of the groundwater level inside the wall is mainly acting on the lower part of the wall, and the lateral pressure on the lower part is larger due to the self-load of the wall and the earth pressure against the upper part of the wall. When freezing-thawing occurs in the winter under such unbalanced pressure conditions, the material of the wall relaxes and the lower part of the wall subject to relatively strong pressure protrudes to the front.
Fig. 5. Schematic model image showing the deviation of southern-side wall in Yeonji.
To quantitatively determine the displacement that occurred in the Yeonji wall, the results showed that 30.25% of the point cloud data was within tolerance range or showing displacement in the direction into the wall, and about 70% of the wall was protruding in the front direction. The distribution of protruding lengths shows a decrease in frequency from about 20 mm to 130 mm above the tolerance range, with a sharp linear decrease
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from 20 mm to 80 mm, but a more moderate decrease beyond 80 mm. Since the wall is under pressure from the inside and towards the outside, it does not show a Gaussian distribution, but is interpreted as having a positive skewed distribution.
4 Discussion In this study, we analyzed the time-series movement and 3D geometric changes of the Yeonji wall using the measurement and 3D scanning data collected from 2014 to 2021. The micro-behavior analysis shows that no movement is observed in both sensors from spring to fall, but a sharp change in tilt occurs in winter. However, the T10 sensor shows a reversible movement where the tilt changes during the winter and returns to its original state in the spring, while the T11 sensor is characterized by an irreversible behavior where the tilt continuously increases. Therefore, there is no difference in the results from the T10 sensor before and after the rapid movement during winter, and it can be interpreted that the wall has recovered from the freeze-thaw action. However, 3D scanning data contradicts this, showing that the actual wall is deformed in the form of a frontal protrusion. This difference is due to the measurement method of the tiltmeter sensors attached to the wall, which means that the actual movement in a three-dimension can be distorted in the process of measuring the two-dimensional space defined by the X and Y axes. It is confirmed that the tilt of the attached stones increases sharply towards the outer side of the wall during the winter, and then returns back towards the inner side in the spring through detailed behavior of the T10 sensor. Thus, it is interpreted that stone of the wall move forward in case of that point where bottom of the stone touches acts as a lever. As the tilt of the stone increases, the lower surface of the masonry is fixated and rotates to the front of the wall, and as the tilt of the masonry decreases, the lower surface of the masonry is pushed to the front by the side pressure and rotates in the opposite direction. In this case, detecting the tilt behavior of the wall is difficult on sensor although real movement has occurred. Sensors that measure the changes in one- or two-dimensional space can distort the movement in a 3D space, and researchers must be aware of the direction of the object’s behavior to interpret it. While it is easy to determine the directionality of the behavior if the change is large enough and to identify structural deformation with the naked eye, most structures experience movements at the microscale. Because the sensors in the form of an attachment to the cultural heritage are measuring the relative motion of a building, there are many factors that can interfere with interpretation. Therefore, in order to improve the reliability of the measurement data, it is necessary to apply a monitoring technique that can apply an absolute coordinate system to perform a cross-comparison analysis with the measurement results. In this study, we used a 3D scanner to identify movements outside the measurement object. The scanner provided sufficient resolution to detect the wall movement, but without a ground-control point we could obtain only the relative deviation, not the absolute position coordinates of the wall. Therefore, establishing a long-term usable coordinate system is essential for building a 3D monitoring system. If the monitoring data are continuously accumulated and compared with past data, the tendency of the microbehavior can be identified. The reliability of short-term monitoring is not guaranteed
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when the wall exhibits only micro-behavior, as the result may fall within the tolerance range. However, it has been confirmed that long-term monitoring over several years can secure accurate data, enabling the stable management of masonry structures such as ramparts. The monitoring data collected over approximately seven years (2014–2021) verified that structural deformation causes continuous wall movement. In particular, we found that the main factors causing the deformation of the fortress wall are moisture inflow and freeze-thaw action in winter, and confirmed that lateral pressure is applied from the inside to the outside of the wall. In addition, previous studies that conducted GPR surveys in the Yeonji area reported the existence of a weakness zone behind the Yeonji wall, raising the possibility that soil was lost in the process of water inflow. Based on these findings, it was decided to dismantle and repair the Yeonji wall, and a structural reinforcement plan was proposed to resist external environmental factors that could cause structural deformation. There are two documented repairs to the Yeonji wall since the excavations in the 1980s, both of which consisted of simple leveling of the wall projecting outwardly. Therefore, the fundamental cause of the deformation remained the same, and the same type of structural deformation would occur again if only the exterior was maintained in the dismantling and repair this time. To control moisture ingress on the inside of the wall, it is necessary to install a water barrier and provide a drainage to allow the water to escape. However, the installation of such culverting and drainage facilities may compromise the authenticity of the cultural heritage. Therefore, the maintenance plan was designed with reference to traditional construction techniques. Although the structural deformation of the walls of Yeonji has been completely resolved, it is influenced by various environmental factors. Groundwater seepage causes soil loss and decreases the structural bearing capacity of the walls. Expansion of moisture caused by freezing imposes physical pressure on the walls. If the balance between structural resilience and external forces is disrupted, the wall may expand again. To detect such changes, the data of a tiltmeter sensor attached at the same location on the repaired wall of Yeonji must be continuously measured and analyzed.
5 Conclusion 1. The Gongsanseong Fortress is a World Cultural Heritage representing Baekje Kingdom, an ancient state in the southwestern part of the Korean Peninsula. More than 20 instrumented sensors are monitoring the microscopic behavior of the wall, with the largest changes detected at the pond site (Yeonji). It is located at the bottom of a valley that extends to the north, where groundwater and surface water from the area is collected. The south wall of the Yeonji, which faces the valley, has undergone structural deformation and is visibly protruding. 2. The sensor for determining the slightest movement of the flexible wall measures the change in the tilt of the wall in a two-dimensional space defined with the X and Y axes centered on the outer surface of the wall. There are two sensors installed in the Yeonji, both of which have a common problem: rapid changes in tilt are observed during the winter months. However, one sensor has a reversible change, while the other has an irreversible change and the tilt continues to increase.
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3. Comparing the environmental measurements with the microscopic behavior of the wall, we found that the movement of the wall is closely related to the temperature. Given that the change in tilt occurs every winter, and no change was detected when the average temperature was recorded, it was interpreted that it is directly affected by the freeze-thaw action of moisture. 4. Deviation analysis was performed by modeling the 3D scan data collected in 2014 and 2021. As a result, the wall of the Yeonji protruded at the front of the wall overall, and the structural deformation was centered aroound the bottom center of the wall. This is where the structural resistance is weakest, most susceptible to the effects of groundwater, and where the lateral pressure due to self-load is the strongest. The most deformed point protruded about 130 mm, and we found that about 70% of the total wall area was deformed. 5. In contrast to the results of the measurement sensors, which showed that the wall was restored after the change in tilt, the 3D deviation analysis showed that most of the wall was protruding forward. This is a distortion caused by the two-dimensional nature of the physical quantities measured by the sensor, which cannot reflect movements in a 3D space. In order to minimize these distortions, a monitoring method that allows the application of an absolute coordinate system should be combined with sensors that are attached to the building to allow observation of relative movements.
References 1. Park, J.H., Park, S.T., Lee, C.H.: Structural stability and microscale behaviors of the fortress wall from the sixth century Baekje Kingdom in ancient Korea. Heritage Science 9(1), 1–16 (2021). https://doi.org/10.1186/s40494-021-00539-8 2. Lee, C.H., Park, J.H.: Variation of paleotopography around the Ssangsujeong pavilion area in Gongsanseong fortress using GIS and 3D geospatial information. J. Conserv. Sci. 38(4), 347–359 (2022) 3. Kim, S.H., Lee, C.H., Jo, Y.H.: Behavioral characteristics and structural stability of the walls in the ancient Korean Royal Tombs from the sixth century Baekje Kingdom. Environ. Earth Sci. 79(3), 1–13 (2020). https://doi.org/10.1007/s12665-020-8819-6 4. Lee, C.H., Jo, Y.H., Kim, S.D.: Three-dimensional image analysis, deterioration evaluation and scientific conservation treatment of the Daechiri dinosaur trackways in Haman country, Korea. J. Geol. Soc. Korea 48(2), 179–191 (2012) 5. Kim, S.H., Lee, C.H., Jo, Y.H.: Digital documentation and short-term monitoring on original rampart wall of the Gyejoksanseong Fortress in Daejeon Korea. Econ. Environ. Geol. 52(2), 169–188 (2019) 6. Choi, I.K., Yang, H.R., Lee, C.H.: A study on digital documentation of precise monitoring for microscale displacements within the Tomb of King Muryeong and the Royal Tombs in Gongju Korea. J. Conserv. Sci. 37(6), 626–637 (2021)
Stability Interpretation for the Tomb of King Muryeong and the Royal Tombs in Baekje Kingdom of Ancient Korea Using 3D Deviation Analysis and Microscale Behavior Measurement Il Kyu Choi , Hye Ri Yang , and Chan Hee Lee(B) Department of Cultural Heritage Conservation Sciences, Kongju National University, Gongju 32588, Republic of Korea [email protected]
Abstract. The Tomb of King Muryeong and the Royal Tombs in Gongju, Republic of Korea has been registered as UNESCO World Heritage sites in 2015 regarding the values as one of the representative cultural heritages of the Woongjin period (475 to 538 AD) in Baekje Kingdom. After the excavation of tombs, several damages occurred due to rapid environmental change. This study uses a 3D precise scanning to visualize microscopic changes in wall composition materials that are difficult to distinguish using sensors and record 3D shape information on vulnerable parts within the tombs. In addition, the obtained data were used to calculate the displacement during the study period through comparative analysis with the previous data of the tomb complex. Based on the RMS deviation analysis, no visible deviation was found in the tolerance ranges ± 2 mm and ± 1 mm. The results indicate that no additional cracks or detachment occurred in all vulnerable parts. However, the displacement analysis confirmed the sagging behavior for the lintel in the Tomb No. 5, which also appeared in the position transducer installed at the Tomb No. 5, indicating that minute movement occurred. It is estimated that the steel supports currently supporting the lintel are not providing adequate support due to corrosion, therefore reinforcement should be considered. The results of this study are expected to be applied as important basic data in preparing and processing conservation measures for the Tomb of King Muryeong and Royal Tombs in Gongju in the future. Keywords: Tomb complex in Baekje Kingdom · 3D scanning · Displacement · Deviation analysis · Conservation measure
1 Introduction The Tomb of King Muryeong and the Royal Tombs in Gongju are registered as UNESCO World Heritage Sites and are preserved as cultural heritages representing the Woongijn period (475 to 538 AD) of Baekje Kingdom in ancient Korea. The targets of this study were the tombs of royal families during the Baekje Kingdom, and more than 20 tombs were known to have existed, but a total of 7 tombs are maintained in the current Royal © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 195–202, 2024. https://doi.org/10.1007/978-3-031-39450-8_16
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Tombs in Gongju (Fig. 1) [1]. In this study, monitoring was performed on the Tomb No. 5, Tomb No. 6 and the Tomb of King Muryeong (Fig. 2). Tomb No. 5 was built using gneiss, which are not uniform in shape. And plaster is applied in each wall, but only traces of it remain. Tomb No. 6 is made of bricks and murals are painted on the walls. The murals in the Tomb No. 6 are the only example in Korea painted on bricks. However, most of the murals have been lost, and only the base layer remains. The Tomb of King Muryeong is the only tomb in the Three Kingdoms Period that records the identity of the deceased and the construction date of the tomb. Since then, the Tomb of King Muryeong has become a standard for the study of tomb culture and chronological research during the Baekje Period, and it is evaluated as a cultural heritage that can examine the historical and cultural influence of neighboring countries at the time. However, after the royal tombs was opened to the public, various damages such as leaks, cracks and behavior of walls have been occurred due to rapid environmental changes inside the tombs [2, 3]. Therefore, scientific analysis was required, and comprehensive research on stability of tombs were studied [4–7]. However, measurement and monitoring of the inside of the tomb have been mainly carried out through precision measurement sensors, and research using three-dimensional scanning has been relatively less performed [8]. In this study, the vulnerable parts within the royal tombs were selected, and three-dimensional precision scanning was performed to visualize the micro displacement occurring inside the tomb compared to the preceding data and to check the progress of the damages.
2 Subject and Methodology Prior to 3D scanning, the vulnerable parts inside the Royal Tombs were selected [8]. In the Tomb No. 5, plastered stone walls with a high possibility of lime loss and lintel stones, which sagging occurred were selected in the four directions of the wall. There are murals inside the Tomb No. 6, and the durability has weakened due to weathering [3]. In this study, the cracks in the mural of the four directions were selected. In the Tomb of King Muryeong, the arch part of the burial entrance where observed downward movement of the bricks was selected as a scanning point. In this study, 3D precision scanning was performed with reference to previous studies [8], and the displacement inside the tomb was visually analyzed by comparing it with precision measurement data. A precision scanner (Artec3D, Eva, Luxembourg) was used to acquire 3D data for each tomb’s monitoring point. In the field, 3D data were acquired using Artec Studio software. The same program was used for post-processing of the received information. The completed polygon mesh was edited using the Geomagic Design X program. In addition, the completed data was analyzed for deviation by calculating the RMS (root mean square) with previous data, and displacement was visualized by comparing the vertical and horizontal distances between members. The analysis compared the changes between the data acquired in 2020 and the data obtained in 2021. And Geomagic Control X software was used for RMS deviation analysis.
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Fig.1. Geographic map of the Tomb of King Muryeong and the Royal Tombs in Gongju.
Fig. 2. Photographs showing the Tomb of King Muryeong and the Royal Tombs in Gongju. (A) Tomb No. 5. (B) Tomb No. 6. (C) Tomb of King Muryeong.
3 Results and Interpretation 3.1 RMS Deviation Analysis Based on the 3D scan data, RMS deviation analysis was performed on the plaster wall of the Tomb No. 5 differences between data were visualized by applying color differences to the results. The standard data was set to images acquired in 2020, and the tolerance range was set to ±2 mm for precise analysis. The deviation was not found in the tolerance range of ±2 mm in the case of the Tomb No. 5. This is believed to be because the tolerance set in the analysis is wider than the actual deviation, and further investigation was conducted by narrowing the tolerance range to ±1 mm for more precise analysis (Fig. 3). In this result, more than 94% of the average data were within the tolerance range (Table 1). Therefore, during the study period, it was interpreted that no additional damages such as peeling, exfoliation or break out occurred on the plaster wall of the Tomb No. 5, and it is observed to be relatively stable. In Tomb No. 6, RMS deviation analysis was conducted to identify microscopic changes, such as cracks and breaks out in the base layer of the mural. The analysis
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Fig. 3. Photographs showing the digital images of RMS deviation analysis of the vulnerable parts in the Tomb No. 5. (A, E) East wall. (B, F) West wall. (C, G) South wall. (D, H) North wall.
Table 1. Results of RMS deviation analysis for the Tomb No. 5 Tomb No. 5 Plaster wall
Within Tolerance
Out of tolerance
±2 mm
±1 mm
±2 mm
±1 mm
East
98.14
96.79
1.86
3.21
West
96.01
94.03
3.99
5.97
South
95.37
93.44
4.63
6.56
North
96.43
94.42
3.57
5.58
conditions were the same as those of the Tomb No. 5, and the tolerance range was set to ±2 mm and ±1 mm to conduct the analysis. And characteristic changes are not identified. But a small amount of deviation is confirmed in the joints between the members. This deviation was caused by the data error acquired between the three-dimensional shape information, not the actual exfoliation or break out of the joint (Fig. 4, Table 2).
Fig. 4. Photographs showing the digital images of RMS deviation analysis of the murals in the Tomb No. 6. (A, E) East wall. (B, F) West wall. (C, G) South wall. (D, H) North wall.
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Table 2. Results of RMS deviation analysis for the Tomb No. 6 Tomb No. 6 Mural
Within Tolerance
Out of tolerance
±2 mm
±1 mm
±2 mm
±1 mm
East
97.52
95.46
2.48
45.45
West
99.03
97.91
0.97
2.09
South
99.47
98.57
0.53
1.43
North
99.52
94.43
0.48
5.57
3.2 Displacement Analysis To analysis the deviation of the plaster wall, displacement on the entrance lintel stone was performed in the Tomb No. 5. The 3D data obtained in the study were used for the displacement analysis, and the distance between the members was measured by selecting 10 points in the vertical and horizontal directions on the lintel stone and the surrounding wall, respectively. Then the data was compared with the previous data in 2020 to identify the behavior of the lintel (Fig. 5).
Fig. 5. Measurement points for vertical and horizontal distances in lintel stone of the Tomb No. 5. (A, B) 3D data acquired in 2020. (C, D) 3D data acquired in 2021.
As a result of the displacement analysis of the lintel stone of the Tomb No. 5, it was found that between the lintel and the bottom of the entrance, the sinking occurred from 0.24 mm to 0.54 mm with average 0.40 mm in vertical direction. In addition, it was confirmed that the horizontal distance between the walls constituting the lintel part increased from 0.03 mm to 0.21 mm and average 0.12 mm (Table 3). It is considered that sinking occurs in the lintel stone of the Tomb No. 5, and that the wall that make up the entrance subjected to vertical loads are slightly pushed to the outside of the tomb. Through this, it was found that the lintel stone is currently in the process of sagging behavior. For the displacement analysis of the entrance arch in the Tomb of King Muryeong, the vertical and horizontal distances were calculated. This study compares the 3D data acquired in 2020 with the research data established in 2021 to review the behavior of the arch (Fig. 6). As a result, the entrance arch had a displacement between –0.11 to 0.09, and the average is −0.03 mm at 10 points appeared. But, both increase and decrease were observed depending on the point where the measurement was performed (Table 4).
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Table 3. Results of displacement in lintel stone within the Tomb No. 5. Point numbers are the same as those of Fig. 5 Displacement (mm) H1
H2
H3
H4
H5
H6
H7
H8
H9
H10
Mean
−0.33 −0.41 −0.32 −0.49 −0.34 −0.54 −0.45 −0.24 −0.41 −0.45 −0.40 W1
W2
W3
W4
W5
W6
W7
W8
W9
W10
Mean
0.12
0.08
0.21
0.13
0.15
0.03
0.12
0.17
0.09
0.11
0.12
The vertical distance was analyzed to examine the behavior of the arch ceiling downward moving member. This also shows the increase and decrease of the distance between the members according to the point in the same way as the arch part. It can be estimated that actual behavior occurred in the entrance arch during this study period. However, considering that the accuracy of the 3D scanner used for precision scanning is 0.1mm, both analysis points show errors within the accuracy, which can be interpreted as not showing actual behavior.
Fig. 6. Measurement points for vertical and horizontal distances in entrance arch within the Tomb of King Muryeong. (A, B) 3D data acquired in 2020. (C, D) 3D data acquired in 2021.
Table 4. Results of displacement in entrance arch within the Tomb of King Muryeong. Point numbers are the same as those of Fig. 6 Displacement(mm) H1
H2
0.03
−0.09 -0.07
H3
H11
H12
0.04
−0.08 -0.10
H13
H4
H5
0.09
−0.05 −0.08 0.05
H6
H7
H8
H9
H10
Mean
−0.06 −0.11 −0.03 −0.03 Mean −0.05
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4 Discussion and Conclusion In this study, to analyze the microscopic change of the Royal Tombs in Gongju, 3D precision scanning was performed to analyze deviation and displacement. An average of 95% appears within the allowable range at all analysis points set to tolerance range ±2 mm, and no damage is confirmed. However, it is possible that the set tolerance was larger than the deviation, so additional analysis was performed by narrowing the tolerance range to ±1 mm. As a result, an average of 93% was confirmed within the tolerance, and it is determined that no additional damage occurred. And it is interpreted that the actual behavior was not shown in the results of the displacement analysis on the arch of the Tomb of King Muryeong. As a results of the displacement analysis, it was found that sagging occurred in the lintel stone of the Tomb No. 5, and it was estimated that the wall of the entrance was outward the tomb. The sag of the lintel stone that occurred during this study period tends to be like the results reported in 2019 (vertical direction; 0.40 mm sag, horizontal direction; about 0.32 mm outward) and 2020 (vertical direction; 0.32 mm sag, horizontal direction; 0.36 mm outward). Considering these results, it can be seen that the lintel stone of the Tomb No. 5 is sagging every year by a certain amount. The sagging behavior of the lintel stone is also confirmed by the position transducer located at the entrance, during this study period, no rapid deflection displacement was found, but fine behavior appeared continuously (Fig. 7). When the results of displacement analysis through 3D scanning and the results of measuring instruments are analyzed together, it is discussed that sagging occurred in the lintel of the Tomb No. 5 during this study period.
Fig. 7. Diagram showing the displacement on position transducer of lintel in the Tomb No. 5.
The behavior of the wall can be checked through the behavior measurement sensor, but there is a limit to identifying the deformation with the naked eye because the behavior of the wall is minute. Therefore, displacement and deviation analysis were performed by constructing 3D shape data to visualize microscopic changes by selecting representative vulnerable parts for each tomb. The deviation was not visualized in both the tolerance
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ranges ± 2 mm and ±1 mm. In the displacement analysis, it is interpreted that behaviors do not occur inside the Tomb of King Muryeong, and the subsidence behavior of the lintel stone in the Tomb No. 5 was confirmed. This unusual behavior was also found in the position transducer. Currently, the steel support supporting the lintel is corroded, and its strength is weakened, so it is judged that the bearing capacity should be restored through reinforcement or replacement. And if changes are identified through continuous monitoring of the same point and reviewed together with precise measurement monitoring data, it will be an essential primary data for evaluating the structural stability of the Tomb of King Muryeong and the Royal Tombs in Gongju.
References 1. Jung, S.K.: A study on the Songsan-ri tombs, Gongju based on the data during the Japanese occupation of Korea. J. Central Inst. Cult. Heritage 10, 249–292 (2012) 2. Suh, M., Park, E.J.: Characteristics of subsurface movement and safety of the Songsanri tomb site of the Baekje dynasty using tiltmeter system. J. Eng. Geol. 7(3), 191–205 (1997) 3. Yoon, Y.H.: Sa-shin-do mural painting of No. 6 tomb in Kongju Songsanri. J. Stud. Korean History 33, 479–508 (2008) 4. Kim, S.H., Lee, C.H., Jo, Y.H.: Behavioral characteristics and structural stability of the walls in the ancient Korean royal tombs from the sixth century Baekje kingdom. Environ. Earth Sci. 79(3), 1–13 (2020). https://doi.org/10.1007/s12665-020-8819-6 5. Kim, S.H., Lee, C.H.: Interpretation on internal microclimatic characteristics and thermal environment stability of the royal tombs at Songsanri in Gongju Korea. J. Conser. Sci. 35(2), 99–115 (2019) 6. Suh, M., Lee, N.S., Choi, S.W., Kim, G.H., Jeong, S.M., Lee, G.B.: In-situ status and conservational strategy of the Muryong royal tomb, the Songsanri tomb No. 5 and the Songsanri Tomb No. 6 of Baekje dynasty. J. Nat. Sci. Kongju Nat. Univ. 7, 147–161 (1998) 7. Suh, M.: Geotechnical consideration on the conservation of the Muryong royal tomb. J. Conserv. Sci. 8(1), 40–50 (1999) 8. Choi, I.K., Yang, H.R., Lee, C.H.: A study on digital documentation of precise monitoring for microscale displacements within the tomb of king Muryeong and the royal tombs in Gongju Korea. J. Conserv. Sci. 37(6), 626–637 (2021)
Structural Analysis of Constructions by Means of Automatic Crack Parameterisation Based on Photographs Friedrich Romstedt1(B) , Sebastian Vetter2 , and Gunnar Siedler2 1 Trabert + Partner, Jean-Sibelius-Straße 18a, 99423 Weimar, Germany
[email protected] 2 fokus GmbH Leipzig, Lauchstädter Straße 20, 04229 Leipzig, Germany
Abstract. Constructions can show cracks due to mechanical stress. Such cracks have been investigated for decades by means of mapping and manual measurement of crack widths. During the formation of a crack, the flanks separate from each other. The shape of the crack flanks and the relative motion of the flanks are independent of each other. To draw precise conclusions from cracks observed in a construction, a quantitative parameterisation of these cracks is desirable. Often the crack opening width and the opening direction can be assumed to be homogenous at least in sections, defining a unique crack opening vector. Here we present algorithms to automatically characterise cracks by determination of their opening vector based on digital images. The algorithms presented here permit to perform a quantitative and reproducible analysis with weak subsidiary conditions imposed on the photographs. The central parameterisation algorithms are robust against many interfering picture properties and do not depend on the exact position of the crack under consideration within the photograph. The precision of the extracted parameters can be estimated based on a statistical analysis. By using the algorithms for the analysis of true-to-scale rectified images metrical quantities can be obtained. It is possible to integrate the developed applications into the documentation process. The methods can be used together with deformation analysis and other complementary techniques. When working with rectified images the rectification parameters might be transferred automatically between similar pictures; this might be used in the analysis of a temporal sequence of images or to improve detail resolution. The algorithms described here might be used as a basis for assessing the precision of the extracted crack parameters without the need of a statistical analysis. In a more distant perspective, patterns consisting of several cracks might be analysed and the overall relative motion of sections separated by cracks might be deduced, to carry out a combined analysis of several cracks. Keywords: Crack parameterisation · Image analysis · Non-destructive testing · Damage investigation · Deformation analysis
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 203–216, 2024. https://doi.org/10.1007/978-3-031-39450-8_17
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1 Introduction In this article, we present a novel method to characterise cracks based on digital photographs. The study is based on a set of sample data, comprised by artificial pictures as well as images derived from a photograph. For the generation of photograph-based input data, the picture shown on the left in Fig. 4 has been used. In many analysis steps, this image has been reduced in resolution and has been cropped to reduce the possible influence of the image regions aside of the crack. For some experiments, the image has also been pre-processed by bi-level threshold conversion, by edge detection and by edge detection followed by bi-level conversion. In addition, a Gauss blur has been applied to some images. Artificial images used were based on a randomised fractal Koch curve, whose lateral size has been reduced to avoid overlap of the artificial crack opening width and the curve’s line. The Koch curve has been chosen since it shows structure on all scales. The curve has been used as an artificial crack flank. By duplication of the single flank, sample pairs of flanks have been deduced. The interior between these flanks has been filled to construct homogenously filled cracks. Paralleling the pre-processing of the photograph, edge detection has also been applied to the artificial homogenously filled cracks. Several methods have been studied in a first attempt to automatically parameterise images from the test set. Some of these are well-known standard techniques in image analysis. The methods are listed here in their principal order of application: • A Fourier-theoretic approach based on the convolution theorem has been investigated. This method is based on the assumption that the input image can be described by a convolution of data describing the pathway of the crack and an image structure defining the local transversal properties of the crack image. Due to the convolution theorem, the two-dimensional Fourier transform of an entire crack picture described by these two components is the product of the component’s Fourier transforms. For such an image, the factor resulting from the second component introduces characteristic straight lines of zero magnitude, which can (in principle) be used to extract the opening vector. • For a set of potential crack opening vectors, both the quadratic difference sum over all corresponding point pairs as well as the autocorrelation of the input data have been investigated for flank pictures. Possible opening vectors optimise these quantities by forming local minima respectively maxima. While these methods partially have been demonstrated for a subset of the artificial data, none of them was applicable to the photograph-based input data. Following from these preliminary approaches, the fundamental methods described in Sects. 2 and 3 have been developed, which since then have successfully been used to analyse many more photographs. Results are given by a detailed example of applying the algorithms to a photograph in Sect. 4, and by describing in Sect. 5 automatic crack parameterisation in true-to-scale images, combined with tracing the crack pathway and together with deformation analysis data and quantity surveying. Sect. 6 discusses the results and the methods found. Subsequent questions and future directions are covered in Sect. 7.
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2 The Congruency Algorithm Since the two flanks of a crack originate from a separation of the whole plane, their shapes can be expected to be congruent with each other. In this case, for each point on one of the two flanks there exists a corresponding point on the other flank. Such pairs of points are called here congruent points. For any two points in the digital picture, we calculate the congruency of these two points as a scalar number. To derive the congruency, the local morphology of the digital input picture at the two positions in question is investigated, utilising a method described in Sect. 3. The congruency is symmetric about reversing the order of the two points involved. In almost all cases the congruency will have identical sign for all pairs of congruent points belonging to the two flanks of a crack. Cracks which lead to positive congruency values for congruent point pairs are called here normal cracks, while cracks with negative congruencies for pairs of congruent points are called antinormal cracks. For two points which are not congruent with each other, the congruency calculated for such a point pair will have zero expectation value. The numerical congruency values of any such two points will have some value, but when sampling different non-congruent point pairs in the photograph, the sign and magnitude of the congruency will vary, depending on the image structure. When all pairs of congruent points along the crack flanks share a common difference vector, this vector can be called the crack separation vector. Possible synonyms are crack opening vector, opening vector and crack vector. Given a certain difference vector, it is possible to add the congruencies of all point pairs in the input picture which are separated by this difference vector. The result is called here the congruency sum of the difference vector under consideration. The difference vector used for this calculation can be chosen freely. When the difference vector matches the opening vector of a crack depicted in the photograph, the congruencies of all congruent point pairs of the crack will accumulate, since their congruencies all have the same sign. If there is no such match with a crack’s opening vector, the congruencies will approximately cancel each other, and the expectation value of the congruency sum will be zero. For normal cracks, the corresponding congruency sum will have positive sign; antinormal cracks feature a negative congruency sum. To apply this method, it is not required to distinguish between pairs of points which are congruent and those which are not congruent with respect to a given crack. The scalar congruency property of point pairs covers both. Furthermore, calculating the congruency sum for a given difference vector does not require a localisation of the crack in question. The value of the congruency sum can be used on its own as a means to identify difference vectors which are characteristic for a specific crack. Tabulating the congruency sum for all possible difference vectors results in a map of the congruency sum. This map is called here the crack map. A position (x, y) in this map corresponds to the difference vector having the same cartesian components. Since the congruency of any point pair is independent of the order of the two points, the congruency sum is symmetric with respect to inversion of the corresponding difference vector, and the value at position (x, y) in the crack map equals the value at (−x, −y). Based on
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→ this observation, each difference vector − v can be identified with its complementary − → counterpart − v , such that both of these representations are considered as equivalent. In Fig. 1 a schematic of a typical situation is given. On the left side of Fig. 1, the coordinate system of a crack map is shown with its origin of coordinates in the centre, together with difference vectors indicated by red and blue arrows, measured from the centre of coordinates. On the right side of Fig. 1, an image map is given with the two flanks of a crack depicted by a pair of bent lines. For two separation vectors, several selected pairs in the crack image are marked by red and blue solid double-sided arrows. Flank points which are part of one of these pairs are highlighted by coloured dots. For each of the separation vectors, the two point-symmetric equivalent orientations are given in the crack map by dashed and dotted vectors of the same length. The red difference vector matches the crack’s opening vector very well, while the signal of the blue difference vector won’t feature a pronounced accumulation of congruencies.
Fig. 1. Illustration of the congruency algorithm.
Difference vectors which are prominent crack vectors can be characterised as local extrema of the crack map. Locations in the crack map constituting a local maximum are called normal signals, while the positions of local minima are called antinormal signals, paralleling the nomenclature introduced for the cracks and their congruency sums.1 For a given difference vector, the congruency contribution to the corresponding location in the crack map can be calculated for a specific point in the picture, which belongs to two point pairs in the image map for such a contribution. For each point in the picture, we calculate the sum of these two congruencies. The resulting plot is called here a localisation map. The localisation map of a crack vector will show large values especially for crack flank points, while featuring a zero-valued background. A localisation map selectively shows the relevant crack structures, and localising a signal calculated by the congruency algorithm can help spotting inhomogeneities of the crack studied, when the localisation signal of the crack vector under consideration is not present in certain sections along a given crack. The crack map covers the zero-difference vector. The congruency sum for this zero vector compares the local morphologies at all image points with themselves. It turns out 1 Important maxima of a crack map are of positive sign, while relevant minima feature negative
values.
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that the corresponding congruencies are of pronounced antinormal character; the sum of this self-congruencies over the whole picture amounts to a large negative value. It is very likely that in this way the crack map’s negative global extremum is located at this point in its origin of coordinates. Most cracks are of normal nature, i.e., they contribute positive congruencies to the total congruency sum of their crack vector. It suffices to locate the global maximum position in the crack map in order to identify the most prominent normal-nature crack vector in the picture.
3 Implementation of the Congruency Algorithm Using Vectorial Autocorrelation of Gradients Let the digital input image be given in the form of a scalar greyscale value s on a rectangular subset of Z2 . We characterise the local morphology by the gradient of s, − → → called − g = ∇ s. For a crack flank point, the local direction of the gradient and the local tangent to the crack flank are assumed to form an orthogonal pair. Under this assumption, the local gradient direction is determined by the shape of the crack flank. The gradient is independent of the orientation of the separation vector. However, given the congruency of the two crack flanks, the gradients at two congruent points can be expected to be either parallel or antiparallel. This situation is outlined in Fig. 2, where the gradients orthogonal to the flanks are shown in antiparallel configuration. → → → → p2 ∈ Z2 , c − p1 , − p2 , as the signWe define the congruency c of two points − p1 , − inverted scalar product of the gradients at the two positions: → − → → − → g − p1 · → g − p2 (1) p2 = −− c − p1 , → For the majority of all crack pictures, the crack interior has a particular characteristic colour, which is different from the colour of the region surrounding the crack. Such → − → p2 along the cracks feature antiparallel gradients for any two congruent points p1 and − − − → → flanks. Thus, these cracks have positive congruency c p1 , p2 for any such point pair. Under certain circumstances, the gradients at congruent flank positions can be oriented in the same direction, being parallel in the narrow sense, when the crack has features leading to dissimilar colour combinations at the flank positions. This can appear when, e.g., one of the two flanks casts a dark shadow while the interior section of the crack has lighter colour than the surrounding region. In such a situation, the congruency will have negative sign—the crack is antinormal. Principal examples for cross sections of both a normal crack as well as of an antinormal crack are shown in Fig. 3. It can be assumed that both cross sections shown in Fig. 3 contain a pair of congruent points. The actual gradients are in most cases not contained by the cross-sectional plane (see Fig. 2); for accuracy, the arrows in Fig. 3 might be assumed to show the one-dimensional projections of the two-dimensional gradients into the plane of the cross section. The left diagram in Fig. 3 shows a dark crack (in the inner section) with light surroundings—a typical configuration. The right diagram of Fig. 3 can be considered as an example showing a dark shadow at the left crack flank with a crack interior otherwise lighter than the area containing the crack.
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Fig. 2. Schematic for pairs of congruent points and the local gradients of the image map s. The two bent lines depict the crack flanks, which are an exact replica of each other. At two positions the separation vector is drawn as a double-sided arrow. For both locations possible gradient directions at the congruent positions are shown by arrows with outward-directed arrow heads.
Fig. 3. Principal behaviour of the gradient directions for two crack topology examples. Shown is the cross section of a normal crack on the left and of an antinormal crack on the right. For both of them, the value of the picture is shown as the ordinate and the position along the picture cross section forms the abscissa. The approximate positions of the crack flanks are shown by vertical dashed lines, their slope in the cross section is depicted by their tangents as dotted lines. The gradient directions are indicated by arrows.
→ → For a given separation vector − v , the congruency sum C − v for this vector is given by: → − → − → − → C − v = − →c p , p + v p
(2)
which is the sum of the congruencies of all point pairs separated by the difference vector − → v . With the definition of c as given by Eq. (1), this amounts to: − → →− → − →− → − → (3) C − v =− − → g p · g p + v p
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→ Writing − g =
g1 g2
, we obtain:
− → − → − → − → → − → − → C − v =− − → g1 p g1 p + v + g2 p g2 p + v
(4)
− − − − − → → → − → → → − → C v =− − − → g1 p g1 p + v − → g2 p g2 p + v
(5)
p
or:
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p
p
The correlation of two scalar-valued functions f and g on Z2 , written as f defined as:
f
g
f p g p
g , is (6)
p
For a scalar-valued function h on Z2 , the correlation h h is termed the auto-correlation of h. The autocorrelation of any such function h is symmetric about inversion of its argument:
h
h
h
h
(7)
The congruency sum C as given by Eq. (5) is a sum of sign-inverted autocorrelations:
C g1
g1 g2
g2
(8)
It inherits the symmetry of the autocorrelations: C(v ) = C(−v )
(9)
→ The map of C over its arguments − v ∈ Z2 is the crack map of the picture analysed. The autocorrelations involved can be calculated using the Discrete Fourier Transform (DFT), which is implemented very efficiently by the Fast Fourier Transform (FFT). Because the congruency sum C, as defined by Eq. (3), can be said to be the → (sign-inverted) autocorrelation of the gradient − g , we call this algorithm a vectorial autocorrelation of gradients.
4 Example of a Crack Parameterisation All figures presented in this section were created using an all-graphical program developed by the first author at Trabert + Partner. This application permits one to open, crop and scale several image files, but does not permit a correction for perspective distortion. Selected regions of the resulting images are then subjected to crack analysis.
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An example for a photograph showing a wall crack is given in the left part of Fig. 4, together with the crack map of the entire photograph in the centre and on the right side. The demonstration picture chosen here has several properties which pose challenges for automatic crack parameterisation: • the crack interior shows a rich structure, resulting from different layers of the cracked material; • the wallpaper covering the cracked wall shows structure due to grains in the wallpaper. The crack vector shown in the centre and on the right of Fig. 4 was extracted from the crack map fully automatically by locating the global maximum of the crack map. Due to the symmetry of the crack map, there are two such locations with mathematically identical congruency sums. The algorithm picks one of the two positions without preference and constructs the other by inverting the found crack vector’s components. To calculate a crack map, the difference vector coordinates considered need to be limited; in Fig. 4 an upper bound is imposed on their absolute value. In the central part of Fig. 4 this bound has been chosen manually, based on a visual guess given graphically in the input image, while on the right side of Fig. 4 the absolute values of the difference vector coordinates are bounded by the longer edge length of the entire picture. The coordinates of the global maximum in the right map of Fig. 4 are identical to those in the central part of that figure; the actual positions in the plots depend on the respective scale. By inserting the crack opening vector found at positions chosen graphically using the mouse cursor the result can be verified. Such a display of the crack vector is provided in the centre part of Fig. 5.
Fig. 4. Example of a wall crack photograph to be analysed (left) together with the resulting crack map (centre and right). Blue dots mark the extracted crack vector. The central part of the figure shows the inner section of the map on the right. Zero congruency sums are shown in mid-grey, positive values are lighter, negative values darker. The origin of coordinates is located in the centre of the two crack maps.
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Localisation maps (cf. Sect. 2) for the determined opening vector are given in the right parts of Figs. 5, 6 and 7. The central parts of these figures and the respective plot on the right show exactly the same section of the input picture. An orange square in the pictures on the left of Figs. 5, 6 and 7 indicates the precise location of the detail sections in the centre and on the right. To visualise the localisation maps, white corresponds to zero value, while the darkness increases with the absolute value of the total congruency contribution of each point. Figure 5 shows a subset of roughly the lower-half input picture, where the signal obtained from the whole input picture is strongly localised. This is in accordance with the abundance of positions in the centre part of Fig. 5, where the human eye can easily spot congruent point pairs along the crack flanks in accordance with the extracted crack vector. The upper-half part of the input image however does not feature pronounced localisation of the overall crack vector, as shown in Figs. 6 and 7. Figure 7 covers a detail of the image together with some example positions of the opening vector extracted from the whole picture. Here, the human eye can clearly discern a discrepancy in the y component. The lack of contribution from the upper part of the image to this signal indicates an inhomogeneity of the opening vector: The most prominent crack opening vector is not present in the upper portion of the image studied.
Fig. 5. Crack vector indicators (blue double-sided arrows in the centre part) and the corresponding crack signal localisation map (on the right) for the lower half of the input picture.
Fig. 6. The crack signal localisation for the upper half of the input picture. The signal resulting from the whole picture is weakly localised in the upper part of the picture, as visible on the right. Because of this low degree of localisation in the sections extending beyond those shown in Fig. 5, the crack vector is not indicated in the central part.
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Fig. 7. Mismatch of the extracted crack vector in a detail of the image studied. The crack vector obtained from the entire image is shown in the centre image by blue double-sided arrows at two positions. The right-hand side plot shows the localisation map corresponding to the detail shown in the centre.
5 Crack Parameterisation in True-to-Scale Image Plans The central algorithm has been integrated into the software metigo® MAP [3], to permit true-to-scale crack parameterisation together with perspective distortion correction, and to combine crack analysis with other techniques in one single image plan. The integration codes have been supplied by the first author; metigo® MAP is developed by fokus GmbH Leipzig. The crack parameterisation algorithm as described in Sect. 2 and 3, applied to one single section of the input image, results in a single crack vector, characterised by opening width and opening direction. Examples of such parameterisations in metigo® MAP are shown in the left part of Fig. 8, together with accompanying data shown in the right section of the same figure. In metigo® MAP, an additional algorithm has been developed to detect the actual pathway of the crack in a rectified image. Based on a simplified polygonal line close to the crack provided by the user, the crack is followed in detail. It is possible to perform automated crack parameterisation repeatedly along the pathway using a sliding window of user-specified size. Based on these multiple measurements, the parameters can be characterised by mean and standard deviation. An example is given in the centre part of Fig. 8. Furthermore, it is possible to combine crack parameterisation with deformation analysis and quantity surveying (see Fig. 9).
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Fig. 8. Performing crack analysis in metigo® MAP. On the left, the congruency algorithm has been applied to two sections (red rectangles), which have been analysed independently from each other. The extracted opening directions and crack widths in millimetres are indicated by red figures. In the centre, metigo® MAP has been used to extract the pathway of a crack, and statistical properties of multiple measurements along the pathway have been determined. The guiding polygonal line provided by the user is shown in green, the detected pathway is displayed in red, and the statistical properties are given in the red annotation. The interface component on the right for the data belonging to the top-right region in the left part of the figure shows the analysed image section and its crack map.
Fig. 9. Combining deformation analysis based on 3D laser scans with automated crack parameterisation and quantity survey in metigo® MAP.
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6 Discussion Several methods using analogue techniques for measuring the opening width of cracks exist, all of them based on estimation of the crack opening width by comparison with some scale held next to the crack. There are only few established methods for crack parameterisation based on digital photographs known to the authors (see [1] and [2]). These are based on identifying cracks in a photograph in terms of their position, and the subsequent extraction of parameters of the cracks detected. For example, [1] uses a Polyline-Fly-Fisher Algorithm to trace the pathway of a given crack, and determines the local crack width by characterising cross-sections of the photograph perpendicular to the extracted crack flank direction. The approach presented here has some advantages with respect to such designs: • To extract the most prominent signal of the crack map, no reference is made to the origin of this signal. There is no need to extract a contiguous polygonal shape of the crack under investigation, and the congruency algorithm does not require the identification of crack flank points. These properties reduce the number of influences limiting the overall stability and robustness of the algorithms. Signal localisation can provide additional information about the actual location of the crack studied and its homogeneity. • As can be seen from Fig. 1 and Fig. 2, the width perpendicular to the flanks of the crack underestimates the entire crack opening width when the crack opening vector is not perpendicular to the crack flanks. Such an estimation technique approximately measures the projection of the total opening distance onto the direction of measurement perpendicular to the tangent. The perpendicular flank distance calculated in this way can vary with the position along the crack with the tangent direction, even when the actual crack opening vector is homogenous. The opening vector extracted using the congruency algorithm is independent of the crack flank orientation. • To calculate a congruency, it is not required to analyse cross sections of the crack. This permits to successfully analyse cracks with rich inner structure between the crack flanks (see Sect. 4). The algorithms presented here can be used to extract a crack vector, but neither the crack map itself nor the localisation of one of its signals can directly provide a way to estimate the precision of such an outcome. A statistical analysis of multiple measurements of the crack parameters in different locations is implemented in metigo® MAP; this statistical method requires the determination of the crack’s pathway. A requirement of the congruency algorithm is the homogeneity of the crack opening direction and opening width in the section analysed. Only under these circumstances can a unique crack opening vector be defined. A way of handling inhomogeneities consists in performing congruency analysis in sections of the entire crack, to reduce the total inhomogeneity in each of the sections. The applicability of the algorithms requires furthermore a sufficient variability of the tangent directions. For example, when the crack flanks analysed feature only one single tangent direction, the crack opening vector cannot be fixed along this tangent direction. A long-standing issue is the automatic detection of antinormal (negative) signals. Algorithms for this task need to distinguish the crack map’s signals of interest from the
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strong negative signal in its centre, which usually forms the global minimum of the crack map. The task is complicated by the fact that this central anti-normal signal has wings reaching into the outer areas (see Fig. 4).
7 Outlook The precision of a crack signal extracted from a crack map might be characterised by derived quantities without the need to perform a statistical analysis. The principal ideas involved do not require the approximation of the crack by a polygon. Such an analysis would complement the estimation of the precision from repeated crack analysis along a pathway as it is already implemented in metigo® MAP. An algorithmic idea to characterise the variability of the tangent directions exists, to indicate insufficient tangent variability. This algorithm does not require a localisation of the crack as well. Upcoming advancements of the algorithms for the automated crack parameterisation might be integrated into metigo® MAP. This would further improve the basis for automated pattern recognition of cracks and for the combination with deformation analysis. In metigo® MAP, it might also be possible to utilise image registration for the analysis of a temporal image sequence or to enhance resolution by using detail images. It might be feasible to analyse crack patterns with respect to the damage-less sections they separate; in this way, the overall relative motion of these sections might be deduced. The localisation map of a crack signal might be useful in automatically determining the pathway of the crack under consideration. To reliably extract antinormal signals some approaches have been identified. In this article, we skipped some questions about how to display crack maps and localisation maps with an appropriate scaling of values. These tasks pose some difficulties since many areas of the respective maps are empty. Furthermore, the details about how to calculate the crack map using FFT have been skipped. Results concerning this questions and mathematical details of the image processing methods will be provided in a forthcoming manuscript. Acknowledgements. The work presented here has been carried out as part of the OPDETRISS project, Verfahren zur optischen Erfassung von Oberflächenveränderungen und Entwicklung einer Software zur Detektion von Rissen und Verformungen an Mauerwerks(konstruktionen), an R&D project supported by the German Federal Ministry for Economic Affairs and Energy (Bundesministerium für Wirtschaft und Energie) on the basis of a decision of the German Bundestag, part of the plan „Zentrales Innovationsprogramm Mittelstand (ZIM)“. OPDETRISS was a collaboration of Trabert + Partner, fokus GmbH Leipzig and the MFPA (Materialforschungs- und -prüfanstalt) Weimar. The MFPA Weimar carried out investigations of damage in two objects caused by drift minerals and, in parallel, conducted laboratory and pilot plant experiments to reproduce the phenomena observed. One focus was research of connections between deformation and crack formation during the creation of drift minerals in gypsum-containing masonry on the basis of stripe light measurements. The first author acknowledges a very constructive and productive collaboration with the second and third author. Thanks for suggestions and proof reading of this manuscript go to Dr. med. Peter Buske, Dr. Frederic V. Hessman, Prof. Dr. Tim Salditt, Dr. Axel Schüler, Dr. Hans-Werner Zier and Katharina Sandmann. The first author wishes to thank especially Dr. Josef Trabert, who generously supported this work in his position as the owner of Trabert + Partner.
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References 1. Niemeier, W., Stratmann, R., et al.: Rissmonitoring in der modernen Bauwerksunterhaltung. Der Prüfingenieur 31, 51–59 (2007) 2. Lins, R.G., Givigi, S.N.: Automatic crack detection and measurement based on image analysis. IEEE Trans. on Instr. and Meas. 65(3), 583–590 (2016) 3. Siedler, G., Vetter, S., Kaminsky, J.: Data acquisition, management and evaluation for stone conservation projects with digital mapping. In: Roca, P., Pelà, L., Molins, C. (eds.): 12th International Conference on Structural Analysis of Historical Constructions SAHC 2020
Simplified Assessment of the in-Plane Seismic Response of Old Brick Masonry Building Aggregates Using DE Macro-Crack Networks Zinan Zhang(B) , Lucy Davis, and Daniele Malomo McGill University, Montréal, QC H3A0C3, Canada [email protected]
Abstract. Old buildings were often constructed adjacent to each other, without the minimum gap recommended by modern codes. This further increases their seismic vulnerability by exposure to the risk of pounding, a complex mechanism involving repeated impacts between adjacent buildings. Although post-earthquake surveys worldwide confirmed that seismic pounding can significantly increase the extent of in-plane damage and cause early collapses, this phenomenon still remains largely unexplored, while ad-hoc assessment guidelines are missing. This preliminary study focuses on investigating the mechanical in-plane interaction among lowrise unreinforced masonry (URM) buildings of clay brick, a seismically vulnerable yet common structural typology across Canada and abroad. The main novelties consist in the unprecedented use for this task of experimentally validated numerical models developed in the Distinct Element Method (DEM) framework, enabling us to map accurately crack propagation up to collapse, as well as the quantification of key material and geometrical factors affecting earthquake performance. To reduce the otherwise prohibitive computational expense typically entailed by DEM and consider building-scale models, a new macro-modelling strategy is devised that idealizes masonry as an assembly of solid rigid blocks connected by nonlinear interface springs, forming an equivalent macro-crack network where failure occurs according to linearized softening joint constitutive laws. Using this expedited yet accurate analysis technique, a comprehensive parametric study is conducted to investigate the pounding of adjacent URM façades of varying height, material degradation levels and opening layout, tested under pushover loading schemes. Preliminary results, which also account for the stochastic nature of the mechanical properties of masonry, seem to suggest that the severity of damage due to building interaction is particularly dependent on the material properties, adjacent building numbers and the building height. These results will inform ongoing research on seismic pounding at McGill University, where the effect of dynamic loading will also be considered. Keywords: Seismic Pounding · Unreinforced Masonry · Clay Brick · Macro-Modelling · Discrete Element Method
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 217–231, 2024. https://doi.org/10.1007/978-3-031-39450-8_18
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1 Introduction The interaction of adjacent buildings in the event of an earthquake, a phenomenon known as pounding, creates large stresses due to continuous impacts which can induce high levels of damage, potentially causing local or global collapse. Masonry structures, already vulnerable to seismic events, are particularly vulnerable to this phenomenon when part of a building aggregate due to the probable variability in dynamic response based on construction technique, geometrical complexity and material properties [1]. To diminish the risk of these interactions, one method modern building codes (i.e., the International Building Code (IBC) 2018, National Building Code of Canada (NBCC) 2015) implement is a separation between adjacent buildings. However, many old urban centers around the world are characterized by predominantly masonry structures constructed progressively with little to no separation between adjacent buildings (see Fig. 1) [2]. Unreinforced masonry (URM) structures, often experiencing poor performance under lateral loads, are the leading cause of seismic fatalities and economic losses worldwide [3]. In old urban centers, many neighboring structures built without separation are non-engineered low-rise URM structures [4], represent a serious threat to public safety and architectural heritage. URM buildings constructed in this pattern (herein referred to as building aggregates) are highly complex structures. Assessment of the seismic vulnerability of existing URM building aggregates is often more challenging than evaluating those of isolated assemblies due to irregular façade openings, multiple construction periods and varying conservation states [5]. While numerous studies in the past decade have reported frequent structural failures in old URM building aggregates during earthquakes, research to assess the effects of pounding on old URM building aggregates is limited. In the 1985 Mexico City (Mexico) earthquake (Mw = 8.0), pounding damage was detected in over 40% of 330 collapsed or severely damaged buildings surveyed and in 15% of all cases it was identified as the main cause of collapse [6]. In the 1971 San Fernando (California, USA) earthquake (Mw = 6.9), a series of pounding-induced failures were observed, of which most of the damages were localized in building aggregates [7]. Additionally, photographic surveys after the 2010 Christchurch (New Zealand) earthquake (Mw = 6.3) portrayed the severe damage present in URM aggregates due to pounding [8]. In the last 30 years, a growing interest in assessing the influence of pounding on the seismic performance of existing buildings has resulted in several studies on steel [9] and reinforced concrete (RC) [10] buildings, focusing on their dynamic interactions [11] either experimentally or numerically. However, limited studies on URM have been conducted thus far [12]. The seismic evaluation of URM buildings is a particularly difficult task, and developing reliable methods for analyzing the earthquake response of URM building aggregates is still an ongoing challenge. This is due, in part, to a lack of experimental data on the seismic response of building aggregates that could be used as a benchmark for calibrating numerical and analytical models in addition to the brittle, highly nonlinear anisotropic behaviour and failure mechanisms typical of URM buildings. Numerical approaches are often utilized to generate representative models of URM buildings under earthquake loading. Accepted in the industry as the most reliable method to gather accurate information on the seismic response, numerical approaches mainly include continuum or discrete element-based techniques. In a continuum-based analysis, Finite Element Modeling (FEM) is a common tool to model the seismic behaviour
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of historical URM buildings under earthquake motion [13], albeit modelling contact, re-contact and separation phenomena typical of pounding motion is challenging due to nodal compatibility issues. Discrete approaches [14-16] and in particular the Distinct Element Method (DEM), based on the mechanical interaction among discrete bodies connected through interface joint springs and originally developed by Cundall [17], are naturally suitable to simulate cracking, material discontinuities and collisions. Due to the high computational expense typically required, very few applications concerning the DEM modelling of large structures are documented in the literature [18-20] and in many cases lack experimental comparisons. In this paper, a novel simplified DEM model based on macro-crack networks is employed to reduce computational burden and allow the discrete simulation of the in-plane response of URM building aggregates. This paper includes results of mechanical interaction among adjacent buildings using quasi-static loading to better understand the main influencing factors of damage extent in seismic pounding cases. These factors are analyzed in a parametric analysis that evaluate the influence on the lateral response of the number of adjacent structures, height difference in adjacent structures and level of material degradation.
Fig. 1. Examples of old URM building aggregates in (left) Québec City (Canada) (right) Siena (Italy)
2 Preliminary Validation Against Experimental and Micro-modelling Results The novel DEM strategy employed in this research, denoted as the DE macro-crack network (Fig. 2a), employs macro-scale blocks representing masonry units and mortar joints. The macro-blocks are sized based on informed crack pattern predictions. In this modelling strategy, previously validated against multiple experimental tests and numerical results [34], the deformability of the system is lumped in the joints. Masonry joints are idealized as zero-thickness nonlinear spring interfaces at contact points between macroblocks where the deformability of the system is lumped and separation (or macro-cracks) occurs. The number of joints is fixed for each URM component (pier, spandrel or node) based on the Equivalent Frame Model (EFM) [21], resulting in multi-scale assemblies of eight rectangular interlocking rigid macro-blocks arranged in three layers. As shown
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in Fig. 2b, this simplified discretization scheme was derived from the observation of the most common in-plane (IP) failure modes of both URM spandrels and piers [22, 23], namely top sliding (TS), diagonal shear (DS), rocking (R) and toe crushing (C). The macro-blocks are arranged to accurately simulate IP and out-of-plane (OOP) failure modes. The resulting macro-crack network is symmetrical, and loads can be applied along any axial direction. An automated geometry-generation code for easily generating the DE macro-crack network of any 2D and 3D configuration was developed using the visual programming language Grasshopper [24], a plugin for the 3D geometrical modelling software Rhinoceros. Figure 2c illustrates how this program meshes a planar element into a 3D solid using the discretization method to instantly generate DE macro-models.
Fig. 2. (a) DE macro-crack networks for a URM panel, (b) IP failure modes and (c) modelgeneration schematic in Grasshopper
Providing that the geometry is rectangular, this program could be applied to any component or façade with different aspect ratios and/or opening layouts. This strategy is particularly suitable for modelling large-scale complex façades, as discussed in the following sections, dramatically reducing geometrical modelling time. Mechanical interaction between adjacent macro-blocks is analyzed along the contact surfaces in the DE macro-crack network. Contact stresses are calculated in the normal (σ) and shear (τ) directions based on the assigned contact stiffness of each spring (normal stiffness kn and shear stiffness ks ) respectively. Inelastic properties of the springs in the normal and shear directions can also be defined, including the tensile strength (ft ), compressive strength (fc ), cohesion (c) and friction angle (φ). The same mechanical properties are assigned to head and bed joints [25]. To account for the complex nonlinear behaviour and to capture all possible failure modes, a new softening contact model developed by Pulatsu et. al [26] was implemented. In this contact model, the nonlinear post-peak response of the material (in tension, compression and shear) is considered according to parabolic, multi-linear or linear functions (see Fig. 3). The preliminary validation of the proposed macro-modelling scheme was conducted on a full-scale two-storey URM façade with regular opening layouts (configuration 1 in Fig. 4a) tested at the University of Pavia [27]. The gravity loads (248.4 kN on the first floor, 236.8 kN on the second floor) and the monotonic pushover loads were applied through a series of isolated steel beams. In the numerical model, the façade was divided
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Fig. 3. Strain-softening model by Pulatsu et. al. [26] in (a) normal and (b) shear directions
into a total of 16 primary URM components and further subdivided into 144 rigid macroblocks. Moreover, the steel beams were modelled as rigid solid elements of reduced thickness (“beam plates” hereinafter) fixed to the façade, to which vertical loads and the horizontal loads were applied to simulate the distributed gravity loads and the pushover loads respectively. To ensure a strong connection, pure elastic material was applied in the joints between the beam plates and the façade so that no tension and shear failure is allowed. Depending on the availability of the experimental data, some parameters are taken from experimental results, whereas other parameters are estimated, considering [28, 29], indicated by the symbol *. The contact properties are summarized in Table 1, where Gc , Gt and Gs are fracture energy in compression, tension and shear, respectively. Young’s modulus of masonry, Em , and the shear modulus, Gm , , (Gm = 0.4Em ) are used to infer normal (kn = Em /H ) and shear (ks = Gm /H ) stiffnesses of the interface springs in the numerical model. Within each macro-crack network the masonry properties of Table 1 were used. At the vertical interfaces between URM components, to represent the expected interlocking strength, inelastic brick properties of Table 1 are assigned. To validate the model, the horizontal displacement of the façade was recorded at the top-left corner of the leftmost steel beam on the second floor indicated in blue dots in Fig. 4a and the force-displacement curve of the macro-model was compared to the experimental results and a similar DEM micro-model [25]. To further validate the modelling accuracy of the proposed modelling strategy when considering irregular opening layouts, four addition tests on clay brick two-storey façades of different opening arrangements were selected according to Parisi and Augenti [30] under IP monotonic pushover loads. Modifications were made to the original façade (configuration 1), pertaining to the layout of door and opening sizes (see Fig. 4a configuration 2–5) [26]. The material properties of the four walls with irregular openings are defined according to Table 1. Force-displacement curves were then compared to equivalent DEM micro-models, replicating original brick sizes and bond patterns of experimental façades [31]. Due to time constraints, the micro-model analysis of configuration 5 was not conducted in the referenced paper, and the result of an Equivalent Frame Method (EFM) analysis (presented in the same paper) is taken as a reference instead [26].
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Gm
fc
ft
c
φ
Gc
GIf
GII f
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[◦ ]
[N/m]
[N/m]
[N/m]
masonry
1491
596*
6.2
0.05
0.075
30
10000*
5*
20*
bricks
1491
596*
15
1*
1.5*
35*
20640*
80*
125*
material ID
Results of the validation, displayed in Fig. 4b, display good correlation between modelling strategies and experimental results. Similar damage patterns, initial lateral stiffness, and shear force capacity were obtained even when analyzed under monotonic load, as compared to the cyclic envelope of the experimental model in both loading. The lateral capacity of configuration 1 is slightly underestimated (approximately 10%) which is likely the result of the different loading protocols, namely monotonic vs. cyclic. Additionally, configurations 2–5 display a good agreement between the micro- and macro-models for initial lateral stiffness and shear force capacity in both negative and positive directions, with a difference under 8% and 10% respectively (see Fig. 4c). The damage patterns between both models (Fig. 4d) are consistent as well.
Fig. 4. (a) DEM macro-models of selected façades; (b) experimental vs numerical forcedisplacement curves and damage patterns; micro- vs macro- (c) initial stiffness and shear force capacity, (d) deformed shape and damage pattern
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It is worth noting that the macro-model, despite proving comparable results, was almost x50 faster than its micro-model counterpart. Due to the good correlation achieved in the validation of the novel macro-modelling strategy, this strategy has been further implemented into the parametric analysis of the URM aggregates presented below.
3 Numerical Parametric Study Methods Masonry building aggregates may originate from progressive construction periods typical of old structures. As cities and towns grow, adjacent masonry buildings may contain materials of various ages. In addition, traditional construction practices do not consistently feature the same structural system in masonry aggregates. In some instances, neighbouring buildings have individual vertical load-resisting systems. Others feature a shared wall supporting the vertical loads of both buildings [32]. It can be difficult to estimate the seismic response of these masonry aggregates because of the complex construction systems present in a single masonry aggregate. Different material use, a variety in the quantity of adjacent buildings and variety of building heights contribute to the large uncertainty experienced in seismic response. The interaction of these parameters and the effect on seismic resistance remains largely unknown thus parametric analyses are one solution to explore the influence of the structural uncertainties on the seismic response of the masonry aggregates and provide reasonable explanations for the effects of this variation. In this work, the parametric study investigates the effects of material degradation, number of adjacent buildings and building height within seismic pounding response. The first parameter studied in this analysis are the material properties. Material properties vary within a single structure depending on the age of the structure, quantity of construction or renovation projects and the level material degradation. Material degradation can occur in old masonry buildings due to the ongoing effects of time, environmental actions, existing damage due to external loads and level of maintenance. Adjacent buildings will often not be built with the same materials – differing time periods, architectural preferences and renovation/maintenance projects ensure some degree of variability in material properties. Building aggregates with different material ages/properties may exhibit significant differences in dynamic behaviour during seismic activity. To reflect this difference in numerical models, the effect of masonry degradation can be included with lower values in strength parameters of masonry [33]. In this research, two levels of degradation from the undamaged condition (DL0) of building material properties were considered. A slight degradation level (DL1) and severe degradation level (DL4) were incorporated in the parametric analysis, based on a probabilistic analysis of brick masonry materials [34]. Under this definition, material parameters mentioned in Table 1 were reduced by 15% (DL1) or 50% (DL4), summarized in Table 2. The building aggregate studied consists of six combinations of three selected material levels (see Fig. 5). For each material property combination, two adjacent façades of the same height with a regular opening layout (configuration 1) were considered. These cases were studied under monotonic pushover analyses and all façades were modelled with the DE macro-crack modelling strategy. In each case, pushover loads were only applied to the steel beams on both floors of the leftmost façade and the horizontal displacements were monitored at the top of the mid-joint between the two adjacent façades (indicated in the blue dot).
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material ID
DL1 (masonry)
Em
Gm
fc
ft
c
φ
Gc
GIf
GII f
[MPa]
[MPa]
[MPa]
[MPa]
[MPa]
[◦ ]
[N/m]
[N/m]
[N/m]
1267
507
5.27
0.0425
0.06
25.5
8500
4.25
17
DL1 (bricks)
1267
507
12.75
0.85
1.275
30
17544
68
106
DL4 (masonry)
745
298
3.38
0.025
0.038
15
5000
2.5
10
DL4 (bricks)
745
298
7.8
0.5
0.75
18.5
10732
40
62.5
Fig. 5. Building aggregates with different material-level combinations
It is important to note that the seismic behaviour of an individual structure can vary based on the quantity of adjacent buildings within a building aggregate. As observed during the 2010 Christchurch earthquake (Mw = 6.3), seismic pounding within a row of URM buildings of similar heights occurred, and severe cracking at the leftmost building was observed during the post-event field investigation. To investigate this phenomenon, the second phase of the parametric analysis investigates the influence of the number of adjacent buildings within a building aggregate on its seismic response. A total of four URM aggregates with one to four façades are compared (see Fig. 6). The studied building aggregates include adjacent façades with a regular opening layout (configuration 1) at the same total building height with original material properties. Monotonic pushover analyses were performed with the respective DE macro-crack models. In each case, the pushover loads were only applied to the steel beams of the leftmost façade in each scenario. Horizontal displacements of the building aggregates were monitored at the top right corner of the rightmost façade (indicated in blue dots).
Fig. 6. Building aggregates with different numbers of adjacent buildings
The final phase of the parametric analysis considers adjacent URM buildings of differing heights. In this situation, local failures due to pounding may arise when the point of impact from the two buildings has different heights, especially when the shorter structure has a larger stiffness than the taller structure [35]. The numerical investigation
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in this study determines the influence factor of building height in seismic response. In configuration 1, A single-storey, 4.5 m tall, URM building with irregular opening layouts (referred to as the shorter wall) and a two-storey, 6.435 m tall, URM building with regular opening layouts (referred to as the taller wall) are analyzed (Fig. 7). Zero separation between the two façades is included to demonstrate the worst-case scenario pounding effects. Both selected façades are modelled with the properties of undamaged masonry (Table 1). Two in-plane monotonic pushover analyses (positive and negative directions) were performed using the DE macro-crack model (Fig. 7). In each analysis, the pushover loads were only applied to one façade directly through to steel beams (highlighted in red) and the horizontal displacements were monitored at the top of the mid-joint between the two façades (indicated in blue dots).
Fig. 7. The numerical model of two unequal-height URM buildings loaded in positive (left) and negative (right) directions
4 DE Macro-Crack Network Numerical Results 4.1 Influence of Material Degradation The macro-model results were processed to display the load-displacement behaviour of varying combinations of degradation levels. Based on lower levels of peak horizontal force (Fig. 8a), a greater level of degradation indicates a progressive reduction in stiffness and peak shear force capacity. In addition, sharp decreases in peak shear force capacity between the combination DL1-DL1 and DL1-DL4 and the combination DL1DL4 and DL4-DL4 were observed. The severely degraded material of DL4 diminishes the structural capacity of the aggregate to the greatest extent, displaying the importance of material degradation on structural capacity. With respect to the failure modes of each masonry aggregate, two distinct crack propagation patterns can be identified. The first pattern occurs when the same material degradation levels are applied (DL0-DL0, DL1-DL1, and DL4-DL4) and shows more early damage in spandrels, while the second pattern is observed in the building aggregates with different material degradation levels (DL0-DL1, DL0-DL4, and DL1-DL4). In both patterns, there were five identifiable damage stages in the crack propagation process (Fig. 8b). In the first pattern, initial cracks were observed in the spandrels on both façades, followed by the failure at the base of the mid-joint. In the second damage stage, shear cracks were first observed at the interface between the façades, followed by the central piers of the loaded façade in
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the third damage stage. In the fourth stage, the cracks propagated towards the exterior pier of the loaded façade and the central pier of the unloaded façade. Finally, in the fifth damage stage, cracks extended to the exterior pier of the unloaded façade. Conversely, in the second pattern, the mid-joint between adjacent façades failed at the beginning of the damage process in the first stage, which is the only difference observed between the two patterns.
(a)
(b)
Fig. 8. (a) Force-displacement curves and (b) crack propagation of two damage patterns
4.2 Influence of the Number of Adjacent Buildings Figure 9a demonstrates that an augmentation in the number of adjoining buildings results in an amplification of the peak shear capacity of the URM building aggregate which is directly proportional to the number of adjacent buildings while the initial stiffness of the URM building aggregate remains unchanged. Upon analyzing the damage characteristics of four clusters of URM buildings (as shown in Fig. 9b), a decrease in damage was noted on the upper floor as the number of buildings in each aggregate increased. Specifically, when three adjacent buildings were present, cracks were predominantly observed at the pier, with shear cracks on the spandrel only occurring on the furthest façade from the pushover load. Spandrels of the remaining two façades remained intact. Additionally, damage to the mid-joint between the two adjacent façades was confined to the pier level and the building as a whole did not lose its integrity. In the four façades case, no diagonal shear cracks were observed in the spandrels of any façade and all mid-joints remained undamaged.
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(a)
(b)
Fig. 9. (a) Force-displacement curve and (b) damage pattern of the URM aggregates with increasing number of façades components
4.3 Influence of Building Height URM building aggregates with façades of two heights were subjected to negative and positive pushover loads and results display different damage patterns and stiffness depending on the loading direction (Fig. 10). In the first damage state, damage to the entire mid-joint and the development of diagonal shear cracks in the spandrel of the taller wall were observed in both loading directions. However, the shorter wall experienced damage above both openings. In the shorter wall, a diagonal shear crack also developed below the window opening in the negative load case and minimal damage under the positive load case. In addition, the shear force at this damage state was higher in the negative direction than in the positive direction (230 kN vs 150 kN). In the second damage state, the extensive damage was visible and diagonal shear cracks characterize the dominant failure mechanism spreading through the spandrel and piers. The shorter façade under the negative load experienced a greater number of cracks above openings than under the positive load. Moreover, in this damaged state, the URM building aggregate displayed higher deformability in the positive loading condition as compared to the negative loading condition. In the third and final damage state, cracks were fully developed in both façades with a greater number of cracks observed in the shorter building subjected to negative loading. Interestingly, the force-displacement curve revealed a significant difference between the positive and negative loading directions. The URM building aggregate only sustained a limited extent of deformability at the peak shear force in the positive loading direction, whereas in the negative loading condition, an increase in shear force was noticed after the displacement of 18 mm. In the negative pushover analysis, the shear force capacity was found to be higher than in the positive pushover analysis (approximately 350 kN and 300 kN, respectively). One explanation for this difference is that the shorter façade is stiffer than the taller façade due to the lower height and smaller number of openings, allowing the URM building aggregate to exhibit a higher lateral capacity and higher ductility in the negative loading direction.
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(a)
(b) Fig. 10. (a) Force-displacement curve, (b) crack patterns of the positive (left) and negative (right) loading directions
5 Conclusions Unreinforced masonry (URM) buildings are characterized by non-uniform material properties, especially as part of a building aggregate, and seismic pounding within these building aggregates can create complex dynamics and collision effects, impacting the seismic response of individual structures. However, the lack of experimental data available towards seismic pounding of masonry aggregates poses a challenge in developing numerical models for simulating the in-plane (IP) response. To address this issue, this research presents a parametric analysis that identifies the effect of varying geometrical and material properties on the response of adjacent buildings in seismic pounding scenarios. A novel macro-crack network model based on the Discrete Element Method (DEM) is utilized in this work, which reduces the computational load while providing reliable and accurate results. The presented macro-crack network modelling strategy is validated against experimental results and a series of DEM façades created using micro-modelling strategies. Through the parametric analysis, this study investigated the influence of material degradation, number of adjacent buildings and varying heights of the URM building aggregate. These preliminary exercises allowed for exploring the mechanical interaction among adjacent buildings in a simplified manner. The parametric analysis led to the following conclusions: • Reduction in stiffness and peak shear force of the URM building aggregate occurs with increased degradation levels. The severe-damaged façade (DL4) displayed the highest level of damage and lowest load capacity of the aggregate.
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• Two distinct crack propagation patterns were observed between adjacent façades: the first observed when each façade had the same level of material degradation and the second when the façades did not have the same material degradation level. • Initial stiffness of the URM aggregate increases with increasing number of adjacent façades. • The peak shear force increases proportionally to the number of adjacent façades. With increasing number of adjacent façades, levels of damage on the upper floors of the middle façades decreased. Level of damage on the piers at the ground floor of each façade remains similar. • Pushover loads originating from the side of the taller façade induced a higher force capacity on the URM building aggregate as compared to those originating from the opposite side. As a result, the shorter façade experienced increased damage in the negative loading direction. The results obtained in this study provide a simplified evaluation of the IP response of URM building aggregates. For evaluating pounding damage, dynamic analyses using artificial and recorded ground motions will be considered in future research.
Acknowledgements. The authors acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2022-03635].
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Accurate and Efficient 2D Modelling of Historical Masonry Buildings Subjected to Settlements in Comparison to 3D Approaches Alfonso Prosperi1(B) , Michele Longo1 , Paul A. Korswagen1 , Mandy Korff1,2 , and Jan G. Rots1 1 Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1,
2628 Delft, The Netherlands [email protected] 2 Deltares, P.O BOX, 177, 2600 MH Delft, The Netherlands
Abstract. This paper presents an improved 2D modelling strategy which aims to represent the behavior of historical unreinforced masonry buildings on shallow foundations subjected to ground settlements. The application is presented with reference to a two-storey building, typical of the Dutch built heritage. The novelty comprises the inclusion of the effect of the lateral house-to-house separation walls of such old buildings. Additionally, the masonry strip foundation is modelled and supported by a boundary interface representing the interaction between the soil and the foundation. Two realistic hogging and sagging settlement configurations are applied to the model and their intensity is characterized using the angular distortion of the settlement shape. The response in terms of damage and deformations of the proposed modelling strategy is compared with the ones of five selected approaches based on the state of the art. For all the selected models, the damage severity is quantified objectively by means of a scalar parameter, which is computed considering the cracks’ number, length, and width. The results of the proposed 2D model agree in terms of displacements, crack patterns and damage with the 3D models. On the contrary, the façade models that do not include the effect of the lateral walls do not exhibit the same cracking and damage, resulting in lower damage and deformations for the same applied angular distortion. Accordingly, the proposed modelling strategy requires less modelling complexity and the analyses are 9 to 28 times faster to run with respect to the 3D models. The efficient and accurate model allows performing a wide number of analyses to easily investigate the role of the various building’s features. Keywords: Settlements · Numerical modelling · Masonry structures · Damage
1 Introduction In many areas of the world, the occurrence of settlements due to human interventions and/or natural processes can harm existing historical structures. Challenges arise in the prediction of the distortions, displacements and damage that are likely to occur on such © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 232–244, 2024. https://doi.org/10.1007/978-3-031-39450-8_19
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buildings, since observations of full-scale structures are often limited or unavailable. Numerical simulations represent a widely adopted alternative to investigate the damage to historical buildings. Three-dimensional analyses may seem more appropriate to predict the response of the entire structure subjected to uneven settlement. However, they require increased computational resources and model complexity, and are thus associated with more uncertainties. Moreover, 3D models should include three-dimensional settlement configurations. The three-dimensional ground movements due to some settlement causes, such as tunnelling, excavation and mining activities, can be estimated with good accuracy [6]. However, for other sources of urban subsidence (e.g. groundwater changes, soil shrinkage, and organic soil oxidation), unpredictable ground profiles can arise [4, 6]. In such cases, the three-dimensional settlement patterns must be retrieved from in-situ survey measurements. Such measurements, however, are difficult to retrieve along all the building’s walls in the case of terraced houses, as they share side walls. This is the case of many buildings in the Netherlands, for which bed-joint measurements are available only along the façades. In this context, two-dimensional models are often used as an alternative to investigate the building’s response. In such 2D models, the effects of the house-to-house separation walls, i.e., the walls transversally connected to the façade, and of the floor system, may or may not be included. Thus, with a focus on historical unreinforced masonry buildings subjected to ground settlements, this study compares the results of six modelling approaches to select the most suitable and less costly in terms of computational resources and modelling burden. Among the selected modelling strategies, a novel 2D model is herein proposed to include the effects of the lateral house-to-house separation walls on the building’s response.
2 Finite Element Models In the last decades, the numerical models that simulate the response of structures undergoing ground movements have become increasingly detailed and accurate [11]. Thanks to the development and availability of computational resources, the modelling approach for structures subjected to settlements improved from elastic beams with equivalent axial and bending properties to complex 2D and 3D models, that include the non-linear behavior of the materials (e.g. in [7, 11, 20, 25–27, 29, 30]). The behavior of soil and of the soil-structure interaction in coupled analyses (i.e. models that include both the structure and the subsurface on which it rests), improved from an elastic continuum to non-linear constitutive laws that accurately predict the ground movements (e.g. in [8, 11, 24, 25]). However, coupled analyses involve the generation of complex meshes and high computational time and effort [11]. Therefore, a compromise is typically found with semi-coupled models. In semi-coupled analyses the ground movements are applied to an interface accounting for the soil and foundation stiffness [11, 26]. A similar approach involves applying the ground displacements to an interface accounting for the soil-foundation interaction, while the strip foundation system is explicitly included in the numerical model [11, 17, 27].
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In this study, six modelling approaches inspired by the state of the art were selected and used for 2D and 3D analyses of a masonry structure subjected to subsidence-related settlements. Figure 1 summarizes the six selected models built with the finite element software Diana FEA 10.5: a) 2D façade model (2DFA in Fig. 1a), a plane stress model of the building’s façade [1, 5, 11]; b) 2D façade model (2DSF in Fig. 1b), a plane stress model with short lateral linear beam elements, with the width of one brick, that simulates the presence of transversal walls [15, 27]; c) 2D façade model (2DLF in Fig. 1c), a novel plane stress model with long lateral linear beam elements, whose cross-section width is wider than one brick, and non-linear springs placed at the sides of the strip foundation; d) 3D façade model (3DFA in Fig. 1d), a three dimensional model of the building’s façade; e) 3D box model (3DBOX in Fig. 1e), a three dimensional model of the entire building, without floors and party walls (similar to [10]); f) 3D full model (3DFULL in Fig. 1f), a three dimensional model of the entire building (similar to [7]).
Fig. 1. The selected modelling approaches for the two-storey masonry building with a width of 8 m for both the façades and the transverse walls, a total height of 7 m and single-wythe (i.e. the width of one brick, equal to 100 mm) walls.: (a) 2D façade model (2DFA); (b) 2D façade with lateral linear short flanges (2DSF); (c) 2D façade with lateral linear long flanges (2DLF); (d) 3D façade model (3DFA); (e) 3D model (3DBOX); (f) 3D full model (3DFULL).
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The models correspond to a two-storey masonry building with a width of 8 m, a total height of 7 m and single-wythe walls (i.e. the width of one brick, equal to 100 mm). Such a building idealizes typical old Dutch structures built before 1945 [13]. The models include the masonry strip foundation system below the walls, commonly observed in such old buildings, with a width and height of 500 and 600 mm respectively for which a soilstructure interaction interface is used [17]. All the models include openings underneath masonry lintels. 8-node quadratic elements with 3 × 3 Gaussian integration schemes were adopted for the façade, lintels, and foundation for both the 2D and 3D analyses. Sixnoded line interface elements were used to model the soil-building interaction. A mesh size of 100 × 100 mm was used for the plane stress elements, and 100 mm for the beam elements. An orthotropic, smeared crack/shear/crush constitutive law was employed to explicitly simulate the cracking behavior of masonry (Engineering Masonry Model, [28]). The material properties of the selected fired clay brick masonry (Table 1) were retrieved from the Dutch Standard [21] and previous studies [14, 28], and were applied to both the façade and foundation. Regarding the models that make use of lateral elements to simulate the effects of transverse walls (2DSF and 2DLF in Fig. 1b and c respectively), class-III Mindlin beam elements were placed on the two lateral sides of the façades, with the Young’s modulus equal to 1/3rd of the one of masonry material (Ey in Table 1) the Poisson’s ratio of 0.15 and the same mass density, following the approach implemented in [15, 27].
Fig. 2. Calculation of the cross-section of the lateral beam elements for the model 2DLF (Fig. 1c) as described in [22, 31]). Measures in meters.
Figure 2 illustrates how the thickness of the cross-section of the lateral elements was computed for the model 2DLF (Fig. 1c). This length corresponds to the sum of three contributions (A1 , A2a and A2b in Fig. 2), which provides the length of the cooperating flange (as described in [22, 31]). The first contribution (A1 in Fig. 2) was computed by considering the minimum of the following transverse wall properties: a fifth of the wall height, half of the internal distance between party walls (Ls /2), or six times the wall thickness (t), as described in [31]. The obtained value (i.e. 0.6 m), is further supplemented
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with the second and the third contributions (A2a and A2b in Fig. 2), which contributes to the normal compression given by the flange (as described in [22]). The total computed thickness for the lateral beam elements (Flange thickness in Fig. 2) is 2.35 m for the selected case. In the case of 3DFULL, the timber floor and roof, commonly observed in the Dutch historical buildings, were modelled using elastic C24 class material for both the class-III Mindlin beam elements, representing the joists, and the orthotropic shell elements for the planks sheeting, calibrated according to [21]. The floor, roof and mid-party wall were disconnected from the front and back façades, thus, the weight of the roof and the floor system is transferred to the transverse walls employing point loads (Fig. 1f). In the proposed model 2DLF (Fig. 1c) the overburden of the floors acting on the lateral walls of the model 3DFULL (Fig. 1f) was simulated applying four equivalent forces, two per floor at each side of the façade (Fig. 1c). The four equivalent forces for the model 2DLF (Fig. 1c) were computed considering the portion of the floor and roof that loads the length of the cooperating flanges. At the foundation, a zero-tension interface was modelled to consider the local soilfoundation interaction by means of boundary interface elements, connected to the bottom edge of the strip foundation [17]. Table 1. Material properties adopted in the FE models. Material Properties
Symbol
Unit of measure
Value
Young’s modulus vertical direction
Ey
[MPa]
5000
Young’s modulus horizontal direction
Ex
[MPa]
2500
Shear modulus
Gxy
[MPa]
2000
Bed joint tensile strength
fty
[MPa]
0.10
Minimum head-joint strength
ftx,min
[MPa]
0.15
Fracture energy in tension
Gft,I
[N/mm]
0.01
Angle between stepped crack and bed-joint
α
[rad]
0.50
Compressive strength
fc
[MPa]
8.50
Fracture energy in compression
Gc
[N/mm]
20.00
Friction angle
ϕ
[rad]
0.70
Cohesion
c
[MPa]
0.15
Fracture energy in shear
Gs
[N/mm]
0.10
Mass density
ρ
[Kg/m3 ]
1708
The interface normal and tangential stiffnesses were computed using the equations reported by [9, 18, 19], on the basis of soil shear modulus G, Poisson’s ratio ν, and foundation thickness (i.e. the base of the foundation in the direction transversal to the masonry façade). The selected soil properties simulate a clayey soil material, with the shear modulus equal to 10 MPa and the Poisson’s ratio equal to 0.45. These stiffness
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values were also adopted in the model 2DLF for the two corner springs (Fig. 1c) placed to support the weight of the lateral beam elements. Two types of asymmetric settlement deformations (i.e. hogging and sagging in Fig. 3) idealize the long-term (i.e. decades) ground displacements that develop during the service life of a historical structure. The settlement shapes, conformed to a Gaussian curve [23] described by Eq. (1), were applied at the base of the foundation. (1) Sv (x) = Sv,max · exp −x2 /2x2i where Sv (x) represents the vertical ground settlement, xi is the distance from the symmetric axis of the curve to the point of inflection and Sv,max is imposed to ensure the same intensity for all the profiles. The angular distortion β (i.e. the slope of the line joining two consecutive points in relation to a line joining the two points at the sides of each settlement profile [3]) was chosen to characterize the intensity of the settlement troughs. Accordingly, all the settlement profiles present the same angular distortion of 1/300. In the case of the 3D models, the settlement shapes were purposely assumed not to vary in the direction perpendicular to the plane of the façade, to exclude the effect of three-dimensional settlement variations. A two-phased load application procedure was adopted for all the models: the self-weight of the structure was applied in 10 steps to compute the initial stress-state, and then the settlement deformation was applied in 195 steps (with a load rate of 0.02 mm/step). The tabulated outputs of the analyses were then used to quantify the damage progression by means of a parameter (, proposed by [16]), based on the number of cracks, their length and opening. The corresponding damage severity was then categorized according to the system proposed by Burland et al. [3] (Table 2).
Fig. 3. Settlement profiles applied in the finite element models: (a) Hogging and (b) Sagging. In the 2D models, only the façade settlement (solid line in the figure) is applied below the interface elements (see Fig. 1), while for the 3D models the entire three-dimensional settlement pattern is applied. The settlement profile of the façade is conformed to a Gaussian distribution and it is characterized by an angular distortion equal to 1/300.
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Table 2. Damage scale with the classification of visible damage and the corresponding discretization of the damage parameter in sub-levels (from [12, 16]). Damage level
Degree of damage
Approximate crack width
Parameter of damage
DL0
No Damage
Imperceptible cracks
12 or more). The response to the seven input records mentioned above is summarized by the median maximum absolute normalized rotation, reported in the plots of the parametric analysis. Hence, for each reference case, 189 dynamic analyses are performed. Table 1. Values of the investigated parameters corresponding to lognormal mean, me, and standard deviation, σ. b
htot / b
Floor parallel
Floor perpendicular
kd
kd
m
-
kN/m
kN/m
(me–σ )
0.35
9
500
400
(me)
0.50
12
1200
1400
(me + σ )
0.70
15
3100
4600
3.2 Results of the Parametric Analysis The parametric study on the thickness b of the wall (Fig. 4), pointed out that, especially for slender walls, the contribute of the flexible diaphragm produces a reverse scale effect: the bigger the wall the less relevant the role of the diaphragm because the inertia force is much larger than the elastic top force. In the configuration where the floor is parallel, this phenomenon is amplified. The effect of the diaphragm stiffness is also investigated. For the configuration where the floor is assumed perpendicular to the façade, the parametric analysis (Fig. 5) highlighted that to an increase in stiffness is associated a decrease in terms of rotations. This trend is usually true also for the configuration where the floor is assumed parallel to the façade, although for extremely slender façades the benefic effect of this stiffness decreases.
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Fig. 4. Median, over seven accelerograms, of the maximum absolute non-dimensional rotations for the bottom body, varying floor orientation with respect to façade, slenderness, wall size.
Fig. 5. Median, over seven accelerograms, of the maximum absolute non-dimensional rotations for the bottom body, varying floor orientation with respect to façade, slenderness, floor stiffness.
4 Conclusions The out-of-plane response of an unreinforced masonry strip wall elastically supported at the top was studied in this paper, accounting for additional masses active on the wall only during the earthquake. Hence, two configurations of the floor orientation were investigated: a) floor parallel to the façade; b) floor perpendicular to the façade. A numerical analysis is carried out to understand the effect of the different parameters that characterize the system on the global response. Therefore, the preliminary investigation of a building portfolio in Emilia-Romagna (region of Italy) was conducted to calculate the mean and standard deviation of a log-normal distribution for the main parameters of the system. The nonlinear time history analyses were performed using seven natural accelerograms compatible with the code spectrum of the city of Mirandola, located in Emilia.
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The analysis outcomes indicated that, for this location, the response of the system is deemed dangerous only when there is a considerable height-to-thickness ratio. Additionally, the investigation on the diaphragm influence revealed that the top spring significantly affect the response of the system. The diaphragm stiffness can notably decrease rotations and, as a result, lower the risk of overturning. Furthermore, when the wall size effect is explored, an inverse scale effect is observed, making the top restraint stiffness less relevant for large walls. Acknowledgments. This work was partially carried out under the research program SISTINA (SIStemi Tradizionali e INnovativi di tirantatura delle Architetture storiche) funded by Sapienza University of Rome and under the research program “Dipartimento di Protezione Civile – Consorzio RELUIS.” The opinions expressed in this publication are those of the authors and are not necessarily endorsed by the funding bodies.
References 1. Paulay, T., Priestley, M.J.N.: Seismic Design of Reinforced Concrete and Masonry Buildings, vol. 768. Wiley, New York (1992) 2. Andreotti, C., Liberatore, D., Sorrentino, L.: Identifying seismic local collapse mechanisms in unreinforced masonry buildings through 3D laser scanning. Key Eng. Mater. 628, 79–84 (2014). https://doi.org/10.4028/www.scientific.net/KEM.628.79 3. Sorrentino, L., Alshawa, O., Liberatore, D.: Observations of out-of-plane rocking in the oratory of san Giuseppe dei Minimi during the 2009 L’Aquila earthquake. Appl. Mech. Mater. 621, 101–106 (2014). https://doi.org/10.4028/www.scientific.net/AMM.621.101 4. de Felice, G., Liberatore, D., De Santis, S., Gobbin, F., Roselli, I., Sangirardi, M., et al.: Seismic behaviour of rubble masonry: shake table test and numerical modelling. Earthq. Eng. Struct. Dyn. 51(5), 1245–1266 (2022) 5. Bruneau, M.: State-of-the-art report on seismic performance of unreinforced masonry buildings. J. Struct. Eng. 120(1), 230–251 (1994) 6. Moon, L., Dizhur, D., Senaldi, I., Derakhshan, H., Griffith, M., Magenes, G., et al.: The demise of the URM building stock in Christchurch during the 2010–2011 Canterbury earthquake sequence. Earthq. Spectra 30(1), 253–276 (2014) 7. Penna, A., Morandi, P., Rota, M., Manzini, C.F., da Porto, F., Magenes, G.: Performance of masonry buildings during the Emilia 2012 earthquake. Bull. Earthq. Eng. 12(5), 2255–2273 (2013). https://doi.org/10.1007/s10518-013-9496-6 8. Zucconi, M., Ferlito, R., Sorrentino, L.: Validation and extension of a statistical usability model for unreinforced masonry buildings with different ground motion intensity measures. Bull. Earthq. Eng. 18(2), 767–795 (2019). https://doi.org/10.1007/s10518-019-00669-2 9. Sisti, R., Di Ludovico, M., Borri, A., Prota, A.: Damage assessment and the effectiveness of prevention: the response of ordinary unreinforced masonry buildings in Norcia during the Central Italy 2016–2017 seismic sequence. Bull. Earthq. Eng. 17, 5609–5629 (2019) 10. Sorrentino, L., Tocci, C.: The structural strengthening of early and mid 20th century reinforced concrete diaphragms. In: Sixth International Conference on Structural Analysis of Historic Construction (2008) 11. AlShawa, O., Liberatore, D., Sorrentino, L.: Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods. Int. J. Architect. Herit. 13(3), 340–357 (2019)
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12. Giuffrè, A.: A Mechanical Model for Statics and Dynamics of Historical Masonry Buildings. Springer, Protection of the architectural heritage against earthquakes (1996) 13. Baggio, C., Masiani, R.: Dynamic behaviour of historical masonry. Brick Block Masonry 1, 473–480 (1991) 14. Doherty, K., Griffith, M.C., Lam, N., Wilson, J.: Displacement-based seismic analysis for outof-plane bending of unreinforced masonry walls. Earthq. Eng. Struct. Dyn. 31(4), 833–850 (2002) 15. Casapulla, C., Giresini, L., Lourenço, P.B.: Rocking and kinematic approaches for rigid block analysis of masonry walls: state of the art and recent developments. Buildings 7(3), 69 (2017) 16. Psycharis, I.N.: Dynamic behaviour of rocking two-block assemblies. Earthq. Eng. Struct. Dyn. 19(4), 555–575 (1990) 17. Spanos, P.D., Roussis, P.C., Politis, N.P.A.: Dynamic analysis of stacked rigid blocks. Soil Dyn. Earthq. Eng. 21(7), 559–578 (2001) 18. Derakhshan, H., Griffith, M.C., Ingham, J.M.: Out-of-plane behavior of one-way spanning unreinforced masonry walls. J. Eng. Mech. 139(4), 409–417 (2013) 19. Gabellieri, R., Landi, L., Diotallevi, P.P.: A 2-DOF model for the dynamic analysis of unreinforced masonry walls in out-of-plane bending. In: Proceedings 4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Kos Island, Greece (2013) 20. Penner, O., Elwood, K.J.: Out-of-plane dynamic stability of unreinforced masonry walls in one-way bending: shake table testing. Earthq. Spectra 32(3), 1675–1697 (2016) 21. Derakhshan, H., Griffith, M.C., Ingham, J.M.: Out-of-plane seismic response of vertically spanning URM walls connected to flexible diaphragms. Earthq. Eng. Struct. Dyn. 45(4), 563–580 (2015) 22. Prajapati, S., Destro Bisol, G., Alshawa, O., Sorrentino, L.: Non-linear dynamic model of a two-bodies vertical spanning wall elastically restrained at the top, pp. 1–21 (2022) 23. Iervolino, I., Galasso, C., Cosenza, E.: REXEL: computer aided record selection for codebased seismic structural analysis. Bull. Earthq. Eng. 8(2), 339–362 (2010) 24. Giresini, L., Sassu, M., Sorrentino, L.: In situ free-vibration tests on unrestrained and restrained rocking masonry walls. Earthq. Eng. Struct. Dyn. 47(15), 3006–3025 (2018)
Investigation of the Structural Performance of Masonry Wharf Cellars in Utrecht Using the Distinct Element Method Yopi Oktiovan(B)
, Anjali Mehrotra , Francesco Messali , and Jan Rots
Department of Materials, Mechanics, Management & Design, Faculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 CN Delft, Netherlands [email protected]
Abstract. One of the characteristic features of the city of Utrecht is its extensive system of canals and wharf cellars, whose constructions date back as early as the 1200s, and which are now considered as one of the historical properties of the city. A typical wharf cellar in Utrecht comprises a masonry barrel vault with multi-layered rings for the cellar interior, masonry piers which are interconnected to the other wharf cellars, and spandrel walls for the façades. Due to increased traffic volume and urbanization which caused the increase of dead load and traffic load, it is important to assess the structural safety and state of maintenance of these historical structures. In this paper, a novel safety assessment framework for these structures is presented and applied to the analysis of a typical masonry wharf cellar in central Utrecht. The geometry of the cellar is first parametrically generated, which is then used to create a block-based numerical model for analysis using the Distinct Element Method (DEM), where bricks units are modelled as discrete blocks separated by zero thickness interfaces. Traffic loads in accordance with the Dutch Standard traffic model for regular vehicles and emergency service vehicles are calculated and the dispersion through the filling soil is modelled. The ultimate load due to these load configurations is then assessed. The analysis results can be used to identify the critical load cases and the failure mechanisms of the wharf cellar, while also providing general insights into the safety and stability of the cellars, thus aiding engineers in their efforts to extend the lifespan of these historical structures. Keywords: Utrecht Wharf Cellar · Distinct Element Method · Traffic Load · Barrel Vault · Boussinesq theory
1 Introductions Masonry arches and vaults have been the basis of the structural elements for many historical constructions since the first ever known masonry arched structures in ancient Egypt and Mesopotamia. The number of masonry arched structure in Europe is estimated to be more than 200,000 within the railway network and is predicted to reach 300,000 if the masonry bridges within the public road system are taken into account [1]. In the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 287–300, 2024. https://doi.org/10.1007/978-3-031-39450-8_24
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Netherlands, a large part of the public road network is still connected to masonry arch bridges and vaults, whose construction dates back to the Middle Ages. These structures still serve as functional infrastructures subjected to relatively large traffic loads every day. The city of Utrecht in the Netherlands is well known for its wharf and street cellars which were built starting from the twelfth century and are now integrated to the public roads. The cellars were initially built to store goods that were transported from the canals. Nowadays, they are used as terraces, office spaces, and other economic functions. The cellars are also considered as one of the historical properties of the city under the National Monument Stadsbinnengrachten en Werven. The construction of the wharf cellar and its typical components are shown in Fig. 1a and Fig. 1b, respectively. The numbers in Fig. 1b are described as follows; 1: cellar’s vault, 2: basement foundation and retaining walls, 3: cracks and leakage, 4: street traffic, 5: wall anchors, 6: basement access, 7: water drain, 8: cable pipes, 9: waterproof layer, 10: new waterproof layer, and 11: wall façades. A typical cellar system comprises a longitudinal bond barrel vault, cross bond masonry piers interconnected to adjacent wharf cellars, and a spandrel wall for the façade. Depending on the span of the cellar system, multi-ring arrangements are used on the cellar’s vault. Due to urbanization and increased traffic volume, the loads sustained by these structures have changed from pedestrian, horses, and carriages to heavier motorized vehicles.
(a)
(b)
Fig. 1. Sketches of (a) construction of wharf with wharf cellars and (b) wharf cellars typical components [2]
Furthermore, the recent collapse of the historical Grimburgwal quay wall in Amsterdam [3] brought to light the importance of assessing the structural safety and state of maintenance of historical structures in Dutch cities. A collaborative work between Witteveen + Bos, Antea Group, and Royal Haskoning DHV for the municipality of Utrecht was started in 2021 to assess the load bearing capacity, investigate the causes of damage in the defective cellars, and check the maximum permissible load for the traffic to safely cross the wharf cellars [2]. The study utilized two-dimensional numerical modelling of the wharf cellar system and the surrounding soil to assess the safety of the cellar in
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accordance with the NEN 8701 Dutch guideline for assessment of existing structures. [4]. The assessment method of the load bearing capacity and serviceability limit of arched structures have been extensively studied, from the empirical MEXE method to nonlinear numerical methods such as finite or discrete element methods. Sarhosis, et. al. [5] summarized the experimental investigations and assessment method for masonry arch bridges but can be easily extended to vault structures as well. Typically for fast and reliable results, empirical methods or limit state based approaches are enough to obtain the collapse load and reactions of the abutments/piers. However, the load bearing capacity seldom overestimated due to the imposed assumptions and information about the displacements and stress distributions are not provided. Recently with the increase of computational power, researchers have leaned into utilizing a micro modelling strategy called distinct element method (DEM) where masonry units are represented as assemblages of block units and mortar joints represented as zero thickness interfaces. This method is widely used for the assessment of masonry arched structures [6, 7, 8]. In this context, this paper introduces a safety assessment framework based on the micro modelling approach and demonstrates it via application to the compliancy assessment of an Utrecht wharf cellar as a case study. The numerical framework utilizes a rigid block formulation where nonlinearities and block deformations are lumped at the interfaces between blocks. The compliancy of the wharf cellar model is checked against the load model in accordance to the Dutch Guideline for traffic loads on bridges and other civil engineering works [9]. If the structure is compliant, the applied load is incrementally increased until failure is reached and the failure mechanism and ultimate load bearing capacity of the cellar is observed. The failure load and mechanism obtained from the numerical model will enable engineers to check the safety and stability of the cellars in their efforts to extend the lifespan of the historical structure.
2 Case Study of the Wharf Cellar in Kromme Nieuwegracht The wharf cellar system shown in the right-hand side of Fig. 2a is located in the Kromme Nieuwegracht canal in the center of Utrecht. The cellar was built possibly in the 12th century, and then rebuilt between 1500–1700 with a higher crown height. The wharves were used as ground-level transport of goods and the cellars were used for storage. The cellar system used for the demonstration of the proposed framework comprises three inter-connected wharf cellars which consist of masonry barrel vaults and load bearing walls with varied springing level. The cross-section drawing of the cellar system is presented in Fig. 2b. The units shown are in mm. The geometrical information is summarized in Table 1 based on the investigation report conducted by Royal Haskoning DHV [10], hereby termed as the investigation report,. The heights were measured based on the N.A.P (Normaal Amsterdams Pell / Normal Amsterdam Level), a reference plane for height in the Netherlands. The interior height is measured between NAP + 2.946 mm and NAP + 2.969 mm. The foundations of the cellar system (below the NAP 0.0 m) are shallow foundations sitting on a loosely packed sand.
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(a)
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Fig. 2. (a) existing situation and (b) cross-section of a reference wharf cellar in Utrecht (all units in mm) [10]
Table 1. Geometrical data of Kromme Nieuwegracht Wharf Cellar Kromme Nieuwegracht
Piers
Arch
Total Length
12.88 m
Width
1.4 m
Span
4.8 m
Height over the N.A.P
3.34 m
Length
4.2 m
Rise at midspan (NAP +)
2.73 m
Number of Arches
3
Height (NAP +)
2.6 m
Vault depth
0.26 m
The material properties, presented in Table 2, are based on the characteristic values specified in the NPR 9998 + C1:2020 [11], the Dutch practical guideline for safety assessment of buildings. The density of the masonry is taken as 23 kN/m3 while the backfill and pavement density are taken at 18 kN/m3 and 23 kN/m3 , respectively. The dilatancy angle is assumed equal to 0. The cross-section of the barrel vault was identified by drilling two boreholes at the highest point of the vault. The drill core result showed that the barrel vault consisted of one brick unit stacked upright with dimensions of 220 × 110 × 55 mm (Length x Width x Height) and another unit stacked horizontally perpendicular to the previous layer, with mortar thickness of approximately 10 mm. Table 2. Masonry material properties as per Table F.2. of NPR 9998 (2020) [11] Properties
Table F.2 NPR 9998 (2020)
Masonry Clay Brickwork (pre 1945)
Units
Elastic modulus
Em
6000
N/mm2
Shear modulus
Gm
2500
N/mm2
Uniaxial tensile strength
fma;b;per
0.1
N/mm2
Initial bed joint shear strength
fma;v;0
0.3
N/mm2
Bed joint shear friction coefficient
μma;m
0.75
[-]
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The illustration of the vault’s cross-section and the investigation footage are presented in Fig. 3a and Fig. 3b, respectively. Finishing layers were found at the top and bottom side of the vaults, while a bituminous layer for waterproofing was observed at the topside. The total vault thickness excluding the finishing layers was 260–270 mm. A cross bond pattern was found at the location of the piers while a longitudinal bond pattern was observed at the vaults. The transition occurred at the springing level, approximately NAP + 1.9 m. According to the investigation report, the assessment results for special traffic load showed that there was a risk of crack formation perpendicular to the direction of travel where the tensile strength at the bottom and top of the arch was exceeded even though the collapse load was considerably higher.
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Fig. 3. (a) Illustration of the cellar vault’s cross-section and (b) Investigation footage at the bottom of barrel vault
3 Distinct Element Modelling of Utrecht Wharf Cellar The presented wharf cellar system is then modelled based on the three-dimensional distinct element method (DEM) [12] using the commercially available software 3DEC 7.0 [13]. This numerical method has been extensively used in the numerical analysis of arched structures and is particularly useful to this research to observe the failure mechanism and damage propagation of the cellar system at a detailed level. In DEM, the masonry blocks are modelled as assemblages of rigid or deformable blocks connected via point contacts comprising interface springs. Interactions between distinct blocks are defined using the soft-contact approach, which allows interpenetration between blocks, the extent of which is controlled by the stiffness of the interface springs. The equation of motion in DEM is solved using an explicit time-marching scheme where central difference algorithm is used. For static problems, the convergence or failure mechanism is reached by introducing dynamic relaxation, a form of artificial damping, to the equation of motion. [14]. The flowchart outlining the block generation and numerical analysis for the safety assessment tool is presented in Fig. 4. The process starts with the parametric generation of the cellar system geometry in Rhino + Grasshopper based on the inputs from Table 1
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Fig. 4. Flowchart of the block generation and analysis for the safety assessment of Utrecht Wharf Cellar model
and on-site inspection. The parametric geometry generation tool contains a series of Grasshopper components with ad-hoc C# scripts that allows fast and robust generation of vault masonry blocks including the longitudinal bond pattern at the barrel vault. Note that the masonry units are modelled with extended dimensions up to half of the mortar joint thickness on all sides of the units. The crown height of the arch elements is uniform for the sake of modelling simplicity. In order to save computational time and reduce the number of blocks modelled, only half of the left and right cellars are defined. The generated geometry is presented in Fig. 5a. In order to retain the joint plane (face-to-face contact) between the vertical units and horizontally stacked units (which in reality would be realized via the layer of mortar), the horizontally stacked units are further discretized into three distinct elements corresponding to the contacting vertical units below them as shown in Fig. 5b.
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Fig. 5. (a) Isometric view of the Rhino 3D model of Utrecht Wharf Cellar and (b) stacking pattern at the arch section
The blocks are then imported into 3DEC and contacts between each of the cellar elements are defined. The blocks are modelled as rigid, while all deformation is lumped into the interface springs. Block density is the only unit input parameter needed under rigid blocks formulation. A Coulomb friction joint constitutive model is applied to the contacting points of the blocks where material properties in Table 2 are used as the joint properties, with zero dilation angle. The joint normal and shear stiffnesses at the contacts between blocks are defined as a function of Young moduli of brick units and mortar over the contact area, as presented in Eq. (1) and Eq. (2) for normal and shear joint stiffness,
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respectively [15]: kn =
Eb · Em (Eb − Em )xhj
(1)
kn 2(1 + v)
(2)
ks =
where Eb and Em are the brick and mortar Young’s moduli, hj is the joint height and v is the Poisson’s Ratio. In terms of boundary conditions, the bottom of both piers are fixed, and in order to simulate symmetric conditions at both ends of the arch vaults, non-physical rigid blocks are defined where blocks are fixed and frictionless contact joints are applied between the blocks and the vault elements. Once the masonry material properties are defined, the 3DEC model is brought to equilibrium under gravity load. Then, the fill material above the cellar system is added as dead load and also brought to equilibrium. The traffic load in accordance with the BM3 of the NEN-EN 1991–2/NB guideline [9] is applied incrementally until the full application of the load. If after full application of the load, the maximum displacement of the structure is still within the specified threshold by the Dutch guideline, which in this case equals to 0.032m, the structure is considered compliant under the applied load. To obtain the failure load, the traffic load is then incrementally increased beyond the full application of the load until collapse occurs to determine the failure load of the cellar system. The failure load is determined when the F (capacity /demand) ratio in Fig. 4 is less than 1, or when the observed displacement keeps increasing to infinity. The backfill load on the arch can be represented as irregularly shaped particles, e.g. Voronoi shape, or be represented as a distributed load over the area. However, with the rigid block formulation in 3DEC, only the latter option is allowed. Since the backfill soil is not explicitly defined in this model, the traffic loads are applied similarly as distributed loads. The load dispersion model follows the Boussinesq distribution [16] along the arch ring while the load is uniformly distributed if it extends beyond the arch ring. By assuming a semi-infinite elastic soil below the level surface, the load dispersion is defined by Eq. (3). The angle definition is presented in Fig. 6. Note that the angles in Eq. (3) are in radians. σz =
q [α + sin α cos(α + 2β)] π
(3)
The assessment approach by Royal Haskoning DHV [10] prescribed eight positions along the travel direction of the wharf cellar. In this paper, the heaviest axle load will be applied at the center of the middle wharf cellar (position #5 in the investigation report). The other positions will be validated as part of the future work of this paper. The BM3 load model in accordance with NEN-EN 1991–2/NB is based on a traffic load in case of emergency deployment of fire services. The ladder fire truck is chosen for the safety assessment since the truck has the heaviest axle load weight. The ladder truck has two axles of 8 tons and 11.5 tons with an axle-to-axle distance of 4.2 m. The rear axle is applied at the center of the middle cellar while the front axle is applied closer to the left
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Fig. 6. Illustration of (a) Boussinesq distribution and (b) Traffic load dispersion
cellar since the cellar system was located in a one-way traffic lane with the direction travel going from the right cellar to the left. According to NEN-EN 1991–2/NB, a magnification factor of 1.4 must be considered when the special vehicles move at a speed of more than 5 km/h. Therefore, the distributed loads for the rear and front axles are 1.4*115kN/(4.2*1.0) = 38.3 kN/m2 and 1.4*80kN/(4.2*1.0) = 26.7 kN/m2 , respectively. Illustration of the load application for BM3 is presented in Fig. 6b. The traffic load dispersion along the arch ring is limited by an angle of dispersion at both ends of the area load. The angle of dispersion, θ, is set to 30° according to Chapter 4.9.1 of NEN-EN 1991–2/NB. The example of the load application in the middle arch is shown in Fig. 7. Once the traffic load magnitude is defined, the area of the arch model that falls within the area limited by the angle of dispersion, the violet arrows in Fig. 7, is searched. The dispersed traffic area load calculated using Eq. (3) is then distributed to the nodes (grid-points) of the blocks within the area.
Force (N)
Fig. 7. Example of traffic load application in the middle arch of the wharf cellar model (BM3 load)
Based on the site inspection report [10], layers of loose sand were found below the floors of the wharf cellar system. Therefore, a lateral earth pressure also needs to be considered as an additional load acting on the cellar system. Similar to the backfill load, since the soil below the floors is not modelled, the lateral earth pressure loads on the piers are applied as displacement-dependent distributed loads, according to the unified model by Ni, et. al. [17]. The lateral pressure load takes the relative displacement of both sides of the pier, converts it to the coefficient of lateral earth pressure and multiplies the coefficient by the unit weight and the soil depth. The lateral load is applied uniformly at the piers.
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4 Analysis Results 4.1 Safety Assessment of Kromme Nieuwegracht Wharf Cellar System Under BM3 Load
Fig. 8. Damage state of the wharf cellar model after 100% application of BM3 load
The quasi-static analysis for load model BM3 managed to reach 100% application of the load with minimal damage. The damage state of the wharf cellar model after 100% application of BM3 load is shown in Fig. 8. The damage started with tensile separation on the interfaces between the vertically (orange-coloured) and horizontally (green-coloured) stacked units, specifically at the region close to the piers before the 100% application of the load. As the analysis underwent the 100% load application, the separation of the bed joints at the centre of the middle arch occurred, which is consistent with the findings from the investigation that there was crack formation on the cellar vault perpendicular to the direction of travel. Note that the damage state in 3DEC occurs when the corresponding strengths (tensile/shear) are exceeded. The maximum displacements at every load increment of each arch is shown in Fig. 9a. The maximum displacement is obtained after equilibrium is reached at the end of each load increment. It can be seen that even after 100% application of BM3 load, the displacement response of the cellar system under traffic load and dead load is linear. It is also important to note that the sudden change of stiffness occurred due to the fact that the backfill load application stage was also included in Fig. 9a (until the total load reached 13.3kN). Meanwhile, the joint normal displacement vectors at the middle arch of the wharf cellar model is presented in Fig. 9b. Even though the normal displacement is relatively small, the separation between the pier and arch has occurred since the tensile damage state has been recorded.
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Fig. 9. (a) vertical displacement vs total applied force and (b) normal displacement vector at middle arch of the wharf cellar model
The calculated displacement requirement in accordance with NEN 9997–1:2016 is found to be 0.032 m. Comparing the required displacement against the maximum observed displacement from the numerical analysis, it can be concluded that the wharf cellar structure in Kromme Nieuwegracht is compliant under the BM3 load model of the NEN-EN 1991–2/NB Dutch guideline when the heaviest axle load is applied at the crown height of the middle arch. Note that different positions and load scenarios are beyond the scope of the present paper, but will be considered as part of the future work of this research. Validation of the cellar model against the site inspection results or other numerical methods such as limit state analysis or finite element analysis are also envisioned. 4.2 Failure Load and Failure Mechanism of Kromme Nieuwegracht Wharf Cellar Model After the compliancy of BM3 load model in accordance to NEN-EN 1991–2/NB is confirmed, the next step is to find the failure load and the governing failure mechanism. Considering the same loading position as specified in Sect. 4.1, the load is increased beyond the full application of BM3 until failure occurs. Failure occurs when the observed displacement keeps on increasing to infinity. It is observed that there is a significant capacity until failure occurs at the cellar system. The damage state of the wharf cellar model at failure load is presented in Fig. 10. It can be seen that the initial separation between vertically and horizontally stacked units were more apparent at failure where separations extended from the springing level up to the highest point of the pier that was in contact with the arch units (Fig. 10a and Fig. 10b). Furthermore, the damage mechanism also changed between the left side and right side arch as it extended towards the crown of each arch. Sliding failure between the vertical and horizontal units was observed on the left arch, while separation failure was found on the interfaces between the arch units of the right arch. Combined slidingseparation failure was also found between the bed joints of the horizontal units on the right-side arch. A similar damage pattern was observed at the middle arch (Fig. 10c) where separation failure at the interfaces of the arch units are continuous from one side of the pier to another. Sliding-separation failure was found towards the depth of the cellar at the area where the traffic load was applied.
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(c)
Fig. 10. Damage state of the wharf cellar under failure load condition at (a) left arch, (b) right arch, and (c) middle arch
The maximum displacement versus the total applied force until failure is presented in Fig. 11a. It is evident that until the onset of the failure load, the displacement response on all arches is relatively stable and as failure occurs the displacement increases significantly. On the middle arch where the heaviest axle load was applied, the displacement response at failure reached −13.85 mm while the displacement at the left arch, where the second axle load was applied, reached −4.78 mm. Due to severe downward movement at the left and middle arches, the right arch experienced extreme uplift where the maximum displacement response reached 18.81 mm. This shows that the failure mechanism of the cellar system involves more than one cellar span. Note that the displacements were taken at the extrados of each arch. To compare with the joint displacement vector plot shown in Fig. 9b, the joint normal displacement vectors of the middle arch at failure are presented in Fig. 11b. It is evident that the separation has extended both ways towards the springing level and towards the crown of the middle arch. Furthermore, the joint normal displacement at regions close to the right pier has reached a maximum value of 3.5 mm. The crack opening at the intrados of the arch close to the crown was also relatively large at 2.5 mm. Although no further inspection was conducted to measure the separation at the inside of the cellar, cracks perpendicular to the traffic direction at the middle wharf cellar was observed according to the Appendix A of the investigation report. Note that separations at the arch skewbacks were also found albeit small.
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Fig. 11. (a) vertical displacement vs force increment and (b) normal displacement vector of the middle arch at failure
Fig. 12. Deformed shape of the wharf cellar model at failure load (magnified 10x)
The deformed shape of the wharf cellar is shown in Fig. 12 (magnified by a factor of 10) while the original shape is presented in a transparent shade of blue. Similar to what has been pointed out from the previous figures, a crack opening at the intrados closer to the crown of the middle arch was observed, while cracking at both the right and left side piers was also clearly shown. Rotation of the right side piers and separations at the right side arch skewbacks were found which was caused by the extreme uplift of the right side arch. In conclusion, the failure load and mechanism of the cellar system is simulated well where the spread of damage and displacement response at the onset of failure is clearly shown. Note that similar to the numerical model in the investigation report, the loosely packed sand was assumed to be pre-loaded, hence no soft soil mechanism occurred at the cellar system which would have caused differential settlements at the piers of the cellar system which could cause a significantly different failure mechanism. It is also important to set a disclaimer that there are many simplifications considered in the numerical model such as the same crown height on each arches, the Boussinesq load dispersion, the blocky piers, and many more. Further calibrations of the numerical model with experimental tests are still needed and will be considered as the future work of this paper.
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5 Conclusions In this study, a micro-modelling approach for the safety assessment of an existing masonry wharf cellar system located in the Kromme Nieuwegracht canal in the city of Utrecht is introduced. A fast and robust geometry generation framework is created using Rhino + Grasshopper. The blocks are then imported to 3DEC for the numerical analysis. Rigid block formulation is used where all deformations and system nonlinearities are lumped at the contacts between blocks. Backfill soil load is applied as a distributed dead load while the traffic load is applied as a dispersed load to the cellar’s arch units according to the Boussinesq theory. The traffic load model in accordance with special emergency vehicle specified in the Dutch guideline is assessed for the wharf cellar structure. The heaviest axle of the traffic load model is applied at the crown of the middle arch while the second axle load is applied 4.2 m to the left side of the heaviest axle load. The analysis results show that under the considered traffic load of the Dutch guideline for traffic loads in bridges, the deformation of the cellar system is overall still within the specified limit despite damage occurring at the intrados of the vault and the arch units close to the pier. The displacement response is also still relatively linear. The next task was to find the failure load and the governing failure mechanism by incrementally increasing the applied load beyond the full application. Failure was predicted for an ultimate load significantly larger than the normative load. At failure, the separation between the arch units was extended to the arch skewbacks on both sides of the middle arch while the failure mechanism at the crown of the left and right arches were different. The crown on the left side arch experienced sliding failure while the right side arch experienced a combination of sliding and separation at the bed joints of the horizontal units. It is important to note that while this three-dimensional safety assessment framework can essentially be substituted by a two-dimensional model due to the 2-D load dispersion model, the intention to introduce the three-dimensional framework in this paper is to set a starting point of introducing a more sophisticated model where the load dispersion model is three-dimensional and that the cellar piers are discretized brick-by-brick as part of the future works. Moreover, the application of different traffic load positions and load scenarios according to the Dutch guidelines, and the variation of thickness of each arch in the vault structures will also be considered in order to simulate the actual condition of the wharf cellar system.
References 1. Brencich, A., Morbiducci, R.: Masonry arches: historical rules and modern mechanics. Int. J. Archit. Heritage 1(2), 165–189 (2007) 2. Utrecht, G.: Kelders in het stadshart Utrecht. Gemeente Utrecht, Utrecht (2020). (in Dutch) 3. Korff, M., Hemel, M., Peters, D.: Collapse of the grimburgwal, a historic quay in Amsterdam. Proc. Inst. Civil Eng. Forensic Eng. 175(4), 96–105 (2022) 4. NEN 8701+A1: Beoordeling van de constructieve veiligheid van een bestaand bouwwerk bij verbouwen en afkeuren – Belastingen. Nieuwe Europese Normen (2011). (in Dutch) 5. Sarhosis, V., De Santis, S., De Felice, G.: A review of experimental investigations and assessment methods for masonry arch bridges. Struct. Infrastruct. Eng. 12(11), 1439–1464 (2016)
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6. Tóth, A.R., Orbán, Z., Bagi, K.: Discrete element analysis of a stone masonry arch. Mech. Res. Commun. 36, 469–480 (2009) 7. Gobbin, F., De Felice, G., Lemos, J.V.: A discrete element model for masonry vaults strengthened with externally bonded reinforcement. Int. J. Archit. Heritage 15(12), 1959–1972 (2021) 8. Lemos, J.V., Gobbin, F., Forgács, T., Sarhosis, V.: Discrete element modelling of masonry arch bridges, arches, and vaults. In: Milani, G., Sarhosis, V. (eds) From Corbel Arches to Double Curvature Vaults. Springer, Cham (2022) 9. NEN-EN 1991-2:2021, Eurocode 1 - Actions on structures - Part 2: Traffic loads on bridges and other civil engineering works, European Committee for Standardization:Brussels (2021) 10. Royal Haskoning, D.H.V.: Verificatieberekening kelder Kromme Nieuwegracht te Utrecht. RHDHV, Utrecht (2021). (in Dutch) 11. NPR 9998:2020: Assessment of structural safety of buildings in case of erection, reconstruction and disapproval - Induced earthquakes - Basis of deisgn, actions, and resistances. Stichting Koninklijk Nederlands Normalisatie Instituut (2020) 12. Cundall, P.: A computer model for simulating progressive large-scale movements in blocky rock systems. In: Proceedings of the International Symposium on Rock Fractures. ISRM, France (1971) 13. Itasca Consulting Group, Inc, Three-Dimensional Distinct Element Code, Ver. 7.0, Minneapolis: Itasca (2020) 14. Lemos, J.V.: Discrete element modeling of the seismic behavior of masonry construction. Buildings 9(2), 43–54 (2019) 15. Centre for Civil Engineering Research and Codes, C: Structural Masonry: An Experimental/ Numerical Basis for Practical Design Rules. CRC Press:Netherlands (2014) 16. Choo, B., Coutie, M., Gong, N.: Finite-element analysis of masonry arch bridges using tapered elements. Proc. Inst. Civil Eng. 91(4), 755–770 (1991) 17. Ni, P., Mangalathu, S., Song, L., Mei, G., Zhao, Y.: Displacement-dependent lateral earth pressure models. J. Eng. Mech. 144(6), 1–12 (2018)
Analytical Model of Bracket Set Frame in Traditional Chinese Timber Structures Qingshan Yang1 , Ke Liu1(B) , and Pan Yu2 1 School of Civil Engineering, Chongqing University, Chongqing 400044, China
[email protected] 2 College of Civil Engineering, Taiyuan University of Technology, Taiyuan 030024, China
Abstract. Bracket set frame (BSF) consists of two column-head bracket sets (CHBSs) and one beam (Tiaojianliang), CHBS consists of bearing blocks (Dou) and short beams (Gong), in a unique manner in traditional Chinese timber structures. The mechanical performances of a BSF is different from a rigid joint or hinge joint exhibiting the behavior of a semi-rigid joint. An analytical model of BSF along y-axis direction of a building is proposed. Based on the structural form of BSF, the analytical model of a BSF is composed of rotational spring elements representing the Mantousun (MTS), Dadou with mortise (DDM) and beam elements representing the beams (Gong, Fang and Tiaojianliang). The accuracy of this model is validated with a solid element model with the same geometric dimensions and mechanical parameters. Effects of the vertical load and section dimension of Tiaojianliang on the load resistance capacity of BSF are analyzed. Result suggests that the load resistance capacity of BSF will increase significantly with the vertical load increases. The load resistance capacity of BSF will decrease with the section dimension of Tiaojianliang decreases. Keywords: Bracket Set Frame · Analytical Model · Rotational Spring Element · Vertical Load · Section dimension of Tiaojianliang
1 Introduction A timber structure is very different from modern concrete or steel structure, and an introduction on its construction is beneficial before discussions on the existing problem in this analytical study. A typical traditional Chinese timber structure usually composes of three structural layers vertically, i.e., the roof frame layer (RFL), the bracket set layer (BSL) and the column frame layer (CFL), as shown in Fig. 1 (a), (b) and (c). The BSL consists of spatial bracket set frame (SBSF), bracket sets (BSs) and beams (Gong, Fang and Tiaojianliang) of different dimensions, as shown in Fig. 1 (b), (d), (e) and (f). BS is also named as Dou-Gong (DG), which consists of bearing blocks (Dou) and short beams (Gong), in a unique manner. The BSs may be broadly classified into three types according to their locations, i.e., the CHBS on top of a side column, the intermediatecolumn bracket set (ICBS) on a beam (E-Fang), and the corner bracket set (CBS) on top of a corner column. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 301–311, 2024. https://doi.org/10.1007/978-3-031-39450-8_25
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The BSL includes spatial bracket set frame (SBSF) as shown in Fig. 1 (b) and (d). The SBSF includes BSF as shown in Fig. 1 (d) and (e). The BSF composes of two CHBSs and a long-span beam (Tiaojianliang) as shown in Fig. 1 (e) and (f). In order to analyze the mechanical properties of traditional Chinese timber structures, it is necessary and efficient to establish their analytical model. Existing models on different components of the BSF are adopted. They included the analytical model of column foot [1], the analytical model of mortise-tenon (MT) connection [2, 3] and the analytical model of single bracket set [4]. The analytical model of BSF will be developed in this study. This study proposes analytical model of BSF in traditional Chinese timber structures. BSF contains two CHBSs and one beam (Tiaojianliang). The CHBS contains MTS which is similar to mortise-tenon (MT) connection, the interface between Dadou and column head is similar to column foot (CF). Based on the above analysis and discussion, the analytical model of BSF is established. Based on the same geometric dimensions and mechanical parameters, the solid element (SE) model has been established to validate the accuracy of the analytical model. Finally, effects of vertical load and section dimension of Tiaojianliang on the load resistance capacity of BSF are discussed.
Linked beam (Fang) (a) RFL
Long-span beam (Tiaojianliang)
(b) BSL
(d) SBSF
CBS ICBS CHBS
Corner column Side column
(e) BSF
y-axis of a building x-axis of a building
(c) CFL
(f) CHBS
Fig. 1. BSF and its location and composition in a traditional Chinese timber structure.
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2 The Proposed Analytical Model of BSF 2.1 Analysis of Structural Form of BSF Vertical load such as the weight of tile, roof board and the snow load are firstly transferred to the RFL via flexural and shear actions, and then to the BSL in the form of concentrated forces. Horizontal loads such as wind load or earthquake load is transferred to the BSL by friction. Therefore, BSF is subjected to both horizontal and vertical loads, as shown in Fig. 2.
Vertical load N
Horizontal load P
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CHBS Long-span beam (Tiaojianliang) Fig. 2. BSF model along the y-axis of a building.
The schematic diagram of relative and absolute rotation in each layer of the CHBS when under vertical load and horizontal load along y-axis direction is shown in Fig. 3 (a). The fourth and fifth layers are joined by Tiaojianliang (Fig. 3 (b)), therefore, there are four interfaces in total, relative and absolute rotation may occur on the four interfaces, which could be simplified as rotational spring elements. Other part, i.e., the component between each interface and the Tiaojianliang could be simplified as beam elements as shown in Fig. 3 (b).
(a) relative and absolute rotation in each layer
(b) Rotational spring element
Fig. 3. The schematic diagram of relative and absolute rotation in each layer and rotational spring element
As shown in Fig. 4 (a), the CHBS has distinct multiple layer construction. The structural decomposition in the y-axis direction is shown in the second column. According
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Fig. 4. Structural form and extrusion deformation of second layer of CHBS.
to different structural form, there are two kinds of rotational springs, named A and B respectively, as shown in the fourth line of Fig. 4, for example, the schematic diagram of structural form of the second layer in the y-axis direction is numbered y2B. Where (a) is the original structure, (b) is the simplified structure, (c) is the schematic diagram of extrusion or compression deformation, and so on in other cases. The extrusion deformation relationship of first layer of CHBS is shown in Fig. 4 (A), which is referred as the analytical model of MTS and the analytical model of DDM as shown in Fig. 10, Fig. 11 and Fig. 12. The extrusion deformation relationship of the y-axis direction from second to fourth layer is shown in Fig. 4 (B), which is referred as the analytical model of MTS as shown in Fig. 10 and Fig. 11, the tenon in Fig. 4 (B) is similar to the MTS in Fig. 4 (A), the difference between them is whether there are gaps between the top of tenon or MTS and the upper components. Based on the analysis of structural form, the analytical model of BSF could be established according
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to those rotational springs. And those rotational springs composed of analytical models of sub-joints. MTS and DDM could be called as sub-joints. 2.2 Analytical Model of BSF The MTS model can be further simplified as a rotational spring element [2], the Dadou (Fig. 5 (a) and Fig. 10) with mortise model (DDm) can be further simplified as a rotational spring element [4], as shown in Appendix, they are the sub-joint analytical model of BSF. Based on the analysis of structural form in the above section, the analytical model of BSF contains these sub-joint analytical model, as shown in Fig. 5. BSF are simulated as rotational spring elements and beam elements in the axis of column head and Dadou. The interface between adjacent layers are modelled as rotational spring elements, the Gong, Fang and Tiaojianliang (Fig. 3 (b)) components have been modelled as beam elements. The simplified model of BSF is shown in Fig. 5. The stiffness matrix (Eq. (1)) of the BSF along the y-axis of a building is then obtained by assembling the stiffness matrices of different types of finite elements as Fig. 5, i.e., the Dadou, Mantousun and the column head (Fig. 3 (b)) is simplified as rotational spring element ➀, the upper interfaces (second layer to fourth layer) of BSF (Fig. 3 (b)) are simplified as rotational spring element ➂, ➄, ➆, the other parts are simplified as beam element ➁, ➃, ➅, ➇, ➈, CHBS on the right and left in BSF are symmetrical.
(1)
where, K donates the stiffness matrix of BSF; ⓔ donates one of the four submatrices of the stiffness matrix of element e; i and j are the node numbers of element e. The load-displacement relationship can be obtained as Eq. (2) F = K where, F and donate the load and displacement, respectively.
Fig. 5. Simplified rotational spring model of BSF.
(2)
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3 Validation of Analytical Model 3.1 Solid Element Model of BSF The BSF model is established in CAD (see Fig. 2), which only have geometric information and could not be analyzed mechanically. Then they have been imported into ABAQUS (see Fig. 6) to input mechanical parameters, interaction, boundary conditions and load condition, etc. 8-node hexahedral finite elements (element C3D8R) is adopted and the mesh of solid element of BSF is shown in Fig. 7. The red coordinates are the local coordinates, and the black coordinates are the global coordinates. The parallel-to-grain direction (the x-axis in the red coordinate system) of the Gong and beam components is perpendicular to the z-axis (in the black coordinate system) as shown in Fig. 6. The parallel-to-grain direction of other components is parallel to the z-axis as shown in Fig. 6 [5]. One step further, the BSF model is calculated and solved in ABAQUS. Finally, the result is output from ABAQUS for mechanical analysis. z y
z
x
y
x z
y y x
z x Fig. 6. Assembly of solid element of BSF.
Fig. 7. Mesh of solid element of BSF.
3.2 Validation of Analytical Model of BSF The load-displacement relationship of the BSF is in good agreement with that from the solid element model as shown in Fig. 8. This indicates the rationality of the analytical model.
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Fig. 8. The load-displacement relationship of BSF.
4 Mechanical Performances of BSF 4.1 The Effect of Vertical Load on the Load Resistance Capacity of BSF Heavy RFL is one of the remarkable features of traditional Chinese timber structures, as it plays an important role in energy dissipation [6] during a seismic event. Vertical loads with a value of 10kN, 20kN, 30kN 40kN and 50kN are applied separately to the top surface of BSF as shown in Fig. 2 respectively, and the load-displacement curve is shown in Fig. 9 (a). The load resistance capacity increases significantly as the vertical load increases, which suggests a heavy RFL would contribute notably to the load resistance capacity of the BSF.
(a) The effect of vertical load
(b) The effect of section dimension of Tiaojianliang
Fig. 9. The load-displacement relationship of BSF.
4.2 The Effect of Section Dimension of Tiaojianliang on the Load Resistance Capacity of BSF The original section dimension of Tiaojianliang is taken as standard and referred as coefficient of section dimension κ. . Considering the large section size of the beam
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(Fig. 1 (d), (e) and Fig. 2), the gradient reduction of section √ area is taken as the variable. κ = 2 means that the width and height of the section are 2 times of the original width and height respectively, and so on in other cases. It could be concluded that the load resistance capacity of BSF will decrease with the section dimension of Tiaojianliang decreases from Fig. 9 (b).
5 Conclusion Owning to the mechanical performances of semi-rigid joint of BSF, a rotational spring model is the core part of analytical model of BSF. The main conclusions of this study are summarized as follow. 1. The analytical model of BSF considering the interaction between the upper and lower components, layer number and components assembly method in the meantime is proposed. 2. Load resistance capacity of BSF increases significantly as vertical load increases, which suggests heavy RFL plays an important structural function in the resistance to lateral load. 3. The load resistance capacity of BSF will decrease with the section dimension of Tiaojianliang decreases. Acknowledgments. The work was supported the 111 project of the Ministry of Education and the Bureau of Foreign Experts of China (No. B18062), National Natural Science Foundation of China (51720105005) and Chongqing Science and Technology Bureau (cstc2020yszx-jcyjX0007).
Appendix When the BSF or CHBS under horizontal and vertical loads, the relative rotation would occur, the bending moment is consistent of two parts, i.e., the first part is extrusion deformation between Dadou and Mantousun, the second part is the compressive deformation between Dadou and column head, as shown in Fig. 10. The derivation of the two parts is referenced from [4]. The bending moment of first part is shown [4] as Eq. (3), and the extrusion deformation volume is in Eq. (4) and (5). ER ER Vt1 + Lc2 + μcosθ Lf 2 Vt2 M1 = Lc1 + μcosθ Lf 1 lt lt wt BC 2 Vt1 = SABC wt = 2 tanθ 2 1 − e−3αlt /2 wt EF Vt2 = + wt EF 2 tanθ α
(3) (4) (5)
where, μ is the frictional coefficient. θ is the rotation angle. Lc1 , Lc2 , Lf 1 and Lf 2 are the arm of force corresponding to Pc1 , Pc2 , Pf 1 and Pf 2 . lt and wt are the length and
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Fig. 10. The extrusion deformation between Dadou and Mantousun.
width of tenon. ER is elastic modulus of ‘Radial’ directions of the timber member. Vt1 and Vt2 are the extrusion deformation volume on the left and right part of Mantousun. The diagram of each symbol is shown in Fig. 10 and Fig. 11. The bending moment of second part is between Dadou and column head [4], there are four working states as shown in Fig. 12. The bending moment and the critical rotational angle of each working state are shown in Eq. (6) to (12). 3 − w l3 EL wdd ldd m m tanθ (6) M2−1 = 12hdd 2hdd NDG θ1 = arctan (7) EL ldd (ldd wdd − lm wm ) EL wm lm3 EL wdd ldd 2 EL wdd 3 tanθ + h1 cotθ − h (cotθ )2 12hdd 4hdd 6hdd 1 8hdd NDG θ2 = arctan EL −4wm lm2 + wdd (ldd + lm )2 2 − lm2 EL wm ldd EL (ldd + 2lm )wm (ldd − lm )2 =− tanθ + h1 48hdd 8hdd EL ldd (wdd − wm ) 2 EL (wdd − wm ) 3 + h1 cotθ − h1 (cotθ )2 4hdd 6hdd 8hdd NDG θ3 = arctan EL wdd (ldd − lm )2 3 h √ 1 2NDG NDG ldd dd − M2−4 = cotθ 2 3 EL wdd
M2−2 = −
M2−3
(8)
(9)
(10)
(11)
(12)
where, EL is elastic modulus of ‘Longitudinal’ directions of the timber member. ldd , wdd and hdd are the length, width and height of Dadou. lm and wm are the length and width of mortise. NDG is the vertical load which is applied to the top surface of CHBS in BSF. The diagram of each symbol is shown in Fig. 10.
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Fig. 11. The schematic diagram of plan extrusion deformation between Dadou and Mantousun.
h4
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(a) Working state 1
h1
(b) Working state 2
h1
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Fig. 12. The load-displacement relationship of BSF.
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The bending moments in the four working states can be summarized as Eq. (13). ⎧ M2−1 0 ≤ θ < θ1 ⎪ ⎪ ⎨ M2−2 θ1 ≤ θ < θ2 M2 = ⎪ M θ ≤ θ < θ3 ⎪ ⎩ 2−3 2 M2−4 θ3 ≤ θ
(13)
The total bending moment is the sum of M1 and M2 , and taking the derivative of the bending moments with respect to rational angle θ , the rotational spring stiffness K could be obtained.
References 1. He, J., Wang, J.: Theoretical model and finite element analysis for restoring moment at column foot during rocking. J. Wood Sci. 64(2), 97–111 (2017). https://doi.org/10.1007/s10086-0171677-5 2. Yang, Q., Yu, P., Law, S.: Load resisting mechanism of the mortise-tenon connection with gaps under in-plane forces and moments. Eng. Struct. 219, 110755 (2020) 3. He, J., Yu, P., Wang, J., Yang, Q., Han, M., Xie, L.: Theoretical model of bending moment for the penetrated mortise-tenon joint involving gaps in traditional timber structure. J. Build. Eng. 42, 103105 (2021) 4. Yu, P., Yang, Q., Law, S., Liu, K.: Seismic performances assessment of heritage timber frame based on energy dissipation. J. Build. Eng. 56, 104762 (2022) 5. Yeo, S., Komatsu, K., Hsu, M., Que, Z.: Mechanical model for complex brackets system of the Taiwanese traditional Dieh-Dou timber structures. Adv. Struct. Eng. 19(1), 65–85 (2016) 6. Meng, X., Li, T., Yang, Q.: Experimental study on the seismic mechanism of a full-scale traditional Chinese timber structure. Eng. Struct. 180, 484–493 (2019)
Stability Assessment of an Ancient Roman Heritage Tunnel: The Crypta Neapolitana Emilio Bilotta1,2(B) , Raoul Paolo Conte1 , Fausto Somma1 and Alessandro Flora1,2
,
1 Department of Civil, Architectural and Environmental Engineering, University of Napoli
Federico II, Via Claudio 21, 80125 Napoli, Italy {emilio.bilotta,alessandro.flora}@unina.it 2 Interdepartmental Centre for Cultural Heritage Engineering, University of Napoli Federico II, CIBeC, p.le Tecchio 80, 80125 Napoli, Italy
Abstract. The Crypta Neapolitana is a historic tunnel attributed to Lucio Cocceio Aucto, a Roman architect of the first century AD. It runs within the current urban area of the city of Naples and crosses the Posillipo hill, that separates the Gulf of Pozzuoli from that of Naples. Since about one century the tunnel has been not used for its original purpose, due to the creation of other larger road and rail tunnels nearby. After being abandoned, several disruptions occurred along its route and the Crypta is not accessible anymore to the public. The tunnel runs across different pyroclastic formations: the deeper layer is a weakly cemented old tuff, with poor mechanical properties, that can be considered a transition material between an uncemented pyroclastic silty sand (pozzolana) and a tuff, with some specific sections in which cohesion is close to zero. To check the current static conditions of the tunnel, an in-situ investigation was conducted and elastic-perfectly plastic 2D analyses were performed with the FE code Plaxis. The main results are briefly summarised in this paper. They indicate that most times the critical instability mechanism is the onset of tension cracks at the sidewalls and the subsequent collapse of blocks, consistently with the evidence of the field survey. Therefore, before the historic tunnel is re-opened to the public, a diffused reinforcement is required. Keywords: Roman tunnel · tuff · stability · renovation · numerical analyses
1 Introduction In the context of the Venice Charter (1964), the conservation of an old heritage monument is a matter of careful discussion concerning its “authenticity” among specialists of several topics, that often requires a correct definition of its originally conceived life cycle. Hence functional integrity, as one of the elements defining the role of the monument in its environment, should be part of the conventional assessment framework that usually considers the material, the iconic and the historical integrity as goals for preservation. The assessment of a monument functional integrity is a matter of highest importance © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 312–322, 2024. https://doi.org/10.1007/978-3-031-39450-8_26
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when the use of an old structure must be allowed, within its original purpose or even in a new way [1]. In this perspective, the preservation of the role of the monument, along with the perception of it within the local historic environment, can usefully help to set filters and criteria to carry out the necessary checks of integrity, smoothing the oftenharsh dispute between extreme conservation and pointless reconstruction that may arise when deciding the clue strategy for conservation and what the design goal should be. Underground structures, such as that we deal with in this paper, require in many cases to take actions to remove the cause of critical mechanisms rather than to mitigate their effects on the structure. Therefore, ground reinforcement with new technologies, that can be classified as a “modern renovation” resulting at an intermediate level of iconic integrity [1], should not be excluded, especially if it contributes to keep the built heritage “alive”, that is “with the highest functional integrity”. Of course, a careful diagnosis of the monument health conditions needs to be made, including all the necessary specialties, among which geotechnical engineering. In this paper we will deal with an ancient Roman tunnel, from a geotechnical point of view. The tunnel, located in the urban area of Naples (Italy), has been in use for centuries to connect two areas of the city, enduring several adaptations and retrofitting before being eventually interdicted to the public use due to critical stability conditions. Almost one century after its closure, re-opening the heritage tunnel to its community is currently under consideration.
2 Historical Background The Crypta Neapolitana is a tunnel running close to the East-West direction across the Posillipo hill that separates the Gulf of Pozzuoli from that of Naples (Fig. 1). It is attributed to the Roman architect Lucio Cocceio Aucto (I BC - I AD), as two other long Roman tunnels in the area (Seiano Grotto e Cocceio Grotto). Some recent studies [2] have supported the hypothesis that a smaller tunnel along its longitudinal axis already existed before, possibly for ritual purposes. In any case, the Roman tunnel of Augustan age had the clear purpose of improving the connection between the growing town of Neapolis (Naples) and the commercial port of Puteolis (Pozzuoli), at that time the largest in the western Mediterranean sea, avoiding the alternative route “per colles” (across the hill). The original Roman cross section of the tunnel was between 4 and 5 m large, and likely no more than 4 m high, with a curved vault and vertical side walls. Its shape is mostly lost, because of subsequent reshaping carried out for centuries. A longitudinal section with the recent shape of the tunnel is reported in Fig. 2. The tunnel is 711 m long, with variable section along its route. Two inclined shafts on the two sides of the hill provide ventilation at about one third of the total length from both entrances.
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Fig. 1. Map of the coastal region called Phlegrean Fields; in evidence the location of the Crypta Neapolitana through the Posillipo hill (The old town of Naples is on the East side). The topography refers to the second half of the XIX century, while nowadays the whole area on both sides of the tunnel is densely urbanized, the two towns of Napoli and Pozzuoli merging into a unique built environment.
Fig. 2. Longitudinal section of the Posillipo hill along the Crypta longitudinal axis, with indication of the geological units
3 Ground Conditions The geological and geotechnical conditions of the tunnel have been explored in the recent past [3, 4]. Figure 2 shows schematically a section of the Posillipo hill the different pyroclastic formations along the route. The deepest layer is a weakly cemented old tuff, with poor mechanical properties, that can be considered a transition material between an uncemented pyroclastic silty sand (pozzolana) and a tuff. In some specific tunnel sections this weak tuff shows an almost null cohesion. Due to the uncomplete cementation process, this formation is not affected by the typical syngenetic cooling fractures observed elsewhere in town in well cemented tuff. The intermediate layer shown in the longitudinal section of Fig. 2 is made of Neapolitan Yellow Tuff, that covers the old tuff in the hill of Posillipo. As well known, this is a soft, light rock with a good
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degree of cementation. The rock mass is characterized by a number of subvertical and sub-horizontal cooling fractures. The Crypta Neapolitana crosses the Neapolitan Yellow Tuff only for about 100 m from the western portal, and only for few meters on the eastern one. Therefore, most of the tunnel is actually excavated in the old tuff. Because of this, the eastern and western parts of the tunnel were unlined, while the central part was lined with masonry. A few parts of the ancient opus reticulatum are still visible.
Fig. 3. Cross section of the Crypta Neapolitana 20 m inside the eastern entrance: current state and reconstruction of the different elevations of the floor in time (modified after [3]).
After more than thousand years from its construction, the route “per cryptam” (through the grotto) was still used but quite undersize compared to the increasing traffic of a growing capital city of the western Europe. It is documented that in 1445 the king Alphonse of Aragòn undertook works to lower the eastern entrance. A century later, the Spanish viceroy Pedro de Toledo further lowered this part of the tunnel, paving the roadway. Other retrofitting works were done under Pedro Antonio of Aragòn (XVII century) and Charles III Bourbon (1748). After Italy reunification, the Municipality of
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Naples undertook further works to strengthen the eastern part of the tunnel with a number of masonry arches (1893). Finally, in 1917 the access and transit though the Crypta Neapolitana was interdicted because of ongoing local collapses and of the risk of collapse of blocks. The role of the tunnel of connecting the two sides of the hill had been taken meanwhile by newly built railways and road tunnels. In 1930, the eastern part of the Crypta was partly filled, and the floor raised back as much as 9 m, to accommodate the entrance to an outside green area. Figure 3 show a schematic reconstruction of the changes of floor elevation in time [3]. Figure 4 shows the two entrances of the tunnel. Recently, bolted steel arches were placed to support the vault in the first 30–40 m on the western side (Fig. 4a).
(a )
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Fig. 4. Western (a) and Eastern (b) entrances of the Crypta Neapolitana in recent photos.
The tunnel is currently in very bad static conditions, with diffused collapse of large blocks along its axis, especially in the central part, where site survey is now almost impossible for safety reasons and only speleologists have been allowed to explore [5]. The Roman masonry lining has collapsed along the whole lined stretch, with only few parts, with no static role, still standing. A large part of the masonry supporting structures placed in the 19th century collapsed. Figure 5 shows some photos of a recent survey [1] from both entrances of the tunnel, giving a clear idea of the widespread state of instability.
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Fig. 5. (a) From top left: pictures from the western entrance till ca. progressive 350 m. Collapse of blocks, tension cracks and collapse of masonry lining are clearly visible; (b) From top left: pictures from the eastern entrance till ca. progressive 150 m. Masonry arches well preserved in the first part, with complete collapse of side walls in the final part. Large subvertical rectangular blocks sometimes on the verge of instability failure (modified after [1]).
4 Analysis of Static Conditions of the Crypta An in-situ investigation was carried out about 20 years ago to check the static conditions of the tunnel. Boreholes from the ground surface and core drills from within the tunnel were executed. Samples retrieved during coring were tested to get the uniaxial compressive strength σc, while flat jack tests were carried out in some sections of the tunnel to quantify the in situ vertical stress (Fig. 8). In the old tuff, i.e. for most of the tunnel length but the parts close to the two entrances, the compressive strength values are in the range 0.5 MPa < σc < 2 MPa, while in the Neapolitan Yellow Tuff σc is as high as 6 MPa. The vertical stress level in the rock, estimated with flat jack, indicates that, for distances from the western entrance between 100 m and 200 m, the rock surrounding the cavity is locally close to failure (σv /σc = 1), consistently with the evidence of diffused collapse.
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Fig. 6. Values of the uniaxial compressive strength of tuff and in situ stress along the axis of the Crypta. Distances taken from the western entrance (modified after [3]).
A detailed geometrical survey of the tunnel was also carried out with a laser scanner (Fig. 7). Values of GSI variable between 55 and 75 were estimated in the western side of the tunnel (sections A to C in Fig. 7), much lower in proximity of the eastern side (GSI = 23 in section E and F in Fig. 7). The characterization of the rock mass was done using the Hoek & Brown failure criterion, according to the values of σc,i (uniaxial compressive strength for intact rock) shown in Fig. 6 and assuming the constant mi (for intact rock) between 8 and 13 [6], then converting the parameters into the ones (c, ϕ) of the Mohr-Coulomb failure criterion, to be used in elastic-perfectly plastic 2D analyses carried out with the 2D Finite Element code Plaxis [7]. Young’s modulus E values were also obtained by using empirical correlations [8]. The history of excavation, further lowering, filling and retrofitting has been simulated, in order to establish as better as possible the current state of stress around the cavity sections. Hence, the safety level has been assessed by a “strength reduction” analysis, that is a common numerical procedure that consists in progressively reducing the original shear strength of the materials. Figure 8 briefly summarises the results in terms of plastic stress points for shear and tension failure [9]. The corresponding value of safety factor corresponding to a mechanism of local collapse (blocks failure) is shown in the figure for each section. While most sections are globally stable, a critical situation is shown in section C (FS≈1), due to extensive tensile failure in the roof. Assuming that yielded volumes progressively collapse, the numerical analyses indicate that most times the critical issue is the creation of tension cracks on the sides and the subsequent collapse of blocks, consistently with the experimental evidence. This mechanism can be reiterated, i.e. local collapses, and subsequent reshaping of the sections, may trigger further collapses and reshaping, and so on. It seems therefore that the preservation of this Roman tunnel requires a diffused reinforcement where critical mechanisms may be progressively activated.
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Fig. 7. Cross sections (obtained by laser scanning) of the Crypta Neapolitana considered in the numerical analyses, with indication of their position (distance from western entrance) along the tunnel axis.
FS 1
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Fig. 8. Results of the numerical analyses in terms of plastic stress points (red and white points corresponding respectively to shear and tension failure). FS is the safety factor corresponding to a mechanism of local collapse (blocks failure)
5 Seismic Behaviour of the Crypta Due to the seismicity of the area, any intervention to improve the stability conditions of the Crypta Neapolitana needs to be seismically assessed through a series of dynamic analyses. In the following, as an example, the dynamic behaviour of the eastern entrance (section F) during the the Irpinia earthquake (Mw = 6.9) that struck the region on 23 November 1980 has been analysed. The event was classified at grade X (Extreme) on
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the Mercalli intensity scale. It left at least 2,483 people dead, at least 7,700 injured, and 250,000 homeless. The maximum PGA value, recorded at the Sturno seismic station (close to the epicenter) was approximately equal to 3.14 m/s2 (Fig. 9a), while the recording station closest to the Crypta Naepolitana, located in Torre del Greco (TDG), recorded a PGA of 0.58 m/s2 (Fig. 9b). Since TDG Station is just 15 km away from the Crypta Neapolitana, and the subsoil sites soil class are the same (class B), this record has been used as input signal for the dynamic analysis, with no further modifications. Since the tunnel of the Crypta Neapolitana is predominantly oriented along the East-West direction, a simple 2D model of the tunnel transves section is practically North-South oriented. For this reason, only North-South and the vertical seismic signals have been applied at the bottom base of the model. Free field boundary conditions were imposed at the sides of the Plaxis numerical model. In addition to the static analysis, a Rayleigh damping ratio of 1.5% was assigned to materials, calibrated with double frequency approach.
(a)
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Fig. 9. (a) Position of recording stations and epicentre of the Irpinia earthquake 1980; (b) TDG Station Records
Figure 10 shows the results in terms of relative shear stress (τ rel ) and total deviatoric strain (γs ), at the instant of time when maximum accelerations are reached at the base of Crypta Neapolitana. Relative shear stress values very close to unity (red in Fig. 10a) in large areas around the section represent possible serious damages scenario. Moreover, Fig. 10b shows the presence of a local mechanism on the right side of the tunnel wall, where block fall may occur. Shear bands around the cavity, reaching the ground surface, also envisage the possibility of a global collapse mechanism affecting the tunnel entrance. At the end of the dynamic calculation, a safety analysis was conducted starting from the stress states generated by the seismic shaking, yielding to a safety factor equal to 1.025 (compared to 1.25 of Fig. 8). Overall, the example confirms that the stability conditions of the tunnel may have been affected by the seismicity of the area and that this issue should be carefully considered, according to code prescriptions, in the design of interventions aimed at reusing the tunnel.
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Fig. 10. (a) Results in terms of relative shear stress; (b) Results in terms of total deviatoric strain.
6 Conclusions The Crypta Neapolitana is a Roman heritage tunnel that played a key role in the development of the city of Naples and deserves a renewed use for the benefit of the community to which historically it belongs. A preliminary study on its current conservation and static conditions provided a clear indication that its preservation and possibility to use requires a wide reinforcement. This brings the discussion to the constraints posed by the relevance of the historic site. The wounds of time are in this case clearly visible, and there is no reason to try and replicate the original Roman cross section, whose traces are mostly lost. The largest part of the tunnel has been naturally reshaped as a result of a stress redistribution within the rock mass or later human interventions. Then, the question arises about what should be preserved. In this case, it seems that the strongest legacy is linked to the role of the Crypta Neapolitana, which is the connection of two neighbourhoods separated by the hill, as demonstrated by their names: Fuorigrotta (literally, out of the grotto) the one on the west side, and Piedigrotta (literally, at the entrance of the grotto) the one on the east side, the grotto obviously being the Crypta Neapolitana. This path has been a living part of the city for at least two thousand years, and still keeps traces of this long-lasting life. Therefore a hard interference with the iconic integrity may be justified in this case to let the Crypta Neapolitana return to its role of a connecting path. In particular, it should become a pedestrian tunnel that would correspond to the best possible preservation of its functional integrity. This is actually a matter of discussion with local authorities. Interventions should include: a new lining in the central part of the tunnel, with new materials and local openings to show details of the old masonry lining; a retrofitting and underpinning of the masonry arches on the eastern side; bolting of potentially instable blocks, and bolted nets in the unlined western part of the tunnel excavated in the Neapolitan Yellow Tuff.ber. Acknowledgements. The work is partly carried out in the frame of the research project GIANO (Geo-risks assessment and mitigation for the protection of cultural heritage) funded by the Italian Ministry of University and Research (PRIN 2020, no. 2020WP2SC9).
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References 1. Flora, A.: Taking care of heritage, a challenge for geotechnical Engineers. In: Geotechnical Engineering for the Preservation of Monuments and Historic Sites III (Lancellotta, Viggiani, Flora, de Silva & Mele Eds), pp. 19–54 (2022) 2. Escalona, F.: Personal communication (2022) 3. Amato, L., Evangelista, A., Nicotera, M.V., Viggiani, C.: The tunnels of Cocceius in Napoli: an example of Roman engineering of the early imperial age. In: Proceedings of AITES/ITA WTC 2001, Progress in Tunneling after 2000, Milan 10–13 June 2001, 1:15–26, Bologna: Pàtron (2001) 4. Viggiani, C.: 2nd Kerisel lecture: geotechnics and heritage. In: Proceedings of the 19th International Conference of ISSMGE, Seoul (2017) 5. Ferrari, G., Lamagna, R., Rognoni, E.: Crypta Neapolitana (Naples, Italy), a multidisciplinary underground heritage site. In: Proceedings of the 3rd international congress of speleology in artificial cavities, Dobrich (Bulgaria), May, 20th –25th 2019, pp. 94–99 (2019) 6. Hoek, E., Brown, E.T.: Practical estimates of rock mass strength. Int. J. of Rock Mech. Min. Sci. 34(8), 1165–1186 (1997) 7. Plaxis: material models manual and reference manual - Plaxis CONNECT Edition V22.02. Bentley (2022) 8. Hoek, E., Brown, E.T.: The Hoek–Brown failure criterion and GSI – 2018 edition. J. Rock Mech. Geotech. Eng. 11(3), 445–463 (2019) 9. Conte, R.P.: La Crypta Neapolitana: analisi numerica di stabilità di una galleria di interesse storico-archeologico. M.Sc. Thesis, University of Napoli Federico II, in Italian (2020)
Contributions of Numerical Modelling to the Stability Analysis of Old Masonry Tunnels O. Moreno Regan(B) Setec TPI, Paris, France [email protected]
Abstract. This paper presents the stability verification of an old masonry tunnel that belongs to the archaeological site of ancient Nemea, Greece. The calculations are carried out using a 2D nonlinear finite element analysis with a damage model. The study presents the results of a structural evaluation in the case that the overburden load above the tunnel increases. This tunnel was initially studied by Alexakis and Makris (2013, 2014) and solutions were provided using Limit Analysis. In this study, a comparison is given regarding the calculated bearing capacity of the tunnel between Limit Analysis and the proposed FE model. Then, several aspects of the numerical modelling of masonry tunnels are discussed. Firstly, the influence of the constitutive law of masonry and the differences between the damage model and two plastic models. Secondly, the stiffness of the surrounding ground, which has an impact on the bearing capacity of the tunnel because the earth pressure is a function of the deformation on the tunnel. And finally, the mesh size, which impacts the depth of the cracked zone and produces a variation of about 15% in the bearing capacity results. From the damage model it was found that horizontal convergences are about 3 cm before failure. This output is a major advantage of the FEM analysis with respect to limit analysis, for it allows to suggest some displacement thresholds. Lastly, a brief discussion is presented regarding the rotational capacity of the hinges as a stability verification criterion. Keywords: Masonry · Damage · Tunnel · Vault · Underground · Nemea · Numerical uncertainty · Soil-structure interaction
1 Introduction In the archaeological site of Ancient Nemea, Greece, south from the temple of Zeus at some 450 m, there can be found the Early Hellenistic Stadium of Nemea. The entrance to this Stadium is made through an open-air passageway that cuts into the slope of the hill on the western side of the Stadium; the passageway is followed by a 36 m vaulted masonry tunnel which remained undiscovered until 1978 (Fig. 1). This tunnel is the subject of this paper and was initially studied by Alexakis and Makris (2013, 2014) based on the findings published by Miller (2001), cited by the former. The objective of the study performed by Alexakis and Makris was to evaluate the structural stability in its current state using limit analysis, as well as an evaluation of its bearing capacity in © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 323–338, 2024. https://doi.org/10.1007/978-3-031-39450-8_27
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the case of an increase of the load above it; also, the objective was to shed some light regarding the exfoliation and damage observed in some stones of the tunnel. Using the preexisting results from limit analysis as a reference solution, the objective of this study is to compare and bring out some intrinsic characteristics (advantages and shortcomings) of the nonlinear FE calculations. To this end, a damage model specially conceived to study masonry is used, accompanied by other nonlinear models as a comparison. Other than the study of the bearing capacity, the objective is also to highlight the importance of the deformations of the structure near failure, which can be obtained by a FE Model. If engineering works are carried out near the tunnel, the displacements are the only thing that can be measured during the works, hence it is important to establish some thresholds on displacements to guarantee the tunnel safety. This aspect is discussed in the paper as well as the uncertainties related to FE modelling through a total of 20 models. This paper is the follow up of previous works about masonry tunnels, see Moreno Regan et al. (2017, 2018, 2022).
2 Modelling Strategy 2.1 Tunnel Description According to Alexakis and Makris (2013, 2014) the tunnel is made up by single limestones blocks 40 cm thick, covering a span of 2.12 m; the rise of the vault is about 0.78 m and the height of the sidewalls is 1.60 m, see Fig. 1 c). There is no mortar between stone blocks, which are freely in contact with each other. The tunnel was built during the 4th century BC as a cut-and-cover tunnel, more details are presented in section Sect. 2.3. The choice was made here to model the tunnel as a continuous medium to study the formation of hinges, the bearing capacity and the deformations, for different configurations. As a reminder, limit analysis also considers the masonry vault as an equivalent continuous medium. The soil around and under the tunnel is also modelled explicitly and the interaction between the tunnel and the soil is modelled with an interface. The calculations were made assuming plane strain conditions.
(a)
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Fig. 1. Tunnel-entrance to the stadium of ancient Nemea: (a) General view of the tunnel, from the west, photo by Miller (2001), (b) Interior of the tunnel, from the East, photo by Miller (2001), (c) Tunnel dimensions (in m), according to Alexakis and Makris (2013, 2014)
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2.2 Masonry Several nonlinear models are considered for the constitutive law of the masonry. The base model is a damage model, and two plastic models are used for comparison. Their description is presented hereafter. Damage Model. A specific model for masonry that combines homogenization and damage was developed in a previous work, Moreno Regan et al. (2017). However, the homogenization part is not considered in this study since the thickness of the tunnel is formed by a single stone block, and the homogenization is not really required. Only the isotropic damage model part is used. This model is a reworked version of the damage model by Mazars (1986), and a thorough description of the numerical model can be found in Moreno Regan et al. (2017). This model produces a damage variable d , that reduces the elastic modulus E as the load increases: σij = (1 − d )Cijkl : εkl
(1)
The variable d ranges from 0 to 1, with 0 corresponding to no damage. This model ∼ considers an equivalent strain ε at each Gauss point, which represents through a single variable the three-dimensional state of strain: σ˜ 1 2− + σ˜ 2 2− + σ˜ 3 2− ∼ 2 2 2 ε= γ ε1 + + ε2 + + ε3 + with γ = − (2) σ˜ 1 − + σ˜ 2 − + σ˜ 3 − where εi (i = 1, 2, 3) are the principal strains and σ˜ i the principal effective stress in the direction i, εi + = εi if εi ≥ 0, or zero otherwise and σ˜ i − = σ˜ i if σ˜ i ≤ 0, or zero otherwise. The value of γ is bounded between 0 and 1 and calculated only when at least one principal effective stress is negative, i.e., in compression. At each material ∼ point, damage starts and evolves if the equivalent strain ε reaches an initial threshold value given by εD0 = ft /E0 , where ft is the tensile strength and E0 is the elastic modulus without damage. The expression of the damage scalar variable d is a linear combination of two variables, dt and dc , associated respectively with the tensile and compression stresses: d = αt dt + αc dc
(3)
where αt + αc = 1. The evolution laws of the two variables of damage are: εD0 (1 − Ac ) Ac − ε˜ M exp Bc − (˜εM − εD0 ) εD0 exp −Bt (˜εM − εD0 ) dt = 1 − ε˜ M
dc = 1 −
(4) (5)
where Ac and Bc are parameters obtained experimentally from the stress-strain curves ∼ of a uniaxial compression test, εD0 the initial threshold and ε M is the actual threshold ∼ equal to εD0 if it has never been reached, or the maximum value reached by ε otherwise.
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Equation for dt in (4), (5) includes a regularization technique in traction, to reduce mesh sensitivity problems in the √ finite element simulations. The parameter Bt depends on the characteristic length lc = S (where S is the area of the finite element to which the integration point belongs), the mode I fracture energy Gft , and the simple uniaxial tensile strength of the material σt according to Bt = lc σt /Gft . Plastic Model 1. The first elastic-plastic model is the classic elastic perfectly plastic model with the Mohr-Coulomb criterion. The choice of the mechanical parameters c (cohesion) and ϕ (friction angle) are proposed in such a way as to find the following relations between compressive and tensile strength: 1 + sin ϕ 2c cos ϕ 2c cos ϕ σc = and σt = , σc = − σt 1 − sin ϕ 1 + sin ϕ 1 − sin ϕ
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Fig. 2. Nonlinear criteria for masonry constitutive law in Plane Strain conditions (σ3 = 0). With σt = 0.1 MPa and σc = 10 MPa
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Plastic Model 2. The second elastic-plastic model is the 3-parameter Willam-Warnke with softening behavior in tension and perfectly plastic behavior in compression. The criterion is described in full detail by Ulm (1996). For all three models, the criterion in the principal stress space as well as the evolution of the stress-strain relations in compression and in tension are illustrated in Fig. 2. It is important to notice that in plane strain conditions there is no limit in biaxial compression for any of the considered models. Properties are presented in Table 1. It was considered that the masonry has a small but no zero tensile resistance, for the sake of numerical stability. The value of σt = 0.1 MPa was chosen, which is consistent with values found experimentally (see Moreno Regan et al. (2018) for instance). The compressive strength σc = 10 MPa is the same as the one suggested by Alexakis and Makris (2013, 2014). The elastic modulus was chosen to take into account the discontinuity between blocks.
Table 1. Masonry material properties Macnnerie kN/m3
Damage model
Mohr-Coulomb
εD0 1.00E-05
c
ρ
2200
E
10000 MPa
Gft
100
ν
0.25
Ac
1.355
σt
0.1
MPa
Bc
1414
σc
10
MPa
Pa.m ϕ
0.500 78.579
William-Warnke MPa
σbi
10
zu
1
Z0
0.8
κ
1000
MPa
2.3 Modelling Stages and Loading According to Alexakis and Makris (2014), the tunnel was built as a cut-and-cover structure, i.e., a trench is first opened up, then the tunnel is built and finally the trench is refilled with earth. This procedure was reproduced in the model, but without considering the trench. In the first stage the tunnel is free standing over the bedrock, then a successive height of backfill of silt soil is added: 1,2,3 and 5 m; and finally, a surface load is applied (see Fig. 3). This load, distributed over the 3 m width of the tunnel, is supposed to represent a theoretical overburden added. Other possibility is to impose a displacement and then find the load by integration. The objective of the calculation is to find the maximum load (height of the overburden). The load is applied only in a 3 m width in order to have the same load case as Alexakis & Makris. Applying the load to all the width of the model would result in an increase in the horizontal load transmitted to the sidewalls and consequently, an increase in the bearing capacity of the tunnel (see Sect. 4.2), however this increase in the horizontal force was not considered by Alexakis & Makris. In order to estimate the failure load of the masonry tunnel with the FE model, the surface load must be discretized and therefore applied by load increments. The results of the nonlinear calculations will depend on how the load is applied: applying small increments reduces the precision of the results, large increments increase it. Here, the calculation was made by discretizing the load into 50 increments. The tolerance of the nonlinear calculations was set to 0.01 and with a maximum number of iterations per
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load increment of 4000. All calculations are made using CESAR-LCPC finite element software with solver rev. 062 (2021).
Fig. 3. Load, mesh, and properties for the FE Model
2.4 Soil and Geotechnical Considerations The tunnel is surrounded by a backfill made of silt soil, and it stands over a formation of bedrock. The soil is modelled as an elastic perfectly plastic material using a MohrCoulomb criterion. Alexakis and Makris (2014) proposed for the cohesion and friction angle of the silt Backfill, respectively, c = 0 kPa and ϕ = 30◦ . As it happens, with a FE model that explicitly models the soil with a surface load (see Fig. 3), it is not possible to consider a backfill with zero cohesion and at the same time search for the failure load (overburden) of the masonry vault: the soil over the vault will fail first (with a mechanism similar to Fig. 9c) before significant loads are transmitted to the masonry vault. This is why a cohesion of 10 kPa was considered for the silt backfill, and ϕ = 30◦ as proposed by Alexakis and Makris (2014). In a similar way, the Bedrock under the sidewalls must be able to bear the vertical load coming from the tunnel sidewalls. Properties presented in Fig. 3 are proposed in such a way as to withstand an unweighted stress of 2000 kPa (see Table 2), i.e., the bearing capacity of a footing of B = 40 cm, using Meyerhof formula. The choice of the elastic modulus E of the soil is a matter of interpretation, because usually the modulus of deformation needs to account for the range of strain expected in the soil next to the tunnel, as explained by Bourgeois et al. (2018). Consequently, a proper soil test should be carried out to estimate E. However, since no tests are available, we can take the plausible range of values for silt soil given, for instance, by Obrzud and Truty (2018), that goes from 2 to 40 MPa, depending on its consistency and plasticity. As a first calculation an elastic modulus of 20 MPa for the backfill is considered; for the bedrock a modulus of 200 MPa is chosen. As it will be discussed later, the value of the stiffness and shear strength properties of the soil next to the sidewalls are crucial when determining the load capacity of a masonry tunnel. The interaction between the tunnel and the surrounding ground is operated by an interface in the model. This interface allows only the sliding of the finite elements of the soil with respect to those of the tunnel. Properties are showed in Fig. 3.
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3 Results: Comparison with Limit Analysis 3.1 Horizontal Earth Pressure State The lateral earth pressure contributes greatly to the stability of the masonry vault, so its determination must be carefully established. Alexakis and Makris (2014) concluded that an active pressure state was unlikely, and therefore the most likely state was the “at rest” state, that is, the horizontal pressure is equal to σh = K0 σv , with K0 = 0.5. To approximate this state, we have set Poisson’s ratio to 0.33. Even if the failure mechanism is different from a sliding wedge along an assumed failure plane behind a retaining wall, we assume that the active coefficient Ka can be obtained with classical approaches. The FE calculation found that the horizontal pressure at the sidewalls, before the extra overburden, lies somewhere between Ka and K0 (Fig. 4); and this is without considering creep and consolidation phenomena that may occurred over the last 2300 years in the backfill (period of stabilization according to Miller (2001)), which can only further complexify the numerical model. The horizontal pressure applied to the tunnel depends on its deformation, and vice versa; its estimation can only be achieved with a model that explicitly takes into account the interaction soil-structure, as will be discussed in Sect. 4.2.
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Fig. 4. Horizontal earth pressure next to the sidewall for different values of the backfill height H : Analytical vs FE Model.
3.2 Bearing Capacity of the Masonry Tunnel Alexakis and Makris (2014) found that the tunnel in its current state has the capacity to withstand large vertical loads. When studying the additional distributed load needed to bring the tunnel to failure, they found that a load of 773 kN (per meter) was necessary, corresponding to a pressure of 258 kPa applied over the 3 m width of the tunnel (see Fig. 3), or an additional column of soil 3 m wide and 14.31 m high. In our study the extra overburden was applied as a distributed load. The results of the damage model indicated that failure occurs for a pressure of 432 kPa. However, in the FE model this load is not entirely supported by the masonry vault alone: the soil by itself is capable of taking some of the load. Consequently, in order to find the actual load supported by the masonry vault, the axial force was investigated at the springer of the vault. Results are presented in Table 2. For the set of parameters chosen, the nonlinear FE model gives a failure load very close to limit analysis results, only 8% greater (total load
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of 1006 kN vs 934 kN). Furthermore (Fig. 5) it was found that the thrust line at failure is almost identical, except at the supports, due to the chosen stiffness of the bedrock. For the calculations carried out here, the thrust line is no other that the eccentricity of the resultant force: e = M /N , where the axial force N and the bending moment M are obtained for each cross section normal to the mean line by integration of the normal stress. The results of the other constitutive laws and further analysis are studied in greater detail in Sect. 3. Table 2. Load carried by the vault, initial and failure Limit Analysis [2]
FEM DAM kN
PLAS 1 kN
PLAS 2 kN
Height m
Volume m3
Weight kN/ m3
Load kN
Each sidewall kN
kPa
Self weight (vault)
–
1.3586
22
30
15
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15
Initial overburden
–
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42.93
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966
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141
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467
1168
503
242
304
1006
483
609
8%
−48%
−35%
Total by sidewall Total
934
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Plastic MC Plastic WW Damage Limit Analysis [2]
Fig. 5. Thrust lines at failure
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4 Results: Advantages and Downsides of the FEM Numerical Modelling 4.1 Bearing Capacity: Compressive Strength or Hinge Mechanism? When studying the masonry vaults of gothic churches, Heyman (1995) stated the following assumptions for masonry arches: deflections are negligible, the mean stresses are low in masonry blocks (so it is safe to assume infinite strength), and the masonry arch becomes unstable if a pattern of hinges appears which corresponds to the mechanism of collapse. In other words, failure would happen then when a hinge mechanism appears, regardless of stress. The problem is viewed as a geometrical one: a sufficient condition of stability is that the arch thickness is large enough to allow the thrust line to lie inside the masonry. However, for the case studied here, Alexakis and Makris (2014) conclude that the theoretical failure of the masonry tunnel is rather related to the increase in stress up to the compressive strength, and not to the creation of a hinge mechanism. Maximum compressive stress happens at the springer, in the intrados (Fig. 6b). Using a FE model, the bearing capacity is reached when the calculation leads to no convergence of the iterative procedure of the solution of the nonlinear problem. However, understanding the reason of the no-convergence is another matter which demands a sometimes-extensive interpretation of the results. In our study we made sure that the no-convergence does not come from the soil failure (see Sect. 1.4), only the masonry. Using the damage model described above, we introduce now the crack related rotation through the angle θ defined by Fig. 12b. In doing so, the intent is to illustrate, if exists, the potential hinge mechanism through the rotational capacity of the hinge, i.e., the maximum angle before the no-convergence. This is clearly a result that Limit Analysis cannot provide. Now, looking at the results obtained for different values of the compressive strength, the numerical FE model suggests that failure may be caused by the fact that the compressive strength is reached, but not in all situations. Figure 6a) shows that for all values inferior to σc = 15 MPa, the maximum overburden load obtained numerically increases as the compressive strength increases (in plane strain conditions, see Fig. 2). This result is similar to the conclusions by Alexakis and Makris (2014). But, for compressive strength values larger than 15 MPa, the bearing capacity of the masonry tunnel no longer increases. From Fig. 6c) we find that stresses do not continue to grow, despite the increasing strength, because the maximum rotation (rotation capacity of the hinge) appears to be limited to a value near to 35 mrad; for a value beyond this rotation, the numerical process leads to no-convergence. These results suggest that if compressive stress is large enough, the tunnel will eventually fail by a hinging mechanism. Several modelling strategies and nonlinear constitutive laws are available in the literature for masonry structures, as comprehensively reviewed by D’Altri et al.(2020). The choice of the constitutive law and its parameters can be a source of uncertainty regarding the estimation of the bearing capacity, contrary to limit analysis, which will only require at most, the compressive strength. On the other hand, however, the prime advantage of the nonlinear FEM, as said before, is that we are able to estimate the displacements near failure, whereas limit analysis does not provide any displacements.
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Fig. 6. Results for different compressive strengths of the masonry (Damage model only): (a) Maximum load (overburden), (b) Maximum compressive stress, (c) Maximum stress and rotation
Three different constitutive laws have been tested here, as described in section Sect. 2.2: the damage model and two plastic models. Results are presented in Fig. 7. It was found that for this geometry and loading scenarios, only the damage model is capable to produce significant displacements (horizontal convergences larger than 10 mm), and to reach greater loads. Plastic models remain conservative when estimating the bearing capacity (Table 2). The shortcomings of an elastic calculation for the masonry have been discussed in Moreno Regan et al. (2022). The evolution of the maximum compressive stress is similar in all models, except the elastic model which underestimates it (Fig. 7b); however only the damage model makes it possible to reach values close to the compressive strength of 14 MPa (see Fig. 2). In Fig. 7c) it can be seen that, when the numerical failure occurs, the damage model produces a greater rotation at the hinge; and a horizontal convergence of about 3 cm; and about 1 cm for the Plastic model. This order of magnitude of the deformations have been observed in practice, see Moreno Regan et al. (2022). If an overburden were actually to take place near the tunnel, the structure will be monitored to measure its deformation, hence the importance of knowing the displacements thresholds, rather than the maximum load, that may indicate if we are near failure or not. The thresholds illustrated is Fig. 7a) could, for instance, be proposed in order to oversee the works and ensure its safety. The “attention threshold” could be placed around 2–3 mm of horizontal convergence, close to the beginning of the nonlinear behavior (whatever the constitutive law), and it could be synonym of extra measures to be taken in the work site; whereas the “warning threshold” could be placed near 20 mm to indicate that we are approaching failure and that the works must be stopped, and reinforcements placed. Figure 8 shows the strain concentration near the cracks for all the constitutive laws. It can clearly be seen that the Mohr-Coulomb criterion will only produce a plastic zone (sometimes large) which does not correspond to any physical crack. Only the damage and the Willam-Warnke models (with strain softening in tension) will produce an accurate strain concentration that represents the crack. Consequently, it can be concluded that the damage model, and to a lesser extent, the Willam-Warnke model, can be expected to predict more accurately the real displacements and deformations of the vault.
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Fig. 7. Results for different models / constitutive laws: (a) Load-convergence (positive convergence means an increase of the distance between sidewalls), (b) Maximum stress and rotation
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Fig. 8. Masonry principal total strain ε1 (tension) for different models
4.2 Impact of the Soil Properties The stiffness and shear strength properties of the soil next to the sidewalls have an important influence on the stability of the tunnel, see Moreno Regan et al. (2022). Six models were built to study the influence of the stiffness of the backfill. The pressures transmitted to the tunnel are a result of the deformation of the structure, and vice versa. From an initial value of the horizontal pressure due to the weight of 5 m of soil (Fig. 4), the pressure increases inexorably with the increasing surface load, in proportion to the stiffness of the ground, contrary to the hypothesis by Alexakis and Makris (2014) who preserve a constant value. The horizontal pressure transmitted to the sidewalls, see Fig. 9 a), increases with stiffer soil, because a more rigid ground will provide a higher lateral reaction. On the contrary, soft soil will allow the deformation of the tunnel providing less lateral reaction, even no reaction at all for a modulus of 5 GPa, until 200 kN of load. The consequence is that the tunnel will have a smaller bearing capacity, since the supports of the vault can move more freely. With a soft ground (5 MPa) the bearing capacity is around 400 kN, whereas for a stiff ground (50 MPa) the bearing capacity is near 700 kN, almost the double.
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In Fig. 9 b) it can be seen that, if the ground modulus is less than 20 MPa, the maximum compressive stress is less than the compressive strength (about 14 MPa), and failure occurs because of the creation of a hinge mechanism: again, the maximum crack related rotation reaches a value close to 35 mrad (see §0) before the no-convergence of the model. If the ground is stiff enough, the deformations will be constrained, and numerical failure occurs when the compressive strength is reached, see Fig. 9 b), in our case for elastic modulus superior to 20 MPa.
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Fig. 9. Impact of the soil properties (damage model): (a) Resultant lateral force for different stiffness of the Backfill, (b) Results for different Backfill modulus, (c) Soil plastic strain at masonry failure (Eb = 20 MPa)
4.3 Mesh Sensitivity and Crack Depth It is known that a damage model with strain softening (see Fig. 2) has dependency issues regarding the mesh size, making it necessary to use a regularization technique to mitigate the problem. This was done in our damage model as explained in Sect. 2.2. In a more general way, it is worth noting that the solution produced by a finite element model will always depends, to some extent, on the mesh size, whatever the constitutive law used in the nonlinear domain. Three different meshes were tested here (see Fig. 10) with the three constitutive laws discussed above to illustrate the range of results that can be found and try to give an estimate, however approximate may be, of the uncertainty related to the mesh size. Results are presented in Fig. 11. As it can be seen in Fig. 11e) the depth of the crack depends on the size of the mesh. The smaller the mesh, the smaller the compressed area in the cracked cross section, producing a higher compressive stress, and this regardless of the constitutive law. For the damage model, we have found a relative standard deviation (RSD) of the maximum compressive stress of 43%, and 30% and 28% for the plastic models, respectively. Regarding the bearing capacity of the masonry tunnel, the RSD is about 14% for the damage model and 16% and 11% for the Plastic models, respectively (Fig. 11a). As it can be seen the uncertainty is greater regarding the maximum compressive stresses.
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Strain-stress relation evolve differently with each mesh. On the other hand, displacements seem to be less uncertain than stresses: in Fig. 11c) we see that for the damage model, meshes 2 and 3 present very similar load-convergence curves (only the coarse mesh gives a different result) contrary to maximum stresses in Fig. 11b). Also, the RSD of the crack related rotation (Fig. 11d) is 23% for the damage model; 45% and 46% for the plastic models.
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Fig. 11. Impact of the size of mesh for the FE Model: (a, b, c, d) Results for different mesh sizes, (e) Principal stress vectors at the crown
5 Rotational Capacity When the stability of an existing masonry tunnel must be verified, usually we verify that the calculated stress and internal forces remain under certain limits, see Moreno Regan et al. (2022), even though the compressive strength is implicitly verified if the model converges. It was found here that a certain value of rotation of the hinge is never exceeded in the calculations, a value close to 35 mrad (around 2 °). It means that from this type of calculation some safe limit can be established a priori (Fig. 12b); then, the rotational capacity of the hinges could be checked as a stability verification.
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The idea of the limitation of the rotation of the hinge is actually not new: it is already a verification demanded by Eurocode 2 (§5.6.3) for cracked reinforced concrete structures when a plastic calculation is made. However, for masonry structures there is no limitation in design codes regarding displacements or rotations; although in a recent addition to Eurocode 6 (masonry structures) it is prescribed that the maximum strain of masonry in uniaxial compression should not exceed 2.0‰ (that we used here, see in Fig. 2 the uniaxial compression curve marked “Damage plane stress”). It appears then that such verification can be used to verify the stability of an existing tunnel, in complement (or sometimes instead) of stress verification which can be uncertain, depending on the properties of the numerical model; displacements been less uncertain in their evolution (see Fig. 12a). This idea will be explored in further research.
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Fig. 12. Study of the crack related rotation at the crown: (a) Influence of the mesh on the maximal values of stress and rotation, (b) Maximum crack related rotation
6 Conclusions The bearing capacity of an existing tunnel can be assessed using a FE nonlinear model and results can be close to those produced by limit analysis. In this study, the ancient masonry tunnel in Nemea was analyzed. With the initial set of assumptions, the calculation showed a bearing capacity of 1006 kN vs 934 kN estimated with limit analysis [1, 2]. For this geometry and load scenario, failure of the masonry tunnel occurs when the compressive strength is reached. Nonetheless, beyond a certain compressive strength and for soft ground around the tunnel, the failure mechanism obtained numerically is rather a hinge mechanism. The apparition of a hinge mechanisms can be interpreted in a FE model when a crack related rotation reaches a certain limit. Our calculations gave a limit close to 35 mrad. It can be suggested to introduce a hinge rotation verification as a complement or instead of a stress check, when assessing the bearing capacity of a masonry vault. This idea will be explored in further research. Also, it is worth point out the fact that a FE model allows to estimate the displacement near failure, which makes it possible to propose threshold values to oversee the works: an “attention threshold” of 2–3 mm and a “warning threshold” of 20 mm, for the horizontal convergence tunnel.
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The FEM assessment comes however with some uncertainties, related to the constitutive law and to the parameters for the masonry and soil. On the other hand, we also have the uncertainties of numerical nature, like the mesh size, the discretization of the load, the parameters of the nonlinear algorithm with its maximum number of iterations, the chosen precision, among others. Here, some of these were tested. Firstly, the constitutive law of the masonry. When modelling quasi-brittle materials like masonry it appears to be more adequate to use a constitutive law with softening behavior, because perfectly plastic behavior may not properly estimate strain concentration (cracks), and thus stresses and deformations. The damage model gives a good estimation regarding the expected strain concentration and deformations of the tunnel. The plastic Willam-Warnke model gives more conservative results regarding maximum compressive stress but follows the same pattern as the damage model. Elastic models will completely underestimate the maximal values of stress and deformations and should be avoided. Secondly, the load and the ground around the tunnel. The pressure applied to the tunnel depends on its deformation, and vice versa. A more rigid ground provides a higher lateral reaction increasing the bearing capacity. A soft soil allows the deformation of the tunnel causing earlier failure through a hinge mechanism. An increase from 5 MPa (unlikely) to 50 MPa in the elastic modulus of the backfill can almost double the bearing capacity. In general, this problem can be treated through a parametric study within a plausible range of values. Also, it should be noted that the no-convergence of the calculation could happen because of soil failure rather than masonry failure, and thus an interpretation of the results is needed. Finally, the mesh size. It was observed that the bearing capacity may present a variation of about 15% and the maximum compressive stress of about 40%. Coarse meshes should be avoided when modeling cracks, since, as it was seen, the crack depth is limited to the size of the elements and if only 2 elements are used, the crack will be limited numerically to half the cross section, which it will not correspond to the physical reality; also, it should be noted that a very refined mesh size can considerably increase the calculation time. As a good measure, at least 10 integration points should be placed in the cross section. In general, the opinion of the author is that results coming from a FE model should be penalized.
References Alexakis, H., Makris, N.: Stability analysis of the underground masonry tunnel of ancient Nemea. In: Bilotta, E., Flora, A., Lirer, S., Viggiani, C. (eds.) Geotechnical Engineering for the Preservation of Monuments and Historic Sites 2013, pp. 113–21. CRC Press (2013). https://doi.org/ 10.1201/b14895 Alexakis, H., Makris, N.: Structural stability and bearing capacity analysis of the tunnel-entrance to the stadium of Ancient Nemea. Int. J. Archit. Heritage 7(6), 673–692 (2014). https://doi. org/10.1080/15583058.2012.662262 Bourgeois, E., Burlon, S., Cuira, F.: Modélisation numérique des ouvrages géotechniques. Techniques de l’ingénieur, Mécanique des sols et géotechnique (2018). https://doi.org/10.51257/av1-c258
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D’Altri, A.M., et al.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27(4), 1153–1185 (2019). https://doi.org/10.1007/s11831-019-09351-x Heyman, J.: The stone skeleton. Structural engineering of masonry architecture. Cambridge University Press, 1st edn, Cambridge, UK (1995) Mazars, J.: A description of micro- and macroscale damage of concrete structures. Eng. Fract. Mech. 25, 729–737 (1986). https://doi.org/10.1016/0013-7944(86)90036-6 Miller, S.G.: Excavations at Nemea II. The early Hellenistic Stadium. University of California Press, Berkley and Los Angeles, USA (2001) Moreno Regan, O., Bourgeois, E., Colas, A.S., Chatellier, P., Desbordes, A., Douroux, J.F.: Application of a coupled homogenization-damage model to masonry tunnel vaults. Comput. Geotechnics 83, 132–141 (2017) https://doi.org/10.1016/j.compgeo.2016.10.024 Moreno Regan, O., Bourgeois, E., Colas, A.S., Chatellier, P., Desbordes, A., Douroux, J.F.: Experimental characterization of the constitutive materials composing an old masonry vaulted tunnel of the Paris subway system. Int. J. Archit. Heritage 12(2), 195–215 (2018). https://doi.org/10. 1080/15583058.2017.1388883 Moreno Regan, O., Bourgeois, E., Douroux, J.F.: On the stability of underground masonry vaults: the case of the mairie d’ivry station of the Paris Metro. Int. J. Archit. Heritage 1–22 (2022). https://doi.org/10.1080/15583058.2022.2108354 Obrzud, R., Truty, A.: The hardening Soil Model – A practical Guidebook. Z_Soil. PC 100707 (2018). report revised 21 Oct 2018 Ulm, F.J.: Un modèle d’endommagement plastique : application aux bétons de structure. Études et Recherches des laboratoires des ponts et chaussées. Série Ouvrages d’Art OA19. LCPC (1996)
Experimental and Numerical Analysis on the Effect of Joint Deformability and Imperfections on the Response of Masonry Arches Subject to Large Support Displacements Chiara Ferrero1(B)
, Chiara Calderini1
, and Pere Roca2
1 Department of Civil, Chemical and Environmental Engineering, University of Genoa,
Via Montallegro 1, 16145 Genoa, Italy [email protected] 2 Department of Civil and Environmental Engineering, Technical University of Catalonia (UPC-BarcelonaTech), Jordi Girona 1-3, 08034 Barcelona, Spain
Abstract. Large support displacements are a major threat for masonry arches. In the last decades, the stability of masonry arches under large support displacements has been often analysed through analytical and numerical methods that adopted Heyman’s assumptions on the behavior of masonry arches and modelled arches as rigid-no tension structures. Although these methods were generally able to capture the collapse mechanisms observed in the experimental tests, they overestimated, even significantly, the experimental displacement capacity. The main aims of this paper are to investigate the reasons why rigid-no tension models fail in accurately predicting the actual response of dry-joint masonry arches to large support displacements and to propose a numerical modelling approach able to obtain a better matching between experimental and numerical responses. To achieve these goals, the case of a small-scale segmental dry-joint masonry arch tested to collapse under vertical, horizontal, and inclined support displacements was investigated. To simulate the experimental tests, a finite element micro-modelling approach was adopted. The arch was schematized as an assemblage of elastic and stiff voussoirs interacting at no-tension friction interfaces, which were considered alternatively rigid or deformable. The comparison between the numerical and experimental results demonstrated that the discrepancies between the predictions by rigid notension models and the experimental outcomes were due to the imperfections and resulting deformability of the joints of the physical model. A strategy to account for this deformability in the adopted modelling approach was thus proposed and validated by comparison with the experimental results. Keywords: Dry-joint masonry arches · Large support displacements · Experimental testing · Finite element micro-modelling · Joint deformability · Geometrical imperfections
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 339–351, 2024. https://doi.org/10.1007/978-3-031-39450-8_28
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1 Introduction Masonry arches play a primary role in the structural behaviour of historic masonry buildings. Consequently, their structural integrity is fundamental to preserve built cultural heritage. Masonry arches are very sensitive to any change in the boundary conditions. However, if small support displacements can be easily accommodated through the opening of three hinges that transform the arch in a statically determinate system, large support displacements can cause severe damage and large deformations, posing a serious threat to stability. Recent years have seen a continuous development of analytical and numerical methods to assess the stability of masonry arches under large support displacements. Most of these methods modelled arches as rigid-no tension structures by adopting the wellknown assumptions introduced by Heyman [1, 2] to describe the behaviour of masonry materials: (i) infinite compressive strength, (ii) no tensile strength, and (iii) no sliding failure. Under these hypotheses, arches behave as assemblages of rigid blocks interacting at no-tension rigid interfaces and collapse by opening a certain number of hinges (four or five in case of symmetrical and asymmetrical geometric and loading conditions, respectively). Starting from Heyman’s assumptions, several authors proposed analytical and computational methods based on a standard application of the theorems of Limit Analysis (e.g., [3, 4, 5, 6, 7]), while others went beyond it by developing rigid block models that couple combinatorial analysis with static and kinematic analyses (see [8, 9, 10]), rely on an incremental limit equilibrium analysis formulation using gap functions for the prediction of failure mechanisms (see [11, 12]) or adopt a variational formulation based on the minimum of the total potential energy (see [13]). In addition, several research works used discrete element (DE) and finite element (FE) methods to study the response of masonry arches to large support displacements under Heyman’s assumptions (see respectively [13, 14] and [7, 12, 15, 16, 17]). As described more in detail in [18], when validated against the results of experimental tests carried out on small or full-scale arches subjected to large support displacements, the large majority of the abovementioned methods correctly captured the experimental collapse mechanisms but overestimated, even significantly, the experimental displacement capacity. The overestimation of the experimental capacity of masonry arches by rigid-no tension models, which was observed also in the case of seismic actions (e.g., [19, 20, 21]), was generally attributed to slight variations in the block dimension, corner rounding due to repeated testing, and inaccurate interlocking between voussoirs. These imperfections reduce the effective thickness of the arches, causing collapse to occur at smaller support displacements or seismic accelerations than those predicted numerically. In the case of arches subjected to seismic actions, decreasing the thickness of the numerical models to account for these imperfections was found to be an effective strategy to better capture the experimental response. In the case of arches subjected to large support displacements, the effect of the imperfections was considered only in [22], where a probabilistic approach was adopted to spread geometrical imperfections on the numerical models. This paper has a twofold aim: (i) to thoroughly investigate the discrepancies between experimental and numerical results obtained when using rigid-no tension models to
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study the response of masonry arches to large support displacement, and (ii) to propose a numerical modelling approach able to accurately simulate the response of dry-joint masonry arches to large support displacements. Such an approach was validated against the results of experimental tests carried out by the authors on a 1:10 small-scale model of a segmental dry-joint masonry arch subjected to vertical, horizontal, and inclined support displacements. Since the experimental mock-up was built as a dry-joint assemblage of voussoirs, the proposed numerical approach adopted a FE micro-modelling strategy, in which the arch was modelled as a set of elastic voussoirs connected by no-tension friction interfaces. The comparison between experimental and numerical results was performed considering both rigid and deformable interfaces. The values of interface stiffness to be adopted were chosen through a sensitivity analysis. Nonlinear static analyses were performed to assess the numerical response of the arch to large support displacements.
2 Experimental Tests and Results The experimental tests, first presented in [23, 24], were performed on a 1:10 small-scale model of a segmental arch supported by two piers (Fig. 1a). As shown in Fig. 1b, the arch has a span length (L) of 533 mm, an angle of embrace of 125°, a rise of 162 mm and a radial thickness of 24 mm, and it consists of 55 voussoirs with dimension 24 × 12 × 120 mm. The voussoirs have a slightly trapezoidal shape to compensate for the lack of mortar in the joints.
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Fig. 1. (a) View of the physical model, (b) geometry of the mockup (dimensions in mm) and investigated displacement directions.
Both the voussoirs and the piers are made of a bicomponent composite material, obtained by mixing a mineral powder with an acrylic polymer in aqueous solution (for further details on the production of the blocks see [24]). The blocks have a density ρ of 1640 kg/m3 , a friction angle μ of 41.2° (corresponding to a friction coefficient of 0.7), a Young’s modulus E of 941 MPa and a compressive strength σ c of 9.1 MPa (measured experimentally in [23]). The high compressive strength and stiffness of the blocks, the null tensile strength of the dry joints and the absence of sliding (resulting from the high friction angle) made the mockup coherent with Heyman’s assumptions on the behaviour of masonry structures.
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The arch was tested to collapse by imposing different combinations of vertical (downward) and horizontal (outward) displacements at the right support. The direction of the imposed inclined displacement δ was identified by the angle α measured from the vertical (Fig. 1b). As shown in Fig. 1b, thirteen directions of imposed displacements were considered, obtained by varying α between 0° (purely vertical displacements) and 90° (purely horizontal displacements). Hereafter, the vertical (δ z ) and horizontal (δ x ) components of the imposed displacement δ (see Fig. 1b) will be expressed in a dimensionless form as δ z /L and δ x /L, where L is the arch span length. Figure 2 depicts the collapse mechanisms obtained for four representative values of α (0°, 20°, 60°, 90°). The thrust line at collapse, drawn on the arch deformed configuration by using graphic statics [25, 26], is also shown. No matter α, the arch initially opened three hinges (A, B and C). Collapse occurred when a fourth hinge (D) opened at the left support. In the case of α = 90°, due to the symmetry in geometry and displacement loading, a further hinge (E) appeared at collapse at the right support (Fig. 2d). The position at collapse of the three initial hinges A, B and C varied with the direction of support displacements. For α between 0° and 15° (see Fig. 2a for α = 0°), hinges A, B and C appeared in the sequence I-E-E (from left to right, where E = extrados; I = intrados). Hinge A was located at the left haunch, whereas the consecutive hinges B and C appeared close to the crown and at the right support, respectively. For α between 20° and 90° (see Fig. 2b-c-d), hinges A, B and C were located alternately between the intrados and the extrados according to the sequence I-E-I. Hinges A and C occurred at the haunches, while hinge B opened near the crown. As shown in Fig. 2b, for α between 20° and 30°, hinge C appeared at the right haunch in the form of minor openings distributed over consecutive joints (for further details see [24]). In correspondence of these openings, the thrust line was almost tangent to the arch intrados without, however, touching it. This behaviour differs from that expected for a rigid-no tension arch complying with Heyman’s assumptions. Such an arch should indeed collapse by the opening of four fully developed hinges, in correspondence of which the thrust line should be tangent to the arch profile. In [24], the authors demonstrated that the minor and distributed openings have the same effect as a hinge in the activation of the collapse mechanism. Figure 3 presents the limit displacement domain of the tested arch, which was computed by plotting the normalized vertical collapse displacement δ z,u /L versus the normalized horizontal collapse displacement δ x,u /L for every value of α. This domain, introduced by the authors in [22], shows the combinations of vertical and horizontal support displacements that the arch can withstand safely (points below the boundary of the domain) as well as those that cause collapse (boundary of the domain and points above it). Different trends in the variation of the collapse displacements with α can be identified. For α between 0° and 15°, the vertical collapse displacement decreases, whereas the horizontal one increases. For α between 15° and 20°, the vertical collapse displacement remains almost constant, while the horizontal one increases. For α between 25° and 90°, the vertical collapse displacement significantly decreases with the increase in α, whereas the horizontal collapse displacement changes only slightly.
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Fig. 2. Collapse mechanisms: (a) α = 0°, (b) α = 20°, (c) α = 60°, (d) α = 90°. (Minor distributed openings indicated with white dotted circles).
Fig. 3. Limit displacement domain of the tested arch.
3 Numerical Model A two-dimensional FE model of the tested arch, not including the piers, was created in the commercial FEM software DIANA FEA [27]. To accurately reproduce the experimental mockup, a micro-modelling approach was adopted, and the arch was modelled as an assemblage of trapezoidal units, representing in size and shape the real voussoirs, connected by zero-thickness interfaces, simulating the dry-joints. Additional interface elements were placed at the arch springings to allow hinge openings at the supports. Pinned boundary conditions were imposed at the edges of these interfaces.
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The FE mesh was created using four-node quadrilateral isoparametric plane stress elements (Q8MEM [27]) for the voussoirs and 2D four-node line interface elements (L8IF [27]) for the interfaces. Following [12] and [17], a mesh size of 2 mm, corresponding to 12 FEs along the arch radial thickness, was adopted. A linear elastic behaviour with infinite compressive strength and a Coulomb friction model with zero cohesion and dilatancy angle were assumed for voussoirs and interfaces, respectively. The Coulomb friction model of the interfaces was extended with a gap criterion with zero tensile strength to allow hinges to open when tensile stresses arise (for further details the reader is referred to [27]). The Young’s modulus and density of the voussoirs as well as the friction coefficient of the interfaces were taken equal to the values measured experimentally (see Sect. 2). The Poisson’s ratio of the blocks was taken equal to 0.2. The values of the normal (k n ) and tangential (k s ) stiffnesses of the interfaces were determined though a sensitivity analysis, as these properties were not measured experimentally. Following the same approach adopted in [12] and [17], the interface normal stiffness k n was varied within a range defined based on literature, while the interface tangential stiffness k s was set equal to 0.5 k n for every value of k n adopted. The sensitivity analysis was first carried out in the case of purely vertical displacements (α = 0°). Subsequently, based on the results obtained, two values of interface normal stiffness, representing either rigid or deformable interfaces, were adopted to perform further numerical simulations and analyse all the directions of support displacements investigated in the experimental tests. The experimental tests were simulated by performing nonlinear static analyses in which support displacement were increased monotonically up to collapse after the application of the self-weight. A regular Newton-Raphson iteration method was adopted in combination with a line search algorithm, which allowed convergence to be reached without experiencing any bifurcation problems. An energy-based convergence criterion of 0.001 was assumed. Geometric nonlinearities were included by adopting the Total Lagrange formulation available in DIANA FEA [27].
4 Comparison Between Numerical and Experimental Results 4.1 Sensitivity Analysis and Comparison for α = 0° Following [12] and [17], the comparison between numerical and experimental results for α = 0° was performed while varying the interface normal stiffness k n between 0.1 and 100 N/mm3 . Figure 4 shows the collapse mechanisms obtained for four representative values of k n (0.1, 1, 10, 1000 N/mm3 ). Regardless of k n , the arch collapsed by an asymmetrical four-hinge mechanism with hinges located in the sequence E-I-E-E. Although this collapse mechanism is in full accordance with the experimental one, hinges appeared in the numerical model either in the form of minor distributed openings (for small values of k n , see Fig. 4a) or in the form of fully developed hinges located at the edge line of the arch (for large values of k n , see Fig. 4c-d). For every value of k n equal or larger than 10 N/mm3 (Fig. 4c-d), all the four hinges A, B, C and D were fully developed and appeared at the edge line of the arch.
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Fig. 4. Collapse mechanisms for different values of the interface normal stiffness k n : (a) k n = 0.1 N/mm3 (δ z,u /L = 3.8%), (b) k n = 1 N/mm3 (δ z,u /L = 12.1%), (c) k n = 10 N/mm3 (δ z,u /L = 20.4%), (d) k n = 100 N/mm3 (δ z,u /L = 21.2%). (Results in terms of compressive stresses in the interfaces) [18].
Figure 5 shows how the predicted collapse displacement δ z,u /L and the location at collapse of hinges A, B and C vary with the interface normal stiffness k n . Note that the interfaces where hinges appear are numbered from left to right, being interface 1 the one at the left support. The collapse displacement increases with increasing k n until reaching a maximum constant value that is not affected by any further stiffness increase (Fig. 5a). The position of hinge C does not change with k n , while the position of hinges A and B varies with k n until k n = 48 N/m3 and remains constant for larger values (Fig. 5b). Since the arch response in terms of collapse displacement and hinge position is not affected by the interface stiffness in the range k n = 48 ÷ 100 N/mm3 , it can be concluded that, for any k n equal or larger than 48 N/mm3 , the interfaces behave as rigid interfaces, and the arch can be considered a rigid-no tension structure. In [12], the authors actually demonstrated that adopting k n = 48 N/mm3 corresponded to simulate rigid interfaces. Figure 5 also shows the experimental results obtained in terms of collapse displacement and hinge position at collapse. For k n = 48 N/mm3 , the FE model significantly overestimates the experimental displacement capacity and does not accurately predict the experimental hinge position at collapse. In contrast, a better matching between experimental and numerical responses is obtained when adopting reduced values of k n , which represent deformable interfaces. This outcome is in full accordance with the overestimation of the displacement capacity of masonry arches by rigid-no tension models observed in the literature (see Sect. 1).
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Fig. 5. (a) Collapse displacement δ z,u /L vs. interface normal stiffness k n , (b) hinge position at collapse vs. interface normal stiffness k n .
4.2 Comparison for α Between 0° and 90° In this section, the numerical and experimental results are compared for all the directions of support displacements investigated in this work (α = 0° ÷ 90°). Based on the results obtained for α = 0° in Sect. 4.1, two different values of interface normal stiffness k n were adopted: 48 and 3 N/mm3 , which represent rigid and deformable interfaces, respectively. Figure 6 presents the limit displacement domain of the arch obtained from experimental tests and numerical simulations. For k n = 48 N/mm3 , the experimental displacement capacity is significantly overestimated, with relative errors varying between 22% and 53% depending on α. In contrast, for k n = 3 N/mm3 , it is accurately predicted with errors ranging between about −5% and 5% for every α, except for 10° (−6.1%) and 90° (8.5%). Despite the differences in terms of displacement capacity obtained for k n = 3 N/mm3 and k n = 48 N/mm3 , for both values of k n the numerical domain compares reasonably well with the experimental one in terms of overall qualitative trend (that is the collapse displacements varies with α in a similar way). However, the abrupt decrease in the vertical collapse displacement obtained in the experiments when α increases from 10° to 15° is perfectly captured only for k n = 3 N/mm3 .
Fig. 6. Limit displacement domain: comparison between experimental and numerical results for k n = 3 N/mm3 and k n = 48 N/mm3 .
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Since adopting k n = 48 N/mm3 corresponds to simulate rigid interfaces, the significant better matching between experimental and numerical results obtained for every α for k n = 3 N/mm3 demonstrates that the joints of the physical model are not rigid but provided with some deformability. Since the voussoirs may be considered rigid due to their high stiffness and compressive strength (see Sect. 2), such deformability can be attributed to imperfections of the contact surfaces between adjacent voussoirs (e.g., roughness and not perfect coplanarity), which are likely to result from the manufacturing process of the blocks. Since these imperfections are pertinent to the contact surfaces between adjacent voussoirs, they are different from those resulting from variations in the block dimension and corner rounding (often simulated in the numerical models by reducing the arch thickness, see Sect. 1). As a further confirmation, in [23] one the authors attempted to gain a better matching between numerical and experimental results by reducing the arch numerical thickness, but the results were not fully satisfactory.
(a)
(b)
(c)
Fig. 7. Collapse mechanisms obtained from FE analyses for k n = 48 N/mm3 (left) and k n = 3 N/mm3 (right): (a) α = 0°, (b) α = 20°, (c) α = 90°. (Minor distributed openings indicated with a dotted circle).
Figure 7 shows the collapse mechanisms obtained for k n = 48 N/mm3 (left) and k n = 3 N/mm3 (right) for three representative values of α (0°, 20°, and 90°). For both values of k n , the FE analyses predicted the same collapse mechanisms obtained in the experimental tests. For α between 0° and 75° (Fig. 7a-b-c), collapse was governed by an asymmetrical four-hinge mechanism with hinges located either according to the sequence E-I-E-E (for α between 0° and 15°, see Fig. 7a) or according to the sequence E-I-E-I (for α between 20° and 75°, see Fig. 7b-c). For α = 90° (Fig. 7d), collapse occurred by a five-hinge
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collapse mechanism with hinges alternating between the intrados and extrados (E-I-EI-E). Differently from the experimental failure mode, which was slightly asymmetrical, the numerical collapse mechanism was perfectly symmetrical, as hinge B opened at both sides of the keystone. The good agreement between experimental and numerical collapse displacements for every α may explains why the numerical and experimental limit displacement domains compared well in terms of overall qualitative trend for both k n = 3 N/mm3 and k n = 48 N/mm3 . Table 1 compares the predicted and experimental positions at collapse of hinges A, B and C. For k n = 3 N/mm3 , the numerical hinge position is generally the same as the experimental one, with differences of one voussoir observed only occasionally. In contrast, for k n = 48 N/mm3 , the numerical and experimental locations do not generally match, except in the case of hinge C for α between 0° and 15°. Table 1. Position at collapse of hinges A, B and C obtained from experimental tests and numerical analyses for k n = 3 N/mm3 and k n = 48 N/mm3 (I = intrados, E = extrados, m.d.o = minor distributed openings). α [°]
Joint no Hinge A
Hinge B
Hinge C
Exp
FEM (k n = 48 N/mm3 )
FEM (k n = 3 N/mm3 )
Exp
FEM (k n = 48 N/mm3 )
FEM (k n = 3 N/mm3 )
Exp
FEM (k n = 48 N/mm3 )
FEM (k n = 3 N/mm3 )
0
9-I
8-I
9-I
28-I
32-I
29-I
56-E
56-E
56-E
5
9-I
8-I
9-I
31-I
32-I
31-I
56-E
56-E
56-E
10
9-I
8-I
9-I
31-I
32-I
31-I
56-E
56-E
56-E
15
10-I
8-I
10-I
31-I
32-I
31-I
56-E
56-E
56-E
20
9-I
8-I
9-I
30-I
32-I
31-I
m.d.o.-I
48-I
m.d.o.-I
25
9-I
7-I
9-I
28-I
30-I
29-I
m.d.o.-I
48-I
m.d.o.-I
30
9-I
7-I
9–10-I
28-I
29-I
29-I
m.d.o.-I
47-I
m.d.o.-I
35
10-I
7-I
9–10-I
28-I
29-I
28-I
45-I
47-I
44–45-46-I
40
10-I
8-I
10-I
28-I
29-I
28-I
44–45-46-I
47-I
44–45-46-I
45
11-I
8-I
10-I
28-I
29-I
28-I
44–45-46-I
48-I
44–45-46-I
60
11-I
9-I
10–11-I
28-I
28-I
28-I
44-I
47-I
45-I
75
11-I
9-I
11-I
28-I
29-I
28-I
45-I
48-I
45–46-I
90
12-I
9-I
11-I
28-I
28–29-I
27–28-I
45-I
48-I
46-I
Looking at Table 1, it can also be observed that, for k n = 3 N/mm3 , the numerical model correctly predicted the occurrence of hinge C in the form as minor distributed openings, as observed in the experimental tests. In contrast, for k n = 48 N/mm3 , hinge C appeared as a fully developed hinge in the numerical simulations. This difference was detected by looking at the distribution of compressive stresses at the arch intrados at the right haunch (see Fig. 8 for α = 20°). For k n = 48 N/mm3 (Fig. 8a), compressive stresses were concentrated in only one FE of the interface mesh, while for k n = 3 N/mm3 (Fig. 8b), they were distributed over several FEs of consecutive interfaces. The stress distribution obtained for k n = 3 N/mm3 correctly reproduces the fact that the thrust line
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at collapse in the physical model did not touch the arch profile at the intrados, but it was almost tangent to it nearby several consecutive voussoirs (see Sect. 2).
(a)
(b)
Fig. 8. Hinge C at collapse in the numerical model for α = 20°: (a) fully developed hinge for k n = 48 N/mm3 and (b) minor and distributed openings for k n = 3 N/mm3 . (Deformation scale factor 2) (adapted from [18]).
5 Conclusions This paper investigated the reasons why rigid-no tension models are not able to accurately predict the response of dry-joint masonry arches to large support displacements and proposed a numerical modelling approach to gain a better matching between numerical and experimental responses. Such an approach, based on FE micro-modelling, was validated by comparison with the results of experimental tests carried out by the authors on a small-scale segmental dry-joint masonry arch subjected to vertical, horizontal, and inclined support displacements. Since the physical model of the arch consisted of a dry-joint assemblage of almost rigid and highly resistant in compression voussoirs, the numerical model was built as a set of elastic and stiff units interacting at no-tension interfaces. The comparison between experimental and numerical results was carried out by adopting two values of interface normal stiffness, simulating either rigid or deformable interfaces, which were determined based on a sensitivity analysis carried out for the case of purely vertical displacements. For every direction of support displacements investigated, the FE model with rigid interfaces correctly captured the experimental collapse mechanisms but overestimated the experimental displacement capacity and did not accurately simulate the experimental hinge position at collapse. Conversely, the FE model with deformable interfaces accurately reproduced the experimental response in terms of collapse mechanisms, displacement capacity and hinge position. These results proved that the joints of the physical model were not rigid but characterized by some deformability, which can be attributed to the imperfections of the contact surfaces between adjacent voussoirs. These imperfections were found to reduce the ultimate displacement capacity of the arch, without, however, affecting its failure modes. This explains why rigid-no tension models, although overestimating the experimental collapse displacement, were generally observed to well capture the experimental collapse mechanisms.
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The comparison between the numerical and experimental results provided further insight into the experimental response of the arch under study. Differently from the FE model with rigid interfaces, the FE model with deformable interfaces was able to capture the deviation of the behaviour of the experimental arch from that expected for a rigid-no tension arch. In particular, it correctly predicted that the collapse mechanisms could occur either by the opening of four (or five) fully developed hinges or by the formation of three fully developed hinges together with minor and distributed openings at a further section of the arch profile. In view of this, it can be concluded that the deviation of the experimental behaviour of the tested arch from that of a rigid-no tension arch was produced by the deformability of the joints, which caused the occurrence of minor and distributed openings and provided the arch with the mobility needed to activate the collapse mechanism when only three fully developed hinges appeared. Calibrating the interface normal stiffness based on the experimental results was found to be an effective strategy to accurately simulate the experimental response and take into account the imperfections of the contact surfaces between adjacent voussoirs. As a further confirmation of this strategy, the value of interface normal stiffness calibrated for the case of purely vertical displacements resulted in a good matching between experimental and numerical results for all the directions of support displacements investigated. Future research will be devoted to deeply investigating the effect of the imperfections and deformability of the joints on the response of masonry arches to large support displacements. First, parametric analyses will be performed on dry-joint masonry arches with different geometries, scales, and materials with the aim of extending the results obtained in this paper to a broader range of arched structures. Subsequently, attention will be paid to the response of masonry arches with mortar joints. In this case, however, the joint deformability is expected to result from the mechanical properties of the mortar, which is far from being rigid, especially in historic masonry constructions.
References 1. Heyman, J.: The stone skeleton. Int. J. Solids Struct. 2(2), 249–279 (1966) 2. Heyman, J.: The Stone Skeleton: Structural Engineering of Masonry Architecture, 1st edn. Cambridge University Press, Cambridge (1995) 3. Smars, P.: Kinematic stability of masonry arches. Adv. Mater. Res. 133–134, 429–434 (2010) 4. Ochsendorf, J.A.: The masonry arch on spreading supports. Struct. Eng. 84(2), 29–35 (2006) 5. Romano, A., Ochsendorf, J.A.: The mechanics of gothic masonry arches. Int. J. Archit. Heritage 4(1), 59–82 (2010) 6. Coccia, S., Di Carlo, F., Rinaldi, Z.: Collapse displacements for a mechanism of spreadinginduced supports in a masonry arch. Int. J. Adv. Struct. Eng. (IJASE) 7(3), 307–320 (2015). https://doi.org/10.1007/s40091-015-0101-x 7. Zampieri, P., Faleschini, F., Zanini, M.A., Simoncello, N.: Collapse mechanisms of masonry arches with settled springing. Eng. Struct. 156, 363–374 (2018) 8. Galassi, S., Misseri, G., Rovero, L., Tempesta, G.: Failure modes prediction of masonry voussoir arches on moving supports. Eng. Struct. 173, 706–717 (2018) 9. Galassi, S., Misseri, G., Rovero, L., Tempesta, G.: Analysis of masonry pointed arches on moving supports: a numeric predictive model and experimental evaluations. In: Carcaterra,A., Paolone, A., Graziani, G. (eds.) XXIV AIMETA Conference, LNME, pp. 2048–2068. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-41057-5_163
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10. Galassi, S., Misseri, G., Rovero, L.: Capacity assessment of masonry arches on moving supports in large displacements: Numerical model and experimental validation. Eng. Failure Anal. 129, 105700 (2021) 11. Portioli, F.P., Cascini, L.: Large displacement analysis of dry-jointed masonry structures subjected to settlements using rigid block modelling. Eng. Struct. 148, 485–496 (2017) 12. Ferrero, C., Calderini, C., Portioli, F.P., Roca, P.: Large displacement analysis of dry-joint masonry arches subject to inclined support movements. Eng. Struct. 238, 112244 (2021) 13. Iannuzzo, A, Dell’Endice, A., Van Mele, T, Block, P.: Numerical limit analysis-based modelling of masonry structures subjected to large displacements. Comput. Struct. 242, 106372 (2021) 14. McInerney, J., DeJong, M.J.: Discrete element modelling of groin vault displacement capacity. Int. J. Archit. Heritage 9(8), 1037–1049 (2015) 15. Masciotta, M.G., et al.: Dynamic characterization of progressively damaged segmental masonry arches with one settled support: experimental and numerical analysis. Frattura ed Integrità Strutturale 51, 423–441 (2020) 16. Alforno, M., Venuti, F., Calderini, C.: Validation of simplified micro-models for the static analysis of masonry arches and vaults. Int. J. Archit. Heritage 15(8), 1196–1212 (2021) 17. Ferrero, C., Rossi, M., Calderini, C., Roca, P.: Experimental and numerical analysis of a scaled dry-joint arch on moving supports. Int. J. Masonry Res. Innov. 6(4), 405–421 (2021) 18. Ferrero, C, Calderini, C, Roca, P.: Effect of joint deformability on the experimental and numerical response of dry-joint masonry arches subjected to large support displacements. Eng. Struct. 275, 115236 (2023) 19. Albuerne, A., Williams, M., Lawson, V.: Prediction of the failure mechanism of arches under base motion using DEM based on the NSCD Method. J. Heritage Conser. 34, 41–47 (2013) 20. DeJong, M, De Lorenzis, L., Adams, S., Ochsendorf, J.A.: Rocking stability of masonry arches in seismic regions. Earthquake Spectra 2, 847–865 (2008) 21. Gaetani, A., Lourenço, P.B., Monti, G., Moroni, M.: Shaking table tests and numerical analyses on a scaled dry-joint arch undergoing windowed sine pulses. Bull. Earthq. Eng. 15(11), 4939–4961 (2017). https://doi.org/10.1007/s10518-017-0156-0 22. Zampieri, P., Cavalagli, N., Gusella, V., Pellegrino, C.: Collapse displacements of masonry arch with geometrical uncertainties on spreading supports. Comput. Struct. 208, 118–129 (2018) 23. Ferrero, C.: Structural behaviour of masonry arches on moving supports: from on-site observation to experimental and numerical analysis. PhD diss., University of Genoa-Technical University of Catalonia (2021) 24. Ferrero, C, Calderini, C, Roca, P.: Experimental response of a scaled dry-joint masonry arch subject to inclined support displacements. Eng. Struct. 253(2), 113804 (2022) 25. Heyman, J.: The Masonry Arch. Ellis Horwood Ltd, Chichester (1982) 26. Huerta, S.: The analysis of masonry architecture: a historical approach. Archit. Sci. Rev. 51(4), 297–328 (2011) 27. TNO DIANA BV. DIANA Finite Element Analysis User’s Manual Release 9.6, Delft, The Netherlands (2014)
Coupled Deformation and Structural Analysis for the Damage Assessment of Cultural Heritage Buildings: The Case of a Masonry Church Exposed to Slow-Moving Landslides Chiara Ferrero , Giulio Lucio Sergio Sacco(B) , Marco Ferrero, Carlo Battini , and Chiara Calderini Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genoa, Italy [email protected]
Abstract. This paper presents the structural damage assessment of Nostra Signora della Bastia sanctuary, a historic masonry church located in the Liguria region (Italy) in an area affected by slow-moving landslides. The church exhibits extensive cracking and large deformations, which are mostly localized in the central and lateral naves. To identify the causes of damage and deformations, structural analysis was carried out in combination with crack-pattern surveys, laser scanner surveys and deformation analysis. The deformation analysis suggested potential causes of damage and allowed damage mechanisms to be preliminary identified. Following what emerged from the deformation analysis, graphic static and kinematic analyses were performed to assess the structural safety of the most damaged elements of the church. Although the graphic analyses indicated the presence of further causes of damage, they provided further insight into the structural response of the church, showing the potential offered by the combined use of deformation and structural analyses for the structural damage assessment of historic masonry structures. Keywords: Historic masonry churches · Structural analysis · Deformation analysis · Graphic statics · Damage assessment · Slow-moving landslides
1 Introduction The structural damage assessment of historic masonry buildings is a challenging task due to the difficulties in dealing with complex geometries, lack of information about material proprieties, and uncertainties about history and past alterations. The task is further complicated by the fact that, during their lifespan, historic masonry structures may be subjected to a range of actions (e.g., earthquakes, landslides, foundation settlements), which, in combination with long-term creep and material degradation, gradually transform the building and modify its geometry with respect to the original one [1]. Structural analysis plays a primary role in the identification of the causes of the damage and deformations of historic masonry buildings and the evaluation of their © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 352–365, 2024. https://doi.org/10.1007/978-3-031-39450-8_29
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structural safety. However, it is first needed to identify and fully characterize past and ongoing damage mechanisms and deformations. Deformation analysis may help in this task. The deformation analysis consists in the study of the deformations experienced by a structure through the comparison between the actual deformed geometry and a hypothetical original undeformed one. It generally takes advantage of the laser-scanner technology available today, which allows the actual geometry of existing buildings to be surveyed with a very high level of accuracy (up to 1 mm). With the aid of laser-scanner surveys, the deformation analysis is able to detect very small deformations (not visible to the naked eye), which may be analyzed together with the crack patterns surveyed on-site to identify the actual damage mechanisms. In view of this, structural analysis should be integrated with deformation analysis for an accurate structural damage assessment. In [2] and [3], the authors identified the displacements fields to be used in the structural analysis of a historic masonry church exposed to slow-moving landslides through a deformation analysis. In this paper, deformation and structural analyses were coupled for a preliminary safety and damage assessment of Nostra Signora della Bastia sanctuary, a listed masonry church located in the Liguria region (Italy) in an area affected by slow-moving landslides. The church exhibits extensive cracking and large deformations that may pose a threat to stability. To identify the causes of damage, structural analysis was integrated with detailed crack-pattern surveys, laser-scanner surveys, and deformations analysis. The deformation analysis suggested that the most significant damage and deformations affecting the church, which were observed in the vault and transverse arches of the central nave, were caused by the point loads transmitted by the roof. Graphic static and kinematic analyses were thus carried out to assess the structural safety of the transverse arches of the central nave under the roof loads and evaluate how far these structural elements were from collapse. The graphic analyses were applied within the framework of the Limit Analysis theory introduced by Heyman [4]. The results of the graphic analyses showed that the roof load could not be the only cause of the damage and deformations observed in the central nave and suggested further investigation and more advanced structural analyses (e.g., numerical analyses).
2 Nostra Signora Della Bastia Sanctuary in Bastia Nostra Signora della Bastia sanctuary (Fig. 1a) is located in Bastia, a small hamlet of the municipality of Busalla (Liguria region). As Fig. 1b shows, the area where the church is situated is close to two active slow-moving landslides: a translational slide (hereafter named landslide I) oriented in the North direction and a complex slide (hereafter named landslide II) oriented in the South-East direction. As suggested in [5], the direction of the either landslide, indicated with an arrow in Fig. 1b, was estimated based on both the contour curves of the area where the church is located and the information provided in [6]. Nostra Signora della Bastia sanctuary as it appears today is the result of significant transformations occurred over centuries. Although historical information is scarce, it is likely that the original core of the building was completed in the first half of the XVIII century and underwent various architectural and structural alterations since 1922 [8].
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Fig. 1. Nostra Signora della Bastia sanctuary: (a) view of the exterior, (b) location in the landslide maps of the Liguria region (church indicated with a red circle, adapted from [7]).
Among these alterations, it is known that the belltower was rebuilt in 1929, the apse was enlarged, the roof was partially re-built between 1986 and 1989, and the church underwent a global restoration by 1933. In 2022, renovation and strengthening works began with the aim of repairing structural damage and ensuring the structural safety of the church. Nowadays, Nostra Signora della Bastia sanctuary has a central nave, two lateral naves, a presbytery, a semi-circular apse, and a belltower. Two rooms used as sacristy and chapel are located on the north-western and south-eastern sides of the presbytery, respectively. A prothyrum with the same width of the central nave stands against the main façade (Fig. 1a). The lateral naves are covered by sail vaults, while the presbytery and the apse are covered with a barrel vault with lunettes and a hemispherical dome, respectively. The central nave was covered with a barrel vault, which was demolished in 2022 during the strengthening intervention due to safety reasons. As shown in Fig. 2ab, the barrel vault was reinforced by a set of transverse arches, three (still standing) located in correspondence of the pillars that separate the central nave from the lateral ones (Fig. 2a, hereafter named intrados arches), three located at mid-span in each bay of the central nave (Fig. 2b, hereafter named extrados arches) and one adjacent to the façade (Fig. 2b). Metallic tie-rods are present at the springings of the transverse arches of the central nave (Fig. 2a), lateral naves, presbytery, and apse. A further tie-rod runs along the inner side of the façade wall. The walls are made of disordered stone masonry, while the vaults of the three naves are made of brick masonry (one layer of bricks laid horizontally). The only exception is the fourth sail vault behind the façade in the north-western lateral nave, which consists of hollow brick masonry. The transverse arches of the central nave are fully made of solid brick masonry, except for the third intrados transverse arch behind the façade, which consists of both solid and hollow bricks. The roof is pitched. A gable roof covers the central nave, while a single-pitched roof covers the lateral naves. On-site inspections and laser scanner surveys were carried out at the extrados of the barrel vault of the central nave, allowing the roof structure to be fully characterized. As shown in Fig. 2b, the roof of the central nave has a timber structure and consists of a series of rafters resting on one side on the perimeter walls and on the other side on two timber ridge beams. The ridge beams are supported either on
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(b)
Fig. 2. (a) Intrados transverse arches and tie-rods at the intrados of the barrel vault of the central nave, (b) extrados transverse arches and roof system at the extrados of the barrel vault of the central nave.
the underlying walls or on solid brick masonry pillars resting on the intrados transverse arches of the barrel vault of the central nave. Above the rafters there are a wooden plank and a covering made of Marseille clay tiles. In the past, the covering was made of slate tiles.
3 Damage and Deformations 3.1 Crack Pattern Survey The crack pattern surveyed in Nostra Signora della Bastia sanctuary is presented in plan in Fig. 3a (in the case of the vaults only the cracks visible at the intrados are reported). The cracks were classified according to three levels of width: (i) thin for a width up to 1 mm (the latter included), (ii) medium for a width between 1 and 5 mm, and (iii) large for a width equal or larger than 5 mm. The most representative damages are illustrated in Fig. 3b-c-d-e. As can be easily seen from Fig. 3a, the damage is concentrated in the central and lateral naves, which presents extensive cracking and deformations in vaults, arches, and floor. The barrel vault of the central nave exhibits a large deformation and extensive cracking in the first, second and third bays behind the façade (Fig. 3b). The cracking pattern is asymmetrical and mainly consists of three cracks that cut longitudinally the vault from the extrados transverse arch at the middle of the first bay behind the façade to the third intrados transverse arch behind the façade. The three cracks are located at mid-span, at the northern springing (at the top of the backfill of the vault) and at an intermediate location between mid-span and the northern springing. They are continuous between the vault and the transverse arches, which show a large deformation similar to that of the vault (Fig. 3c, for further details on the deformation of the intrados transverse arches see Sect. 3.2). The crack at mid-span and the one between mid-span and the northern springing show the largest opening at the intrados and extrados, respectively, and they progress over the entire thickness of both the barrel vault and the first and second intrados transverse arches behind the façade (the third intrados arch only presents hairline cracks visible from the intrados). The crack at the northern springing is visible only at the intrados. In addition to the abovementioned cracks, two large cracks affect the
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barrel vault at both sides of the intrados transverse arch situated between the third and fourth bays behind the façade, indicating an inadequate connection between vault and arch (Fig. 3a). As shown in Fig. 3a, the sail vaults of both the lateral naves are affected by thin diagonal cracks oriented at 45° with respect to the longitudinal axis of the church and developing almost perpendicular to the direction of landslide I. Extensive damage can also be observed in the floor. In the lateral naves, the floor presents a series of diagonal cracks having the same orientation as the cracks of the vaults of the lateral naves (Fig. 3d). These cracks generally develop along the joints of the tiles and have a width ranging between 2 and 8 mm. An important sinking of the floor is detected in correspondence of the pillars that separate the central nave from the lateral ones (Fig. 3e). Differently from vaults, arches, and floor, the walls of the naves do not exhibit extensive damage but are only affected by a few minor and localized cracks. A large vertical crack can be, however, observed in the fourth bay of the north-western lateral nave at the intersection between the longitudinal and transverse walls (see Fig. 3a). This crack, which continues up into the vault, is likely to result from an inadequate connection between contiguous structural elements.
(a)
(c)
(b)
(d)
(e)
Fig. 3. Damage survey of Nostra Signora della Bastia sanctuary: (a) crack pattern in plan, (b) cracking pattern and deformation of the barrel vault of the central nave, (c) cracking pattern and deformation of the first intrados transverse arch behind the façade, (d) diagonal cracks in the floor of the lateral naves, (e) sinking of the pillars.
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3.2 Deformation Analysis With the aim of assessing and quantifying the deformations experienced by Nostra Signora della Bastia sanctuary, a deformation analysis was carried out with the aid of a laser scanner survey. A first laser scanner survey campaign was performed in 2017 using the Z + F 5006h laser scanner and the Topcon GPT-2006 total station. This laser scanner ensured the acquisition of about 25 million points per station and an accuracy of approximately 1 mm per surveyed point. The second laser scanner survey campaign was performed in 2021 with the aim of surveying the roof structure and the extrados of the barrel vault of the central nave, which became accessible due to the ongoing renovation works. The deformation analysis focused on the central and lateral naves, which are the most damaged parts of the church according to the crack pattern survey (see Sect. 3.1). As depicted in Fig. 4, three transverse sections (AA’, BB’ and CC’) passing through the transverse arches that divide the bays were analysed. A deformation analysis of the entire floor of the church, illustrated in Fig. 5, was also performed. The deformation analysis of the transverse sections AA’, BB’ and CC’ was aimed at assessing and quantifying the deformation of walls, pillars, arches, tie-rods, and floor. The surveyed geometry of walls, tie-rods, and floor was compared with a hypothetical undeformed geometry represented by vertical or horizontal reference lines (dashed blue lines in Fig. 4). For each architectural element analysed, a reference point was identified (marked with a blue dot in Fig. 4) and used as both rotation centre to calculate the tilting of walls, pillars and tie-rods and reference point to assess the vertical displacement of the floor. The overall tilting measured on each face of walls and pillars is reported in Fig. 4 as an inclined line (orange dashed line) alongside the deformed geometry, both amplified by a factor of ten for clarity. The most significant vertical displacements of the floor are indicated with red arrows. The rotations measured in the walls and pillars are relatively small, with a maximum of 1° (see angle ω in section CC’), which corresponds to a deviation from the vertical of approximately 7 cm. Both positive (to the North-West) and negative (to the South-East) rotations can be observed. The positive rotations affect the south-eastern lateral nave in sections AA’ and BB’ and the entirety of the church in section CC’. Conversely, the negative rotations are detected in the north-western lateral nave in section AA’ and in the north-western longitudinal wall in section BB’. The tie-rod at the springings of the first transverse arch of the central nave behind the façade (section AA’) does not exhibit any rotation but only a deflection that is probably due to its self-weight. The two tie-rods at the second and third transverse arches of the central nave (sections BB’ and CC’) are inclined downwards towards South-East, while the tie-rods of the both the lateral naves are inclined downwards towards North-West. The deformation analysis of the floor suggests that all the pillars of the central nave experienced a vertical settlement, as a significant sinking of the floor was detected near each pillar. This is in full accordance with the damage surveyed in the floor (Sect. 3.1). Furthermore, the floor shows an overall downward rotation towards North-West in section AA’.
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Fig. 4. Deformation analysis of the transverse section of Nostra Signora della Bastia sanctuary: (a) section AA’, (b) section BB’, (c) section CC’. (Deformed geometry amplified by 10 times).
The deformation of the transverse arches was assessed by evaluating the distance between a reference undeformed geometry (blue dashed line in Fig. 4), which was assumed to be semi-circular, and the actual deformed geometry, obtained from the laser scanner survey (red solid line, amplified by ten times). The deformations observed in the transverse arches of sections AA’ and BB’ are in good agreement with the surveyed crack pattern. The most significant changes in the arch curvature are indeed detected at the positions where cracks opened (mid-span, north-western springing and at intermediate location between mid-span and the springing). A further change in the curvature is detected at the south-eastern haunch. The most deformed transverse arch is that of section AA’, which exhibits a deflection of the crown of about 12 cm and a rise of the north-western portion of about 4 cm. The deformation exhibited by the transverse arches of sections AA’ and BB’ is compatible with that observed in masonry arches subjected to point loads at mid-span. Although the theoretical deformed geometry would be symmetrical, asymmetrical deformed geometries characterized by a significant rise at only one haunch were indeed observed in small-scale masonry arches tested to collapse under a point load applied at the crown [9]. Differently from the arches of sections AA’ and BB’, the transverse arch of section CC’ only exhibits a deflection at mid-span. The occurrence of support displacements in the transverse arches of the central nave is still under investigation due to the difficulty in accurately defining the top level of the capitals from the laser scanner surveys. However, vertical displacements similar to those observed in the tie-rods may have occurred.
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To further investigate the occurrence of differential settlements in Nostra Signora della Bastia sanctuary, a deformation analysis of the entire floor was performed. The floor was isolated from the surveyed point cloud data and its vertical displacements were estimated based on the distance between the surveyed geometry and reference planes specifically identified. In the central and lateral naves, a tilted plane with an inclination of 1.12° was used as reference plane. This plane was identified through a fitting operation on the point cloud data of the floor of the naves. In this way, the inclination of the floor in the longitudinal direction towards the apse, which is often observed in historic masonry churches, was considered. For the analysis of the floor of presbytery, apse and sacristy, a horizontal plane was used as reference plane. The results of deformation analysis of the floor, reported in Fig. 5, show that the most significant settlements are localized in the northern corner of the north-western lateral nave and in the southern corner of the south-eastern lateral nave, with a concentration of vertical displacements close to the pillars of the central nave and the façade. These deformations are in good agreement with those observed in the transverse sections.
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Fig. 5. Deformation analysis of the floor (represented in terms of out-of-plane displacements): (a) plan, (b) amplified 3D representation. (The areas of the floor indicated in white are portions of the floor obstructed by furniture and altars).
4 Structural Analysis Structural analysis was performed with the aim of assessing the structural safety of the transverse arches of the central nave under the loads transmitted by the roof. The deformation analysis presented in Sect. 3.2, indeed, suggested that the deformations and crack patterns of the transverse arches could be attributed to the point loads transmitted by the roof. The first intrados transverse arch behind the façade was analysed, being the most deformed one according to the deformation analysis. To perform structural analysis, the loads transmitted by the roof to the transverse arch under consideration were first evaluated and graphic analyses were then carried out.
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The analysis of the loads transmitted by the roof of the central nave to the transverse arch under study was carried out by using Ftool software [10]. Figure 6a-b shows the static schemes adopted for the rafters and the ridge beams, respectively. The ridge beam RB1 was modelled as a continuous beam on four supports (the façade wall and the three brick masonry pillars resting on the transverse arches of the central nave), while the ridge beam RB2, resting on two brick masonry pillars, was modelled as a simply supported beam. The spacing and the dimensions of the cross-section of the rafters were measured on-site and were taken equal to 500 mm and 70 × 125 mm, respectively. The dimension of the cross-section of the ridge beams was estimated from the laser-scanner survey and was taken equal to 140 × 172 mm and 240 × 200 mm for the ridge beams RB1 and RB2, respectively. The thickness of the wooden plank above the rafters was estimated at 20 mm. A density of 4.5 kN/m3 was adopted for all the timber elements, which were assumed to be made of spruce (typical of the roof systems of the buildings located in the municipality of Busalla). Since the roof covering was originally made of slate tiles but is currently made of Marseille clay tiles, the load analysis was carried out considering the weight of both types of tiles (0.42 kN/m2 and 0.8 kN/m2 , respectively). The total vertical load V acting on the transverse arch was obtained by summing the vertical load transmitted by the roof to the self-weight of the brick masonry pillar (dimensions 0.12 × 0.24 × 1.13 m) resting on the arch. A total vertical load V equal to 5.41 kN and 8.35 kN equal was obtained in the case of Marseille clay tiles and slate tiles, respectively.
Fig. 6. Static schemes adopted for the rafters (a) and the ridge beams (b).
The graphic analyses were carried out on both the undeformed and deformed geometries of the transverse arch under consideration. In both cases, two different analyses were performed: (i) a first analysis in which only the arch was assumed to carry the load transmitted by the roof (configuration A), and (ii) a second analysis in which the barrel vault and the extrados transverse arches were assumed to contribute to withstand the roof load and transfer it to the longitudinal walls (configuration B). This second analysis is justified by the fact that the longitudinal cracks of the barrel vault are continuous with those of the transverse arches. In both analyses, the resistant cross-section was taken equal to that of the transverse arch. However, while in the first analysis only the self-weight of the transverse arch was taken into account, in the second analysis the self-weight of the portion of the barrel vault and the extrados transverse arches indicated in Fig. 7 was also considered. To calculate the values of the self-weight to be used in the graphic analyses, a density of 18 kN/m3 was assumed for the brick masonry of both the barrel vault and the transverse arches.
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Fig. 7. Portion of the barrel vault and the extrados transverse arches considered in configuration B: (a) plan (see the red rectangle), (b) 3D view. (The intrados and extrados transverse arches are coloured in blue and red, respectively).
The graphic analyses carried out on the undeformed geometry of the transverse arch were aimed at evaluating the ultimate load V u transmitted by the roof that causes the arch to collapse. A lower bound and an upper bound of such a load were obtained by applying, respectively, the static and kinematic theorems of Limit Analysis as introduced by Heyman [4] in combination with the uniqueness theorem. According to the static theorem, a structure is safe if at least one thrust line in equilibrium with the external loads and falling within the boundaries of the structure can be found. According to the kinematic theorem, collapse occurs if a kinetically admissible mechanism for which the work done by the external forces is positive or zero can be found. The uniqueness theorem states that a limit condition is reached if a both statically and kinematically admissible collapsing mechanism can be found, that is collapse occurs when the thrust line touches the arch boundary in as many points (corresponding to hinges) as needed to activate a mechanism. Under this condition, the mechanism is the true ultimate mechanism, the load is the true ultimate load, and the thrust line is unique [4, 11]. The results obtained from the graphic static and kinematic analyses in the case of configuration B are shown in Fig. 8a-b, respectively. For the sake of conciseness, the results obtained for configuration A will not be graphically shown but only reported in the text. Since the arch undeformed geometry is symmetrical and the point load acts at mid-span, a symmetrical five-hinge collapse mechanism with two hinges opening at the springings was assumed to occur. To obtain a lower bound V lb of the ultimate load leading to collapse, a thrust line tangent to the arch in five points was sought (Fig. 8a). To do this, the thrust line was assumed to pass through the hinges A, B and C (whose location was considered fixed) and the load V lb was increased until the thrust line became tangent to the arch at two further points at the intrados. Values of V lb equal to 8.7 kN and 35.0 kN allowed a thrust line fully inside the arch profile and tangent to it in five points to be found in the configurations A and B, respectively. These values are a lower-bound of the ultimate load V u causing collapse in the two configurations. To obtain an upper-bound V ub of the ultimate load leading to collapse, a kinematically admissible five-hinge mechanism for which the work done by the external forces was equal to zero was sought (Fig. 8b). The five hinges were placed at the same positions identified by the static analysis to verify if they could actually result in the true collapse mechanism (see the uniqueness theorem mentioned above). The kinematic theorem was
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Fig. 8. Graphic analyses carried out on the undeformed geometry of the first transverse arch behind the façade in the case of configuration B: (a) static analysis, (b) kinematic analysis.
applied considering values of the vertical load V ub corresponding to 105% of the vertical load V lb obtained by the static analysis and, thus, equal to 9.14 kN and 36.75 kN for configurations A and B, respectively. The arch was then divided in four blocks rotating around five hinges and the Principle of Virtual Works was used to calculate the multiplier of the vertical load λ for which the work done by the external forces was equal to zero. Values of λ equal to 0.95 and 0.97, corresponding to values of the vertical load V ub equal to 8.72 kN and 35.7 kN, were obtained for configurations A and B, respectively. These values are an upper-bound of the ultimate load V u causing collapse in the two configurations. Since the difference between the lower- and upper-bound of the ultimate load obtained from the static and kinematic analyses, respectively, is lower than 3% for both the configurations A and B, the assumed collapse mechanisms are the true collapse mechanisms and the true ultimate load V u can be taken equal to 8.7 kN and 35.0 ÷ 35.7 kN for configurations A and B, respectively. Graphic static analyses were performed on the deformed geometry of the transverse arch with the aim of evaluating how far collapse was to occur (Fig. 9). As the arch shows an asymmetrical deformed geometry, collapse is expected to occur by the opening of four hinges. The three cracks surveyed in the arch (see Sect. 3.1) can be considered as hinges, as the deformation analysis detected a change in the arch curvature at their locations. A thrust line passing through these three hinges was thus sought through graphic statics. As shown in Fig. 9 for configuration B, the cracks at the springing and mid-span were assumed to correspond to two hinges (A and C, respectively) located at the extrados, while the crack at an intermediate position between the springing and mid-span was considered to be a hinge (B) located at the intrados. The structural safety of the transverse arch in both the configurations A and B was first evaluated under the total vertical load V estimated by the load analysis, which was equal to 5.41 kN and 8.35 kN in the case of Marseille clay tiles and slate tiles, respectively. Under this load, the thrust line passing through hinges A, B and C is unique, as arches are statically determinate structures when three hinges open. No matter the type of tiles considered, a thrust line fully inside the arch boundaries and passing through the three hinges A, B and C was not found in either configuration (see Fig. 9a for the case of Marseille clay tiles in configuration B). The vertical load transmitted by the roof was
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thus reduced until finding a thrust line fully inside the arch profile. This occurred for values of the total vertical load V equal to about 1.1 kN and 4.2 kN for configurations A and B, respectively. As shown in Fig. 9b, in this case, the thrust line was found to pass very close to the intrados at the right haunch and to be almost tangent to it nearby one or two consecutive voussoirs. Although the values of the vertical load estimated in this way cannot be considered as the real ones acting on the arch, the deformation analysis detected a change in the curvature of the arch at the south-eastern (right in Fig. 9a) haunch, next to the location where the thrust line is almost tangent to the intrados at one or two consecutive voussoirs. As described in [12] and [13], this condition indicates the occurrence of minor and distributed openings, which have the same effect as a hinge in the activation of the collapse mechanism. As a result, the arch can be considered in limit conditions and close to collapse for the estimated values of the vertical load V.
Fig. 9. Graphic static analyses carried out on the deformed geometry of the first transverse arch behind the façade in configuration B under a total vertical load V of 5.4 kN (a) and 4.2 kN (b).
5 Discussion and Conclusions In this paper, a preliminary structural assessment of Nostra Signora della Bastia church (Italy) was performed by integrating structural analysis with crack pattern surveys, laserscanner surveys, and deformation analysis. The church exhibited extensive cracking and large deformations in the vaults and transverse arches of the central nave. The deformation analysis performed with the aid of the laser-scanner surveys allowed some hypotheses on the causes of damage to be put forward. The point load transmitted by the roof at the extrados of the transverse arches of the central nave was identified as potential cause of damage, as the deformed geometry of the arches was compatible with that observed in masonry arches subjected to point loads at mid-span. To assess the structural safety of the transverse arches under the roof loads, structural analysis was performed. Graphic (static and kinematic) analyses were carried out on both the actual deformed geometry and a hypothetical undeformed reference geometry of the first transverse arch behind the façade. For each geometry, two analyses were performed, one considering only the arch (configuration A) and the other also taking into account the contribution of the barrel vault and extrados arches of the central nave in carrying the roof loads (configuration B). The graphic static analyses carried out on the arch deformed geometry showed that the point loads that the transverse arch can withstand in its deformed configuration
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without collapsing (i.e., the thrust line is fully inside the arch profile) is smaller than the roof load calculated through the load analysis in both configurations A and B. Since the arch and the vault were stable before the vault was intentionally demolished, two possible conclusions can be made. First, the actual load transmitted by the roof was overestimated by the load analysis. Such overestimation may result from modelling the supports of the ridge beams on the pillars and underlying transverse arches as perfectly rigid supports instead of elastic supports, as they probably are. Second, the tensile strength of masonry, neglected under Heyman’s assumption of Limit Analysis, enhances the capacity of the arch to withstand the roof load. In any case, since the maximum load that the arch can withstand in configuration A is significantly smaller than the one calculated through the load analysis, it is likely that the barrel vault and the extrados transverse arches of the central nave contribute to carry the load transferred by the roof. The graphic kinematic analyses carried out on the arch undeformed geometry showed that the ultimate load causing the arch to collapse under the action of the roof is significantly larger than the one that the arch can withstand in its current deformed geometry in both configurations A and B. This result suggests that the roof load is not the only cause of damage, but further phenomena may be involved. Since the tie-rods at the springings of the barrel vault are not horizontal according to the deformation analysis, it is likely that the transverse arches of the central nave experienced support displacements. Such displacements may have reduced the capacity of the arches to withstand point loads and resulted in the asymmetrical cracking and deformation pattern observed. As commented in Sect. 3.2, the occurrence of displacements at the arch springings has not been investigated yet. When dealing with support displacements evolving slowly over time, like those produced by foundation settlements or slow-moving landslides, the arch response should be analysed in the framework of large displacements instead of small displacements, as done in this paper. This suggests that the graphical analyses should be complemented with more advanced numerical analyses that consider geometrical nonlinearities. In view of the result obtained, this paper shows the potential offered by the combined use of deformation and structural analyses and represents a first step for the development of a methodology that systematically integrates the two types of analysis for the structural damage assessment of historic masonry structures. Acknowledgements. The authors would like to thank Arch. Andrea Mamone for the material provided on the case study and the possibility to access the building during the renovation works.
References 1. Roca, P.: Considerations on the significance of history for the structural analysis of ancient constructions. In: Lourenço, P.B., Modena, C., Roca, P. (eds.) IV International Conference on Structural Analysis of Historical Constructions, pp. 63–73. Balkema, Amsterdam (2004) 2. Sacco, G.L.S., Ferrero, C., Calderini, C., Battini, C., Vecchiattini, R.: Effect of slow-moving landslides on a vaulted masonry building: the case of San Carlo Borromeo church in Cassingheno (Genova). In: Lancellotta, R., Viggiani, C., De Silva, F., Mele, L. (eds). Third international symposium on Geotechnical Engineering for the Preservation of Monuments and Historic Sites (2022)
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3. Sacco, G.L.S., Ferrero, C., Battini, C., Calderini, C.: Combined use of deformation and structural analysis for the structural damage assessment of heritage buildings: a case study in the Liguria region (Italy). Eng. Failure Anal. 147, 107154 (2023) 4. Heyman, J.: The stone skeleton. Int. J. Solids Struct. 2(2), 249–279 (1966) 5. Ferrero, C., Cambiaggi, L., Vecchiattini, R., Calderini, C.: Damage assessment of historic masonry churches exposed to slow-moving landslides. Int. J. Archit. Heritage 15(8), 1170– 1195 (2021) 6. Federici, P.R., Capitani, M., Chelli, A., Del Seppia, N., Serani, A.: Atlante dei Centri Abitati Instabili della Liguria. II. Provincia di Genova (Atlas of the unstable inhabited centres of Liguria. II. Genova province). Regione Liguria, Genova, Italy (2004) 7. Autorità di bacino distrettuale del fiume Po. Atlante dei Rischi Idraulici e Idrogeologici, Accessed 25 Oct 2018 8. Mamone, A.: Survey, analysis and diagnosis of Nostra Signora della Bastia Sanctuary in Busalla. University of Genoa (2017) 9. Shapiro, E.E.: Collapse mechanism of small-scale unreinforced masonry vaults. M.S. thesis in Building Technology, MIT (2012) 10. Ftool Software. https://www.ftool.com.br/Ftool/. Accessed 02 Jan 2023 11. Roca, P., Cervera, M., Gariup, G., Pelà, L.; Structural analysis of masonry historical constructions. Classical and advanced approaches. Arch. Comput. Methods Eng. 17, 299–325 (2010) 12. Ferrero, C, Calderini, C, Roca, P.: Experimental response of a scaled dry-joint masonry arch subject to inclined support displacements. Eng. Struct. 253(2), 113804 (2022) 13. Ferrero, C, Calderini, C, Roca, P.: Effect of joint deformability on the experimental and numerical response of dry-joint masonry arches subjected to large support displacements. Eng. Struct. 275, 115236 (2023)
3D Non-periodic Masonry Texture Generation of Cultural Heritage Structures M. Pereira1 , A. M. D’Altri1,2(B) , S. de Miranda2 , and B. Glisic1 1 Department of Civil and Environmental Engineering, Princeton University, Princeton, USA 2 Department of Civil, Chemical, Environmental, and Materials Engineering, University of
Bologna, Bologna, Italy [email protected]
Abstract. Block-based models, which can account for the actual block-by-block masonry texture, are becoming more commonly used for the analysis of historical masonry structures, given their high accuracy in representing masonry mechanics and their computational demand which has become lately approachable. However, the implementation of full-scale models where every single masonry block is accurately represented can be time-consuming, and even impossible, due to lack of relevant data. In this contribution, a 3D non-periodic masonry pattern generator is proposed for the block-based analysis of full-scale historical structures. This approach uses as input the digital solid model of the structure, in terms of voxels, and a representative texture of a small portion of a wall. The generator automatically creates the block-by-block arrangement of the whole structure through a pseudo-statistically meaningful representation, also in case of multi-leaf walls. An example of cultural heritage structure is used to assess the effectiveness of the automatic generator. Then, pushover-like analyses are conducted by means of an available block-based model, investigating the masonry texture influence on full-scale mechanical responses. Keywords: Multi-leaf masonry · Masonry mechanics · Non-periodic texture · Historical monumental buildings · Voxel
1 Introduction Numerical modelling of masonry and historical structures can result essential to apply conservation strategies on cultural heritage (CH) buildings. In this framework, blockbased models (that account for the actual block-by-block masonry texture) represent the most accurate option for the structural analysis of masonry structures [1], including also multi-leaf non-periodic masonry [2, 3]. The main drawbacks that characterize blockbased models are: (i) their considerable computational demand, and (ii) the impossibility to geometrically accurately represent every single block in a full-scale masonry structure, due to non-periodic patterns and lack of relevant data [4]. Concerning drawback (i), the recent enhancement of computational facilities together with the recent development of efficient models allowed the block-based simulation of large-scale masonry structures, as shown in [5, 6]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 366–373, 2024. https://doi.org/10.1007/978-3-031-39450-8_30
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Concerning drawback (ii), a possible recent way to solve the issue, beyond imagebased methods [7, 8] limited to plane and single-layer structures, considers pattern generators which can automatically generate the block-by-block geometry of the structure to be used in structural analysis. In this framework, a 2D generator for historic stone masonry has been developed in [9], whereas a 3D generator for stone masonry walls has been developed in [10]. Particularly, a multi-objective optimization packing approach has been developed to place the blocks in the wall and to fill the overall volume. Although this method allows to create realistic non-periodic multi-leaf masonry walls, also based on irregular blocks, the resulting finite element (FE) meshes have a large number of degrees of freedom and, so, a considerable computational effort. Therefore, the utilization of these FE meshes appears limited to homogenization and multiscale analyses, while their full-scale application appears still unlikely. In this contribution, a 3D non-periodic masonry pattern generator is proposed for the block-based analysis of full-scale historical structures. This approach requires as input (in terms of voxels): (i) the digital solid model of the structure, and (ii) a representative texture of a small portion of a wall. Input (i) is also obtainable directly from point clouds of CH structures [11], while input (ii) could be obtained automatically from images [12]. The generator automatically fills the volume of the structure through a block-byblock arrangement that attempts to keep the blocks statistics of the representative texture, also in case of multi-leaf walls. Such 3D block-by-block texture is directly employable in block-based computational analysis of full-scale historical masonry structures. An example of CH structure, namely the Alcaçova wall of the Guimarães castle (Portugal) [13, 14] characterized by 2 leaves of non-periodic granite blocks, is used to assess the effectiveness of the automatic texture generator. The generated texture is then employed in pushover-like analyses by adopting a 3D damaging block-based model previously developed in [15]. Finally, the influence of masonry texture on full-scale mechanical responses is discussed.
2 Masonry Texture Generator The 3D masonry texture generator here proposed is based on voxels and requires as input: (i) the digital solid model of the structure (target volume); and (ii) a representative texture of a small portion of a wall. The target volume allows the specification of fillable and non-fillable regions (e.g. openings), while all the block types and their statistics to be considered in the structure can be found in the representative texture. Firstly, lintels are inserted above openings. Particularly, openings are automatically identified and lintels of a suitable size are introduced as special blocks. Then, edges and corners are filled. This filling procedure moves vertically, up to the edge/corner is eventually filled.
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Finally, all the inner regions of the volume are filled with blocks. This last operation is carried out block-by-block, starting from the bottom row of a first leaf and repeated for the rows above. While filling a row, head joints are detected and a set of block types suitable to be inserted without vertical alignment are determined. If the available block types cannot guarantee to perfectly fill the volume, ad hoc block types are introduced to fill any remaining gap. A follow-up adjustment step, which tries to minimize the number of ad hoc blocks through the merging with neighboring blocks, is finally performed. The interested reader is referred to [16] for further details. A preliminary check of the consistency of the generator is here shown and discussed (Fig. 1). An example of representative texture used as reference is shown in Fig. 1a, arbitrarily taken from the case study in [13] with 10 block types, 2 of which are throughthickness. The target volume is created by scaling 3 times the width and the height of the representative texture (Fig. 1a), considering a thickness of 3 leaves. Hence, 3 samples are generated and considered. The block type content percentages (p) of the reference texture and the 3 generated samples are shown in Fig. 1b, while the arrangements of the 3 generated samples are shown in Fig. 1c. As it can be noted from these preliminary results, the generator produces statistically-consistent textures in a robust way.
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Fig. 1. Example of masonry texture generation. (a) Representative texture (reference). (b) Reference (black markers) and generated samples block type content percentages. (c) Arrangements of the generated masonry samples.
The generator is then employed for a CH structure, i.e. the Alcaçova wall of the Guimarães castle (Portugal) [13, 14], see Fig. 2. The target volume of this structure is taken from [13], where few geometrical simplifications were adopted. Accordingly, the target volume is composed of 2 leaves of blocks and 7 openings (Fig. 2a). The masonry
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texture generated by means of the representative texture in Fig. 1a is shown in Fig. 2b (“Actual texture”), while the texture generated with the same representative texture, but without through-thickness blocks, is shown in Fig. 2c (“Without through-thickness blocks”). As it can be noted, the overall filling of the target volume is guaranteed by means of this 3D masonry texture generator.
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Fig. 2. CH structure texture generation. (a) Simplified digital solid model of the Alcáçova wall. Masonry textures of the two leaves: (b) Actual texture (through-thickness blocks are highlighted in dark grey), (c) Without though-thickness blocks.
3 Structural Analysis 3.1 Numerical Modelling The generated textures (Fig. 2b-c) are then employed in pushover-like analyses using the 3D damaging block-based model developed in [15]. Such model is characterized by 3D damaging blocks and zero-thickness joints modeled through contact-based cohesivefrictional interfaces. The interested reader is referred to [15] for additional details. The mechanical characterization has been conducted in agreement with [13].
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The damaging behavior of blocks relies on the plastic-damage continuum constitutive law developed in [17]. Such law accounts for isotropic damage by means of two damage scalar variables, 0 ≤ dt < 1 for tension and 0 ≤ dc < 1 for compression. The main input of the continuum constitutive law is represented by tensile and compressive uniaxial stress-strain curves, which are given for the case study in Table 1 together with the elastic properties of blocks. Table 1. Block mechanical properties. Young’s modulus [MPa]
4800
Poisson’s ratio [\]
0.17
Density [kg/m3 ]
2700
Tensile uniaxial nonlinear response
Compressive uniaxial nonlinear response
Stress [MPa]
Inelastic strain
dt [\]
Stress [MPa]
Inelastic strain
dc [\]
1.0
0
0
12.0
0
0
0.1
0.001
0.9
12.0
0.004
0
1.2
0.012
0.9
The joint response relies on a node-to-surface cohesive-frictional contact formulation. In the normal direction, the contact constrain is enforced by means of the Lagrange multiplier method. In addition, a cohesive response is activated in tension, governed by the normal cohesive stiffness Kt , the tensile strength ft , and the excursion of normal displacement uF in the softening branch, assumed linear. In the shear direction, a cohesive-frictional response is activated. The cohesive response is governed by the shear cohesive stiffness Ksc , the cohesion c, and the slip excursion δ F in the softening branch (linear), while the frictional response is merely governed by the friction angle φ. In particular, the frictional contribution is assumed to reach the plateau contemporarily to the peak of cohesion. The joint mechanical properties used for the CH example are given in Table 2. It should be pointed out that the intralayer joints have been assumed without cohesion, i.e. only friction has been considered. Table 2. Joint mechanical properties. Tensile response ft [MPa] uF [mm] Kt [N/m3 ]
Shear response 0.05
c [MPa]
0.05
0.5
δ F [mm] Ksc [N/m3 ]
0.5
φ [°]
30
1.0· 1010
0.5 · 1010
The generated models are then employed in nonlinear static analyses. Particularly, the wall is uniformly loaded out-of-plane, clamped at the base, and horizontal supports
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are placed on two vertical edges of the sides (that attempts to mimic the constraint given by orthogonal walls). 3.2 Numerical Results In this section, the results of the out-of-plane analyses for the “Actual texture” and the case “Without through-thickness blocks” are shown and discussed (Fig. 3). In particular, the pushover curves are shown in Fig. 3a, while the collapse mechanisms are shown in Fig. 3b, in terms of horizontal displacement contour plots. As it can be noted, considerable differences appear between the “Actual texture” and the case “Without throughthickness blocks”, both in terms of (i) pushover curves (Fig. 3a), where a remarkably lower horizontal capacity and overall stiffness is observed in the case “Without throughthickness blocks” with respect to “Actual texture, and (ii) collapse mechanisms (Fig. 3b), where a complete detachment between leaves is only observed in the case “Without through-thickness blocks”.
(a)
(b)
Fig. 3. Numerical results of the out-of-plane loaded CH structure: (a) pushover curves, and (b) collapse mechanisms.
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According to these preliminary results, the presence of few through-thickness blocks appears to have a beneficial contribution to the out-of-plane capacity of the wall, preventing the detachment between leaves.
4 Conclusions In this contribution, a pattern generator for 3D non-periodic masonry structures has been proposed. This generator requires as input the digital solid model of the structure and a representative texture of the wall, both in terms of voxels, to automatically fill the overall volume of the structure through a block-by-block arrangement that attempts to keep the blocks statistics of the representative texture. This approach showed to be effective also in case of multi-leaf walls, and appeared directly employable in block-based computational analysis of full-scale historical masonry structures. The Alcaçova wall of the Guimarães castle (Portugal), characterized by 2 leaves of non-periodic granite blocks, has been used as benchmark to assess the effectiveness of the automatic texture generator, which proved to be robust and efficient in providing convenient inputs for full-scale block-based analysis of CH structures. The generated textures have been then employed in out-of-plane pushover analyses by adopting an available damaging block-based model. Preliminary results highlighted that the presence of few through-thickness blocks appears to have a beneficial contribution to the out-of-plane capacity of the structure, preventing the detachment between leaves. Acknowledgments. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101029792 (HOLAHERIS project, “A holistic structural analysis method for cultural heritage structures conservation”).
References 1. D’Altri, A.M., et al.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27(4), 1153–1185 (2020) 2. Tiberti, S., Milani, G.: 3D homogenized limit analysis of non-periodic multi-leaf masonry walls. Comput. Struct. 234, 106253 (2020) 3. Cavalagli, N., Cluni, F., Gusella, V.: Evaluation of a statistically equivalent periodic unit cell for a quasi-periodic masonry. Int. J. Solids Struct. 50(25–26), 4226–4240 (2013) 4. Pantoja-Rosero, B.G., Saloustros, S., Achanta, R., Beyer, K.: Image-based geometric digital twinning for stone masonry elements. Autom. Constr. 145, 104632 (2023) 5. Ferrante, A., et al.: Discontinuous approaches for nonlinear dynamic analyses of an ancient masonry tower. Eng. Struct. 230, 111626 (2021) 6. Malena, M., Portioli, F., Gagliardo, R., Tomaselli, G., Cascini, L., de Felice, G.: Collapse mechanism analysis of historic masonry structures subjected to lateral loads: a comparison between continuous and discrete models. Comput. Struct. 220, 14–31 (2019)
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7. Loverdos, D., Sarhosis, V., Adamopoulos, E., Drougkas, A.: An innovative image processingbased framework for the numerical modelling of cracked masonry structures. Autom. Constr. 125, 103633 (2021) 8. Valero, E., Bosché, F., Forster, A.: Automatic segmentation of 3D point clouds of rubble masonry walls, and its application to building surveying, repair and maintenance. Autom. Constr. 96, 29–39 (2018) 9. Zhang, S., Hofmann, M., Beyer, K.: A 2D typology generator for historical masonry elements. Constr. Build. Mater. 184, 440–453 (2018) 10. Shaqfa, M., Beyer, K.: A virtual microstructure generator for 3D stone masonry walls. Eur. Journal of Mechanics-A/Solids 96, 104656 (2022) 11. Castellazzi, G., Presti, N.L., D’Altri, A.M., de Miranda, S.: Cloud2FEM: a finite element mesh generator based on point clouds of existing/historical structures. SoftwareX 18, 101099 (2022) 12. Ibrahim, Y., Nagy, B., Benedek, C.: Deep learning-based masonry wall image analysis. Remote Sens. 12(23), 3918 (2020) 13. Milani, G., Esquivel, Y.W., Lourenço, P.B., Riveiro, B., Oliveira, D.V.: Characterization of the response of quasi-periodic masonry: geometrical investigation, homogenization and application to the Guimarães castle. Portugal. Eng. Struct. 56, 621–641 (2013) 14. Riveiro, B., Lourenço, P.B., Oliveira, D.V., González-Jorge, H., Arias, P.: Automatic morphologic analysis of quasi-periodic masonry walls from LiDAR. Comput.-Aided Civil Infrast. Eng. 31(4), 305–319 (2016) 15. D’Altri, A.M., Messali, F., Rots, J., Castellazzi, G., de Miranda, S.: A damaging block-based model for the analysis of the cyclic behaviour of full-scale masonry structures. Eng. Fract. Mech. 209, 423–448 (2019) 16. Pereira, M., D’Altri, A.M., de Miranda, S., Glisic, B.: Automatic multi-leaf nonperiodic blockby-block pattern generation and computational analysis of historical masonry structures. Eng. Struct. 283, 115945 (2023) 17. Lee, J., Fenves, G.L.: Plastic-damage model for cyclic loading of concrete structures. J. Eng. Mech. 124(8), 892–900 (1998)
Stability of Masonry Vaulted Tunnels in Purely Frictional and Cohesive-Frictional Grounds A. Menil1(B) , A.-S. Colas1 , D. Subrin2 , and M. Bost1 1 Université Gustave Eiffel, Lyon, France [email protected] 2 Centre d’Etudes des Tunnels (CETU), Lyon, France
Abstract. Masonry tunnels are underground structures which can experience degradation due to ageing resulting in damage or cracking. In this work, the stability of these structures is studied using the upper-bound kinematic approach of yield design theory. This method allows estimating the ultimate load of any system knowing the geometry and the strength of its constitutive materials. However, the determination of the optimal failure mechanism, that is to say the one giving the upper-bound of the ultimate load, can be tricky as regards the interactions between the ground and the structure itself. To overcome this issue, it has been chosen to decompose the problem in two sub-problems. On the one hand, existing kinematic models dealing with the stability of excavations are extended to cohesive-frictional grounds. On the other hand, a mechanism representing the deformation observed on-field is explored to assess the masonry lining stability. Yield design theory is used to determine upper-bound estimations of the ultimate load for excavations in purely frictional grounds, cohesive-frictional grounds, and for a masonry vault subjected to a concentrated load. Keywords: Stability · Yield design · Masonry vault · Shallow tunnel
1 Introduction Masonry tunnels are underground structures constructed between the 19th and the first half of the 20th centuries in Europe and worldwide for the development of transport or hydraulic infrastructures. These constructions have long proved their robustness; nevertheless, they can experience degradation due to ageing resulting in damage or cracking. Furthermore, in an urban context, creation and enlargement of transportation networks can have an impact on these existing structures. The stability of masonry lining has been the subject of several studies and models that have been developed on the basis of observed degradation. Some of them have tried, for instance, to take into account an elasto-plastic behaviour for the ground and to describe in detail the behaviour of the structure itself through a homogenized model with damage for the masonry lining and the unreinforced concrete sidewalls [1, 2]. This paper is part of a study aiming at better understanding the behaviour of a masonry tunnel subjected to ageing or an evolution of its environment. In a preliminary approach, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 374–386, 2024. https://doi.org/10.1007/978-3-031-39450-8_31
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it has been decided to evaluate the bearing capacities (ultimate limit state) of masonry tunnels resorting to upper-bound yield design. Yield design allows assessing the stability of a system resorting to the compatibility between the quasi-static equilibrium and the strength properties of its constitutive materials. The kinematic upper-bound approach of yield design states that, for any kinematically admissible virtual velocity field, if the virtual work by a given load exceeds the maximum resisting work, then this load is certainly unsafe [3].
2 Problem Statement and Resolution Method The system under consideration is a tunnel composed of a masonry vault, seated on sidewalls and invert made of concrete (see Fig. 1). The three categories of input data needed for the resolution by yield design are detailed below. 2.1 System Geometry The tunnel has a diameter D and the lining a thickness e. It is made of a masonry vault, which forms an angle θn with the horizontal at its skewback. The keystone forms an angle of θc with the horizontal. The tunnel is embedded in the ground with a cover depth C. The length of the structure is very long compared toits diameter, thus leading to consider plane strains hypothesis in the transversal plane ex , ey . 2.2 Loadings The ground-structure system is subjected to the ground specific weight γ, the masonry specific weight γm and a uniformly distributed overload σS at the ground surface. 2.3 Materials Strength The ground is considered as cohesive-frictional following Coulomb’s strength criterion with a cohesion c and an internal friction angle ϕ. Masonry blocks, side walls and invert are considered as infinitely resistant while the joints between the blocks follow Coulomb’s strength criterion with a cohesion cm and a friction angle ϕm . Using the kinematic approach of yield design, this criterion can be written using the π support functions: π d = ccotanϕtrd if trd ≥ (|d1 | + |d2 |)sinϕ (1a) π n, v = ccotanϕ v if v .n ≥ v sinϕ
(1b)
The problem symmetry allows considering half problems in the following. In order to identify the failure mechanisms of the ground-structure system, it has been decided to solve this problem by studying two complementary problems as a first attempt: the stability of the sole ground (see Fig. 2a) and the stability of the sole masonry vault (see Fig. 2b).
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Fig. 1. Schematic description of the masonry tunnel embedded in the ground: geometry, load and strength parameters
(a)
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Fig. 2. Problem decomposition: study of the ground stability (a) and the masonry vault stability (b)
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3 Yield Design Analytical Solutions for Unlined Openings in Cohesive-Frictional Grounds Considering the problem as described in Fig. 2a, the problem data are the ones described in Sect. 2 except for the tunnel lining which is replaced by a uniform support load σ T : σ T = σT e r
(2)
Relying on [4] and [5], the stability of the ground is assessed using two families of virtual failure mechanisms illustrated in Fig. 3. These mechanisms involve virtual rigid body translations of edges of the ground, represented in grey in Fig. 3, whereas the remaining part of the ground remains still.
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Fig. 3. Description of the “roof” failure mechanism (a) and the “sides and roof” failure mechanism (b): volume of ground in translation are represented in grey
3.1 “Roof” Failure Mechanism (a) Mechanism description. The virtual failure mechanism is described in Fig. 3A: an edge of ground at the tunnel roof defined by the volume abe is subjected to a vertical translation U : U = −U ey The ground around remains still.
(3)
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V = abe represents the volume of ground in translation, and is given by: π D2 cotanϕ − + ϕ = V = Vabc − V bce 8 2
(4)
= ab represents the discontinuity surface between the edge of ground in translation and the ground remaining still, and is given by: =
D cotan0 2
(5)
St = be represents the surface inside the excavation in contact with the edge of ground 1 1 in translation. The mechanism remains under the ground surface when C D ≥ 2 sin0 − 1 . In this case, the overload σS does not affect the mechanism. Since the rigid body mechanism does not involve internal deformation, the relevancy condition boils to Eq. (1b), and is fulfilled as soon as the velocity jump U forms an angle ϕ with the discontinuity surface = ab. Upper-bound solution. The virtual work of the external forces Pext and maximum resisting work Prm can be written using Eqs. (2), (3), (4) and (5). The kinematic theorem given by [3] finally gives: Pext ≤ Prm γ D2 8 cotanϕ −
π 2
+ ϕ − σT D cos ϕ ≤ cD cos ϕ cotan ϕ
(6)
In order to make easier the parametric representation and analysis of the results, the upper-bound estimation of the ultimate support load can be written in its dimensionless form: σT 1 c ≥ Nγ (ϕ) − γD tanϕ γD
(6a)
With Nγ (ϕ), a function of the geometric parameters representing the specific weight contribution to the ultimate load result, given by:
1 1 π − +ϕ (6b) Nγ (ϕ) = 8cosϕ tanϕ 2
3.2 “Sides and Roof” Failure Mechanism (b) Mechanism description. The virtual failure mechanism is described in Fig. 3B: an edge of ground at the tunnel roof defined by the volume abe is subjected to a vertical translation U 1 and another edge of ground on the excavation sides defined by the volume bce is moved by a translation U 2 : U 1 = −U1 ey
(7a)
U 2 = −cosαex − sinαey
(7b)
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With α = cbe. The ground around remains still. V1 = abe and V2 = bce represent the volumes of ground in translation, and are given by: D2 8tanϕtan2 α2 α D2 2cotan − π + α = V2 = Vbcde − V cde 8 2 V1 = Vabe =
(8a) (8b)
1 = ab, 2 = bc and 12 = be represent the discontinuity surfaces between an edge of the ground in translation and the ground remaining still or the other edge of the ground in translation, and are given by: 1 =
D 2sinϕtan α2
(9a)
D 2tan α2
(9b)
2 = 12
D = 2cotan α2
(9c)
St = ce represents the surface inside the excavation in contact with the edge of ground D in translation. The mechanism remains under the ground surface when C D ≥ 2tanϕtan( α2 ) . In this case, the overload σS does not affect the mechanism. Since the rigid body mechanism does not involve internal deformation, the relevancy condition boils to Eq. (1b), and is fulfilled as soon as the velocity jumps U 1 , U 2 and U − U form an angle ϕ with the discontinuities surfaces 1 = ab, 2 = bc and 1 2 12 = be respectively. Upper-bond solution. The virtual work of the external forces Pext and maximum resisting work Prm can be written using Eqs. (2), (7a), (7b), (8a), (8b), (9a), (9b) and (9c). The kinematic theorem given by [3] finally gives: Pext ≤ Prm 2
cos ϕ sin(α−ϕ) γ U1 D 1 + cotan α2 + α−π 4 2 sin(α−2ϕ) 2 tan ϕ tan2 ( α2 ) cos ϕ 1 −σT DU ϕ + cos(α − ϕ)) (cos 2 sin(α−2ϕ)
ϕ+cos(α−ϕ) sin ϕ ≤ cU21 D cotanϕ cotan α2 1 + cos ϕ sinsin(α−2ϕ)
(10)
In order to make easier the parametric representation and analysis of the results, the upper-bond estimation of the ultimate support load can be written in its dimensionless form: σT c ≥ Nγ (ϕ) ± Nc (ϕ) (10a) γD γD With Nγ (ϕ), a function of the geometric parameters representing the specific weight contribution to the ultimate load result and Nc (ϕ) a function of the geometric parameters
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representing the strength parameters of the ground contribution to the ultimate load result, given by: Nγ (ϕ) =
sin(α−2ϕ) 2 2sinϕtan( α2 )
+ sin(α − ϕ)(cotan
α 2
+
α−π 2 )
2cosϕ + cos(α − ϕ) α
2ϕ − cotan 2 1 cosϕ + cos(α − ϕ) + Nc (ϕ) = cosϕ + cos(α − ϕ) sinϕ sin(α − 2ϕ)
(10b) (10c)
The upper-bound load is finally given by optimising expression (10a) with respect to the variation of angle α meaning the α that gives the highest estimation of the ultimate load for the considered parameters in this configuration. 3.3 Modelling in Optum CE The analytical approach has been completed by a numerical simulation using Optum CE, see Fig. 4. This finite element software makes it possible to determine numerically the values of the ultimate load, relying on the upper-bound approach of yield design theory. The input parameters are thus the same as the ones used for the analytical resolution: system geometry, loadings and material strength criterion. The results obtained are compared with the results determined by the analytical formulation. Figure 4 represents half the problem, the geometry and loading being symmetrical. The displacements are blocked in both directions on the lateral and lower outer limits. At the axis of symmetry, only the horizontal displacements are blocked. The mesh is automatically generated by the program. Figure 4 represents the case where the ratio C/D between the ground cover C and the excavation diameter D is equal to 3. The strength (c, ϕ) and load parameters (σT , γ ) are set to obtain ratio σT /c that can be compared to the ones explored in the analytical results. The program determines the specific weight γ to be applied in order to achieve failure by the upper-bound approach of yield design. This result is used to calculate the corresponding σT /γ D. Figure 4 presents the distribution of the displacement norm of the ground. It is possible then to compare the mechanism determined analytically and numerically.
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Fig. 4. Modelling on Optum CE, distribution of the displacement norm of the ground
3.4 Results The evolution of the dimensionless support load σT /γ D is represented in Fig. 5.a with respect to the friction angle of the ground ϕ for a purely frictional or cohesive-frictional ground for different c/γ D values. The solid lines correspond to the results for the roof mechanism A and the dashed lines to those for the sides and roof mechanism B. The results shown here for the mechanism A are identical to those given by [5]. The kinematic approach undertaken in this work provides an upper-bound of the critical load. However, σT being a resistance parameter, the analytical kinematic approach leads here to lowerbounds of the critical pressure meaning that the optimal estimates are given by the greatest values.
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The circle markers correspond to the values obtained with Optum CE for a purely frictional ground. These results obtained numerically are higher than those given by the closed-form solutions. This is due to the fact that Optum CE can scan a very large number of failure mechanisms, using velocity discontinuities as well as smooth deformations. For a friction angle of the ground below 40°, Mechanism B gives higher thus better lowerbound estimates of the critical pressure than Mechanism A, and incidentally closer to the results obtained numerically. Since grounds over 40° are very specific, mechanism B is selected as the best estimate from the kinematical approach in the present analysis. The internal pressure to be applied within the opening decreases for greater internal friction angle ϕ as well as greater cohesion c, both parameters expressing the shear resistance of the ground. The evolution of the dimensionless load γ D/c with respect to the friction angle of the ground ϕ for different σT /c values for a cohesive-frictional ground is represented in Fig. 5.b with the same conventional representation of the analytical and numerical results. The kinematic exterior approach given by the mechanism B appears relatively close to the optimal critical loads expressed by the numerical results.
Fig. 5. Dimensionless maximum load as a function of ϕ for purely cohesive grounds and cohesivefrictional grounds (a, left) compared to results obtained with Optum CE (b, right), solid and dashed lines correspond to mechanisms A and B respectively
4 Yield Design Analytical Solution for a Masonry Vault Subjected to a Punctual Load 4.1 Mechanism Description Considering the problem as described in Fig. 2b, the problem data are the ones described in Sect. 2 except for the ground, which is replaced by a concentrated load called Q and applied at the keystone centre. This simplified loading is chosen so as to simulate the deformation that can be observed in masonry tunnels. This mechanism involves a convergence between the keystone and the invert and a divergence between both sidewalls. The underground pressure being more difficult to simulate and analyse, it will be explored in further studies.
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The virtual failure mechanism of the vault is described in Fig. 6. Keystone is animated with a vertical translation U to comply with the problem symmetry. The section of the vault comprised between the keystone (of angle θc ) and a masonry joint of angle α is given a rotation W2 around Ce of angular velocity ω2 and a translation U . The section of the vault comprised between the skewback (of angle θn ) and the masonry joint of angle α is given a rotation W1 around Ne of angular velocity ω1 .
Fig. 6. Description of the rotational failure mechanism for the vault
4.2 Upper-Bound Solution Relevancy conditions give ω1 and ω2 expressions as functions of U . The kinematic theorem as presented above can be applied to get the ultimate load. The obtained equation with the form Q ≤ f (D, e, θc , θn , γ , c, ϕ, α) may be written in a dimensionless Q e c form given by γ D2 ≤ f D , θc , θn , γ D , ϕ, α . Finally, an optimisation on the kinematic parameter α provides an upper-bound estimation of the ultimate load that the vault can + sustain: γ QD2 ≤ f + De , θc , θn , γcD , ϕ .
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4.3 Results 1 , with ϕ Figure 8 represents the dimensionless maximum load as a function of tanϕ between 10 and 45° (i.e. 1/tanϕ between 1 and 5.7), with realistic values for block interface friction angle ϕ chosen as 25, 30 and 35° (i.e. 1/tanϕ as 2.1, 1.7 and 1.4). A thin vault is considered thus De ≤ 0.1, and the influence of this parameter being minor, the value De = 0.06 is set. γcD is taken between 0 and 20 to explore significant ranges for masonry specific weight and shear properties [6]. Modelling results obtained with Optum CE as described in Fig. 7 are represented with dots on the graphs. Results show that, for the defined system, increasing masonry specific weight lowers the maximum load. It also decreases if the internal friction angle defined at the contact between masonry blocks increases. This comes from the fact that for a given cohesion value (according to an ideal Coulomb strength criterion not truncated in the field of negative stresses) increasing the frictional angle means decreasing tensile resistance. The comparison of the graphics given Fig. 8 shows that the ultimate load increases if an angle θn is introduced, simulating higher lateral sidewalls.
Fig. 7. Modelling on Optum CE, results showing the distribution of the displacement norm of the vault
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1 for θ = 0◦ (a, left) and θ = 20◦ Fig. 8. Dimensionless maximum load as a function of tanϕ n n (b, right)
5 Conclusions The results given in this paper are limited to the study of mechanisms in the ground alone and for a single vault subjected to a concentrated load at the keystone. Perspectives on this work include the combination of these two approaches in a comprehensive ground-structure yield design simulation combined with finite element modelling in order to describe accurately the deformation of masonry tunnels.
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References 1. Kamel Daca, T. : Contribution au diagnostic expert et à l’analyse de risques dans les ouvrages souterrains en maçonnerie par la modélisation numérique. Ph.D. thesis, INSA de Lyon, 2013. Consulté le: 11 mai 2022. [En ligne]. Disponible sur: https://tel.archives-ouvertes.fr/tel-010 80902 2. Moreno Regan, O. : Etude du comportement des tunnels en maçonnerie du métro parisien », phdthesis, Université Paris-Est, 2016. Consulté le: 11 mai 2022. [En ligne]. Disponible sur: https://tel.archives-ouvertes.fr/tel-01355701 3. Salençon, J.: Yield design (2013) 4. Davis, E.H., Gunn, M.J., Mair, R.J., Seneviratine, H.N.: The stability of shallow tunnels and underground openings in cohesive material. Géotechnique 30(4), 397–416 (1980). https://doi. org/10.1680/geot.1980.30.4.397 5. Atkinson, J.H., Potts, D.M.: Stability of a shallow circular tunnel in cohesionless soil. Géotechnique. 27(2), 203-215 (1977). https://doi.org/10.1680/geot.1977.27.2.203 6. Delbecq, J.-M.: Les ponts en maçonnerie (1982)
Numerical Modelling and Structural Analysis of Armoury Museum at City Palace Udaipur, Rajasthan, India Omkar S. Adhikari1(B) and João M. Pereira2 1 Indian National Trust for Art and Cultural Heritage, Lodi Road, New Delhi, India
[email protected]
2 ISISE – Institute for Sustainability and Innovation in Structural Engineering), University of
Minho, Campus de Azurem, Guimarães, Portugal [email protected]
Abstract. The work intends to study and analyse a case study of the City Palace Udaipur in Rajasthan, India. The City Palace complex, Udaipur is an exemplary model of the Rajput palace fortress and its construction lasted 400 years, starting from 1553C.E [1]. The Saleh Khana (armoury museum) had been intervened due to the presence of structural damage [2]. This work focusses on the analysis of the structural condition of the Saleh Khana (armoury museum), within the City Palace of Udaipur, India. In general, two main objectives are achieved. First, the modelling and assessment of the condition of the structure before the interventions are carried out. The obtained results are then compared with the documented damage present in the structure before the interventions to verify if the damage present at the structure was reflected properly while modelling and its only due to the vertical forces acting on the building. Secondly, the modelling and assessment of the condition of the structure after the interventions is carried out. The obtained results are then compared with structural analysis before the intervention to verify the improvements made with the interventions that were proposed and executed. To achieve these objectives, different 3D finite element models of the structure were analysed. The research was able to justify several important damage features of the building. Particularly, good consistency was obtained regarding the damage patterns of the stone frames and the vaulted roofs. Furthermore, the results indicate that the numerical model developed within the scope of this work can properly replicate the overall behaviour of the structure. The efficiency of the interventions executed in the Saleh Khana was estimated, and an improvement on the overall capacity of the structure under vertical loads of 67% can be expected. Keywords: FE modelling · Structural Analysis · Masonry structures · Stone masonry · Non-linear static analysis
1 Salehkhana – Armory Museum The city palace complex is a monumental site with an ensemble of built form and courtyard spaces at varying levels built on a over the time period of 400 years. Salehkhana was built in 16th century CE, comprises of a series of vaulted spaces with smaller vaulted © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 387–399, 2024. https://doi.org/10.1007/978-3-031-39450-8_32
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rooms (a Fig. 1) which served as the waiting hall for the guests that came to meet the King [2].
(a)
(b)
(c)
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Fig. 1. Salehkhana: (a) main façade highlighting Salehkhana area; (b) interior openings; (c) main vault; (d) corbelled stone vaults.
In current scenario Salehkhana is partially functioning as an Armoury gallery in Mardana Mahal, City Palace Museum. The revised museum plan focused on the restoration of the Salehkhana to its original Grandeur by removing additions and alteration done due to structural distress in later periods in past. The proposal intended to improve the structural safety of the existing structure, also regain the long-spanned hall spaces while reorganizing circulation pattern. to crater museum theme. 1.1 Defect Mapping Detail measured drawings and photographic survey were primary mode of data collection and defect identification. The observations were reflected on drawing in form of defect maps. Damage observed were of two types: a) opening of joints between adjacent stones (Fig. 2a); b) structural cracks (Fig. 2b). The alarming damage observed (Fig. 2) were the cracks in the stone beams (within stone frames).
(a)
(b)
Fig. 2. Defect examples: (a) cracks: center of top beam (b) opening of joints: side walls
1.2 Proposed Interventions Based on detail assessment, It was difficult to revert back to original opening size by removing total infill due to heavy loading and existing crack in stone beam above Therefore, mid-way was suggested to introduce additional system which support the crack beam and help to increase opening size for museum. The two systems were introduced firstly Arch system with width of opening is 1.2 m (3 stone beams) and second system of steel frame with 0.8 m (2 stone beams).
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During scientific investigation historic decorative stone column were found embedded in the infill wall. Thus, the proposal was revised from stone arches in all four frames to only two stone arches (marked in red) and two steel frames (marked in yellow) making the columns visible for the visitors (Fig. 3).
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(b)
(c)
Fig. 3. (a) Location of the interventions. (b) steel frame system (c) Arch system
1.3 Numerical Modelling In this case Finite Element Modelling was performed using DIANA10.2 software. Due to simplicity and the lesser calculation requirements, macro modelling approach was used for the analysis of the Salehkhana structure. The model was constructed using 3D solid elements. Building the geometry of the model is an important and complex task as there is, often, no distinction between decorative and structural elements. Due the complexity of historic construction and several simplifications in geometry were assumed. Here, the focus was to keep the geometry idealization as simple as possible, while being able to properly reproduce the behavior of the structure. Some of the simplification undertaken while building the model can be seen in (Fig. 4).
(a)
(b) Fig. 4. (a) simplification of the corbelled roof; (b) stone columns.
Besides this kind of geometrical simplifications, one important simplification was the fact that only the ground floor was modelled. Because only vertical loads are to be considered in this analysis, only the first floor was modelled. However, the weight from the upper floors was considered by introducing additional elements aligned with the walls from the upper floors. These extra elements were considered linear elastic but with specific densities that take into account the extra weight of the upper floors.
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1.4 Modelling Procedure The modelling procedure was as follows (Fig. 5): a) A simplified floor plan was firstly drawn in CAD and latter imported to DIANA; b)The stone columns and beams were added; c)The floor plan was extruded in height forming the walls of the structure; d)With the walls created, the openings were introduced; e)The vaults were created and attached to the structure; f)The remaining of the roof structure (filling) was built; Additional blocks were created aligned with the walls from the upper floors in order to apply the load from the upper floors.
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(b)
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Fig. 5. The modelling procedure
1.5 Loads and Boundary Conditions Regarding the loads, two different types of loads were considered: a) self-weight; b) hydrostatic pressure. The procedure of applying the loads was first, the self-weight of the structure was applied to the model (100%), then hydrostatic pressure was applied to the retaining walls (100%), then self-weight of the structure was increased gradually until the structure presented excessive damage (>100%). The hydrostatic pressure was considered since the building is inserted in a mountain, having certain walls in direct contact with the soil (retaining walls) (Fig. 6).
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Fig. 6. (a) Numerical model with the hydrostatic pressure on the retaining walls, (b) Numerical model with the extra elements with equivalent densities for the extra mass, (c) Numerical model with the support conditions.
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Because the 3D model only considered the first floor of the structure and the weight from the upper floors, as well as the roof needed to be taken into consideration in the analysis, the second, the total mass of the upper floors (walls and roofs) and top domes was estimated considering their volume and their specific mass and was added above each wall and with help of mass unloading on each wall, it was possible to calculate an equivalent density for the extra elements considering the total mass of the upper floors. This was only possible because only vertical loading was considered in the analysis. Because the building lays on top of a very thick stone layer (>2 m), the model was considered pinned at the bottom of its walls and columns. Additional supports were placed on the south end of the structure and the displacement in the XX direction was blocked, considering the connection of the building to the remaining adjacent structures. 1.6 Meshing Four different types of regular solid elements were employed for meshing the numerical model: a) eight-node isoparametric solid brick element; b) five-node isoparametric solid pyramid element; c) four-node, The HX24L an eight-node isoparametric solid brick element; d) six-node isoparametric solid wedge element. The final mesh was composed of 369662 nodes and 65652 elements. The distribution of element types can be seen in (Fig. 7).
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Fig. 7. Mesh in DIANA: (a) Bottom view (b) roof; (c) corner
1.7 Constitutive Material Laws and Mechanical Properties The non-linear behavior of masonry was modeled using a total strain based constitutive model – Total Strain Crack model [3]. The input for the Total Strain Crack model, in its rotating form, comprises two parts: (1) the definition of the behavior in tension and compression, and the corresponding non-linear material properties; and (2) the basic parameters and linear-elastic properties such as material density, Young’s modulus and Poisson’s ratio. The fracture energy is defined as the energy necessary to create a unit area of a fully developed crack (Fig. 8).
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Fig. 8. Stress-strain curves: (a) Exponential softening curve for tensile masonry behavior; (b) parabolic curve for compressive masonry behavior.
Due to the lack of information regarding the physical and mechanical properties of masonry present at Salehkhana, typical values were estimated and adopted based on the literature [4]. Only for the compressive strength of the granite stones (monolithic stone) tests were performed and a value of 21.16 MPa was available. In this model there are three types of materials to be considered and the final mechanical properties assumed in the model can be seen in Table 1: a) Ashlar masonry with good bond and lime mortar joint. It is a three-leaf wall made with rectangular stone unit. It is located on the west end of the Salehkhana (Fig. 9a); b) Rubble masonry with small irregular units and a good quality thick mortar joint. The wall is three-leaf with thickness of 1.2 to 1.6 m (Fig. 9b); c) Monolithic stone (granite).
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Fig. 9. Types of masonry considered in model: a) ashlar masonry; b) rubble masonry.
The values for the density, compressive strength and Young’s Modulus were taken directly from the available literature. The tensile strength was assumed as 7% to 10% of the compressive strength. As far as the softening behavior of masonry is considered, the tensile and compressive fracture energy values, necessary for the presented constitutive models, can be derived according to the tensile and compressive strength and each ductility index, according to: d = G/f
(1)
For the compressive fracture energy [5], it is suggested a value of d = 1.6 mm for compressive strength lower than 12 MPa. The recommendation [6] is to increase this value for lower strength materials (typically more ductile): d = 2.8 − 0.1fc [mm]
(2)
For the tensile fracture energy, no relation can be found between strength and fracture energy and a value of 0.02 N/mm is recommended [7].
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Table 1. Mechanical properties assumed in the numerical model. Mechanical property
Ashlar masonry
Rubble masonry
Granite stone
E (Young’s modulus) [MPa]
2400
1020
12243
fc (Compressive strength) [MPa]
4.00
1.50
21.16
Gc (Fracture energy) [N/mm]
9.60
3.98
24.0
ft (Tensile strength) [MPa]
0.30
0.10
1.97
Gf (Fracture energy Mode-I) [N/mm]
0.02
0.01
0.02
ρ (density) [kg/m3 ]
2200
2000
2700
1.8 Results for Non-linear Analysis Before Intervention In order to track the behavior of the structure during the analysis, several nodes were highlighted and tracked (Fig. 10). These are nodes in the stone beams (center and ends) and center of the vaults. These nodes were chosen considering the defect map previously presented and in which most of the damage was concentrated in the stone frames and roofs (vaults) (Fig. 11).
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Fig. 10. Interest nodes: (a) plan view schematic; (b) 3D view, Deformed mesh at maximum displacement: a) 3D top view; b) 3D bottom view.
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Fig. 11. (a) Comparison of displacement curves between center of stone beam (P4) and center of vault (P1), (b) Comparison of displacement curves between all stone beams.
In order to identify the location of the damage within the structure, the maximum principal strains were used. From the numerical model it was possible to see that the stone frames and the vaults were the areas with the highest maximum principal strains. Figure 12 shows the maximum principal strains at maximum displacement for the stone frames was shown in the model (Fig. 13a) and it is possible to see that in the stone frames, the damage is concentrated at the center point of the beam. In the vaults (Fig. 13b), the damage is concentrated on the top edge of the vault, and some cracks are starting from the corners moving towards the center. In the rest of the structure, it was possible to see that the masonry walls did not show any considerable damage (Fig. 13c).
Fig. 12. Opening of stone frame with node P8.
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Fig. 13. Maximum principal strains: a) stone frame with node P4; b) vaults (bottom view); c) masonry walls (same color scale).
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1.9 Numerical Model vs. Defect Map One of the objectives was comparing the results of the non-linear static analysis using finite element method with the damaged identified within the real structure. So, if damage patterns were similar, it would be possible to assume that the damage present in the structure is only due to the vertical loads acting on the structure. From the defect mapping it was seen that the areas with the most damage were the stone frames and the vaults. And this was concluded in the numerical model as well (Fig. 14).
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Fig. 14. Comparison of damage for the stone frames: (a) FEM with maximum principal strains; (b) crack at center point of stone beam. Comparison of damage for the vaults: (c) FEM with maximum principal strains; (d) crack distribution.
Some areas in the numerical model seem more damaged when compared with the damage map of the existing structure. However, this can be explained by the existence of a decorative cover of plaster within the vaults, making it possible that not all damage is visible. 1.10 Non-linear Structural Analysis After Intervention The second analysis was the structural analysis of the structure after the interventions. Here, the objective is to quantify the influence of the interventions in the overall capacity of the structure considering vertical loading. The second analysis was the structural analysis of the structure after the interventions. Here, the objective is to quantify the influence of the interventions in the overall capacity of the structure considering vertical loading. 1.11 Numerical Modelling The addition of two different substructures was done in existing model: a) two stone arches; b) two steel frames. (Fig. 15) shows the introduction of the substructures into the base model and Fig. 16 show finite element mesh used for these sub-structures. For the stone arch, the material properties of the existing rectangular stone masonry were used (Table 1), for the steel a linear elastic behavior was used with a Young’s Modulus of 200 GPa.
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Fig. 15. (a) building the sub-structures considered in the intervention; (b) placing the substructures into the base model; (c) front view of the stone arch geometry; (d) front view of the steel frame geometry.
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Fig. 16. Finite element mesh of the sub-structures: a) stone arch; b) steel frame.
1.12 Results for Non-linear Analysis After Intervention To assess the structural behavior of the building, a static non-linear analysis is performed for vertical loading, using the finite element software DIANA 10.2. The procedure for applying the load was the same as the one presented in the previous Section. The overall capacity of the structure to vertical loads is 5.56 g (Fig. 17), meaning that is 5.56 times its own self-weight. The deformed mesh of the building at maximum displacement can be seen in (Fig. 18).
Fig. 17. Vertical load factor vs. displacement at node P8 (beam).
It is possible to see that the behavior of the structure differs from the structure before interventions. The frames with the highest displacement are now the frames with the steel reinforcement frame and the stone arches (Fig. 19).
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Fig. 18. Deformed mesh at max displacement: (a) 3D top view; (b) 3D bottom view.
Similarly, to the previous model, in order to identify the location of the damage within the structure, the maximum principal strains were used. From the numerical model, it was notice that the intervention is having the desired effect, lowering the strain values at the center of the beams (Fig. 20a). The strain in the roof reduced and it does not show any further damage pattern (Fig. 20b). The masonry walls also did not have any considerable strains as before (Fig. 20c).
Fig. 19. Comparison of displacement curves between center of stone beam (P4) and (P8).
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Fig. 20. Maximum principal strain: (a) stone frame at node P8; (b) vaults (bottom view); (c) masonry walls (same color scale).
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1.13 Effectiveness of the Intervention Measures In order to access the effectiveness of the intervention measures, both models were compared: a) before interventions; b) after interventions. Here, the comparison was performed in terms of capacity curves. (Fig. 21) shows the comparison in capacity curves for both models before and after the intervention at different locations of the structure. It was seen the model with the interventions presents an overall capacity 1.67 times greater than the overall capacity of the model before the interventions. In fact, this can be translated as a 67% improvement in the overall capacity of the structure.
Fig. 21. Comparison of capacity curves for models before and after the interventions: (a) Node P8; (b) node P8.
2 Conclusions In general, two main objectives were achieved. The first objective was modelling and assessment of the Salehkhana before the interventions. The results of this non-linear static analysis were compared with the damage map of the structure. The second objective was modelling and assessment of the Salehkhana after the interventions. The results of this assessment were compared with the results of the analysis before the interventions so that the effectiveness of the proposed intervention could be assessed. Based on the works, the following conclusions can be formulated: a) The 3D non-linear numerical model developed within the scope of this work is able to reproduce the overall behaviour of the Salehkhana structure. b) By comparing the damage patterns of the numerical model and the defect map available from the structure before the intervention it was possible to conclude that the damage present at the structure is due to its own vertical loading. c) From the result of 3D non-linear numerical model with the interventions it was possible to conclude that the performed interventions were able to increase the overall capacity of the structure by 67%. Acknowledgement. I am thankful to all the Professors who taught me during the course, specially, to Professor Paulo B. Lourenço for guiding me during the course and sustained my choice of the
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topic of the thesis. I am also grateful to Shriji Arvind Singh Mewar of Udaipur, Chairman and Managing Trustee, Maharana of Mewar Charitable Foundation (MMCF), The City Palace, Udaipur for his support and guidance during my stay in Udaipur. I am thankful to MMCF for scholarship and Dr. Shikha Jain for all the learning and experience they provided me in field of Conservation. Also thank you to Dr. Vaishali Latkar for always being my mentor and guide since my journey of conservation.
References 1. DRONAH: Conservation Master Plan an Overview. The City Palace Complex, Udaipur, Final Report, Maharana of Mewar Charitable Foundation, Udaipur, India, p. 84, Udaipur, India (2009) 2. MMCF: Detailed project Report Salehkhana Ground Floor and Salehkhana First Floor (Nikkaki-Chopad): Arms and Armoury Related Exhibition. The City Palace Museum Udaipur, Rajasthan, India, Maharana of Mewar Charitable Foundation, 171 p. Udaipur, India (2015) 3. TNO DIANA (2009) DIANA, Displacement methods Analyser, release 9.4, User’s Manual 4. NTC Norme tecniche per le costruzioni - Il Capo del Dipartimento della Protezione Civile. With Circolare no. 617 (2009). Il Ministro Delle Infrastrutture, Italy (in Italian) (2008) 5. MC 2010: fib Model Code 2010, first complete draft, vol-2. Fib bulletin 56, 17p. (2010) 6. Lourenço, P.B.: Recent advances in masonry modelling: micro modelling and homogenization. Multiscale Modeling in Solid Mechanics, pp. 251–294 (2009a) 7. Lourenço, P.B.: Recent advances in masonry modelling: micro modelling and homogenization. Multiscale Modeling in Solid Mechanics, pp. 251–294 (2009b)
Numerical Modeling of FRP-Strengthened Masonry Structures Using Equivalent Frame Models Ivana Božuli´c1(B) , Francesco Vanin2 , and Katrin Beyer1 1 Earthquake Engineering and Structural Dynamics Laboratory (EESD), EPFL, Lausanne,
Switzerland [email protected] 2 Résonance Ingénieurs-Conseils SA, 1227 Carouge, Switzerland
Abstract. The present study focuses on enhancing the seismic resistance of existing masonry structures. To that aim, the use of fiber-reinforced polymer (FRP) strengthening serves to improve structural behavior by attaching FRP strips to the masonry walls. Despite substantial study on the influence of such strengthening interventions on structural elements, computationally efficient numerical models capable of adequately depicting this phenomenon remain scarce. This paper therefore endeavors to develop and validate a numerical modeling approach to capture the effect of FRP strengthening on masonry panels. The proposed modeling approach leverages a newly developed macro-element, capable of capturing both in-plane and out-of-plane modes of failure. This is achieved by incorporating the FRP intervention into the section model through the addition of fibers, while the effect of transversal FRP strips on shear strength is accounted for by a proportional increase in the cohesion within the shear strength equation. This approach is further illustrated through a case study of a masonry building tested on a shake table. Overall, the suggested modeling strategy successfully predicts both the in-plane and out-of-plane response, indicating that equivalent frame models may successfully describe the response of masonry structures with FRP-strengthened walls. To conclude, the models discussed in this study can be employed for a time-effective analysis. Additionally, it can assist in determining the best strengthening strategy for potential retrofitting. For cultural heritage sites, where unnecessary retrofitting should be avoided, this aspect is particularly essential. Keywords: fiber-reinforced polymer · equivalent frame models · masonry · strengthening · in-plane capacity · shear reinforcement
1 Introduction A substantial portion of residential buildings and most heritage structures in Europe are comprised of unreinforced masonry (URM). Recent earthquakes, such as those in Central Italy (2009, 2016) and Croatia (2020), have once again highlighted the significant seismic vulnerability of these structures [1–3]. While retrofit measures can be implemented © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 400–406, 2024. https://doi.org/10.1007/978-3-031-39450-8_33
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to enhance the seismic resistance of URM structures [4], accurately predicting their behavior in a real seismic event proves to be a challenging task. In order to plan effective retrofit interventions and assess their performance, the engineering community requires reliable tools for capturing the seismic response of both unstrengthened and, where applicable, strengthened URM structures. The interaction of building components demands a thorough assessment of the response of the entire system through a numerical model of the whole structure. For this purpose, we employ equivalent frame models of complete buildings since they have been shown to be an effective, computationally inexpensive, and reliable tool [5]. Current equivalent frame model (EFM) macro-element formulations, as published in earlier publications as [6–9], only consider the in-plane behavior of masonry elements. To verify the out-of-plane response of masonry walls, supplementary calculations were required. The inclusion of out-of-plane behaviour of masonry panels is one of the most recent developments [10]. Our study is based on the novel macro-element; therefore, both in-plane and out-of-plane response can be accounted for. The objective of this study is to develop and validate a modeling approach for FRPreinforced URM structures utilizing equivalent frame models (EFMs). In this paper, we present a modeling strategy for masonry wall retrofitting approaches that appropriately reflect the increase in shear and flexural capacity of the masonry elements. Furthermore, the investigation of the change in the overall building behavior caused by various retrofitting procedures will be conducted.
2 Numerical Modeling Approach As previously mentioned, our EFM technique for retrofitting masonry walls is built on the three-dimensional macro-element created by [10], which has been integrated into the OpenSees software [11]. When simulating the effects of FRP strengthening, we take into consideration the separate contributions of the increase in both shear and flexural capacities. Furthermore, by separately addressing the shear and flexural capacity, the model can provide valuable insights into the specific contributions of FRP reinforcement in enhancing the overall strength and stability of the masonry wall. All the analyses that produced the results presented in this research were carried out using OpenSees software [11]. 2.1 Increase in Flexural Capacity The flexural properties of the masonry panel may be studied using fiber sections, which require slicing the cross-section of the wall into individual fibers and assigning each its unique material characteristic. The macro-element contains three fiber sections, at the extremities and at the center. This feature is important for identifying the difference between FRPs that are and are not anchored to the slabs. Tensile strength is negligible in the fiber model used for masonry fibers, compressive strength is limited, it exhibits damage under compression, and there is no strength reduction. The material model chosen for the FRP reinforcement fibers is linearly elastic in tension up to the point of failure and has no compressive strength.
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When the FRP fibers are anchored to the slabs, all three sections of the macro-element are modeled as fiber sections comprised of both masonry and FRP fibers. However, if the anchorage is not present, only the central segment of the macro-element is reinforced, and the upper and lower sections consist solely of masonry fibers. This distinction is important as it can have a significant impact on the overall behavior of the retrofitted masonry building. Due to formulation of macro-element, the explicit modeling of debonding and delamination of fibers is not possible. In line with the methodology proposed by [12], we specify the maximum attainable effective strain of the FRP reinforcement under tension, which incorporates the potential for debonding and delamination failure. 2.2 Increase in Shear Capacity In the macro-element developed by [10], the in-plane forces are imposed as nodal forces at the two nodes at extremities, resulting in constant in-plane shear deformations along the axis of the element. The hypothesis we make is that the FRP strengthening does not alter the shear stiffness of the masonry component, but only its shear strength. This means that the enhancement in shear strength resulting from the FRP reinforcement can be modeled by increasing the cohesive component, since it is independent of the axial load. The enhancement of shear strength as a result of FRP reinforcement can be estimated using engineering models that predict the shear resistance of FRP-retrofitted masonry walls. A review of the existing models can be found in [13] and [14]. The total shear strength of an FRP-strengthened masonry panel is calculated as the sum of the shear strength of the intact masonry wall and the contribution from the FRP reinforcement. The difference in the increase due to grid and diagonal FRP layouts is also considered. In accordance with the macro-element formulation, this increase in shear strength is reflected in the value assigned to cohesion.
3 Numerical Approach Application One of the key benefits of using macro-element modeling is its ability to conduct multiple dynamic assessments with minimal computational effort and in a relatively short period of time. This provides a valuable opportunity to study the impact of strengthening on both the overall and local response of a building. In this study, we demonstrate the potential of our numerical approach for modeling FRP-strengthened masonry walls by applying it to a real-world structure that was previously tested. The CoMa-WallS building, a mixed reinforced concrete and unreinforced masonry structure, was selected for this purpose. The building was first tested on an uni-axial shake table by [14] and then modelled in its unretrofitted state in [15]. The results of these tests showed that the building experienced out-of-plane failure in the top story, as well as in-plane failures in the first and second story. By utilizing our proposed approach, we aim to evaluate various hypothetical retrofit solutions for this building and analyze the effect of FRP strengthening on its global and local behavior.
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(b )
Fig. 1. Equivalent frame model of the building tested by [14] modelled in unstrengthened configuration in [15] with applied CFRPs: a) RetrConfig A - FRPs applied only to the walls that are loaded out-of-plane; b) RetrConfig B - FRPs applied to all the masonry walls, without anchorage to the slab.
Three hypothetical reinforcement scenarios were examined by numerical simulations. The first scenario included adding carbon fibers to both faces of the wall in a diagonal pattern; strengthening was only applied to walls that were perpendicular to the seismic loading axis, meaning that they were the only ones that experienced out-of-plane deformation (RetrConfig A –Fig. 1). The second scenario involved applying FRPs to every wall, but with no anchoring in the slab (RetrConfig B – Fig. 1). In the third scenario, all walls that were susceptible to in-plane or out-of-plane loads were expected to be reinforced with FRPs and connected to the slab (RetrConfig C). Using the Montenegro record in the NS direction of the building as in the experimental campaign [15], incremental dynamic analyses were carried out. A comparison of the out-of-plane displacement of the central portion of the uppermost story wall in the unretrofitted configuration (i.e., the configuration validated through experimentation), and the suggested reinforced configurations is displayed in Fig. 2. The results of the FRP-reinforced simulation demonstrate the efficacy of fibers in mitigating excessive out-of-plane displacements, therefore averting local failures, and enhancing the building’s overall response.
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Fig. 2. The output of our model (RetrConfigA), which simulates the shake table conducted by [14], was modelled in unstrengthened configuration by [15]. Comparison of the time-history responses for Run 9 of the out-of-plane deformation at midheight of the out-of-plane loaded URM wall flanked by URM walls, at the top story.
The RetrConfig B and RetrConfig C models were developed to demonstrate the impact of strengthening on the overall response of the building. The IDA curves for the maximum absolute displacements of the uppermost floor are plotted in Fig. 3. The implementation of CFRP significantly reduces the maximum displacement, even in the absence of anchorage in the slabs (RetrConfig B). Furthermore, when CFRP is anchored in the slabs, reinforcing the top, bottom, and central sections (RetrConfig C), the building’s capacity to withstand PGA increases in comparison to reinforcing only the central section. Additionally, the failure mode underwent a transformation, with the development of shear failure instead of flexural failure.
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Fig. 3. The output of our model (Configurations RetrConfig B and RetrConfigC) which simulated the shake table tests performed by [14] and was modelled for the unstrenghtened by [15]. A comparison of the overall response in terms of maximum displacement.
4 Conclusions The purpose of this study was to create and validate a computationally efficient method for modeling FRP-strengthened masonry buildings, which takes into account the impact of FRP strengthening on the in-plane and out-of-plane capacity. The proposed method is an equivalent frame model (EFM) that utilizes the novel macro-element model developed by [10] and implemented in OpenSees [11]. The proposed methodology can effectively capture the seismic performance of masonry buildings with FRP-strengthened walls. EFMs are a suitable choice in terms of computational effort and analysis time, enabling multiple dynamic analyses that consider parameter uncertainty, therefore, allowing predictions of potential failure mechanisms for various types of FRP materials and retrofitting layouts. This understanding is essential in determining the impact of an intervention on the overall building response, which is a necessary input for force-based or displacement-based assessment methods. This method can also be used to evaluate the performance of retrofitted masonry and mixed constructions. Furthermore, through this approach, we can get a better understanding of the benefits and limitations of FRP reinforcement. Moreover, the models proposed here can support the decision-making process when it comes to selecting the optimal strengthening strategy, especially in the case of cultural heritage structures where over-strengthening should be avoided. Further research could expand on this work by exploring the use of textile-reinforced mortars (TRMs) as an alternative to FRPs.
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Acknowledgements. The project was supported by the Swiss National Science Foundation through grant 200021_175903/1 Equivalent frame models for the in-plane and out-of-plane response of unreinforced masonry building.
References 1. D’Ayala, D.F., Paganoni, S.: Assessment and analysis of damage in L’Aquila historic city centre after 6th April 2009. Bull. Earthq. Eng. 9, 81–104 (2011). https://doi.org/10.1007/s10 518-010-9224-4 2. Sorrentino, L., Cattari, S., daPorto, F., Magenes, G., Penna, A.: Seismic behaviour of ordinary masonry buildings during the 2016 central Italy earthquakes. Bull. Earthq. Eng. 17(10), 5583– 5607 (2018). https://doi.org/10.1007/s10518-018-0370-4 3. Stepinac, M., et al.: Damage classification of residential buildings in historical downtown after the ML5.5 earthquake in Zagreb, Croatia in 2020. Int. J. Disaster Risk Reduct. 56, 102140 (2021). https://doi.org/10.1016/j.ijdrr.2021.102140 4. Quagliarini, E., Maracchini, G., Clementi, F.: Uses and limits of the Equivalent Frame Model on existing unreinforced masonry buildings for assessing their seismic risk: a review. J. Build. Eng. 10, 166–182 (2017). https://doi.org/10.1016/j.jobe.2017.03.004 5. Lagomarsino, S., Penna, A., Galasco, A., Cattari, S.: TREMURI program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng. Struct. 56, 1787–1799 (2013). https://doi.org/10.1016/j.engstruct.2013.08.002 6. Penna, A., Lagomarsino, S., Galasco, A.: A nonlinear macroelement model for the seismic analysis of masonry. Earthq. Eng. Struct. Dynam. (2014). https://doi.org/10.1002/eqe 7. Addessi, D., Liberatore, D., Masiani, R.: Force-based beam finite element (FE) for the pushover analysis of masonry buildings. Int. J. Architect. Herit. 9(3), 231–243 (2014). https:// doi.org/10.1080/15583058.2013.768309 8. Siano, R., et al.: Numerical investigation of non-linear equivalent-frame models for regular masonry walls. Eng. Struct. 173, 512–529 (2018). https://doi.org/10.1016/j.engstruct.2018. 07.006 9. Vanin, F., Penna, A., Beyer, K.: A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls. Earthq. Eng. Struct. Dyn.49, 1–23, (2020a). https://doi.org/10.1002/eqe.3277 10. McKenna, F., Fenves, G., Scott, M., Jeremic, B.: Open system for earthquake engineering simulation (OpenSees). University of California, Berkeley, CA. http://opensees.berkeley.edu 11. Grande, E., Imbimbo, M., Sacco, E.: A beam finite element for nonlinear analysis of masonry elements with or without fiber-reinforced plastic (FRP) reinforcements. Int. J. Architect. Herit. 5(6), 693–716 (2011). https://doi.org/10.1080/15583058.2010.490616 12. Zhuge, Y.: FRP-retrofitted URM walls under in-plane shear: review and assessment of available models. J. Compos. Constr. 14(6), 743–753 (2010). https://doi.org/10.1061/(ASCE)CC. 1943-5614.0000135 13. Kišiˇcek, T., Stepinac, M., Reni´c, T., Hafner, I., Luli´c, L.: Strengthening of masonry walls with FRP or TRM, Gradevinar. 72(10), 937–953 (2020). https://doi.org/10.14256/JCE.2983.2020 14. Beyer, K., Tondelli, M., Petry, S., Peloso, S.: Dynamic testing of a four-storey building with reinforced concrete and unreinforced masonry walls: prediction, test results and data set. Bull. Earthq. Eng. (2015). https://doi.org/10.1007/s10518-015-9752 15. Vanin, F., Penna, A., Beyer, K.: Equivalent-frame modeling of two shaking table tests of masonry buildings accounting for their out-of-plane response. Front. Built Environ. (2020). https://doi.org/10.3389/fbuil.2020.00042
The Evaluation of the Wooden Structural System in Hijazi Heritage Building via Heritage BIM Ahmad Baik(B) Geomatics Department, Architecture and Planning Faculty, King Abdulaziz University, Jeddah 21589, Saudi Arabia [email protected]
Abstract. The historic district of Jeddah city has a unique traditional building structural system known as the Hijazi style. The structure system of historic Jeddah buildings is based on load-bearing walls and through a unique horizontal load distribution wooden system known as the "Tkalil" system. Moreover, exact identification of this Hijazi building style deficiency necessitates information besides familiarity through the original structural system, as well as the construction method of the Hijazi building style. This can be combined through an advanced scientific method for exploration. This paper will focus on evaluating the Tkalil structural system based on 3D laser scanning and Heritage Building Information Modelling (HBIM) techniques, through different case studies of the historical building in historic Jeddah, Saudi Arabia. Furthermore, the traditional construction technique for historic buildings in historic is multiple-leaf coral-stone masonry load-bearing walls. Moreover, there are several structural deficiencies patterns in these heritage walls which can lead to instability of these heritage buildings structures, as well as the degradation of the structural condition of these heritage buildings’ foundations, as well as the flat timber ceilings. Indeed, using advanced techniques for data acquisition (Photogrammetry and 3D laser scanning), then analysing these data via the BIM platform can help to understand the core issues of these heritage buildings before applying any solutions. The 3D laser scanning will provide very detailed and accurate 3D point cloud models. These models will be the base for the heritage BIM models to be evaluated and to indicate the stability of these heritage structural systems. Keywords: Hijazi · HBIM · 3D Laser Scanning · Jeddah · Wooden Structural
1 Introduction 1.1 The Architectural Characteristics of Hijazi Region Over the years Hijazi architecture has developed and shown its identity all over the region. The historical houses in Jeddah have unique architectural characteristics which make it a rich source of information for architects, structural engineers, artists, and people who are interested in heritage buildings. The architectural characteristics are not only used for structural or aesthetical reasons, but it can be used for many different reasons © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 407–420, 2024. https://doi.org/10.1007/978-3-031-39450-8_34
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such as coping with the climatic changes and challenges and dictated by the geographical location and availability of resources in the region. As a result, there are different architectural characteristics that serve different needs such as the Roshan, Mashrabiyah, Manjur Pattern and Plaster decoration. Moreover, according to Ragette (2003), “these historical houses have remarkable and simple design and architecture that represent a rich heritage, demonstrating how local craftsmen and builders adapted designs to respond to social demands and other environmental factors in earlier periods”. As a consequence of this evolution, the old houses designs have a unique pattern, as well as being authentic and functional. Moreover, the uniqueness of pattern takes a turn for the better in reducing humidity and increasing thermal comfort, as the buildings increase cross ventilation (Eleish 2009). According to SCTA (2013), the historical houses of Jeddah have to be “understood as an urban unit active in the making of the city”, therefore these houses need to be “studied as typo-morphological responses to climate, material and sociospatial practices”. By focusing on the Roshan, it can be found that it is the basic and primary urban unit of the historic Jeddah houses. These Roshans had a significant role in the shaping of the urban fabric, which was originally comprised of tightly knit areas integrating commercial, residential functions, and organised around the main market and the social identity of the historical city. Furthermore, SCTA (2013), pointed out, "Through its programmatic, climatic, spatial and visual characteristics, it contributed to the shaping of the urban morphology, land use patterns and the overall character of Jeddah". In recent years, the historical houses have been used as multi-purpose buildings that house residential and commercial activities. Additionally, the historical houses are private spaces that equal to the street level and connected with semi-private spaces such as offices, markets, warehouses. Also, it could be used as hotels during the season of Al-Hajj. Jeddah historic houses are designed effectively to meet the considerations of climate challenges. As a result, historical Jeddah houses are very efficient and critical in shaping the morphology and the urban fabric of the historic city. In addition, the orientation of the street network of the historic city is designed to correspond to the prevailing breezes, north and northwest to make the pedestrian movement more comfortable. Furthermore, the impact of the shade and light, the alternation of cool and warm surfaces, and hot and cool spaces is clearly allowing the airflow of the city. In general, the Hijazi historical houses, could be described as individual or semi-individual units in a humid and hot area. As a result, it creates larger street network and increases the air flow and cross ventilation. The distribution and dimension of the historical Jeddah houses are important elements to keep the streets protected from heat and sunrays and keep it in the shade. Moreover, the houses are distributed according to their heights, the high houses are used as “wind catchers” to allow the breeze that comes from the sea to maintain continuous vertical air circulation inside the houses, based on the natural upward movement of hot air across stairwells and shafts, pulling air over the windows (Roshan and Mashrabiyah), which in turn cools the inside and favours air circulation. An important architectural solution for dealing with Jeddah’s climate is “Al-Mabit in Arabic”, which was used for sleeping during the summer nights; it was normally built from panelled wood with louvers and a light roof (Fig. 1). Moreover, Al-Lyaly (1990) defines it as, “Al-Mabit on the uppermost floor is like an air pavilion”, furthermore, “The louvered timber walls surrounding it on two or
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Fig. 1. (a) The dense fabric of the old city (b) Example of the Roshan
sometimes three sides allow the air to circulate freely in the space and at body level thus enhancing the comfort of the occupants”. The most common architectural characteristics in historical Jeddah are the Roshan and Mashrabiyah, which create a rich and distinct visual character for the old Jeddah city. Further, both Roshan and Mashrabiyah play an important part in different ways, such as allowing for cross ventilation, water-cooling, views, and decoration, and offering privacy. The next part will explain more about Roshan and Mashrabiyah. Roshan and Mashrabiyah. Roshan and Mashrabiyah; “wooden bay windows” are the most striking of Jeddah’s historic houses, but these architectural features are also common in many Middle Eastern Islamic cities such as Istanbul, Damascus, Cairo, Baghdad, and Suakin. Moreover, in historic Jeddah, both Roshan and Mashrabiyah are unique for many reasons. For example, these features are connected from floor to floor, are larger in size, more diverse in sculptural techniques and decorations, and contain a mix of different elements. Influences from Asia and India (SCTA 2013). Additionally, due to the diversity of the population and the multicultural influence of visiting artisans and artisans, these influences are reflected in the Roshan and Mashrabiyah variations in historic Jeddah. The taste and wealth of the owner influenced the quality, size, and decorative design of these Roshans and Mashrabiyah. Roshans and Mashrabiyah were created in different sizes and styles. In some buildings in Historic Jeddah, the entire facade is covered with a large Roshan. The Roshan, on the other hand, can have the usual width, four or five bays, but the span over two or more floors of the house (multistorey), or even the entire height of the building. Roshan and Mashrabiyah, can be connected vertically, connecting the top of one to the base of the other with wooden strips, or horizontally, joining the caps together into a single hat stretched across many Roshans and the spaces between them. Next to Roshan or Mashrabiyah, inside, there is usually a flat platform "30 to 50 cm high"; this platform is used to sit during the day and sleep at night (SCTA, 2013). Manjur Pattern. The Manjur pattern can be defined as a lattice grille of wood or a shish net, always in the upper part of Roshan or Mashrabiyah. The main purpose of Manjur is to catch soft light and maintain shade, besides, to catch a cool breeze, which is desirable in the hot climate of Jeddah. Culturally, the Manjur provided a veil, allowing
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families inside the house to look outside without being seen (A. Baik & Boehm, 2017). The idea of Manjur’s beautiful designs is to have specially cut wooden slats interlocking at right angles (criss-crossed) and housed in a frame. These Manjur designs provide a pleasing look from the outside as well as the inside. The shape in which the edges of the laths are cut determines the shape of the gaps created between the two laths, as well as the complete style of the Manjur net (A. H. Baik, 2020).The Shish (wooden net) usually contains two or more shapes arranged in sequence to give the Manjur the desired form, and in general, the size and shape of the Manjur pattern are chosen to give the Manjur the desired pattern, and a balanced combination of shade, delicate light, pleasant breeze, and privacy (A. Baik et al., 2014). Gates and Doors. Another important architectural characteristic in the historic city of Jeddah is the gates, both internal and external. In addition, these wooden gates have compound leaves and are decorated with carved panels depicting some of the finest woodwork and ornamentation in Arabia. The main entrance gate receives considerable attention in traditional buildings in Jeddah. Regarding the design of these gates, it can be noticed that these gates are quite tall, have rich decorative panels, and carved patterns on both sides, and are framed with carved stone or decorative plaster. Moreover, these designs appear as repeated floral as well as asterisk motifs connected by geometric patterns and/or polygonal polygons or pointed stars. In addition, it can be noted that in some parts of the gate its carved patterns are shallower and deeper than in others. Plaster Decoration. As a result of the humid and salty weather in Jeddah, the limestone and coral blocks were affected. The main solution to protect the walls and surfaces of these buildings is the use of the plaster. Over time, plaster craft improved and developed, resulting in decorative plaster sculptures on the facade. As can be easily seen, decorative plaster is always concentrated on the ground floor of facades, especially around windows and main gates of the buildings in historic Jeddah. Regarding the plastering and decorating process, the work is applied to the coral walls while they are still wet. The beauty of plaster decoration lies in the contrast between carved and uncarved surfaces, creating a difference in shadow and shadow. Excellent examples of carved plaster decoration can be found in the historic house of Jokhdar and Ribat al-Khonji. Although there is no scientific study of the plaster decorations in the historic city of Jeddah, it seems that the old decorations were simpler and more geometric, while the plaster one’s Later carvings became more complex with intricate decorative patterns being carved more deeply into plaster and remaining in its thickness. An interesting aspect that has been found in some of the main facades of buildings in the historic city of Jeddah is the sgraffito. Sgraffito is always located on the ground floor corner of the two facades and this sgraffito was created by scraping a surface to reveal the contrasting colour underneath. These sgraffiti are usually in the form of rectangular or square slabs; otherwise, they are rarely available in relief form as on the Nasif Historic House (Fig. 2). Hijazi Structural Technique (Takalee). The Hijazi houses are considered one of the types of evidence of creativity in the Hijazi heritage architecture, as they stand for hundreds of years. Each part and detail contain many lessons and concepts. There is no pointless part in it, there is a reason behind every detail. As a result, it is built arbitrarily in the Hijaz heritage architecture, either to prove a right or to improve behaviour. During
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Fig. 2. (a) Decorated doorways (b) Manjurs in Jeddah houses (c) An example of the wooden doors in Jeddah.
the past years, there are many travellers and tourists who record their fascination with Hijaz heritage architecture by describing the height of its buildings. The observations of most of the travellers who passed through Jeddah cantered on three main points: that it is a clean city, and its people are suffering from a lack of access to clean water. Moreover, many travellers described its buildings as one of the tallest buildings at that time. The buildings reach a height of about 30 m which was not usual 500 years ago. As a result, how could the people of Jeddah with their simple capabilities and limited resources construct buildings that reach a height of seven and eight floors. Especially it is constructed with coral rocks extracted from the sea in the form of large pieces and then cut into smaller pieces as needed (which is considered as one of the non-solid stones and according to its physical components, it cannot bear more than two floors only). This came by using some special construction techniques such as (Takleh or Takaleel) which is a frame made of solid wood; builders used to put it horizontally at specific heights (usually 1m) to increase the stability of the building leading to having a greater number of the floors and increase the height of the building. These Takleh have main six uses first, it is a very important structural element that helps in transferring the loads horizontally, rather than vertically nature. Thus, the entire wall supports and cooperates with each other to bear the loads above it, the strong stone is supported by the weak stone. Therefore, the capacity of these stones’ doubles, and they can bear more with having the Takleh. Besides, the other techniques such as the thickness of the walls, the method of their construction, and emptying the walls as much as possible from the inside and outside…etc. The second use of Takleh lies in holding other building elements such as doors, windows, beams, etc. The coral rock is fragile and full of voids and cavities, and it cannot hold anything on it, so Takleh were used for having more stabilization, especially since they are made of the hardest wood. The third use of Takleh is measuring the level of the building. Builders used to place Takleh at close and specific heights between 70 cm to 100 cm approximately, and it helps to hide the differences in the building or between the sizes of the excavated stones, which were formed manually. As a result, the builders ensure that the heights of the building from all sides are equal. Fourth, the Takleh is used to inspect the apparent safety of the buildings, if there is any bending in the Takleh that means the loads are not distributed properly and the building needs maintenance. Fifthly, the Takleh is the most important element to be used during maintenance, as the builder suspends the building over the damaged part (the part that needs repair) by placing strong supports of wood under the overlay which maintenance is required, and then the wall
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under that overlay is removed and rebuilt. This is an advantage that you will not be found in any other house. The Hijazi house could be destroyed and rebuilt again, which helps to facilitate maintenance work and increase the life span of the Hijazi buildings, as many buildings are more than 500 years old. Finally, these Takleh are considered an aesthetic element in the Hijaz buildings, their horizontal extension breaks the sharpness of the vertical height of the buildings and makes it more acceptable to the human eye. Therefore, the builders, when they finish the buildings from the outside do not cover the Takleh, but they highlight them in a striking way, so people can enjoy their beauty. However, the invention of Takleh by the ancient builders is considered one of the greatest inventions that have had a significant impact on architecture in the Hijazi region (Figs. 3 and 4).
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Fig. 3. (a) Takalee on the interior facades (b) Mangabi stone. (c) Takalee on the facade
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Fig. 4. (a) This image illustrates the construction materials used in building Red Sea houses. (b) Wall construction details (Source: Alharbi, 1989, p.241)
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2 3D Reality Capture Technique in Heritage The 3D reality capture techniques are methods used to capture detailed 3D data of a heritage building or structure, which can be used to create digital representations of the heritage building. These techniques include: – Laser scanning: This method involves using a laser scanner in order to capture detailed 3D data of the building’s surface geometry, including its walls, roof, windows, and other features. The scanner emits a laser beam that reflects off the building’s surfaces, and the scanner’s sensor captures the reflection and records the distance from the scanner to each point on the building’s surface (A. H. Baik 2020). – Photogrammetry: This method involves taking photographs of the building from different angles and using software to process the images and create a 3D model of the building’s surfaces. This can be done using a camera mounted on a drone or a ground-based camera (Alshawabkeh et al. 2021). – Structure from Motion (SfM): This method uses a series of overlapping photographs taken from different viewpoints to generate a 3D model of the building or structure (A. H. Baik 2020). Once the data has been captured, it can be used to create detailed engineering drawings, maps, and other visualizations of the building’s structure, including its geometry, dimensions, and surface details. This data can be used to identify potential issues, such as cracks, deformations, or damage, that might not be visible during a visual inspection. It can also be used to create a digital twin of the structure, which can be used for ongoing monitoring and analysis, and to simulate different scenarios in order to help with the decision-making procedure(A. H. Baik 2020). 2.1 Terrestrial Laser Scanning “TLS” Terrestrial laser scanning is an automated measurement technique that measures the surface 3D coordinates of a selected object. Laser scan output data is displayed in point cloud format. Each of these points has x, y, and z coordinates of the scanned surface. Furthermore, several laser scanning systems are available on the engineering market today. However, these systems have three types of scanners methods. These can be suitable for metric heritage studies: (time-of-flight) scanners, triangulation, and phase comparison (Murphy 2013). Additionally, the difference between these scanners systems has to do with how the scanner calculates 3D coordinate measurements. For example, for the triangulation type, the scanner uses laser beam points on the surface of the object captured with one or more cameras (A. Baik 2016). Alternatively, according to Boehler et al. (2003) “time of flight scanners calculate the range, or distance, from the time taken for a laser pulse to travel from its source to an object and be reflected back to a receiving detector”. 2.2 Terrestrial Laser Scanning Data Processing Laser scanning captures a variety of data representing 3D coordinates known as "point cloud data". These point cloud date need a professional program in order to deal with the
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huge amount of data. Moreover, usually capturing millions of accurate 3D points could take a few minutes, on the other hand, there is enormous work in transporting this point cloud data into a 3D model which containing useable information (Baik et al. 2014). Moreover, there are several programs in the market which can deal with the point cloud date. For examples, Leica Cloud-Works, Polyworks, Autodesk ReCap and RiScanpro which have greatly improved the processing, manipulation and analysis of vector and image data from point clouds. Also, these software platforms are combined algorithms for triangulation and point cloud surfacing (Remondino 2003). After the scanner point cloud has been transferred, there are a number of suitable software programs that can be dealt with troubleshoot and remove the noise or the point cloud distortion from the scanner data. In addition, each system of these laser scanners has its own software package. For example, Leica Cyclone® carries the Leica laser scanning system. Overall, the Leica Cyclone® modelling approach is to generate an optimally shaped object from a point cloud data. Additionally, the Leica Cyclone® has several object-specific utilities that the user can select according to the topology of the scanned point cloud (A. Baik et al. 2013). On the other hand, other software programs are applied instead of polygonal 3D models; NURBS surface models, or editable feature-based CAD models (Ikeuchi 2001) (Fig. 5).
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(b) Fig. 5. (a) Point Cloud Data processing. (b) Using laser scanning
2.3 Combining Laser Scanning and Digital Images Most modern laser scanning systems have a built-in camera for image data. Additionally, 3D point clouds can be coloured by applying stacks of multiple images to the point cloud data. RGB colour data from an image can be mapped to range data taking into account point translation, instrument rotation and perspective projection (Abmayr et al. 2005). This requires geometrically correct calibration of both the laser and the camera as well as the Camera corrections are presented to correct for camera lens distortion, and via mapping to a point cloud, the image Viewpoints contained in are removed (Murphy 2013). Furthermore, a High Dynamic Range "HDR" colour image can be accurately mapped onto a geometric model represented via the point cloud if the position as well as
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the orientation of the camera in the coordinate system of the geometric model is known (Beraldin 2004). 2.4 Heritage BIM HBIM stands for "Heritage Building Information Modelling." It is a process of creating a digital representation of a Heritage building or structure using Building Information Modelling (BIM) technology and tools. This representation can include information about the heritage building’s architecture, construction, materials, and history, as well as data on its current condition and maintenance needs. Heritage BIM can be used in order to aid in the preservation and restoration of heritage buildings, as well as in their ongoing management and use (A. Baik et al. 2013). Moreover, Heritage BIM is an interactive solution representing interactive engineering 3D model. Usually, this 3D model is based on terrestrial laser scanning data "TLS", Architectural photogrammetry, and culture heritage data (A. Baik et al. 2014). In addition, Heritage BIM automatically provides complete technical drawings, orthographic views, sections, and 3D models. Regarding the Heritage Conservation and Preservation sectors in Historic Jeddah, Heritage BIM can support in several aspects, such as improve the understanding of heritage buildings and the context, Knowledge of the building materials, construction as well as the structural techniques, and the building pathologies, understanding the heritage building materials (A. H. Baik 2020). The field of heritage conservation will also benefit from Heritage BIM in a variety of ways, including by enabling a thorough analysis of proposed renovations and changes before final decisions are made, assisting with the heritage building maintenance, helping with budgeting for repairs and maintenance, and enabling a wider public building experience because models can be viewed using free viewer application from remote locations (A. Baik et al. 2013). Furthermore, the opportunity to develop details about the object’s methods of construction and material makeup is also provided by introducing the culture heritage information of Jeddah and the Hijazi region. Through the use of various program platform management techniques, the prototypes of the libraries of parametric objects are modelled onto the photogrammetry as well as the point cloud data during the Heritage BIM process (A. H. Baik 2020) (Fig. 6).
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Fig. 6. (a) HBIM model for Nasif House (A. H. Baik 2020) (b) Combining the laser data with the photogrammetry
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3 The Evaluation of the Wooden Structural System (the Method) 3.1 Visual Inspections Visual inspection for heritage structures is an important aspect of their preservation and maintenance. These inspections involve a thorough examination of the heritage building’s exterior and interior, including its roof, walls, windows, doors, and other structural elements. Usually, during the visual inspection, an inspector will look for signs of wear and tear, damage, or deterioration, as well as any potential safety hazards. They may also take photographs or make notes to document their findings. Furthermore, The inspector may also use specialized tools and equipment, such as binoculars, ladders, scaffolding, or drones, to access hard-to-reach areas of the structure (Van Balen and Verstrynge 2016). Moreover, the results of the visual inspection can be used to identify potential issues that need to be addressed, and to develop a plan for preservation and maintenance. This can include repairs, restoration, or conservation work, as well as ongoing monitoring and maintenance to ensure the building’s continued stability and integrity. In the case of this paper, the first step was to be coding the building elevations. Then taking pictures and ortho pictures for these elevations, celling, and floors. And determine the damages. This step is very important to produce any 2D as-built CAD drawings from both laser scanning and the visual inspections. Then, drawing this elevation in 2D CAD drawings. These drawings will contain the as-built condition with all damages (Fig. 7).
Fig. 7. Visual inspections, coding and taking pictures for the elevations.
3.2 Terrestrial Laser Scanning Phase Laser scanning is a technology that can be used for structure evaluation of heritage buildings and structures. It involves using a laser scanner to capture detailed 3D data of the building’s surface geometry, including its walls, roof, windows, and other features. The scanner emits a laser beam that reflects off the building’s surfaces, and the scanner’s sensor captures the reflection and records the distance from the scanner to each point on the building’s surface. This process is repeated many times to capture a large number of data points, creating a detailed 3D model of the building (Schueremans and Van Genechten 2009). Furthermore, Once the data has been captured, it can be used to create
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detailed drawings, maps, and other visualizations of the building’s structure, including its geometry, dimensions, and surface details. This data can be used to identify potential issues, such as cracks, deformations, or damage, that might not be visible during a visual inspection. Moreover, The data can also be used to create a digital twin of the structure, which can be used for ongoing monitoring and analysis, and to simulate different scenarios to help with the decision-making process (Cuartero et al. 2019). In the case of this paper, it was very important to use the laser scanning to document the as-built condition in 3D digital environment. The first step was to get the georeferenced coordinates of the buildings. The second step was to plan for this phase and to determine the best locations for both the laser scanning spots and the black and white (B/W) targets. The third step was to scan the buildings from outside to inside the buildings. The fourth step was to process the point cloud data to be registered and include all laser scanning spots (both outside and inside scans). The final step was to paper the data to be use for Heritage BIM process. It is very important to emphasize that the outcomes of laser scanning phase are very important to be used in processing the 2D as-built CAD drawings. That is because of the high accuracy and accurate measurements that laser scanning provides (Figs. 8 and 9).
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Fig. 8. (a) georeferencing the targets (b) canning the building’s facades (c) Scanning the building from inside
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Fig. 9. (a) the exterior façade of case 1 (b) the interior façade of case 1 (c) Section
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3.3 HBIM for Structure Simulation Heritage BIM can be used for structure simulation of heritage buildings and structures. Furthermore, once the HBIM model has been created, it can be used to simulate different scenarios, such as load-bearing capacity, structural behavior, and environmental effects, on the building’s structure (A. Baik et al. 2013). This can help to identify potential issues and to develop a plan for preservation and maintenance. For example, the HBIM model can be used to simulate the effects of different loads, such as wind, snow, or earthquakes, on the building’s structure. This can help to identify potential weak points or areas of the building that may be at risk of failure. Additionally, the HBIM model can be used to simulate the effects of different conservation and restoration treatments, such as the addition of new structural elements or the removal of old ones, on the building’s structural integrity (A. H. Baik 2020). Furthermore, Heritage BIM can also be used to model the building’s environmental behavior and energy consumption, which can be used to improve building’s performance. It can also be used to create virtual tours, which can be used for education, awareness and for the promotion of the heritage building. In the case of this paper, the heritage BIM modelling was built based on the 3D point cloud data. In these steps it was very important to identify the LoD for both information (iLoD) and elements (eLoD). The second step was to prepare the model for different engineering simulations, for example, structural, environmental, MEP and many more (Figs. 10 and 11).
Fig. 10. The vertical section shows the HBIM modelling process
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Fig. 11. Section shows the interior façade in BIM modelling process.
4 Conclusions The evaluation of the wooden structural system in Hijazi heritage buildings using Heritage BIM is an important aspect of preservation and conservation efforts for these buildings. Hijazi heritage buildings are a type of traditional architecture found in the Hijaz region of Saudi Arabia, and they often feature wooden structural systems that are unique and complex. Using Heritage BIM, a detailed digital representation of the building can be created, which includes information on the building’s architecture, construction, materials, and history, as well as data on its current condition and maintenance needs. This model can be used to simulate different scenarios, such as load-bearing capacity, structural behavior, and environmental effects, on the building’s wooden structural system. For example, the Heritage BIM model can be used to simulate the effects of different loads, such as wind, snow, or earthquakes, on the building’s wooden structural system. This can help to identify potential weak points or areas of the building that may be at risk of failure. Additionally, the Heritage BIM model can be used to simulate the effects of different conservation and restoration treatments, such as the addition of new structural elements or the removal of old ones, on the building’s structural integrity. The Heritage BIM model can also be used to evaluate the building’s environmental behavior and energy consumption, which can be used to improve the building’s performance.
References Abmayr, T., Härtl, F., Reinköster, M., Fröhlich, C.: Terrestrial laser scanning–applications in cultural heritage conservation and civil engineering. Proceedings of the ISPRS Working Group V/4 Workshop 3D-ARCH 2005, Virtual Reconstruction and Visualization of Complex Architectures, International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Mestre-Venice (2005). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10. 1.1.153.6557&rep=rep1&type=pdf
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Al-Lyaly, S.M.Z.: The traditional house of Jeddah: A study of the interaction between climate, form and living patterns. University of Edinburgh (1990) Alshawabkeh, Y., Baik, A., Miky, Y.: Integration of laser scanner and photogrammetry for heritage BIM enhancement. ISPRS Int. J. Geo Inf. 10(5), 316 (2021) Baik, A.: Documentation of the Nasif Historical House, in Historical Jeddah, Saudi Arabia, Using Terrestrial Laser Scanning and Image Survey Methods. Proceedings of the Eighth Saudi Students Conference in the UK, pp. 767–780 (2016) Baik, A., Alitany, A., Boehm, J., Robson, S.: Jeddah historical building information modelling ‘JHBIM’–object library. ISPRS Ann. Photogram. Rem. Sens. Spatial Inf. Sci. 2(5), 41 (2014) Baik, A., Boehm, J.: Hijazi architectural object library (HAOL). ISPRS-Int. Arch. Photogram. Rem. Sens. Spat. Inf. Sci. 42, 55–62 (2017) Baik, A., Boehm, J., Robson, S.: Jeddah historical building information modeling “JHBIM” old Jeddah – Saudi Arabia. Int. Arch. Photogram. Rem. Sens. Spatial Inf. Sci. XL-5/W2, 73–78 (2013). https://doi.org/10.5194/isprsarchives-XL-5-W2-73-2013 Baik, A.H.: Heritage Building Information Modelling for Implementing UNESCO Procedures: Challenges, Potentialities, and Issues. Routledge (2020) Beraldin, J.-A.: Integration of laser scanning and close-range photogrammetry-the last decade and beyond. International Society for Photogrammetry and Remote Sensing (2004) Cuartero, J., Cabaleiro, M., Sousa, H.S., Branco, J.M.: Tridimensional parametric model for prediction of structural safety of existing timber roofs using laser scanner and drilling resistance tests. Eng. Struct. 185, 58–67 (2019) Eleish, A.: Heritage Conservation in Saudi Arabia. Proceedings of the Joint International Symposium of IAPS-CSBE & Housing Networks: Revitalizing Built Environments: Re-Qualifying Old Places for New Uses (2009) Ikeuchi, K.: Modeling from reality. In: Proceedings of 2001 Third International Conference On 3-D Digital Imaging and Modeling, pp. 117–124 (2001) Murphy, M.: Historic building information modelling adding intelligence to laser and image based surveys of European classical architecture. ISPRS J. Photogramm. Remote. Sens. 76, 89–102 (2013) Ragette, F.: Traditional domestic architecture of the Arab Region. Edition Axel Menges (2003) Remondino, F.: From point cloud to surface: The modeling and visualization problem. In: International Workshop on Visualization and Animation of Reality-Based 3D Models, vol. 34, 5p. (2003) Schueremans, L., Van Genechten, B.: The use of 3D-laser scanning in assessing the safety of masonry vaults—a case study on the church of Saint-Jacobs. Opt. Lasers Eng. 47(3–4), 329–335 (2009) SCTA. (2013). historic Jeddah, the gate to Makkah (p. 697). Saudi Commission for Tourism and Antiquities Van Balen, K., Verstrynge, E.: Structural Analysis of Historical Constructions: Anamnesis, Diagnosis, Therapy, Controls: Proceedings of the 10th International Conference on Structural Analysis of Historical Constructions (SAHC, Leuven, Belgium, 13–15 September 2016). CRC Press (2016)
Modeling of Masonry Bridges in Presence of Damage: The Case Study of San Marcello Pistoiese Bridge Daniela Addessi1 , Domenico Liberatore2 , and Andrea Battisti1(B) 1 Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via
Eudossiana 18, 00184 Rome, RM, Italy {daniela.addessi,an.battisti}@uniroma1.it 2 Department of History, Representation and Restoration of Architecture, Sapienza University of Rome, Piazza Borghese 9, 00186 Rome, RM, Italy [email protected]
Abstract. Safeguard of the heritage of masonry infrastructural constructions is a relevant concern nowadays. The historical-monumental value of a large part of these artifacts, combined with their current functional reuse in the transport networks, make them interesting case studies. These structures are generally afflicted by structural weaknesses that make them vulnerable under dynamic actions, strongly present in the Italian peninsula, due to its widespread and high seismicity. In this framework, Finite Element analysis turns out to be a useful tool to better understand the structural behavior of masonry artifacts. In this paper, the seismic assessment of a masonry arch bridge, located in Italy, is proposed by means of a 3D FE modeling. The masonry material is described through the adoption of a constitutive law with damage, capable of capturing the degrading behavior of masonry under cyclic actions, characterized by a strain softening response. The phenomenological law is characterized by the presence of a scalar damage variable, describing the material degradation evolving during the analysis. After the investigation of modal shapes of the bridge, the horizontal capacity curve was estimated through a pushover analysis, and finally the structure was subjected to a set of natural accelerograms. The health state of the case study was consequently defined by means of damage indexes, and the most critical areas of the bridge were highlighted through the study of the damage patterns. Keywords: Masonry Arch Bridge · Finite Element Modeling · Damage · Time History Analysis · Damage Index
1 Introduction A growing interest from the scientific community is developing in the study of masonry bridges. This type of artifacts is indeed widely spread both in Italian and European countries, referring to multiple ages of construction. Nowadays, it is possible to find numerous examples of these structures, ranging from monumental walking bridges to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 421–432, 2024. https://doi.org/10.1007/978-3-031-39450-8_35
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other few centuries old examples, which are currently re-used as part of road and rail transport networks. The interest in the study of these constructions, therefore, ranges from the field of architectural heritage conservation to infrastructural safety [1–3]. However, these are very vulnerable to seismic actions, due to the limited building knowledge of the past, and the numerous structural deficiencies. These latter are, in some respects, like those found in masonry buildings, such as the absence of transverse connections and the poor mechanical properties of the mortar adopted. In this framework, a survey made after 2016 Central Italy earthquake [4] focused the attention again on the issue of seismic vulnerability of Italian masonry bridges, showing the damage scenarios in several infrastructural constructions located in the epicenter area. Finite element (FE) analysis turns out to be a particularly useful tool to investigate masonry artifacts: it gives the possibility to carry out an extensive study that first allows to discover the structural deficiencies, thus performing a seismic vulnerability analysis, and then moves on to model possible reinforcement scenarios [5], obtaining a predictive evaluation of their effectiveness. Several approaches are now available to describe masonry response, such as micromechanical, macromechanical and multiscale models [6–8]. While modeling real-scale structures, a macromechanical modeling approach is employed. Accordingly, masonry heterogeneous material is treated as an equivalent homogeneous continuous medium, characterized by a phenomenological constitutive law whose parameters are derived by means of homogenization and identification techniques [3]. Classical constitutive laws are generally adopted to characterize materials, as commonly implemented in computational codes [9], but these are often not suitable to correctly reproduce the structural response of masonry in the nonlinear field. In the present work, the linear and nonlinear study of a masonry arch bridge is carried out, aiming at investigating its horizontal capacity and the structural damage activated under seismic actions. A constitutive law with damage is adopted, which models material degradation caused by tensile strain states, allowing global estimation of this by means of damage indexes and local-level assessment by means of damage patterns. The detailed formulation is contained in Addessi and Sacco 2016 [6]. The adopted model was originally formulated for micromechanical modeling of bricks, and later used for the macromechanical analysis of the “Ponte delle Torri” in Spoleto, showing that it is capable of reproducing, with good approximation, some of the damage scenarios currently present in the artifact [10, 11]. With the aim of estimating the structural response under seismic actions, a threedimensional (3D) model of the bridge is developed, applying the three components of seismic actions and monitoring displacements and damage evolution history.
2 Description of the Bridge The studied bridge, also known as the “Lizzanese” bridge, connects the towns of San Marcello Pistoiese and Lizzano, in Tuscany, crossing a natural riverbed. The artifact reasonably dates back to the 18th-19th centuries but underwent heavy reconstructions after World War II. The structure, regarding geometry and adopted materials, is strongly characteristic of many bridges present in central Italy, which makes its study even more significant for general concerns. In terms of geometry, the bridge has 3 arches, two symmetrical side arches of 8 m span and the central one of 21.5 m; the two central piers
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are founded in the riverbed, while the abutments follow the slope of the terrain. Overall, the structure has a length of 72.5 m, 5.8 m in cross-section, and an overall height from the base of the piers of 24.25 m including parapets. A large part of the construction is made of sandstone masonry, grouted with cement mortar in the external areas and lime mortar in the internal areas. The vaults are made of brick masonry and cement mortar, and the internal filling is in loose soil. Foundations are in reinforced concrete, over stratified rocks [12].
3 3D Modeling of the Structure The bridge was modelled using the Finite Element Program FEAP [13], adopting 8node 3D brick user-type elements, in which the constitutive law with damage described in [6] was implemented. 3 degrees of freedom are defined at each node, i.e., the three displacements uk , vk , wk , and the displacement fields are interpolated by trilinear shape functions. The Gauss integration technique, with a 2x2x2 rule, is used to perform the required element computations. The bridge is fully restrained at the ground. Figure 1 shows the whole bridge and an exploded view separating the different materials, with reference to the discretization adopted for the analyses, consisting of 2724 FE. This mesh was selected to get a good match between accuracy of the results and computational burden. In Fig. 1 it is possible to notice the different materials employed and the way they are distributed in the structure: piers, spandrel walls, and abutments are made of sandstone masonry (red), the internal backfill is made of soil (yellow), and the vaults are made of brick masonry (blue).
Fig. 1. 3D model of the bridge (a); exploded view of the adopted materials: sandstone masonry (b), brick masonry (c), backfill (d).
3.1 Damage Law Formulation The adopted constitutive law was presented in Addessi and Sacco 2016 [6], and already applied in the field of macromechanical modeling of masonry bridges for the study of "Ponte delle Torri”, in Spoleto. This latter was first subjected to a seismic assessment [10] and then, underwent a simulation of a seismic sequence adherent to the main events that involved the structure during its life [11], obtaining good agreement with the current damage state. The constitutive model is meant to describe damage related to microfractures process for prevailing tensile strain states. The formulation involves the use of a
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single scalar damage variable D, acting equally on each term of the elastic matrix and modeling isotropic damage. The relationship is as follows: σ = (1 − D)E ε
(1)
with σ denoting the 6-component stress vector, E the 6x6 elastic constitutive matrix, and ε the 6-component strain vector. Damage onset and evolution is driven by an associated variable, which measures an equivalent strain state. This is defined on the basis of the positive principal strains εi/j, also accounting for the effects of negative principal strains. The parameter ε0 is a regularization factor that ensures the convexity of the limit domain and k regulates the effect of the negative strains. Therefore, the definition of the equivalent strain measure is given by: 3 3 3 1 − δij 2 εi − εj − + − ε0 εeq = εi + ε0 + − k (2) 2 i=1
i=1 j=1
To overcome the mesh dependency problems arising in presence of strain-softening materials, such as masonry, the nonlocal integral regularization technique is here adopted. This involves the use of a weighting function ψ with Gaussian shape, which permits to account for the influence, on each Gauss point, of the average strain state occurring at points lying in its neighborhood. The size of this latter is regulated by the nonlocal radius, defined based on the masonry size. Then, the equivalent strain is defined as the following nonlocal measure: 1 ψ(x − y)εeq (y)dV ε eq (x) = (3) ψ(y)dV The adoption of the nonlocal regularization technique allows to overcome the meshdependency of the FE solutions leading to objective numerical results. The damage evolution law uses the nonlocal strain measure and depends on the following mechanical parameters: β governs the shape of the softening branch, εt the tensile strain threshold, and εu the value of the equivalent strain corresponding to the completely damaged state. For a detailed discussion of the parameters, refer to [6, 10, 14]. ˜ =1+ D
1 εeq (εt − εu )
2
−β (ε eq −εt ) 2 ε e ε − ε ε + ε ε − 2ε eq u eq u eq t t 3
(4)
Damage estimation during the analyses, at each time step, is performed according to the following relation:
˜ 1 D = max 0, min D, (5) history
also considering the assumption of thermodynamics irreversibility of damage, for which ˙ ≥ 0. The physical variation range of the damage scalar variable D is between 0 and D 1, corresponding to the undamaged and fully damaged condition.
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3.2 Modal Analysis The bridge model was first validated in the linear elastic field to test the efficiency of the geometric modeling and restraint scheme. The modal analysis was performed. Mode 1 and mode 5, representing out-of-plane and vertical mode, respectively, obtained with the FE model were compared to the data shown in literature [9, 12, 15]. The bridge, already studied in literature, was modeled by means of other computational software and an in situ dynamic investigation, with accelerometers, was also performed. Sandstone masonry was characterized by a Young’s modulus E of 10x109 N/m2 and a material density γ of 2200 kg/m3 ; the brick masonry was characterized by a Young’s modulus of 12x109 N/m2 and a material density γ of 1800 kg/m3 ; for the backfill a Young’s modulus of 5x109 N/m2 and a γ of 1800 kg/m3 were assumed. For all the materials, a value of Poisson ratio ν equal to 0.2 was adopted. The chosen FE discretization, made of 2724 FEs was defined after an updating process within modal analysis, reaching a good match with literature benchmarks. The same mesh was kept in the following nonlinear analyses, where it showed good accuracy and efficiency properties, despite the heavy computational burdens. Periods and frequencies are given in Table 1, and Fig. 2 shows the associated modal shapes. Table 1. Periods and frequencies for mode 1 and mode 5: FEAP model vs Experimental. Modal analysis
FEAP model T [s]
FEAP model f [Hz]
Experimental f [Hz]
Variation of f %
Mode 1 (out-of-plane)
0.23
4.21
3.998
5.3
Mode 5 (vertical)
0.07
14.50
13.911
4.2
Fig. 2. Modal shapes: Out-of-plane mode 1 (a), vertical mode 5 (b).
4 Nonlinear Analyses After the modal validation, nonlinear analyses were performed, starting with a pushover followed by time history analyses. In all these analyses, the backfill was considered as a non-structural material, assigning to it a linear elastic constitutive law so that it does not influence the damage scenario of the structure during the analyses. Performing analyses in the nonlinear field, and considering the uncertainties in the moduli of materials, as
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well as possible ageing phenomena, it was considered appropriate to reduce Young’s moduli. Similar considerations are given in [12, 15]. Backfill therefore results in the same values of ν and γ as mentioned before, and the Young’s modulus E equal to 5x108 N/m2 . Regarding the structural materials, sandstone and brick masonry, the same Poisson ratio ν and γ mentioned above were adopted, while the tensile and compressive thresholds were deduced from the Italian Guidelines NTC [16]. Sandstone masonry was characterized by a compressive strength f c equal to 8.5 MPa and tensile strength f t equal to 0.55 MPa, brick masonry by f c equal to 4.2 MPa and f t equal to 0.3 MPa. Figure 3 shows the damage laws adopted for the structural materials, and Table 2 shows the related set of parameters.
Fig. 3. Constitutive laws with damage: sandstone masonry (a), brick masonry (b).
Table 2. Parameters adopted for the damage law of sandstone masonry and brick masonry. Material
E [N/m2 ]
ν
εt
k
εu
ε0
βt
βc
α
Sandstone masonry
5x109
0.2
0.4x10–4
0.03
5x10–2
10–5
5000
750
6000
Brick masonry
6x109
0.2
0.05x10–4
0.03
500x10–2
10–5
12000
1800
4000
4.1 Pushover Analysis Considering the structural symmetry of the bridge, restraints and loading conditions, the pushover analysis was conducted on a half-bridge model (1362 FE), reducing the computational burden. The analysis was performed by first applying the self-weight and then, a distribution of horizontal mass proportional forces. The structural response was monitored through two control nodes: a point on the road surface at the center of the central arch, at centerline, called TOP, and a point at the height of the center of mass called CM, at an elevation of 14 m from the base of central pier, at centerline. The arc-length solution algorithm was adopted, as it allows to follow the post-peak softening branches. This behavior is due to the strain softening of the constitutive laws employed, which well-represent the real behavior of masonry. The curve presents a first elastic branch, then
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a peak zone corresponding to the maximum base shear and, finally, a softening branch with loss of strength and increase of displacement. Given the adopted laws, as expected, the shape of the curve and the maximum force and displacement values differ from those evaluated in [12], where the authors adopted elastic-plastic laws without damage. As obvious, the reading at the TOP control node provides a higher displacement compared to the CM, as also highlighted in [9], where the issue of the choice of control points for bridges is discussed. The displacement monitoring of point CM thus results in a more conservative capacity curve, with the same maximum base shear but lower subtended area. Figure 4 shows the pushover curves and damage patterns detected at the end of the analysis: structural damage is highlighted in the crowns of the arches, at the base of the pier, and mainly in the abutment zone of the pushing side, where tensile states are more concentrated.
Fig. 4. Pushover curve for TOP and CM control nodes (a); Damage patterns at the final step of the analysis: South side view (b), North side view (c).
4.2 Time History Analysis A time history analysis campaign was performed relying on the study of the seismic history of the site where the bridge is situated. The investigations were articulated starting from the Italian Macroseismic Database DBMI [17], where the major events in the municipality of San Marcello Pistoiese were found and completed with data for the adjacent town of Pistoia. By means of the Italian Accelerometric Archive ITACA [18], the main fault mechanisms found in recent seismic events of the area were identified. A subsequent phase followed, searching for natural records that had characteristics related to the seismic history of the site and using the Engineering Strong Motion Database [19]. A set of 7 events was created, and the spectral compatibility procedure was performed in the period range between 0.1 and 1 s, taking care to keep the scaling factors as small as possible, not to excessively alter the signal. The set has events with a M w value between 5.6 and 6.5, epicentral distance less than 30 km, and focal mechanisms of normal or thrust type. To perform analyses well matching the real conditions, the three components of earthquake N-S, E-W, Z were considered simultaneously. In addition, 3 return periods were considered: 201, 475, 975 years for the purpose of investigating increasing damage scenarios. In this process, each component was scaled regarding its relative response spectrum from NTC Code [16], for each return period. N-S and E-W components were scaled with respect to the horizontal response spectrum, Z component
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with respect to the vertical response spectrum of the site. Figure 5 shows the spectral compatibility procedure for the N-S direction, assigned along the out-of-plane direction of the bridge, for the 3 return periods. E-W component was assigned along the longitudinal direction of the structure, Z component was assigned along the vertical direction. A Rayleigh damping method was adopted, considering the first two angular frequencies of the structure and a 5% damping ratio. A Newmark implicit integration with β and γ equal to 1/4 and 1/2, respectively, is used to solve the dynamic problem, combined with a Newton-Raphson algorithm for the solution of the non-linear behavior.
Fig. 5. Elastic spectra of the 7 ground motions selected, NTC18 elastic spectrum for San Marcello Pistoiese site (black), average spectrum of the 7 ground motions set (red): 201 years return period (a), 475 years return period (b), 975 years return period (c).
The same group of analysis was carried out for both the damage and elastic model of the entire bridge, in order to compare the responses. Analyzing the maximum displacements for the out-of-plane direction, read at the TOP point, where the most significant displacements are displayed, and comparing the three return periods and the two models (Fig. 6), some interesting observations can be made. As for the 201 years return period, four out of seven events with maximum displacement reached by the elastic model are observed. This scenario varies considerably for the 975 years return period graph, where five out of seven events present a maximum response shown by the damage model. Examples of this are the Greece 1999 and South Italy 1998 events, where it is possible to notice this amplification in the damage model response for 975 years return period. The bridge experiencing damage, thus varying its modal periods, will experience new resonance conditions towards the seismic action. As an example, for the Greece 1999 event with 975 years return period, all the results of the analysis are shown in Fig. 7. The greatest displacements, as expected, are reached along the out-of-plane direction, where an amplification phenomenon is observed in the response evaluated by the damage model. The responses along the E-W and Z directions are considerably less significant. It is interesting to note, along the Z direction, how the oscillations start from an initial value of attestation, then stabilize on a new value corresponding to a residual displacement at the end of the analysis. The transition between the initial and residual displacement has a trend closely related to the growth of damage in the structure. This latter is highlighted, for the damage model, through damage indexes, evaluated at each time step of the analyses. The Global Damage Index (GDI) [10] and its modified version based on fractile at 95%, (D0.95 ) [11], were implemented by the authors. Regarding the damage patterns, it is possible to track the
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Fig. 6. Maximum displacements of the TOP point along the out-of-plane direction (N-S) for damage and elastic models: 201 years return period (a), 475 years return period (b), 975 years return period (c).
damage evolution. Referring again to the Greece 1999 event in case of 975 years return period, at the end of the analysis, a damage pattern with an approximately symmetrical damage distribution is obtained. Symmetry is broken only locally near the spandrel walls above the west arch, where a peak of the damage can be detected. Maximum damage is localized around the crowns of the three arches. In other events, such as the Turkey 1999, for the same return period, non-symmetrical damage pattern could be observed, indicating that the E-W components has a non-negligible effect in the directionality of damage propagation. Moreover, the bridge experiences an excitation of the higher modes.
Fig. 7. Response of the bridge under Greece 1999 record with 975 years return period: N-S displacement (a), Z displacement (b), E-W displacement (c), damage indexes (d), damage pattern south side view (e), damage pattern north side view (f).
More investigations regarding dynamic amplification were conducted by means of the Fast Fourier Transform (FFT) of the displacement response (Fig. 8). By evaluating the damaged period through frequency peaks and highlighting this value into the scaled N-S displacement spectrum of the earthquake, good agreement was found with the response
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reported before. The damage model shows an increased period compared to that of the elastic model. However, the displacement spectrum refers to one direction only, that out-of-plane for the bridge, and therefore to only one predominant modal form, the first one. However, the structure is subjected to accelerations along the three directions experiencing multiple modes excitation, resulting in a simplified procedure for the study of the phenomenon. This explains the variation between the maximum displacement shown in Fig. 7 and what is evaluated using the spectrum in Fig. 8. For all the analyses performed adopting the damage model, the evolution of damage in the bridge is also followed by means of the damage indexes mentioned above. A summary graph of the D0.95 index for the analyses with 975 years return period is shown in Fig. 9. This index, by evaluating the average damage identified in the structural volume, turns out to be a synthetic measure of the structural health, showing during the time of the analysis the progression of degradation. It is worth noting the different gradient through which the various events reach the threshold of maximum damage; more impulsive earthquakes explicate in few instants the total damage, as in the case of Southern Italy 1998 or Balkans 1979 events. Once the maximum peaks in earthquake acceleration are attained, given the condition of thermodynamic irreversibility, damage reaches the maximum value and remains constant until the end of analysis. Regarding the set employed, the most severe earthquakes, which reach the most severe degradation, turned out to be Balkans 1979 and Central Italy 2016, with an index value higher than 0.8.
Fig. 8. Fast Fourier Transform (FFT) of the out-of-plane displacement for the damage and elastic models for Greece 1999 record with 975 years return period (a); elastic and damaged mode 1 period compared to the elastic displacement spectrum (b).
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Fig. 9. Damage index D0.95 for the 7 records with 975 years return period.
5 Conclusions The present study adopted a macromechanical constitutive law with damage to study the static and dynamic nonlinear response of a masonry arch bridge. The isotropic phenomenological law, characterized by the introduction of one scalar damage variable, is quite reliable in reproducing the behavior of masonry under seismic loading conditions. This formulation, after initial applications in the micromechanical framework, and subsequent extensions to the macromechanical framework, sees in this work a further field of testing. The study of a three-arch masonry road bridge, with a recurring construction scheme for small-sized historical bridges in Italy, is definitely useful for both in-depth investigation of the structural response and comparative analyses with other modeling choices for similar case studies. Adopting a 3D FE model and accounting for seismic action in the three directions, an intent was made to reproduce realistic conditions as accurately as possible to obtain a more reliable response. Therefore, after modal validation of the model and estimation of the horizontal capacity with pushover curve, an investigation at different damage levels, considering three return periods, employing a set with heterogeneous characteristics, stands as a fundamental tool to survey the structural weaknesses. Among the potentialities of the FEAP user finite element, where the formulation was implemented, is the ability to show damage maps, relevant to identify areas where damage is localized during the earthquake, and thus being able to hypothesize incipient collapse mechanisms. Moreover, being able to follow the progression of damage by means of damage indexes, allows a view of the overall damage on the structure, and thus shows how severe an earthquake is, with respect to the bridge in terms of the velocity of damage evolution and maximum damage reached. Performing a comparison with an elastic model of the bridge for the time history analyses, offered the opportunity for evaluations of the dynamic amplification of the response, which in most cases occurred for the damage model. Future studies could see interest in modeling structural reinforcement techniques designed to repair the most vulnerable areas of the structure, as well as more in-depth investigations into the incidence of the Z component for earthquakes in near-fault events.
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References 1. Gönen, S., Soyöz, S.: Seismic analysis of a masonry arch bridge using multiple methodologies. Eng. Struct. 226, 111354 (2021). ISSN 0141-0296 2. Roselli, I., et al.: Health assessment and ambient vibration testing of the “Ponte delle Torri” of Spoleto during the 2016–2017 Central Italy seismic sequence. J. Civ. Struct. Heal. Monit. 8(2), 199–216 (2018). https://doi.org/10.1007/s13349-018-0268-5 3. Karaton, M., Aksoy, H. S., Sayın, E., Calayır, Y.: Nonlinear seismic performance of a 12th century historical masonry bridge under different earthquake levels. Eng. Failure Anal. 79, 408–421 (2017). ISSN 1350-6307 4. Di Sarno, L., da Porto, F., Guerrini, G., Calvi, P.M., Camata, G., Prota, A.: Seismic performance of bridges during the 2016 Central Italy earthquakes. Bull. Earthq. Eng. 17(10), 5729–5761 (2018). https://doi.org/10.1007/s10518-018-0419-4 5. Gattulli, V., Lofrano E., Paolone A., Pirolli G.: Performances of FRP reinforcements on masonry buildings evaluated by fragility curves. Comput. Struct. 190, 150–161 (2017). ISSN 0045-7949 6. Addessi, D., Sacco, E.: Nonlinear analysis of masonry panels using a kinematic enriched plane state formulation. Int. J. Solids Struct. 90, 194–214 (2016) 7. Di Re, P., Addessi, D., Sacco, E.: A multiscale force-based curved beam element for masonry arches. Comput. Struct. 208, 17–31 (2018) 8. Addessi, D., Di Re, P., Gatta, C., Sacco, E.: Multiscale analysis of out-of-plane masonry elements using different structural models at macro and microscale. Comput. Struct. 247, 106477 (2021) 9. Pelà, L., Aprile, A., Benedetti, A.: Comparison of seismic assessment procedures for masonry arch bridges. Construct. Build. Mater. 38, 381–394 (2013). ISSN 0950-0618 10. Addessi, D., Liberatore, D., Nocera, M.: Damaging Behavior of Masonry Arch Bridges: Analysis of ‘Ponte delle Torri’ in Spoleto, Italy. Journal of Earthquake Engineering (2020) 11. Addessi, D., Gatta, C., Nocera, M., Liberatore, D.: Nonlinear dynamic analysis of a masonry arch bridge accounting for damage evolution. Geosciences 11, 343 (2021) 12. Pelà, L., Aprile, A., Benedetti, A.: Seismic assessment of masonry arch bridges. Eng. Struct. 31(8), 1777–1788 (2009) 13. Taylor, R.L.: FEAP—A Finite Element Analysis Program, Version 8.5; Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA, USA (2017) 14. Addessi, D., Sacco, E.: Enriched plane state formulation for nonlinear homogenization of inplane masonry wall. Meccanica 51(11), 2891–2907 (2016). https://doi.org/10.1007/s11012016-0484-1 15. Aprile, A., Pelà, L., Benedetti, A.: Analisi pushover di ponti in muratura. PONTI E VIADOTTI: ASPETTI PROGETTUALI, STRUTTURALI E DI MANUTENZIONE (2006). [in Italian] 16. NTC 2018: Italian Building Code for Constructions (Norme Tecniche per le Costruzioni). D.M. 17th January 2018 – S.O. n. 8, G.U. n. 42; 20th February 2018. [in Italian] 17. Locati, M., Camassi, R., Stucchi, M.: DBMI11, la versione 2011 del Database Macrosismico Italiano. Milano, Bologna. Accessed September 12 (2018). http://emidius.mi.ingv.it/DBMI11 18. Russo, E., et al.: Italian Accelerometric Archive v3.2 - Istituto Nazionale di Geofisica e Vulcanologia, Dipartimento della Protezione Civile Nazionale (2022) 19. Luzi, L., Puglia, R., Russo, E., Orfeus, W.: Engineering Strong Motion Database; Version 1.0; Istituto Nazionale di Geofisica e Vulcanologia, Observatories & Research Facilities for European Seismology: Roma, Italy, vol. 10 (2016)
Macroelement Modelling Based on a Bouc – Wen Formulation with Degradation for the Dynamic Analysis of Masonry Walls Domenico Liberatore1 , Daniela Addessi2 , and Alessandra Paoloni2(B) 1 Department of History, Representation and Restoration of Architecture,
Sapienza University of Rome, Piazza Borghese 9, 00186 Rome, RM, Italy 2 Department of Structural and Geotechnical Engineering, Sapienza Universtity of Rome,
Via Eudossiana 18, 00184 Rome, RM, Italy [email protected]
Abstract. Among the different finite element modelling approaches available for the description of unreinforced masonry structures, the equivalent frame method is widely diffused. It is, in fact, capable of describing the response of masonry walls with good accuracy, thanks to the possibility of reproducing its main in-plane collapse mechanisms through the schematization of piers, spandrels and rigid zones with one-dimensional macroelements. Nonlinear hinges completed with appropriate constitutive laws are employed for the description of the nonlinear characteristics of masonry, both for shear and flexural mechanisms. In particular, a Bouc-Wen formulation is considered in this study and modified with the introduction of degradation by means of a scalar variable for damage and an additional parameter for flexibility increase, to properly account for the strength and stiffness degrade typical of masonry under cyclic actions. The dynamic behavior of a squat masonry wall under different types of excitations is investigated, as well as the effects of the damage and flexibility increase in the dynamic response of the panel. Keywords: Equivalent Frame · Force-based macroelement · Bouc–Wen Hysteresis · Damage · Flexibility Increase
1 Introduction The use of the equivalent frame approach for modelling the response of masonry structures and elements, such as arches or panels, is a widespread practice nowadays, especially in practitioners’ field. This approach can be usually applied when these are unreinforced and regular, with either rigid or flexible floor diaphragms, and the structural response can be assumed to be box-like. Despite the specific typology of cases that can be analysed, the spread of this modelling method is due to numerous advantages, which come from the combination of a low computational burden, a reduced number of input parameters and a quite satisfactory accuracy of the results [1]. This latter, often investigated in literature [2, 3], can be given by both the adequacy of the equivalent frame assumption and the nonlinear models used for the behaviour of the structural elements © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 433–444, 2024. https://doi.org/10.1007/978-3-031-39450-8_36
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[4]. Moreover, the aforementioned advantages are acknowledged mostly when the seismic or dynamic response of these buildings or panels are concerned, considering the complexity of both the dynamic actions and the remarkable nonlinear response of the system. According to the equivalent frame method, piers and spandrels are modelled as macroelements in which the deformations are allowed, while nodes are schematized as rigid panels or as rigid offsets at the ends of the deformable elements [5]. To model these latter, different formulations are proposed in literature. In some cases, they are modelled as two-dimensional elements either with bi-linear behaviour for the description of the shear and flexural mechanisms [6], or as discrete quadrilateral elements whose nonlinear behaviour is described through springs located at the edges of the element, at its centre and the interfaces [7]. However, more often, beam elements are employed to describe the elements of the equivalent frame system. In particular, two main approaches can be distinguished, namely a lumped approach, in which the nonlinearity is considered through nonlinear hinges [8–10], and a distributed nonlinear approach [2, 4, 11]. In this framework, to accurately consider the complex hysteretic and degrading phenomena experienced by masonry during cyclic actions, the in-plane flexural and shear behaviour of piers and spandrels, as well as the typical nonlinear mechanisms of masonry material, are properly described by means of a lumped hinge approach. The proposed force-based macroelement, based on the formulation proposed in [10], is composed of an elastic beam in series with two flexural hinges lumped at the end nodes for the description of the flexural mechanisms and a shear link for the characterization of the shear mechanism. The constitutive relationship adopted to describe the nonlinear behaviour of masonry is based on a modified and enriched Bouc-Wen law. The BoucWen model [12, 13], was often used in literature for the description of a wide class of complex materials, such as masonry, confirming to be a reliable tool for the representation of the related hysteresis phenomena. In previous works [14, 15], it was enhanced through the introduction of two scalar parameters, representing damage and flexibility increase effects, respectively. While the first controls both strength and stiffness degradation, the second only regulates stiffness decay, permitting to efficiently drive the two phenomena. Pinching is also considered for slender panels, to properly account for the flexural behaviour, through the introduction of a proper device in the hinge formulation [14]. The macroelement formulation is extended to the dynamic field, considering a lumped mass approach and a classical Rayleigh damping. The aim is to investigate damage evolution under dynamic actions and its interaction with the hysteretic behaviour of the system. The model is used to study both static and dynamic responses of masonry panels, considering different geometric configurations and loading conditions. In particular, the performances of the enriched Bouc–Wen model are accurately examined, with the aim of analysing the effect of the degradation on the global response of masonry.
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2 Dynamic Force-Based Macroelement Formulation The present formulation is based on the macroelement proposed in [10], which was enhanced with the introduction of flexibility increase in the hysteretic law adopted for the nonlinear hinges, and properly modified to represent the dynamic behavior of the system. It consists of a force-based beam element which allows the description of the in-plane behavior of masonry elements through a lumped hinge approach, implemented in the global displacement-based finite element code FEAP [16]. 2.1 Equivalent Frame Dynamic Formulation The macroelement is composed of a 2D elastic beam element in series with two flexural hinges located at the ends and a shear link, which enclose the flexural and shear nonlinear mechanisms, respectively. The detailed formulation is described in [10]. The lumped hinge approach adopted for the macroelement permits to introduce a proper constitutive law in each hinge, with the aim of reproducing the nonlinear response characterizing masonry structures. In particular, the Bouc-Wen hysteretic model modified with the introduction of damage and flexibility increase, described in the following section, is considered. However, despite the squat panels being properly represented by the selected constitutive law, the complex behavior of slender panels is not completely represented by the modified Bouc-Wen model only. It is, in fact, necessary to use additional devices to the Bouc-Wen constitutive law to capture particular mechanisms, such as pinching. To this end, a nonlinear elastic device is considered in parallel to the modified BoucWen hysteretic model, which permits to obtain the S-shaped cycles typical of panels which experience pinching. An elastic negative device is added afterwards, with the aim to reproduce more accurately the initial stiffness of slender systems observed in experimental results. To also describe the dynamic behavior of masonry structures, which is relevant especially when structures located in seismic prone areas are considered, the cyclic model has been extended to the dynamic field. To this end, the following finite element equations are introduced: M¨u + C˙u + Pint (u) = Pext
(1)
In Eq. (1), the global nodal acceleration, velocity, and displacement vectors are ¨ u˙ and u, respectively, where the dot symbols represent the derivative with denoted as u, respect to time. Pint (u) is the internal force vector, which is evaluated from the structural response at each iteration of each step of the global nonlinear analysis. The global mass matrix M is a lumped matrix; its diagonal contains the translational and rotational masses of each node. Moreover, the damping matrix C is evaluated considering the Rayleigh approach, by combining at each step of the analysis the mass and the stiffness matrices using the coefficients a0 and a1 respectively, assumed equal to 13.7 and 0.00073. Lastly, Pext is the global external force vector, which contains the value of the dynamic excitation assigned at each node of the system at every time step.
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2.2 Hinges Constitutive Law Despite the large employment of classical constitutive laws implemented in largely diffused commercial software, the complex nonlinear behavior of masonry needs to be properly described, also accounting for the strong degradation experienced during cyclic performance. In accordance to this, a modified Bouc-Wen hysteretic model with damage, already formulated in [14], is considered, and further enriched with the introduction of a flexibility increase term. The Bouc-Wen model can be exemplified through the location of an elastic spring in parallel with a hysteretic spring. This latter, in [14] has been modified with the introduction of a scalar damage variable D, which reduces the hysteretic force F h , resulting in the following equation: F = F el + F h = a k vy u + (1−D) (1−a)k vy z
(2)
In the equation, a is the hardening parameter, k is the initial stiffness, vy is the maximum elastic displacement, u is the nondimensional displacement and z is the hysteretic variable which represents an elastic displacement. The differential equation which regulates the evolution of this latter parameter remains unchanged with respect to the equation formulated in the classic Bouc-wen model [14]. The damage parameter D, which is a nondimensional scalar variable, ranges from 0 to 1, where 0 refers to the undamaged and 1 the fully damaged state. Its evolution is related to the progression of the dissipated energy U h through a positive scalar parameter δ D which is set by the user and has the dimension of the inverse of an energy. The damage variable is, therefore, evaluated as D = δ D U h and its increasing values are ruled by the assumption of thermodynamic admissibility. Despite the accordance with experimental results proves the model to be enough accurate [10, 14], a further modification is considered, to have a better respondence of the numerical curves in the loading and unloading branches. It is, in fact, necessary to capture a more marked stiffness reduction in these sections of the numerical response of both squat and slender panels. To this end, a flexibility increase term is added in the evaluation of the elastic displacement and the dissipated energy, which are evaluated as: v = vy [(1 + δK U h )z + up ] and: Uh =
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3 Squat Panel Response In the following paragraph, the response of a squat wall to different types of dynamic excitations is analyzed. Three harmonic horizontal forces are applied at the base of the panel, thus simulating an acceleration time history. The amplitude of the excitations is the same for all three cases and set equal to 15 m/s2 , while the ratio between the angular frequency of the excitation Ω and the one of the panel ω distinguishes the three harmonic actions. This latter is fixed and equal to 0.95 in the first case, proximate to resonance condition, while in the second and third case it has increasing and decreasing values, respectively: in fact, the ratio between the two periods ranges between 0.2 and 1.5 in these latter cases. The geometry and restraining conditions of the masonry panel simulate the squat wall analyzed at the Joint Research Centre of Ispra in [17]: the ratio between the height of the wall L e and its base l is equal to 1.35, while the width t is 0.25 m. Moreover, the rotation is restrained at both the top and base of the wall, thus allowing the horizontal translation of the top only. The material mechanical parameters reproduce the behavior of unreinforced masonry made of bricks and lime mortar. The Young’s modulus E is equal to 1700x103 kN/m2 , the shear modulus G is 300x103 kN/m2 and the compressive f c and shear f v strengths are set equal to 6200 kN/m2 and 225 kN/m2 , respectively. The evaluation of the maximum elastic displacement vy , which indicates the elastic range threshold, follows the Italian Guidelines [18], according to the procedure described in [10, 19]. Regarding the dynamic parameters of the system, a 5% damping factor is considered for the Rayleigh damping matrix, and a density mass equal to 4.8 t/m3 is set, increased with respect to the literature reference value to get a high natural period for the panel, which permits to attain high displacement amplitudes, to better emphasize the shape of the hysteretic cycles. Table 1 contains the values adopted for the modified Bouc-Wen hysteretic model for the first set of analyses, in which the Bouc-Wen hysteretic model with damage and flexibility increase (red solid line in the following figures) is compared to a classical Bouc-Wen formulation (dashed blue line) and the elastic case (dashed black line) for the three excitations. In particular, only the results related to the shear hinge are presented, considering that the contribution of the flexural hinge for the squat panel results as negligible. Table 1. Constitutive parameters of the modified Bouc-Wen hysteresis. Shear Hinge
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Figures 1, 2 and 3 show the response of the panel to the excitation with fixed, increasing and decreasing Ω/ω ratio respectively, considering a flexibility increase parameter δ K set equal to 0.3. In each figure, the horizontal global displacement Δ experienced at the top of the panel, the progression of the damage variable for the shear hinge evaluated at each step of the analysis, and the response of the hysteretic hinge in terms of shear stress T sh versus shear strain γ can be detected. Horizontal Global Displacement
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The case with fixed Ω/ω ratio is analyzed first. Although in the first cycle the classical and modified Bouc-Wen models experience similar behavior, they depart immediately after, due to the higher displacement, and consequently the higher period, reached by the latter. Of course, only this case experiences damage. The damage variable, thanks to the irreversibility thermodynamic assumption and its dependency on the dissipated energy, results to be increasing during the entire analysis. In the first 0.1 s, its growth is more rapid, and the value of 0.1, corresponding to almost a quarter of the maximum value of damage, is reached. This is strictly connected to the first cycles of the analysis, which reach the largest displacements. After reaching the maximum displacement, in fact, the following cycles show strength reduction, highlighting the effect of damage on the panel strength. Nonetheless, these cycles, which reach displacement levels that are almost constant, correspond to an increase of the damage variable, due to the presence of both strength and stiffness reduction, which is spread during the rest of the analysis and shows a smooth trend. The hysteretic cycles are then narrower, and their equivalent stiffness tends to be reduced at each cycle. In Fig. 2 and 3, the response to the excitations with increasing and decreasing Ω/ω ratio are represented. The different frequency content of the two forcing actions allows the panel to experience significantly different behaviors. In the first case, in fact, the most evident evolution of damage is concentrated between 0.2 and 0.6 s, where the damage variable goes from 0 to almost 0.9. A global displacement with increasing cycle amplitude is experienced, to which shear cycles with fat shape and increasing
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amplitude correspond. Moreover, even if the initial cycles of the classic Bouc-Wen case are overlapped to those of the modified Bouc-Wen case, when damage becomes overriding, strength reduction can be detected. Simultaneously, the flexibility increase, which reduces the stiffness in the loading and unloading branches of the curve, consents to reach significantly higher displacements with respect to those of the classic BoucWen. In the last part of the curves, instead, a reduction of the displacement amplitude occurs, together with a lower number of experienced cycles in about 0.4 s. A less rapid increase of the damage variable is detected in this last part of the curve, going from 0.9 to the maximum value experienced of 0.95. This latter is in correspondence of the thinner hysteretic cycles, which undergo a more severe strength and stiffness reduction, arriving to an almost null area of the cycle.
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Regarding the third case (Fig. 3), in which the Ω/ω ratio is decreasing, the modified and classic Bouc-Wen models experience similar behavior. Both cases, in fact, show a discording trend with respect to the elastic case. This latter shows an increasing displacement amplitude until about 0.35 s, followed by a rapid decrease of the response until an almost null oscillation around the zero displacement. In contrast, the two Bouc-Wen models show a short and rapid raise of the amplitude in the first couple of cycles, followed by an almost constant decrease for the rest of the duration of the signal, until reaching a stationary response assessed on really low values of residual displacement, with an amplitude of the oscillation that is almost null. Also, the classical Bouc-Wen model shows a residual displacement more pronounced than that of the modified formulation. Regarding the behavior of the shear hinges, the modified constitutive model clearly shows strength and stiffness degradation; moreover, the flexibility increase shrinks the cycles and enhances their trend to reduce the equivalent stiffness. The damage variable shows a rapid increase in the first 0.2 s of the analysis, reaching few steps later its maximum value of 0.34. It should be noted that even if in this case damage increases from the very beginning of the analysis, with respect to Fig. 2 where it starts increasing after 0.2 s, its growth is more rapid and is concentrated in a lapse of time that is almost half as much as the case with increasing forcing frequency, while the maximum reached value is a third with respect to the other case. After this first lapse of time, the damage variable experiences a short and smooth increasing phase, and then is kept constant for the rest of the analysis, during which the decreasing hysteretic cycles tend to have a null area and no further damage is experienced. 100
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Further considerations are made regarding the constitutive behavior in presence and absence of flexibility increase, for the same squat panel and the three considered excitations. The elastic (black dashed line) and modified Bouc-Wen (solid red line) models are then compared to a case with damage only (dashed blue line) [10, 14].
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However, to better appreciate the difference between the cases, the flexibility increase parameter δ K is increased from the value of 0.3 to the value of 5 kJ−1 , while the damage parameter δ D remains equal to 0.2 kJ−1 , as reported in Table 1. Figure 4 shows the response of the panel to the excitation with fixed Ω/ω ratio. Both Fig. 4 a) and Fig. 4 b) reports the same curve, but highlighting different sections. The figure on the left (Fig. 4 a) displays with colors the initial cycles, where the flexibility increase contribution is detectible from the rapid thinning of the cycles with respect to the case with pure damage, even if the same strength degradation level is experienced. The more the analysis evolves, the higher the flexibility contribution is, thanks to its dependency from the evolution of the dissipated energy, and the thinner the cycles get. Moreover, the shear strain values reached at each cycle are visibly higher with respect to those with damage only, and consequently also the maximum reached shear strain is higher. Figure 4 b), which focuses on the second part of the cycles, emphasizes how the resonant response experiences cycles that are almost reduced to lines, and whose slope tends to decrease, while the cycles with damage only tend to maintain the large shape typical of the Bouc-Wen cycles, also showing the strength reduction. Interesting considerations concerning the evolution of damage can be made. It is, in fact, evident that the case without flexibility increase experiences a higher damage with respect to the case with flexibility increase during the entire duration of the analysis, with the exception of the first cycle, when the two behaviors are almost coincident. The reduction of the area of the cycles, caused by the increase of the elastic displacement, leads to a lower dissipated energy for each cycle. Consequently, considering that the scalar damage variable D directly depends on the evaluation of the dissipated energy, the values of damage reached by the case with flexibility increase are significantly lower, equal to 0.1 versus 0.6 for the case with damage only. This can be clearly seen in Fig. 4 b), in the graph relative to damage, where after 0.1 s the level of damage experienced in the case with flexibility increase is almost constant, as the experienced cycles are really thin and with almost null area, while the case with pure damage experiences a significant smooth increase of the variable D that lasts until the end of the analysis. In Fig. 5 a), a similar behavior to the previous case can be seen, with cycles visibly thinner regarding the modified Bouc-Wen hysteresis. The onset of damage in the two cases starts after about 0.2 s from the beginning of the analysis, when the panel response exits from the elastic range, and continues until about 0.5 s for the case with flexibility increase and 0.6 for the case with damage only. After that, it continues almost constant until the end of the analysis. As can be seen in Fig. 5 b), this latter section of the curve corresponds in both cases to thin cycles with low area and consequently experiencing low energy dissipation. Moreover, the case with null δ K almost reaches the fully damaged state, with D equal to 1, while the case with δ K equal to 5 kJ−1 reaches a maximum value of damage equal to 0.4, even if its hysteretic cycles are already reduced to straight lines. The presence of the flexibility increase thus reduces the values of the damage variable D reached during the analysis.
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Finally, Figs. 6 a) and b) present a behavior in agreement with the results shown in Figs. 4 and 5, confirming that the case with damage only reaches a higher damage variable value. The two hysteretic curves clearly show the influence of the flexibility increase even in the first cycles of the analysis, where it allows the panel to reach higher values of distortion with considerably lower stiffness in the loading and unloading branches. Figure 6 b) also shows that the cycles rapidly collapse around the origin in both cases, as the decreasing angular frequency of the excitation makes the panel experience cycles with lower amplitudes with the progression of the analysis. This condition leads the panel with a parameter δ K equal to 5 kJ−1 , to immediately have cycles with almost null
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amplitude and a damage variable which does not increase anymore. On the contrary, the case with pure damage still shows an increasing variable D, as some of the subsequent cycles still have a non-null amplitude and show strength degradation.
4 Conclusions A macroelement for the dynamic analysis of masonry walls through the use of the equivalent frame method and an enhanced Bouc-Wen constitutive law is presented, with the possibility of describing damage by means of two scalar variables affecting strength and stiffness degradation. The model, based on an existing modification to the classic Bouc-Wen hysteretic formulation, enhances the characterization of damage through a parameter which allows to describe the flexibility increase, depending on the dissipated energy, observed in the loading and unloading branches of experimental curves available in literature. Additional terms are included in the elastic displacement and in the dissipated energy calculations to account for it. Consistently with the forcebased formulation, Rayleigh damping and lumped mass approach are implemented for the description of the dynamic behavior. A squat panel is modeled with the proposed macroelement and subjected to three different excitations with ratio between the angular frequencies Ω/ω fixed to a condition proximate to resonance, increasing and decreasing, respectively. The behavior for the case with flexibility increase is compared to the elastic case and the classical Bouc-Wen model in first instance, and then to the case with pure damage, with the aim of comparing the dynamic behavior in presence and absence of flexibility increase. As expected, the presence of flexibility increase allows the system to reach higher shear strain values with respect to the classical Bouc-Wen models, also driving the cycles to be thinner and to have a lower equivalent stiffness during the progression of the cycles. Comparing this latter case with the model with damage only, a higher value of the damage variable D regarding the case with damage only, with respect to the case with flexibility increase, can be detected. This is caused by the lower value of dissipated energy reached during the analysis due to the increase of the elastic displacement and the thinner cycles experienced in this latter case. Further studies for the extension of the presented macroelement to the threedimensional behavior are ongoing, with the aim of also describing the principal out-of-plane collapse mechanisms commonly experienced by masonry walls.
References 1. Quagliarini, E., Maracchini, G., Clementi, F.: Uses and limits of the equivalent frame model on existing unreinforced masonry buildings for assessing their seismic risk: a review. J. Build. Eng. 10, 166–182 (2017). https://doi.org/10.1016/j.jobe.2017.03.004 2. Siano, R., et al.: Numerical investigation of non-linear equivalent-frame models for regular masonry walls. Eng. Struct. 173, 512–529 (2018). ISSN 0141-0296 3. Cattari, S., Camilletti, D., D’Altri, A.M., Lagomarsino S.: On the use of continuum Finite Element and Equivalent Frame models for the seismic assessment of masonry walls. J. Build. Eng. 43, 102519 (2021). ISSN 2352-7102
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4. Peruch, M., EnricoSpacone, P., Shing, B.: Cyclic analyses of reinforced concrete masonry panels using a force-based frame element. J. Struct. Eng. 145(7), 04019063 (2019). https:// doi.org/10.1061/(ASCE)ST.1943-541X.0002335 5. Dolce, M.: Schematizzazione e Modellazione degli Edifici in Muratura Soggetti ad Azioni Sismiche. L’industria delle costruzioni. 25(242), 44–57. (1991). [In Italian] 6. Lagomarsino, S., Penna, A., Galasco, A., Cattari, S.: TREMURI program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng. Struct. 56, 1787–1799 (2013) 7. Caliò, I., Marletta, M., Pantò, B.: A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings. Eng. Struct. 40, 327–338 (2012). https:// doi.org/10.1016/j.engstruct.2012.02.039 8. Addessi, D., Liberatore, D., Masiani, R.: Force-based beam finite element (FE) for the pushover analysis of masonry buildings. Int. J. Archit. Heritage 9(3), 231–243 (2015) 9. Addessi, D., Mastrandrea, A., Sacco, E.: A force-based equivalent frame element for pushover analysis of masonry structures. Key Eng. Mater. 624, 405–412 (2014). https://doi.org/ 10.4028/www.scientific.net/KEM.624.405 10. Sangirardi, M., Liberatore, D., Addessi, D.: Equivalent frame modelling of masonry walls based on plasticity and damage. Int. J. Architect. Heritage 13(7), 1098–1109 (2019) 11. Raka, E., Spacone, E., Sepe, V., Camata, G.: Advanced frame element for seismic analysis of masonry structures: model formulation and validation. Earthq. Eng. Struct. Dyn. 44(14), 2489–2506 (2015) 12. Bouc, R.: A mathematical model for hysteresis. Acta Acust. Acust. 24(1), 16–25 (1971) 13. Wen, Y.K.: Method for random vibration of hysteretic systems. J. Eng. Mech. Div. Proc. ASCE 102, 249–263 (1976) 14. Liberatore, D., Addessi, D., Sangirardi, M.: An enriched Bouc-Wen model with damage. Eur. J. Mech. - A/Solids 77, 103771 (2019). https://doi.org/10.1016/j.euromechsol.2019.04.006 15. Liberatore, D., Addessi, D., Paoloni, A.: (Submitted) Hysteretic models with degradation 16. Taylor, R.L.: FEAP – A finite element analysis program, Version 8.5. California: Department of Civil and Environmental Engineering, University of California at Berkeley (2017) 17. Anthoine, A., Magonette, G., Magenes, G.: Shear-compression testing and analysis of brick masonry walls. In: Proceedings of the 10th European Conference on Earthquake Engineering, Balkema, Rotterdam (The Netherlands), pp. 1657–1662 (1995) 18. NTC. 2018. Italian Building Code for Constructions. (Norme Tecniche per le Costruzioni). D.M. 17th January 2018 – S.O. n. 8, G.U. n. 42; (2018) [in Italian] 19. Liberatore, D., Addessi, D., Sangirardi, M.: Nonlinear analysis of masonry walls based on a damage-plastic formulation. In: Aguilar, R., Torrealva, D., Moreira, S., Pando, M.A., Ramos, L.F. (eds.) Structural Analysis of Historical Constructions. RB, vol. 18, pp. 1009–1017. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-99441-3_109
Structural Analysis of Historic Absorption Building in Turner Valley, Alberta Emina Burzic(B) , George Iskander, Neil A. Duncan, and Nigel G. Shrive Department of Civil Engineering, Faculty of Engineering, University of Calgary, Calgary, AB, Canada [email protected]
Abstract. Many historic structures in Canada are deemed unsafe and are closed or of limited access to the public. An “unsafe” steel and concrete heritage building rebuilt in 1930 has been analysed structurally. The building in question is the absorption building at the Turner Valley Gas Plant (TVGP), a National Historic site. Throughout the building lifespan the structural skeleton has been adapted to accommodate changes in the oil and gas processing. The TVGP was Alberta’s first natural gas plant built and thus the birthplace of the energy sector in Western Canada. The absorption building housed the first ever absorption plant in Canada in 1914. The load path, effects of modified and missing members, and capacity of elements were assessed. Due to a lack of historical records, Non-destructive testing methods were used to determine building properties. Geometrical data was collected with laser scanners and ground penetrating radar systems. X-ray diffraction, scanning electron microscopy, hardness tests and tension/compression tests were used to determine material stiffness, strength, and chemical microstructure. Four finite element models were developed to conduct a linear-elastic analysis to assess the effects of changes in structural integrity which may have occurred due to structural member modifications. A load test was performed to validate the models. Results confirmed the load path and the effects of modifying members as an initial assessment towards a complete safety analysis. The research also exposed gaps within current standards and provided a guide to future engineers on structural interventions in heritage structures as standards are developed. Keywords: Structural Analysis · Historical Structures · Finite Element Modelling · Non-destructive Testing · Heritage Conservation
1 Introduction Historical structures are a key component in understanding past culture and engineering methods. The Canadian construction industry is shifting to reusing existing structures in an effort to reduce environmental impacts, like our European neighbors [1]. In the last 20 years more and more buildings have been designated as historical, with many of them closed to the public as they are considered unsafe. However, the amount of funding for conservation has not increased with the number of designations [2]. The lack of funding does not allow for structural assessments to be conducted on all buildings and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 445–457, 2024. https://doi.org/10.1007/978-3-031-39450-8_37
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therefore many are closed to the public due to safety concerns [2]. We conducted a structural assessment on a historical building located in Turner Valley, Alberta, Canada which is currently closed and designated as “unsafe”. The building in question is the absorption building of the Turner Valley Gas Plant (TVGP), a National Historic site [3]. The structure was rebuilt in the early 1930s using steel, corrugated iron sheathing, and concrete when the original 1914 wooden building burnt down in 1920 [3]. The site is historically known as the birthplace of the energy sector in Western Canada and the absorption building was one of the first of its kind [3]. Due to adaptations in oil and gas processing the building’s structural skeleton underwent many adaptations, i.e., structural members were removed or deformed to accommodate gas piping. The building requires a structural analysis to consider whether it can be designated as safe and opened to the public. Conducting a structural analysis on a historical structure provides unique challenges. It is common that the structure will have no engineering records on the geometrical or material properties. The lack of records creates a need for geometrical, material, and structural data to be collected as these data are required to create a finite element model and conduct a structural analysis. Engineers must consider how the building is constructed to ensure the structure can safely withstand the loads to which it is subjected. Historical structures are protected by law against any damage during remediation, adding another layer of complexity to the analysis. Non-destructive and minor destructive methods were used to collect data. In Canada, the guidelines in the National Building Code of Canada (NBCC) and the Standards and Guidelines for the Conservation of Historic Places (SGCHP) from Parks Canada are used to set an expectation and roadmap in restoring structures based on internationally agreed principles [4, 5]. The NBCC is vague on how to conduct a structural assessment on historical structures and the SGCHP does not consider the technical process [4, 5]. Additionally, neither of these documents are mandatory when conducting an intervention - resulting in lack of guidance and inconsistent interventions. This poses a safety issue and public risk because engineers and the structures they are dealing with are not held to the same standards as applied to new structures. Our objective was to determine if the building is safe to be open to the public, either in its current state or after an intervention. A structural analysis was conducted based on an applied test load. Multiple models were created to compare various characteristics of the building and determine their impact, i.e., the removal of members, and the effects of the corrugated iron sheathing surrounding the building.
2 Methodology To conduct a structural analysis using FEM, the building’s geometries and material properties need to be obtained as structural engineering records were not available for the absorption building at TVGP. The section below describes the various models that were developed to best represent and simulate the conditions seen on site at the absorption building.
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Fig. 1. The absorption building at the Turner Valley Gas Plant.
2.1 Geometrical Properties A geometrical survey was conducted to obtain the geometrical properties of the building. The building is 6.1 m wide and 13 m long. The height of the apex is 5.2 m and the roof slopes 26–27° (Fig. 1). Five 1-m-wide absorption tanks run through the middle of the building. The tanks obscure the view of trusses and roof members. Additionally, the building has vaulted ceilings and missing or deformed members (Fig. 2).
(a)
(b)
(c)
Fig. 2. a) Shows the vaulted ceilings and absorption tanks, b) Shows a member that was deformed to allow a pipe to run through the building, c) Shows a member that was removed which are typical throughout the building.
The complex building geometries and obstructions restricted the ability to use hand tools to determine measurements in various locations, especially in the roof [6]. Laser scanning was used to conduct a geometrical survey of the building and the results were validated against hand measurements [6]. The values obtained were within 5 mm of each
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other and therefore they were used in the modelling of the absorption building [6]. The cross sections of members were determined using calipers as the error present within the laser scanning cloud model was not reliable for such small measurements. Five structural members were used in the modelling of the building, i.e., pipe columns, pipe beams, roof angles, beam angles, and corrugated iron sheathing (typical cross-sections are shown in Fig. 3).
(a)
(b)
(c)
Fig. 3. Common cross sections within the absorption building. a) Cross section of all pipe members, b) Cross section of roof angle members, c) Cross section of beam angle members.
2.2 Material Properties No records of material properties were available, i.e., the type of steel, whether piles were used, or if the concrete was structurally reinforced with steel. These structural and material properties were collected through various non-destructive or minor destructive tests. To determine the concrete strength a sample of the foundation was taken from a spalled area and tested until failure under compressive loads. A scaled version of the ASTM standards for compression tests was used to determine the height to diameter ratio for the samples as the concrete thickness available was limited [7]. Cylinders were created with a 2:1 height to diameter ratio (Fig. 4a). The compressive strength of concrete was determined to be 21 MPa. To determine the steel properties a 30 mm long section of pipe was cut from a modified member in the building and tested until failure under tension loads. A SNC machine was used to create a scaled version of the ATSM E6 standard dog-bone samples for testing [8] (Fig. 4b). The ultimate stress for the steel specimens was determined to be 390 MPa. Due to the size of the samples strain gauges were not applicable to the sample and Young’s Modulus could not be verified. A value of 200 000 MPa was used [9]. Ground penetrating radar (GPR) was used to determine the foundation depth, if the concrete was reinforced, and if piles exist. The results found no reinforcement or piles were present within the concrete and the foundation was 15 cm thick. To test the chemical microstructure of the steel and concrete, X-ray diffraction, scanning electron microscopy, and hardness tests were used. The chemical composition results indicated that the concrete had a high cement ratio, and the steel was considered a mild steel with a high carbon content. The corrugated iron sheathing was measured to be 1.5 mm thick with a corrugated pitch of 73.6 mm. When compared to standard sheet sizes, an appropriately similar
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(b)
Fig. 4. a) A concrete test sample for compression tests, b) A steel test sample for tension tests.
industry size is a 1.5-mm-thick sheet with a depth of 19 mm and corrugated pitch of 75 mm [10]. Therefore, the standard sheet size was carried in further calculations. 2.3 Load Path To understand the load path, we must understand the construction of the building. The building consists of 7 main frames – two exterior and five interiors. Of the five interior frames, all are repetitive except for one (Fig. 5).
Fig. 5. a) Interior repetitive section, b) Interior section used at one location.
The gravitational load system consists of the roof sheathing tied to the roof angles, and roof angles tied to the angled pipe columns, which are simply supported on the top of the wall. The walls consist of corrugated sheathing tied to both horizontal beam angles and column pipes as seen in Fig. 6a. The column pipes were connected to a horizontal pipe beam at their base, tying all the frames together. For extra rigidity the horizontal pipe beam was cast into a concrete ledge. The ledge then carried the load to the ground. Figure 6b depicts pipe columns encased in the concrete ledge. The corrugated iron sheathing had begun corroding in various areas, but the corrosion was not significant to raise concerns (Fig. 6c). A goal of the modeling was to determine if the sheathing is carrying loads and if the corrosion and connections should be addressed.
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Fig. 6. a) Depicts the corrugated iron sheathing wall connected to both a pipe column using bolts and an angle beam using ties on an interior repetitive section, b) Depicts the concrete ledge in which a pipe beam is encased, c) Depicts corrosion that is seen throughout the sheathing.
2.4 Connections The connections within the building lack consistency and vary from welds, to ties and bolt connections. The exact method used to create the tie connections is unknown, however they are best described as bent nails. Figure 6a shows tie connections and bolt connections. The connection strength was not tested in this case study. However, it was noted that the connections between the sheathing and the columns at the base of the walls were beginning to fail in various locations. 2.5 Finite Element Model The finite element method in the linear elastic range was used to conduct a structural analysis of the absorption building. The results of the GPR scanning showed that piles were not present, rebar did not exist, and the foundation was about 15 cm thick. Based on these results, we decided modelling the foundation was not beneficial. To account for the foundation and concrete ledge, fixed boundary conditions were used at the base of the wall in all models. All FEMs were analyzed in SAP2000 and Abaqus. The steel material properties used were that of typical mild steel as historical values were not obtainable (Young’s Modulus was set to 200000 MPa, and Poisson’s Ratio to 0.3) [9]. All cross sections previously mentioned in the geometrical properties section were used in the creation of the framework. The sinusoidal profile of the 1.5-mm-thick corrugated iron was converted to an equivalent rectangular block shell element, as we were interested in the addition of sheathing to overall stiffness and not the structural analysis of the sheathing itself. The effective stiffness was calculated to represent that of the sheathing. The equivalence properties based on industry sheet sizes is listed in Table 1 [10]. The ratio of the moment of inertia for the corrugated sheathing and equivalent rectangular shell section was found to be 168.6. This value was used as a multiplier in the FEM material properties, i. e., the strong axis moment of inertia, and bending, to account for corrugation of the sheathing. The resulting equivalently stiff rectangular shell element was 1.8 mm thick. The equivalent stiffness was calculated for the shell elements and is reported in the last row of Table 1 demonstrating the equivalent stiffness to the corrugated iron sheathing.
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Table 1. Equivalent structural properties of rectangular shell element and corrugated sheathing [9]. Corrugated Sheathing
Equivalent Rectangular Shell Element
Cross-Sectional Area (mm2 (in2))
1974 (3.06)
---
Moment of Inertia (mm4 (in4))
81 935 (0.06)
486
EI (Stiffness) (N-mm2 x1010)
1.6387
1.6388*
* This value was determined by multiplying the equivalent rectangular shell element moment of
inertia by the equivalence ratio of 168.6 and by Young’s Modulus
Four different FEMs were created with the same material properties and overall geometry but with differences in structural arrangement and boundary conditions of the members. Fully Fixed Framework Model. This model used the skeleton of the building with all members in place and all connections fully fixed (Fig. 7). Fully fixed constraints mean translation and rotational degrees of freedom are fully linked between members at all joints. Moments, shear, and axial forces are transferable at all connections. The model was constructed using beam elements and had no sheathing and no missing members. This was done to mimic the model once construction had been completed and to act as a baseline for all other models. The displacement results obtained from this model would be the minimum displacement allowed for the building. Thus, creating a limit for any validation testing. This model was also created to determine if the sheathing was affecting the structural integrity of the building. The remaining models used this model as a base.
Fig. 7. Depicts the Fully Fixed Framework Model. The green members depict roof angle sections, yellow depicts angle beam sections, and red depicts both pipe column and beam sections.
Fully Fixed Shell Model. Shell elements were added to the Fully Fixed Framework Model on all faces of the building with continuity at all edges (Fig. 8). The shell elements
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were designed to account for the sheathing. This model, like the framework model, acts as an idealized model of the post original construction version of the building to assess a potential structural role of the sheathing. Additionally, this model was used in further models as a base.
Fig. 8. Depicts the Fully Fixed Shell Model. The shell elements shown in yellow were added to the original framework shown in Fig. 7.
Partially Fixed Shell Model. In the Partially Fixed Shell Model, connections were modified to simulate the reality of the connections on site. All beam connections in the Fully Fixed Framework Model were converted to pinned connections as the angle beams were usually cut to surround the column and join to the pipe. This is shown in Fig. 6a. After further observations on site, it was discovered that the sloped roof pipes were only semi-welded to the beam at the top of the wall. The shell edges at the top of the walls and bottom of the roof were released to pinned connections as the roof sheathing is not connected to the wall sheathing on site. Additionally, the shell edges at the bottom of the wall and bottom of the columns were released to pinned connections to simulate the failing connections between the sheathing and framework as observed. Figure 9 highlights the shell elements that were released in green. As the connections on site were not tested, we were limited in the number of connections we could release. The shell edges, beam to column connections, and sloped beam weld connections were released as they were visually observed as disconnected or partially connected. The pin connections allow shear and axial loads to transfer through the building, but not moments and torsion. Existing Building Shell Model. This model was developed to simulate the building in its current form with missing members and appropriate connections. Twenty-nine members were missing or deformed and therefore unable to carry load, and these connections were completely removed from this model. The most affected faces of the building are depicted in Fig. 10. The remaining connections were simulated the same as in the Partially Fixed Shell Model. This model sought to determine if the removed
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Fig. 9. Depicts the shell edges in green that were released to pin connections.
members affected the structural integrity of the building and was also used to compare to load test results conducted on the building.
Fig. 10. Depicts an example of the missing or deformed members in blue that were removed from the existing building model. a) Depicts the front of the absorption building, and b) Depicts the side profile of the building.
2.6 Validation A load test was conducted and measured on site at the absorption building. The same test load was applied at the same location to all the above-described models. This was done to confirm and validate the model results. The test load location was strategically selected for feasibility both on site and in the model’s space. The load was applied to the bottom chord of the interior frame closest to the back wall as shown in Fig. 11. The geometry of this frame does not distribute the loads as well as the other interior frames, therefore displacements will be most visible at this location. Additionally, this location had no obstructions and thus provided the best access on site. The length of the loaded member was 1124 mm and using the limit of L/360 the allowable deflection is 3.12 mm [4]. The load test was conducted on a still spring morning with no snow load and wind load present. A 55-kg weight (532.7 N) was applied at the above specified location. Dial
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Fig. 11. Depicts the interior rare section with a load of 532.7 N
gauges were set at the top of the columns and at the location of load application. The dial gauges have a minimal resolution of one thousandth of an inch (0.0254 mm) A reading was taken immediately after loading and a half hour after loading with the loading still applied.
3 Results The following results were obtained when the same test load was applied on site and in the models. Figure 12 depicts the vertical displacements of the Framework model compared to the Shell model for the same test load (Table 2).
(a)
(b)
Fig. 12. a) Depicts the vertical displacements of the Fully Fixed Framework Model with displacements shown magnified by a factor of 500, b) Depicts the vertical displacements of the Existing Building Shell Model with displacements magnified by a factor of 500 as well illustrating the significantly reduced displacements.
Based on the above, the following observations were noted: • The fully fixed shell model predicted the smallest vertical displacement.
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Table 2. Load test results for vertical displacement at point of load application. Model Names
Vertical Displacement (mm)
Fully Fixed Shell
0.1036
Partially Fixed Shell
0.1059
Existing Building
0.1061
Fully Fixed Framework
1.3154
On-site Dataa
0.0508–0.12701
a The tabulated value for on-site data is a range from instantaneous deflection to post half an hour
deflection
• The shell models all predicted very similar displacements. • The fully fixed framework model predicted the largest displacement and when compared to the on-site data it is the only value that does not fall within the range. • The on-site deflection is within the range of allowable deflections based on the simply supported member.
4 Discussion Based on our analyses and experimental measurements, the shell models were found to be accurate within marginal error. The displacements measured during the on-site load test are under the allowable 3.12 mm based on the NBCC [4]. This result is a step in the right direction to determining if the building is safe to be reopened to the public. The fully fixed framework was intended to act as a minimum, which was found not to be the case. The corrugated sheathing (here modelled with shell elements) appears to be carrying a significant portion of the load and needs to be considered in the structural analysis of the building. The results between the framework and shell model show that the sheathing adds stiffness to the walls, reducing horizontal displacements and adds stiffness to the roof which reduces vertical displacements. Figure 11 b and c show the deformed structure with and without shell elements for the same scale. It is visible that the sheathing is acting as a support to the framework by preventing displacement of the framework itself. It was observed that connections at the base of the sheathing were failing. This is of concern as the sheathing is carrying load. If the load is unable to transfer through the sheathing the displacements will increase and could result in failure of the building or entire walls. The connections should be monitored and tracked as a preventative measure. Proper maintenance of the sheathing and connections would prolong the service life of the building. Further studies should be conducted on the connections, their design, strength, and constructability. Additionally, material tests should be run on the corroded corrugated iron sheathing to determine the rate at which its structural capacity is diminishing. Based on the results obtained, the model has been validated and now can be used to model other potential load cases that will determine if the building can be opened to the public. Potential load cases would include wind and snow loads based off survey data from Turner Valley.
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The Fully Fixed Shell Model is acting as a minimum. The 29 insufficient members in the Existing Building Model accounts for the difference with the Partially Fixed Shell Model but their absence has not significantly affected the overall structural response of the building. However, locally, there could be a more significant effect on adjacent members which will have to be considered. Complexities of the building’s structural joints are difficult to fully incorporate in the model, possibly resulting in variations between the shell models and the on-site data: further consideration for better simulati0n of the types of connections used may be needed. Systemic errors from the use of sensitive dial gauges with a resolution of 0.0254 mm, material and geometrical data collection, and the setup used for load testing the building were present. Future studies should include more test locations and the effects of horizontally loading the building. As previously mentioned, no code exists for conducting structural reviews on historical structures in Canada. Recommendations are in place based on the Parks Canada Guidelines [5]; however, they are not enforced, and the document does not aid in the technical portion of the review. For the current study, the guidelines were followed as applicable with the non-destructive testing and minimal impact on the building. However, the tests completed were not specified and methods for conducting studies are open to interpretation which can lead to inconsistences in evaluations. This case study could be used as a reference for the load testing conducted and the appropriate material, geometrical, and structural studies conducted. A set of structural guidelines should be created and enforced for historical structures in Canada.
5 Conclusion Two main conclusions from this study are: (1) the sheathing around the building is carrying loads, and (2) the missing and deformed members in the building had minimal structural effect on the vertical load-displacement response of the building. Intervention methods on the absorption building should take the sheathing into consideration and be careful in the event of removal or replacement. The Parks Canada Guidelines and National Building Code of Canada were considered throughout this study [4, 5]. Material, geometrical, and structural properties were all collected in a non-destructive or minordestructive manner. The on-site experimental testing conducted for model validation was done with minimal weight to ensure the structure was not overloaded or caused permanent damages. The minimal differences between the displacements measured on site and in the FEM predictions provide confidence to the validation of the models for use in future studies. This research exposed gaps within current standards and provided a guide to future engineers on how to conduct a structural analysis on a steel structure as standards are developed. Acknowledgement. The authors would like to acknowledge funding from the Natural Sciences and Engineering Research Council of Canada and the University of Calgary’s Geomatics Engineering Department for providing the Lecia BLK 360 for laser scanning at the Turner Valley Gas Plant. Many thanks to Elisa Rubalcava Cobo, from Heritage Conservation, Alberta Culture, the site contact for the absorption building at the Turner Valley Gas Plant, for providing access to the site.
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References 1. Ross S.: Addressing climate change by retrofitting Canada’s existing buildings. Policy Options. Montreal, Canada (2021). https://policyoptions.irpp.org/magazines/june-2021/add ressing-climate-change-by-retrofitting-canadas-existing-buildings/ 2. Goulet, J., Gomez, S.: Report 2: Conserving Federal Heritage Properties. Office of the Auditor General of Canada. Ottawa, Canada (2018). https://www.oagbvg.gc.ca/internet/English/ parl_oag_201811_02_e_43200.html 3. Turner Valley Gas Plant National Historic Site of Canada. Parks Canada. Montreal, Canada. https://www.pc.gc.ca/apps/dfhd/page_nhs_eng.aspx?id=858. Accessed 20 June 2021 4. Canadian Commission on Building and Fire Codes: National Building Code of Canada, 14th ed. National Research Council of Canada (2015) 5. Canada’s Historic Places. Standards and Guidelines, 2nd ed. (2010). https://www.historicp laces.ca/media/18072/81468-parks-s+g-eng-web2.pdf. Accessed 18 Nov 2020 6. Burzic, E., Iskander, G., Duncan, N., Shrive, N.: Geometric survey through laser scanning of a historical building in Alberta. Transforming Construction with Reality Capture Technologies. Fredericton, New Brunswick, Canada (2022). https://doi.org/10.57922/tcrc.607 7. ASTM: ASTM C39/C39M-21 – Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. ASTM, West Conshohocken (2021) 8. ASTM: ASTM E8–04 – Standard Test Methods for Tension Testing of Metallic Materials. ASTM, West Conshohocken (2010) 9. Engineering toolbox, Metal and Alloys – Young’s Modulus of Elasticity, https://www.engine eringtoolbox.com/young-modulus-d_773.html. Accessed 10 Feb 2021 10. 2016 Sinewave Load Tables for Corrugated Metals, Inc. (2016). https://www.corrugated-met als.com/product/sinewave-2-67-x-3-4/#single/0. Accessed 10 Jan 2023
Sensibility Analysis of Traditional Span Frame Lawrence Kauffmann(B) , Jean-Luc Coureau, Alain Cointe, and Philippe Galimard I2M GCE, 351 Cours de la Libération, 33405 Grenoble, Talence, France {lawrence.kauffmann,jean-luc.coureau,alain.cointe, philippe.galimard}@u-bordeaux.fr
Abstract. This article deals with the restoration of the wooden frame of the NotreDame de Paris Cathedral as part of a scientific project after the 2019 burning. The purpose is to conserve the architectural heritage while ensuring the craftsmanship of the medieval age as described in [1], by Thibaut, Caré and Maurin in 2022. In this context, we have reproduced a part of the timber frame on the basis of the original schemes of the nave. Through an in-situ monitoring, this structure represents a study case in order to provide data relative to the kinetics of displacements of this structure composed of green oak. These informations allow to evaluate the global behaviour of the structure and its vulnerability by taking several deformability sources into account. A numerical bar model has been developed by using finite element software, like in the article [2] by Vannucci. P in 2021, to analyse the sensibility of material properties and geometry with data identified experimentally. We have also performed a retro-analysis focused on the axial stiffness of each connection in the model, by fitting data to reproduce the real displacements measured from static tests realized on the wooden frame. Similarly to the full scale tests performed on the article [3, 4] or [5], from full scale tests in-situ, we examine the effects of static vertical forces involving bending moment of the principal beams and including the influence of the scale factor and the global effects of this traditional timber frame. Furthermore, we carried out an experimental campaign consisting of tryout press on different traditional types of joints. The goal was to characterise their stiffnesses and their specific failure modes using images correlation like in the article [6] by Koch and Eisenhut in 2013. Concomitantly, numerical simulation are developed in order to investigate the dependence of the stiffness with contact gaps between the pieces, which is relative to the know-how of the carpenter and moisture content variations. Keywords: Timber frame · Traditional joints · Finite element · Green oak · Characterisation · Images correlation
1 Instruction The catastrophic fire of “Notre Dame de Paris” in April 2019 initiated a restoration and reconstruction project in which several laboratories collaborate. The preservation of our cultural heritage and the respect as closely as possible of the intention of the old master carpenters cope with the modern construction standards, that are essential to © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 458–471, 2024. https://doi.org/10.1007/978-3-031-39450-8_38
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the project of this magnitude. Previous studies like [7], demonstrated the significance of joint stiffnesses in the calculation of overall displacements and force distribution in traditional frame. However, artisanal wood-to-wood connections may present some pathologies, leading to a lack of information relative to their performance in-situ when moisture content can vary, despite their wide use in existing heritage structures. The shift towards modern calculation methods in the field of heritage structures must be accompanied by stringent justifications to eliminate any indeterminacies associated with medieval techniques, despite their proven reliability. We want to examine the influence of the mechanical performance of traditional joint on the structural behaviour, as well as sources of variability. To this end, we will proceed to two scales of analysis. The first is a structural analysis at the macroscopic scale of a frame. The second, a local check design at the local scale relative to the connections. These both studies, which are respectively described in parts 1 and 2, are based on experimental tests which are then reproduced numerically by finite elements in the elastic field. The first part of this article focuses on a full scale replication of the framework span of Notre Dame de Paris. The originality of this structure is the possibility offered to perform a large scale tests and to measure the instantaneous response of the structure under known loading conditions. At first, the global analysis is performed through a 2D simulation of a truss, modelled as 1D bar elements connected by nodal joints. The stiffnesses of this nodal elements are modified to include their influence on the behaviour of structure. The second part of this article is focused on laboratory compression tests on connections at 1/3 scale. The deformations of the surfaces specimens are assessed through image correlation analysis. A method for characterizing joint stiffnesses is proposed and the average value and variability of six samples are estimated. The study then proceeds to the joint check design by joint modelling using finite elements. We try to explain the variability of the experimental results using physical gaps like contact defects between the pieces due to moisture content.
2 Global Analysis of the Main Frame 2.1 Replica of the Historical Span In a collaborative effort with the Professional High School for Building Trades in Felletin (France), a part of the framework Nave of Notre-Dame de Paris, was built under the guidance of carpenters. This structure is a full-scale replica of Span No. 9, placed between the trusses N° 4 and 5, based on the historical plans. The wooden structure is 11 m high on a base of 13 m wide and 3,5 m deep. But the replica serves as a study case rather than a faithful reproduction of the Notre-Dame-de-Paris Framework. In fact, we can enumerate a non-exhaustive lists of differences like the age and the diameter and wood species, the cutting methods of beams, the nature of traditionally joints, mounting history, its natural exposure… The span was erected in December 2020 outside, suspended above the ground and covered with a wooden roof. The truss structure is comprised of two repeating structural units: 2 main trusses and 4 pairs of evenly spaced truss rafters (70 cm interval). It is supported by 4 wall plate bars and 2 consoles, which are anchored to concrete blocks and slabs equivalent to the long-walls of the cathedral. The truss design reflects a clear
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(a)
(b)
Fig. 1. Span replica of the nave (a), Tenon joint gap contact (b).
hierarchy of components. The trusses are comprised of rafters that distribute weight to the main tie-beam which assemblies the rafters and maintains their spacing. This is the connection where the load rate is maximum. The joint which, to facilitate mounting steps, has been chosen to ensure this function is the Tenon-oulice. We will give the closest attention to the mechanical performance of this connection, which is likely to have the greatest impact on the good redistribution of forces between the elements and therefore the overall deformation of the structure. Timber elements are often visible, which facilitate the inspection and the characterization of details and assessment of pathology. After two years, the structure has evolved significantly under its long-term loading. The wood dried out, reduced the beam sections and introduced or reinforced gaps in the contacts connections, like the Fig. 1b. It was also necessary to empty the pockets of water that had been formed in the mortises of the Tenon-oulice joints, which undoubtedly contributed to reinforce the shrinkage in these connections. Finally, the evaluation of in-situ displacements is a crucial aspect of timber structure inspection and is essential to supply a good level of knowledge on the deformations kinetics. A monitoring system recording to displacements and climate conditions provides real-time data according to our needs. Moreover, a series of tacheometer readings taken at periodic intervals, measure the movements of 40 targets distributed on the connections over the two main frames. The use of reflective targets enhances the measurement accuracy to ± 1 mm and provides a comprehensive understanding of the three-dimensional behaviour of the frame over time. 2.2 Static Load Test on Full Scale This study aims to evaluating the behaviour of the structure under proof load test. To do this, the ends of the second third tie-beam were locally solicited at the level of the joints with rafters. Figure 2a shows a picture of the device test and the Fig. 2b represent the diagram of static loading ramp. This article focuses on the results of an asymmetrical loading test on frame N°4.
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sheave block
Hand winch 20°
(a)
Force sensor
7,5m
(b)
Fig. 2. Devise static test (a) Diagram of static loading ramp (b)
The sheave blocks were set at the points of application of the loads with a cable passed in and connected at these ends to a concrete slab on the ground. A hand winch was used to produce a progressive tension where a force sensor was placed to record device. The test is set up at both ends of the third tie-beam to the frame and using onsite measurements, to calculate the vertical load F_v at the nodes with the following equation: Fv = 2.F t .cos(10◦ )
(1)
This test needs the installation of two sensors (accurate at 0.05 mm) and real-time signal processing software and their calibration. To localise the sensors optimally, a structural calculation type simulation is used to evaluate the stresses and deformations of the loading configuration. This simulation is presented in part 2.3. Four measurement points on the tie-beam and the rafters were identified for this loading (vectors drawn on the Fig. 4.a): • The first point corresponds to the maximum deflection (yellow vector) and the second at minimum inflection (red vector) under the main tie-beam of the frame N°4. Two resistive sensors of displacement are added, called 1st sensor and the 2nd sensor respectively at points 1 and 2. • The two other points of the loading beam, the point 3 in green and point 4 in blue, which are less easily accessible with classic sensors, are respectively represented by the 1st and 2nd marker used to the tacheometer measurement drawn Fig. 3d. During the same loading cycle, the sensors signals are obtained per point in volts. The first one, Fig. 3.a, represented the load measured by the force cell, while the two second (Fig. 3b and 3c) represented the absolute vertical deflection of the 1st and 2nd sensors.
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(b)
(c)
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Fig. 3. Signal of load sensor in N (a), Signal of displacements of the 1st sensor (b), Signal of displacements of the 2nd sensor (c), Diagram of tacheometer implantation (d).
Representative data are summarized in the Table 1 for each cycle. The displacements measured by monitoring are taken for a load measured at Ft = 9000 N (Fig. 3a, red line) or, with Eq. 1, Fv = 17800 N. This value is choosen because of the corresponding displacement signal Fig. 3b was cut after 2mm due to the end of the LVDT sensor. Those measured with the total station, at the maximum load of cycles 3 and 4, respectively for Ft = 10500 N and 11500 or approximatively for a vertical load of Fv = 20700 N and 22600 N. The average values are balanced by the load and expressed for an equivalent load of Fv = 20 KN in the last column. Table 1. Recapitulative table of the measurements deflection by load cycle. Cycles
1st sensor
2nd sensor
1st marker
2nd marker
1 cycle
−1.90 mm
−0.32 mm
2 cycle
−1.93 mm
−0.26 mm
3 cycle
−1.96 mm
−0.19 mm
−2,0 ± 0.5 mm
3,3 ± 0.5 mm
4 cycle
−1.95 mm
−0.29 mm
−2,7 ± 0.5 mm
3,1 ± 0.5 mm
Prediction at Fv = 20KN
−1.94 mm
−0.27 mm
−2.1 mm
2.9 mm
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2.3 Finite-Elements Modelling This part proposes the use a numerical bar model to replicate the behaviour of frame No. 4 during a static test. The model is developed with Cast3M and it consists in bar elements connected each other, which takes into account the elastic properties of timber. By limiting the analysis to static and elastic behaviour, the model corresponds to the one use by design office. We reproduce the frame and we implement the average sections and properties of the oak beams [8]. The boundary conditions of the truss and the consoles were also defined: the consoles were placed in single contact with the ground and the truss beam are supported vertically by the walls, corresponding to simply supported beam located at the wall plate bars connections are also defined hinged. In fact, the historical frames are designed with many elements where contacts are present, which produces low bending joint stiffnesses. Nevertheless, the axial stiffness should be investigated, because wood has different modulus according to force direction in the joints.
(a)
(b)
Fig. 4. Truss deformation (a), Points deflection as a function of the average stiffness K (N/mm) (b).
The numerical computations were then used to supply the elastic response of the system by adding the static load from the full scale test (20 KN), the own weight is not taken into account. The results, Fig. 4a, showed that the deformations agreed with the experimental data (sign of the tacheometer measures), however the experimental deflections at the measurement points were two times upper than the hinged model results. There first results inform us about the path taken by the forces and about the most stressed joint in tension (6 KN) and compression (-11 KN) between the rafter and the truss beam. The offset between the numerical and experimental results maybe influence by inaccuracies with which the model describes the global rigidity of the structure and therefore the real distribution of the loads in the elements. This maybe mainly influences by material properties or stiffness of joints or the both at the same time.
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Connections should be considered as semi-rigid connections. We add stiffnesses defined in the axial direction of one of the two beams involved. According to [9], we have defined two stiffnesses for each joints. We consider at first an isotropic value of both directions and they are the same all over the truss. The Fig. 4(b) displays 4 curves for each measurement points which represent the displacements as a function of the average stiffnesses according to decade variation (as log 10 (Kmean )). As average stiffnesses increases, the curves reach the asymptotic value fixed by the hinged model (for log10 K = 9). We finally retro-analyse by assessing the magnitude of the displacements obtained experimentally. The values measured with the tacheometer are not precise enough for this method. By taking the displacements measured at points 1 and 2, on the curve (red and yellow) of the semi-rigid model, we finally obtain an average value of 1e7 N/m. However, it was clear that the assembly stiffnesses are neither isotropic not homogeneous. So to test the influence of the variability of these stiffnesses, the Monte-Carlo method was employed similarly at the article [10]. This method consists in changing the parameter of a type of element according to it’s a Gaussian law and randomly distributing these parameters in the model. To reproduce a realistic dispersion of the parameters, an average value and a standard deviation were defined. The retro-analysis of the translational stiffnesses of an assembly revealed an average value of 1e7N/m. To obtain the Fig. 5a we generate a coefficient of variance equivalent to 10%. This allows the orthotropic stiffnesses in the connections. In order to compare the effects of variability of Young’s modulus, at first, a gaussian law is generated Fig. 5b. It referred to European recommendations for timber D30 of third class [11]. The first model tested is based on the hinged model without joint stiffnesses but including the variability of the Young’s Modulus. The second model have uniform Young’s modulus distribution and including the variability of the orthotropic joints stiffnesses.
Fig. 5. Gaussian of the Young modulus (a), Gaussian for the stiffnesses variability (N/m) (b).
We investigate the influence of parameters and their variations on elastic response through the use of 1000 calculations of structure. A large number of structural response samples were obtained, which were represented in the form of cumulative frequencies curves. The average displacements and variance coefficient provided information on the influence of the parameters and their variations on the elastic response (Fig. 6).
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Fig. 6. Cumulative frequency of the point 1 Table 2. Summary table of input/output coefficients. Input 1st model
Input 2nd model
Output 1st model
Output 2nd model
Mean value
11e9 MPa
1e7 N/m
−1.21mm
−1.96mm
COV
8%
10%
9.4%
4%
The variability of the mechanical quality of wood seems to have little influence on the global response of the structure. However, the variation coefficient of the output parameters, shown that, for 10% of variability, the stifness influence is also insignificant. Furthermore, the lack of knowledge and in-situ experimental data on the performance of traditional assemblies will present challenges in informing the model on a case-by-case basis. To overcome these challenges, we suggest further investigation into the local scale assembly to characterise a large number of samples (Table 2).
3 Investigation of a Traditional Joint 3.1 Experimental Tests The design of wood-to-wood joints is studied in order to evaluate the performance of the different types of assembly focusing on the most stressed assembly, the Tenon-oulice which connects the rafters to tie-beam in the replica described part 1.1. It is a joint oriented at 55° with a triangular Tenon cut square with the current rafter section drawn in the Fig. 9a. An experimental campaign was performed to test Tenon-oulice specimens in maritime pine presented in Fig. 7a. Its scale corresponds to 1/3 of the real connection in order to test the experimental protocol. The goal is to provide experimental support to estimate the joint stiffness as it is proposed in the article [12] that treat of the major role of the joint in the structural behaviour. During this study we decide to limit the characterization of the stiffness at the longitudinal rafter direction.
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Fig. 7. Picture of the Tenon-oulice type joint (a), Rupture mode of the end of truss beam (b).
The specimen was placed on a rigid support, with the rafter portion in the axis of the cylinder. The loading head allow rotations in order to conserve the contact with the rafter. A plate composed of teflon was used to allow the sliding between tie-beam and the support. The loading ramp is performed by displacement controlled at a speed equal to 0.8 mm/min, and two cycles were completed at 30% of the failure load, in order to obtain the linear elastic regime. A force sensor was used to measure the load at each displacement increments. The results of the test showed a crushing of the tenon extremity which were generally accompanied by a rupture of the end of truss beam represented Fig. 7a. The kinematics of the deformations were tracked image correlation, which recorded the displacements at a frequency of 2 Hz with a capacity of 1.4 × 1.4 thousand pixels/picture. Beforehand, a black speckles applied to the surface. The pattern formed by the speckle is analysed one by one, making possible the reconstruction of the displacements at the surface of the pieces as it was done in the article [13] and [14]. The absolute displacement of each pixel with respect to the reference image at a vertical load of 10 KN is shown in Fig. 8b and the interest area is denoted by the white rectangle projected along the rafter, in the vertical characterization direction. 3.2 Characterization of Joint Stiffnesses The displacements field in the interest area, are normalize in the elastic field. These data are averaged per pixel to obtain a flexibility field. We then reduce the problem to one dimension by averaging the vertical displacement for each section of the interest area. Therefore, we obtain, Fig. 8a the evolution of the axial flexibility of the joint along the neutral axis. It supply interesting approach to characterise the axial stiffness assumed to the rafter between the point A and B.
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Fig. 8. Average rigidity by section along the interest zone (a), Vertical displacement shading maps (b).
Three distinct linear phases may be declined in the Fig. 8a. The second phase can be seen as an image of the joint. It may be also regarded as the mixed zone, between the rafter and the tie-beam. We can therefore evaluate a critical length LAB (which starts from point A to point B, along the rafter neutral axis) and which represents the stiffness variation according to wooden pieces and contact zones. This transition zone can be represented by a spring between points A and point B which is equal to the inverse of the stiffness KX ,AB , Fig. 8b.
X
A
B
Fig. 9. Equivalent bar model and local stiffness.
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Experimental stiffness
A5
32306 N/mm
A6
23555 N/mm
A8
9352 N/mm
A9
33666 N/mm
A10
14260 N/mm
A11
43281 N/mm
mean
26070 N/mm
COV
49%
3.3 Numerical Twins of the Joint We aim at using 3D finite-elements to estimate the real stiffness of the Tenon-oulice joint. We reproduce the geometry and the corresponding loading with boundary conditions as part of linear elasticity by using mechanical properties of the Maritime pin which was investigated in the experimental campaign. The unilateral contact conditions with the support were reproduced, respectively, in blue and red on the Fig. 10a according to the experimental configuration Fig. 5a. The load is imposed uniformly on the upper section of the rafter.
(a)
(b)
Fig. 10. boundary conditions and loading surface (a), Displacements field in the rafter direction with perfect contacts (b).
The displacements field, show Fig. 9b, in the rafter direction is obtained with perfect contacts. If we compare the numerical results with the experimental one, we obtained a
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similar evolution of the axial stiffness along the neutral axis. Nevertheless, the magnitude of the signal seems to be low (blue Fig. 10b) for the numerical model idealising perfect contact between piece of wood. The interest of such a model is to be able to consider contact defects such as the joint gap due to the drying, Fig. 1(b). In fact, wood is a hygroscopic material: the change of humidity in the hygroscopic domain produces swelling and shrinkage in the wood. The longitudinal shrinkage coefficient is approximately 0.01%/%, the radial and tangential coefficients of 0.3%/%. A drying of 10% is modeled, by taking into account a uniform distribution of the moisture content in the sections. The Fig. 11b represented the displacements field in the rafter direction with the shrinkage of the mesh. A special attention should be paid to the contact between the mortice and the Tenon. Indeed, the shift due to the shrinkage modifies the mechanic involved between the beams. Then another simulation is launched with the load as part of elasticity. The difference between both simulations, give the displacements field reflecting the gap joint due to the drying. The average of flexibility curves along the neutral fibre obtained with and without shrinkage (continuous curves) are then superimposed on the experimental results (dotted curves) on the Fig. 11a. The flexibility curve resulted exceeds some experimental curves. The implemented phenomena of shrinkage help to explain their variability (COV Table 3).
(a)
(b)
Fig. 11. Experimental and numerical mean line flexibility (a), Displacements field in the rafter direction with shrinkage (b).
4 Conclusion The sturdy propose an overview on full-scale tests performed on a replica of a part of the carpentery of Notre Dame de Paris. It aims at measuring the displacements from static proof loading. Classic design rules of structure calculations are not sufficient to describe the real linear behavior without considering semi-rigid connection between bars. However, the literature does not provide an accurate prediction of the traditional connection stiffness. The proposed retro-analysis reproduce the global static rigidity of the structure by imposing an isotropic translation stiffness in its nodes. Although the
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new model can give the deflection of one or two points, it is uncertain that it restores the entire frame behaviour with a single isotropic and elastic value of the joint stiffness. Finally, we have explored, the influence of the orthotropic stiffnesses variability of the connections on the overall structure behavior. The comparison with the influence with the Young modulus variability emphasizes the need to characterize the stiffnesses of wood-wood assemblies. Consequently, we have proposed a method to characterize the stiffnesses of these connections. These experiments allowed us to determine the variability of rigidity along one bar representative of the distribution of the forces between the upper and lower part of the joint. Subsequently, a numerical twin was established to model the joint behavior. This approach, from experimental to digital, enabling better-controlled 3D simulation, coupled with a characterization method. This model can be declined to evaluate the stiffnesses of the traditional joints according to their typology and its own loading. In addition, the possibility of adding defects to the geometry or contacts offers a way to reconstruct the failure tree of the real trusts. This can subsequently be used to calibrate the 2D frame model by restoring the equivalent stiffness to the nodes and thus provide useful knowledge for the safety analysis of the architectural heritage diagnosis.
References 1. Thibaut, B., Caré, S., Maurin, E.: Oak beams in medieval frameworks: constraints and advantages for restoration. J. Cult. Herit. (2022) 2. Vannucci, P.: A study on the structural functioning of the ancient charpente of Notre-Dame, with a historical perspective. J. Cult. Herit. 49 (2021) 3. Suzuki, Y., Maeno, M.: Structural mechanism of traditional wooden frames by dynamic and static tests. Struct. Control Health Monitor. 13(1), 508–522 (2006). https://doi.org/10.1002/ stc.153 4. Arangjelovski, T., Gramatikov, K., Docevska, M.: Assessment of damaged timber structures using proof load test – experience from case studies. Constr. Build. Mater. 101, 1271–1277 (2015). https://doi.org/10.1016/j.conbuildmat.2015.07.010 5. Richard, J., Schmidt Robert, G., Erikson, A.: Behaviour of traditional timber frame sructures, report on research co-sponsored by: Department of Civil and Architectural Engineering University of Wyoming Laramie, USDA NRI/CGP (2003) 6. Koch, H., Eisenhut, L., Seim, W.: Multi-mode failure of form-fitting timber connections – Experimental and numerical studies on the tapered tenon joint. Eng. Struct. 48, 727–738 (2013). https://doi.org/10.1016/j.engstruct.2012.12.002 7. Descamps, T., Avez, C., Carpentier, O., Antczak, E., Jeong, G.Y.: Historic timber roofs modelling: prosthesis and resin repairs. Wiadomosci Konserwatorskie – J. Herit. Conserv. (2016) 8. Guitard, D.: mécanique du materiau bois et composites, CEPAD, pp. 110–113 (1987) 9. Jorissen, A.J.M., den Hamer, J., Leijten, A.J.M.: Traditional timber frames. In: 2014 World Conference on Timber Engineering, FPInnovations (2014) 10. Kefei, W., Hongwei, X., Fuzheng, O.: A reliability analysis framework with Monte Carlo simulation for weld structure of crane’s beam. In: AIP Conference Proceedings (2018) 11. The European Union Per Regulation 305/2011, EN 1995-1-1: Design of timber structures Part 1-1: General - Common rules and rules for buildings (2004) 12. Branco, M., Descamps, T.: Analysis and strengthening of carpentry joints. Constr. Build. Mater. 97 (2015)
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13. Braun, M., Pantscharowitsch, M., Kromoser, B.: Experimental investigations on the loadbearing behaviour of traditional and newly developed step joints for timber structures. Constr. Build. Mater. 323 (2022) 14. Komlan, R.T.: Caractérisation expérimentale des propriétés mécaniques d’assemblages à tenon-mortaise par mesures de champs cinématiques. 40èmes Rencontres Universitaires de Génie Civil (2022)
Structural Behaviour Assessment of the Anastylosis Reconstruction of the Ruins of Kfar Synagogue in Bar’am (Israel) Yaacov Schaffer1 , Raffaele Italia1 , Aharon Levi1 , Meir Ronen2(B) , Matteo Salvalaggio3 , Maria Rosa Valluzzi3 , Marco Mocellini4 , Sonia Bellin4 , and Filippo Casarin4 1 Schaffer & Ronen Engineers Ltd., 34 Ben Yehuda, 9423001 Jerusalem, Israel 2 Western Galilee College, Hamichlala Road, 2412101 Akko, Israel
[email protected]
3 Department of Cultural Heritage, University of Padova, Piazza Capitaniato 7, 35139 Padova,
Italy 4 R-Struct Engineering srl, Via Vigonovese 31, 35127 Padova, Italy
Abstract. The ruins of the Kfar synagogue are located inside Bar’am National Park, in Northern Israel, near the Lebanon border, once part of an ancient Jewish village inhabited from 200 B.C. to Middle Age. The synagogue dates back to the 3rd century A.D. and was built using stones elements from pre-existing RomanByzantine public buildings. The building was heavily damaged by the Galilee Earthquake in 1837, which caused the collapse of the roof and part of walls and columns. Nowadays the ruins include 4 columns of the front porch, the main façade complete up to the second floor and part of inner walls and columns, while the entablature is almost completely collapsed.Considering the important historical value of the entablature - a unique example in Israel - the Bar’am National Park Authority decided to start historical, architectural, and structural studies with the aim of restoring its remains, planning to reconstruct the ancient front porch by anastylosis. The structural behavior of the remains has been analyzed through the Distinct Element Method (DEM), introducing the anastylosis reconstruction of the entablature to predict the seismic response of resulting structure. The stone elements have been modelled through rigid blocks and non-linear deformable interfaces; dynamic analysis has been performed based on local standard spectrum and accelerograms compatible with the seismological history and site soil condition.DEM simulation allowed to evaluate the seismic behavior of the reconstructed configuration, evaluating the opportunity of i) using monolithic or multidrum new columns for the bearing of reconstructed entablature and ii) introducing connections between stone elements, addressing the design phase. Keywords: Anastylosis · Ancient synagogue · Distinct element modeling · Rigid block analysis · Time history analysis
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 472–483, 2024. https://doi.org/10.1007/978-3-031-39450-8_39
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1 Introduction The main aim of the study discussed in this paper concerns the conservation and partly reconstruction of the Ancient Kfar Synagogue in the National Park of Bar’am, whose last known conservation activities were carried out in the 80s. Historical, architectural and structural studies have been recently started by the Bar’am National Park, in order to promote the restoration of the remains and the reconstruction of the collapsed entablature, funded by Israeli National Park Authority and private donations. In the framework of these activities, this study helped to evaluate the structural behavior of the remains and to address to following design phases. The preservation of the archaeological heritage requires a particular care, in order to keep unaltered its historical, economic and social values. However, such conservation activities must be addressed also to the vulnerability of the structure to ordinary (e.g., weathering) and exceptional (e.g., earthquakes) events. In such a framework, the reconstruction design of the Kfar Synagogue porch requires i) the detailed anastylosis of the available stone remains and new material additions and ii) the structural assessment of the viable reconstruction approaches. The structural assessment of the Kfar Synagogue was performed via the Distinct Element Modeling (DEM). Since nowadays the structure consists of incomplete archaeological remains, its structural capacity relies on its equilibrium capacity rather than material strength. Such capacity was assessed by time-history nonlinear dynamic analyses, for both current and reassembled (i.e., anastylosis) status. 1.1 The Bar’am National Park The remains of the ancient Kfar Synagogue in Bar’am, - apart from the remains of a smaller synagogue - have been already mentioned in the Middle Ages by Jewish travelers and have been excavated in the village of Bar’am. The archaeological remains of the synagogue were excavated by the historians C. Watzinger and H. Kohl at the beginning of the XIX century and dated to the II century BC (based on their architectural decorations) [1]. The archeologists N. Avigad and G.Foerster, completed the excavations in the 60s as part of the works for the creation of the ‘Bar’am National Park’. The archeologists G. Foerster and Y.Tsafrir dated the synagogue to the II and III centuries CE [2], whereas the archeologist Z. Ma‘oz concluded that it was the first typical architecture building of the Galilean synagogues [3]. The Kfar Synagogue has not been dated on the basis of scientific archaeological data yet. 1.2 The Current Remains of the Kfar Synagogue The current remains of the Kfar Synagogue, heavily damaged by the Galilee earthquake in 1837, consist of the ancient main façade (approximately 5 m tall), with the eastern section of its porch partially still standing (Fig. 1a). The façade is made of large limestone blocks, approximately 50-cm thick, whilst doors lintels and the central arch are made of 70-cm size elements. The front of the building has a large porch, which is an unusual for Byzantium Period synagogues. Based on the original layout, totally or partially new
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columns were installed during the reconstruction of the 60s. Four are still standing: a larger corner one, with rectangular section, and three slender ones with a circular base, approximately 60cm-diameter, with a height similar to the façade. The twin corner column appears halved.
(a)
(b)
Fig. 1. The Kfar Synagogue: a) main façade and porch of the current remains; b) inner yard.
Bar’am Nation Park Authority plans to proceed with the restoration of the remains, including the reconstruction by anastylosis of the ancient entablature, which has been recomposed on the ground and waits for the repositioning on top of the columns. The Synagogue of Baraam is a 3rd century building (A.E.C.), built with RomanByzantine elements, obtained from pre-existing public buildings. In particular, the type of building with a Portico is unique in Israel, and during the 1960s it underwent reconstruction with methods and materials currently now recognized as non-conservative by scientific community. The aim of the work is to carry out a seismic improvement of the building, with calculation programs and innovative methods and materials.
2 Materials and Method The structural design of the anastylosis of archaeological remains can be challenging since such structures are lying in an incomplete form and thus, they do not follow the rules of traditional intervention design. Moreover, their structural (and seismic) behavior relies on the equilibrium capacity more than material strength, which is in a poor conservation status due to exposure to weathering and time [4, 5]. The structural design of the anastylosis of Kfar Synagogue entablature has thus been assessed via the Distinct Element Method, a powerful tool able to detect the potential rocking behavior of the structural components and their possible overturning. Once estimated the seismic action according to Israeli code [6], compatible time histories were obtained by natural seismic records of the ESM European Strong Motion Database [7]. Dynamic nonlinear analyses were conducted, and outcomes processed as control points displacements in function of time. Rocking and residual displacements were detected, allowing to assess the structural and seismic behavior of the current remains and the reassembled configurations. The comparison of results permitted to select the proper intervention for the reconstruction of the porch and entablature of Kfar Synagogue.
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2.1 Distinct Element Model of the Kfar Synagogue The Distinct Element Model of the Kfar Synagogue has been constructed in the framework of the Itasca 3DEC code [8], which proved to be an effective tool for the simulation of dry block masonry [9]. Stone blocks were modeled as rigid blocks (assuming unlimited compressive strength), whereas nonlinear behavior was lumped at deformable interfaces according to the Mohr-Coulomb law, with no tensile strength (because the consistency of mortar is unknown). Since no destructive tests have been provided, material characterization was based on scientific literature data for the archaeological block masonry and columns [10–12], crosschecked with numerical modal outcomes (i.e., plausibility of mode shapes and frequencies) [5]. The main aim of the paper is the structural assessment of the reassembled configurations of the entablature and porch, also by evaluating the use of fastening systems. Five models were constructed and evaluated, as described in Table 1 and Fig. 2. The AsB model simulates the current status of the Kfar Synagogue. Four reconstruction scenarios were simulated, based on monolithic or multi-drum design of the new columns of the porch, without (MN-B and DR-B) or with (MN-R and DR-R) fastening systems. Reconstructed columns were assumed made of new stone, with optimal matching between blocks mutual faces. Each multi-drum new column was composed of a basement, four drums and the capital; each monolithic column was made of a unique element instead. These hypotheses were made as boundary scenarios, to detect benefits and drawbacks of the two structural approaches.
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Fig. 2. 3D Distinct Element Model of Kfar Synagogue: a) current remains (AsB) b) detail of reconstructed entablature, c) monolithic columns models (DR-B and DR-R, in transparency), d) multi-drum columns models (MN-B and MN-R, in transparency).
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Current State
Design assumptions
Anastylosis Dry assembling without fasteners
Dry assembling with steel fasteners
AsB
-
-
-
-
Multi-drum columns
MN-B
MN-R
-
Monolithic columns
DR-B
DR-R
2.2 Material Characterization Connectors were assumed made of titanium, as successfully applied in the Parthenon retrofitting [13], since was proven to be mechanically and chemically compatible with ancient stone elements. Based on the studies of [14, 15], Grade 2 B348 Titanium was chosen for ∅ 16 mm a) 10-cm long bars inserted between drums and base (DR-R) or b) 150-cm long rod retaining the monolithic columns (MN-R). Slip model for connectors was derived from the study about granite-hydraulic mortar behavior [16]. As practiced in the reassembling of the columns of the Temple of Apollo Pythios in Gortyn [4], properties of axial reinforcements elements used in the 3DEC code were derived according to [17]. Table 2 reports the main characteristics of the materials. Table 2. Current state and reassembled layouts studied. Block interface
Connectors Mortar-stone interface
Titanium
jkn [Pa/m]
jks [Pa/m]
Friction angle [°]
c [MPa]
µ [-]
E [GPa] and v [-]
fy [MPa]
Wall blocks
3.2•109
1.6•109
30
-
-
-
-
Columns blocks
109
109
30
0.359
0.630
105, 0.32 275
2.3 Characterization of the Seismic Action The site of Bar’am is located in the Upper Galilee region, geologically characterized by dolomite and limestone rock deposits; a B soil category was hence assumed. This is a seismic prone area close to Safed, where various seismic events have been recorded. According to [18], the Hula fault is crossing such area, and, among the many, the following earthquakes (year, surface seismic magnitude MS or magnitude MW ) were felt: 1759 Ms = 6.5, 1837 Ms = 7.4, 1927 Ms = 6.2, 2013 MW = 3.7, 2018 MW = 4.6.
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The seismic action was calculated according to Israeli code [6]. The Peak Ground Acceleration (PGA) expected for the site is equal to 0.14 g; spectral acceleration at ground level was calculated as 0.17 g for the B soil category (period T = 0). Figure 3a reports the elastic spectrum calculated for Life Limit State (LLS). Seven couples (North-South and East-West directions) of natural time histories were obtained through the matching within the European Strong Motion database via the RexelWEB service [7], for expected magnitude (6-to-7) and soil class B. Figure 3b shows a sample of such velocigrams couples. Viscous damping was neglected in TH analyses, since it was evaluated as a proper solution for the simulation of free-standing columns undergoing the strong motion part of an earthquake [10].
Fig. 3. Characterization of seismic action for the B soil category: a) LLS elastic spectrum; b) a sample of the compatible natural velocigrams.
3 Results 3.1 Reassembled Configuration The reconstruction of the porch entablature consists in the anastylosis of the ancient stone elements and their eventual completion with new stone (Fig. 4a). Moreover, new columns are installed, apart the C8 one, underneath the only portion of the entablature still in place. Hence, such reconstruction bears the two corners of the main façade. Prior to the anastylosis of the entire porch, i.e., columns and entablature, the latter one was reassembled separately (Fig. 4b), in order to detect the lacks and fill them. Incomplete elements were reconstructed by their re-shaping with addition of the newstone elements and the insertion of inner steel ties among them (Fig. 4c). Although the preliminary restoration project is defined, the structural design, based on both static and seismic conditions, should support the executive design of the anastylosis procedure. In particular, the potential adoption of multi-drum or monolithic columns and fastening systems. 3.2 Modal Analysis Modal analysis was first carried out to characterize the dynamic behavior of the Kfar Synagogue remains (i.e., façade wall and columns no. 2, 3, 4, 8, Fig. 2a). Table 3
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(a)
(b)
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Fig. 4. Anastylosis of the synagogue porch entablature: a) current remains and anastylosis design (in transparent grey), courtesy of Architect Amir Freundlich and Conservator David Zell, b) reconstruction of the entablature, c) detail of elements reconstruction with steel ties.
reports the frequency values of the first mode shapes of the columns (simple bending) and façade (simple out-of-plane bending). Outcomes revealed that interface stiffness can significantly affect frequency values, especially when higher than 109 Pa/m, for columns, and 6.4•109 Pa/m, for façade blocks. Since no experimental characterization was available, reference values of normal and shear stiffnesses equal to 109 Pa/m were assumed for columns interfaces [10], whereas 3.2•109 Pa/m and 1.6•109 Pa/m were assumed for façade blocks. Although such values still need to be updated based on in-situ investigations, in this framework a former plausibility check was carried out [5]. 3.3 Time-History Analysis Nonlinear time-history analyses (THA) were conducted for the five configurations (AsB, MN-B, MN-R, DR-B, DR-R). In this sub-section, results for a sample velocigram are presented. Figure 2a-b describe the position of the control points. The AsB model, i.e., the one which simulates current remains status, was able to withstand the 7 velocigram couples compatible with LLS spectrum (PGA = 0.17 g), by the production of rocking phenomena without equilibrium loss (Fig. 5). The largest displacements were recorded for column C3, which is the slenderest among the four still standing. Columns C4 and C2 showed more limited displacements due to lower height and larger section, respectively. The smallest displacements were detected in column C8, which benefits of a lintel to façade eastern corner. Façade and central arch didn’t display significant movements instead. The AsB model was able to stand against the seven couples of natural velocigrams compatible with LLS state spectrum of B soil, i.e., the expected seismic action, according to [19]. This is in accordance with the fact that such structural configuration is still standing nowadays.
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Table 3. Frequency values of structural components in function of interface stiffnesses (in italic values selected for the final model). First frequency values [Hz] Component
Interface normal and shear stiffness jkn and jks [Pa/m] 108 6.4 • 108 109 6.4 • 109 108
3.2 • 108
109
3.2 • 109
C2
1.11
2.80
3.51
8.66
C3
1.14
2.88
3.61
9.13
C4
1.85
4.67
5.87
14.78
C8
1.16
2.92
3.66
9.25
Interface normal and shear stiffness jkn and jks [Pa/m]
Façade
109
1.6 • 109
3.2 • 109
6.4 • 109
5 • 108
9 • 108
1.6 • 109
3.2 • 109
3.17
4.07
5.76
8.15
Fig. 5. X- and Y-displacement of control points in function of velocity time-history input: arch keystone, eastern corner of façade, columns top.
The reassembled configurations, i.e., MN-B, MN-R, DR-B, DR-R, were assessed for the same seismic action. From a macroscopic point of view, the four reconstruction scenarios can withstand the expected LLS seismic action for a B category soil. The
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component most vulnerable to seismic shocks was the two-ring lintel arch. Their global displacements (i.e., not relative to base motion) were recorded and plotted for the four reconstruction scenarios (Fig. 6). It emerged that the highest settlements occurred in the arch crown (three voussoirs). The adoption of multi-drum columns (DR-B) induced larger displacement at the skewbacks and a larger slipping of the keystone, compared to monolithic assumption (MN-B). The use of fastening systems appeared to be capable of reducing such settlements, although the assumption of monolithic columns (with a 1.5m-long titanium rope) was still preferable compared to drums connected via titanium bars. Figure 7 shows the settlements of the arch keystone and the relative displacement of skewbacks. In the case of bare anastylosis procedures (i.e., no fastenings), residual vertical (Z) settlement of keystone is higher than 3 cm (DR-B) or 1 cm (MN-B), due also to the mutual turning away of skewbacks along springing line. The best benefit in terms of settlement reduction is confirmed in the case of MN-R, where both skewbacks and keystone recorded negligible displacements.
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(b)
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(d)
Fig. 6. Displacement magnitude diagram [meters] of reconstructed two-ring arch: a) DR-B, b) DR-R, c) MN-B, d) MN-R.
Finally, the validity of the rigid block assumption (unlimited compressive strength with deformability neglected) was assessed by checking that compressive stresses aroused during THA did not overcome the compressive strength of stone blocks. Maximum compressive stresses detected were equal to 1.2 MPa and 1.8 MPa, for MN-R and DR-R models, respectively. Such values were found compatible with expected compressive strength of stone blocks, expected higher than 6 MPa. Interfaces shear failure and sliding were detected, according to the aim of the study of assessing the equilibrium capacity of the reconstruction other than strength provided by materials.
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(a)
(b)
(c)
(d)
Fig. 7. Ground referenced displacement of key stone (on left) and relative settlements of skewbacks (on right, moving towards if positive, away if negative) for 0.17g compatible seismic action: a) DR-B, b) DR-R, c) MN-B, d) MN-R.
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4 Conclusions The DE numerical modeling performed for the structural and seismic design of Kfar Synagogue anastylosis permitted to assess the proper approach for the reconstruction by anastylosis of the synagogue porch and entablature. The current remains should be capable of withstanding the expected seismic action, as witnessed by their conservation until the current days. The reconstruction of the outer entablature can thus rely on the existing façade, whereas a new porch colonnade must be assembled. The use of multi-drum and monolithic columns were assessed, in both fastened/non-fastened configurations with/without ∅ 16-mm titanium bars or rods. It was revealed that, for the expected LLS seismic action (i.e., 0.17g PGA), all reconstruction approaches appeared capable of bearing the seismic loads. However, the use of multi-drum columns could lead to higher deformability than monolithic ones, which induced also larger slips between arch skewbacks and key stone settlements. The use of titanium bars (DR models) or rods (MN models) can reduce the displacements suffered. The configuration MN-R with monolithic columns and a 1.5m-long titanium rod to foundation resulted the layout able to provide the lower displacements. Hence, although free-standing multi-drum columns showed to be capable of withstanding higher base acceleration compared to monolithic counterparts (based also on frequency content of the time-history record) [20, 21], the latter ones should be preferable in the reconstruction of the Kfar Synagogue porch, due to their capacity of producing limited displacement (at expected LLS seismic action). The study discussed in this paper was aimed at guiding the structural design of the anastylosis of the Kfar Synagogue porch and entablature. Thanks to the distinct element modeling of the archaeological remains and anastylosis hypothesis, it was possible to detect the potential benefits of some engineering approaches, i.e., the use of multi-drum and monolithic columns, with or without the use of fasteners. In provision of the executive design of the anastylosis, detailed characterization of the soil and the structural materials (e.g., ambient vibration tests, tests on stone samples) will be performed and provided. In such a way, the seismic action will be adjusted, as well as blocks interfaces laws (i.e., stiffnesses and friction angle). Furthermore, the sizing of titanium fasteners will be optimized, based on iterative analyses on acting shear and tensile forces.
References 1. Kohl, H., Watzinger, C.: Antike Synagogen in Galilaea (1916) 2. Foerster, G.: Has there indeed been a revolution in the dating of galilean synagogues? In: Levine, L. (ed.) Continuity and Renewal: Jews and Judaism in Byzantine-Christian Palestine, pp. 526–529. Hebrew University, Jerusalem, Yad Ben-Zvi and Dinur Center for the Study of Jewish History (2004) 3. Ma’oz, Z.U.: On ancient synagogues in Galilee and the Golan. Archaostyle Sci. Res. Ser. 16. 22–44 (2017), Prof. Archeologist Mordechai Aviam (Israel Antiquities Authority) and Archeologist Yosi Bordowicz (Israel Nature and Parks Authority) 4. Salvalaggio, M., Bonetto, J., Zampar, M., Valluzzi, M.R.: Numerical prediction of the seismic behavior of reassembled columns in ancient structures: an anastylosis model for the temple of apollo Pythios in Gortyn (Crete). Heritage 4, 3421–3441 (2021). https://doi.org/10.3390/ heritage4040190
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5. Valluzzi, M.R., Salvalaggio, M., Lorenzoni, F., Politi, M., Boaga, J.: The Engineering approach to conservation of massive archaeological structures in seismic areas: the apollo nymphaeum in Hierapolis of Phrygia. Int. J. Archit. Herit. 00, 1–17 (2022). https://doi.org/ 10.1080/15583058.2022.2056545 6. The Standards Institution of Israel: Israel Standard SI 413 - Amendment No. 5. Design Provisions for Earthquake Resistance of Structures, Israel (2013) 7. Sgobba, S., et al.: The online graphical user interface of REXELweb for the selection of accelerograms from the Engineering Strong Motion database (ESM). In: 39° Convegno Nazionale Gruppo Nazionale Geofisica della Terra Solida (GNGTS), 22 – 24 giugno 2021 (2021) 8. Itasca Consulting Group Inc.: 3DEC 5.0: 3-Dimensional Distinct Element Code, Theory and Background, (2013) 9. Colombo, C., Savalle, N., Mehrotra, A., Funari, M.F., Lourenço, P.B.: Experimental, numerical and analytical investigations of masonry corners: Influence of the horizontal pseudo-static load orientation. Constr. Build. Mater. 344, 127969 (2022). https://doi.org/10.1016/j.conbui ldmat.2022.127969 10. Papantonopoulos, C., Psycharis, I.N., Papastamatiou, D.Y., Lemos, J.V., Mouzakis, H.P.: Numerical prediction of the earthquake response of classical columns using the distinct element method. Earthq. Eng. Struct. Dyn. 31, 1699–1717 (2002). https://doi.org/10.1002/ eqe.185 11. Kim, J., Lorenzoni, F., Salvalaggio, M., Valluzzi, M.R.: Seismic vulnerability assessment of free-standing massive masonry columns by the 3D discrete element method. Eng. Struct. 246, 113004 (2021). https://doi.org/10.1016/j.engstruct.2021.113004 12. Lemos, J.V.: Discrete element modeling of masonry structures. Int. J. Archit. Herit. 1, 190–213 (2007). https://doi.org/10.1080/15583050601176868 13. LZambas, C.: Structural repairs to the monuments of the acropolis - the Parthenon. Proc. Inst. Civil Eng. Civil Eng. 92(4), 166–176 (1992). https://doi.org/10.1680/icien.1992.21497 14. Papadopoulos, K., Vintzileou, E.: New titanium connectors for the columns capitals of the classical temple of apollo Epikourios. Int. J. Archit. Herit. 10, 749–765 (2016). https://doi. org/10.1080/15583058.2015.1113342 15. Papadopoulos, K., Vayas, I.: Restoration and strengthening techniques for ancient-Greek monuments. Int. J. Archit. Herit. 13, 33–46 (2019). https://doi.org/10.1080/15583058.2018. 1497233 16. Vasconcelos, G., Lourenço, P.B.: Experimental characterization of stone masonry in shear and compression. Constr. Build. Mater. 23, 3337–3345 (2009). https://doi.org/10.1016/j.con buildmat.2009.06.045 17. Dasiou, M.E., Psycharis, I.N., Vrouva, A.: Numerical investigation of the seismic behaviour of connections of ancient colonnades. In: ECCOMAS Thematic Conference - COMPDYN 2011 3rd International Conference Computer Methods Structuring Dynamics Earthquake Engineering An IACM Special Interest Conference Programs, pp. 25–28 (2011) 18. Zohar, M., Salamon, A., Rubin, R.: Earthquake damage history in Israel and its close surrounding - evaluation of spatial and temporal patterns. Tectonophysics 696–697, 1–13 (2017). https://doi.org/10.1016/j.tecto.2016.12.015 19. EN 1998:2004 + A1: Eurocode 8: Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings (2013) 20. Sarhosis, V., Baraldi, D., Lemos, J.V., Milani, G.: Dynamic behaviour of ancient freestanding multi-drum and monolithic columns subjected to horizontal and vertical excitations. Soil Dyn. Earthq. Eng. 120, 39–57 (2019). https://doi.org/10.1016/j.soildyn.2019.01.024 21. Psycharis, I.N., Papastamatiou, D.Y., Alexandris, A.P.: Parametric investigation of the stability of classical columns under harmonic and earthquake excitations. Earthq. Eng. Struct. Dyn. 29, 1093–1109 (2000). https://doi.org/10.1002/1096-9845(200008)
Discontinuous Dynamics of Santa Maria Annunziata Church Under Seismic Loading: A Non-smooth Contact Dynamics Approach Mattia Schiavoni , Gianluca Standoli , Francesca Bianconi , Ersilia Giordano , and Francesco Clementi(B) Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Via Brecce Bianche n.12, 60131 Ancona, Italy [email protected]
Abstract. The dynamics the Santa Maria Annunziata church located in Camerino (Macerata province, Italy), subjected to transversal dynamic loadings has been analysed by using a distinct element code which implements the Non-Smooth Contact dynamics method. Since the contact between blocks is governed by the Signorini’s impenetrability condition and the dry-friction Coulomb’s law, the church exhibit discontinuous dynamics. The sliding motions of blocks are non-smooth functions of time. Numerical simulations are performed with the aim of investigating the influence of the friction coefficient and of some past retrofitting interventions on the global response. The results obtained are compared with the real damage that the Church suffered following the seismic sequence in central Italy in 2016, and for this reason the four main shock that strocked the area were used in the numerical analyses. A good agreement between the numerical and the real damages are finally obtained but it might be interesting to elaborate additional models in which the building presents different degrees of connection with the towers. Keywords: Masonry · Historical Structure · Discontinuous Approach · Non-Smooth Contact Dynamic Method · Damage Cumulation
1 Introduction Existing masonry structures are typically distinguished by their exceedingly flexible floors and their perpendicular walls’ unclear interlocking [1, 2]. Due to these factors, post-earthquake surveys reveal collapses involving single panels collapsing out-of-plane or macroblocks (parts of structures) forming a partial failure mechanism [3]. These scenarios require targeted and specially designed retrofitting interventions [4, 5]. For structures characterized by a correct distribution of the openings and by the absence of staggered floors, it is possible to use the equivalent frame method [6, 7]. These conditions are not easily identifiable in historic buildings [8, 9], for this reason in recent years two advanced methods have been developed that allow for a numerical response with respect to the real damage, i.e., the continuous and the discontinuous © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 484–493, 2024. https://doi.org/10.1007/978-3-031-39450-8_40
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models. In the continuous model there is a homogenization of the material without a distinction between mortar and brick. The material is therefore assumed as a continuous deformable body capable of simulating the behaviour under static and dynamic loads through constitutive laws obtained by experimental tests or through values obtained for masonry with similar characteristics [10–13]. In the discontinuous models, on the other hand, in detailed micro-modeling the masonry is represented by considering blocks and mortar [14, 15], otherwise in simplified micro-modeling the thickness of the mortar is incorporated in the blocks [16–18]. These interact with each other through contact surfaces governed by smooth or non-smooth laws [19–22]. The advantage of using this approach lies in the fact that it is possible to consider the separation of the blocks thus reproducing both in-plane and out-of-plane behavior [23–25]. Recently it has been possible to find a combination of the two methods [26, 27]. In this work the dynamic behavior of the Church of the Santa Maria Annunziata located in Camerino, in the province of Macerata (Central Italy) is chosen. The Church was studied through the discontinuous approach using the Non-Smooth Contact Dynamic (NSCD) method implemented in the LMGC90© open-source code. Following the intense seismic sequence that stroke the central Italy in 2016, the Church was seriously damaged and closed for safety reasons.
2 The Case Study The case study is the Santa Maria Annunziata Church, located in Camerino, in the province of Macerata, Italy. The Church is in the heart of the city and is the most relevant structure in Camerino (Fig. 1). The Church dates to the XIII century, the first testimonies speak of a Romanesque church dedicated to San Giuseppe. In 1268 there was the first overhaul of the building, made necessary both because of the devastation suffered in 1259 at the hands of the Swabians headed by Percivalle Doria and because of the needs of the city to expand economically and demographically. Other renovations took place following the earthquake of 1279, when the bell tower collapsed. In 1748–1749 there was an important revision of the main façade, the thirteenthcentury style gave way to the baroque style. Due to the earthquake of 1799, the reconstruction of the structure was necessary. The works involve demolishing the remaining structures and completely rebuilding the Latin cross church with a longer longitudinal axis than the previous one. Other changes concerning the facade were made to this project, for this purpose it was necessary to move the plan of the Church to the NorthEast. It has built with traditional techniques, it is realized in masonry exception of the North-West façade which is realized in stone. On 8th September 1832, the Church was dedicated to the Santa Maria Annunziata and was consecrated. Over the years the church has resisted several earthquakes, without significant damages to the structure. Differently, the shocks of 1979 (Valnerina) and 1997 (UmbriaMarche) caused injuries that are still identifiable thanks to the chromatic diversity of the material used in local interventions. The nave of the Church develops for a total length of 66.60 m and a height of 30.50 m. In the Church, there is a semi-basement floor placed at a depth of 5.30 m. Compared to
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Fig. 1. The Santa Maria Annunziata Church (Camerino, Macerata province, Italy) and the Italian macroseismic intensity map.
the height at the entrance, the gable is at a height of 17,95 m while the towers reach a height of 40.10 m (Fig. 2). Following the seismic events that hit central Italy in 2016, the Church is in a poor state. The seriously damaged parts are the façade, the towers and the connection towerschurch. It is shown how the façade, due to a poor connection with the orthogonal walls was subject to the phenomenon of hammering with the consequent formation of lesions in the upper part. In the towers, on the other hand, vertical cracks can be seen that start from the openings and reach the base. Further damage has been reported to the historical-artistic heritage present inside the Church, there are shear cracks which have caused damage to the statues inside the niches.
3 Discrete Element Method: Non-smooth Contact Dynamics Method The masonry is represented as a collection of 3D rigid elements, where the mortar thickness is included. The elements interact each other at points of contact that are regulated by specific constitutive laws. Typically, the iteration between the bodies at the
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(c)
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(d)
Fig. 2. Horizontal section (a), transversal section A-A (b), transversal section B-B (c) and longitudinal section C-C (d).
contact points is done by normal and shear components, which depend on the speed and relative displacement of the bodies. A realistic overall behaviour may be obtained by considering a good number of contact points. In particular, the dynamic response of the Church of Santa Maria Annunziata is evaluated using the Non-Smooth Contact Dynamics (NSCD) method. The NSCD method is implemented in LMGC90© code [28]. This method was proposed by [29, 30] distinguishing it from the Distinct Element Method (DEM) because: (i) does not consider structural damping; (ii) integrates the non-smooth contact laws; (iii) it uses an implicit integration scheme. Considering two bodies Bi and Bj and calling respectively Pi and Pj their possible points of contact (Fig. 3a), if n is the orthogonal unit vector at the point Pi , g is the distance between the two bodies: (1) g = Pj − Pi · n. Calling respectively rn and rt the normal and tangential forces of Bi and Bj and u˙ n , u˙ t respectively the normal and tangential velocities of Pj respect Pi , we use two contact laws:
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1. Signorini’s law of impenetrability (Fig. 3b): g ≥ 0, rn ≥ 0, gr n = 0,
(2)
if g = 0 → u˙ n ≥ 0, rn ≥ 0, u˙ n rn = 0.
(3)
This law indicates a perfect plastic impact, i.e. Newton’s law returns a coefficient equal to zero. In this way, due to the impact, there are no bounces, this can be justified by the fact that bricks and stones have a low coefficient of return, which allows to neglect bounces. 2. Dry-friction Coulomb’s law (Fig. 3c): rt < μr n → u˙ t = 0 |rt | ≤ μr n : (4) |rt | = μr n → u˙ t = −λ |rrtt | where the friction coefficient is μ and λ is a positive real arbitrary number. The motion equation can be expressed as: M q¨ = f (q, q˙ , t) + l,
(5)
where M is the matrix of masses, q¨ the acceleration, f (q, q˙ , t) the vector of internal and external forces operating discretely on the system and l the contact’s resultant. The characteristic pairs of each contact (˙un , u˙ t ) and (rn , rt ) are connected to the global vectors q˙ and l by linear mappings that depend on q, respectively. Reactions l and velocity q˙ are discontinuous functions of time due to the non-smooth nature of the contact Eq. (2)–(4). When the velocities are discontinuous, Eq. (5) is integrated into time t. The equation of motion is integrated into the interval ti , ti+1 : M (˙qi+1 − q˙ i ) =
ti+1 ti
qi+1 = qi +
f (q, q˙ , t)dt + l i+1 , ti+1
q˙ (t)dt,
(6.2) (6.2)
ti
where l i+1 is the pulse inthe interval ti , ti+1 , q˙ i+1 is the variable that approximated the speed in the time ti+1 . In (6) and in the local contact Eqs. (2) and (3), reactions are approximated by the average of the pulse where the contact is concentrated at the local level. In this work the deformability of the blocks is neglected, in this way, there are no internal deformations but only the sliding and oscillation of the blocks that composed the Church. The main purpose of the model is to reproduce as faithfully as possible the geometry and structural elements that make up the Church of the Santa Maria Annunziata. To reduce computational burdens, it was considered appropriate to use a large block modelling, the 3D model was made with the Midas FEA NX© software, reproducing the
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(a)
(b)
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(c)
Fig. 3. Contact between bodies (a), Signorini’s law (b) and dry-friction Coulomb’s law (c).
blocks one by one, avoiding complex shapes, and simplifying the shape when deemed necessary. The masonry is represented by rigid non-convex three-dimensional blocks reproducing a good interlocking between them. The openings, vaults and arches were discretized with regular blocks, and the foundation was represented with a rigid block. It was decided to model only the vaulted floors inside the towers, for the others it was chosen to consider their contribution in terms of loads. This simplification was possible thanks to the accurate survey, which made it possible to identify the various floors. In this way, the model counts 27850 blocks (Fig. 4).
Fig. 4. View of the numerical model of the Church of Santa Maria Annunziata (Camerino, Macerata province, Italy).
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The material survey shows the presence of two different materials: solid brick masonry with lime mortar (1800 kg/m3 ) and cut stone with good bonding (2100 kg/m3 ) in the North-West façade. The energy dissipation in the LMGC90© is regulated by the restitution coefficient, and in this case it is imposed equal to zero (no bouncing). A friction coefficient equal to μ = 0.50 was used in the interface between the blocks and equal to μ = 0.90 in the interface between the blocks and the base.
4 Numerical Results The Church is subjected to the seismic sequence of central Italy of 2016. Initially, the structure was subjected only to the gravitational force, then the seismic sequence was applied, using Matelica (MTL) as a reference seismic station. In order to reproduce the cumulative damage the four main events of the seismic sequence were considered (Table 1). For each event, the velocities in the three main directions are taken, considering 10 s of peak and 2 s of null velocities between the different shocks. In this way, the total duration of the analysis is equal to 46 s. Table 1. The main characteristics of the four quakes considered. Seismic Event
ML
Depth Station Class Rjb [km] EC8a [km]
Rrup [km]
Repi [km]
NS PGA EW [cm/s2 ] PGA [cm/s2 ]
U PGA [cm/s2 ]
24/08/2016 6.00 63.90 MTL (01:36:32)
B
44.49 44.49 63.90 −66.71
69.95
31.02
26/10/2016 5.40 42.70 MTL (17:10:36)
B
39.64 40.08 42.70 −44.58
−30.00
17.63
26/10/2016 5.90 39.10 MTL (19:18:06)
B
28.18 28.19 39.10 −240.47 −122.18 −77.86
30/10/2016 6.10 47.10 MTL (06:40:18)
B
35.33 35.32 47.10 −122.44 75.96
−44.08
a Classification of site not based on direct measure of V s,30
In Table 1 are reported the main data of the forum shocks considered where Rjb is the Joyner-Boore distance, or rather the smallest spacing between the rupture site and the rupture surface projection; Rrup is the shortest distance between the rupture site and the rupture surface and Repi is the distance calculated by the geometric swap. Finally, in Fig. 5 the damages obtained from the numerical model are compared with those that occurred following the seismic sequence in 2016. The results obtained from the numerical model are in good agreement with the real ones. The approximation of the blocks does not faithfully trace the lesions but still identifies the most vulnerable parts. On the South-West façade (Fig. 5) the parts that have been most affected by the seismic sequence of central Italy are the two bell-towers.
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Fig. 5. Comparison between the numerical and real damages after the seismic sequence of central Italy in 2016.
Lesions can be seen in correspondence with the clock and in correspondence with the tower-to-church connection caused by hammering between the walls. On the North-West façade (Fig. 5), on the other hand, the most evident cracks concern the whole part of the bell tower and the openings placed on the nave of the Church.
5 Conclusions The Church of Santa Maria Annunziata placed in Camerino (Macerata province, central Italy) was analysed with the seismic sequence of central Italy in 2016. To reproduce the cumulative damage, the four main shocks are applied in sequence. To investigate the dynamic behaviour of historical masonry structure the discrete approach is used, specifically trougth the NSCD method developed in the LMGC90© code. Thanks to the approximations used in the NSCD method, i.e., (i) does not consider structural damping; (ii) integrates the non-smooth contact laws; (iii) it uses an implicit integration scheme, it was possible to obtain great predictive capabilities. In agreement with the real damage, it is possible to notice how the numerical model identifies the most vulnerable parts, i.e., the bell cells and the tower-to-church connection. Therefore, to obtain extremely more accurate results it is necessary to use a more accurate discretization (with extremely high computational costs).
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References 1. Solarino, F., Oliveira, D.V., Giresini, L.: Wall-to-horizontal diaphragm connections in historical buildings: a state-of-the-art review. Eng. Struct. 199, 109559 (2019). https://doi.org/10. 1016/j.engstruct.2019.109559 2. Lourenço, P.B., Mendes, N., Ramos, L.F., Oliveira, D.V.: Analysis of masonry structures without box behavior. Int. J. Archit. Herit. 5, 369–382 (2011). https://doi.org/10.1080/155 83058.2010.528824 3. Malena, M., Portioli, F., Gagliardo, R., Tomaselli, G., Cascini, L., de Felice, G.: Collapse mechanism analysis of historic masonry structures subjected to lateral loads: a comparison between continuous and discrete models. Comput. Struct. 220, 14–31 (2019). https://doi.org/ 10.1016/j.compstruc.2019.04.005 4. Mosoarca, M., Apostol, I., Keller, A., Formisano, A.: Consolidation methods of romanian historical building with composite materials. Key Eng. Mater. 747, 406–413 (2017). https:// doi.org/10.4028/www.scientific.net/KEM.747.406 5. Formisano, A., Milani, G.: Seismic vulnerability analysis and retrofitting of the SS. Rosario Church Bell tower in Finale Emilia (Modena, Italy). Front. Built Environ. 5, 1–12 (2019). https://doi.org/10.3389/fbuil.2019.00070 6. Lagomarsino, S., Penna, A., Galasco, A., Cattari, S.: TREMURI program: an equivalent frame model for the nonlinear seismic analysis of masonry buildings. Eng. Struct. 56, 1787–1799 (2013). https://doi.org/10.1016/j.engstruct.2013.08.002 7. Quagliarini, E., Maracchini, G., Clementi, F.: Uses and limits of the equivalent frame model on existing unreinforced masonry buildings for assessing their seismic risk: a review. J. Build. Eng. 10, 166–182 (2017). https://doi.org/10.1016/j.jobe.2017.03.004 8. Lemos, J.: Discrete element modeling of the seismic behavior of masonry construction. Buildings 9, 43 (2019). https://doi.org/10.3390/buildings9020043 9. D’Altri, A.M., et al.: Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification. Arch. Comput. Methods Eng. 27(4), 1153–1185 (2019). https://doi.org/10.1007/s11831-019-09351-x 10. Giordano, E., Clementi, F., Nespeca, A., Lenci, S.: Damage assessment by numerical modeling of Sant’Agostino’s sanctuary in Offida during the central Italy 2016–2017 seismic sequence. Front. Built Environ. 4 (2019). https://doi.org/10.3389/fbuil.2018.00087 11. Facchini, L., Betti, M., Corazzi, R., Kovacevic, V.C.: Nonlinear seismic behavior of historical masonry towers by means of different numerical models. Proc. Eng. 199, 601–606 (2017). https://doi.org/10.1016/j.proeng.2017.09.103 12. Illampas, R., Ioannou, I., Lourenço, P.B.: Seismic appraisal of heritage ruins: the case study of the St. Mary of Carmel church in Cyprus. Eng. Struct. 224, 111209 (2020). https://doi.org/ 10.1016/j.engstruct.2020.111209 13. Valente, M., Milani, G.: Seismic assessment of historical masonry structures through advanced nonlinear dynamic simulations: applications to castles, churches, and palaces. In: Numerical Modeling of Masonry Historical Structures pp. 163–200. Elsevier (2019). https://doi.org/10. 1016/B978-0-08-102439-3.00005-1 14. Sandoval, C., Arnau, O.: Experimental characterization and detailed micro-modeling of multiperforated clay brick masonry structural response. Mater. Struct. 50(1), 1–17 (2016). https:// doi.org/10.1617/s11527-016-0888-3 15. Calderón, S., Sandoval, C., Arnau, O.: Shear response of partially-grouted reinforced masonry walls with a central opening: testing and detailed micro-modelling. Mater. Des. 118, 122–137 (2017). https://doi.org/10.1016/j.matdes.2017.01.019 16. Schiavoni, M., Ferrante, A., Salachoris, G.P., Mariotti, C., Clementi, F.: Out-of-plane seismic response of a masonry facade using distinct element methods. Int. J. Mason. Res. Innov. 1, 1 (2022). https://doi.org/10.1504/IJMRI.2022.10051745
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17. Ferrante, A., Schiavoni, M., Bianconi, F., Milani, G., Clementi, F.: Influence of stereotomy on discrete approaches applied to an ancient church in Muccia, Italy. J. Eng. Mech. 147, 04021103 (2021). https://doi.org/10.1061/(ASCE)EM.1943-7889.0002000 18. Lourenço, P.B., Rots, J.G.: Multisurface interface model for analysis of masonry structures. J. Eng. Mech. 123, 660–668 (1997). https://doi.org/10.1061/(ASCE)0733-9399 19. Mendes, N., Zanotti, S., Lemos, J.V.: Seismic performance of historical buildings based on discrete element method: an adobe church. J. Earthq. Eng. 24, 1270–1289 (2020). https://doi. org/10.1080/13632469.2018.1463879 20. Sarhosis, G.M.V., Bagi, K., Lemos, J.V.: Computational Modeling of Masonry Structures Using the Discrete Element Method. IGI Global (2016).https://doi.org/10.4018/978-1-52250231-9 21. Chetouane, B., Dubois, F., Vinches, M., Bohatier, C.: NSCD discrete element method for modelling masonry structures. Int. J. Numer. Methods Eng. 64, 65–94 (2005). https://doi.org/ 10.1002/nme.1358 22. Lancioni, G., Lenci, S., Piattoni, Q., Quagliarini, E.: Dynamics and failure mechanisms of ancient masonry churches subjected to seismic actions by using the NSCD method: the case of the medieval church of S. Maria in Portuno. Eng. Struct. 56, 1527–1546 (2013). https:// doi.org/10.1016/j.engstruct.2013.07.027 23. Pulatsu, B., Erdogmus, E., Lourenço, P.B.: Comparison of in-plane and out-of-plane failure modes of masonry arch bridges using discontinuum analysis. Eng. Struct. 178, 24–36 (2019). https://doi.org/10.1016/j.engstruct.2018.10.016 24. Lemos, J.V., Sarhosis, V.: Discrete element bonded-block models for detailed analysis of masonry. Infrastructures. 7, 31 (2022). https://doi.org/10.3390/infrastructures7030031 25. Lemos, J.V., Sarhosis, V.: Dynamic analysis of masonry arches using Maxwell damping. Structures 49, 583–592 (2023). https://doi.org/10.1016/j.istruc.2023.01.139 26. Bagnéris, M., et al.: A complete methodology for the mechanical diagnosis of statue provided by innovative uses of 3D model. Application to the imperial marble statue of Alba-la-Romaine (France). J. Cult. Herit. 28, 109–116 (2017). https://doi.org/10.1016/j.culher.2017.05.002 27. Reccia, E., Cazzani, A., Cecchi, A.: FEM-DEM modeling for out-of-plane loaded masonry panels: a limit analysis approach. Open Civ. Eng. J. 6, 231–238 (2012). https://doi.org/10. 2174/1874149501206010231 28. Dubois, F., Acary, V., Jean, M.: The contact dynamics method: a nonsmooth story. Comptes Rendus Mécanique. 346, 247–262 (2018). https://doi.org/10.1016/j.crme.2017.12.009 29. Moreau, J.J.: Unilateral contact and dry friction in finite freedom dynamics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds.) Nonsmooth Mechanics and Applications. ICMS, vol. 302, pp. 1–82. Springer, Vienna (1988). https://doi.org/10.1007/978-3-7091-2624-0_1 30. Jean, M.: The non-smooth contact dynamics method. Comput. Methods Appl. Mech. Eng. 177, 235–257 (1999). https://doi.org/10.1016/S0045-7825(98)00383-1
Dynamic Numerical Study of Traditional Dry-Stone Walls with YADE Paola Ita1 , Sandra Santa-Cruz1(B) , Dominique Daudon2 , and Nicola Tarque1,3 1 GERDIS Research Group, Civil Engineering Division, Pontificia Universidad Católica del
Perú, Lima, Peru [email protected] 2 Univ. Grenoble Alpes, CNRS, Grenoble INP 3SR, F-38000 Grenoble, France 3 Department of Continuum Mechanics and Structures, Universidad Politécnica de Madrid, C/Prof, Aranguren 3, 28040 Madrid, Spain
Abstract. On the hills of some Andean cities in South America, the population has built their homes on terraces supported by traditional dry-stone retaining walls (“pircas”) without any regulation or code. Because this zone is prone to strong earthquake ground motions, it is necessary a better understanding of the pircas’s out-of-plane behavior and collapse mechanism for risk prevention and mitigation. However, no dynamic studies of this traditional construction exist to date. This work addresses a numerical study of the response of pircas subjected to ground motions in the out-of-plane direction and how different construction techniques (i.e. block arrangements and wall configurations) can affect this response. The dynamic analysis was carried out with the YADE (open-source software for discrete numerical models and focused on the Discrete Element Method, DEM). By varying the vertical separation of Through stones (tie stones) and overlap of stones in the cross-section of the walls, we obtained 5 models which were subjected to a representative seismic signal. Regular and parallelepiped clumps (groups of rigidly joined spheres) were selected for modeling the wall blocks due to their versatility in their geometry and lower computational cost than other types of particles supported by YADE [1]. The effect of the backfill has not been considered yet, since we are focused on the wall configuration effects on the dynamic response. In the absence of dynamic experimental results, the precise calibration of the numerical model has yet to be sought. The results obtained are preliminary. At a later stage, an experimental dynamic test will be carried out, and they can be properly calibrated. The numerical results showed that when the wall presents a cross-section with adequate overlap, the amount of Through Stone (from 2.2 to 3.6 per m2) is not important. On the other hand, when the wall cross-section has no overlap, the wall presents the least resistance to moderate damage levels and collapse. Additionally, it was possible to verify that the pseudo-static out-of-plane response (obtained in a previous study) is more conservative than the dynamic one. Keywords: DEM · Dynamic analysis · DSRW · Earthquake · Overturning · Damage · YADE
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 494–504, 2024. https://doi.org/10.1007/978-3-031-39450-8_41
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1 Introduction The slopes of some cities in the Andes are being informally occupied by residents who build their houses on terraces supported by a traditional Dry stone retaining wall, DSRW, called “pirca”. Pircas are built in community works without technical assistance, which is why they present a high seismic risk [2]. Despite numerous studies in Europe [3–7] to evaluate the out-of-plane behavior of DRWS, the pircas behavior cannot be extrapolated from those results because the construction characteristics (geometry, material, shape, disposition of the stones, and percentage of voids) are different. For example, the percentage of voids for stone walls varies between 32% and 38% [8], which is high compared to European walls (25% for walls composed of small blocks and 15% for those built with large blocks) [9]. This work is part of a research project that studies the out-of-plane behavior of pircas. In previous stages, the following was studied: a) the characterization of the traditional construction technique of the pircas of the Central Andes. b) numerical and experimental pseudo-static study of walls on a natural scale with local labor, without considering the backfill, following the habitual practice of the inhabitants of the southern zone of Lima [10]. c) numerical pseudo-static study of the out-of-plane behavior of different configurations of stone walls. At this stage, 70 walls with different configurations were studied [11]. This work aimed to study, through dynamic numerical models, the out-of-plane behavior of different pircas arrangements to provide recommendations for their construction process. The software used for modeling was YADE, an open-source package focused on DEM. The dynamic results made it possible to validate the recommendations obtained in the numerical and experimental pseudo-static study by Ita et al. [11]. On the other hand, it was obtained that the pseudo-static results are more conservative than the dynamic ones. The numerical models were subjected to a Peruvian seismic signal scaled at various amplitudes to get the maximum ground accelerations (PGA) that cause the initiation of damage and collapse of the walls. In a future study, this range of accelerations will be one of the control factors that can be used to design a full-scale dynamic test on a seismic table.
2 Wall Configuration Two critical parameters affect the out-of-plane behavior of the stone walls: Through stones (tie stones that pass through the cross-section) and the overlap of stones in the cross-section [11]. For this reason, three longitudinal sections (longitudinal configuration) and three transversal sections were considered to define the different configurations of the wall. The configurations studied are a combination of both sections. The spacing in the height of the Through stones met the requirements set out by Schacher and Ali [12] (at least every 600 mm). The configurations are based on Ita et al.’s numerical pseudo-static study [11]. The location of the through stone was represented by longitudinal configurations 1, 2, and 3, shown in Sect. 2.1. On the other hand, since the overlap is a complex factor to control in the field, three sections with different overlap lengths were considered, as shown in Sect. 2.2.
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2.1 Longitudinal Section The parameter that defines the longitudinal sections is the horizontal separation and the vertical separation of the Through stone, which effectively improves the out-of-plane seismic performance of stone walls, as Meyer et al. [13] demonstrated in dynamic tests using a shaking table. In Fig. 1, the three sections studied are shown. The Through stones are represented with black blocks; their horizontal spacing is 1000 mm, and their vertical spacing is 300 mm or 600 mm. Longitudinal configurations 1, 2, and 3 present 3.6, 2.5, and 2.2 Through stone per m2 .
(a) (b) Longitudinal configuration 1 (23 Through stones) Longitudinal configuration 2 (16 Through stones)
(c) Longitudinal configuration 3 (14 Through stones)
Fig. 1. Longitudinal configurations. Note that configurations 1 and 2 have the same side edges. However, configuration 1 presents 44% more Through stone than configuration 2. On the other hand, configurations 2 and 3 present the same arrangement of Through stones except for the lateral edges.
2.2 Cross Section The parameter that defines the cross sections is the overlap (OV). Three cross sections were considered, called “OVTdA”, where “d” represents the percentage of OV concerning A (see Fig. 2).
3 Damage Level Qualitative criteria were applied to describe the damage levels and their relationship with the global response to the wall. The result of evaluating the damage in terms of the mechanisms is only partially objective. However, the damage descriptions are welldefined, limiting the judgment dispersion (see Table 1). Further work will explore more quantitative criteria and their relation to the qualitative ones used here.
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Fig. 2. Cross Sections (0V0A, OV33A, OV66A) Table 1. Damage Level Damage Level
Descripción
1
Slight damage
Small or moderate slippage between the blocks
2
Moderate damage
Collapse (by sliding) of some blocks of the wall
3
Collapse
Collapse at the end-sides of the wall or along the wall
4 Numerical Model 4.1 Mechanical Properties The software used is YADE, which is open-source and focuses on DEM. The type of element chosen was clump (group of rigidly bonded spheres) due to its low computational cost compared to other particle types (clumps, regular polyhedrals, and irregular polyhedrals) available in the software [1]. Regular blocks were considered to generate the different configurations of the walls. DEM allows structures or materials to be modeled as groups of rigid or deformable blocks using the appropriate mechanical laws and assumes that the deformations are concentrated at the joints or contacts. A linear elastic-frictional non-cohesive constitutive law was used. This constitutive law was chosen because it is the most usually used in DEM and has been suggested in the literature. Collisions (interactions between particles) must be detected at each time step, as the relative positions of the particles can change due to their motion (i.e., the spatial rotation and velocity of the spheres at the point of contact). At each step, given the normal displacement (uN ) and shear (uT ), the normal force (F N ) and shear force (FTt ), which are proportional to the displacements (Eqs. (1), (2)), are calculated. If uN > 0, the contact is deleted without generating forces. KN is the normal stiffness, and KT is the shear stiffness. The shear force (FT ) depends on the friction angle (F), Eq. (3), depending on whether the test shear force is greater or less than F N tanF. FN = KN uN
(1)
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FTt = KT uT FT = FTt FT =
(2)
|FN | tan t , if |FT | > |FN | tan F T
FTt , if |FT |
(3)
≤ |FN | tan
The mechanical properties of the blocks were based on the results obtained in a previous study [10, 11], in which the pseudo-static numerical models were calibrated based on experimental results. Table 2 shows the mechanical properties of the blocks and joints chosen. A damping value was not considered in the numerical model. The geometry of the clumps contributes to the dissipation of energy by friction, for which the behavior generally is conservative. A computer running Ubuntu 16.04 LTS with 62.8 GB RAM and a 2.2 GHz processor was used to analyze the walls; the average computational time was one hour per one second of the signal. In the absence of dynamic experimental results, the precise calibration of the numerical model has yet to be sought. The results obtained are preliminary results. Table 2. Mechanical properties of blocks and joints
Blocks Joints Others
Parameter
Value
Specific weight (KN /m3)
27.67
KN (Pa/m)
10 (x 107 )
KN /KS
2
F(°)
20
Timestep t (s)
0.00015
Damping(ξ)
None
4.2 Seismic Signal The seismic signal considered is the earthquake in Peru on May 31, 1970, its moment magnitude was 7.9 Mw, and the peak ground acceleration (PGA) was 0.1 g. This earthquake has a broad frequency content and is representative of Peruvian earthquakes. The time history analysis was not performed with the original signal. A signal processed and scaled to a maximum ground displacement (PGD) of 10mm was considered, which we will call the “base signal”. Subsequently, this signal was amplified by values in a range from 2 to 15. This allowed find for which PGA or PGD the damage initiation and the wall collapse occurs. In Fig. 3, the base signal is plotted regarding acceleration and displacement.
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(a)
(b) Fig. 3. Base seismic signal. a) Displacement signal (PGD = 10 mm). b) Acceleration signal (PGA = 1.7 m/s2 )
5 Configuration Effect 5.1 Effect of Cross-Section The configuration formed by the longitudinal configuration 2 and the cross-section OV0A, OV33A, and OV66A was considered to study the effect of the cross-section on the wall’s out-of-plane behavior. Table 3 shows the PGD the signal should have for the wall to present the different levels of damage. All sections show light damage for a 10mm PGD. The non-overlapping section (OV0A) presents the lowest resistance to collapse due to the lack of overlap. On the other hand, section OV66A presents the least resistance among the remaining sections since it presents blocks of a small width (1/6 width of the wall) that slide and contribute to collapse. On the other hand, Fig. 4 shows the PGA the signal should have for the wall to present the different levels of damage. Section OV33A and OV66A have 40% and 20% higher collapse resistance, respectively than section OV0A. This result presents the same trend as that obtained in the pseudo-static analysis, where sections OV33A and OV66A present a greater resistance collapse than section OV0. The cross-sections considered are ideal. In a constructed wall, there will be variability in the overlap. Therefore, to account for all cases, a range of values is presented that considers the cross sections found in self-constructions (OV0A) to the overlapping sections (OV33A, OV66A). Table 4 shows a range of PGA and PGD values that generate
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Table 3. Configuration 2: Peak ground displacement (PGD) for the three transversal sections Configuration 2: Peak ground displacement, PGD (mm) Cross section
Damage level Slight damage
Moderate damage
Collapse
OV0A
10
40
50
OV33A
10
50
70
OV66A
10
10
60
Fig. 4. Configuration 2: Peak ground acceleration (PGA) for the three transversal sections
different levels of damage in a configuration 2 wall. It is obtained that this configuration can have moderate damage and collapse from a PGA of 0.18 g and 0.9 g, respectively. Regarding PGD, configuration 2 can deal moderate damage and collapse from 10mm and 50mm, respectively. Table 4. Configuration 2. PGA y PGD ( range of values) Cross section
Damage level
PGD (mm)
PGA (g)
Configuration 2: OV0A, OV33A, OV66A
Slight damage
< 10; >
< 0.18; >
Moderate damage
< 10; 40 >
< 0.18; 0.9 >
Collapse
< 50; 60 >
< 0.9; 1.26 >
Figure 5 shows the collapse mechanism for a signal with a PGD of 150 mm. This magnitude was chosen to appreciate the generated mechanisms. It is obtained that for the non-overlapping section (OV0A), the collapse is due to delamination. In section OV33A, there is a collapse in part of the wall because the overlap of the blocks of the cross-section
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is ideal and allows the blocks of the wall to work as one mostly. The collapse occurs at the ends because there is no restriction at the lateral ends of the wall. On the other hand, in section OV66A, there is a block overturning due to the presence of blocks 1/6 of the width of the wall. These blocks slide and contribute to the overturning of the wall (Fig. 5c).
(a)
(b)
(c)
Fig. 5. Configuration 2: Collapse mechanisms (PGD = 150 mm) (a)OV0A: delamination (b) OV33A: collapse at the ends of the wall (c) OV66A: overturning of the wall
5.2 Effect of Longitudinal Configuration The cross-section OV33A and the longitudinal configuration 1, 2, and 3 were considered to study the effect of the longitudinal configuration on the out-of-plane performance of the wall. Table 5 shows the PGD the signal should have for the wall to present the different levels of damage. All sections present the same damage levels for the indicated displacements. The walls with cross-section OV33A presented slight damage, moderate damage, and collapse for 10, 50, and 70 mm, respectively. No value is presented for the collapse of configuration 1 because it did not collapse for a PGD of 150mm. Table 5. OV33A: Peak ground displacement (PGD) for the three configuration OV33A: Peak ground displacement, PGD (mm) Configuration
Damage level Slight damage
Moderate damage
Collapse
1
10
50
___
2
10
50
70
3
10
50
70
On the other hand, Fig. 6 shows the PGA that the signal should have for the wall to present the different levels of damage. The three configurations resist the same magnitudes because they have the same OV33A cross-section. This result is similar to that
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obtained in the pseudo-static analyses, where when considering a cross-section with an overlap of 1/3 the width of the wall, the amount of Through stone is a non-significant factor (for walls between 2.2 and 3.6 Through stone per m2 ). Configurations 2 and 3 present the same arrangement of Through stones except for the lateral edges. However, the effect of confinement at the ends of the wall is not appreciated. It is necessary to perform more runs with the other cross sections (OV0A and OV66A) to reach an adequate conclusion.
Fig. 6. OV33A: Peak ground acceleration (PGA) for the three configuration
Figure 7 shows the collapse mechanism for a signal with a PGD of 150 mm. This magnitude was chosen to appreciate the generated mechanisms. Configuration 1 fails to collapse by presenting the most considerable amount of Through stone. On the other hand, in longitudinal configurations 2 and 3, collapse occurs at the ends of the wall by having free lateral edges (without restrictions).
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Fig. 7. Collapse mechanisms (PGD = 150 mm) (a) Configuration 1, block sliding (b) Configuration 2, collapse at the ends (c) Configuration 3, collapse at the ends
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6 Pseudo-Static Versus Dynamic Results Table 6 shows the PGAs that produce the collapse of the wall for configuration 2 (pseudostatic and dynamic case). The basal force resisting the wall was obtained in the pseudostatic analysis without considering the backfill. Subsequently, considering that the earthquake’s only force is the wall’s inertia force, the pseudo-static collapse acceleration is obtained. The relationship between the dynamic and pseudo-static collapse acceleration is between 3 and 4. The pseudo-static results are more conservative than the dynamic ones. Scaled-down harmonic shaking table tests confirm that pseudo-static approaches are too conservative [7]. Table 6. Peak ground acceleration (PGA): Pseudo-static versus dynamic results Cross section
Configuration 2: PGA (g) Pseudo static
Dynamic
OV0A
0.26
0.90
OV33A
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1.26
OV66A
0.28
1.08
7 Conclusions The numerical results showed that even complying with the recommendations on the vertical separations of the Through stones, the presence of overlap causes the resistance out of the plane of the stone walls to increase up to 30% concerning a cross-section without overlap. On the other hand, it is essential to avoid small stones (1/6 width) at the ends of the cross-section of the wall as they slide and contribute to its collapse. Although there is no precise calibration of the model, since there are no dynamic experimental results, the conclusions regarding the configurations are similar (same trend) as those obtained in the pseudo-static study by Ita et al. [11]. There is a limitation when considering only a quantitative method to define damage levels. Quantitative criteria will also be explored in subsequent work. It was possible to carry out the dynamic numerical modeling of the stone walls in YADE. The limitation is that the damping was not implemented (ξ = 0). The geometry of the clumps contributes to the dissipation of energy by friction, for which the behavior generally is conservative. On the other hand, the numerical models of the stone blocks are regular and uniform, the effect of irregular joints was not taken into account because the exact geometry of the stones was not sought to be represented in this investigation. The pseudo-static results, obtained at an earlier stage, are more conservative than the dynamic results. The relationship between dynamic and pseudo-static acceleration is between 3 and 4. These results do not consider the effect of the backfill. Therefore, it is necessary to consider this factor in future work.
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For configuration 2, the PGA of collapse is between 0.18 and 0.9 g. However, the values presented do not consider any security factor. Therefore, considering a security factor of 2, the collapse of a wall of configuration 2 is between 0.09 g and 0.45 g. The range presented can be verified in a future study where experimental tests will be carried out. Acknowledgments. The numerical part was founded by Dirección de Gestión de la Investigación at the PUCP through grant DGI-2020-PI0770.
References 1. SantaCruz, S., Daudon, D., Tarque, N., Zanelli, C., Alcántara, J.: Out-of-plane analysis of dry-stone walls using a pseudo-static experimental and numerical approach in scaled-down specimens. Eng. Struct. 245, 112875 (2021) 2. Zanelli, C.: Evaluación de vulnerabilidad sísmica de las pircas mediante modelación numérica en elementos discretos: aplicación al caso de las pircas en carabayllo, lima. Tesis para optar el título de Magíster en Ingeniería Civil. Pontificia Universidad Católica del Perú. Lima (2019) 3. Mundell, C., McCombie, P., Heath, A., Harkness, J., Walker, P.: Behavior of drystone retaining structures. Proc. Inst. Civil Eng. Struct. Build. 163(1), 3–12 (2010) 4. Anon: Experiments carried on at Chatham by the late Lieutenant Hope, Royal Engineers, on the pressure of earth against revetments and the best form of retaining walls. Corps. R. Eng. 7, 64–86 (1845) 5. Burgoyne, J.: Revetments of retaining walls. Corps R. Eng. Pap. 3, 154–159 (1853) 6. Savalle, N., Vincens, É., Hans, S.: Experimental and numerical studies on scaled-down dryjoint retaining walls: pseudo-static approach to quantify the resistance of a dry-joint brick retaining wall. Bull. Earthq. Eng. 18(2), 581–606 (2019) 7. Savalle, N., BlancGonnet, J., Vincens, E., Hans, S.: Dynamic behaviour of drystone retaining walls: shaking table scaled-down tests. Eur. J. Environ. Civil Eng. 26(10), 4527–4547 (2020). https://doi.org/10.1080/19648189.2020.1855477 8. Evaluación, R.V.: del riesgo sísmico en viviendas sobre pircas en un asentamiento humano en el distrito de Villa María del Triunfo. Tesis para optar al título de Ingeniero Civil. Pontificia Universidad Católica del Perú. Lima (2021) 9. Colas, A.S., Morel, J.C., Garnier, D.: Assessing the two-dimensional behavior of drystone retaining walls by full-scale experiments and yield design simulation. Géotechnique 63(2), 107–117 (2013) 10. Ita, P., Santa-Cruz, S., Daudon, D., Tarque, N., Párraga, A., Ramos, V.: Out-of-plane analysis of dry-stone walls using a pseudo-static experimental and numerical approach in natural-scale specimens. Eng. Struct. 288, 116153 (2023). https://doi.org/10.1016/j.engstruct.2023.116153 11. Ita, P., Santa Cruz, S., Daudon, D., Tarque, N.: Numerical studies on dry joint stone masonry: a pseudo-static approach for the study of the out-of-plane performance of different wall configurations. In: 14th North American Masonry Conference (2023) 12. Schacher, T., Ali, Q.: Dhajji construction. United Nations Pakistan and NDMA Pakistan (2009) 13. Meyer, P., Ochsendorf, J., Germaine, J., Kausel, E.: The impact of high-frequency/ low-energy seismic waves on unreinforced masonry. Earthq. Spect. 23(1), 77–94 (2007). https://doi.org/ 10.1193/1.2431211
Material Characterization, Dynamic Identification and Mechanical Modelling of the Fifth Minaret of Herat, Afghanistan G. Misseri1(B) , G. Lacanna2 , R. Grazzini1 , F. Fratini3 , A. Boostani4 , and L. Rovero1 1 Department of Architecture -Materials and Structures Division, Florence University, Firenze,
Italy [email protected] 2 Department of Earth Sciences, Florence University, Firenze, Italy 3 Institute of Heritage Science, National Research Council, Firenze, Italy 4 Aga Khan Cultural Services Afghanistan, Kabul, Afghanistan
Abstract. The Fifth Minaret of Heart, part of the “Musalla” complex, 15th century, is the only one still standing in the Gawhar Shad area. The 42 m tower, whose external surfaces were completely covered by glazed tiles, used to corner the Madrasa, which was demolished at the end of the 19th Cent. This fact, coupled with several low-intensity earthquakes and recursive floods, has induced increasing leaning for over a decade starting from the end of the 80s, and the formation of an extensive crack at the base of the shaft. An emergency intervention carried out in 2003 prevented the collapse. The study pointed at a broad, multi-discipline knowledge path to systematize available information and determine the intrinsic material characteristics, the building technology solutions, the damage and vulnerability sources, the behavior under dynamic loading and the structural response in the current configuration. To determine the material characteristics, the following tests were carried out: uniaxial compression and indirect tension tests on bricks, penetrometer tests on mortar joints on site, porosity tests on bricks, X-ray diffraction tests and observation of thin sections at the optical microscope in polarized light on bricks and mortars and clay mineral composition. The building technology solutions were inspected at the site and supported by the analysis of borescope images. A seismic network composed of five seismometers was installed to implement Operational Modal Analysis. Results were exploited to calibrate the mechanical properties of the 3D solid mesh of the Minaret, retrieved by the Terrestrial Laser Scanner survey, and a set of modal pushover analyses were employed to determine the expected damage areas in the current configuration. Keywords: Minaret · Afghanistan · seismic interferometry · XRD tests · mechanical tests · modal pushover analysis
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 505–516, 2024. https://doi.org/10.1007/978-3-031-39450-8_42
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1 Introduction 1.1 Short Historical Account The Fifth Minaret (M5) belongs to the Gawar Shad area of the Musalla complex in Herat; the name Gawar Shad recalls her patroness, the wife of the sovereign of the Timurid Empire, [1]. Sultan Shah Rukh made Herat the capital, moving it from Samarkand at the beginning of his reign in 1405 A.D., and worked for a cultural renaissance of the old city, Alexandria in Ariana, which was one of the far east Alexandria of the Macedonian empire. The Gawar Shad area was completed by 1438 and hosted a Mosque and a koranic school, Madrasa, and a Mausoleum; the Fifth Minaret used to corner the Madrasa. The successor of Shah Rukh, Husayn Bayqra, erected a second Madrasa in the area. In fact, the word Musalla (a space outside a mosque used for praying) is generally employed by the population to identify the complex. Today, only five Minarets and the Mausoleum remain in the complex; although in 1915 nine towers could still be visible, Fig. 1; most of the minarets were also leaning at that time. As shown in Fig. 1, the site appeared in a state of abandonment as reported by several travellers’ drawings, [2]. In fact, the buildings that stood with the minarets were intentionally demolished in 1885, to provide a free battlefield for a supposed forthcoming war against Russians, who however never attacked there. Early 19th Cent. images show a seriously eroded base of the Fifth Minaret (M5), hence a pedestal was added reasonably after the 1921 and 1932 earthquakes, which had caused the collapse of minarets marked with an X in Fig. 1b. The leaning of the minaret is confirmed stable in the period 1915– 1975, [3], but after Soviet occupation (1979) a large avenue crossing the area was built, and between 1984 and 1989 a grenade hit the M5 causing a large hole. Also, two further earthquakes (Mw = 4.6 in 1982 and Mw = 4.5 in 1990, [4]) occurred not too far from Herat and hit the area which suffered, in that period, from recursive floods of the Hari Rud river, [3], hence water penetration in the soil must have been serious. Therefore, the M5 lean seriously worsened in the period 1982–2002, and connected to the leaning increase a deep crack at the top of the pedestal formed. In 2002, during UNESCO’s surveying activities, the leaning of the M5 appeared so marked, around 2.4 m out-of-plumb, that installation of emergency steel stays, anchored to concrete blocks embedded in the soil at 25 m distance from the M5 base, was quickly implemented in a few months, [6]. Several studies could then take place to understand structural, [7], geotechnical, [3], and archaeological, [8] characteristics. Evidence collected shows that the M5 foundations, made of stone masonry, are 5.25 m deep; they reasonably show, similarly to M6, a circular layout with varying depth; M5 foundations were dug before, deeper and raised up to 1.5 m, then, Madrasa foundation walls start reconnecting to the M5 ones. In fact, in the drained condition, the bearing capacity of soil shows no settlement susceptibility for stress levels induced by M5. In case of soil saturation, reduction of bearing capacity, foundation depth discontinuity, lack of lateral constraints and earthquake occurrence, robustly justify the serious leaning increase. In 2016, a monitoring system for crack growth and tilting control and structural strengthening works at the base of the M5 were implemented, [9]. The studies and actions implemented up to 2020 permitted the minaret’s survival and the understating of important soil and foundation characteristics. Based on this, the
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Fig. 1. a) Plan of the Musalla site, in green the Gawhar Shad Area, in Brown the Husayn Bayqra area; b) the still standing minarets in 1915; photo by Oskar von Niedermayer. Minarets marked from 1 to 4 belong to the Husayn Bayqra area, and 5 and 6 to the Gawhar Shad area, minarets marked with X collapsed during the 1921 and 1932 earthquakes; c) East-West cross section from TLS survey and d) plans at + 15.00 m, + 20.00 m and + 28.00 m, [5].
authors continued investigations designing and implementing a seismic network, a wide experimental campaign (both on-site and in the laboratory), detailed surveying activities and refined structural modeling. 1.2 Geometry and Building Technology The M5 42 m-tall gently tapered and curved shaft shows a solid core up to around 10m from ground, where the entrance door (on top of the Madrasa walls) is placed. The inner space is shaped by a core masonry “shaft” on which a conical spire staircase of massive thickness (around 3 m) twists for five times. At the time of the erection, steps reasonably used to be, for the powerful meaning of the number in the Muslim culture, 99, today only 97 remained, each spacing a π/10 wide angle. The only openings are the entrance door, at the muquarnas balcony and on the top, damaged over time. All the original exterior surfaces used to be covered by glazed tiles of dazzling colors, [10]. Analyses on the decorated surface elements were also carried out and are being processed, they are not reported here for conciseness. The thickness of the external masonry walls reduces from around 60 cm at the entrance to 35 cm on top. Although the external geometry appears markedly slender and light, inside, apart from the lower part, which is completely solid, the space occupied by
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the staircase is as wide as the space left for the passage, as shown by the cross-section of Fig. 1c, which was obtained from slicing the point cloud of the terrestrial laser scanning survey. Direct inspection activities revealed that the structure of the spiral stairs is the leading element of the structure to which the external curved masonry ties. The masonry structure of the stairs crosses through the curved external masonry, which turns out to be discontinuous. Such a discontinuity cannot be tackled by observing the monument from the outside, since the masonry system hosting the decorative apparatus covers the internal bearing masonry. Indeed, the glazed tiles belong to a second system of external masonry dedicated to the accommodation of blocks of tiles into a cloisonné logic. Interestingly, the part of the shaft that used to be connected to the masonry of the madrasa clearly reveals the presence of wood tying elements to support a stitching effect of the Minaret to the building.
2 Experimental Campaign 2.1 Laboratory Tests Mechanical Characterization Tests. Seven bricks belonging to the masonry of the structural system were sampled and subject to uniaxial compression tests (27 specimens), according to [11] and indirect traction tests (27 specimens), according to [12], each specimen had a cubic shape with a nominal edge equal to 40 mm, see Fig. 2. All the mechanical tests were carried out employing an INSTRON SATEC 5592-315HVLF2-G2 test machine, equipped with a 600 kN load cell. The tests were conducted in displacement control. The acquisition of the displacement measures took place through a Linear Variable Differential Transformer (LVDT) integrated into the test machine, Fig. 2b-c. For each brick, one of the specimens was cut into four smaller specimens dedicated to the determination of the water accessible porosity and bulk volume through the hydrostatic balance test, which provided an average bulk density of 1.67 g/cm3 . Concerning compressive strength, tests showed an average value of fc = 19.95 MPa, the highest average value is for the sample Brick 1 (9 specimens), equal to 33.05 MPa, while the lowest value is of the Brick 3 (3 specimens) equal to 9.10 MPa. The strength of Brick 3 is 27% of Brick 1, this difference is linked also to the remarkably varying porosity among the bricks, Fig. 3a. In fact, assuming that brick 1 does not belong to the original masonry texture, consisting of smaller bricks of different shapes, the compressive strength was calculated without the value of brick 1, obtaining fc = 17.91 MPa with a lower coefficient of variation (CV = 0.28 vs CV = 0.38 for the complete set). Results are comparable with results of investigations on similar bricks, [13–15]. Concerning results of the splitting tests, they provided an average tensile strength ft = 1.81 MPa (CV = 0.24) ranging between 1.24 MPa (Brick 3) and 2.47 MPa (Brick 1). Test results prove that the seven brick samples exhibit different mechanical properties; in particular, brick Br-1 showed the best mechanical properties in terms of strength, while brick Br-3 the weakest, and, consistently, samples Br-1 and Br-3 showed the lowest and highest porosity, respectively, see Fig. 3b. The overall results show also that the ratio tensile-compressive strength is almost constant, i.e. 7%(Br-1), 8% (Br-2), 11% (Br-3), 8% (Br-4), 13% (Br-5), 10% (Br-6) and 7% (Br-7).
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Fig. 2. Compression test: a) Specimens b) C-Br1–6 specimen after test c) stress-strain diagrams of Brick 1 specimens
Fig. 3. a) Results of uniaxial compressive tests, each pointer represents the average value obtained by specimens tested and belonging to the same brick. b) Results of splitting tests.
Mineralogical Characterization Tests. Eleven mortar samples belonging to the decorated system and to bedding joints were subject to mineralogical analysis. In particular, the determination of the mineralogical composition through X-ray diffraction (XRD) and petrographic study through observations on thin sections at the optical microscope in transmitted polarized light were carried out. In Fig. 4, reference specimens of mortar are reported. All the mortar samples, with the exclusion of the mortar sampled from the restoration work implemented to restore the lacunas left by the rocket impact, are all based on a binder obtained from the firing of a chalky rock (gypsum) and the aggregate often shows the presence of brick fragments. The amount of binder with respect to the aggregate is not constant, showing both scarce and abundant levels. The granulometry is in general bimodal with finer grain size more abundant than the coarser grain size in those specimens showing abundant binder ratio. The coarser grain size in general ranges 1–1.5 mm in all specimens reasonably connected to older mortars (e.g., sampled from the inside of the base crack), while up to 4mm grain size can be connected to a different type of work, maybe carried out by successive interventions.
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Fig. 4. Thin sections of mortar reference samples tested through XRD.
2.2 On Site Tests Penetrometer Tests. In order to estimate the mechanical properties of the gypsum mortar, penetrometer tests were carried out on internal bed joints of mortar at each level of the stairs (each complete twist) corresponding to the NSEW directions at a height of 1m from the step, for a total of 26 valid measuring points. The historical masonry mortar penetration test is based on the principle of penetration, and the test result is the penetration load as a function of the penetration depth. As a result, for each sample (masonry mortar) several penetrations were made (from 15 to 20), and only the fifteen penetration values which have more or less than 25% of their mean value were selected. The average value of the selected measurement points is calculated to estimate mortar compressive strength providing fc = 3.24 MPa (CV = 0.23). Using the T Student test, for the set of 26 valid measurement points, the confidence interval for the theoretical average compressive strength is (3.05 MPa;3.43 MPa) with 78% probability. It is worth highlighting that the penetrometer fitting curves are calibrated on lime mortars, which generally show higher grain-binder cohesive capacity and bigger aggregate size, hence the reported value is reasonably a safe lower threshold of the uniaxial compressive strength. Observation of data subsets belonging to the same twist suggests that mortar belonging to levels 1, 2, and 3 show slightly lower compressive strength values (3.19 MPa, 2.52 MPa, 2.93 MPa, respectively) compared to level 4 and 5 (with values 3.97 MPa and 3.74 MPa, respectively). Borescope Observations. At the base of the minaret, accurate inspections revealed that the lowest set of holes once accommodating the wood elements stitching the minaret to the madrasa is effectively the location of the base crack. Hence, borescope images revealed on the lateral surface of the cylindrical void left by the absence of wood, that the crack developed deep inside the base of the shaft. It was possible to evaluate the length of the visible crack ranging 1.4–1.45 m from the external surface.
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Fig. 5. Three-dimensional representation of the six modes.
3 Operational Modal Analysis and Seismic Interferometry In recent few decades, Operational Modal Analysis (OMA), also known as Output Only or Ambient Vibration Test, has become a powerful tool for a wide range of applications in the field of civil engineering [16, 17]. In the last ten years, several authors, in addition to monitoring the modal frequencies, have presented new approaches to structural dynamic analysis based on seismic interferometry of ambient vibration [18–21] to investigate the seismic wave propagation in the building. Seismic interferometry evaluates the impulse response function (IFR) of an elastic medium from one point to another. Wave phase velocity of impulse response functions (IRFs) is uncoupled with soil-structure interaction, being directly linked to the stiffness of the building [22, 23]. The recorded data concerns five stations located at different levels (1.45 m, 10.58 m, 20.47 m, 28.31 m and 40.44 m) of the 5th Minaret of Herat relative to about 39 h (from 11:00 UTC on 27 May to 01:00 UTC on 29 May) with no gap at all five stations. Each seismic station was equipped with 3-component seismometers with Lennartz 3D/1s seismometers. Seismic data were digitized using a 24 bits Lunitec Atlas Digitizer at
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500 Hz, and the time synchronization between stations was achieved using GPS. The time series has been divided into 30 min long consecutive blocks. For each data set the spectral analysis was performed using Welch’s technique with an overlap of 66% and a Hanning weighting function of 120 s with a frequency resolution of 0.0076 Hz. Results provide the frequencies, directions and damping ratios of the first six modal shapes, see Fig. 5. Each couple of modal shapes exhibits substantial orthogonality with movement trending in the 60°–240° N direction (Mode 1) and in the 155°–335° N direction (Mode 2). The first two modal shapes show a frequency of 0.483 Hz and a damping ratio of 1.62%, and 0.613 Hz and a damping ratio of 1.08%. The third and fourth modes show frequencies of 1.941 Hz and 2.301 Hz, and damping of 1.11% and 0.92%, respectively. The fifth and sixth modes have frequencies of 4.728 Hz and 5.452 Hz and a damping ratio of 1.05% and 0.96% respectively.
4 Structural Investigation Based on the results of all the investigations reported in the previous sections it has been possible to implement a 3D model of the minaret to be represented into a FE environment and possibly modelled to understand its response to different loading conditions. The high complexity of the spiral staircase, the presence of a remarkable crack at the bottom of the base, and the crucial intervention of strand installation, discouraged the use of more simplified methods of structural analysis. The analyses carried out included vertical loads, eigenfrequencies and modal pushover. The 3D model was directly meshed from the TLS survey carried in 2021 by AKCSA. The 2D meshes were refined from the point cloud in CAD environment and “sealed” to effectively create a 3D volume. The model was employed in DIANA FEA environment, [24]. The fixed constraints were applied at the surface of the base. The presence of strands literally preventing the structure from instability, were modelled as a set of 54 3D point forces. To prevent stress concentration, a rigid “service” plate coincident with the meshed surface of the minaret, was modelled to apply cables forces on. The direction and intensities of the forces were evaluated one by one, from an inverse thrust line analysis procedure. Knowing from the past reports the expected thrust in the strand cables, the topographic survey of the cables path, and through TLS survey the 3d path attached to the Minaret, the resultant forces and directions of each component became defined, so that the intensities of each component could be defined. The volume was meshed with 89649 non-linear 16-nodes brick elements of nominal length 300 mm. The values assigned to the material properties are reported in Table 1. To provide a sound, reliable FE model, the OMA results were employed. In particular, starting from the results of the first 6 modal shapes, and frequencies it was decided to fit the experimental data by refining the position and depth of the base fracture, keeping the mechanical properties of the masonry fixed, which is acceptably homogenous at the building scale. By step-by-step refinement of results of the eigenfrequency analyses, through a trial-and-error procedure, it was possible to define the geometrical model with modal shapes, directions, and frequencies, satisfactory similar to experimental data. Directions fitted with the experimental one and the obtained modal frequencies are 0.48 Hz, 0.55 Hz, 2.16 Hz, 2.36 Hz, 5.18 Hz, 5.47 Hz. The position and dimensions of
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Table 1. Mechanical parameters employed in the FE analyses. Name
Value
Material model
Total strain-based crack model
Young’s modulus
1 800 MPa
Poisson’s ratio
0.1
Mass density
1800 kg/m3
Crack orientation
Fixed
Tensile curve
Linear-ultimate crack strain
Tensile strength
0.1 MPa
Ultimate strain
0.005
Residual tensile strength
0.01 MPa
Shear retention function
Constant
Shear retention factor
0.01
the crack was implemented by creating a real disconnection at the base of the model by subtracting a wedge volume of 187 cm depth and 3 cm width at the crack mouth. The fitted direction obtained lays substantially in the direction of the mode 1 modal shape. In other words, the first modal shapes and frequencies tested on site by OMA can be simulated in the FE model by assuming the presence of a deep fracture at the base orientated on the place in the same direction of the first modal shape. Only after having defined a reliable model in terms of self-frequencies, the vertical and seismic load non-linear analyses were carried out. It is worth underlining that the linear static analysis carried out removing the effect of the strand cables could not be carried out; hence, the whole system is effectively in equilibrium only for the geometry of the external forces layout. The response under vertical loads assuming a nonlinear behavior of masonry, had to be carried out iteratively. This fact shows that for the current displaced condition, the only presence of the Minaret self-weight, induces with reasonable accuracy, some damage state to the material itself. The highest damage is connected to the crack mouth at the base. Also, for gravity loads, the maximum value for the out-of-plane principal stress components at the base of the minaret reach at most 1.07 MPa, in very good agreement with results from [3], and acceptable only in drained condition of the soil strata under foundations. After the analysis for vertical loads, the response of the minaret against earthquake loading has been investigated. The probabilistic seismic hazard curves for the site, according to USGS, [4], are reported in Fig. 6. Based on the expected acceleration values at site and the results of the eigenfrequency analyses, a set of modal push over analyses have been carried out to understand the expected damage level in case of earthquake. The modal pushover analysis was conceived to improve the standard push-over method. Basically, a series of push over analyses is carried out according to higher vibration modes that activate a remarkable amount of modal mass. Standard static non-linear analyses are based on loading transversely the structure under investigation
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through force or displacement distributions proportional to the first modal shape or to mass distribution. However, it is widely acknowledged that tall buildings are vulnerable to the response according to the higher vibration modes, which generally shows frequencies correspondent to the highest values (plateau interval) of the acceleration spectrum, causing cracks forming on the higher half of the shaft rather than at its base. In the case of the minaret, the vulnerability to the first modal shaped is markedly pronounced due to the presence of the base crack. Through modal pushover analysis, the first five vibrations shapes became the displacement-based loading profiles, in positive and negative directions. This approach has the advantage of “following” the damage of the building loaded, since as soon as the material enters a non-linear phase in some areas, showing increased strains, the displacement-based loading profile adapts to the new (damaged) shape. The results are summarized in Fig. 7, in terms of crack strains, which show how the expected damage is concentrated in the lower part of the minaret. With lower values, there are crack strains also expected at the intersection lines between the staircase and the vertical masonry, revealing that the area will need cautious reinforcement interventions, in addition to those aimed at reducing the effect of the base crack.
Fig. 6. Hazard curves for Herat for PGA, 0.2-s SA, and 1.0-s SA. The horizontal dashed black lines correspond to a 10- (upper) and 2- (lower) percent probability of exceedance in 50 years or a return period of about 500 and 2,500 years, respectively. The solid black line is the seismic hazard curve resulting from a combination of all sources. The dashed-dot curves reflect contributions to seismic hazard using the ground-motion relation of Ambraseys and others (1996), while the solid curves represent Western United States ground-motion relations. The red curves are the contribution to seismic hazard from fault sources that are characteristic, and the green curves are for Gutenberg-Richter. The blue curves represent contributions from background seismicity less than 50-km depth, while the cyan curves represent contributions from seismicity between 50- and 100-km depth (solid) and 100- and 250-km depth (dashed-dot). Adapted from USGS [4]
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Fig. 7. Results of pushover analyses in terms of crack strains, for accelerations levels as per predicted by USGS levels.
5 Closing Remarks The paper reports a series of investigations aimed at understanding the vulnerability of the Fifth Minaret of Herat. Tests were carried out on site and in laboratory and covered physical, mechanical, and mineralogical aspects. The complete Terrestrial Laser Scanning survey combined with Operational Modal Analysis and seismic interferometry constituted the knowledge basis for the 3D Finite Element model, which has been provided with mechanical parameters of the material obtained by laboratory tests and refined based on the outcomes of direct inspections and results of the modal shapes tested on site. Still a great research work is duly necessary to provide this monument appropriate consolidation and conservation strategies.
References 1. Manz, B.F.: Gowhar-˘S¯ad¯A¯g¯a. Encyclopædia Iranica XI, pp. 180–181.600 (2002) 2. O’Kane, B.: Timurid Architecture in Khurasan. Costa Mesa (1987) 3. Margottini, C.: Emergency consolidation of the 5th minaret in Herat (Afghanistan): report on the mission 25th november – 2nd december 2010. 603 Technical Report. UNESCO (2010) 4. USGS Homepage. https://earthexplorer.usgs.gov 5. Lico, A.: Il Quinto Minareto di Herat (Afghanistan, 1432 d. C.): percorso della conoscenza per un progetto di consolidamento (in Italian). Master’s thesis at the University of Florence (2021) 6. Macchi, G.: Saving minarets at risk in afghanistan. Structural Analysis of Historical Constructions-Modena i Lourenco& Roca, pp. 1375–1382 (2005) 7. Perrone, C., Pie, S., Seiler, U., Ziegert, C.: Long-term conservation proposal for the permanent structural safety of the fifth minaret in Herat. Technical report. UNESCO (2012) 8. Urban, T.: Gawhar Shad Madrasa Mission (Oct-Nov 2010). Archaeological excavations and topographical Mapping. Technical report. UNESCO (2010) 9. De Vito, S.: Implementation of monitoring system and structural strengthening work of the base of the 5th Minaret. Technical report. UNESCO (2016)
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10. Aube, S., Lorain, T., BendezuSarmiento, J.: The complex of Gawhar Shad in Herat: new findings about its architecture and ceramic tile decorations. Iran J. Br. Inst. Persian Stud. 58(1), 62–83 (2020) 11. EN 772–1: Methods of test for masonry units - Determination of compressive strength. European Committee for Standardization (2011) 12. EN 12390–6: Testing hardened concrete – Tensile splitting strength of test specimens. European Committee for Standardization (2010) 13. Lourenço, P.B., Fernandes, F.M., Castro, F.: Handmade clay bricks: chemical, physical and mechanical properties. Int. J. Architect. Herit. 4(1), 38–58 (2010) 14. Shu, C.X., et al.: China’s brick history and conservation: laboratory results of Shanghai samples from 19th to 20th century. Constr. Build. Mater. 151, 789–800 (2017) 15. Matysek, P., Witkowski, M.: A comparative study on the compressive strength of bricks from different historical periods. Int. J. Architect. Herit. 10(4), 396–405 (2016) 16. Brinker, R., Zhang, L., Andersen, P.: Modal identification from ambient responses using frequency domain decomposition. In: Proc. of the 18th International Modal Analysis Conference (IMAC), San Antonio, Texas (2000) 17. Rainieri, C., Fabbrocino, G., Cosenza, E.: Automated Operational Modal analysis as structural health monitoring tool: theoretical and applicative aspects. Key Eng. Mater. 347, 479–484 (2007) 18. Sneider, R., Safak, E.: Extracting the building response using seismic interferometry: theory and application to the Millikan library in Pasadena, California. Bull. Seismol. Soc. Am. 96(2), 586–598 (2006) 19. Nakata, N., Snieder, R.: Monitoring a building using deconvolution interferometry. II: Ambient-vibration analysis. Bull. Seismol. Soc. Am. 104(1), 204–213 (2014). https://doi. org/10.1785/0120130050 20. Bindi, D., et al.: Seismic response of an 8-story RC-building from ambient vibration analysis. Bull. Earthq. Eng. 13(7), 2095–2120 (2014). https://doi.org/10.1007/s10518-014-9713-y 21. Lacanna, G., Ripepe, M., Coli, M., Genco, R., Marchetti, M.: Full structural dynamic response from ambient vibration of Giotto’s bell tower in Firenze (Italy), using modal analysis and seismic interferometry. NTD and E Int. 102, 9–15 (2019) 22. Todorovska, M.I., Trifunac, M.D.: Impulse response analysis of the Van Nuys 7 storey hotel during 11 earthquakes and earthquake damage detection. Struct. Control. Health Monit. 15, 90–116 (2008) 23. Todorovska, M.I.: Seismic interferometry of a soil-structure interaction model with coupled horizontal and rocking response. Bull. Seismol. Soc. Am. 99(2A), 611–625 (2009) 24. DIANA TNO BV https://dianafea.com/
FE Model Update of a Historic Masonry Building After Restoration. The Case of the Palacio Pereira in Santiago, Chile María I. Valenzuela1 , Wilson Torres2 , Cristián Sandoval1(B) , and Diego Lopez-Garcia1,3 1 Department of Structural and Geotechnical Engineering, Pontificia Universidad Católica de
Chile, Santiago, Chile [email protected], {csandoval,dlg}@ing.puc.cl 2 Department of Civil Engineering, Universidad Politécnica Salesiana, Campus Sur, Quito, Ecuador [email protected] 3 Research Center for Integrated Disaster Risk Management (CIGIDEN) ANID FONDAP 1522A0005, Santiago, Chile
Abstract. The Palacio Pereira, located in Santiago - Chile, is a historic masonry building that was severely damaged by the March 3, 1985 (Mw 8.0) and February 27, 2010 (Mw 8.8) earthquakes. This building was declared a National Monument in 1981, and its restoration began in 2016 after more than 30 years of complete abandonment. The seismic upgrade process included the repair of the existing structural damage and the execution of strengthening strategies to improve the seismic performance. In this context, this paper presents a brief description of the main works aimed at returning structural integrity, as well as the strengthening interventions carried out to improve the future seismic performance. In addition, the main results of an in-situ experimental campaign, aimed at identifying modal parameters from the response to ambient vibrations, are presented and discussed. Finally, a 3D Finite Element (FE) model of the building is updated by modifying the density and Young modulus of masonry to improve the matching between experimental and analytical frequencies. Results show that the new floor system provides a certain degree of diagram constraint. Keywords: Heritage building · Restoration · Seismic strengthening · OMA test · Model updating
1 Introduction In Chile, historic and heritage masonry constructions are relatively scarce mainly due to the high seismic activity of the country. As an example, after the Maule earthquake (Mw 8.8) on February 27, 2010, significant losses of built heritage were reported [1, 2]. Consequently, improvements in the seismic performance of this type of construction should be undertaken to avoid further losses in future events. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 517–531, 2024. https://doi.org/10.1007/978-3-031-39450-8_43
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In the last decade, different technical methods have been developed for repairing and strengthening unreinforced masonry (URM) structures. However, the choice of the most suitable technical solutions is part of the complex, multidisciplinary procedure of conservation and restoration of architectural heritage. In this context, interventions causing only a reduced impact on the original structure should be preferred, provided that they are enough to warrant the required safety level [3]. Seismic rehabilitation of historic structures is often very challenging from a scientific and technical point of view due to their unique structural configurations and the inherent uncertainties associated with existing structures. Therefore, the validation process of the structural model of the building under study is of critical importance. In this scenario, ambient vibration testing has become the main experimental method available for assessing the structure’s natural frequencies and modal shapes [4, 5]. The modal properties thus defined can be used to calibrate the numerical model by adjusting some uncertain parameters. Through this methodological approach, a representative numerical model of the current state of the structure can be achieved. The Palacio Pereira, built in 1872, is a historic URM building located in Santiago, Chile. This construction was in a stage of neglect since 1980 and its state of damage before restoration was mainly due to the accumulated action of two large earthquakes (the 1985 [Mw 8.0] and 2010 [Mw 8.8] earthquakes). In 2012, a public architecture competition was called for its restoration and finally, between 2016 and 2019, the building underwent an architectural restoration and seismic retrofit project. Figure 1 shows views of the exterior of the Palacio Pereira before and after its restoration. Taking advantage of the project, the Palacio Pereira was the subject of some studies since it is one of the first seismic rehabilitation works in Chile that is carried out following the present-day conservation and restoration principles. For instance, its pre-restoration seismic response was numerically assessed using linear elastic analyses [6] and nonlinear time-history analyses [7]. Also, a 3D FE model of the Palacio Pereira was used for validating a multi-directional pushover approach which can be used for the seismic analysis of irregular URM buildings without box behavior [8]. This paper presents a brief description of the main works aimed at restoring structural integrity to the Palacio Pereira, as well as the strengthening interventions carried out to improve its future seismic performance. In addition, the main results of an in-situ experimental campaign, aimed at identifying modal parameters of the restored structure due to ambient vibrations, are presented and discussed. Finally, a 3D FE model of the building in its current condition is updated by modifying some structural parameters to improve the matching between experimental and analytical frequencies.
2 Palacio Pereira 2.1 Previous Work The Palacio Pereira is a two-story building with two main façades, the south and eastern facades, as shown in Fig. 2a. Its main earthquake-resistant system is made up of URM shear walls with an average thickness of 65 cm. As can be seen, this historical building presents structural irregularity both in plan (Fig. 2b, L-shaped) and in elevation and
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Fig. 1. Exterior of the Pereira Palace before (a) and after (b) the restoration carried out in the period 2016–2019.
exhibited structural deficiencies (flexible timber floors, inadequate floor-to-wall and wall-to-wall connections) when it was struck by the 2010 Chile earthquake.
Fig. 2. (a) Isometric view of the Palacio Pereira; (b) Plan view of 1° floor.
Previous investigations [6–8] summarized the major damage observed in the building: large diagonal cracks at inner walls and above windows and doors, as well as a lack of connection of some perpendicular walls with the eastern façade. In addition, due to the abandonment, there was no wooden diaphragm on the second floor either. Figure 3 shows the main cracks in the south and eastern facades of the Palacio Pereira registered after the 2010 Maule earthquake. Several laboratory and in-situ tests were carried out to determine the main mechanical properties of the existing masonry in the structure [7]. Samples of historic mortar and bricks obtained from Palacio Pereira were characterized in the laboratory following standard methods. In addition, two in-situ campaigns were performed. The first one was for determining the masonry shear strength through a shear-compression test. It was performed on a portion of an existing wall located on the first floor of the building. This in-situ test was essential to obtain and calibrate some important parameters of a numerical model. It should be noted that the in-situ shear test provided a shear strength of 0.23 MPa for the existing masonry. The second campaign was a single and double flat
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jack test oriented to obtain the stress state under gravitational loading in a given wall and the elastic modulus of masonry. The Young’s modulus value found was E = 1785 MPa. The experimental values obtained and other assumed parameters were used in the corresponding 3D FE model of the building. Subsequent analyses carried out with the entire model showed that most of the modes of the structure were essentially local modes, as expected due to the absence of rigid diaphragms. Several modal shapes showed out-ofplane deformations in some walls mainly in the east-facing façade which could explain (in part) the deformed state and observed damage to the structure. Finally, a good general agreement was observed between the existing damage patterns and the damage predicted by the numerical model [7].
Fig. 3. Main cracks registered in the south (a) and eastern (b) façades of the building before restoration.
2.2 Main Structural Interventions The repair and strengthening of a URM building against earthquakes represent a complex procedure. The interventions to be carried out must ensure a good performance of the whole structural system. Therefore, some measures such as the following should be promoted: to provide floor diaphragm action, to restore and ensure a good connection between structural walls, to restore the integrity of the structural elements through crack injection or reconstruction of damaged parts, and to provide the seismic resistant elements with a greater capacity in shear resistance and ductility. In this framework, the retrofitting interventions aimed at restoring the Palacio Pereira took all previous studies into account. Specifically, the main interventions may be grouped as follows: • Replacement and strengthening of wooden beams (oak) used in floor systems (Fig. 4a) • Reconstruction of the most damaged parts of the walls (Fig. 4b) and use of embedding steel bars in the horizontal mortar joints of damaged spandrels (bed-joint structural repointing) (see [9]). • Injection of cracks using natural hydraulic lime mortar (Fig. 4c) • Construction of a floor system composed of wooden beams and RC slab on the second floor and the roof level (Fig. 4d-e). The RC slab was only 7 cm thick. This intervention is intended to ensure a uniform distribution of seismic loads among the shear walls while not adding a lot of mass to the structure. Additionally, given the numerous openings present in the building and the observed post-earthquake damage (see Fig. 3), all doors and windows of the Palacio Pereira were
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Fig. 4. Summary of some of the main structural interventions in the Palacio Pereira.
reinforced with a 200 mm wide and 10 mm thick steel ring all around. The fastening of these rings to the masonry was based on the assembly of rod anchors with a diameter of 16 mm and a length of 1 m. Such anchors, placed every 30 cm on average, were embedded in the masonry using epoxy and then joined to the steel ring by welding. Figure 5 shows a schematization of the solution and some details of its execution. This intervention seeks to provide the structural walls, mainly on the first floor, with a greater capacity for shear resistance and ductility. Note that a similar solution has been implemented in restoration projects of historic buildings in Turkey [10] and Italy [11].
3 Dynamic Identification 3.1 Experimental Campaign An experimental campaign to estimate the modal properties of the Palacio Pereira after the restoration was designed and implemented. The dynamic identification approach used in this research was the same as that used in the Metropolitan Cathedral of Santiago, Chile [5, 12]. The experimental campaign consisted of measuring the response to ambient vibrations of the structure at selected points. During the experimental campaign, five accelerometers were used. These devices measure accelerations and velocity in the 3 orthogonal directions. The synchronization of the sensors was adjusted based on radio signals that connect them to each other. The vibration of the structure was recorded by measuring velocity due to its larger signal-to-noise ratio. At least 10 setups were made
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Fig. 5. Reinforcing of openings with a steel ring and embedded anchors: (a) schematization (dimensions in mm) and (b-e) construction sequence.
during the campaign, however, only 5 of them were finally used to measure the response of the structure. Figure 6 shows the location of the five setups considered. A set-up is an array of instruments where the dynamic response of the structure is recorded for at least 20 min. A sampling rate of 128 Hz was used. In all set-ups, two reference instruments were used, i.e., always located at the same position (called Ref-T1 and Ref-T2 in Fig. 6). These two sensors were located on the second-floor level (+5.9 m). As can be seen, the number of sensors considered in each setup was different because some readings had to be discarded due to problems such as loss of synchronization and close hits to some equipment, among others. It should be noted that setup #3 included two sensors on the roof level (+11.5m).
Fig. 6. Location of the sensors for all set-ups.
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3.2 Signal Processing Before identification, each of the signals was filtered through a low-pass filter with a cutoff frequency of 16 Hz. These records were then analyzed in the ARTEMIS software [13]. The identification method used was EFDD (Enhanced Frequency Domain Decomposition) [14]. As the name implies, this method is an improved version of the wellknown FDD method (Frequency Domain Decomposition) [15]. These improvements consist mainly of determining frequencies and damping by the correlation function and determining the mode shape by the weighted sum of the singular vector decomposition. The EFDD method was applied using a manual peak-picking process on singular value curves (Fig. 7a). The obtained natural frequencies of the structure were the following: 4.98, 5.71, and 6.32 Hz. The independence between them is validated based on the determination of MAC between the three proposed modes (Fig. 7b). A small dependency is observed between the second and third-mode shape vectors.
Fig. 7. (a) Singular values of the spectral densities marking natural frequencies; (b) MAC between experimental modes.
3.3 Experimental Modes Figure 8 shows the three modal shapes obtained by the application of EFDD methodology. As can be seen, the first mode involves translation mainly in the NS direction and activates the entire south façade of the Palacio Pereira; the second one involves translation in the EW direction, while the third mode is rotational and activates the walls in the short and long directions at the same time. It is important to note that these experimental results show that the floor system built during the restoration process (wooden beams plus RC slab) is not capable of generating a rigid diaphragm as such, neither at the second-floor level nor at the roof level. Consequently, the corresponding 3D FE model of the building must consider this important aspect through a proper modeling of the elements that make up the floor systems.
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Fig. 8. Experimental modal shapes (plan view of the structure): (a) freq. 4.97 Hz; (b) freq. 5.71 Hz; (c) freq. 6.32 Hz.
4 Model Update 4.1 Model Description To perform a 3D structural analysis of the Palacio Pereira, a FE model was implemented in the DIANA software [16]. The FE model was updated based on a numerical model previously generated by Sandoval et al. [7]. The model was intended to be representative of the restored condition of the building and consequently, some aspects of the geometry of the model had to be updated. Figure 9a shows the load-bearing walls with all modifications done during the restoration project. Meanwhile, Fig. 9b shows the areas where RC slabs were built (which agrees with the areas indicated in gray in Fig. 6). It should be noted that wooden beams and RC slabs were modeled in an independent way to realistically simulate the structural behavior of the new floor system. Figure 9c shows the steel roof structure of the gallery area which was modeled with an equivalent floor system. Last, Fig. 9d shows a view of the FE model along with its meshing.
Fig. 9. FE model of the Palacio Pereira: (a) URM masonry walls, (b) RC slabs, (c) equivalent steel roof, and (d) meshing
As in Sandoval et al. [7], the roof system and the parapets were not explicitly included in the model because their stiffness properties were deemed to have no influence on the seismic response of the building. Their mass properties, however, were included in the
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model as tributary lumped masses at the nodes located at the roof level (roof system and parapets). Likewise, the weight of these elements was also included in the model as tributary concentrated loads. All the walls of the Palacio Pereira were modeled by shell elements; in particular, curved triangular shell elements (CT30S), with an average element size of 0.5 m. An average thickness of 0.65 m was assigned to all walls. Regarding the horizontal floor system, RC slabs were also modeled with curved triangular shell elements (CT30S) and a thickness equal to 0.085 m was assigned to these elements. Meanwhile, all the wooden beams were modelled with truss elements (L2TRU) and were spaced 0.5 m between their centerlines. The steel beams of the gallery area were separated by 0.52 m in the NS direction and 0.48 m in the EW direction and a section whose area is equal to 0.0225 m2 was assigned These beams represent the existing trusses in the gallery area. As for the support conditions, all the existing walls on the first floor were restricted at their base to translation in the X, Y and Z directions. The entire model shown in Fig. 9d was built with around 49,400 shell-type elements and 530 truss-type elements, all of which are connected by more than 100,240 nodes. Table 1 summarizes all the values of the parameters initially assumed in the FE model. The mechanical properties of the materials that were used for the elements are those necessary to update the model in the elastic range since it is assumed that environmental vibration only develops in the linear elastic range of the component materials. Table 1. Initial mechanical properties of materials Material property
Symbol
Unit
Masonry
RC (H25)
Wooden beam (Oak)
Steel (A370-240ES)
Young´s Modulus
E
MPa
1785
21200
12300
210000
Density
ρ
Kg/m3
1800
2500
550
7850
Poisson’s ratio
ν
-
0.2
0.2
0.2
0.3
4.2 Modal Parameter Identification The purpose of the modal identification is to get the frequencies and modal shapes of the Palacio Pereira. These properties will be compared with those obtained from the analytical model generated, that is, based on the environmental vibration test described in Sect. 3 and then obtaining an updated version of the FE model of the building. The update of the calibration parameters of the model represents average values of some mechanical properties of the material that constitutes the structure and also the changes made to the structure in the restoration process between the years 2016–2019. As previously mentioned, the masonry walls were modeled as a homogeneous material that included steel reinforcement in openings of doors and windows, therefore, to calibrate the model, only the linear elastic properties of this material were modified: Young’s modulus and density.
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The first step before modifying any parameter is to perform a modal analysis on the analytical model of the structure to obtain the initial errors with respect to the experimental frequencies obtained from the ARTEMIS software (Fig. 10). The initial values of the calibration parameters are called nominal values in the optimization process. In Table 2, the experimental and nominal frequencies are compared; an error of 4.44% is obtained for the first mode, 7.32% is obtained for the second one, and the third one shows an error equal to 2.78%. The sum of these values gives a global error equal to 14.53%. The nominal error for each mode is defined by Eq. (1). It should be noted that when obtaining the modal shapes and frequencies, the local deformations in the gallery area are pronounced; therefore, to show the global mode shapes of the analytical model, this area was hidden in Fig. 10. f anai − f expi · 100 (1) %Errornomi = f expi where fanai corresponds to the analytical frequency, and fexpi to the experimental frequency. Table 2. The error between analytical and experimental frequency (initial properties). Mode description
Experimental Analytical frequency (Hz) frequency (Hz)
Effective modal mass (%)
Nominal error (%)
Global error (%)
Mode 1: N-S translation
4.98
5.21
23
4.44
14.53
Mode 2: E-W translation
5.71
6.13
33
7.32
Mode 3: Torsion
6.32
6.50
Dir NS: 23; Dir EW: 17
2.78
Fig. 10. Adimensional displacements of modal shapes with initial values: (a) translation NS, (b) translation EW, (c) torsion.
4.3 Calibration Process The following describes the mathematical method used to update the calibration parameters of the analytical model of Palacio Pereira based on the experimental model. It is
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necessary to take into account that the analytical values are greater than those required, therefore, it is necessary to decrease the values of the analytical modal frequencies by modifying the values of the elastic properties of the masonry. This decision is based on the intervention solution implemented in all openings of the building. Thus, the proposed method is an analysis in stages where the parameters are adjusted from the most influential to the one that least affects the change in the frequencies of the structure. First, a sensitivity analysis was carried out for two parameters related to masonry: density and Young’s modulus. The assessment of each parameter was carried out separately; that is, when one varies, the other two remained at their nominal value. Each one was increased and decreased by 5%, 10% and 15% of the nominal value (see Table 3), and then, the frequencies for each of these cases were obtained. The study thus sought to see its influence on the response of the model. Figure 11 shows the variation of the frequencies in each mode of the structure concerning the variation of the values of the parameters. It is possible to conclude that density is the most influential parameter since the highest rate of change in the frequencies is obtained. Therefore, the order of adjustment of the masonry parameters to achieve the calibration of the analytical model is the following: first density and then the Young’s modulus. Secondly, the adjustment of the masonry parameters was carried out in stages. The frequency values of the three modes of the FE model were obtained by varying the density ±15%, ±10% and ±5% to the nominal value. Then, the obtained frequency values were plotted and the interpolating second-degree polynomial expression was obtained, which represents the variation of the frequencies for modes as a function of the density. Subtracting from this expression the nominal experimental value and squaring this difference, the error for each of the modes was obtained. A general way for each calibration parameter is represented by Eq. (2). Errormodei = (Fanai − f expi )2
(2)
where Fanai corresponds to the function of the second-degree polynomial curve of the analytical frequency and fexpi is the value of the experimental frequency of the same mode. Given the error for each mode, the Excel SOLVER function, which optimizes linear or non-linear, smoothed or non-smoothed problems, was used to obtain the density value that minimizes the total error, which is given by the sum of the errors of the first, second, and third modes. Table 3. Variation of masonry parameters for sensibility analysis Property
85%
90%
95%
Nominal Value
105%
110%
115%
Young’s modulus (MPa)
1517
1607
1696
1785
1874
1964
2053
Density (kg/m3 )
1530
1620
1710
1800
1890
1980
2070
Finally, the value of the calibrated density is obtained. The value in the DIANA model is updated and the process is repeated, which now minimizes the total error of the frequencies for the modulus of elasticity. It should be noted that the order is important
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since it is necessary to accomplish the influenceability in the variation of the frequencies of the model for the proper functioning of the exposed method. Based on Fig. 11, it can be seen that Young’s modulus has less influence than density on the change of frequencies. It must be noted that density is related to the mass of the model but not to its stiffness, hence a change in density can be expected to significantly influence the modal frequencies. Likewise, Young’s modulus is related to the stiffness of the model but not to its mass, hence a change in Young’s modulus can also be expected to significantly influence the modal frequencies. In other words, the results of the sensitivity analysis are consistent with physics-based observations.
Fig. 11. Frequency variation of each mode based on the variation of each calibration parameter.
4.4 Results The analytical model presented global errors decreasing each stage when calibrating the masonry parameters. After several iterations, a total error of 5.84% was obtained between the analytical frequencies and those obtained experimentally. The values of density and Young’s modulus that minimize the frequency errors are 1979.7 kg/m3 and 1789.4 MPa respectively. These values are presented in Table 4. Table 4. Calibrated properties. Property
Nominal value
Calibrated value
Density (kg/m3 )
1800
1979.7
Young’s modulus (MPa)
1785
1789.4
As a summary, the analytical frequencies ofthe FE model with the finally calibrated parameters can be found in Table 5, while the corresponding mode shapes are presented in Fig. 12. The results of the calibrated model, in particular of effective modal mass, show that the new floor system provides a certain degree of diaphragm constraint in relation to the condition prior to the restoration of the building.
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Table 5. The error between experimental and analytical frequencies with calibrated parameters. Mode description
Experimental Analytical frecuency (Hz) frecuency (Hz)
Effective modal mass (%)
Nominal error (%)
Global error (%)
Mode 1: N-S translation
4.98
5.00
19
0.32
5.84
Mode 2: E-W translation
5.71
5.89
39
3.12
Mode 3: Torsion
6.32
6.17
Dir NS: 26; Dir EW: 5
2.40
Fig. 12. Adimensional displacements of modal shapes with calibrated properties: (a) translation NS, (b) translation EW, (c) torsion.
5 Conclusions The Palacio Pereira, a heritage structure recently restored, was studied based on measurements of its modal properties. A process of identification of frequencies and modal forms of the existing building in its restored condition was developed. Then, the update of the FE model of the building was carried out by modifying the density and elastic modulus of the masonry present in the load-bearing walls. The update was carried out in a process of minimizing the error between experimental and analytical frequencies. This study allows us to conclude the following: • The results of the dynamic identification of the Palacio Pereira showed that the new floor systems do not constitute a rigid diaphragm as such. This may be due to the lack of stiffness of the implemented solution compared to the stiffness of masonry walls. The implications of this fact should be investigated in future studies. • The obtained values for the calibration parameters are average values that get a nearby analytical model to the experimental one. In some locations of the structure, these values can be bigger or lower than these averages, but they represent adequate values to get the objective and minimize the errors between analytical and experimental frequencies. • The final values of calibration parameters seem logical taking into account the interventions performed in the Palacio Pereira. In particular, the steel reinforcement solution executed in each opening of the building increased the mass of the masonry (density) and very slightly increased its elastic modulus.
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• The calibrated model can now be used to carry out non-linear time history analyses in order to assess the performance of the building in its restored condition against future seismic events. Acknowledgements. This research has received financial support provided by ANID-Fondecyt through grant No. 1221407. Further support was provided by the Research Center for Integrated Disaster Risk Management (CIGIDEN) ANID FONDAP 1522A0005 (Santiago, Chile).
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13. Structural Vibration Solutions A / S. ARTeMIS (2015) 14. Brincker, R., Ventura, C.E., Andersen, P.: Damping estimation by frequency domain decomposition. In: 19th International Seminar on Modal Analysis, pp. 698–703 (2001) 15. Brincker, R., Zhang, L., Andersen, P.: Modal identification from ambient responses using Frequency Domain Decomposition. In 18th International Seminar on Modal Analysis (2000) 16. DIANA FEA. DIANA—Finite element analysi. Diana release 10.4 (2018)
Preliminary Assessment of the Resistance Characteristics and Dynamic Behavior of the San Francisco of Assis Church in Marcapata, Cusco-Perú Mijail Montesinos(B) , Julio Rojas-Bravo, Matt Valer, and Susan Choquemaqui National University San Antonio Abad of Cusco, Cusco, Perú {mijail.montesinos,julio.rojasb}@unsaac.edu.pe Abstract. The San Francisco de Assis church of Marcapata is a historical rubble masonry with mud mortar structure built between XVI and XVII centuries, located in the province of Quispicanchi, Cusco-Perú. Despite the importance of this monument, structural studies for its conservation and preservation are unknown. Those facts have motivated the realization of this study, with the objective to obtain data for the assessment of its actual structural condition. The paper begins with a brief description of the historical aspects of the Marcapata site and the Church, followed by the on-site structural inspection both at the exterior and interior of the monument. Based on in-situ non-destructive approach, Operational Modal Analysis (OMA) tests was further developed with reference to a representative wall of the monument. The results of the experimental field campaign were used to develop calibrated finite element models of the wall, and to indirectly estimate mechanical characteristics of the masonry. The initial structural inspection revealed the precarious state of conservation of the monument and the need for more detailed studies. Three-ruble-stone-mud-mortar wallets of 60 × 60 × 30 cm3 (height × length × width), made with materials like the original, collected around the site, were subjected to uniaxial compression monotonic load. A maximum compression resistance of 0.82 MPa was obtained. The dynamic properties of west wall of the church were identify through OMA tests. Three highly sensitive piezoelectric accelerometers and a data acquisition system were used. A fundamental frequency of 3.1 Hz was obtained using the enhance frequency domain decomposition approach. OMA tests also allowed to indirectly estimate a modulus of elasticity of 720 MPa for the masonry. The results obtained in this preliminary study will be used in the ongoing structural assessment of the Marcapata Church. Keywords: Marcapata Church · Rubble Stone Masonry · Compression Resistance · Operational Modal Analysis · Frequencies of Vibration · Modulus of Elasticity
1 Introduction The San Francisco de Assis Church of Marcapata is a historical construction built around the second half of the 17th century. Is located in the province of Quispicanchi, CuscoPerú. Its main support structure is made of rubble stone masonry with mud mortar © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 532–542, 2024. https://doi.org/10.1007/978-3-031-39450-8_44
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(Fig. 1a). The roof structure is made of wood, cover by traditional straw or “paja” periodically renewed. This pre-hispanic ancient construction tradition, which is held for the surrounding communities every four years as "Know practices and rituals associated with the communal work of the “repaje or wasichakuy (quechua language)” was declare in 2015, Cultural Patrimony of the Nation [1] (Fig. 1b). Likewise, the characteristics of the masonry in this monument show similar features to that founded in the area during pre-hispanic period. At its interior, Marcapata Church contain valuable mural paintings. Due to its location the church is exposed to natural hazards such as earthquakes, so that it is necessary to understand its structural behavior in order to secure its preservation. This paper shows preliminary studies carried out with the aim to obtain data for the structural evaluation. The study includes on-site visual inspection, compression uniaxial tests, operational modal analysis and numerical calibration of FE models.
2 Brief Historical Review 2.1 Marcapata Site Marcapata, in the time of the Incas, in the period of the government of the Inca Tupac Yupanqui, was strategically located at the confluence between the Araza and Cachic rivers. It was the gateway to the Cuchoa valleys, today called Quincemil, Tambopata and Puerto Maldonado, towns located in the jurisdiction and strip of Antisuyu. These original populations were called Manaries or “Iscay-Singas”, there were also the Arasaires. Areas that produced coca, gold, feathers and cedar wood. In the viceroyalty it was known as "Los Andes de Marcapata” [2]. In the second half of the 16th century, in the Cuchoa Valley, the purchase and sale of coca fields was intensely promoted, which was boosted by mining production in the Villa Imperial de Potosi. This is how in 1583, Juan Alonso Palomino, a resident of the city of Cusco, granted a coca farm in favor of Alonso Rivero for sale, in the Cuchoa valley, in the site called Miraflores, the transfer of such farms was made according to the manner in which they had been purchased from the "Indians of Marcapata, of the Cuchoa Valley” [3]. Towards the end of the 18th century, the Marcapata-Cuchoa valley suffered a major flood catastrophe caused by the collapse of the “Huahuallani" hill. Regarding this natural event, the Italian naturalist Antonio Raimondi (1865) made a geographical description of the disasters in Marcapata and surroundings. [4]. 2.2 The San Francisco of Assis Church The Marcapata Church, also named as Templo de San Francisco de Assis, is the church of the District of Marcapata, in the Quispicanchi Province in Cusco, Peru. Marcapata is a rural village of 5,300 inhabitants, located at 173 km east of the city of Cusco. The colonial town was located on a plain that follows the natural slope of the land, at a height of 3150 m above sea level. The primitive colonial settlement of the church was built around the middle of seventeen century. Probably, the humid climate conditions of the place, determined that the
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temple of San Francisco de Asís de Marcapata, was built using stone walls and tamped mud and not adobe as in other neighboring churches in the Ocongate region. At its interior, Marcapata Church contain valuable mural paintings. The Church was continuously used by the community since its construction in the seventeenth century and it is an important gathering and religious place for the community members. One of the unique remains in the Marcapata Church is the pre-hispanic ancient construction tradition, which is held for the surrounding communities every four years as “Know practices and rituals associated with the communal work of the ‘repaje’ or wasichakuy” was declare in 2015, Cultural Patrimony of the Nation. Likewise, the characteristics of the masonry in this monument show similar features to that founded in the area during pre-Hispanic period.
(a)
(b)
Fig. 1. (a) Location of The San Francisco de Assis Church of Marcapata (b) Communal work of the “repaje or wasichakuy (Quechua word)”.
3 On-Site Visual Inspection 3.1 Visual Inspection and Evaluation Criteria In this stage it was defined five structural macro-components: Foundation, Walls, Buttresses, Sub-structure of the Choir and Roof (Fig. 2) for which qualitative evaluation criteria were applied in order to determine the vulnerability of the structure and the need for further evaluation [5]. Table 1 shows the criteria for the preliminary evaluation of the structural macro-components.
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Fig. 2. Interaction among macro-components of the structure of the San Francisco of Assis Church. Table 1. Criteria for the preliminary evaluation of the structural macro components Qualification
Resilience
Connections
Construction
Deterioration
A
High, when the structural conception is competent with the demand
Well, when they are very appropriate for the demand
Very good quality
Very good state of conservation, when it does not require more than periodic maintenance;
B
Medium, the structural conception is good although in a few aspects it is not competent
Regular, when Good quality they work moderately and do not fully meet the demand
Good state of conservation, when it requires some repair treatment to continue fulfilling its function properly
C
Low, the structural conception is not in accordance with the demand, however it presents some appropriate aspects
Bad, when demand compliance is low
Regular state of conservation, when the intervention required can mean replacement parts
Regular quality
(continued)
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Qualification
Resilience
Connections
Construction
Deterioration
D
Very Low, the structural design is not appropriate for the function required
Very Bad, when the connection is completely deficient before the demand
Poor quality
Poor state of conservation, when it requires the replacement of the element or partial or total reconstruction
3.2 Results and Conclusions of the Visual Inspection and Evaluation Criteria Based on the visual inspection and the criteria given in Table 1, an evaluation for the San Francisco of Assis Church was carried out. Table 2 presents the results of the qualitative structural evaluation of the different macro-structural elements. Geotechnical studies concluded that the structure lays on rock bed. Likewise, Table 3 shows the evaluation of the interaction between such elements. Table 2. Evaluation Summary of the San Francisco de Asís Church of Marcapata Macro Element
Resilience
Connections
Construction
Deterioration
Façade Wall
B
B
B
B
Longitudinal Walls
C
C
B
B
Buttresses
C
N/A
B
B
Sacristy
B
B
C
B
Baptistery
B
B
C
B
Roof
C
D
B
D
Chorus
C
D
B
B
Front end Wall
C
C
B
B
There was observed three principal interactions mechanisms of macro-components. The first mechanism corresponds to the interaction between the longitudinal walls and the roof structure. The pairs of the roof structure are assumed to be supported by a wooden beam (arrocabe), which extends continuously over the longitudinal wall. This interaction is necessary for the support of the roof but it exerts horizontal thrust forces on the wall, because the “knuckle” in many cases is not enough to counteract said push. This motivates the wooden braces that connect the longitudinal walls to become in a second element of interaction. The braces are located under the arrocabe and their function is to counteract the horizontal force produced by the thrust of the ceiling. It is observed that most of the braces, due to the deterioration they present, do not fulfill this important function. Likewise, the brace above the choir has been removed.
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Table 3. Interaction between Macro Structural Elements Façade Longitudinal Buttresses Sacristy Baptiste Roof Chorus Front Wall Walls end Wall Façade Wall
Yes
Longitudinal Yes Walls
Yes
No
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Yes
No
No
No
Yes
No
No
No
No
Yes
Buttresses
Yes
Yes
Sacristy
No
Yes
No
Baptiste
Yes
Yes
No
No
Roof
Yes
Yes
No
No
No
Chorus
Yes
Yes
No
No
No
No
Front end Wall
No
Yes
Yes
Yes
No
Yes
No No
The second mechanism corresponds to the interaction between the longitudinal walls and the front-end wall. The interaction between these two macro- elements helps to maintain stability in the face of horizontal seismic forces. However, pronounced cracks are observed in both corners of these wall encounters. The action of the buttresses placed, possibly, after this phenomenon has occurred, does not help to control it due to the separation between these buttresses and the walls, probably caused by a settling and outward rotation of these elements. The third mechanism corresponds to the interaction between the façade wall and the wooden roof structure. The interaction between these elements occurs at the edge of the tympanum and is precarious since there are no important structural elements that connect the roof with the tympanum of the façade. Only the wooden straps are supported on the façade wall without apparently showing a special connection in said zones. According to these preliminary observations, it is concluded that the Temple of Marcapata is in a situation of vulnerability and more detailed studies are required to evaluate its structural capacity for adequate preservation measures.
4 Uniaxial Compression Tests Three-ruble-stone-mud-mortar wallets of 60 × 60 × 30 cm3 (height × length × width) made with materials collected around the site, were subjected to uniaxial compression monotonic load. The material used consisted in andesite ruble stone with 7 –10 diameter (Fig. 3a), and a 1 thickness mortar made with clay soil mixed with cut straw fibers (Fig. 3b and 3c). Reinforced concrete beams of 120 × 20 × 30 cm3 (length x height x width) were placed up and bottom the specimens to guarantee uniform compression stress in the material, and a cement mortar was placed in the interface specimen-beams to prevent local failure in this zone (Fig. 3d). The tests were force controlled at a velocity rate of 7200 N/min. A similar failure mode was observed in the three specimens. The
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first significant crack appeared in the narrow side of the specimen, then cracks spread in the front face. The failure initiates in the mortar and continues through the test. There was no evidence of failure in the stones (Fig. 3e-f).
Fig. 3. Uniaxial compresion test (a) andesite stone units (b) mud mortar (c) fabrication process (d) cement mortar and concrete lintel (e) wallet tested (f) specimen failure mode.
An average value of 0.82 MPa with a coefficient of variation of 5.7% was obtained for the maximum compression resistance of the material. This value is in the range obtained in other studies for ruble-stone masonry [6] and [7]. According to ASTM C1314–22 [8], a slenderness factor of 1.0 was used for determining the maximum compression resistance (see Table 4). Table 4. Maximum compression resistance during tests Specimen Axial Load (N) Length (mm) Width (mm) Maximum Compression Resistance (MPa) 1
15971.1
30.1
59.9
0.87
2
14524.8
30.05
59.95
0.79
3
14520.2
30.02
60.05
0.79
Average
0.82
C.V
5.7%
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5 Operational Modal Analysis Tests and Calibration of the FE Model 5.1 OMA Tests Dynamic properties of the representative west wall of the monument (Fig. 4a) were identified by means of operational modal analysis. Three highly sensitive piezoelectric accelerometers (10 V/g) with a measurement range of ±0.5 g, and a 24-bit data acquisition system connected to a laptop were used (Fig. 4b). One accelerometer was placed at the middle top of the west wall as a fixed reference sensor, the zone with major displacements expected [9], while the others accelerometers were mobile sensor located along the wall. Ambient vibration was acquired with a sample frequency of 256 Hz in time lapses of 25 min, there were seven measurements points in five set ups (Fig. 4a).
(a)
(b)
Fig. 4. OMA set up test (a) West wall and location of sensors and (b) Accelerometer and DAQ System.
Using the enhance frequency domain decomposition approach [10] implemented in ARTeMIS [11], an average normalized density spectrum was obtained for the west wall (Fig. 5a). Major energies are observed at frequencies of 3.2 Hz and 6.2 Hz, which correspond to the first and second mode of vibration respectively. For such modes, a damping ratio of 4.33% and 5.45% were identified. Mode shapes and dynamic properties of west wall are shown in Fig. 5b.
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(a)
(b)
Fig. 5. (a) Density spectrum for the epistle wall and (b) Mode shapes and dynamic properties of west wall.
5.2 Calibration of the FE Model The numerical modelling of the structure was carried out using the SAP2000 software [12]. Dynamic properties namely frequencies and mode shapes obtained from OMA tests, and numerical modal analysis were compare using de Modal Assurance Criterion (MAC) in order to calibrate the numerical model [13]. The sensitivity analysis showed that the variables with the greatest influence during model calibration were the boundary conditions and the modulus of elasticity of the ruble-stone masonry. MAC values were calculated for three numerical models with different boundary conditions and E-values (Fig. 6). Fully connected linear elastic shell and frame elements were used to model masonry walls and wood elements respectively. The support conditions were considered fully constrained at the base of the walls. The geometry of the structural elements corresponds to the one observed at field. Regarding to materials, a volumetric weight of 22.5 kN/m3 was used for the ruble-stone masonry (based on laboratory tests); E-values were obtained matching the numerical fundamental frequency with the one obtained in OMA tests. For wood material a volumetric weight of 6.86 kN/m3 and a modulus of elasticity of 9806 MPa were used [14]. The roof structure was modelled as forces applied at the top of the walls. Model 1
Model 2
Model 3
(a) E – modulus: 696 MPa West wall’s boundary conditions: Transversal and longitudinal walls of the church nave and wood tensors at roof.
(b) E – modulus: 693 MPa West wall’s boundary conditions: Transversal and longitudinal walls of the church nave and wood tensors at roof and at choir loft zone.
(c) E – modulus: 687 MPa West wall’s boundary conditions: Elements considered in Model 2 plus walls and wood beam of sacristy and baptistery.
Fig. 6. Models used during calibration process (a) Model 1, (b) Model 2, and (c) Model 3.
From the analysis carried out, Model 3 had the highest MAC values, 0.95 y 0.84 for the first and second mode respectively, and can be used for structural analysis of
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the church. Furthermore, from numerical calibration a E-modulus of the ruble-stone masonry of 687 MPa was obtained. Table 5 summarizes the results of the calibration process. Figure 7 shows the numerical mode shapes from Model 3 and the corresponding modes from OMA tests. Table 5. MAC values for numerical models. OMA Tests
Model 1
Experimental Frequency (Hz)
Frequency (Hz)
MAC
Frequency (Hz)
MAC
Frequency (Hz)
MAC
1st Mode
3.20
3.20
0.90
3.20
0.90
3.20
0.95
2nd Mode
6.21
6.28
0.46
6.29
0.45
6.74
0.84
(a)
Model 2
Model 3
(b)
Fig. 7. Comparisson of numerical and experimental modal parameters (a) first mode and (b) second mode.
6 Conclusions This paper is a preliminary study aiming the structural condition of the San Francisco Church of Marcapata. Visual inspection of the monument, based upon a qualitative study of interaction among main structural elements, concludes that the Temple of Marcapata is in a situation of vulnerability and more detailed studies are required to evaluate its structural capacity for adequate preservation measures. From uniaxial compression tests of ruble-stone masonry, an average maximum resistance of 0.82 MPa was obtained. Operational modal analysis using the enhanced frequency domain decomposition technique of the selected wall, identified mode shapes and frequencies of 3.20 Hz and
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6.21 Hz, associated with damping ratios of 4.33% and 5.45% respectively. These data through the application of MAC criteria were used for indirectly estimate the modulus of elasticity and calibrate the numerical model of the structure. Three numerical models with different boundary conditions and E-modulus were calibrated using Modal Assurance Criterion (MAC). The highest MAC values of 0.95 and 0.84 for the first and second mode corresponded to model 3. According to this model, an E-modulus of 687 MPa for the ruble-stone masonry was established. Mechanical parameters found for the San Francisco de Assis church can be used in future studies of seismic vulnerability evaluation, and as a reference in structural evaluation of historical structures made with similar materials. Acknowledgements. The authors would like to thank Ms. Lidia Caller, Mr. Juan Caller and students research group “Sayri Tupac” of the University San Antonio Abad of Cusco-Perú for their kind support during this work. These studies were partly founded by The Order of The Company of Jesus in charge of the Marcapata Parish.
References 1. Resolution Nro. 097–2015-VMPCIC-MC. Culture Ministry. Lima (2015) 2. Gonzales A. Proceso Histórico del hermoso Valle de Marcapata-Cuchoa, Cuzco. Personal communication (2019) 3. Alonso Palomino, Q.J.: A resident of the great city of Cuzco, sells a coca field in the Cuchoa Valley in favor of Alonso Rivero, Cuzco. Cusco Historical Archive 4. Raimondi, A.: Editores Técnicos Asociados. Vol. IlI, pp. 129–130. Perú, Lima (1966) 5. Torrealva, D.: Personal communication (2017) 6. Lourenço, P., Karanikoloudis, G.: Structural performance and seismic vulnerability of adobe historical constructions. The Kuño Tambo Case Study. Terra Lyon 2016. p. 5. Cusco (2016) 7. Meimaroglou, N., Mouzakis, H.: Mechanical properties of three-leaf masonry walls constructed with natural stones and mud mortar. Eng. Struct. 172, 869–876 (2018). https://doi. org/10.1016/j.engstruct.2018.06.015 8. Standard Test Method for Compressive Strength of Masonry Prisms. ASTM-C1314 - 2022A EDITION (2022) 9. Pachón, P.: Structural assessment of historical buildings by using the Operational Modal Analysis (OMA) technique. (OMA). p. 34. Sevilla (2014) 10. Brinker, R., Ventura, C.: Introduction to Operational Modal Analysis. 1st ed. John Wiley & Sons, Ltd, United Kingdom (2015) 11. Software SVS. ARTeMIS Modal 6.0., http://www.svibs.com (2019) 12. CSI SAP2000 v.22 - Computer and Structures, Inc., Berkeley, CA, USA, 2022 13. Aguilar, R.: Investigations on the structural behavior of archaeological heritage in Peru: From survey to seismic assessment. Engineering Structures. pp. 99–100. Peru (2015) 14. NTE.010. Reglamento Nacional de edificaciones del Perú, Norma técnica E.010: Madera (“Peruvian design code for wood structures”), (2006)
Detailed Numerical Micro-modelling of Masonry TRM Reinforcements La Scala Armando1,2(B) , Javier Pereiro-Barceló2 and Salvador Ivorra2
, Dora Foti1
,
1 Department of Civil, Engineering Sciences and Architecture, Polytechnic University of Bari,
70124 Bari, Italy [email protected] 2 Department of Civil Engineering, University of Alicante, San Vicente del Raspeig, 03080 Alicante, Spain
Abstract. The need to safeguard and often restore the historical-architectural heritage has led over the years to the introduction of different types of structural reinforcements based on the use of fibres made of different materials capable of increasing the tensile strength of a given structural element. Such solutions are certainly valid in the case of seismic phenomena, while their behaviour in the case of another highly destructive phenomenon that can affect buildings is little investigated: fires. In the present paper, the behaviour of different types of reinforcements based on glass, carbon and basalt fibres, subjected to high temperatures was investigated. This work starts from some experimental data obtained through laboratory tests on suitably prepared specimens to build a numerical model capable of describing the evolution of the behaviour of these materials as temperature increases. Keywords: TRM · FRCM · High-temperatures · Numerical modelling
1 Introduction In recent years, the scientific community has been strongly interested in the need to identify increasingly effective and less invasive systems for the reinforcement and seismic upgrading of historic buildings, both masonry and non-masonry. One of the most adopted solutions is the use of fibre-reinforced polymer matrix (FRP) materials [1]. The main problem with the use of such materials is their very poor fire resistance, due to the high variability in terms of mechanical parameters of epoxy resins exposed to significant thermal gradients. Further shortcomings lie in the irreversibility of their application, which makes them impossible to use in the case of structures of great cultural value, and in their high cost. To overcome these problems, in recent years, a new system of structural reinforcement has been developed, which uses textile fibres of various kinds (glass fibre, carbon fibre, basalt, etc.) in a cement matrix, usually consisting of common mortar (TRM). This solution, in fact, in addition to reducing the out-of-pocket costs of processing, allows for © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 543–555, 2024. https://doi.org/10.1007/978-3-031-39450-8_45
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a better applicability of this system even in the case of buildings of significant historicalarchitectural value because mortar is a significantly less invasive element than the epoxy resins that form the basis for FRP-type reinforcements, as well as having a much better fire resistance, thanks to the fireproof nature of the materials used [2]. The importance of the fire resistance capacity of structures, historical and otherwise, is highlighted by the renewed interest of the scientific community in the subject [3–6]. The wide diffusion that TRM is reaching is testified both by the good number of researches that can be found in the literature, related to the reinforcement of different structural elements in both masonry [7–9] and reinforced concrete [10, 11], and by the development of the Standards that regulate the application of these solutions, such as found in the ACI 549.4R-20 for North America, or the CNR-DT 215/2018 Standard in use in Italy [12, 13]. On the basis of what is found in the literature [14–16], it is possible to preliminarily identify a particular behaviour of TRM from a mechanical point of view; such reinforcements, in fact, exhibit three phases when subjected to tensile stresses. In the first phase, the mortar does not show any cracking phenomena, so that the elastic modulus of the composite material will be roughly the same as that of the mesh of fibres, with the stresses, however, referring to the homogenised section given by the mortar plus the fibres. When the first cracks are formed, this initiates the second phase, in which we see the development of a certain cracking framework in the cement matrix; here there is a considerable reduction in the elastic modulus, and a considerable increase in deformations. The third and final phase sees the complete cracking of the matrix and the tensional state entirely at the expense of the TRM mesh; from a mechanical point of view, one notes an almost perfectly plastic behaviour, with an almost horizontal trend in the stress-strain curve [17]. The objective of the present work is to analyse in a numerical environment the damage development of TRM composites in case of exposure to high temperatures; the numerical modelling was conducted by adopting different finite element solutions for the modelling of the fibre mesh. The final aim is to be able to fully define the creep interaction found in the experimental tests between the fibres and the mortar matrix.
2 Materials This work is based on some previous studies carried out by Estevan et al. [18] regarding the tensile behaviour of TRM reinforcement systems. The experimental tests initially carried out, from which it was decided to start from for the realisation and calibration of the numerical models, saw the use of four different types of fibres marketed by Mapei; two of these are glass fibre meshes (Mapenet EM40 and Mapegrid G220), while the other two are high-strength carbon fibre (Mapegrid C170) and basalt fibre (Mapegrid B250). In the following, the different nets will be referred to as type A, B, C, D. About the mortars used, these are two commonly used types, again supplied by Mapei (MapeWall Render & Strengthen and Planitop HDM Restauro); they will be referred to below as M1 and M2. As far as mechanical properties are concerned, tables prepared with data provided by the parent company are given below (Tables 1 and 2).
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Table 1. Fibre properties Supplier characteristics
Mesh A
Mesh B
Mesh C
Mesh D
Fibre type
Mapenet EM40
Mapegrid G220
Mapegrid C170
Mapegrid G250
Materials
Glass
Glass
Carbon
Basalt
Mesh size
40 x 40
25 x 25
10 x 10
6x6
Weight (g/m2 )
270
225
170
250
Resistant area (mm2 /m)
35.82
35.27
48
38.91
Tensile strength (kN/m)
56.25
45
240
60
Young’s modulus (GPa)
33
72
252
89
Elongation at failure (%)
4
1.8
2
1.8
Table 2. Mortar properties Supplier characteristics
M1
M2
Type of mortar
MapeWall Render & Strengthen
Planitop HDM Restoration
Compressive strength (MPa)
15
15
Young’s Modulus (GPa)
10
8
The use of TRM reinforcements, although advantageous when compared with classical methods of confinement by means of FRP, nevertheless presents some criticalities; in particular, an extremely important phenomenon to be understood is the loss of adherence between mortar and fibres. In the case of TRM, in fact, already under normal operating conditions, the adherence between the cement matrix and the fibre network is not so effective; in fact, the mortar is not able to impregnate the fibres in the best possible way, contrary to what happens with the epoxy resins of FRP [19, 20]. The consequence of this imperfection is an unevenness in the stress transfer paths within the resistant section, and throughout the longitudinal development of the reinforcement; this causes a type of failure known as ‘telescopic failure’, i.e., there is a mutual sliding between the parts, without visible damage. In practice, this problem can be remedied by placing a layer of epoxy resin between the fibres and the mortar, prior to pouring the mortar. 2.1 Test Setup Tests for the mechanical characterisation of TRM reinforcements were conducted by Prof. Estevan et al. at the laboratory of the Universidad de Alicante [18]; for this purpose, rectangular-shaped TRM specimens were manufactured in accordance with the
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requirements of the AC-434 guide and the RILEM TC 232-TDT recommendations [21, 22]. The specimens were made 500 mm long, 100 mm wide and 10 mm thick. Anchorage zones were defined at the head and foot of the test specimen of 100 mm each, leaving a central area of 300 mm free for measurements. The width was determined to ensure at least three vertical fibres for the mesh with the largest mesh size (Mapenet EM40). The specimens were manufactured in stages: first a 4 ÷ 5 mm thick layer of mortar was cast, then the fibre mesh was placed and finally the final layer of mortar was cast. For each type of reinforcement, 20 specimens were produced, which were then subjected to different temperatures; specifically, the different thermal steps performed were at 20, 100, 200, 400 and 600 °C. Heating was carried out by means of an electric oven at constant increments of 10 °C/min until the target temperature was reached, which was then maintained for approximately one hour. The heated specimens were then left to cool for 24 h until room temperature was reached. 2.2 Tensile Tests The test specimens were then subjected to a tensile test according to the guidelines provided by AC 434 and RILEM TC 232-TDT. The test setup involved anchoring the specimens at the head and foot by bolting them between two 10-mm-thick steel plates. The load was applied by means of an hydraulic machine with a capacity of 50 kN; the tensile load was applied by means of displacement control, with steps of 0.2 mm/min until failure of the test specimen. The displacement control was carried out by means of an LVDT on one side, connected to an HBK QuantumX MX1615B acquisition system and attached to the steel plates, with an initial measured length of 300 mm; on the opposite side, the relative elongation was monitored by means of a Digital Image Correlation (DIC) system, realised by positioning a 16 MP digital camera, placed 75 cm away from the test specimen. For a better result, the specimen was treated with a layer of paint to make the contrast between the cracked and healthy parts more evident and thus improve the analysis process [23].
3 Numerical Modelling The next step following the analysis of the experimental data obtained from the test campaigns conducted at the Universidad de Alicante, was to model in a software environment the A20 specimen, among all those analysed, in order to obtain an effective and precise numerical model, through calibration with the experimental data, with the ultimate objective of carrying out predictive analyses on the behaviour of these materials, under different, and more extreme, conditions than those realised during the experimental tests. The numerical model that will be presented below was realised with the Abaqus CAE software. The FEM model was realised considering a pushed micro-modelling, in which both the mortar matrix and the glass fibre mesh were defined as C3D8R type brick elements. These elements are 8-node linear bricks, with reduced integration and hourglass control. Due to the reduced integration, the locking phenomena observed in the C3D8 element
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do not show. However, the element exhibits other shortcomings: the element tends to be not stiff enough in bending; stresses, strains, etc. are most accurate in the integration points. The integration point of the C3D8R element is in the middle of the element. Thus, small elements are required to capture a stress concentration at the boundary of a structure. There are 12 spurious zero energy modes leading to massive hourglassing: this means that the correct solution is superposed by arbitrarily large displacements corresponding to the zero energy modes. Thus, the displacements are completely wrong. Since the zero energy modes do not lead to any stresses, the stress field is still correct. In practice, the C3D8R element is not very useful without hourglass control. Reduced integration elements are chosen to reduce computational time, which would be excessive in case of higher order elements. In addition, reduced integration is preferred in plasticity problems because elements do not exhibit volumetric locking when plastic flow occurs, and incompressible material behaviour takes place; it was preferred to use a denser mesh and low order elements [24]. As far as solving methods are concerned, two different routes were followed: one by means of a linear static analysis and another by means of a non-linear dynamic analysis [25]. The first case is the more classical one, which is expected to be adopted in the representation of a quasi-static experimental test such as the one examined; the second case, on the other hand, represents an innovative solving strategy provided by the software, which makes it possible to obviate the various convergence problems that can sometimes arise in the case of classical static analyses. A basic concept in Abaqus is the division of the problem history into steps. A step is any convenient phase of the history-a thermal transient, a creep hold, a dynamic transient, etc. In its simplest form a step can be just a static analysis in Abaqus/Standard of a load change from one magnitude to another. There are two kinds of steps in Abaqus: general analysis steps, which can be used to analyse linear or nonlinear responses, and linear perturbation steps, which can only be used to analyse linear problems. General analysis steps can be included in an Abaqus/Standard or Abaqus/Explicit analysis. A static stress analysis is used when inertia effects can be neglected; can be linear or nonlinear; and ignores time-dependent material effects (creep, swelling, viscoelasticity) but takes rate-dependent plasticity and hysteretic behaviour for hyperelastic materials into account. Linear static analysis involves the specification of load cases and appropriate boundary conditions. The direct-integration dynamic procedure provided in Abaqus/Standard uses the implicit Hilber-Hughes-Taylor operator for integration of the equations of motion, while Abaqus/Explicit uses the central-difference operator. In an implicit dynamic analysis, the integration operator matrix must be inverted, and a set of nonlinear equilibrium equations must be solved at each time increment. In an explicit dynamic analysis displacements and velocities are calculated in terms of quantities that are known at the beginning of an increment; therefore, the global mass and stiffness matrices need not be formed and inverted, which means that each increment is relatively inexpensive compared to the increments in an implicit integration scheme. The size of the time increment in an explicit dynamic analysis is limited, however, because the central-difference operator is
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only conditionally stable; whereas the Hilber-Hughes-Taylor operator is unconditionally stable and, thus, there is no such limit on the size of the time increment that can be used for most analyses in Abaqus/Standard (accuracy governs the time increment in Abaqus/Standard) [26]. The stability limit for the central-difference method (the largest time increment that can be taken without the method generating large, rapidly growing errors) is closely related to the time required for a stress wave to cross the smallest element dimension in the model; thus, the time increment in an explicit dynamic analysis can be very short if the mesh contains small elements or if the stress wave speed in the material is very high. The method is, therefore, computationally attractive for problems in which the total dynamic response time that must be modelled is only a few orders of magnitude longer than this stability limit; for example, wave propagation studies or some “event and response” applications. Many of the advantages of the explicit procedure also apply to slower (quasi-static) processes for cases in which it is appropriate to use mass scaling to reduce the wave speed. [24] (Fig. 1).
Fig. 1. Brick Finite Element C3D8R
3.1 Material Properties and Constitutive Equations The combination of materials used, i.e., cement mortar matrix and glass fibre mesh, poses a considerable challenge in numerical modelling. The mechanical properties of the two materials are, in fact, extremely different, and their interaction is not as intuitive as it might seem. From a purely theoretical point of view, it was assumed that these two coupled materials should behave similarly to what occurs in reinforced concrete between, precisely, concrete and steel bars. The experimental evidence [17, 18], however, showed that in the case of TRM reinforcements, it is not possible to adopt the same constitutive simplifications that are commonly adopted in the design field for reinforced concrete (preservation of flat sections and perfect adhesion). It was therefore necessary to identify an ad-hoc constitutive bond for this composite. The mechanical characteristics of the individual materials constituting the composite analysed are presented in the Tables 3 and 4 below; in this case, also based on the
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experimental evidence already available, it was decided to consider the glass fibre mesh as infinitely elastic, while the behaviour of the mortar was defined as elasto-plastic, which is described quite precisely using the Concrete Damage Plasticity method [27–29]. The need to define a breaking criterion for mortar led to its definition as a set of brick elements of the type described in the previous point. For the modelling of the fibre network, the initial idea was to use T3D2 truss type elements, inserted within the mortar matrix by means of an ‘embedded region’ type constraint; the problem with this approach was that this constraint, in practice, consisted in adopting the hypothesis of perfect adherence between the network and the mortar, which, as demonstrated by the experimental tests, does not occur. For this reason, it was then preferred to also model the mesh with brick elements, to be able to consider a “bond slip” between the two materials as the imposed stress state changes. The definition of the mesh as a 3D element required, first of all, to define the characteristics of the material in a complete manner, but also to define a sort of constitutive bond of the entire conglomerate formed by the mortar and the fibres. The definition of this overall constitutive bond was made possible through the definition of certain particular ‘interaction properties’. In this case, the behaviour at the interface was defined, both in the normal and transversal sense, of an attritive type; in addition, a cohesive behaviour was defined, which made it possible to describe as precisely as possible the behaviour of the test specimen during the cracking phase of the mortar (although in this sense, completely satisfactory results have not yet been obtained); finally, the damage mechanism was defined, which entails the plasticisation of the TRM sections and the definitive flattening of the stress-strain curve. Table 3. Elastic properties of materials Material
E (MPa)
ν
Mortar
10000
0.24
TRM (glass fibre)
33000
0.30
Table 4. Concrete damage plasticity parameters [24] Material
Dilation Angle
Eccentricity
fb0/fc0
K
Viscosity parameter
Mortar
30
0.10
1.20
0.6667
0.001
Regarding the imposed boundary conditions, the plate attachment of the experimental test was replicated, and the load was also applied by means of displacement control. 3.2 FEM Results Various models were realised to understand and appropriately define the mechanical behaviour of reinforcement in TRM. The most relevant results found during the numerical analyses are presented below.
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The models created were calibrated with the results of tests conducted at room temperature, as a matter of greater precision in defining the mechanical characteristics of the materials, for which both the results obtained from experimental tests and those provided by the manufacturer are available. Briefly, simulations were conducted in two directions: one using a simplified model, with the mesh modelled as truss elements (2D), and a more complex one, with the mesh modelled as 3D elements (Fig. 2).
Fig. 2. a) 2D mesh model b) Plastic deformations at the cracks in the mortar
In the case of the simplified model, in which the only possible interaction between mortar and mesh was possible with the application of a constraint of the “embedded region” type, the behaviour of the first elastic section of the composite is simulated with good approximation. Unfortunately, the assumption of perfect adherence means that the two components of the reinforcement always remain in contact and therefore the mutual sliding caused by the progressive cracking that occurs in the mortar does not occur. As can be seen from the graph below, in fact, the model curves present a well-defined yield point, and an almost perfectly plastic behaviour from that point. It should be emphasised that the model with the 2D mesh shows a significantly lower ‘yield’ stress of the composite than that shown by the experimental tests (Fig. 3).
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Fig. 3. 2D Mesh - Force-Displacement Diagram
Following the tests carried out on a simplified model and wishing to achieve a greater degree of precision in the micro-modelling of this structural element, a considerably more complex numerical model was elaborated, in which the interaction between mortar and mesh is given by the interaction between three-dimensional brick elements (Fig. 4).
Fig. 4. a) 3D mesh model b) Plastic deformations at mortar cracks
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In this case, the definition of the behaviour of the two materials is given by the interface properties defined in the software. The progressive damage pattern that was attempted to simulate saw the implementation of a friction-type behaviour in the tangential direction to the contact surfaces (a friction coefficient μ = 0.7 was defined), while a stiffness was defined in the normal direction that could simulate the interpenetration between the parts once a certain tension state was reached. It was also necessary to define the characteristics of the material’s cracking phase by means of cohesive behaviour, and finally to describe the maximum stresses at which the material’s crisis would occur (Fig. 5).
Fig. 5. 3D Mesh - Force-Displacement Diagram
The results obtained showed a good level of approximation in the description of the behaviour of the composite, although in this case, it was practically impossible to describe the initial trend given by the solidarity between fibres and mortar. A next step in this direction, to be developed in the future, will be to make the coefficients describing the interactions at the interfaces variable over time, with the hope of achieving an even better degree of precision. In any case, the degree of approximation achieved still makes it possible to precisely describe the critical points of the material, i.e., the transition to the plastic phase and its breakage. It was also possible to define the complex phenomenon of mutual sliding between the mesh and the mortar with a satisfactory level of accuracy. It should be noted that, in the case of both the 2D model and the 3D model, the static test tends to return forces that are tendentially greater than those expressed by the dynamic test at the yield point; this may probably be due to a better ability to describe the phenomenon in relation to the loading speed, which evidently, and despite the small
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size of the specimen (for which the inertia forces could be considered negligible), was not sufficiently small to allow the test pattern to be considered perfectly static.
4 Conclusions This study involved the reproduction in a numerical environment of experimental tests conducted on a composite material, such as TRM, whose heterogeneity, both geometric and constitutive, is still an obstacle to the comprehension of its mechanical behaviour. Investigations conducted in Abaqus have shown that: 1. At room temperature, the material roughly reflects the expected behaviour, as the values at the tension and deformation levels achieved reflect the manufacturer’s statements. 2. To understand which modelling strategy was the most effective, various tests were conducted, both on mixed models (truss + brick) and on three-dimensional models only. Analyses of a different nature, both static and dynamic, were also conducted. 3. The various numerical models developed allowed for the elaboration of various considerations regarding the physics of the tests performed and the behaviour of the material. It is relevant to note the difficulty of numerically defining the trilinear behaviour of the constitutive bond of the composite. 4. The model with the 2D network, by means of the ‘embedded region’ constraint, made it possible to simulate the synergetic behaviour of the two constituent materials of the TRM composite. Unfortunately, this model, due to its limitations, is not sufficiently adaptive to consider the progression of the physiological phenomenon within the mortar and thus the consequent reduction in elastic modulus. 5. The all-element brick model, on the other hand, made it possible to achieve a good degree of approximation in the representation of the behaviour of the TRM under tensile stress. The next step in the refinement of this solution will be to make it adaptive, by implementing a variation equation of the parameters defining the properties of the constituent materials and the boundary characteristics at the interfaces, as the tensional state increases. 6. It was also interesting to note that, the two types of analyses conducted, static and dynamic, almost always gave similar results, with stress values always higher for static analyses. We believe that this better adherence can be attributed to a better ability of the dynamic test to simulate the quasi-static experiment conducted in the laboratory; the static test, on the other hand, suffers from a load application rate that is probably already too high. 7. In the near future, once the “constitutive” characterisation of the TRM composite has been refined, the aim is to verify the adherence of the model obtained even when the temperature varies, in order to be able to have reliable predictive models, which will then allow the case histories already studied in the experimental phase to be expanded.
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References 1. Foti, D.: On the numerical and experimental strengthening assessment of tufa masonry with FRP. Mech. Adv. Mater. Struct. 20(2), 163–175 (2013). https://doi.org/10.1080/15376494. 2012.743634 2. Kouris, L.A.S., Triantafillou, T.C.: State-of-the-art on strengthening of masonry structures with textile reinforced mortar (TRM). Constr. Build. Mater. 188, 1221–1233 (2018). https:// doi.org/10.1016/j.conbuildmat.2018.08.039 3. Caggegi, C.: Experimental analysis on tensile and bond properties of PBO and aramid fabric reinforced cementitious matrix for strengthening masonry structures. Compos. Part B. Eng. 127, 175–195 (2017). https://doi.org/10.1016/j.compositesb.2017.05.048 4. Fantilli, A.P., Burello, N.S.: Masonry arches and vaults under fire. J. Build. Eng. 56 (2022). https://doi.org/10.1016/j.jobe.2022.104740. ISSN 2352-7102 5. La Scala, A., Sabbà, M. F., Foti, D.: Fire hazard of electric vehicles in enclosed structures. In: 2022 AEIT International Annual Conference (AEIT), Rome, Italy, pp. 1–6, (2022). https:// doi.org/10.23919/AEIT56783.2022.9951769 6. Foti, D.: Prestressed slab beams subjected to high temperatures, Composites. Part B, Engineering, vol. 58, March 2014, p. 242–250, 2014. ISSN: 1359–8368 7. Ivorra, S., BenjamínTorres, F., Baeza, J., Bru, D.: In-plane shear cyclic behavior of windowed masonry walls reinforced with textile reinforced mortars. Eng. Struct. 226, 111343 (2021). https://doi.org/10.1016/j.engstruct.2020.111343 8. Estevan, L., Baeza, F.J., Bru, D., Ivorra, S.: Stone masonry confinement with FRP and FRCM composites. Constr. Build. Mater. 237, 117612 (2020). https://doi.org/10.1016/j.conbuildmat. 2019.117612 9. Bertolesi, E., Torres, B., Adam, J.M., Calderón, P.A., Moragues, J.J.: Effectiveness of textile reinforced mortar (TRM) materials for the repair of full-scale timbrel masonry cross vaults. Eng. Struct. 220, 110978 (2020). https://doi.org/10.1016/j.engstruct.2020.110978 10. Ivorra, S., Bru, D., Galvan, A., Silverstri, S., Apera, C., Foti, D.: TRM reinforcement of masonry specimens for seismic areas. Int. J. Saf. Secur. Eng. 7(4), 463–474 (2017). https:// doi.org/10.2495/SAFE-V7-N4-463-474 11. Koutas, L.N., Tetta, Z., Bournas, D.A., Triantafillou, T.C.: Strengthening of concrete structures with textile reinforced mortars: state-of-the-art review. J. Compos. Constr. 23(1), 03118001 (2019). https://doi.org/10.1061/(ASCE)CC.1943-5614.0000882 12. ACI 549.4R-20: Guide to Design and Construction of Externally Bonded Fabric-Reinforced Cementitious Matrix and Steel-Reinforced Grout Systems for Repair and Strengthening of Concrete Structures, American Concrete Institute, ACI Committee 549 (2020) 13. CNR-DT 215/2018: Guide for the Design and Construction of Externally Bonded Fibre Reinforced Inorganic Matrix Systems for Strengthening Existing Structures, CNR - Advisory Committee on Technical Recommendations for Construction, Rome, Italy, (2020) 14. Carozzi, F.G., Poggi, C.: Mechanical properties and debonding strength of Fabric Reinforced Cementitious Matrix (FRCM) systems for masonry strengthening. Compos. Part B Eng. 70, 215–230 (2015). https://doi.org/10.1016/j.compositesb.2014.10.056 15. deFelice, G., et al.: Mortar-based systems for externally bonded strengthening of masonry. Mater. Struct. 47(12), 2021–2037 (2014). https://doi.org/10.1617/s11527-014-0360-1 16. Papanicolaou, C.G., Triantafillou, T.C., Papathanasiou, M., Karlos, K.: Textile reinforced mortar (TRM) versus FRP as strengthening material of URM walls: out-of-plane cyclic loading. Mater. Struct. 41, 143–157 (2008). https://doi.org/10.1617/s11527-007-9226-0 17. Estevan, L., Torres, B., Varona, F.B., Baeza, F.J., Ivorra, S.: Shear strengthening of masonry walls with Textile Reinforced Mortars (TRM) under high temperature exposure. J. Build. Eng. 63, 105511 (2023). https://doi.org/10.1016/j.jobe.2022.105511
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18. Estevan, L., Varona, F.B., JavierBaeza, F., Torres, B., Bru, D.: Textile Reinforced Mortars (TRM) tensile behavior after high temperature exposure. Constr. Build. Mater. 328, 127116 (2022). https://doi.org/10.1016/j.conbuildmat.2022.127116 19. Bisby, L., Stratford, T., Courtney, H., Farren, S.: Fire performance of well-anchored TRM, FRCM and FRP flexural strengthening systems. Advanced Composites in Construction 2013. Network Group for Composites in Construction (2013) 20. Bournas, D., Lontou, P.V., Papanicolaou, C., Triantafillou, T.: Textile-reinforced mortar versus fiber-reinforced polymer confinement in reinforced concrete columns. ACI Struct. J. 104, 740–748 (2007) 21. AC434: Acceptance Criteria for Masonry and Concrete Strengthening Using Fiber-Reinforced Cementitious Matrix (FRCM) Composite Systems, ICC Evaluation Service (2016) 22. RILEM Technical Committee 232-TDT (Wolfgang Brameshuber): Recommendation of RILEM TC 232-TDT: test methods and design of textile reinforced concrete. Uniaxial tensile test: test method to determine the load bearing behavior of tensile specimens made of textile reinforced concrete. Mater. Struct. 49, 4923–4927 (2016). https://doi.org/10.1617/s11527016-0839-z 23. Torres, B., Varona, F.B., JavierBaeza, F., Bru, D., Ivorra, S.: Study on retrofitted masonry elements under shear using digital image correlation. Sensors 20(7), 2122 (2020). https://doi. org/10.3390/s20072122 24. Simulia ABAQUS: Users’ Manual Documentation, Version 6.13; Simulia: Johnston, RI, USA (2013) 25. Rizzo, F., Ricciardelli, F., Maddaloni, G., Bonati, A., Occhiuzzi, A.: Experimental error analysis of dynamic properties for a reduced-scale high-rise building model and implications on full-scale behavior. J. Build. Eng. (2020) 26. Lapidus, L., Pinder, G.F.: Numerical Solution of Partial Differential Equations in Science and Engineering. John Wiley & sons Inc., New York (1999) 27. Bolhassani, M., Hamid, A.A., Lau, A.C.W., Moon, F.: Simplified micro modeling of partially grouted masonry assemblages. Constr. Build. Mater. 83, 159–173 (2015). https://doi.org/10. 1016/j.conbuildmat.2015.03.021 28. Rousakis, T., et al.: deformable polyurethane joints and fibre grids for resilient seismic performance of reinforced concrete frames with orthoblock brick infills. Polymers 12, 2869 (2020) 29. Dauda, J., Iuorio, O., Lourenco, P.: Characterization of brick masonry: study towards retrofitting URM walls with timber-panels. In: 10th International Masonry Conference Milan, vol. 10 (2018)
Parametric Study of In-Plane Collapse Mechanism of Panels with Different Masonry Geometric Bond Patterns Hoi Lon Wan and Chi Chiu Lam(B) Department of Civil and Environmental Engineering, Faculty of Science and Technology, University of Macau, Macau SAR, China [email protected]
Abstract. Masonry structures are built by laying brick or block elements, usually with mortar as cohesive joint, which results in its property that masonry is relatively strong in compression while weak in tension. Load capacity and the associated failure mechanism of a masonry wall or structure under lateral and vertical load depends on different parameters such as material (blockwork and joint) used, dimension of block elements and wall, different arrangement and workmanship of laying block elements. The historical center of Macau was recognized by UNESCO as one of the world heritages on 2005. Many of the historical buildings in this historical center were traditional masonry buildings in the south-east of China. Three types of masonry wall pattern, namely as the stretcher bond, Flemish bond and common bond, were commonly used in the construction of those masonry buildings. In this paper, the load capacity and the associated failure mechanism of these three different types of masonry wall pattern were investigated. Parametric study of these three different types of masonry wall pattern was performed by mean of limit analysis and Macro-block methods. The corresponding loading capacity results and failure mechanism obtained by these two methods were compared and discussed. It is found that lateral loading capacity for common bond and normal arrangement are smaller than Flemish bond. For Flemish bond, wall failed in sliding mechanism in the largest failure loading among these three patterns. Keywords: Unreinforced Masonry (URM) · Collapse Mechanism · Limit Analysis · Historical buildings · Masonry wall pattern
1 Introduction 1.1 Background As development of construction material and technique, reinforced concrete (RC) and steelworks are most widely applied in today’s building construction due to their flexibility and larger loading capacity. However, masonry has been used as building material in the old ages and some of them are reserved nowadays, whether in structural or non-structural purpose such as partition wall or outer face as building façade. In Macau, it can be found in many places especially in the old city area, which used to be the residential and © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 556–565, 2024. https://doi.org/10.1007/978-3-031-39450-8_46
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commercial center of the city in the past [1]. Therefore, vulnerability assessment of the existing historical masonry structures, which can be studied through design codes and numerical simulation, is a concerning issue because of the declined material properties may cause strength problem to the structures. 1.2 Objectives Masonry elements are nonhomogeneous and anisotropic materials composited with brick or block elements and usually with mortar as cohesive joint. Brick or block elements of masonry can be stone such as marble, granite and limestone and can also be concrete block, etc. Mortar is made up with cement, sand, lime water and sometimes with other mixtures to increase its durability. Structural stability is mainly provided by block-block interaction, where sliding and separation between surfaces are the dominating mode of mechanism. For a masonry wall or structure, properties would highly depend on the chosen block elements and mortar joint used, nevertheless, another dominating factor is the blocks arrangement to form a panel. Due to complexity and difficulty of modelling of masonry structures, many numerical approaches, such as the finite element method [2], equivalent frame method [3], limit analysis [4] and macro-block method [5], are developed for analyzing masonry structures. In this paper, the load capacity, and the associated failure mechanism of these three different types of masonry wall pattern were investigated. Parametric study of these three different types of masonry wall pattern was performed by mean of limit analysis and macro-block methods.
2 Masonry Modelling Methodology 2.1 Limit Analysis Approach As masonry structures consist of at least two different materials, block element and mortar, numerical modelling of masonry structures could be done in micro and/or macro levels. In the micro level, although very detailed modelling of masonry structures could be carried out by using finite element method, the analysis is very time consuming. In the macro level, limit analysis which considers the equilibrium of discrete rigid block element is one of the methods which balanced the analyzing cost and accuracy. In this study, the computer program, LiABlock_3D v1.0 [6], is applied for analyzing the collapse mechanism and ultimate capacity of masonry wall with different geometric bond patterns. A two layers masonry wall constructed in normal arrangement is shown in Fig. 1 with basic information shown in Table 1. The wall is subjected to uniform lateral distributed loading. Frictional coefficient μ is set as variable while staggering ratio (s/h) and wall ratio (L/H) is unchanged. The corresponding load factor calculated from LiABlock_3D v1.0 with varying staggering ratio (s/h) is shown in Fig. 2. The results showed that when μ is less than or equals to 0.4, as a turning point, the load factor is exactly equals to the frictional coefficient and associated mechanism is sliding along the base. On the other hand, when μ is larger than 0.4, the mechanism is defined as overturning along different angles and crack line, where load factor α calculated by limit analysis is larger with greater μ value.
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To determine the collapse mechanism of masonry wall subjected to uniform lateral loading, D’Ayala and Speranza [5] proposed a simple analytical model for calculating load factors associated with various collapse mechanisms of wall assemblies. According to their assumptions, failure of the masonry panel is assumed to be triggered by a crack line and portion of failure is either sliding along the crack line or overturning. Angle of crack line could be varied, and different angle of crack line resulted in different failure loading and mechanism. This analytical model is also known as the Marco-block method and its assumptions included: (1) There is no tensile strength developed by bonding from mortar joints and only gravitational acceleration acting as vertical load. Therefore, this method is considered relatively conservative, (2) The failure pattern is a diagonal crack from the toe and goes along the whole wall and any openings of the wall are neglected for development of crack path, (3) Blocks are rigid elements, meaning that crack will not happen across the block internally while it will only go along the block-block interface. (4) The diagonal crack divided the wall into two portions and the mechanism of upper portion wall is whether sliding or overturning about the toe. (5) The collapse load factor λ is defined as the ratio between the lateral acceleration and the gravitation acceleration (a/g), therefore, the collapse load can be obtained by multiplying the gravity of failure portion and the collapse load factor. With the same parameters showed in Table 1, the load factors of the masonry walls were calculated by using the Marco-block method and the results were shown in Fig. 3. It is found that the results obtained by using the Marco-block method are very closed to that obtained from limit analysis. Therefore, both methods were further applied to analyze masonry walls with (1) different staggering ratio, (2) loading conditions and (3) geometric bond patterns and the results were shown in the following sections. Table 1. Basic information of masonry wall Unit Weight
Wall Size (mm) Brick Size (mm)
Staggering Ratio s/h
Wall Ratio L/H
Frictional Coeff. μ
18 kN/m3
1920 × 2400 × 240 × h × 240 120 (L × H × W) (l × h × b)
Vary from 0.6 to 3.0
0.8
Varied from 0 to 1.8
* s = half of the length of brick
3 Parametric Study 3.1 Masonry Wall with Different Loading Conditions For masonry building, there are many structural elements composed with different materials. Besides brick elements, timbers are most widely used material in masonry buildings such as slab, roof, curtain wall, wall ties, etc. Structural elements resist loading including permanent and live loads which are transferred to the masonry walls and eventually to
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Fig. 1. Two layers masonry wall constructed in normal arrangement subjected to uniform lateral distributed loading with different staggering ratio (s/h)
Fig. 2. Load factor α (from limit analysis) vs. frictional coefficient μ
the foundation. In such situation, loading capacity of masonry structural wall is influenced by these existing loadings. In this section, additional surcharges are applied to the masonry walls to investigate how this factor affects wall’s lateral loading capacity. Four masonry walls with different loading conditions as shown in Fig. 4 were analyzed by both limit analysis and Marco-block method. The dimension of walls is set as
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Fig. 3. Load factor α (from Macro-block method) vs. frictional coefficient μ
1920 mm × 2400 mm × 240 mm (L × H × W) and brick size is 240 mm × 100 mm × 120 mm (l × h × b) with frictional coefficient (μ) between brick as 0.7. The loading conditions included: (1) wall with lateral load only, (2) wall with lateral load and fixed vertical load (2 kN/m) on top, (3) wall with lateral load and fixed vertical load (5 kN/m) on top and (4) wall with lateral load and fixed vertical load (5 kN/m) on top and middle height of wall. The corresponding results of failure mode and failure load predicted by both limit analysis (LiABlock_3D) and Marco-block method were shown in Fig. 5. Taking limit analysis as reference, it is shown from the results that the different of failure load varied from 0.69 to 0.93. The results predicted by Marco-block method were conversative for all four cases. When the vertical load is larger, the failure loads of masonry walls were increased as well due to the additional resisting moment given by the vertical loading. As the staggering ratio (s/h) of the wall is the same for all four cases, the failure angle predicted by Marco-block method is 50.20 for all four cases. 3.2 Masonry Wall with Different Geometric Bond Order Different principle of bricks laying and composing of masonry wall is very common which results in different geometric bond order. Currently, there are quite several different bond types which have unique characteristic. In Chinese tradition, it is believed that different construction of masonry wall and arrangement may have influence on the fortune and geomantic omen. In respective of different purposes for brick bond pattern, this section studied how those type of bond patterns would affect the failure load. Terms that are used in masonry composition can be classified as course, header, stretcher and joints. As illustrated in Fig. 6, a stretcher is a horizontal laid masonry unit whose length is along or parallel to the face of the wall while header is perpendicular to the face of the wall. Size and laying orders of stretchers and headers formed different brick bond types of masonry wall. Three different types of geometric bond order are shown in Fig. 7, which are identified as (1) Stretcher bond, (2) Flemish bond and (3) Common
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Fig. 4. Masonry walls with different loading conditions
bond. Stretcher bond pattern is the most common and simplest type of pattern in today’s masonry construction; therefore, it is named as normal arrangement hereafter. Stretchers are the main elements while headers exist at two sides of the wall. Common bond is also known as American bond in which headers are inserted every certain row of stretchers, e.g. three rows (also called “三順一丁” in Chinese). The pattern of Flemish bond was prepared by placing stretchers and headers alternatively in every course and header is centrally between the stretchers immediately above and below to be evenly bonded. In Chinese, it is also named as “梅花丁式”. Walls sizes are set as 1920 × 2400 × 240 mm (L × H × W) with different brick size and staggering ratio (s/h). Frictional coefficient (μ) is 0.6 and no vertical loadings were applied. Limit analysis and Macro-block methods are conducted to obtain the failure load and mechanism. Results for both limit analysis (LiABlock_3D) and Macro-block method are shown in Fig. 8, from which it was found that failure load predicted by Macro-block method are all less than that predicted by limit analysis (LiABlock_3D) and the ratio varied from 0.61 to 0.76. Failure load and crack angles for normal arrangement and common bond are closed to each other. From limit analysis (LiABlock_3D), the failure loads are 10.45 and 10.14 kN and from Macro-block calculation, they are 6.41 kN at 46.4° and 6.94 kN at 50° respectively. As the staggering ratio (s/h) for normal arrangement and common bond are similar, their failure modes and failure load were found similar as well. On the other hand, as sliding mechanism happened for Flemish bond pattern, it was shown that largest value of failure load could
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Fig. 5. Comparison of failure mode and failure load with different loading conditions
be achieved for this pattern. The results of failure modes from both analyses are close to each other with both sliding at staggering angle of 62.5°. By both limit analysis approach and Macro-block calculation, lateral loading capacity for common bond and normal arrangement are smaller than Flemish bond, indicating different block-block position and arrangement will have impacts on the whole wall capacity. For Flemish bond, wall failed in sliding mechanism in largest failure loading.
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It is because the wall has greater staggering ratio (s/h), and most importantly for Flemish bond pattern, there is an interlocking effect between brick keeping them to be locked tightly with each other. In today’s construction of masonry wall, this factor should be considered not only aesthetically but also in structural stability point of view.
Fig. 6. Masonry unit and composition
Fig. 7. Three types of masonry wall patterns
4 Summary and Conclusions 4.1 Parameters Affecting Stability of Masonry Structures According to parametric study of masonry walls, several parameters which would affect the stability and corresponding failure mechanism under lateral loading of the masonry were found. Those parameters are discussed as following: (1) General geometry of the walls and block elements composition such as wall ratio (L/H) and block staggering ratio (s/h) are very important parameters. As the wall is slender, overturning mechanism is easier to happen and vice versa. On the other hand, when the block elements are very flat and with higher staggering ratio (s/h), overturning failure of the wall could be prevented. With both consideration of L/H and s/h ratio for designing the preliminary sizing of the masonry structures, the whole structure’s stability is mostly settled.
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Fig. 8. Comparison of failure mode and failure load of wall with different geometric bond order
(2) The frictional coefficient (μ) is another important parameter. The magnitude of μ by roughness between brick and brick interface would affect the sliding mechanism as well as corresponding collapse loading. However, the value of μ would not be varied too much practically and is usually within a reasonable range. (3) For typical masonry structures, gravity loading from slabs or roofs is usually transferred as vertical load on walls supporting them. Permanent or impose loads are transferred vertically to the wall and foundation. As shown in the analytical solutions, masonry walls with vertical loading could resist larger lateral loading to collapse. When the vertical loading is larger, the collapse load also became larger. (4) Wall construction pattern could affect the collapse load capacity as well. As it is shown in this study, lateral loading capacity for common bond and normal arrangement are smaller than Flemish bond, indicating different block-block position and arrangement will have impacts on the whole wall capacity.
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(5) For the limit analysis by using LiABlock_3D software, the failure mode of the masonry wall could be captured more precisely. However, the computational cost and time is much higher than that of the Marco-block method. Although the Macroblock method seems to be more conservative than that of limit analysis, it provides a faster way for predicting the failure load capacity and failure mode of the masonry walls considered. Acknowledgement. The authors would like to acknowledge the conference grant (CG-FST-2023) and the research grant (MYRG2022-00186-FST) from the University of Macau for supporting this research.
References 1. World Heritage Committee: The Historic Centre of Macao. UNESCO document (2005). https:// whc.unesco.org/uploads/nominations/1110.pdf 2. Lourenço, P.B.: Computations on historic masonry structures. Prog. Struct. Eng. Mater. 4, 301–319 (2002). https://doi.org/10.1002/pse.120 3. Salonikios, T., Karakostas, C., Lekidis, V., Anthoine, A.: Comparative inelastic pushover analysis of masonry frames. Eng. Struct. 25(12), 1515–1523 (2003) 4. Milani, G., Lourenco, P.B., Tralli, A.: Homogenised limit analysis of masonry walls, Part I: failure surfaces. Comput. Struct. 84, 181–195 (2006) 5. D’Ayala, D.F., Speranza, E.: Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings. Earthquake Spectra 19, 479–509 (2003) 6. Cascini, L., Gagliardo, R., Portioli, F.: LiABlock_3D: a software tool for collapse mechanism analysis of historic masonry structures. Int. J. Archit. Herit. 14(1), 75–94 (2018)
A P-Delta Discrete Macro-Element Model for Rocking Masonry Walls Valeria Cusmano1(B) , Bartolomeo Pantò2 , Davide Rapicavoli1 , and Ivo Caliò1 1 Department of Civil Engineering and Architecture (DICAR), University of Catania, Catania,
Italy [email protected] 2 Department of Engineering, University of Durham, Durham, UK
Abstract. This paper presents a robust and accurate P-Delta Discrete MacroElement Method (DMEM) formulation to assess the out-of-plane (OOP) rocking behavior of masonry walls, allowing for both mechanical and geometric nonlinearities with a limited computational cost. OOPs mechanisms are one of the main causes of failure or severe damage involving historical and monumental masonry constructions subjected to earthquake loading. These mechanisms can be activated at low-magnitude seismic actions mainly at the upper levels of masonry buildings due to the amplification of the dynamic response and wall displacements. In this paper, according to the DMEM, the wall is discretised in a number of sheardeformable macro-portions (macro-elements) interacting by interfaces allowing for flexural cracks and sliding at the joints. According to the proposed strategy, the equilibrium is imposed considering the system’s undeformed configuration, while the global load vector is computed at each step of the analysis according to the current position of loads. The model is validated against rigid-block numerical solutions accounting for large displacements and experimental tests. Finally, a real church façade is analysed, investigating the influence of the geometrical layout, boundary conditions, and masonry deformability on the structural response. The results confirmed the accuracy and efficiency of the model and its potential to be employed for real seismic assessments. Keywords: Rocking behavior · Unreinforced masonry (URM) walls · Out-of-Plane mechanisms · P-Delta effects · Discrete Macro-Elements · DMEM
1 Introduction Masonry structures, including monumental and historical constructions, represent a significant percentage of the existing buildings worldwide. The seismic response of masonry monumental structures is generally governed by the coupling between the in-plane (IP) and out-of-plane (OOP) responses of the masonry wall. In-situ post-earthquake observations clearly show that for unreinforced masonry (URM) constructions, the OOP behaviour of masonry walls is the most likely cause of structural damage or collapse [1, 2] being activated at a low level of displacement magnitude but evolving towards moderate and large displacements related to a rigid-block-like kinematic [3]. Hence, apart from © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 566–577, 2024. https://doi.org/10.1007/978-3-031-39450-8_47
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constitutive nonlinearities, geometric nonlinearities assume great importance, entailing a significant increase in analysis complexity. These OOP mechanisms are typically assessed using macro-block limit-analysis models within the force-based approach (FBA) to evaluate the ultimate load multiplier activating the failure mechanism [4–6]. However, these more evolved methods do not account for masonry deformability and progressive damage (tensile cracking and plastic sliding) at masonry joints. On the other hand, refined Finite Element (FE) and Distinct Element (DE) approaches explicitly account for the actual masonry bond and geometric nonlinearities and can effectively predict the OOP response of masonry walls [7, 8]. However, they need complex 3D constitutive laws and calibration procedures and require high computational costs, making them generally unsuitable for engineering applications [9, 10]. Several researchers developed simplified alternative modelling approaches and practical tools to cover these limits decreasing the computational cost of nonlinear static and dynamic analyses. In this field, macro-element approaches were proposed in which structures are described as an assemblage of macroscopic structural elements, often modelled by means of an equivalent frame model (EFM) or plane element [11]. Nevertheless, these approaches generally neglect the OOP response of masonry walls, and its use is restricted to the assessment of the global response of masonry buildings. Few attempts have been made to extend the plane models to incorporate the OOP response of masonry panels [12, 13]. The present study aims to cover this research gap by upgrading the discrete macroelement method (DMEM), and introducing geometrical nonlinearities related to P-Delta effects. The DMEM was originally proposed for the in-plane response of masonry walls [14] and subsequently extended to 3D kinematics to account for the coupled IP and OOP responses of masonry walls when subjected to earthquake loadings [15, 16]. More specifically, the paper presents a simple but accurate P-Delta formulation of the DMEM method to assess the rocking response of masonry walls, allowing for an effective description of second-order effects related to geometric nonlinearities. The model is used to describe the response of rigid-block panels, comparing the results with those obtained using the classical rocking theory proposed by Housner [17], accounting for large displacement and experimental tests. Finally, a real church façade is analysed, investigating the influence of the geometrical layout, boundary conditions, and masonry deformability on the structural response. The results confirmed the accuracy and efficiency of the model and its potential to be employed for real seismic assessments.
2 The P-Delta Discrete Macro-Element Method The DMEM has been initially proposed with the aim of introducing a low computational cost numerical strategy alternative to FEM and DEM models. In its first proposal, the DMEM approach was restricted to the IP simulation proposing an alternative to the EFM models. Subsequently, the model was extended to 3D kinematics, enabling the strategy to simulate both the IP and the OOP behavior of masonry walls [15, 18]. According to the DMEM approach, a masonry wall is divided into macro-portions, represented by shear-deformable spatial elements (macro-element) connected to the other elements through nonlinear zero-thickness interfaces. Each macro-element is characterised by four vertexes (v1 , …,v4 ), and its kinematics is governed by seven Lagrangian
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parameters (Fig. 1.a) collected in the vector dT = U V W γ . The first six components are associated with the rigid motion of the element, while the last one represents the generalized shear deformation. Each interface is composed of a set of nonlinear mono-dimensional links calibrated following a straightforward fiber procedure [19, 20]. A distribution of n rows of orthogonal links (Fig. 1.b) concentrates the axial and flexural deformability of masonry, both in-plane and OOP; a longitudinal shear link (Fig. 1.c) governs the shear-sliding mechanism between masonry joints; two transversal out-of-plane shear links (Fig. 1.d) control the out-of-plane sliding mechanism as well as the torsional and a further diagonal link rules the diagonal shear behaviour (Fig. 1.e). The number n of rows of orthogonal links is chosen according to the desired level of accuracy to be reached for interface integration. It is worth noticing that no additional Lagrangian parameters are needed to describe the kinematics of interfaces. Therefore, the total degrees of freedom of the model are directly given by 7xN being N the number of macro-elements; this aspect strongly contributes to containing the model computational burden. However, a rigorous description of geometrical nonlinearities, as required for a rigorous description of OOP rocking response, would require the adoption of exact large displacement kinematics with the step-by-step update of the geometrical stiffness matrix and current configuration, compromising the model complexity and efficiency. Aiming at maintaining the benefits of the DMEM, a simplified but robust and efficient P-Delta approach is proposed, characterized by a reasonable accuracy for engineering applications, although maintaining a simple theoretical formulation and low computational effort. More specifically, the P-Delta effects are accounted for by updating the current positions of the external and along-interface internal forces applied to the macro-elements.
Fig. 1. (a) Lagrangian parameters; (b) orthogonal links, (c) IP sliding link, (d) OOP sliding links, (e) shear-diagonal links
3 Numerical Application This section applies the novel P-Delta DMEM formulation to simulate the rocking response of masonry walls. In particular, static nonlinear analyses are performed on single rectangular blocks whose mechanisms are characterized by the rotation around horizontal hinges and on a benchmark already tested in literature, while nonlinear dynamic analyses are performed on a real masonry façade. The results highlight the need to consider geometric nonlinearities when the OOP behavior wants to be studied.
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3.1 Static Nonlinear Simulations In this section, the numerical predictions obtained by the proposed model are compared to the analytical results obtained by considering the rigid block assumption. As benchmark models, two single walls, whose mechanisms are characterized by the rotation around horizontal hinges, are considered. More specifically, a parapet wall (PW) of height h, thickness t, and weight W, and a simply-supported wall (SSW), constituted by two rigid blocks of height h1 and h2 , weight W 1 and W 2 respectively and thickness t, spanning vertically between supports at ceiling/floor levels, are considered. For the sake of simplicity, in the analyzed SSW specimens, it was assumed that h1 = h2 = h/2 and, as a consequence, W1 = W2 . The capacity curves obtained by pushover analyses are superposed to a rigid-linear softening force-displacement relationship until the achievement of the displacement value ucr , corresponding to the condition in which the lateral resisting force approaches to zero. The DMEM models are developed considering a single panel with height h = 1.00 m and thickness t = 0.12 m in the case of the PW and two panels for the SSW. The interface links of the macro-element are characterised by assuming a no-tension material, linear elastic in compression, with k n representing the stiffness of a unitary area, which is set sufficiently high to approximate an almost rigid block (k n = 5E+08 N/m3 ). The results obtained by the DMEM for the two (PW and SSW) walls are shown in Fig. 2. Compared to the corresponding analytical capacity curves of the rigid-block models. The results are normalised by the ultimate force (F 0 ) and critical displacement (ucr ) of the analytical solution. In the analyses, the number of interface transversal links rows, discretising the wall thickness, has changed from 5 to 50 to investigate the influence of this discretization parameter on the wall response. It can be noted that the DMEM model well describes the overall response of the walls since the force-displacement curve tends to the theoretical rigid-block response as the number of links increases. Small differences between the numerical and the analytical responses are observed in the pre-peak and peak load stages due to the finite stiffness of the DMEM model. In all the cases, the response is very close to the analytical limit case when more than twenty rows are employed in the discretization. It is worth noticing that the number of links does not significantly affect the computational burden and computing time since the overall degrees of freedom are associated to the number of macro-elements only.
Fig. 2. Force-displacement relationship of PW and SSW prototypes (a) PW (b) SSW
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Fig. 3. Force-displacement relationship with (continue line) and without (dashed line) P-Delta effects compared to the analytical curve (dotted line) (a) PW (b) SSW
Moreover, the influence of an applied axial load is also evaluated by comparing numerical and analytical results in terms of force-displacement relationships (F-u) by varying the axial compression force applied at the top of the wall. It can be observed (Fig. 3) how the presence of a vertical pre-compression σv plays a fundamental role in the stability of these types of mechanisms as it increases the value of the capacity in terms of strength but decreases its capacity in terms of displacement. Finally, in Fig. 3. The role of P-Delta effects is also quantified by comparing the results obtained by the previous and novel formulations of the DMEM model, neglecting and considering the P-Delta effects, respectively. The comparisons highlight how neglecting the P-Delta effects not only influences the prediction of the ultimate displacement but also affects the accuracy in terms of peak load prediction. From Fig. 3, it is also evident how the P-Delta effects become significant at a rather low displacement magnitude. Considering the cases investigated in this section, that threshold can be assumed to be around 10% of the ultimate displacement. As the next investigation, the proposed P-Delta DMEM model is employed to simulate a series of experimental tests of an isolated brick wall subjected to OOP loading carried out by Doherty (2000) [21] and numerically investigated by different authors [22–24]. The tests have been carried out on simply-supported walls with and without pre-compression, representing load-bearing and non-load-bearing walls in URM buildings, which were subjected to monotonic static loads and dynamic excitations along the OOP direction. The specimens consisted of single-leaf brick-masonry walls, 0.11 m thick, 1.50 m height, and 0.95 m wide. The tests were conducted on uncracked and cracked specimens to investigate the influence of pre-existing structural damage on the OOP wall response, but in the present study, only the uncracked configuration and the non-load bearing condition are considered. In all the static tests, the lateral load (F) was uniformly applied at the wall mid-height using a hand pump-driven hydraulic actuator Fig. 4a. The DMEM model has been performed by adopting a refined mesh. Namely, a number of 18 macro-elements, corresponding to the number of bricklayers of the specimen, and 19 interfaces equally distributed along the wall height discretized with seven rows of links have been considered. The elastic and nonlinear masonry mechanical parameters required to calibrate the DMEM model have been chosen according to [23] and [24] and are summarised in Table 1. In the analysed specimen, the pre-peak branch is linear elastic with high stiffness,
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up to a maximum force. Once the maximum force is reached, which corresponds to the cracking of the mid-height interface element, the curve shows a sudden drop in resistance; the softening continues up to the residual strength of approximately 0.4 kN (Fig. 4a). The overall DMEM response agrees very well with experimental results and FEM predictions for both the specimen investigated.
Fig. 4. (a) Static push test configuration; (b) Pushover curves
Table 1. Mechanical parameters of masonry Em [MPa] Young’s modulus
σt [MPa] Tensile strength
σc [MPa] Compressive strength
Gt [N/mm] Fracture energy in tension
Gc [N/mm] Fracture energy in compression
c [MPa] Cohesion
tg(ϕ) [−] Friction coefficient
1560
0.163
6.2
0.05
1.00
0.23
0.58
3.2 Dynamic Nonlinear Application In this section, the dynamic behavior of the façade of San Michele church located in Lisciano, central Italy, which exhibited an incipient out-of-plane response of the main façade during the 2016–2017 earthquake swarm of Central Italy, is investigated. The church is a benchmark since has been already investigated in [25, 26]. The single nave church has a rectangular plan (10 m × 20 m), with a bell tower located on one side of the church and structure integrated into the building Fig. 5a–b. The façade is 9.30 m wide, 0.65 m thick and 9.70 m high. Its slenderness ratio α is about 0.07, obtained as the arctangent of the ratio of half-thickness and the height of the center of mass (0.325 m/4.6 m) (Fig. 5c). More details on the features of the church can be found in [25, 26]. The DMEM model of the church façade is supposed to be elastic being the nonlinearities concentrated only at the rocking interface, which is characterised by a no-tension constitutive law with stiffness in compression for a unit area equal to
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5E+08 N/m3 . An adequate number of nonlinear orthogonal links has been chosen in order to obtain an accurate dynamic response. A free-standing condition of the façade is considered.
Fig. 5. San Michele church; (a) global view, (b) view from inside, (c) dimensions of the façade (in meters)
Harmonic Inputs. A set of harmonic nonlinear dynamic analyses were carried out on the structural model applying a sinusoidal input in the direction orthogonal to the plane of the façade. In particular, 840 nonlinear dynamic analyses were carried out considering seven values of the amplitude (A [cm/s2 ]) and varying the frequency (ω [Hz]), for each amplitude, between 0.025 Hz and 3.0 Hz. The analyses were conducted considering and neglecting the P-Delta effects. From Fig. 6a, it is apparent that the range of frequencies which, with the same amplitude, identify collapse condition for overturning is wider when P-Delta effects are taken into account. Moreover, it is also evident (Fig. 6b) that when the P-Delta effects are considered, the value of the frequency for which we have the maximum displacement of the control point is smaller. Finally, in Fig. 7, the “safe domain” is reported where it is also clear that the safe region is greater when the P-Delta effects are neglected. In particular, in this figure, the ratio between the maximum and the critical displacement is plotted against the amplitude of the signal, being the critical displacement equal to the thickness of the façade. In particular, when the P-Delta effects are taken into consideration, the displacements of the control points, corresponding to “safe” (i.e. no overturning) are about the 50% of the critical displacement. Conversely, when the PDelta effects are neglected, the value of displacements identifying “safe” conditions
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assume valuer around 150% of the critical displacement. Finally, regarding the “safe” range of the amplitude, when the P-Delta effects are considered, the range which is considered “safe” is approximately 35% smaller than that obtained by neglecting the P-Delta effects. In view of the above considerations it is apparent how P-Delta effects should be considered when investigating the out-of-plane behaviour of masonry walls.
Fig. 6. Displacement response spectra of the wall prototype subjected to harmonic oscillations.
Fig. 7. “Safe” domain under harmonic oscillations.
Earthquake Inputs. The earthquakes selected for the nonlinear time-histories analyses are those recorded in the 2016–2017 Central Italy earthquakes [26], which are characterized by high values of PGA, PGV, and PGA/PGV ratio. The considered earthquakes and their parameters are reported in Table 2. Namely, AMT and T1213 have the highest PGA and PGV, while NOR has the highest PGV/PGA ratio. The relative accelerograms are reported in Fig. 8. For all three seismic records, Incremental Dynamics Analyses (IDAs) are performed with and without P-Delta effects. The constructions of the IDA curves involves performing a series of nonlinear dynamic analysis for each record by scaling it to multiple levels of intensity. In this work, the displacement of the control point was defined as
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Engineering Demand Parameter (EDP), while the PGA and the PGV were selected as IMs. The IDAs curves were built considering different scale factors of the seismic signal, in terms of PGA, starting from SF = 0.05, which means reducing the signal to 5% of the recorded one up to a maximum scale factor of 1.20 which is equivalent to increasing the recorded signal by 20%. For each scaled accelerogram, the maximum value of the displacement of the control point is registered. The effects of the tensile strength of the rocking interface are studied using three different values of σt . Namely, a no-tension material, σt = 0 MPa, and two finite values, σt = 0.05 MPa and σt = 0.1 MPa, are considered. The IDAs curves are reported in Fig. 9 both in terms of PGA and PGV for all the seismic records. From Fig. 9 it is evident that for small values of displacements, there are small differences between the curves obtained considering the P-Delta effects and the curves obtained neglecting their effects. In particular, for AMT and T1213, which have the highest PGA and PGV, the curves with and without P-Delta effects have the same trend up to a displacement that is equal to half of the wall thickness (32.5 cm) approximately, instead for NOR, they have the same trend up to almost 80% of the wall thickness (52 cm). Moreover, from the same figure, it is also apparent that when the P-Delta effects are considered, the bearing capacity of the façade, both in terms of PGA and PGV, is less sensitive to the signal with respect to the analyses conducted neglecting them. Finally, the same observation can be made for the influence of the tensile strength of the rocking interface, and this is because when the displacements are large, the geometric effects have a greater influence, also in the dynamic response, than the constitutive nonlinearities.
Table 2. IMs of the seismic records PGA [m/s2]
PGV [m/s]
PGV/PGV [s]
AMT
5.216
0.379
0.07
NOR
3.057
0.562
0.18
T1213
7.793
0.607
0.08
Fig. 8. Seismic records
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Fig. 9. IDAs curves obtained considering the different selected earthquake signals.
4 Conclusions The paper presents and applies an enhanced Discrete Macro-Element (DMEM) model that consists in including P-Delta effects aiming at accounting for geometric nonlinearities in a simplified way but maintaining the very low computational cost of the strategy. After a brief description of the model, it is applied to simulate the response of rigid blocks, comparing the DMEM predictions with the analytical application of the classical theory and with some experimental tests carried out in the experimental campaign conducted by Doherty [21]. The results of the static nonlinear application evidence that the proposed model can reliably predict the ultimate lateral strength and displacement capacity of masonry walls exhibiting OOP rocking mechanisms. In the second part of the paper, a case study represented by a church façade has been subjected to dynamic loads in order to study the influence of considering the P-Delta effects in a structural model of masonry buildings. In particular, harmonic and earthquake dynamic nonlinear analyses were conducted. More specifically, a set of nonlinear analyses considering a sinusoidal signal with seven values of the amplitude and varying the load frequency, for each amplitude, between 0.025 Hz and 3.0 Hz, have been considered. The analyses were conducted considering and neglecting the P-Delta effects, respectively. The analyses confirmed that larger is the collapse region, both in terms of displacement and amplitude, when the P-Delta effects are taken into account. Finally, incremental dynamic analyses were conducted considering three different seismic inputs characterized by different magnitude levels. This latter analysis pointed out the lower sensitivity to signal and mechanical parameters of the model when P-Delta effects are considered.
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Overall, the presented results demonstrate the importance of including geometric nonlinearities in assessing masonry walls subjected to seismic rocking motion and confirm the accuracy of the proposed model, which can provide good predictions of the ultimate behavior of rocking walls to large lateral displacements, maintain the advantage of the DMEM strategy consisting in limiting the computational effort.
References 1. Ingham, J.M., Griffith, M.C.: Performance of unreinforced masonry buildings during the 2010 darfield (Christchurch, NZ) earthquake. Aust. J. Struct. Eng. 11(3), 207–224 (2011) 2. Vlachakis, G., Vlachaki, E., Lourenço, P.B.: Learning from failure: damage and failure of masonry structures, after the 2017 Lesvos earthquake (Greece). Eng. Fail. Anal. 117, 104803 (2020) 3. Lagomarsino, S.: Seismic assessment of rocking masonry structures. Bull. Earthq. Eng. 13(1), 97–128 (2014). https://doi.org/10.1007/s10518-014-9609-x 4. Giuffré, A.: A mechanical model for statics and dynamics of historical masonry buildings. In: Petrini, V., Save, M. (eds.) Protection of the Architectural Heritage Against Earthquakes. ICMS, vol. 359, pp. 71–152. Springer, Vienna (1996). https://doi.org/10.1007/978-3-70912656-1_4 5. Casapulla, C., Cascini, L., Portioli, F., Landolfo, R.: 3D macro and micro-block models for limit analysis of out-of-plane loaded masonry walls with non-associative Coulomb friction. Meccanica 49(7), 1653–1678 (2014). https://doi.org/10.1007/s11012-014-9943-8 6. Casapulla, C., Giresini, L., Lourenço, P.B.: Rocking and kinematic approaches for rigid block analysis of masonry walls: State of the art and recent developments. Buildings 7(3), 69 (2017) 7. Macorini, L., Izzuddin, B.A.: A nonlinear interface element for 3D mesoscale analysis of brick-masonry structures. Int. J. Numer. Methods Eng. 85, 1584–1608 (2011) 8. Lemos, J.V.: Discrete element modeling of the seismic behavior of masonry construction. Buildings 9(2), 43 (2019) 9. Chisari, C., Macorini, L., Amadio, C., Izzuddin, B.A.: An inverse analysis procedure for material parameter identification of mortar joints in unreinforced masonry. Comput. Struct. 155, 97–105 (2015) 10. Pantò, B., Caliò, I.: Numerical modeling for the seismic assessment of masonry structures. In: Civ. Struct. Eng., pp. 85–126 (2022) 11. Brencich, A., Gambarotta, L., Lagomarsino, S.: A macroelement approach to the threedimensional seismic analysis of masonry buildings. In: 11th European Conference on Earthquake Engineering, vol. 90, pp. 1–10 (1998) 12. Vanin, F., Penna, A., Beyer, K.: A three-dimensional macroelement for modelling the in-plane and out-of-plane response of masonry walls. Earthq. Eng. Struct. Dyn. 49(14), 1365–1387 (2020) 13. Bracchi, S., Galasco, A., Penna, A.: A novel macroelement model for the nonlinear analysis of masonry buildings. Part 1: axial and flexural behavior. Earthq. Eng. Struct. Dyn. 50(8), 2233–2252 (2021) 14. Caliò, I., Marletta, M., Pantò, B.: A new discrete element model for the evaluation of the seismic behaviour of unreinforced masonry buildings. Eng. Struct. 40, 327–338 (2012). https:// doi.org/10.1016/j.engstruct.2012.02.039 15. Pantò, B., Cannizzaro, F., Caliò, I., Lourenço, P.B.: Numerical and experimental validation of a 3D macro-model for the in-plane and out-of-plane behavior of unreinforced masonry walls. Int. J. Archit. Herit. 11(7), 946–964 (2017)
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16. Chácara, C., Cannizzaro, F., Pantò, B., Caliò, I., Lourenço, P.B.: Seismic vulnerability of URM structures based on a Discrete Macro-Element Modeling (DMEM) approach. Eng. Struct. 201, 109715 (2019) 17. Housner, G.W.: The behavior of inverted pendulum structures during earthquakes. Bull. Seismol. Soc. Am. 53(2), 403–417 (1963) 18. Vadalà, F., Cusmano, V., Funari, M.F., Caliò, I., Lourenço, P.B.: On the use of a mesoscale masonry pattern representation in discrete macro-element approach. J. Build. Eng. 50, 2022 (2021) 19. Pantò, B., Cannizzaro, F., Caddemi, S., Caliò, I.: 3D macro-element modelling approach for seismic assessment of historical masonry churches. Adv. Eng. Softw. 97, 40–59 (2016) 20. Cannizzaro, F., Pantò, B., Caddemi, S., Caliò, I.: A Discrete Macro-Element Method (DMEM) for the nonlinear structural assessment of masonry arches. Eng. Struct. 168, 243–256 (2018) 21. Doherty K.T.: An investigation of the weak links in the seismic load path of unreinforced masonary buildings (2000) 22. Griffith, M.C., Lam, N.T.K., Wilson, J.L., Doherty, K.T.: Experimental investigations of unreinforced brick masonry walls in flexure. J. Struct. Eng. 130(3), 423–432 (2004) 23. Minga, E.: 3D Meso- and Macro-Scale Models for Nonlinear Analysis of Masonry Systems. Imperial College, London (2017) 24. Pantò, B., Macorini, L., Izzuddin, B.A.: A two-level macroscale continuum description with embedded discontinuities for nonlinear analysis of brick/block masonry. Comput. Mech. 69(3), 865–890 (2022). https://doi.org/10.1007/s00466-021-02118-x 25. Giresini, L., Casapulla, C., Denysiuk, R., Matos, J., Sassu, M.: Fragility curves for free and restrained rocking masonry façades in one-sided motion. Eng. Struct. 164(March), 195–213 (2018) 26. Giresini, L., Pantò, B., Caddemi, S., Caliò, I.: Out-of-plane seismic response of masonry façades using discrete macro-element and rigid block models. In: COMPDYN Proceedings, vol. 1, pp. 702–717 (2019)
Numerical Modelling and Structural Health Monitoring for Built Heritage Management: The Case of the Church of Santa Croce in Ravenna Francesca Ferretti(B)
, Chiara Monteferrante, and Claudio Mazzotti
DICAM Department, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy [email protected]
Abstract. The conservation of the built heritage represents nowadays a great challenge for the scientific community and for the heritage managers since historical buildings can typically face both seismic and climate related hazards. To increase the resilience and reduce the vulnerability of historical constructions, specific strategies and methodologies should be developed and applied. In the framework of the Shelter project, funded by the European Union’s Horizon 2020 program, the Church of Santa Croce in Ravenna (Italy) was taken as a case study for the validation of such methodologies, involving a multidisciplinary approach. In this work, the structural behavior of the Church of Santa Croce was investigated through the development of a finite element model and the implementation of a Structural Health Monitoring system, with the possibility of accessing data in realtime. First, the historical analysis of the construction and slightly-destructive tests were carried out to investigate the constructive details, the state of damage, and the mechanical properties of the materials. After acquiring a detailed knowledge level of the construction, modal analyses and nonlinear static numerical simulations were carried out to assess the modal parameters and to reproduce the existing crack pattern. On the one hand, the numerical analyses supported the design of the monitoring system itself; on the other hand, a model updating was carried out to calibrate mechanical parameters not explicitly obtained through testing. The adopted methodologies and approaches are described in the paper, together with the results of the numerical simulations and preliminary results acquired from the monitoring system. Keywords: Cultural heritage · Historical buildings · Vulnerability · Finite Element Model · Structural Health Monitoring
1 Introduction Risks related to the effects of climate change and natural hazards are increasingly threatening the cultural heritage. In order to reduce the vulnerability of historical buildings, to promote their exploitation and foster their conservation, it is necessary to identify and develop intervention plans and protocols to improve the resilience of the buildings and of the areas in which they are located [1–3]. The European SHELTER project (Sustainable © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 578–590, 2024. https://doi.org/10.1007/978-3-031-39450-8_48
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Historic Environments hoListic reconstruction through Technological Enhancement and community-based Resilience), financed by the Horizon 2020 Research and Innovation Programme, aims to establish cross-scale, multidimensional, data driven and community based operational knowledge framework for cultural heritage and conservation-friendly resilience enhancement and sustainable reconstruction of historic areas to cope with climate change and seismic hazard. The multidisciplinary activities undertaken within the SHELTER project made it possible to analyze the main challenges identified in five case studies, representative of different cultural heritage construction typologies from small to large scale, for the validation of the proposed methodologies. The urban open lab identified in the Italian territory is the Church of Santa Croce and the surrounding archaeological site in Ravenna, which represent an area affected by subsidence, alluvial phenomena and seismic events. In this framework, the present work focuses on the case study from a structural point of view and it is structured as follows. Introduction to the case study and the presentation of the knowledge path are given in Sect. 2 in order to investigate the constructive details, the state of damage, and the mechanical properties of the materials [4–6]. Section 3 presents the installed real-time monitoring system and the dynamic identification. In Sect. 4, modal analyses and nonlinear static numerical simulations were carried out to calibrate the mechanical parameters used ad input in the numerical simulations and to assess the vulnerability of the church, trying to reproduce the existing crack pattern. Finally, Sect. 5 collects the main conclusions of this work.
2 The Case Study: Church of Santa Croce in Ravenna The Church of Santa Croce is located in the city center of Ravenna (Italy) within an archeological site inscribed as UNESCO cultural property since 1996 (Fig. 1). The area in which the Church is located is characterized by subsidence phenomena which, together with the conformation of the site itself, determines the constant presence of water. The area is therefore prone to sudden flood, especially in case of heavy rainfall, which have become increasingly frequent due to climate change. Currently, a drainage system allows the site to be maintained in a dry condition. 2.1 Knowledge Path In the framework of the safety evaluation of existing historical buildings, the knowledge of the construction is one of the most important aspects, to be achieved prior to the execution of numerical analyses and to the design of relevant interventions [4–6]. In order to plan the monitoring activities and to model the Church of Santa Croce, a specific knowledge path was followed, as described in the following sections. Historical Analysis. The initial configuration of the Church of Santa Croce, built around 450 BC, was more complex with respect to the current one (Fig. 1). Through the collection of information about the origin of the construction and its evolution over time [7–9], it was possible to determine the chronological sequence of the main modifications occurred in the past centuries (Fig. 2). After centuries of demolitions and partial reconstructions, at the end of the XX century, the timber roof was rebuilt after a fire and
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(b) Fig. 1. Church of Santa Croce: (a) plan view from Google Maps, (b) south-east view.
strengthening interventions were carried out on the apsis, with reinforced plaster, and on the foundations.
Fig. 2. Evolution of the configuration of the Church of Santa Croce.
Geometry and Details. A survey of the Church of Santa Croce was carried out to precisely describe its geometry and identify the structural elements and details. The vertical structural elements are double-leaves masonry walls, composed of several masonry typologies, due to the evolution of the construction through the centuries, all made by bricks and poor lime-based mortar. The roof is composed by timber trusses and wooden beams supported by a reinforced concrete corbel built at the top of the longitudinal walls and the apsis arch. The access to the Church is located on the west side, on Galla Placidia street, running close to the façade in the XX century, at a higher level with respect to the Church’s floor. Regarding the state of damage of the Church, the survey of the crack pattern was carried out (Fig. 3). Major cracks were located in correspondence with the connections
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between orthogonal walls, on the southern wall and in correspondence with the apsis, both at the roof level and at the base. Moreover, a severe problem highlighted during the on-site inspections was the detection of the groundwater level higher than the floor level of the Church, leading to problems related to capillary rising damp and, more in general, to the presence of water on the site.
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Fig. 3. Damage survey: (a) plan view, (b) southern wall.
On-Site Experimental Campaign. Given the historical character of the Church of Santa Croce, non-destructive and minor-destructive on-site tests were conducted with the objective of identifying the structural details and evaluate material properties to be used in the numerical simulations. In more details, the following investigations were carried out: (i) endoscopies to detect the wall stratigraphy, (ii) sonic tests to evaluate the homogeneity of the masonry walls and the presence of cracks/defects, and (iii) sampling of bricks and mortar for the determination of their compressive strength. The test locations are reported in Fig. 4. Endoscopies, conducted on the southern and western walls, having a total thickness of 62 cm, allowed to evaluate the walls stratigraphy which is entirely composed by clay bricks and lime-based mortar. Within the thickness, it was not detected the present of a disorganized core. Sonic tests may be performed according to different methodologies, mainly distinguished as direct and indirect sonic tests [10, 11]. Considering the features of the construction and the possibility to easily access both wall sides or one side only, in the present work both methodologies were adopted: one direct sonic test and three indirect sonic tests were performed. The tests were conducted using two piezoelectric probes, positioned on opposite sides of the walls (direct tests) or on the same side (indirect test), considering the testing points represented in Fig. 5a. In more detail, for indirect sonic tests, the emitting probe was positioned in correspondence of the testing point “0”, while the receiving probe was progressively moved in correspondence with the other testing points (1–16). For the direct sonic tests, the two probes were positioned in the same testing point on the opposite sides of the wall. By knowing the time of flight, which is the
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Fig. 4. Plan view with indication about the test locations.
time the sonic waves take to travel, and the distance within the probes, it was possible to evaluate the wave velocity, that can be directly related to the material quality. The results of an indirect sonic test are presented in Fig. 5b, where the velocity contour plot was obtained by interpolating the results obtained at the different testing points. In Fig. 6, the comparison between the sonic wave velocities obtained for all the tests is presented. It is possible to observe that lower values of the wave velocities were obtained for the indirect sonic tests and this can be explained by the irregularities detectable on the wall surfaces, mainly due to damages and degradation of the mortar joints.
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Fig. 5. Sonic tests: (a) location of testing points, (b) representative map of wave velocities for the indirect sonic test Sc_i3.
Concerning the determination of material properties, 7 bricks and 2 mortar joint samples were extracted from different masonry portions. Due to the quality and state of conservation of the mortar, it was not possible to extract a larger number of undamaged samples. The obtained samples were then tested in the laboratory. In more detail, bricks were cored to obtain specimens having a unitary aspect ratio, which were then subjected
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Fig. 6. Sonic test results.
to uniaxial compression test [12], obtaining an average brick compressive strength equal to 11.1 MPa. Double punch tests [13] were performed on the mortar joint samples, for the evaluation of the mortar compressive strength, resulted equal to 2.6 MPa. By knowing the compressive properties of the constituent materials, the masonry compressive strength was estimated by using the Eurocode 6 formula, obtaining 3.2 MPa.
3 Structural Health Monitoring System 3.1 Real-Time Monitoring System On the basis of the knowledge acquired about the state of conservation of the Church of Santa Croce, a proper design of the monitoring system was carried out by first identifying the typologies of the sensors to be adopted. Considering the subsidence problems and the pre-existing cracks detected through the damage survey, the following sensors were chosen: (i) 5 linear potentiometers, with a gauge length of 50 mm, to measure the opening of main cracks, (ii) 2 biaxial clinometers (measurement range of ±5°, resolution equal to 0.001°) to measure rotations of the longitudinal walls, (iii) 5 level meters (measurement range of ±40 mm, sensitivity equal to 0.01 mm) to monitor vertical displacements of the walls, and (iv) 6 uniaxial accelerometers for the dynamic identification. They were all installed inside the Church in the positions reported in the plan view of Fig. 7. A web dashboard was also developed for the real-time visualization of the data registered by the acquisition system. The data were transmitted to the web platform through wireless protocols. The structural monitoring began at the end of April 2021 and is currently in operation. The data registered by potentiometers, clinometers and level meters from April 2021 to December 2022 are presented in Fig. 8. In general, it can be observed that the only crack for which a consistent opening is registered is the crack in correspondence with the potentiometer P5, positioned at the base of the apsis, where the access to the crypt is located. Angle variations registered by the clinometers are comparable for the two longitudinal walls. Concerning vertical displacements, even if a global trend cannot be identified, consistently with the fact that the external walls of the church are not
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Fig. 7. Monitoring system: type and positions of the sensors.
Fig. 8. Real-time monitoring data from April 2021 until December 2022 (grey area: no data due to flooding of the Church).
adequately connected in correspondence with the corners, it is possible to notice that, at the end of 2022, a negative increment of the displacements is registered by all the level meters. The grey area indicated in the graphs of Fig. 8 represents a period of time in which the monitoring activities stopped due to the fact that the Church was flooded as a result of severe thunderstorms and of the malfunctioning of the drainage system. 3.2 Dynamic Identification As previously described, uniaxial piezoelectric accelerometers (sensitivity of 10 V/g and measurement range of ±0.5 g) were also installed, for a limited period of time, to perform ambient vibration tests for the dynamic identification of the construction. They were positioned at a height of 5 m from the base of the Church (Fig. 7). Ten different registrations obtained under dynamic excitation induced by ambient vibrations
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were considered. For each registration, signals were acquired with a frequency equal to 200 Hz for a total duration of 100 s. The dynamic characteristics of the structure were identified by means of the Enhanced Frequency Domain Decomposition (EFDD) method [14], which is based on a singular value decomposition of the Power Spectral Density (PSD) matrix to separate the contribution of each vibration mode. Once the singular value decomposition is performed, the Peak-Picking identification technique [15] can be adopted for the identification of natural frequencies. Considering the different registrations for each accelerometer, it was possible to identify recurrent ranges of resonance frequencies, leading to the identification of the first five natural frequencies of the Church as the average between the ones obtained for all the registrations. Moreover, modal displacement values were derived for each accelerometer and for each registration, then averaged with respect to the total number of registrations, to evaluate the mode shapes associated to the natural frequencies previously identified. Results in terms of natural frequencies, periods and damping ratios of the first modes of the structure are reported in Table 1. They were used for the calibration of the numerical model, as will be explained in the following. Mode shapes are presented in Sect. 4, in comparison with the mode shapes obtained from the eigenvalue analysis. Table 1. Natural frequencies, periods and damping ratios of the first fives modes of the structure. Mode
Frequency (Hz)
Period (s)
Damping ratio (%)
I
2.716
0.368
3.90
II
3.926
0.255
1.93
III
4.656
0.215
1.97
IV
5.618
0.178
1.89
V
6.847
0.146
0.84
4 Numerical Model A 3D solid continuum finite element model (Fig. 9) of the Church of Santa Croce was developed by using the commercial software DIANA FEA v. 10.6. The geometry was defined on the basis of the geometric survey and of the on-site inspections previously described. The structural elements (masonry walls, apsis strengthened with reinforced plaster, reinforced concrete ring beam, timber roof elements) were modelled by adopting isotropic continuum models and quadratic brick elements. The elastic material properties are summarized in Table 2. It is worth mentioning that the elastic properties of the masonry were set by considering the values proposed by the Italian Building Code commentary [16] for poor-quality brick masonry. Indeed, information about the elastic modulus or the Poisson’s ratio were not obtained during the on-site investigations. The soil was modelled according to the Winkler model, i.e. by considering mutually independent springs of stiffness k, through boundary interface elements. Values concerning the mechanical characteristics of the soil were established on the basis of previous
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surveys conducted in the area, i.e. investigation on the soil type and monitoring activities in which vertical displacements of the masonry walls were measured [7]. In more detail, to simulate the real behaviour of the foundations due to soil subsidence, different elastic stiffness constants were adopted under the masonry structural elements: 155.6 MPa/m for the façade, 155.5 MPa/m for the southern wall, 165.46 MPa/m for the northern wall, 45.1 MP/m for the bell tower, and 151.7 MPa/m for the apsis. To reproduce the presence of the street adjacent to the main façade, a horizontal constraint was considered in the model to account for the restraint to horizontal translations provided by the street itself. As observed during the damage survey, the walls were not properly connected in correspondence with the corners of the building. For this reason, quadratic interface elements were introduced at the connection between orthogonal walls. The stiffness parameters of these elements, i.e. one normal component (kz) and two shear components (kx and ky), were calibrated by considering the results obtained during the dynamic identification process, as described in the following. The loads considered during the analyses were the ones related to the self-weight of the structural and non-structural elements. Table 2. Material properties adopted in the FE model. Material
Young’s modulus E [MPa]
Poisson’s ratio ν [-]
Mass density w [kN/m3 ]
Masonry
1800
0.2
18
Timber
9000
0.2
7.5
Reinforced concrete
32000
0.2
25
Fig. 9. Finite Element Model of the Church of Santa Croce.
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4.1 Eigenvalue Analysis The dynamic behaviour of the church was investigate by performing an eigenvalue analysis on the 3D FE model with the objective of calibrating the stiffness parameters of the interface elements inserted in correspondence with the walls connections. With this purpose, a modal analysis was initially carried out on a model in which infinite stiffness values were assigned to these interface elements. As expected, natural frequency values much higher than the experimental ones were obtained. Subsequently, the stiffnesses were calibrated by using the experimental frequencies as a reference: first the normal stiffness k z was calibrated, then the shear stiffnesses k x and k y were varied until convergences with the experimental data. Eventually, the stiffness values obtained were: k z = 0.6 N/mm3 and k x = k y = 0.06 N/mm3 . In Fig. 10, a comparison between the experimental and numerical first vibration modes is presented. Values of the displacements were taken from the FE model considering the points where the real accelerometers were placed during the dynamic testing, then normalized and amplified. As it can be seen, a quite good agreement was obtained between the experimental results and those from the calibrated model, demonstrating the reliability of the model itself.
Fig. 10. Comparison between numerical and experimental mode shapes.
4.2 Nonlinear Analysis In addition to the eigenvalue analysis, a nonlinear analysis was also performed with the aim of simulating the existing cracking scenario. In order to model the nonlinear mechanical behaviour of the masonry, the Mohr-Coulomb plasticity model was adopted, with cohesion and angle of internal friction equal to 0.075 MPa and 0.38 rad, respectively. The dilatancy angle was set to zero and cohesion or friction hardening were not considered. A tension cut-off was set at 0.05 MPa. Adopted values of the mechanical properties were set according to indications available in the Italian Building Code commentary [16] for existing masonry buildings and based on preliminary parametric analyses. The nonlinear static analysis was performed by applying the dead loads in 10 subsequent load increments. The regular Newton-Raphson method was used to solve the nonlinear problem. The results of the nonlinear analysis are presented in Fig. 11 for the last load step, i.e. total dead load applied, in terms of vertical displacements (Fig. 11a), in-plane
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principal stresses (Fig. 11b), vertical plastic strain (Fig. 11c), and normal stresses at the interfaces (Fig. 11d).
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Fig. 11. Results of the nonlinear analyses: (a) vertical displacements, (b) in-plane principal stress components, (c) vertical plastic strains, (d) interface normal tractions.
It can be noticed that the most stressed masonry portions are located below the opening on the main façade, in correspondence with the apsis and, in general, in the lower portions of the masonry walls. Plastic strains can also be observed at the connection between the bell tower and the southern wall and between the bell tower and the apsis. Even if the presented results cannot precisely describe the crack pattern, it is worth mentioning that these locations are the ones in which most of the pre-existing damage was concentrated (Fig. 12). Due to the presence of the Galla Placidia street, it was not possible to investigate cracks in the masonry portion below the opening of the main façade. Along the interface elements at the corners, it can be observed that positive normal relative displacements are detected in many points, thus indicating the opening of cracks in those positions.
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Fig. 12. Real damage pattern: (a) connection between the bell tower and the southern wall, (b) connection between the street and the southern wall.
5 Conclusions In this work, a methodology which can be applied for the evaluation and monitoring of the state of conservation of existing buildings belonging to the cultural heritage was presented. The information related to the knowledge of the construction, to be achieved with historical analyses, on-site surveys and investigations about structural details and material properties, adopting non-invasive techniques, represent a key factor for the subsequent phases and, more specifically, for the accurate design of a Structural Health Monitoring system and for the numerical modeling. The possibility to access monitoring data in real-time through a web dashboard was investigated and developed to provide a tool for the technicians, who can have the possibility to receive updated information about the monitored entities and to intervene in case of problems or specific events which might be dangerous for the historical building. Moreover, the information obtained through the monitoring system could be useful for the numerical model updating. The numerical model is, indeed, essential for the study of the safety of the building, e.g. against seismic events, and it should be the closer as possible to the reality. Within this perspective, the monitoring activities will continue in the following months, providing a basis for the definition of maintenance protocols supporting decision making processes. Acknowledgments. This research was carried out in the framework of the SHELTER project, funded by the European Union’s Horizon 2020 research program, grant N. 821282. The contribution of Massimo Gardini (CSM Sistemi) to the design of the monitoring system is gratefully acknowledged.
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References 1. Chiabrando, F., Colucci, E., Lingua, A., Matrone, F., Noardo, F., Spanò, A.: A European Interoperable Database (EID) to increase resilience of cultural heritage. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci. 42, 151–158 (2018) 2. Sharifi, A.: A critical review of selected tools for assessing community resilience. Ecol. Ind. 69, 629–647 (2016) 3. Ahern, J.: From fail-safe to safe-to-fail: sustainability and resilience in the new urban world. Landsc. Urban Plan. 100(4), 341–343 (2011) 4. Ministero delle Infrastrutture e dei Trasporti: Aggiornamento delle ‘Norme Tecniche per le Costruzioni’. Gazzetta Ufficiale della Repubblica Italiana, Rome (2018) 5. EN 1998-3: Eurocode 8: design of structures for earthquake resistance-part 3: assessment and retrofitting of buildings. CEN (European Committee for Standardization), Brussels (2005) 6. DPCM 9/2/2011: Linee guida per la valutazione e la riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme tecniche delle costruzioni di cui al decreto del Ministero delle Infrastrutture e dei trasporti del 14 gennaio, Rome (2008) 7. Ricceri, G.: Studi e ricerche nell’area di San Vitale, Galla Placidia e Santa Croce in Ravenna. SGEditoriali, Padova (1992) 8. Gelichi, S., Piolanti, P.N.: La chiesa di S. Croce a Ravenna: la sequenza architettonica. In: XLII corso di cultura sull’arte ravennate e bizantina. Ravenna, Edizioni del girasole (1995) 9. Massimiliano, D.: La basilica di Santa Croce - Nuovi contributi per Ravenna tardoantica, Edizioni del Girasole (2013) 10. Binda, L., Saisi, A., Tiraboschi, C.: Investigation procedures for the diagnosis of historic masonries. Constr. Build. Mater. 14(4), 199–233 (2000) 11. Binda, L., Saisi, A., Tiraboschi, C.: Application of sonic tests to the diagnosis of damaged and repaired structures. NDT E Int. 34(2), 123–138 (2001) 12. EN 772-1: Methods of test for masonry units-Part 1: Determination of compressive strength. Brussels. Comité Européen de Normalisation, Brussels (2011) 13. Henzel, J., Karl, S.: Determination of strength of mortar in the joints of masonry by compression tests on small specimens. Darmstadt Concrete 2(1), 123–136 (1987) 14. Allemang, R.J., Brown, D.L.: A unified matrix polynomial approach to modal identification. J. Sound Vib. 211(3), 301–322 (1998) 15. Ewins, D.J.: Modal Testing: Theory and Practice. Wiley, New York (2000) 16. Ministero delle Infrastrutture e dei Trasporti: Circolare n. 7 del 21 Gennaio 2019. Istruzioni per l’applicazione dell’«Aggiornamento delle “Norme tecniche per le costruzioni”» di cui al DM 17 gennaio 2018. CS LL. PP (2019)
Micro Modeling of Irregular Stone Masonry Walls Using Mathematical Programming Qianqing Wang1(B) , Ketson Roberto Maximiano dos Santos2 , and Katrin Beyer1 1 École Polytechnique Fédérale de Lausanne EPFL, Earthquake Engineering and Structural
Dynamics EESD, Lausanne, Switzerland [email protected] 2 Stochastic Analysis and Signal Processing Lab, Department of Civil, Environmental, and Geo-Engineering (CEGE), University of Minnesota Twin Cities, Minneapolis, USA
Abstract. While understanding the shear strength of stone masonry structures is important for the design and the maintenance, we still lack computational tools for predicting the strength as a function of the stone layout. Here we implement an end-to-end image based kinematic analysis framework that converts the image of a stone layout of a wall into a 2D kinematic model. Machine learning and image processing techniques are applied to convert a wall image into a rigid block model, which is then used as the geometry input for an existing limit analysis approach using mathematical programming. This existing approach is extended such that also cohesion, limited tensile and compressive strength can be considered in the point-based formulation of interface failure. We apply the method to simulate the strength of stone masonry walls with mortar that are subjected to shearcompression loading and show that our method can demonstrate the influence of the stone masonry typology on the shear strength. Keywords: Stone masonry · Shear strength · Limit analysis · Model generation · Micro modeling
1 Introduction Shear strength is a fundamental concept in the field of structural engineering that refers to the maximum load-carrying capacity of a material or structure when subjected to a lateral force. In the context of stone masonry walls, understanding the shear strength is essential for determining the ability of the wall to withstand external loads in the design, such as those caused by wind or earthquakes, or to identify and address any weaknesses or damage that may compromise the structural integrity of the wall in the maintenance and repair processes. Next to the mortar strength, the shear strength of a stone masonry wall depends mainly on its microstructure, including their size and shape, bonding pattern, and the mortar quality. The shear strength of stone masonry walls is typically analyzed with computer simulations. Among them, microscale modeling simulates the behavior of masonry walls at the scale of stones by explicitly modeling the individual characteristics of each stone © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 591–602, 2024. https://doi.org/10.1007/978-3-031-39450-8_49
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unit such as their size, shapes, material properties, and the properties of the mortar connecting the units. Most of the contributions related to this topic are focused on finite element modeling [1–3]. Zhang et al. conducted finite element analysis to study the influence of typology on the compressive strength [2] and shear resistance [3] of stone masonry walls. In their case, a simulation lasted around 20 h using a high-performance computing cluster with processors running at 2.6 GHz and using 64 GB of RAM [2]. Compared to finite element analysis, limit analysis is computationally efficient as one obtains limit (load multiplier and failure mechanism) directly without going through the loading history [4]. In this regard, Krabbenhoft et al. formulated the limit analysis theorem as an optimization problem, which can be solved as a mathematical programming problem [5]. Portioli et al. extended this method and applied it to simplified microscale modeling of mortar-joint stone masonry using surface contact models [6] and point contact models for cohesionless joints [7]. Point-based contact models that include cohesion, and therefore also a limited tensile strength, has not yet been treated. This is relevant for modelling stone masonry with mortar joints. Apart from the challenge of modeling mortar joints, stone masonry has an irregular layout, which is a challenge for the geometry idealization. The common practice is to use image processing tools to generate finite element meshes [2] or discrete bodies [8– 10] from sketches or photos. However, such meshing tools cannot be directly used in kinematic analysis as they do not compute the location of contact points and contact interfaces. Herein, we propose an end-to-end image-based kinematic analysis framework to investigate the shear strength of 2D irregular rubble stone masonry wall at microscale. To this end, we develop an image-based preprocessing algorithm that uses machine learning and image processing techniques to convert image data into a simulation model. For the limit analysis, we use the 4-point schema proposed by Portioli [7]. In our problem, we included cohesion, limited tensile and compressive strength in the formulation of the interface failure criterion. We apply the framework to simulate the shear strength of various stone masonry typologies.
2 Method The limit analysis is performed based on the kinematic analysis formulation proposed by Krabbenhoft [5]. Portioli used this approach to analyze masonry structures with regular stone layouts considering tensionless and cohesionless interfaces [7]. In this section, we first present a new numerical formulation that includes friction, cohesion, tensile strength and compressive strength at interfaces. The second part is dedicated to the preprocessing algorithm that converts the image of a masonry wall into a geometry model for the computer simulation. 2.1 Rigid Block Modeling of Mortar-Joint Masonry Structures Using Mathematical Programming Masonry is modeled as an assembly of stone and mortar elements. A stone element is represented as a polygon which shape is determined by the border of a stone extracted
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from the input image (the preprocessing steps are explained in Sect. 2.2). Mortar is divided into triangles, each representing an individual element in the model (Fig. 1 left). Four contact points are introduced on each interface, which is represented by the incident edges including stone-mortar interfaces, stone-stone interfaces, and mortarmortar interfaces (Fig. 1 right). In the context of simulating shear-compression tests on walls, we also introduce ground and beam elements, where both are represented as polygons in contact with neighboring elements. The center of the beam element is located horizontally at the center of the wall such that there is zero moment at the horizontal section in the middle of the wall.
Fig. 1. Rigid block model of stone masonry wall
The physical constraints of the problem, including equilibrium of elements and failure at interfaces, are formulated based on the rigid block model. Equilibrium is maintained at the center of each element: AFc = FD + αFL ,
(1)
where Fc is the contact force vector including a normal component and a tangential component: Fck = (tk , nk ),
(2)
where tk and nk are the tangential force and the normal force acting at the contact point k. A is the equilibrium matrix, whose entries are determined based on the location of contact points and element centers. FD and FL are the dead and live load, respectively, which are only applied on the beam element. α is the load multiplier of the live load. The equilibrium of the ground element is not considered, such that the magnitude of the contact force on the ground-mortar interface is only constraint by material properties. Failure occurs at the interfaces by imposing constrains on the contact forces on contact points, including sliding, cracking and crushing. Sliding failure is governed by a Coulomb-type criterion, written as: tk + μnk ≤ Ck
(3)
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Ck is the cohesive force at contact point k and μ is the friction coefficient. The value of Ck is approximated as a function of the cohesion c and the length of the interface lj : Ck = 0.25clj
(4)
Cracking and crushing are conditioned on the normal force and the moment at interfaces with a perfect plastic behavior in compression and tension, as shown by dashed lines in Fig. 2. The failure surface is written as the following: − ft lj − aj + fc aj − Nj = 0 2 0.5fc aj2 + 0.5ft lj − aj + Nj 0.5lj − aj − Mj = 0 (5) Here ft and fc are the tensile strength and compressive strength respectively. aj is the distance from the edge of interface j to its neutral axis in the plastic state, lj is the length of interface j. The function is approximated by eight uniform segments such that the resulting optimization problem is linear (solid lines in Fig. 2). The forces on interfaces can be obtained by aggregating the forces on contact points: Nj = Mj =
4 k=1
nk
1 4 nk lj k=1 2
(6) (7)
The work of Krabbenhoft [5] shows that by assuming associative flow rule, the maximum load multiplier α can be obtained through the following linear optimization problem, and that the displacement of elements can be obtained by Lagrange multiplier associated with the solution of the same optimization problem. max α subject to Eqs.(1), (3) and (5) In this study, the optimization problem is solved with optimization solver Mosek [11]. The iterative procedure proposed by Gilbert et al. [12] is also implemented to consider non-associative flow rule in sliding. 2.2 Automated Model Generation from Images Images can depict the microstructure of stone masonry walls. Figure 1 shows a stone masonry wall generated by Zhang and Beyer [3] as a typical representation of a typology A wall according to the Italian code [13]. Herein, we developed an image processing tool to translate such data into the rigid block model shown in Fig. 3. To identify stone and mortar elements, we first detect the boundaries of stones using the marching squares algorithm (Fig. 4 left), which is a widely used method for finding the contours of objects in images [14]. The obtained pixel-wise contour points are then downsampled using a pixel grid downsampling method. When the contour vanishes or becomes one-dimensional (verified through linear regression) due to downsampling, the original pixel-wise points of the contour are utilized instead. The resulting points
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Fig. 2. Cracking and crushing failure on interfaces
Fig. 3. A stone masonry wall generated by Zhang and Beyer [3]
Fig. 4. Detected stone edges and downsampled stone edges
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are rearranged in counter-clockwise order using Quickhull algorithm [15] such that connecting the points result in continuous non-self-intersecting polygons (Fig. 4 right). The stone contours serve as the geometric input for the generation of a finite element mesh of the mortar. The mesh generated by Gmsh [16] is composed of three-point triangles, with each triangle representing a mortar element (Fig. 5). The interfaces are defined by the edges of the triangles (Fig. 6), with two contact points identified at the two ends of each edge. The direction of the normal force on a contact point is perpendicular to the direction of the edge, while the direction of the tangential force is parallel to it.
Fig. 5. Meshed mortar where each triangle is a mortar element in kinematic analysis
The incidence information of contact points, meaning which two elements are in contact through which points, is identified by matching the contact pairs. A contact pair comprises two points placed at the same location but belonging to different elements. In the current 4-point contact kinematic analysis formulation, one interface comprises 2 contact pairs, each includes 2 contact points. We iterated all the contact points and found the counter points using R tree search. An R tree is a tree-based data structure that organized spatial data in a hierarchical manner, which each node in the tree is a 4-d vector representing the coordinate and the direction of normal force of a point. As contact pairs share the same coordinates with opposite normal directions, the counter point of a point (xi , yi ) with normal direction (nxi , nyi ) is the node (xi , yi , −nxi , −nyi ) in the R tree and can be found efficiently through nearest neighbor search.
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Fig. 6. Rigid block model for kinematic analysis where the red points are the center of stone elements, the green points are the center of mortar elements. Black triangle shows the center of the ground element and blue triangle shows the center of loading beam. Stone-mortar interface is colored in orange, mortar-mortar interface is in light blue.
3 Results 3.1 Material Properties and Reference Simulation Different interface properties can be assigned to different contact point. The material parameters have been summarized in Table 1. Most parameters were taken from the reference simulation [3]. We made the following assumptions for parameters that are unavailable: • The compressive strength of mortar is 2.0 MPa. • The compressive strength at stone-mortar interface is 1000 times larger than the compressive strength at mortar-mortar interface. • The material properties of stone-stone interface are the same as those of stone-mortar interface. • The ground-mortar and beam-mortar interfaces are 10 times stronger than the stonemortar interface in terms of tensile strength and cohesion.
Table 1. Material properties used in the simulation Interface
fc (MPa)
Mortar-mortar Stone-mortar
μ
ft (MPa)
c (MPa)
2.0
0.15
0.3
0.5
2000
0.05
0.1
0.5
Stone-stone
2000
0.05
0.1
0.5
Ground/beam-mortar
2000
0.5
1.0
0.5
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3.2 Influence of the Model Size The pixel grid downsampling step in the developed preprocessing algorithm changes the model size (i.e., number of contact points and number of elements) by varying the grid size. To investigate its influence on the outcome of the computer simulation, we consider 2, 5, 10, 15 pixels per grid to generate four models from the stone masonry wall image shown in Fig. 3. The results are illustrated in Fig. 7.
Fig. 7. Models corresponding to different grid size: (a) 2, (b) 5, (c) 10, and (d) 15 pixels per grid.
It can be seen that increasing precision (the reverse of number of pixels per grid) leads to quadratic increase in the number of elements and contact points in the model due to the dimensionality of digital images. For the coarsest model, the mortar element sizes are not uniformly distributed. This characteristic results from the employed downsampling criterion saying that if the downsampled vertices of one stone is colinear, the original vertices of that stone should be used. Such criterion ensures that all stones are represented in the obtained model, no matter how small it is. Therefore, a dense mesh around small stones are inevitable despite the grid size.
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Double bending shear simulations for three levels of axial stress (0.1, 0.5, 1.0 MPa) are conducted for all four models. The obtained load multipliers are shown in Fig. 8a. For a low compression level (0.1 MPa) and a medium compression level (0.5 MPa), the load multiplier is barely influenced by the model size. On the other hand, for high compression level (1.0 MPa), there is a large difference between the results obtained from the model of grid size 15 and model of grid size 10. To understand this phenomenon, the displaced elements with crack maps are shown in Fig. 9. The crack width of an interface is calculated as the difference in displacement of contact pairs on that interface. Large cracks are shown in read whereas smaller ones are shown in blue. It can be seen that the crack propagates easily in the coarse model (grid size 15). In refined models, the interlocking between stones are well represented, improving the shear strength of the wall. In terms of computational cost, Fig. 8b shows the computing time for each simulation. The time increases exponentially with grid precision. Therefore, we use 10 pixels per grid to balance efficiency and accuracy for the rest of the simulations in this study.
Fig. 8. (a) Load multiplier and (b) computation time for different grid sizes.
3.3 Influence of Various Typologies To validate the proposed method, we analyzed the shear strength of a sample of 15 walls as presented in the reference simulation [3]. The wall samples were classified into five categories, corresponding to the typologies A, B, C, D and E defined in the Italian code [13]. For each sample, three compression levels were applied: 0.1 MPa, 0.5 MPa, 1.0 MPa. The horizontal load is applied in two directions, from left to right and from right to left. A total of 90 simulations were conducted in total. The obtained shear strength for double bending boundary condition are summarized in Fig. 10. It can be seen that for low compression level (0.1 MPa), the typology of the wall has little influence on the load multiplier. For medium and high compression level (0.5 MPa and 1.0 MPa), the shear strength increases from typology A to typology E. This is because the failure mode is dominated by flexural failure at low compression level, which is independent of the wall typology, whereas the wall fails in shear at high compression level. The same phenomenon is found in the reference simulation [3]. We also noticed
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Fig. 9. Crack patterns for compression level of 1.0 MPa and, horizontal force from right to left for distinct grid sizes: (a) 2, (b) 5, (c) 10, and (d) 15 pixels per grid.
that for a given typology, the shear strength at high compression level has a larger variance than that at low compression level, especially for typology A, B and C, where the largest load multiplier is 2.6, 3.0, and 2.7 times respectively larger than the smallest value. This shows that shear strength at high compression level is more sensitive to the microstructure. The proposed kinematic analysis method with detailed microscale modeling is able to differentiate the walls with different micro structure at a reasonably computation cost. The average computation time for one simulation was 7 min on a computer running at 2.9 GHz with 32 GB of RAM.
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Fig. 10. Load multiplier with different typology for three compression level
4 Conclusion The current study proposed a microscale modeling method to analyze the shear strength of irregular stone masonry walls. To this end, we developed an automated preprocessor that converted image data into a rigid block model. With the generated model, one can obtain the limit load multiplier of masonry wall of any typology using mathematical programming method proposed by Krabbenhoft [5]. Using the proposed method, we conducted simulations of a single wall using different grid sizes. The results showed that it was important to represent the interlocking between stones when analyzing shear strength at high compression level. For different walls, the proposed method can predict the shear failure and the flexural failure, differentiating the shear strength of stone masonry walls of different typologies. In conclusion, this work provided an efficient tool for the microscale modeling of irregular stone masonry walls.
References 1. Salachoris, G.P., Magagnini, E., Clementi, F.: Mechanical characterization of “Scaglia Rossa” stone masonry through experimental and numerical analyses. Constr. Build. Mater. 303, 124572 (2021) 2. Zhang, S., Mousavi, S.M.T., Richart, N., Molinari, J.F., Beyer, K.: Micro-mechanical finite element modeling of diagonal compression test for historical stone masonry structure. Int. J. Solids Struct. 112, 122–132 (2017) 3. Zhang, S., Beyer, K.: Numerical investigation of the role of masonry typology on shear strength. Eng. Struct. 192, 86–102 (2019) 4. Tiberti, S., Milani, G.: 2D pixel homogenized limit analysis of non-periodic masonry walls. Comput. Struct. 219, 16–57 (2019) 5. Krabbenhoft, K., Lyamin, A.V., Huang, J., da Silva, M.V.: Granular contact dynamics using mathematical programming methods. Comput. Geotech. 43, 165–176 (2012)
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6. Portioli, F., Cascini, L., Casapulla, C., D’Aniello, M.: Limit analysis of masonry walls by rigid block modelling with cracking units and cohesive joints using linear programming. Eng. Struct. 57, 232–247 (2013) 7. Portioli, F.P.A.: Rigid block modelling of historic masonry structures using mathematical programming: a unified formulation for non-linear time history, static pushover and limit equilibrium analysis. Bull. Earthq. Eng. 18(1), 211–239 (2019). https://doi.org/10.1007/s10 518-019-00722-0 8. De Felice, G.: Out-of-plane seismic capacity of masonry depending on wall section morphology. Int. J. Archit. Herit. 5(4–5), 466–482 (2011) 9. Abu-Haifa, M., Lee, S.J.: Image-based modeling-to-simulation of masonry walls. J. Archit. Eng. 28(4), 06022001 (2022) 10. Loverdos, D., Sarhosis, V., Adamopoulos, E., Drougkas, A.: An innovative image processingbased framework for the numerical modelling of cracked masonry structures. Autom. Constr. 125, 103633 (2021) 11. MOSEK ApS: MOSEK Optimizer API for Python 9.3.21 (2019). https://docs.mosek.com/lat est/pythonapi/index.html 12. Gilbert, M., Casapulla, C., Ahmed, H.M.: Limit analysis of masonry block structures with nonassociative frictional joints using linear programming. Comput. Struct. 84(13–14), 873–887 (2006) 13. MIT, Ministry of Infrastructures and Transportation, Circ. C.S.Ll.Pp. No. 617 of 2/2/2009: Istruzioni per l’applicazione delle nuove norme tecniche per le costruzioni di cui al Decreto Ministeriale 14 Gennaio 2008, G.U.S.O. n.27 of 26/2/2009, No. 47, 2008 in, Technical report (2009) 14. Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. ACM Siggraph Comput. Graph. 21(4), 163–169 (1987) 15. Barber, C.B., Dobkin, D.P., Huhdanpaa, H.: The quickhull algorithm for convex hulls. ACM Trans. Math. Softw. (TOMS) 22(4), 469–483 (1996) 16. Geuzaine, C., Remacle, J.F.: Gmsh: A 3-D finite element mesh generator with built-in pre-and post-processing facilities. Int. J. Numer. Meth. Eng. 79(11), 1309–1331 (2009)
Simulation of Brittle Collapse Mechanisms in Historical Masonry Using Sequentially Linear Analysis (SLA) Manimaran Pari(B) and Jan Rots Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands [email protected]
Abstract. Sequentially Linear Analysis (SLA) is known for robust and reliable finite element simulations of masonry constructions, often considered challenging because of the brittle behaviour of the masonry material. Herein a sequence of scaled linear analyses is performed with decreasing secant stiffness of one integration point per analysis, representing local damage increments. This procedure is especially suited to simulate highly nonlinear collapse mechanisms. In this article, a benchmark experiment on structural historical masonry is first chosen. This benchmark is simulated using SLA, using the micro-modelling approach, with linear blocks/bricks and nonlinear interfaces using a multi-surface interface model. The results are compared against those of the experiment, nonlinear finite element analysis, and the Discrete Element Method (DEM), good agreement is found with those of the experiment, and the collapse mechanisms are also captured in a robust manner. Keywords: Sequentially Linear Analysis (SLA) · Robust simulations · Brittle failures · Multi-surface interface model · Micro-modelling
1 Introduction Historical constructions are known to collapse in a rather brittle manner when subject to extreme loadings like torrential rains, earthquakes and extreme winds. Nonlinear finite element analyses, NLFEA, of such collapsing structures is a proven advanced numerical tool. However, traditional incremental-iterative solution procedures in NLFEA are often considered challenging because of the convergence troubles that arise owing to the softening behaviour of the masonry material [1]. This can be controlled using path following methods like arc-length control, at the expense of several trial runs, or other solution procedures like explicit dynamic methods. Alternatively, there exists a class of solution procedures based on the Sequentially Linear Analysis (SLA), to achieve robust and reliable finite element (FE) simulations, wherein a sequence of scaled linear analyses is performed with decreasing secant stiffness of one integration point per analysis, representing local damage increments. This procedure is a proven alternative for masonry analyses and is especially suited to simulate highly nonlinear collapse mechanisms. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 603–616, 2024. https://doi.org/10.1007/978-3-031-39450-8_50
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In this article, a benchmark experiment in masonry showcasing collapse mechanism is chosen. This is simulated using SLA, with its latest constitutive and solver developments [2–4], in order to capture collapse mechanisms under non-proportional loading conditions. The case is modelled using the micro-modelling approach of masonry [5], differentiating the continuum into linear elastic bricks and potential failure planes represented by interface elements: along head and bed joints, and additionally, a potential vertical brick cracking plane in the middle of each brick (if necessary). Furthermore, a case-study of a pushover experiment presentative of historical masonry structure – the part of the cloister’s facade of the Sao Vicente de Fora monastery in Lisbon [6, 7] is studied. The results of the SLA simulations are compared with those of an NLFEA and the Discrete Element Method (DEM) [8]. The paper first presents the SLA methodology and the constitutive model used therein, followed by the benchmark experiment and the simulation results. Finally, the historical masonry structure simulation results and conclusions are presented.
2 Sequentially Linear Analysis: Methodology The Sequentially linear analysis (SLA), a non-incremental (total) solution approach [1], helps simulate the damage process in quasi-brittle materials by allowing for one damage event at a time. The crux of the approach relies on sequentially running linear analyses, i.e., an event-by-event approach, each of which identifies a critical integration point in the FE model with the maximum stress. The strength and stiffness of this critical point are then reduced based on a discretised step-wise constitutive relation called the sawtooth law shown in Fig. 2. Thereafter, the linear analysis results, i.e., the displacements, forces, stresses and strains, are scaled using the critical load multiplier λcrit , the least ratio of the allowable strength to the governing stress over all integration points. For a scalable load L, the load multiplier for each IP i and the overall critical load multiplier (minimum of all positive load multipliers) are defined as follows: λi(ft/σ gov); λcrit = min(λi); Lcrit = λcrit L
(1)
Herein, the nonlinear modelling of quasi brittle fracture is alleviated of multiple cracks attempting to survive and the use of secant stiffness makes the procedure additionally very robust. The sequence of linear analysis continues until a predefined termination criterion is reached. A composite-interface formulation, previously proposed to be used in conjunction with the sequentially linear framework [2] is used herein. The failure surface (2D and 3D) shown in Fig. 1 has: (a) a tension-cut-off criterion coupled with a uniaxial tension softening law; (b) a compression-cap cut-off criterion, dependent purely on the normal traction, coupled with a uniaxial parabolic hardening–softening law; and (c) a step-wise secant Coulomb friction law which decouples the tension and shear modes, the dilatancy effects are neglected because of no coupling, i.e. the dilatancy angle ψ = 0, an assumption that yields good results for masonry structures in general [2]. Step-wise secant saw-tooth laws address all aforementioned uniaxial behaviour (See Fig. 2). For further details on the model the reader is referred to Reference [2].
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Fig. 1. Failure surface for the 2D line interfaces (left) and 3D planar interfaces (right)
Fig. 2. Linear tension softening (a), cohesion softening (b) and compression hardening-softening (c) saw tooth constitutive laws
The critical load multiplier in SLA for non-proportional loading conditions involving a constant load, for e.g., deadweight, and a variable load like a wind load, is different from Eq. 1. In case of the interfaces for example, the tractions are expressed as the superposition of the tractions due to the constant and scaled variable loads as shown in Eq. (2) for each integration point i. The governing stress is then limited by the allowable strengths f , corresponding to the failure criterion, as shown in Eq. (3), such that only the critical integration point i lies on the failure surface while all non-critical points lie below it. These equations could apply for any of the failure possibilities i.e., cracking, crushing or shearing. As long as Eq. (3) holds, Eq. (4) applies at the global level. Contrarily, when Eq. (3) fails in a certain analysis step j, the procedure is steered into the Intermittent Proportional Loading (denoted by subscript ipl hereon) [9, 10] in the next step ( j + 1), while implicitly reducing the constant load, as shown in Eq. (5a), (5b) to reinstate Eq. (3). Such regions indicate the need for multiple failures representing a sudden propagation of damage. Once the critical integration point and the load multiplier is determined, the strength and stiffness corresponding to the failure type is reduced stepwise, the linear analysis results are scaled, and the procedure moves to the next linear analysis. Alternatively, in an incremental version of SLA i.e., the Force-Release method [4], the non-proportional load path is discretised into a series of piece-wise proportional loading paths. Linear analyses are performed with load increments of a certain load vector, each of which may or may not lead to damage at a critical integration point i according to Eq. (6), wherein all quantities with are the corresponding incremental values caused by the load increment. Upon damage, the stress from a damaged element is released gradually through a sequentially linear redistribution loop wherein the unbalanced forces due to the previous damage are applied as loads on the FE model, while all previously applied loads are kept constant, and other elements may be damaged. When the redistribution
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loop does not lead to further damage, the response stays in equilibrium. Otherwise, it evolves through states of disequilibrium and eventually returns to equilibrium. ti = ti, con + λ ti, var
(2)
(ti, con + λti, var) = f ∧ ∀i = k : (tk, con + λtk, var) < f
(3)
Lcrit, j = λcon Lcon + λvar Lvar with λcon = 1 and λvar = λcrit, j
(4)
Lipl = Lcon + λcrit, (j − 1) Lvar and Lipl, j = λcrit, j Lipl
(5)
(ti + λ ti) = f ∧ ∀i = k : (tk + λ tk) < f
(6)
3 Structural Masonry Benchmark In this section, the validity of the sequentially linear approach in conjunction with the micro-modelling approach using the multi-surface interface constitutive model is revisited. The SLA study on the experiment on a solid clay brick masonry wall [2], tested by Raijmakers and Vermeltfoort [11, 12] and popularly used by fellow researchers as a benchmark case, is briefed upon. 3.1 Experiment and Finite Element Model The solid clay brick masonry wall tested by Raijmakers and Vermeltfoort [11, 12], wall was made of 18 courses of bricks, with dimensions of 210 mm × 52 mm × 100 mm, and mortar layers of 10 mm thickness. The top and bottom courses of bricks were clamped to a steel beam to constrain the rotation along both edges, additionally preventing the free vertical movement of the top edge. The walls were loaded initially by an overburden pressure of 0.30 N/mm2 , followed by a monotonically increasing lateral load d applied under displacement control. The walls are discretised using the simplified micro-modelling strategy [5], wherein mortar joints and the brick–mortar interfaces are lumped together into a zero-thickness interface, and the bricks are extended to account for the mortar thickness. Appropriate boundary conditions are applied and the bricks are modelled using 4-noded iso-parametric plane stress elements (27.5 mm × 27.5 mm in size) with linear interpolation shape functions and a 2 × 2 Gaussian integration scheme. Zero-thickness interfaces are modelled using 2 + 2 noded interface elements in conjunction with a 2-point Newton–Cotes integration scheme. The FE model is as shown in the Fig. 3 alongside material properties listed in Table 1. For further details on the model, the reader is referred to Reference [2].
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Fig. 3. Schematic representation of the experiment on solids clay brick masonry walls and the FE Model
3.2 SLA Results and Discussion The wall firstly exhibits flexural failure which is visible as horizontal cracks along bed joints at the bottom-right and top-left corners of the wall (See Fig. 4). After the flexural cracks are fully developed (before 2 mm top displacement), compressive strut action results in a staggered step-like crack along the diagonal to the toe (left bottom corner) of the wall. This damage propagation includes both sliding failure along the bed joints, resulting in loss of shear stiffness, and tensile cracking along head joints, resulting in loss of both normal and shear stiffnesses. The fully developed flexural cracks and propagating diagonal step cracks at 2 mm top displacement are shown as tensile cracking and shear failure plots in Fig. 4. Furthermore, the stress flow into the toe of the wall leads to the onset of the crushing failure, which can be seen as loss of normal stiffness in the crushing plots of Fig. 4. The damage plots DmTeNN and DmCoNN indicate loss of normal stiffness due to cracking and crushing respectively. The DmTeSS damage plots indicate loss of shear stiffness which is either due to a pure-sliding failure or the damage based shear reduction associated with the cracking/crushing modes. All damage plots herein range from 0 to 1 which refer to undamaged and fully damaged cases for the corresponding failure criteria. Upon further increase of the lateral displacement to 4 mm, the damage along the diagonal shear crack increases and localises, leading to a widening of the head joints and simultaneous sliding along bed joints, along the diagonal of the wall. Furthermore, the stepped crack also involves vertical splitting cracks through the bricks along the courses at mid-height of the wall, which often appear as sudden drops/instabilities in traditional NLFEA [5]. This is adequately captured by SLA. Simultaneously, the toe of the wall is completely crushed along half the length of an entire brick. This results in a clear drop of lateral capacity which is observed in the force–displacement curve, indicating structural collapse. The case is also simulated using the Force-Release method and the results compare well with SLA and is mostly an envelope of the SLA response. There exists close similarity in the damage plots of the SLA and Force-Release simulations for continuum FE studies unlike lattice element models [4], and therefore Force-Release plots aren’t
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Units
Parameters
Elastic
Bricks
Young’s Modulus E0 [GPa]
16.7
Poisson’s ratio v0
0.15
Normal stiffness kn [N/mm3 ]
106
Shear stiffness kt [N/mm3 ]
106
Brick Cracks
Head & Bed Joints
Compression
Tension
Tensile Strength ft [MPa]
2
Fracture energy GIf [N/mm]
0.08
Saw-teeth discretisation factor
0.2
Softening relation
Linear
Shear retention factor β
Damage-based [10]
Normal stiffness kn [N/mm3 ]
82
Shear stiffness kt [N/mm3 ]
36
Shear
Strength fc, ft, c0 [MPa]
6.0
0.25
0.35
Fracture energy Gc ,
1.8
0.018
0.125
Saw-teeth discretisation factor
0.1
0.15
0.05
Softening relation
Parabolic
Linear
Exponential
Shear retention factor β
Damagebased [10]
Damage-based [10]
–
GIf , GII f [N/mm]
shown herein (refer [2]). The differences become apparent whenever SLA returns to the Intermittent Proportional Loading (IPL), wherein the last successful load combination is scaled proportionally to avoid violation of the constitutive law anywhere in the FE model. Under such conditions, the overburden load in SLA is implicitly reduced to enforce equilibrium during a quasi-static damage driven failure propagation. This becomes significant starting ~3.7 mm prescribed lateral displacement, marked as a yellow circle in the force-displacement plot of Fig. 4, indicating onset of collapse. The constant load drops to extremely low values through this region but is also recovered
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immediately (Fig. 4), which appears as large snap-backs in the post-collapse region at prescribed lateral displacements around 4 mm. Since every damaged element’s stress is released instantaneously in SLA, the neighbouring integration points of the critical integration point whose stresses are close to their respective allowable strengths subsequently become critical at a considerably lower load. In summary, the performance of the non-proportional loading strategy of SLA is successful in this problem leading to collapse, which in turn is described using its inherent redistribution procedure i.e., the IPL. On the other hand, these regions are simulated in disequilibrium using the Force-Release method appearing as instabilities or drops of load for a constant imposed displacement. The collapse mechanism herein is captured by both approaches adequately. However, the drop of load corresponding to the eventual instability is described by the SLA and the Force-Release methods in diametrically opposite ways, with regard to the time scales for the redistribution. This is in line with the differences observed between the approaches to typical explosive failure in the previous case studies [9], and is clear from how the loading is modified in case of SLA (Fig. 4) during collapse. SLA describes the entire collapse while maintaining equilibrium by reducing the constant load, while the ForceRelease method addresses it using the avalanche of damage states in disequilibrium which appear as vertical drops of the capacity.
Fig. 4. The deformed profile, and damage plots indicating tensile, shear and crushing failures for the pushover study, with discrete cracking-shearing-crushing interfaces, using the SLA method at 2 mm and 4 mm prescribed lateral displacements. Force–displacement curves of the experiments compared against those of the SLA and the Force-Release simulations, and (b) the evolution of constant load of pre-compression during the simulations.
The suitability of the two sequentially linear methods depends on the type of experiment being simulated. Force-Release method is suitable for typical displacementcontrolled experiments which actually exhibit instabilities. These would be consistent with the drops of loads observed in Force-Release simulations. On the other hand, it may not be suitable for physical processes which exhibit snap backs or for truly quasi-static
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experiments. SLA is more preferable when the damage process zone is unique and controlled for quasi-static evolution in an experiment [9, 10]. However, for a Crack Mouth Opening Displacement (CMOD) controlled experiment with multiple cracking zones, SLA may also not be appropriate because it does not control a unique damage process zone as in the experiment, and contrarily may incorrectly decrease it due to release of previously applied loads while allowing the structure to relax. Force-Release method, in this case, may increase the CMOD due to the redistribution. In a quasi-static sequentially linear setup, a truly CMOD controlled experiment with multiple evolving damage zones can be appropriately simulated by the so-called general method [9]. For a detailed analysis on the applicability of the approaches, the reader is referred to References [9, 10].
4 Historical Masonry Benchmark 4.1 Experiment and Finite Element Model Experiments on the behaviour of full-scale masonry structures representative of historical masonry, is very limited. Historical masonry are therefore usually analysed directly by first calibration and validation of numerical models based on experimental benchmarks on structural walls or facades. In this regard, the experiment conducted at the ELSA laboratory of the Joint Research Centre of the European Commission, on a full-scale model of part of the cloisters of the Sao Vicente de Fora monastery in Lisbon (Fig. 5) is unique. Details of the experimental findings are presented in Ref. [6] and the tested model features three stone block columns, two complete arches and two half arches, as shown in Fig. 5 [7].
Fig. 5. Cloisters of the Sao Vicente de Fora monastery (internal view – left) and the experimental set-up (image from Reference [7] - right).
The experimental set-up is as shown in Fig. 5. The FE model is made using the simplified micro-modelling strategy [5] as in the previous section, wherein mortar joints and the stone block-mortar interfaces are lumped together into a zero-thickness interface, and the stone blocks are extended to account for the mortar thickness. The stone blocks are modelled linear elastically using 8-noded iso-parametric plane stress elements, roughly
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Fig. 6. FE micro-model of the structure showing head and bed joints in black, stone masonry in grey, infill brick masonry in brown, loads in dark green and the bottom supports in red.
75 mm in size with a 2 × 2 Gaussian integration scheme. The zero-thickness interfaces are modelled using 3 + 3 noded interface elements, in conjunction with a 3-point Newton–Cotes integration scheme. The infill brick masonry and the stone blocks are kept linear elastic. Material parameters are as shown in Table 2. The thickness of the wall is assumed to be 500 mm after a sensitivity analysis for initial stiffness and dead weight, as information on cross section is sparse. The boundary conditions that have been provided try to simulate the test setup as well as possible. The base nodes are pinned and the nodes at top of the two external pillars have been constrained to have equal vertical displacements. As far as loading is concerned, firstly vertical dead loads are applied so as to result in 400 kN per pillar/panel distributed in a 4/1 ratio, alongside self-weight. Secondly, prescribed displacements were applied to the top edge of the structure to simulate the static equivalence of seismic action. The structure is supported at the bottom in both horizontal and vertical direction to simulate the fixed boundary condition. Two analyses were run on the FE model. Firstly, a Sequentially linear analysis is performed. Secondly, for comparison purposes, a Non-Linear Finite Element Analysis (NLFEA) with the traditional incremental-iterative approach was done with the two loading stages. Lateral load was applied to a total of 30mm top displacements in 100 steps of 0.3mm, wherein the Newton Raphson iteration scheme that converges to an energy norm of 0.0001 was used. Aside the differences from the load application procedure, it is to be noted that the coulomb friction model with gapping criterion [14]
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used in NLFEA has no cohesion/tension softening, while in SLA softening is allowed as described in Table 2 (Fig. 6). Table 2. FE Model parameters Units
Parameters
Elastic
Stone
Young’s Modulus E0 [GPa]
23
Poisson’s ratio v0
0.2
Self-Weight (kg/mm3 )
2500
Young’s Modulus E0 [GPa]
2.3
Poisson’s ratio v0
0.2
Brick infill
Tension
Shear
Strength ft , c0 [MPa]
0.1
0.1
Fracture energy
0.1
10
Saw-teeth discretisation factor
0.2
0.05
Softening relation
Linear
Exponential
Shear retention factor β
Damage-based [10]
–
Self-Weight (kg/mm3 ) 2500 Head & Bed Joints
Normal stiffness kn [N/mm3 ]
115
Shear stiffness kt [N/mm3 ]
47.9
GIf , GII f [N/mm]
4.2 Results and Discussion The results from SLA on the structure are compared against the experimental monotonic envelope and other numerical simulations in Fig. 7. SLA slightly underestimates the ultimate strength but with regard to the initial stiffness degradation and damage formation, the result is appreciable. The SLA curve is qualitatively quite comparable and reasonable in relation to similar block-based modelling results from literature i.e. the joint model in CASTEM 2000 or the distinct element method with deformable bocks [13] and also the NLFEA analysis performed herein. The differences arise owing to the inherent differences in the approaches. CASTEM 2000 joint model is assumed to follow a simple elasto-plastic Coulomb friction law with no cohesion or tensile strength, while SLA allows for both cohesion and tensile softening. The damage pattern from the CASTEM model shown in Fig. 10 shows concentration of deformation in joints as
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expected and is somewhat similar to the SLA damage pattern in Fig. 9. SLA, however, allows for asymmetric failure localisation and propagation unlike the traditional solution procedure and this is evident in the large opening and sliding damage close to the left column/infill interface, while in CASTEM the damage is more distributed. NLFEA results also are similar to SLA but suffer from convergence issues typical of implicit solvers (unconverged points are shown in Fig. 7.), and this alongside the differences in the constitutive modelling i.e., no softening in tension/cohesion give rise to the disparity in damage shown in Fig. 11 for NLFEA. DEM damage plots/results were not shown in the work of reference [13] and are therefore not compared herein. In summary, the performance of SLA seems quite appreciable. With regard to the non-proportional loading algorithm, as shown in Fig. 8, the constant load of overburden and self-weight are applied over 1000 steps initially involving damage before reaching the full value of unity. Thereafter, when the lateral load is applied, the drops in constant load seen in Fig. 8 correspond to the intermittent proportional loading, necessary during highly nonlinear regions of the structural response, when a linearly scaled combination of loads is not possible anymore. This has been previously shown to be acceptable as long as the loads don’t completely start to decrease to zero which is a sign of the onset of structural collapse [9]. Therefore, the current SLA simulation is appreciable from this point of view considering that this has been an ongoing topic of debate [9, 10].
Fig. 7. Experimental and numerical curves from this study (NLFEA, SLA) and from literature (DEM and CASTEM) [13].
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Fig. 8. Evolution and fluctuation of the first load i.e., the overburden and self-weight during SLA to allow for admissible damage
Fig. 9. Normal and tangential displacements (Left-Opening and Right-sliding) at the interfaces for the SLA model
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Fig. 10. CASTEM 2000 displaced mesh [13]
Fig. 11. Normal and tangential displacements (Left-Opening and Right-sliding) at the interfaces for the NLFEA model
5 Conclusions This article presents an overview of the sequentially linear analysis approach, in conjunction with a composite interface formulation, for micro-modelling or block-based approach to the analysis of masonry structures. A structural historical masonry benchmark is chosen and simulated using SLA quite appreciably. This shows potential of the method, especially in highly nonlinear and brittle collapse mechanisms, to provide results in a numerically robust manner compared to the traditional incremental iterative solution in the finite element method. The method is also comparable to block-based modelling strategies in literature, while being a more robust alternative. The method is currently being investigated for geometrically nonlinear, plasticity and other loading/stress history-related problems.
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References 1. Rots, J.G., Invernizzi, S.: Regularized sequentially linear saw-tooth softening model. Int. J. Numer. Anal. Meth. Geomech. 28(7–8), 821–856 (2004) 2. Pari, M., Van de Graaf, A.V., Hendriks, M.A.N., Rots, J.G.: A multi-surface interface model for sequentially linear methods to analyse masonry structures. Eng. Struct. 238, 112123 (2021) 3. Pari, M., Swart, W., van Gijzen, M.B., Hendriks, M.A.N., Rots, J.G.: Two solution strategies to improve the computational performance of sequentially linear analysis for quasi-brittle structures. Int. J. Numer. Meth. Eng. 121(10), 2128–2146 (2020) 4. Eliáš, J., Frantík, P., Voˇrechovský, M.: Improved sequentially linear solution procedure. Eng. Fract. Mech. 77(12), 2263–2276 (2010) 5. Lourenco, P.B.: Computational strategies for masonry structures. Ph.D. thesis, Delft University of Technology (1996) 6. Pinto, A.V., et al.: Laboratory tests on full scale monument. In: Proceedings of the 11th European Conference on Earthquake Engineering, Paris (France) (1998) 7. Pegon, P., Pinto, A.V.: Seismic Study of Monumental Structures Structural Analysis, Modelling and Definition of Experimental Model. Report EUR 16387 EN, European Laboratory for Structural Assessment (1996) 8. Pulatsu, B., Bretas, E.M., Lourenco, P.B.: Discrete element modeling of masonry structures: validation and application. Geomech. Eng. 11(4), 563–582 (2016) 9. Pari, M., Hendriks, M.A.N., Rots, J.G.: Non-proportional loading in sequentially linear solution procedures for quasi-brittle fracture: a comparison and perspective on the mechanism of stress redistribution. Eng. Fract. Mech. 230, 106960 (2020) 10. Pari, M.: Simulating quasi-brittle failure in structures using sequentially linear methods: Studies on non-proportional loading, constitutive modelling, and computational efficiency. Ph.D. thesis, Delft University of Technology (2020) 11. Raijmakers, T., Vermeltfoort, A.T.: Deformation controlled tests in masonry shear walls, Report B-92-1156, TNO-Bouw, Delft (1992) 12. Raijmakers, T., Vermeltfoort, A.T.: Deformation controlled tests in masonry shear walls: Part 2, Report TUE/BKO/93.08, Eindhoven university of technology (1993) 13. Giordano, A., Mele, E., De Luca, A.: Modelling of historical masonry structures: comparison of different approaches through a case study. Eng. Struct. 24(8), 1057–1069 (2002) 14. Ferrera, D.: Diana User’s Manual, Release 10.5. DIANA FEA BV (2022)
Numerical Study of Three-Point Bending Fracture Tests for Examination of Wood in Mode II Václav Sebera1(B) and Jiˇrí Kunecký2 1 Department of Wood Science and Technology, Mendel University in Brno, Brno,
Czech Republic [email protected] 2 Institute of Theoretical and Applied Mechanics, Czech Academy of Sciences, Prague, Czech Republic
Abstract. Fracture properties belong to one of the most important properties of wood due to its safety consequences that come out of the wood cellular structure and natural phenomena occurring in wood such as cracks. Cracks in wood may substantially decrease mechanical performance of wooden beams because they create stress contraction spots and, therefore, they should be studied with appropriate attention. To test fracture properties of wood, one can employ many techniques and tests. Specific testing procedures have certain requirements on specimens with respect to wood nature – grain angle, moisture, species and others. The general goal of this work is to analyze so called end-notched flexure test in three-point bending (ENF-3PB) scheme to provide fracture behavior of wood using such a test. The work consisted of utilizing 3D finite element analysis (FEA) to analyze sensitivity of testing procedure to various variables introduced to a specimen such as span-to-height ratio, friction coefficient and length of initial crack. The analyses considered wood as orthotropic material including both elastic and plastic regions of deformation using Hill’s plasticity. The crack path is modeled using cohesive zone models, contact between specimen and loading grips and supports was modeled using contact algorithms. Results show that ENF-3PB test is very sensitive to setup and in case of cumulative effect of studied phenomena, the measurement error might not be negligible. Keywords: wood · fracture · end-notched flexure test · finite element analysis · mode II
1 Introduction Wood belongs to structural renewable materials with high strength-to-density ratio when fiber direction is concerned and, therefore, it can be used with an advantage as a construction material [1]. However, due to its cellular nature, it is susceptible to fracture in the fiber direction, mainly in applications where dowels, knots, drills, notches etc. are in way of high stresses, but also due to shrinkage causing drying cracks [2]. On one hand, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 617–625, 2024. https://doi.org/10.1007/978-3-031-39450-8_51
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wood behaves as a quasi-brittle material showing typical fracture behavior [3], on the other it shows substantial plasticity when loaded by a compression, especially perpendicular to fiber which can be handled by both damage and fracture approaches [4–6]. Therefore, it is important to study fracture behavior, but at the same time, it is important to examine the fracture tests themselves because wood, especially soft woods, showing this specific plastic behavior might negatively influence the fracture characteristics to be measured. This behavior is wood species specific, but one has to also consider that it is often the case that the examination procedures were taken from testing very different materials such as synthetic composites that don’t show plastic behavior. This work focuses on wood when loaded in fracture mode II that is induced by shear stresses by bending wood. Experimentally, fracture properties of wood in mode II have been measured using end-notched flexure by three-point bending (ENF-3PB) for a long time [7]. It was shown that fracture properties of wood in ENF-3PB are dependent on a ratio of initial crack length and half span which has to be reflected in an experiment design [8]. Fracture of wood in mode II may also be obtained by the compact shear (CS) tests, but it was shown that CS test result in higher proportion of mixed mode due to non-simultaneous crack opening at two crack planes [9, 10]. Another promising approach is to employ the asymmetric four-point bend fracture (AFPBF) tests that may be advantageous for scenarios where a certain proportion of mode I occurs [11]. One of the difficulties in mode II is to monitor crack onset and propagation. To overcome these issues, one can utilize the equivalent crack length approach incorporated into the compliance-based beam method (CBBM) [12]. This combination showed to have benefits because it did not require tracking of crack propagation which was, to a convenience, derived directly from the current compliance of a beam. The equivalent crack length method applied on a pine, spruce and beech wood was examined by [13, 14, 15]. These authors also developed the finite element (FE) model of a crack propagation of wood in mode II that was successfully verified using an equivalent crack length approach. The procedure of equivalent crack was successfully tested experimentally and numerically on an end-load split (ELS) scheme when examining fracture properties of pine wood in mode II [16]. Because of its relative ease, the ENF-3PB with equivalent crack approach is also well suited for wood bonds [17], and for determination of cohesive zone models of material itself or adhesive bonds that may be used in numerical simulations [18]. Using an optimization technique within a combination of finite element simulation and DIC analysis to characterize fracture behavior of Douglas fir wood (Pseudotsuga menziesii L.) in mixed mode was shown [19]. Both tools conveniently provided data that enabled separation of mode I and mode II without taking into account local elastic mechanical properties. More recently, simulation of crack propagation and finding strategies to prevent it to design more durable cross-laminated timber (CLT) was shown in [20]. Hygral strains developed due to shrinkage may also occur in the timber elements, especially at RT plane, one of the possible approaches to predict them was shown in [21]. However, the numerical prediction of the fracture behavior is dependent on experimental data that are obtained from adequate tests that are not inducing error when applied on wood or wood-based materials. Therefore, the goal of the paper is to develop
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a numerical model of crack propagation in wood along the fiber in mode II with use of elasto-plastic material model of wood and examine its usability with respect to material and geometry of test (span-to-height ratio).
2 Material and Methods The total work consists of two parts: (i) numerical simulations using finite elements (FE) and (ii) experimental work. The first part – numerical analyses – is presented here in the paper, meanwhile the second one – experiments – is planned to be carried out within the spring and summer of 2023 and will be, therefore, included only in the final presentation at the conference. Within the numerical part, we developed the FE model of the 3ENF test (see Fig. 1). The 3D FE model was developed to investigate force-deflection response in dependency of various factors (see below) as well as for strain distribution, imprint and total strain energy in the model under the loading head and above supports.
Fig. 1. Geometry of sample and sketch of the 3ENF test
Experimental work will consist of a series of 3ENF tests with various configurations reflecting numerical predictions and they will be accompanied by digital image correlation technique to monitor crack onset and propagation. Further, the experiments will serve as a basis for numerical model validations. 2.1 Finite Element Analysis For a development of the 3D FE model (Fig. 2), computational package Ansys v 19.2 (Ansys Inc., USA) was used. The FE model employed 4 different types of finite elements: 1) Solid95 for modeling the main body of the sample, this element was chosen because it supports bilinear orthotropic plasticity based on Hill potential theory. It is quadratic finite element consisting of 20 nodes, each node has three degrees of freedom (displacements in X, Y and Z directions); 2) contact elements Targe170 and Conta174 for modeling contact phenomena between the sample and supports, between specimen and loading head, and between the lamellae around introduced initial crack. The supports and loading grip were modeled as perfectly rigid because they are made of steel and, hence, the contact pairs were defined as rigid-flexible; 3) interface finite element Inter204 for modeling cohesive zone in the middle of specimen at the path of assumed crack propagation due to shear stress. It is a quadratic 16node finite element.
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The FE analyses were solved with a nonlinear option “large deformation”. Material model used for spruce wood was elasto-plastic orthotropic taken from [20], its elastic part is as follows: E L = 17 850 MPa, E T = 289 MPa, E R = 352 MPa, GLR = 573 MPa, GLT = 474 MPa, GRT = 53 MPa, ν LR = 0.023, ν LT = 0.014, ν RT = 0.557, where E i is normal modulus, Gij is shear modulus and ν ij is Poisson’s ratio, and L, R and T are longitudinal, radial, and tangential directions, respectively. The plastic part of the material was defined as follows: 1) three yield stresses in normal directions: σ L = 49 MPa, σ R = 6.4 MPa, σ T = 7.1 MPa; 2) three tangent moduli in normal directions: E L,tan = 140 MPa, E R,tan = 1.8 MPa, E T,tan = 2.3 MPa; 3) three shear yield stresses: σ LR = 6.7 MPa, σ RT = 6.7 MPa and σ LT = 3.1 MPa.; 4) three shear tangent moduli: E LR,tan = 5.73 MPa, E LT,tan = 4.74 MPa, E RT,tan = 0.53 MPa. The elasto-plasticity was simplified in a way that we assumed the same properties in tension and compression mode. For the cohesive zone, we employed bilinear model of traction-separation law with maximal shear stress τ = 5 MPa at separation of 0.096 mm, and total separation 0.224 mm.
Fig. 2. Geometrical model (top) and FE mesh of 3D specimen for mode II (bottom)
FE analyses investigated the following: (i) influence of initial crack length on total force-displacement response; (ii) influence of span-to-heigh ratio on plastic strain energy developed in wood at contacts with loading head; and (iii) influence of friction on force-displacement response.
3 Results 3.1 Influence of Crack Length The first analysis was to assess the influence of the initial crack length on specimen force-displacement (F/d) response and development of vertical strains under the load head. The results for initial crack lengths between 12 and 20 cm with a step of 2 cm is depicted in Fig. 3. We can see at Fig. 3a that as the crack length increases, both stiffness and maximal reached force decreases. Stiffness of specimen with 20 cm long crack is reduced to approximately 60% of the value for 12 cm initial crack length. For the initial crack length of 12 cm, the crack did not open, so peak force is not achieved and, consequently, the nonlinear F/d response is done only by development of plastic strains
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in wood – horizontal plastic strains due to bending and vertical compression plastic strains as seen Fig. 3b. However, assuming maximal force (F max ) for 12 cm crack length to be about 550 N, then the value of F max for 20 cm crack length dropped to 66% of original value, i.e. similarly as for stiffness. We also see that for the phase after reaching F max , the F/d response has various character for different initial crack lengths. The longer the initial crack length is, the less rapid decrease of F occurs after crack onset, so the crack propagation is more stable (self-similar). However, from an experimental point of view, this parameter is controlled by speed of loading. If we look at the plastic strains developed under the loading head (Fig. 3b), we see that specimens with initial crack length above 16 cm have very similar responses (the specimen with 14 cm long initial crack did not converge to the end). These specimens got plastic strains developed after full separation occurred (till center of specimen), so it is visible as strains going to negative values.
Fig. 3. FEM predicted force-displacement response for various lengths of initial crack length (a) and average vertical plastic strain developed under the loading head at corresponding initial crack lengths (b)
From beam theory it is known that to have a stable crack growth, the initial crack length should be at least 0.7 of halfspan – L [21]. In this study it is a crack length of 16 cm that has a ratio 0.71 L. We see that for greater initial cracks (18 cm equals 0.8 L, 20 cm equals 0.89 L), the crack propagation is very stable without any drops of force. 3.2 Influence of Span-to-Height Ratio The second analysis was to determine an influence of span-to-height ratio (s/h ratio) on resulting F/d response and strains developed under the loading head. Within the numerical analyses, following s/h ratios were predicted: 5, 7.5, 9.75, 12.5, 15, 17.5, 20, 22.5. Figure 4a shows the F/d response changes substantially with change of s/h ratio, the maximal force for s/h ratio of 5 is approx. 4.5 times higher than for s/h ratio of 22.5. The results in total strains (plastic plus elastic) developed under the loading head (1 cm from center of load head to both sides) is depicted in Fig. 4b and Fig. 4c. The Fig. 4b shows the development of total strains at Y axis in linear perspective, which makes the interpretation more difficult because for higher s/h ratios, the curves overlap. Therefore, the graph was modified to logarithmic Y axis (Fig. 4c), which enables us to
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see the effect of s/h ratio on total strain energy. This concludes in a fact that the lower s/h ratio, the higher total strain energy under loading head. If we analyze the proportion of plastic strain energy in total strain energy when plateau is reached (for deflection beyond 0.01 m), we can conclude following: for s/h ratios 22.5 and 20, there is 0%, for s/h ratios 17.5, 15, 12.5, 9.75, 7.5, and 5, there is 3%, 21%, 34%, 61%, 74%, and 80% of plastic strain energy proportion, respectively. In general, it is recommended s/h ratio is above 17, which represents very good fit with our model (for scenario s/h = 17.5), because it contains only 3% of plastic strain energy. The ENF setup for wood with s/h ratio above 20 is plastic-strain free, which is in agreement with [8] that recommends the same ratio. However, for woods that have higher proportions between E L and GLR , than in our case (approx. 31), the convenient s/h ratio might be different, so each species should be treated individually when using 3ENF test.
Fig. 4. FEM predicted force-displacement response for various lengths of initial crack length (a) total strain energy at loading head (b), total strain energy at loading head in logarithmic scale (c).
For clarity, a stress and strain distributions in the specimen including the imprint of the loading head into the wood is depicted in Fig. 5. Figure 5a and Fig. 5b represent scenario S/h = 17.5, and Fig. 5c and Fig. 5d. Represents a scenario with S/h = 5. We see that for ratio S/h = 17.5, the imprint occurs, but it is minimal. For the ratio S/h = 5, the imprint of load head into wood is substantial, but this scenario is not realistic, it rather shows a capability to compute permanent strains using bilinear orthotropic elasto-plastic model of wood. It is also necessary to say that the showed stress and strain distributions for the ratio S/h = 17.5 is after the crack opened meanwhile for the ratio S/h = 5, the stress and strain distributions represent situation without crack, so these images cannot be compared directly and have rather illustrative character to show the principle. 3.3 Influence of Friction Coefficient The friction coefficient (μ) that is defined in the FE model for surfaces where both lamellae get into the contact with each other influences the global F/d response. Therefore, the μ consequently influences the amount of energy needed to develop a certain deflection of specimen that causes crack onset and its propagation which introduces an error into fracture toughness evaluation. In experimental measurement, this negative impact is often reduced by inserting Teflon stripe between lamellae, which lowers the friction between them. However, as we see at Fig. 6, the μ somehow impacts the maximal force (F max ), so there is 5.1% difference when comparing scenarios with minimal and maximal μ. Despite the fact that it seems as low impact, we have to recall that the 3ENF is used for
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Fig. 5. a) von Mises stress for S/h = 17.5 at deflection of 25 mm b) von Mises strain for S/h = 17.5 at deflection of 25 mm c) von Mises stress for S/h = 5 at deflection of 6 mm b) von Mises strain for S/h = 5 at deflection of 6 mm, All images are in true scale.
measuring critical energy strain release rate (GIIc ) that is taken from the maximal force achieved. Therefore, even such a difference should not be neglected.
Fig. 6. a) The effect of friction coefficient on global F/d response, b) detail on F max from rectangle at (a)
4 Conclusions Even despite the fact that experimental part of the work is to be done after deadline of this conference contribution, the presented numerical model resulted in several conclusions that might be interesting for a reader. The specific conclusions coming out of this work are following: (i) length of initial crack length rapidly influences F/d response and fracture toughness consequently, so the experiment should be designed with respect to appropriate crack length related to specific wood properties (for instance, proportion of E L and GLR ); (ii) even though the ratio S/h = 17.5 is recommended from beam theory and other analyses, a certain error is still introduced due to development of plastic strains under load head and supports for such ratio; (iii) influence of friction on F/d response is
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rather small, but still represents an introduction of a certain error into interpretation of data. The general conclusion of the work is hence following: even though the numerically studied individual effects on 3ENF test can be minimized and reveals their rather lower impact, when all would be present at the same time and created composite scenario, it may introduce an error of measurement that is not negligible. Acknowledgement. Experimental and numerical assessment of the bearing capacity of notches in timber beams at arbitrary locations using LEFM [Grant Agreement #21-29389S].
References 1. Kollmann, F.F., Côte, W.A.: Principles of wood science and technology I. Solid wood. In: Principles of Wood Science and Technology. Springer, New York (1968). https://doi.org/10. 1007/978-3-642-87928-9 2. Smith, I., Landis, E. Gong, M.: Fracture and Fatigue in Wood, 1st edn. Wiley, Hoboken (2003) 3. de Moura, M.S.F.S., Dourado, N.: Wood Fracture Characterization, 1st edn. CRC Press, Boca Raton (2018) 4. Danielsson, H., Gustafsson, P.J.: A three dimensional plasticity model for perpendicular to grain cohesive fracture in wood. Eng. Fract. Mech. 98, 137–152 (2013) 5. Mackenzie-Helnwein, P., Eberhardsteiner, J., Mang, H.A.: A multi-surface plasticity model for clear wood and its application to the finite element analysis of structural details. Comput. Mech. 31, 204–218 (2003) 6. Benvenuti, E., Orlando, N., Gebhardt, C., Kaliske, M.: An orthotropic multi-surface damageplasticity FE-formulation for wood: Part I - constitutive model. Comput. Struct. 240, 106350 (2020) 7. Yoshihara, H., Ohta, M.: Measurement of mode II fracture toughness of wood by the endnotched flexure test. J. Wood Sci. 46(4), 273–278 (2000). https://doi.org/10.1007/BF0076 6216 8. Yoshihara, H.: Influence of span/depth ratio on the measurement of mode II fracture toughness of wood by end-notched flexure test, 8–12 (2001) 9. Reiner, J., Wood, J., Subhani, M.: Mode II fracture of wood: comparison between EndNotched Flexure and Compact Shear testing. Eng. Fract. Mech. 270, 108561 (2022) 10. Biswal, S., Singh, G.: Determination of fracture toughness and traction–separation relation in Mode I/II of a natural quasi-brittle orthotropic composite using multi-specimen approach. Eng. Fract. Mech. 282, 109163 (2023) 11. Yoshihara, H., Maruta, M.: Mode II critical stress intensity factor of solid wood obtained from the asymmetric four-point bend fracture test using groove-free and side-grooved samples. Eng. Fract. Mech. 258, 108043 (2021) 12. de Moura, M.F.S.F., Silva, M.A.L., de Morais, A.B., Morais, J.J.L.: Equivalent crack based mode II fracture characterization of wood. Eng. Fract. Mech. 73(8), 978–993 (2006) 13. Silva, M.A.L., de Moura, M.F.S.F., Morais, J.J.L.: Numerical analysis of the ENF test for mode II wood fracture. Compos. A Appl. Sci. Manuf. 37(9), 1334–1344 (2006) 14. Gómez-Royuela, J.L., Majano-Majano, A., Lara-Bocanegra, A.J., Xavier, J., de Moura, M.F.S.F.: Shear traction-separation laws of European beech under mode II loading by 3D digital image correlation. Wood Sci. Technol. 56, 1631–1655 (2022) 15. Sorin, E., Coureau, J.-L., Pérez, C.: Mode I and II R-curves characterization of the Maritime Pine and Spruce under the same geometry. Eng. Fract. Mech. 269, 108472 (2022)
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16. Silva, M.A.L., Morais, J.J.L., de Moura, M.F.S.F., Lousada, J.L.: Mode II wood fracture characterization using the ELS test. Eng. Fract. Mech. 74(14), 2133–2147 (2007) 17. Xavier, J., Morais, J., Dourado, N., De Moura, M.F.S.F.: Measurement of mode I and mode II fracture properties of wood-bonded joints. J. Adhes. Sci. Technol. 25(20), 2881–2895 (2011) 18. Silva, F.G.A., Morais, J.J.L., Dourado, N., Xavier, J., Pereira, F.A.M., De Moura, M.F.S.F.: Determination of cohesive laws in wood bonded joints under mode II loading using the ENF test. Int. J. Adhes. Adhes. 51, 54–61 (2014) 19. Méité, M., Dubois, F., Pop, O., Absi, J.: Mixed mode fracture properties characterization for wood by digital images correlation and finite element method coupling. Eng. Fract. Mech. 105, 86–100 (2013) 20. Nairn, J.A.: Predicting layer cracks in cross-laminated timber with evaluations of strategies for suppressing them. Eur. J. Wood Wood Products 77(3), 405–419 (2019). https://doi.org/ 10.1007/s00107-019-01399-7 21. Chen, K., Qiu, H., Sun, M., Lam, F.: Experimental and numerical study of moisture distribution and shrinkage crack propagation in cross section of timber members. Constr. Build. Mater. 221, 219–231 (2019) 22. Milch, J., Tippner, J., Sebera, V., Brabec, M.: Determination of the elasto-plastic material characteristics of Norway spruce and European beech wood by experimental and numerical analyses. Holzforschung 70, 1081–1092 (2016) 23. Yoshihara, H.: Mode II initiation fracture toughness analysis for wood obtained by 3-ENF test. Compos. Sci. Technol. 65(14), 2198–2207 (2005). https://doi.org/10.1016/j.compscitech. 2005.04.019
Thrust Layout Optimization for the Analysis of Historic Masonry Structures Isuru Nanayakkara(B)
, Andrew Liew , and Matthew Gilbert
Department of Civil and Structural Engineering, The University of Sheffield, Sheffield S1 3JD, UK [email protected]
Abstract. Historic masonry structures form an important part of the world’s collective cultural heritage. Many methods have been developed for assessing the load carrying capacity of masonry gravity structures, from simple hanging chain representations to much more complex non-linear finite element models, though tools that can provide rapid and reliable assessments are still sought after. Here, a new automated procedure, termed thrust layout optimization (TLO) is presented. This is designed to overcome limitations of the traditional thrust line method, and more recently developed computer based alternatives such as the thrust network analysis (TNA) method. The new procedure is capable of automatically identifying admissible thrust lines in masonry gravity structures comprising general arrangements of masonry blocks, without the need to specify in advance the form of the thrust line or thrust network layout. As well as providing a rapid assessment of load carrying capacity, the TLO method provides a clear visual presentation of load paths. Also, sliding friction can be accounted for and large-scale problems involving complex geometries can be tackled, as demonstrated via various examples described in this contribution. Keywords: Thrust Line Analysis · Masonry Structures · Computational Analysis
1 Introduction Historic masonry structures form an important part of the world’s collective cultural heritage—ranging from the grand arches of the Sassanian Empire in the 3rd Century AD to Saint Peter’s Basilica in Rome in the 17th Century AD [1]. Assessment of their load carrying capacity and making any necessary corrective measures to strengthen them is necessary for the preservation of this cultural heritage [2]. Thrust lines generated by funiculars—from physical models (e.g., hanging chain models [3]), graphical methods (e.g., [4]), or numerical methods (e.g., particle spring models [5])—have been extensively used in the analysis of masonry gravity structures such as arches, buttresses and gothic apses (in 2D) as well as in vaults and domes (in 3D). The usage of funicular thrust lines stems from Hooke’s observation of hanging chains—‘as hangs the flexible cable, so but inverted stands the rigid arch’ [6]. From © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 626–638, 2024. https://doi.org/10.1007/978-3-031-39450-8_52
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this, it follows that if one can find a catenary form (with the appropriate loading and support conditions) that can be contained within the masonry gravity structure under consideration, then that structure will be safe under those loads and support conditions. This was further formalised by Heyman in his eponymous ‘safe theorem’, formulated as a limit analysis problem [7]. More recently, computer based methods implementing finite element models and limit analysis approaches have also been used for the analysis of masonry structures. While traditional linear elastic finite element models are of limited use for the analysis of masonry structures, non-linear finite element methods can be applied but are computationally expensive and demand higher levels of user expertise [2]. Limit analysis approaches, which directly model the collapse limit state, have been more popular and have seen significant improvements over the years. Building on the work of Kooharian [8] and Heyman [7], Livesley [9] proposed a rigid block limit analysis method, later extended by others (e.g., [10–12]). However, rigid block methods require explicit modelling of constituent units, or taking a macro-block approach (e.g., [13]): While the former can be time-consuming to model and solve when the blocks are numerous, the latter runs the danger of overestimating the stability when the failure planes do not coincide with actual interfaces between blocks. A resurgence of computer based implementation of graphic static models has been observed. This has primarily been due to the popularity of the thrust network analysis (TNA) procedure developed by Block and Ochsendorf [14], building on work by O’Dwyer [15]. TNA can be used to evaluate the safety of masonry gravity structures by computing a geometric safety factor, or by considering limiting horizontal thrusts at the supports [16]. However, the dependence of the results obtained on the topology of the initially defined thrust network remains an issue. Thrust line method have inherent limitations, regardless of the mode of implementation. Apart from the explicit limitations of unlimited friction capacity (which is not a reasonable assumption for flying buttresses [17]), there are ambiguities related the way tension is treated (although the solution is purported to be compression only, it does implicitly assume tension to allow material below the thrust line to be ‘lifted up’), and case specific modifications (such as the need to determine an inclined crack in masonry buttresses [18]). Also, there are acknowledged limitations in using funiculars as thrust lines, where the method implicitly assumes vertical cuts, disregarding the actual block stereotomy [19–21]. Furthermore, when complex geometries are involved (e.g., consider a gothic cathedral) it is often necessary to analyse parts of the structure separately and to then combine these to check overall stability, a somewhat cumbersome process [18]. In this work, a new computational means of identifying admissible thrust lines in masonry gravity structures is proposed to overcome the aforementioned issues. The proposed procedure takes advantage of powerful layout (or ‘topology’) optimization techniques that have already been successfully used to automate the so-called ‘strut and tie’ method of design for reinforced concrete structures, where the goal is to identify tensile and compressive force paths in deep beams and other elements, enabling efficient layouts of tensile reinforcement to be identified [22]. In a traditional unreinforced masonry structure, the goal is somewhat different, with the priority being to identify compressive force paths, with self-weight effects handled appropriately. In the present
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contribution it will be shown that a formulation employing truss layout optimization [23, 24], used in tandem with transmissible loads [25–27], can be built upon to directly identify compressive force paths and to establish margins of safety. It will be shown that this requires the introduction of interfaces to represent weak masonry joints, thereby allowing both tensile and sliding failures to be modelled, as well as changes to the optimization objective function. The present paper is organized as follows. In Sect. 2 identifying the shortcomings in the funicular thrust lines, thrust layouts are proposed; thrust layout optimisation procedure to automatically obtain thrust layouts is formulated in Sect. 3 and is then applied to typical examples of historical masonry structures in Sect. 4; conclusions are drawn in Sect. 5.
2 Thrust Layouts Although funicular thrust lines have been successfully used in applying Heyman’s safe theorem to masonry gravity structures, Heyman himself later noted some limitations of the thrust line method [19–21]. Specifically, funicular thrust lines implicitly assume vertical cuts, disregarding the actual stereotomy of the constituent blocks, thus allowing for the possibility of self-weight loads being ‘lifted up’ across weak interfaces. Furthermore, the treatment of tensile strength in the funicular thrust lines is not clear—although the solution visualised is compression only, implicitly the self-weight of masonry lying below the thrust line is lifted up to this. Also, whereas the block material possesses some limited tensile strength, the interfaces have negligible tensile strength, and thus need to be treated differently. The two simple examples shown in Fig. 1 and Fig. 2 demonstrate how these errors can lead to incorrect results. In Fig. 1, as vertical cuts are assumed instead of the actual cut, which is horizontal, the funicular thrust line predicts a higher collapse load than that can be carried by the assembly. This is by allowing the self-weight of the bottom block to be lifted across the tension-weak interface. This is clearer when the tensile lines are drawn from the centres of mass of the blocks to the thrust line—it is evident that the tensile link from the bottom block cuts across the weak interface between blocks. In Fig. 2, although a compression only thrust line cannot be constructed, an equilibrium solution exists as demonstrated by the force flow plotted in (b). This force flow is now allowed to carry tensile forces within the block but not across weak interfaces between blocks. Note that the force T in the tensile link introduced (5 force units, horizontal) is significantly less than the implicit tension pulling the self-weight of the top block (40 force units, vertical). And there is no reason for these two tensile forces to be treated any differently. Following these observations, the following rules are applied to correct funicular thrust lines and to arrive at thrust layouts: • self-weight forces are only allowed to be transmitted within a given block (when attempting to attach itself to the thrust layout);
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Fig. 1. Constraining load transmissibility in funicular thrust lines: (a) the funicular thrust line generated from graphic statics disregards the weak interface between blocks and implicitly assumes a tensile link across it, overestimating load capacity; (b) the self-weight of the bottom block is not pulled across the weak interface, but is allowed to be carried by the supports, giving the exact collapse load (compression and tension links in blue and red respectively; the geometry is as indicated; unit weight of 2 units and width of 2 units considered).
Fig. 2. Incorporating tension explicitly in thrust lines: (a) a valid thrust line cannot be drawn if only compressive links are allowed; (b) a thrust layout contained within the structure can be constructed with the help of a tensile link (the geometry is as indicated; unit weight of 2 units and width of 2 units considered).
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• links carrying tensile forces are permitted within blocks (but not across weak interfaces). Thrust layouts give a valid representation of the equilibrium of individual blocks making up the structure, while respecting the weak interfaces that exist between blocks, and visualising a (possible) force flow within the structure.
3 Thrust Layout Optimisation (TLO) A relationship exists between graphic statics (GS) and ground-structure layout optimisation (LO), in their application to pin jointed structures. GS enforces equilibrium at nodes and allows exploration of a design space by letting nodes move, thereby changing the geometry of the structure (which is usually of pre-defined topology). Similarly, LO too enforces equilibrium at nodes; however, in this case, the nodal coordinates are usually fixed but a fully connected ground-structure is considered (i.e., all possible members connecting all the pin joints are considered first). And thereafter, in LO, member yield strengths are imposed to enable a minimum volume structure to be found. Given this relationship between the two methods, LO appears to be a viable candidate to automate the generation of thrust layouts, albeit some modifications are required. Direct application of the LO process would generate a ‘truss-like’ force flow within a masonry structure, but (i) would fail to recognise the weak interfaces in masonry gravity structures, and (ii) self-weights fixed at nodes would not generate force flows resembling typical thrust lines. To address these issues, interface nodes representing weak masonry bonds can be introduced and self-weight loads can be allowed to move along their lines of action via the use of ‘transmissible’ loads contained within a given block. Using the two block assembly in Fig. 3, the proposed thrust layout optimization (TLO) process is now described in more detail (see [28] for additional details). Interface nodes share the same physical location at a weak interface, but with each being associated with one of the adjacent blocks. This gives rise to node pairs that are each connected via a normal force qn and a shear force qs , respectively aligned perpendicular and parallel to the interface (Fig. 3b). The weak interface is enforced by constraining the normal force to always be compressive, and the shear force to be limited by the normal force and the friction coefficient between blocks at the interface. Transmissible loads have previously been used in conjunction with the standard ground structure layout optimisation procedure [25–27]. These are loads that are shared across multiple nodes lying along a given vertical line of action when self-weight loads are involved. To respect the weak block interfaces, the transmissibility is restricted to the extents of a given block (Fig. 3c). When assessing the stability of a masonry gravity structure, a common goal is to seek the magnitude of applied load that can be applied before collapse occurs. To achieve this, the collapse load factor (the multiplier on a given load required to initiate failure) is sought. This can be achieved by maximizing the load factor subject to equilibrium and yield constraints, using the defined ground structure and set of transmissible self-weight loads—resulting in the formulation given in Eq. (1) below:
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max λ q, qn , qs , w, λ
(1a)
s.t. Bq + Bn qn + Bs qs − w − λf = 0
(1b)
ˆ Hw = w
(1c)
t q ≤ qmax 1
(1d)
qn ≤ 0
(1e)
μqn ≤ qs ≤ −μqn
(1f)
w ≥ 0
(1g)
λ ≥ 0
(1h)
where λ is the load factor on the externally applied loads; B is a 2n × m matrix containing direction cosines of links, q = [q1 , q2 , … , qm ]T is a vector of internal member forces, t being the maximum tensile force allowed. Also f = [f1x , f1y , f2x , f2y , … , with qmax fnx , fny ]T is a vector of external applied loads and Bn and Bs are interface equilibrium matrices of size 2n × p (where p is the number of interface node pairs) containing direction cosines on the basis of notional zero-length members oriented respectively perpendicular and parallel to the corresponding interface; qn = [qn,1 , qn,2 , … , qn,p ]T is the interface normal force vector and qs = [qs,1 , qs,2 , … , qs,p ]T is the interface shear force vector; w = [0, w1 , 0, w2 , … , 0, wn ]T is the nodal self-weight load vector (note that as self-weight loads are applied in the vertical direction, only vertical equilibrium ˆ 2, … , w ˆ g ]T is the load group vector, where g is the constraints are affected); w ˆ = [w ˆ 1, w number of transmissible self-weight load groups in the problem, with w ˆ i being the total load applied in transmissible load group i. Finally, H is a binary matrix that specifies which nodal load components in w belong to which load group in w, ˆ where H is of size g × 2n and is given by: 1;if load component j exist in load group i Hij = . (2) 0; otherwise Thus, the factor on externally applied loads is maximized under the constraints of (i) static equilibrium at nodes, Eq. (1b) and Eq. (1c); (ii) a maximum tensile force allowed within blocks, Eq. (1d), with no tensile forces allowed across weak interfaces, Eq. (1e); and (iii) interface friction force limited by friction coefficient, Eq. (1f). Additionally, the constraint in Eq. (1g) is needed to avoid spurious solutions from being identified [26]. The linear nature of the objective function and constraints means that the problem can be solved using an efficient linear programming (LP) solver.
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Finally, although solving Eq. (1) will determine the collapse load factor, the associated solution may include spurious self-equilibrating force networks, since these are not explicitly penalized in Eq. (1). This will in turn lead to thrust layouts that are not visually clear. To address this, a volume minimization post-processing step can be performed, with the computed load factor constrained to lie at the value found in the load evaluation step. This is carried out using the basic layout optimization formulation (i.e., that typically used for trusses), with interface nodes and transmissible self-weights now also included in the model. Outcomes from the process are shown in Fig. 3d–e. A further post processing geometry optimization rationalization step (after [29]) can help further improve the visual clarity of the force flow; see Fig. 3f. Furthermore, in addition to the thrust lines obtained via the TLO process (shown in Fig. 3d–f), the vertical selfweight vectors hidden by the assumed transmissibility of self-weight loads can also be optionally plotted to provide additional visual information; see Fig. 3g.
Fig. 3. Application of proposed thrust layout optimization (TLO) procedure to a simple two block problem: (a) geometry of blocks and location of external load P and support; (b) problem discretized via nodes and links; (c) masonry self-weight represented by transmissible loads W 1 and W 2 ; (d) collapse load and thrust layout found by solving the associated layout optimization problem; (e) thrust layout obtained when using a finer resolution nodal grid (as indicated); (f) thrust layout obtained after also performing a post-processing geometry optimization rationalization step; (g) layout with transmissible self-weight vectors also plotted—compression and tensile transmissible self-weight vectors are shown in blue and red, respectively, with line thicknesses indicating the magnitude of the forces.
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4 Examples A set of three examples are provided to showcase the potential of TLO in the analysis of historic masonry gravity structures—(i) an arch with holes; (ii) a flying buttress; and (iii) a section of a gothic cathedral. 4.1 Segmental Arch A segmental arch having equally sized voussoirs, with three ornamental internal holes positioned on the arch centreline is considered (see Fig. 4). The arch is subjected to an off-centre point load. A friction coefficient of 1 is assumed to eliminate sliding failures. A funicular thrust line (see Fig. 4a) contained fully within the structure, and not passing through the holes, would give a very conservative estimate of the collapse load (P of 27.6 kN). Recognizing the likely limited, albeit finite, tensile strength of the masonry voussoirs, the funicular thrust line can instead be restrained to lie within the structure only at weak interfaces between the blocks (see Fig. 4b). This, now, gives a much higher collapse load, P of 57.4 kN. However, the thrust line no longer stays within the arch section, thus making the status of the force flow and hence the validity of the solution unclear. Now, the corresponding thrust layout optimization solution (see Fig. 4c) gives a collapse load P of 58.1 kN. This, while slightly higher than that estimated via the thrust line method, makes the load path clearer. While the force flow remains entirely within the structure, the presence of tensile forces where the thrust line would move out of the structure, and the bifurcation of the thrust line around the internal holes are clearly visualised (Additionally, this justifies constraining the thrust line only at weak interfaces in Fig. 4b). The slight increase in collapse load arises due to a situation akin to that in Fig. 2—where the tensile links in the first voussoir pulls back its self-weight and does not correspond to a location of the thrust line moving out of the structure. The same collapse load estimated by TLO is also predicted by the rigid block method (Fig. 4d). However, this method does not provide information on the force flow within the structure, whereas TLO provides a valuable perspective on how forces flow in masonry gravity structures. 4.2 Flying Buttress In the traditional thrust line method, it is generally assumed that no sliding failures will occur, which can be unsafe, particularly in the case of flying buttresses [17]. However, limited friction capacity at block interfaces can readily be accounted for via the interface nodes in TLO. This leads to a more realistic visualisation of the force flow within masonry gravity structures of the sort shown in Fig. 5. The flying buttress of Mallorca Cathedral, as presented by [30], is considered. It is subjected only to its self-weight. The thrust line in Fig. 5a (reproduced from [30]) gives a thrust line passing through the bottom corner of the head of the flyer to a point on the base support, while touching both the extrados and intrados along the way; this would lead to a collapse only if the abutments spread enough to enable formation of a ‘snap through’ collapse mechanism. Now considering the angle of incidence of thrust at supports (i.e., the angle between the thrust and the perpendicular to the support), at the
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Fig. 4. Segmental arch - solutions obtained via: (a) traditional thrust line method; (b) thrust line method with thrust constrained at block interfaces only; (c) TLO, showing force flows confined to areas where material is present; (d) rigid block method, showing collapse mechanisms only (arch span: 5.80 m, rise 1.85 m, width 0.1 m, unit weight: 25 kN/m3 ; circular voids on arch centreline at locations indicated have diameter of 0.35 m; collapse load P in kN applied 0.72 m from left support; thrust lines obtained assuming self-weight lumped at block centroids; thrust t = 250 N; thrust layouts obtained using internal and boundary node spacings of 0.05 m and qmax layout tensile force line thickness scaled by a factor of 2 for emphasis).
flyer head it is 47.6° and at the base it is 13.4°. Although the thrust line is fully contained within the structure, the friction angle of the material (assumed to be 40° in this case) is not sufficient to avoid sliding failure at the flyer head. Considering the stereotomy of the blocks and limited friction capacity of the material via TLO, a more realistic force flow can be found (see Fig. 5b). The resulting thrust layout indicates that the load will be carried primarily by the arch ring, giving a shallower angle of incidence for the thrust at the head. As a result, the horizontal thrust and the vertical reaction at base are increased. This would in turn increase the loading on the elements carrying those reaction forces—e.g., a masonry buttress. 4.3 Gothic Cathedral TLO can also be used to analyse more complex structures, rapidly providing information on load carrying capacity and internal force flows. To demonstrate this, a section of a gothic cathedral is considered. Thus, a gothic cathedral section—inspired by Tortosa Cathedral in Tarragona, Spain [31]—is now considered. It has two side aisles, at either side of the nave, all of which having barrel vaulted roofs and a set of single flying buttresses above. The nave is of 10.96 m span and the aisles are of 4.71 m and 3.92 m span, while the roofs of the nave
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Fig. 5. Flying buttress - subjected only to its self-weight, is assessed via (a) traditional thrust line method (reproduced from [30]); (b) TLO, considering actual stereotomy and friction capacity limited by a friction coefficient of 0.85 (horizontal (H) and vertical (V1 and V2 ) support reactions are as indicated; thrust layouts obtained using internal and boundary node spacings of 0.05 m).
and side aisles are at 23.68 m, 17.04 m, and 11.15 m, respectively, from ground level. Buttress piers are of 20.36 m and 14.12 m in height. The section considered for the analysis has varying widths; buttress piers are of 2 m width, flying buttresses of 1 m width, and the vaulted roof of 6m width, as indicted in Fig. 6. The cathedral is built using stone of unit weight 18 kN/m3 , while the ballast filling of the vaulted roof has a unit weight of 15 kN/m3 (see Fig. 6). A friction angle limit of 40° is assumed for all interfaces.
Fig. 6. Gothic cathedral: width and unit weight variation of the assessed section. Width of the flying buttresses, piers and vaults are 1m, 2 m, and 6 m respectively. Unit weight of stone (in grey) is 18 kN/m3 and unit weight of ballast fill (in brown) is 15 kN/m3 .
The gothic cathedral is assessed under a point load applied on the keystone of the nave barrel vault. The block discretization indicated in Fig. 7 is used. The ground-structure was in this case made up of 43,192 nodes, 4,038,868 internal links and 12,962 interface
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node pairs. The corresponding CPU times were 55 s for the load evaluation step, and 263 s for the volume minimization postprocessing step. The resulting thrust layout is shown in Fig. 7, where the left and the right hand sides of the figure use different cut-off limits for the forces plotted; on the left only forces greater than fmax /100 are plotted, while on the right forces greater than fmax /10000 are plotted, where fmax is the maximum thrust in the thrust layout. As the cut-off is increased the main elements of the thrust layout emerge. Note that when only the higher forces are plotted (left hand side) no thrust lines appear on the flying buttresses, since the forces present in these are small, particularly when no external applied loads are present.
Fig. 7. Gothic cathedral: thrust layout for load applied on the keystone of nave vault. On the left hand side, forces lower than 1/100 of fmax are cut off and on the right forces lower than 1/10000 of fmax are cut off (tensile link thickness scaled by a factor of 2 for emphasis; qt max of 10 kN, boundary node spacing of 0.05 m and internal node spacing of 0.2 m).
5 Concluding Remarks A new procedure has been developed that allows both the safety of masonry gravity structures to be evaluated and the transmission of internal forces to be clearly visualized. The procedure builds on the truss layout optimization with transmissible loads formulation, using this to model self-weight, and with interfaces included in the formulation to model weak masonry joints. The new procedure is herein termed thrust layout optimization (TLO).
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Although the traditional thrust line analysis method has proved useful for many years, it has some limitations. For example, block stereotomy is not considered, leading to self-weight being ‘lifted up’ across weak interfaces. Also, the treatment of tensile forces is not clear. Thrust layouts—where transmissibility of self-weights is restrained and the limited, albeit present, tensile strength of the block material is made use of—are presented here. Furthermore, the TLO process proposed to obtain thrust layouts readily incorporate limiting friction at block interfaces. The thrust layouts identified via TLO provide a rich visual representation of force flows in masonry gravity structures. The procedure takes on board the limited tensile capacity of masonry blocks and makes no prior assumptions about the topology of thrust layouts. This enables visualisation of forces flowing around internal holes, with the force flows associated with blocks rocking about vertices often resembling classical Michell structures; more familiar funicular thrust line solutions can also be identified. It is also possible to plot transmissible self-weight vectors, eliminating ambiguity as to how self-weight forces are mobilized.
References 1. Kurrer, K.E.: The History of the Theory of Structures, 2nd edn. Ernst & Sohn, Berlin (2008) 2. Roca, P., Cervera, M., Gariup, G., Pela’, L.: Structural analysis of masonry historical construction. Classical and advanced approaches. Arch. Comput. Methods Eng. 17, 299–325 (2010) 3. Graefe, R.: The catenary and the line of thrust as a means for shaping arches and vaults. In: Addis, B. (ed.) Physical Models: Their Historical and Current Use in Civil and Building Engineering Design, pp. 79–126. Ernst & Sohn (2021) 4. Paris, V., Ruscica, G., Roberti, G.M.: Graphical modelling of hoop force distribution for equilibrium analysis of masonry domes. Nexus Netw. J. 23, 855–878 (2021) 5. Kilian, A., Ochsendorf, J.: Particle-spring systems for structural form finding. J. Int. Assoc. Shell Spat. Struct. 46(147), 77–84 (2005) 6. Heyman, J.: The Masonry Arch. Ellis Horwood, Chichester (1982) 7. Heyman, J.: The stone skeleton. Int. J. Solids Struct. 2, 249–279 (1966) 8. Kooharian, A.: Limit analysis of voussoir (segmental) and concrete arches. J. Am. Concr. Inst. 24, 317–328 (1952) 9. Livesley, R.K.: Limit analysis of structures formed from rigid blocks. Int. J. Numer. Meth. Eng. 12, 1853–1871 (1978) 10. Ferris, M., Tin-Loi, F.: Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int. J. Mech. Sci. 43, 209–224 (2001) 11. Orduña, A., Lourenço, P.B.: Cap model for limit analysis and strengthening of masonry structures. J. Struct. Eng. 129, 1367–1375 (2003) 12. Gilbert, M., Casapulla, C., Ahmed, H.M.: Limit analysis of masonry block structures with nonassociative frictional joints using linear programming. Comput. Struct. 84, 873–887 (2006) 13. Casapulla, C., Portioli, F., Maione, A., Landolfo, R.: A macro-block model for in-plane loaded masonry walls with non-associative Coulomb friction. Meccanica 48(9), 2107–2126 (2013). https://doi.org/10.1007/s11012-013-9728-5 14. Block, P., Ochsendorf, J.: Thrust network analysis: a new methodology for three dimensional equilibrium. J. Int. Assoc. Shell Spat. Struct. 48, 167–173 (2007) 15. O’Dwyer, D.: Funicular analysis of masonry vaults. Comput. Struct. 73, 187–197 (1999)
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16. Avelino, R.M., Iannuzzo, A., Van Mele, T., Block, P.: Assessing the safety of vaulted masonry structures using thrust network analysis. Comput. Struct. 257, 106647 (2021) 17. Nikolinakou, M.-K., Tallon, A.J., Ochsendorf, J.A.: Structure and form of early Gothic flying buttresses. Revue Européenne de Génie Civil 9(9–10), 1191–1217 (2005) 18. Huerta, S.: The safety of masonry buttresses. Proc. Inst. Civil Eng. Eng. Hist. Herit. 163, 3–24 (2010) 19. Heyman, J.: La coupe des pierres. In: Kurrer, K.E., Lorenz, W., Wetzk, V. (eds.) Proceedings of the 3rd International Congress on Construction History, Cottbus, Germany, pp. 807–812 (2009) 20. Ochsendorf, J.: The masonry arch on spreading supports. Struct. Eng. 84(2), 29–35 (2006) 21. Alexakis, H., Makris, N.: Limit equilibrium analysis of masonry arches. Arch. Appl. Mech. 85(9–10), 1363–1381 (2014). https://doi.org/10.1007/s00419-014-0963-6 22. Xia, Y., Langelaar, M., Hendriks, M.A.N.: A critical evaluation of topology optimization results for strut-and-tie modelling of reinforced concrete. Comput. Aided Civil Infrastruct. Eng. 35, 850–869 (2020) 23. Dorn, W.S., Gomory, R.E., Greenberg, H.J.: Automatic design of optimal structures. J. Mech. 3, 25–52 (1964) 24. Gilbert, M., Tyas, A.: Layout optimization of large-scale pin-jointed frames. Eng. Comput. 20, 1044–1064 (2003) 25. Darwich, W., Gilbert, M., Tyas, A.: Optimum structure to carry a uniform load between pinned supports. Struct. Multidiscip. Optim. 42, 33–42 (2010) 26. Lu, H., Tyas, A., Gilbert, M., Pichugin, A.V.: On transmissible load formulations in topology optimization. Struct. Multidiscip. Optim. 64(1), 23–37 (2021). https://doi.org/10.1007/s00 158-021-02932-0 27. Fuchs, M.B., Moses, E.: Optimal structural topologies with transmissible loads. Struct. Multidiscip. Optim. 19, 263–273 (2000) 28. Nanayakkara, K.I.U., Liew, A., Gilbert, M.: Application of thrust layout optimization to masonry structures. Proc. Royal Society A 20230053 (2023). https://doi.org/10.1098/rspa. 2023.0053 29. He, L., Gilbert, M.: Rationalization of trusses generated via layout optimization. Struct. Multidiscip. Optim. 52(4), 677–694 (2015). https://doi.org/10.1007/s00158-015-1260-x 30. Fuentes, P.: Mechanics of flying buttresses: the case of the cathedral of Mallorca. J. Mech. Mater. Struct. 13(5), 617–630 (2018) 31. Lluís i Ginovart, J., Jover, A.C.: Design and medieval construction: the case of Tortosa cathedral (1345–1441). Constr. Hist. 29(1), 1–24 (2014)
Vernacular Constructions: Conservation and Management
Double Quincha in Lima, Peru: Innovation, Adaptation and Comfort in the XVII–XIX Centuries A. Scaletti, T. Montoya, and M. Wieser(B) Department of Architecture, CIAC & PAPUCP, Pontificia Universidad Católica del Perú, Avenida Universitaria 1801, San Miguel, Lima, Peru [email protected], {tmontoya,mwieser}@pucp.edu.pe
Abstract. Peruvian construction technology has an original tradition of thousands of years, from a completely indigenous remote past to the cultural mixture of the viceroyalty centuries and the encounter with the rest of the world. This tradition has been, as is to be expected, strongly conditioned by the material characteristics of the geographical, climatic and territorial environment, with multiple adaptations and innovations. One of these innovations is the quincha, used throughout the coast of the Peruvian viceroyalty for the second and third levels of all structures. But the documentation indicates the use of a variant, the “double quincha” as an element that, using the width of more rigid supports, created an internal air chamber. This work references colonial and contemporary documentation and case studies in Lima, to verify the properties for thermal comfort of the double quincha, in one of the first studies of its kind for this material. Architectural surveys and systematic temperature measurements were carried out at multiple buildings in the center of the historic city- as well as the use of models in an energy simulator program. The results allow us to understand a little more both the constructive reasoning of quincha and the possibilities of this traditional method. Keywords: traditional architecture · double quincha · thermal comfort · Peru
1 Framework Traditional construction in the Viceroyalty of Peru (16th–19th centuries) experienced some pivotal moments as it sought to respond to the requirements of the geographical, material and human environment. This was especially true for the case of the Peruvian coast, a long desertic line crossed by small valleys and resting directly on the Nazca Plate, part of the so-called “Ring of Fire of the Pacific”. This situation meant, then as now, the recurrence of high-intensity earthquakes, some of them accompanied by tsunamis. For this work, it is especially important to consider the two great historical earthquakes centered around the area of Lima -the viceregal capital back then and of modern Double Quincha-The word, of indigenous origin, was already found in chronicles such as those of the priest Bernabé Cobo (History of the New World... p. 210–211). In Spain, similar elements were called “looms”. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 641–654, 2024. https://doi.org/10.1007/978-3-031-39450-8_53
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Peru today- that occurred in 1687 and 1746. After the first, it was considered prudent to promote the use in upper levels of a hybrid construction system of local origin, the quincha: it is a succession of straight posts in squared wood, with the space of the low generally understood as the official popularization of this system in the viceregal capital, but it is an objective fact that quincha was already used throughout the territory, as it is up to the present. The traditional interpretation, however, understands it as a single panel made of wood, cane and mud/clay: this paper seeks to suggest that a double-panel version, with a thin interior air chamber, was also widely used in large and small houses of the viceregal capital.er part filled with stone, adobe or brick, with wooden diagonals or crosses to avoid deformations. The upper two thirds typically present a weft of thin reeds or cane1 or wooden slats -hence the Spanish name, “loom”- tied to the uprights with damp leather, “huasca” in Quechua. The whole element is covered in mud on both sides and can later be also covered with plaster or lime and painted. It is, in short, a flexible and relatively light element, but it was not very successful among the rich elite of Lima at the time, as it was considered a precarious and humble solution. The second great earthquake, that of 1746, was the most important and destructive that was recorded in the Peruvian viceregal period and, as the main consequence for our topic, it was the trigger for the first anti-seismic regulations on the continent. Faced with the expert recommendations of the time and with the possibility of limiting all constructions in Lima and the coast of the viceroyalty to a single floor -including cathedrals, towers and churches, even palaces- Viceroy José Antonio Manso de Velasco, later Count of Superunda, decided to order that over the height of five varas2 (about 4.5 modern meters) quincha would be the only permitted building material. That moment is generally understood as the official popularization of this system in the viceregal capital, but it is an objective fact that quincha was already used throughout the territory, as it is up to the present. The traditional interpretation, however, understands it as a single panel made of wood, cane and mud/clay: this paper seeks to suggest that a double-panel version, with a thin interior air chamber, was also widely used in large and small houses of the viceregal capital.
2 References to the Double Quincha in the Historic Center of the City of Lima The viceregal documentation regarding double quincha is relatively scarce, and bibliographical references even more scarce. However, texts such as Crespo’s cite as the oldest documentary reference for the quincha in general a notarial protocol from 1662, and then in similar documents in 1667, where terms such as “brick and plaster loom” or “cane loom” were used in second levels of residences3 . For example, Crespo indicates
1 Commonly named in Peru “caña brava”, its scientific name is “Gynerium sagittatum”. 2 About 0.83 m. 3 Crespo cites the San Cristóbal Archives, at the General Archive of the Nation (AGN), Notarial
Protocols, Antonio de Figueroa (1662), n. 640 fol. 1079 et seq. See CRESPO RODRÍGUEZ, María Dolores (2006). Domestic architecture of the City of Kings (1535–1750). Seville: EEHA, CSIC, University of Seville, Diputación de Sevilla, p. 91–93.
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that “the quincha loom could be used either to enclose load-bearing areas, or as a nonbearing dividing loom, and depending on whether it fulfilled one function or another, its thickness and resistance were different…”.4 Then, in documents such as the 1669 protocol by Pedro Pérez Landero, the “double loom” is already found, although restricted to a “chácara” or country house, in the Lurigancho valley5 . The work executed there, carried out for Don José del Corral by the master mason Juan De Los Ríos, was actually the repairing of one quincha wall damaged by the earthquake of 1668, which had to be redone on its remains on the second floor. For this, De Los Ríos undertook the redoing of the oratory “of brick loom, all of it with a baheda of reeds and plaster. And the four main walls of said house must be made of adobe. And the divisions and medianías [of the upper level] have to be of cane looms”.6 And if a “simple loom” was understood as flexible and light, the “double looms” of quincha apparently had in their favor the creation of an intermediate space, an air chamber between its two panels or frames that was understood as useful to provide a certain thermic control, which -Crespo suggests- made it especially popular on facades7 . As mentioned, originally -and to a certain extent up to the present- quincha was generally understood as a poor element, without prestige. Great earthquakes, especially that of 1746 and the subsequent official Ordinances served to reassess that idea, since according to authorities such as Viceroy Manso de Velasco “experience has forced looms to be made of wood and cane that are tremor-proof and with more comfortable patios so that any event does not make it necessary to abandon the homes themselves and experience the damages and impairments that have been suffered for having left them…”8 . Crespo insists that although this type of construction was understood as necessary, society’s impulse to dissimulate it led to promote its plastering and covering with paint. It was used, then, but it was not something people wanted to expose. In the specific of the double variant, Pacón y Velarde9 explore the concept of an intertwined format with a couple of schemes in their bachelor’s thesis. On the other hand, Marussi proposes the existence of a scheme with reeds tied with huasca -leather strips 4 Crespo Rodríguez, Op. Cit., p. 91. 5 SUITO, Giovanni. The Lima house and characteristic elements during the 16th, 17th and
6 7
8
9
18th centuries. Federico Villareal National University, Architecture and Urbanism Program, Bachelor Thesis directed by the architect A. Linder, Lima: 1971 (unpublished). The original document, cited by both Suito and Crespo, is from the San Cristóbal file in the AGN, Notarial Protocols, Pedro Pérez Landero (1669), n. 1470, fol. 620 et seq. The author mentions “…double looms, a cane framework superimposed on a brick or mud structure, which left a gap between the two panels, preferably used on the facades”. See Domestic Architecture in the City of Kings…, p. 92. General Archive of the Indies (AGI), Lima 983, On the reductions to the censuses… December 1748. The quote is also found in PÉREZ-MALLAÍNA BUENO, Pablo Emilio (2001). Portrait of a city in crisis. Lima society before the seismic movement of 1746. Seville: CSIC-EEHARiva-Agüero Institute. The viceroy insists saying that “experience has taught that only the buildings of this material do not fall apart with tremors easily.”. PACÓN LUNG, María Cristina y Cecilia VELARDE LÓPEZ (1989). La profesionalización de la mano de obra como principio de una adecuada praxis en conservación - Lima. Universidad Ricardo Palma, Facultad de Arquitectura y Urbanismo. Tesis de Bachiller dirigida por el arquitecto E. Gastelumendi, Lima: (inédita), lámina 22.
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used still wet, as previously mentioned- to the crossbar and not intertwined. Describing it, he indicates: “...there was an empty space between the two layers of reed creating a thermal protection space that increased the comfort conditions inside these buildings, this double membrane solution was generally used on walls that were not attached to other belonging to neighboring buildings”.10 Suito insists on the idea of the use of double quincha mainly on the façade of buildings: “The double loom is frequently used on facades; with studs of greater section in relation to the thickness of the loom, and carrying a double braid of cane and in the lower part of the loom a brick set with mud or plaster and sand. So that there was an empty space between the two panels, thus increasing the resistance of the wall and creating an athermic space with which to counteract the heat of the sun that hit the façade”.11 However, as we will see as a result of what has been investigated for this paper, it is not strictly true that double quincha was only used in load-bearing walls, nor that it was preferably used in facades due to thermal insulation issues.
3 The Study To understand the double quincha issue, architectural surveys were carried out and analyzed in the traditional houses of half a block of the historic center of the city of Lima, capital of Peru and historically the most important city of the Spanish Viceroyalty (16th–19th centuries) in South America. The block chosen for the study (Fig. 1) is located two streets from the main square of the city and in past centuries was the seat of very important families: today the Riva-Agüero and O’Higgins houses stand out in it, both patio-houses of important dimensions and traditional construction, although the area studied also includes more modest buildings, especially from the 18th and 19th centuries, significantly modified. This meant carrying out very detailed planimetries, where significant dimensional discrepancies were found, since it had been assumed a priori that all quincha to be found would correspond to the simple, single model. By our findings, it was immediately evident that in the half block analyzed in detail, more than 60% of the rooms are built with double quincha walls with a thickness of 0,30 m or more, on all the walls of the rooms (Fig. 2). This corresponds to the oldest documentary reference in this regard, for the Riva-Agüero complex:
10 In Marussi, Ferruccio. Historical Background of the Quincha…, p. 26. The same author had
already developed the subject in his doctoral thesis of 1981 (“The quincha in the monumental buildings of the Viceroyalty of Peru”), presented at the Higher Technical School of Architecture of the Polytechnic University of Madrid. 11 SUITO, Marco, Op. Cit.
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Fig. 1. Location of the sector of the block studied (red), located close to the Plaza Mayor and important religious institutions (yellow) such as Los Agustinos, Las Mercedarias and the Cathedral of Lima. Based on Pedro Nolasco’s plan of 168712
“In a survey carried out on July 10, 1779, the master builders Marcos Lucio - at the same time also a Master Builder for the city - and Alonso de Rivera maintained that they found the house looms in good condition “both double and single”.13 Similarly, in Annex 6 of the Historical Study Report carried out by Zamora on the houses on the same block -it is an internal document provided by the current owner, the Pontificia Universidad Católica del Perú, prepared by its Infrastructure office- the reference to the assignment of Ramírez de Arellano to Pérez la Torre stands out. In a document registered by notary Francisco Palacios, on October 5, 1865, the materiality of the second level of the south east area of the block is described indicating that “the looms are semi-double, with the exception of several insignificant quinchas inside the top floor.”14 For this paper, two types of studies were carried out: the first, the observation and constructive analysis of the double thatch, taking as case study 1 the property located towards Huancavelica street (Fig. 3a). For case study 2, an analysis was carried out with 12 Extracted from Gunther Doering, Juan (1983) Plans of Lima, 1613–1983. Municipality of
Metropolitan Lima: Petróleos del Perú. 13 From the Riva-Agüero Historical Archive, AHRA C-23, 69r. The citation is found in
SCALETTI, A. N. (2015). «…having recognized its stonework factory and looms…»: the Riva-Agüero house (Lima, Peru - 18th century). In the First Hispano-American International Congress on the History of Construction. (pp. 1591–1602) MADRID: Juan de Herrera Institute. 14 From Protocol No.: 567. Folio: 671r–672r (32 pages-Inserts), 21vF. Terán Collection, General Archive of the Nation.
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simulation of the thermal behavior of the environment that includes one of the façade walls; towards De La Unión street, oriented towards the southeast (Fig. 3b).
Fig. 2. General plan of the second floor of the area studied. Own elaboration based on files of the PUCP Infrastructure Department15 .
3.1 Constructive Analysis (Case Study 1) The housing unit studied in this case has access from Huancavelica street and involves only the second floor. Almost the entire house has double quincha walls with a medium thickness of more than 0,33 m, in situations of being façade walls, dividing walls, walls exposed to the patios, internal load-bearing and non-load-bearing walls. It was decided to carry out the constructive analysis in this sector because it has two damaged walls and consequently part of the plaster layer had been lost (Fig. 4a), which allowed the characteristics of the wall to be observed: the structure, wall head (Fig. 4b), the order of the canes, the internal cavity (Fig. 5) and the plaster layers. To complement the characterization of the wall, three exploration perforations were made, taking special 15 Access to the properties was possible thanks to the support of the Pontificia Universidad Católica
del Perú (PUCP), owner of the majority of the block, through its Office of the Administrative Vice President and its Infrastructure Department. Specifically, the Riva-Agüero and O’Higgins houses operate under the administration of the IRA-PUCP.
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Fig. 3. a & b. Quincha façades of houses in Huancavelica and De la Union streets. (T. Montoya 2022).
care on the inside and outside of the façade to check, among other things, the thickness of the plaster.
Fig. 4. a. Quincha without plaster, b. High part of the same wall. (T. Montoya 2022).
As average, the rooms in vice royal houses are 4 or 4,5 m. tall, with maximum longitudes of 5 m. The distance between the support elements of a typical quincha wall was 0,80 m, with horizontal elements approximately every 0,90 m. The wooden frame of quincha, be it simple or double, react in a flexible way when confronted with earthquakes, allowing it to resist them with relatively few damages. Most of those are frequently evident on the mud plaster covering, which are fortunately easy to repair. As indicated, the double quincha in the case study is mostly 0,33 m thick: it is typically structured with wooden studs of rough surface, with a 4 (0,10 or 0,12 m)
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Fig. 5. Void between double quincha canes (T. Montoya 2022).
square base spaced every 0,80 m to axis. These rest on a wooden base that itself rests on the top of the masonry wall (adobe or brick) of the first level of the building. Rectangular wooden crossbars are attached to these columns on both sides of the column, with huasca, which was placed wet and in which the drying contraction was counted on to keep all the elements fixed. The total interior height of the second level is 3.80 m, a little less than what is present in other more important houses of the same block. The first quarter of the height of the wall is filled with adobes to increase the weight of the base and between studs there are diagonal timbers that provide rigidity to the structure. The top part of the quincha wall also presents filling of 2 rows of adobes on the “collar” or mooring beam. The cane braiding was carried out with 2.80 m long canes, inserted on the side on which the cane is curved. Approximately 40 reeds were used in one section. The thicknesses of these oscillate between 0,01 and 0,02 m, with the average of the measurements being 0,017 m. Currently, this type of reeds are classified as “third” or “fourth” types, being understood as the ideal thickness to be able to carry out the curvature of the braid. In the columns, 4 reeds are tied together with the huasca to level and receive the mud that covers them. In the most deteriorated wall of the building studied -indicated in Fig. 2 as “1”four strata of plasters have been identified, but the fourth has not been considered in the measurements because it was identified as the product of a modern remodeling, with a layer of industrial paint. The three plasters thus considered are: the first, applied directly over the reeds and the one that allows a first “leveling”. The mud adheres to and covers the surface of the canes with a thickness that varies between 0,02 and 0,04 m depending on the sector it covers. The next layer of plaster displays more presence of fibers, it is 0,02 m thick; and finally the third plaster is 0,01 m thick. Over these, the wall receives a thin layer of plaster and paint as finish. The total thickness of the plaster up to the cane is 0,06 m (Fig. 6a and 6b). At first glance and for the uninitiated, a wall of this thickness gives the impression of being made of a more solid or heavier material than what it is, providing a sensation similar to that of an adobe wall. With this thickness, when opening a door it remains within the limits of the spillway of the entrance, which fundamentally means a different
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perception of the space of a room. Here the shape and characteristics of the double quincha come into value, being wider than the usual simple one, and therefore perceptible as solid and more easily concealed as a more prestigious material.
Fig. 6. a. Plastic 1/10 scale of double quincha wall. b. Double quincha construction detail. Own elaboration, 2022.
3.2 Thermal Performance Analysis (Case Study 2) For the analysis, two types of commercial software have been used: Opaque and Design Builder. With the first, the thermal properties of the historical components (adobe t = 0,44 m; simple quincha t = 0,12 m; and double quincha t = 0,33 m) and the contemporary ones (brick masonry t = 0,15 m and concrete plates t = 0,12 m) were compared. With the second, a thermal simulation has been carried out under conditions of summer and winter to compare a second-floor room on the façade with a double quincha (Fig. 7a) and another with a simple quincha, both with a simple-layer mud roof. The simulated environment for the Opaque analysis was designed with a height from floor to ceiling of 4,20 m. The window has a wooden frame with simple transparent glass closure (t = 0.006 m) and no sill. It is oriented with a view to the East, rotated 33° to the South (Fig. 7b). The use of the environment is an exhibition or meeting room, without the presence of electrical equipment of any kind, or heating, or air conditioning, only the presence of people. The weather registered for Lima’s Jorge Chávez Airport was used (EPW, nine kilometers east of the Historic Center of Lima). March 5–11/August 19–25 were the date ranges used for summer and winter, respectively. Interior curtains were considered when the temperature was above 20 °C, 30% window opening capacity, the infiltration level was set at 2 air changes per hour (air tightness). Finally, the natural ventilation factor was considered, but taking into account that windows are closed below
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Fig. 7. a. Typical room dimensions. b. Geometry of O ‘Higgins’ house, in De la Union street, in the Design Builder program. Own elaboration 2022.
24 °C. Which gives a ventilation capacity up to 10 cah according to requirements. The floor and side walls are adiabatic surfaces, through which there is no heat exchange.
4 Results and Discussion The number of double quincha walls found in the buildings of the block under study does not correspond to the common idea of its relative scarcity. It is a very important quantity with respect to the total, to the point of being possible to consider double quincha the majority of the walls preserved. Its constructive characteristics would allow us to understand that these are standardized products to a certain extent and rather common in the range of options of viceroyalty architecture. For the cases studied, it is not possible at present, due to the absence of exact records and documentation, to understand if they come from the same historical moment. Table 1. Thermal properties of components (wall and roof). Own elaboration 2022.16 Wall
Thermal Transmittance (U-Value) W/m2 ·K
Decrement factor
Time lag (h)
Adobe
1,070
0,07
7,11
Viceroyal Quincha
1,563
0,74
4,59
Viceroyal double Quincha
0,778
0,40
9,50
Brick
2,183
0,79
3,98
Concrete
4,245
0,77
3,39
Mud cake (roof)
1,494
0,62
5,20
16 Software calculated OPAQUE 3.0. A U-value, Time Lag, and Decrement Factor calculator
opaque wall or roof surfaces. https://www.sbse.org/resources/opaque
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The thermal properties of the materials and the thicknesses of the components suggest great differences (as can be seen in Fig. 11) regarding the thermal performance of the five hypothetical walls considered in detail. From the results of thermal transmittance (insulation capacity), decrease factor (dampening capacity) and delay time (delay capacity), a significant improvement of the double quincha compared to the simple one is evident in the three aspects. Compared to adobe, the double quincha presents similar features in terms of thermal inertia and delay time, but the thermal inertia of adobe is much higher due to its great mass. Finally, the simple quincha, and to a greater extent the double quincha, have an insulation capacity far superior to contemporary construction options. (Table 1 and Fig. 8).
Fig. 8. Thermal transmittance and decrement factor of wall types. To the left more insulation, to the right more thermal inertia. Own elaboration 2022.
Assigning the properties described in the single and double quincha walls within the dynamic thermal simulation software (Design Builder), and considering the other conditions previously presented (climate, geometry, use, ventilation and infiltration), the results show operating interior temperature conditions very similar between both types of wall. This situation occurs both in the warmest week of summer and in the coldest week of winter. In summer, in the hottest hours, the temperatures inside the environment with a double quincha are slightly lower compared to those with a simple quincha, but the difference is very small, around 0.20 °C and 0.30 °C. In winter, at the coldest time, the double quincha allows higher internal temperatures, but again with quite low values, between 0.30 °C and 0.40 °C. In both situations, the incorporation of the double quincha compared to the simple one is not decisive. Considering the average temperature values of the analyzed weeks, 23.85 °C in the warmest and 16.46 °C in the coldest, taking into account the adaptive thermal comfort
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method validated by ASHRAE and using the CBE Thermal Comfort Tool17 online resource, it can be deduced that the thermal comfort limits in summer to satisfy 80% of the users are between 21.7 °C and 28.7 °C; in winter between 19.4 °C and 26.4 °C (Fig. 9). In the case of summer, both the simple and the double quincha allow comfortable conditions, although very close to the upper limit, while in winter, both constructive solutions do not ensure minimum thermal comfort conditions, since temperatures tend to be almost everywhere below, but close to, the lower limit of the comfort limit. Beyond the material of the wall, the other elements of the envelope and the high degree of infiltration of the construction explain these results in winter.
Fig. 9. a & b: Comparative graphic of outside and inside temperatures in summer and winter in the cases studied, Design builder program. Own elaboration 2022.
17 Tartarini, F., Schiavon, S., Cheung, T., & Hoyt, T. (2020). CBE Thermal Comfort Tool: Online
tool for thermal comfort calculations and visualizations. SoftwareX, 12, 100563.
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5 Conclusions Double quincha was more prevalent than is commonly understood in large Lima residences. The little knowledge of its specificity in the general literature suggests that it was grouped with the simple quincha and, perhaps, even indicates a certain contempt by specialists given its perceived precariousness. The greater width of the double quincha could also serve to hide its nature, in line with the viceroyalty’s intention to hide a material not considered “noble”. The thermal benefits of the double quincha wall are superior to those of the simple quincha, and both exceed those presented by the walls currently built in the city of Lima. The better thermal performance of the double quincha shows a slightly better thermal performance compared to the use of the simple version, but said improvement is not relevant both in summer and in winter in a city with few annual temperature variations. The additional conditions of traditional buildings, such as the density and the properties of the other exposed surfaces, in addition to the little rigor of the Lima climate, explain the low impact of the wall material on the final results. Additionally, it is important to highlight the fact of urban compactness in Lima: the rooms, except for the roof, have few surfaces exposed to the outside, which helps to cushion the interior from a climate that is devoid of large thermal oscillations. At present there are not enough studies comparing the structural resistance between the two versions of quincha studied, but in terms of architectural space, the double version is clearly perceived as more solid, perceptibly denser and aesthetically more sensorially satisfying. More research will be necessary to understand if these factors actually played a determining role in their use in the historic city.
References 1. Cobo, B.: Obras del Padre Bernabé Cobo de la Compañía de Jesús. Historia del Nuevo Mundo - Fundación de Lima, I y II. Biblioteca de Autores Españoles, Madrid (1653 [1956]) 2. Crespo Rodríguez, M.D.: Arquitectura doméstica de la Ciudad de los Reyes (1535-1750). Sevilla: EEHA, CSIC, Universidad de Sevilla, Diputación de Sevilla (2006) 3. Gunther Doering, J.: Planos de Lima, 1613–1983. Municipalidad de Lima Metropolitana: Petróleos del Perú (1983) 4. Marussi Castellán, F.: Antecedentes históricos de la quincha. Documento técnico del Instituto Nacional de investigación y normalización de la vivienda ININVI (1989) 5. Pacón Lung, M.C., Velarde López, C.: La profesionalización de la mano de obra como principio de una adecuada praxis en conservación - Lima. Universidad Ricardo Palma, Facultad de Arquitectura y Urbanismo. Tesis de Bachiller dirigida por el arquitecto E. Gastelumendi, Lima: (inédita) (1989) 6. Pérez-Mallaína Bueno, P.E.: Retrato de una ciudad en crisis. La sociedad limeña ante el movimiento sísmico de 1746. Sevilla: CSIC-EEHA-Instituto Riva-Agüero (2001) 7. Suito, G.: La vivienda limeña y elementos característicos durante los siglos XVI, XVII y XVIII. Universidad Nacional Federico Villareal, Programa de Arquitectura y Urbanismo, Tesis de Bachiller dirigida por el arquitecto A. Linder, Lima: (inédita) (1971)
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8. Torrealva Dávila, D., Vicente Meléndez, E.: Experimental behavior of traditional seismic retrofitting techniques in earthen buildings in Peru. In: Proceedings of the SAHC 2014 9th International Conference on Structural Analysis of Historical Constructions, Mexico City, Mexico, 14–17 October 2014, Breslavia, Poland (2014) 9. Wieser, M., Onnis, S., Meli, G.: Conductividad térmica de la tierra alivianada con fibras naturales en paneles de quincha. Proceedings of the SIACOT, pp. 199–208 (2018)
Exploration on the Original Architecture of a Vernacular Workshop in East Sichuan Basin of China Bowen Qiu1
, Chi Jin1 , Lingyan Xu1 , Yongkang Cao1,2,3 , and Qian Du1,3(B)
1 International Research Centre for Architectural Heritage Conservation, Shanghai Jiao Tong
University, 601 Huadin Tower, 2368 West Zhongshan Road, Xuhui District, Shanghai 200235, China [email protected] 2 Chongqing Research Institute, Shanghai Jiao Tong University, 5/F 598-A2 Liangjiang Avenue, Yubei District, Chongqing 404100, China 3 School of Design, Shanghai Jiao Tong University, 800 Dongchuan Road, Minhang District, Shanghai 200240, China
Abstract. Q¯ıuji¯a Zhàcaì Zu¯ofang was a vernacular building cluster in East Sichuan Basin of China with a history of more than a century. A Siheyuan quadrangles of the cluster, called as Shàngyuàn, was alternated and finally demolished after mid-20th century. The aim of this research was to define and reason the status of Shàngyuàn after its original finish and before demolition. As a result of this research, the history of the building cluster was first clarified. Architecturally, the historic length measurement system adopted to construct Shàngyuàn was defined, and the original architecture of Shàngyuàn around 1900s and before demolition were reasoned. This research was an application of existing study and theory about the vernacular buildings in Sichuan Basin and showed a methodology to verify historic building archives for built heritage conservation projects. It also provided a feasible approach to reason original building for the remains of Szechuan vernacular buildings, especially for those lacking reliable archives or photos. Keywords: Archaeotecture · Original Design Research · 20th Century Heritage · Vernacular Building · Archaeology Site
1 Introduction Q¯ıuji¯a Zhàcaì Zu¯ofang (literally The Qiu’s Zhacai Workshop) is a late-Qing Dynasty vernacular building cluster in Fuling, Municipality of Chongqing, China. The cluster is consisted of two parts – Shàngyuàn (literally Upper Courtyard) and Xiàyuàn (literally Lower Courtyard), among which Xiàyuàn is a single building being preserved while Shàngyuàn is a Siheyuan (Chinese quadrangles) being completely demolished in the past decades. Historical records showed that Shou’an Qiu, the inventor of the world-famous pickle Zhacai, used to live and to produce Zhacai at the workshop. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 655–668, 2024. https://doi.org/10.1007/978-3-031-39450-8_54
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This research aimed to clarify the changes of Shàngyuàn from its origin design to alteration and demolition over 20th century based on historical documentation and archaeological discovery. Cross-verification among various sources of information was precisely conducted, in order to clarify the status of Shàngyuàn in different eras in 20th century.
2 Social and Historical Context of the Site Q¯ıuji¯a Zhàcaì Zu¯ofang was located at a hillside field of the right bank of Yangtze River in western part of the town of Fuiling. This mountain area was considered as the east end of Sichuan Basin, where it shared similar climate and culture with the rest of the Basin. The traditional buildings in Fuling were in typical Szechuan style, usually adopting characteristic Chu¯andˇou timber frame Structure and unnoticeably-curved or non-curved roof. This was the most characteristic feature of Szechuan vernacular building. The design and layout of Szechuan vernacular buildings were also in a freer style than the ones in Central and East China as lacking flat ground in the Basin [1]. Buildings were typically built with stone and earth base, timber frame and earth or brick wall [2]. Q¯ıuji¯a Zhàcaì Zu¯ofang was built in late 19th century, but the exact year of construction remained unknown. Local chronicles of Fuling indicate that the owner of this building cluster – Shou’an Qiu – invented and manufactured Zhacai at the workshop in 1898 [3]. This reveals that the construction of Q¯ıuji¯a Zhàcaì Zu¯ofang shall not be later than then. In the coming decades after Qiu invented Zhacai, the workshop was once the only place producing this popular pickle. Q¯ıuji¯a Zhàcaì Zu¯ofang was the house of the Qius’ family and business. The building cluster continued owned by the Qius after Shou’an’s death in the Republican Era. By entering the second half of 20th century, the building cluster was allotted to local people as a result of Socialism revolution, and the Qius continued living at a part of the cluster. Alteration to the building occurred, due to the shortage of space caused by excessive number of residents living inside the cluster. In 1960s, the originally opened gateway hall of Shàngyuàn was walled with earth bricks to create more interior space. Two Zhacai cellars were also dig in the building – as the local residents at the community narrated. Nevertheless, the quadrangles layout of Shàngyuàn remained. Satellite images indistinctly showed the origin layout of the cluster, with a courtyard at the centre. From 1970s to 1990s, massive alteration was applied to Shàngyuàn. Survey drawings conducted in 1997 showed contemporary intervention to the main hall. It is found that there were considerable differences between the status of Shàngyuàn to typical Szechuan traditional building style and the demolition of the west wing building. In the coming decade, the remaining parts of Shàngyuàn – main hall, east wing building and gateway hall – were gradually demolished. Shàngyuàn was not shown in the satellite image captured in 2010, and newspaper article published in 2013 recorded the complete loss of Shàngyuàn [4]. By 2020, archaeologist excavated the site of Shàngyuàn. The origin quadrangles layout was clarified, and the longitudinal bays (K¯aiji¯an) of the building were clearly discovered and positioned. Two cellars were also found at the site of gateway hall, verifying the credibility of oral history narrated by the current residents from local community.
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3 Understanding of Information 3.1 Available Information Though Shàngyuàn had no longer existed, information and documentation about the building cluster were discovered. Base on available primary sources – including archaeological discovery, survey implemented in 1997, photos, oral history and article records, etc. – it was possible to reveal the origin and change of this building cluster in the 20th century. Other supplementary materials, such as other local vernacular buildings and relevant academic research, were also referred to fill the gap of information among primary sources. Archaeological Discovery. Archaeological excavation of Shàngyuàn was conducted from 22 December 2020 to 24 January 2021, covering an area of 1600 square metres. The work confirmed the quadrangles layout of Shàngyuàn: the site consisted of main hall, east and west wing buildings, gateway hall, front steps, drainage, etc. Building foundations were built with rammed earth enclosed with strip stones, among which the foundation of main hall’s central bay was well preserved (Fig. 1). Alteration to the buildings after 1950 were also discovered by excavation work. Two Zhacai cellars were found at the northwestern part of the site, with lime-treated surface and approximate 0.6-m spacing in between.
Fig. 1. Drone image and plan of Shàngyuàn archaeology site (Provided by Fuling District Committee of Culture and Tourism)
Drawings of 1997 Survey. Survey of Q¯ıuji¯a Zhàcaì Zu¯ofang was implemented in January 1997. The survey drawing set provided a general plan for Shàngyuàn and Xiàyuàn, 9 views of Shàngyuàn buildings, and 8 views of Xiàyuàn. The content of the drawing set is summarised in Table 1. The west wing building of Shàngyuàn was marked as destructed on the general plan. By cross-verifying the measurements on the drawings and comparing them with archaeological discovery, it was obviously found that there were errors and mistakes on
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Cluster and Building
Drawing
Shàngyuàn Main hall
Plan, front elevation, back elevation, left-side elevation, cross section
East wing building
Plan, front elevation, left-side elevation, cross section
West wing building N/A Gateway hall
N/A (cross section contour shown on the front elevation view of the east wing building)
Xiàyuàn
1/F plan, G/F plans, front elevation, back elevation, left-side elevation, 2 cross sections, element details
Others
General plan for both building Shàngyuàn and Xiàyuàn
the drawings. Nevertheless, this drawing set was the only properly conducted measurements of Shàngyuàn, and it provided the general image of the cluster before its complete loss. Historic and Satellite Photo. There was only one historic photo (Fig. 2a) of Shàngyuàn found, directly indicating the details about the gateway hall in 1990s. It not only recorded the stone front steps of the cluster, but also revealed the detail about the materials and structure of the gateway hall. The elevation measurements of the gateway hall can also be speculated by scaling the photo with archaeology site. This filled the information gap about gateway hall of 1997 survey. Moreover, it also showed the dark grey tiles on the main hall as well as the intersecting roof between the main hall and east wing building, through the gateway on the photo. Apart from historic photo, satellite images also showed the changes of site in the second half of 20th century. In 1960s, American satellite system The Keyhole captured a series of images of Fuling. These images were declassified in 1990s and available on United States Geological Survey (USGS) website. The earliest Stereo High image available online was taken on 25 March 1971, with resolution about three metres on the ground (Fig. 2b). Although the image was still not clear enough to tell the appearance of roof, it still expressed the quadrangles layout of Shàngyuàn, whereas another satellite photo captured on 22 October 2010 by Maxar Technologies showed that the building cluster was completely disappear. Combining the records of 1997 survey, it can be assumed that the quadrangles layout had been kept until Shàngyuàn’s complete loss between 1997 to 2010. Oral History and Published Article. The impression and records by local people were important clues to understand the past of the site. Local cultural heritage authority had collected the narratives about the site from the olds from local community and descendants of the Qius. Local media Chóngqìng Zhèngxié Bào also reported the loss of Shàngyuàn in 2017, with a photo showing the status of site [4]. Apart from these primary sources mentioned above, there were other sources of information could be referred to understand the design and style of Shàngyuàn, such as
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(a) Historic photo of Shàngyuàn’s gateway hall (Provided by Fuling District Committee of Culture and Tourism)
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(b) Keyhole satellite image of the site (Entity ID: DS11141006DA045, available on USGS website)
Fig. 2. The historic photo and satellite image of Shàngyuàn
other vernacular buildings in Fuling and relevant publications about Szechuan vernacular buildings.
3.2 Priority of Acceptance Priority of acceptance was set for the available sources of information according to their credibility. The layout, plan, structural frame, location of columns, roof style, building elevations and building elements were the objectives to be clarified, in order to understand the buildings of Shàngyuàn. The priority of acceptance for each objective was summarised as Table 2. Table 2. Objectives and corresponding priority of acceptance of information source Objective
Priority of acceptance
Layout
[1]>[4]>[5]>[6]>[8]>[9]
Plan
[4]>[5]>[6]
Structural Frame
[4]>[5]>[8]>[9]
Location of columns
[4]>[5]>[8]>[9]
Roof style
[5]>[8]>[9]
Building elevations
[3]>[5]>[8]>[9]
Building elements
[5]>[8]>[9]
Note: [1] The Keyhole satellite photo captured in 1971; [2] Maxar satellite photo captured in 2010; [3] Historic photo; [4] Archaeological discovery in 2020; [5] Drawings of 1997 survey; [6] Oral history; [7] Published article; [8] Examples of local vernacular building (eg. the building of Xiàyuàn); [9] Publications about Szechuan vernacular buildings
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3.3 System of Length Measurement The system of measurement for building construction varied in ancient China, especially for vernacular buildings. To define which system was applied to Shàngyuàn was the preliminary step to understand building dimensions. The main Chinese traditional length units were zhàng, chˇı, cùn and f¯en, with conversion relation of 1 zhàng = 10 chˇı = 100 cùn = 1000 f¯en. The length measurement system for Shàngyuàn could be either the official Yíngzàochˇı Kùpíngzhì system, carpentry system (Mùg¯ongchˇı) or Lˇub¯anchˇı (Wéng¯ongchˇı). Carpentry system and Lˇub¯anchˇı varied according to region. Documents, publications and evidences showed that there were five possible lengths of chˇı for this research [5]. In the building practice, quarter, half and integer were the common digits used for length [5]. The possibility of each length of chˇı could be evaluated through dividing dimensions on the archaeology site by every quarter chˇı. Equation (1) defined the standard deviation of clearly positioned dimensions (Table 3) on the site floating on the multiple of quarter chˇı. It enabled to quantitatively define the most likely length of chˇı for this research finding the minimum standard deviation [6]. 2 4L 4L i=1−n x i − x i (1) σ = N in which Li was the dimensions on the site, x was the length of 1 in each system, and N was the number of dimensions on the site which was 8 in this case. The minimum result occurred when one chˇı equalled to 320 mm (Table 4), so that 320 mm was the one-chˇı length that dimensions on the site were closest to the multiple of quarter chˇı. Hence, it could be confirmed that the official Yíngzàochˇı Kùpíngzhì system was applied to Shàngyuàn, and 320 mm is the length of chˇı for this research. Table 3. Dimensions for calculation Building of Shàngyuàn
Dimension
Measurement (mm)
Main hall
Central bay
4639
East secondary bay
4313
West secondary bay
4725
East end bay
5152
East wing building
West end bay
4708
Front elevation to back elevation
6221
Central bay
4508
South secondary bay
3600
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Table 4. Possible length measurement systems and corresponding standard deviation calculated System of length measurement
Length of 1 chˇı in metric system (mm)
Standard deviation
Official system (Yíngzàochˇı Kùpíngzhì)
320
0.248
Carpentry system (Szechuan Region)
301
0.331
Carpentry system (Chengdu Region)
318
0.204
Lˇub¯anchˇı (discovered in Lizhuang, Sichuan)
433
0.277
Lˇub¯anchˇı (collection of the Palace Museum, Beijing)
460
0.287
4 Reasoning of Historic Appearance The historic appearances of Shàngyuàn both in 1990s and around 1900 was reasoned in this research. The appearance in 1990s was the one that could be directly reasoned from the sources of information but was with contradictions to typical vernacular building style in Fuling. Based on it, an appearance without those contradictions was reasoned which was believed as the original status of Shàngyuàn around 1900. 4.1 Historic Appearance in 1990s From the history clarified of Shàngyuàn, the cluster was intervened after the moving in of exceed residents in 1960s, and gradually demolished before 2010. The archaeology excavation in 2020 and survey in 1997 provided details about the building cluster, which made it possible to reason the status of Shàngyuàn in 1990s. Layout. The layout of Shàngyuàn was clear, and it reflected the adaptation to its local geography. Survey drawings and archaeological discovery, as well as historic satellite image, showed that Shàngyuàn was in a quadrangles layout facing towards northeast. The central axis of the quadrangles was approximately 15° east-northeast. The cluster was built on several stone-enclosed terraces on the hillside. The main hall was at the highest location, whereas that of the gateway hall was at the lowest. Stone front steps were laid at the entrances of each building. The altitude of Shàngyuàn was between 203.89 m to 205.16 m above sea level. Drainage was laid at the southwestern, southeastern and eastern sides of the site. Plan. The plan of the buildings could be clarified based on the 2020 archaeological discovery and 1997 survey drawings. Nevertheless, contradictions between these two sources of information were found by overlapping the plans (Fig. 3). Rectangular plan of main hall was expressed on the survey drawings, whereas the plan was found in right-angled trapezoid as the excavation outcomes. There were also several parts that
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the contours on survey drawing lay beyond the edge of the site (marked with red dashed lines on Fig. 3), and the footprints of column on the survey drawing were not located on the plinths (Zhùchˇu) (marked with yellow dashed lines on Fig. 3). Considering the survey instruments were less accurate and errors of survey were found by cross-verifying the survey plan and elevations, the excavation outcomes were believed more credible than survey drawings. The excavated footprint on the site was considered as the primary source the define the general plan of Shàngyuàn.
Fig. 3. Overlapping drawings of 2010 archaeological discovery (in black) and 1997 survey (in blue)
As the excavation only provided the approximate location of the building contours and longitudinal bays, the dimensions of building contours and bays were going to defined as the multiple of integral or half cùn, which was the multiple of 16 mm (Fig. 4). The location of columns would be defined according to the structural frame of the buildings. Structural Frame. The structural frame of buildings was defined mainly according to the drawings of 1997 survey, as this information could not be acquired from archaeology discovery. Historic photos and other vernacular buildings in Fuling, especially Xiàyuàn, were also referred to. Main Hall. The structure of the main hall was defined by the section view among the survey drawing. The building was a timber-earth structure, whose timber frame was with 6 purlins and 6 columns and back elevation was built with rammed earth. The ridge was at the third purlin from front elevation (Fig. 5a). East Wing Building. There was the section view of east wing building in the survey drawing set, showing the building was a timber structure. Its timber frame was with 8 purlins and 8 columns, and the ridge was at the fourth purlin from front elevation. There was also a gallery at the back of the building. However, archaeology excavation showed the east wing building was located at a two-level terrace with difference of
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Fig. 4. Dimensions of building contours and bays overlapping on archaeology excavation plan (unit: f¯en = 3.2 mm)
approximately 1.28 m in height. This was different from the single-level terrace base on the survey drawing. Considering the back elevation on survey drawing was beyond the footprint of east wing building, excavation outcomes were considered more credible than the drawings. The back part of east wing building was reasoned as stilted building (Diàojiˇaolóu) by referring to the examples of local vernacular building (Fig. 5b) [7, 8]. Gateway Hall. There was no purposed drawing for the gateway hall, but there was a section contour on the elevation of east wing building. It revealed that there were six purlins in the building, and the ridge was at the third purlin from front elevation. Historic image showed that the gateway hall was a timber-earth structure, whose rammed earth brick wall did not reach the eaves and upper part was timber-framed (Fig. 5c). West Wing Building. No drawing of the west wing building was discovered because of its early loss. The structure of the west wing building was defined as timber structure by referring to the east wing building. The frame was believed as 8 purlins 8 columns in order to keep similar spacing between two purlins and fit the footprint of the building, and the ridge was at the central purlin. The slope of roof was defined as 25° as same slope was adapted to the other buildings of Shàngyuàn and Xiàyuàn (Fig. 5d) [2].
Fig. 5. Section views of the Shàngyuàn buildings in 1990s
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Location of Columns. As the number of columns had been defined by structural frames, the columns could be therefore positioned on the plan. By compromising the data of survey drawing, the integral length of Yíngzàochˇı Kùpíngzhì and the location of the plinths on the archaeology site, the location of columns of Shàngyuàn could reasoned as Fig. 6, with data summarised in Table 5.
Fig. 6. Location of columns
Table 5. Dimensions of the column location Building
Purlin-to-purlin spacing (transversal bay)
Dimension in chˇı
Dimension in metre
Main hall
All
3.690
1.180
East wing building
1st and 3rd from front
4.200
1.344
3.900
1.248
4th , 5th and 7th from front 4.050
1.296
elevation 2nd from front elevation elevation 6th from front elevation
3.750
1.200
Gateway hall
All
2.600
0.832
West wing building
All
3.500
1.120
Particularly, the dimension of the gateway hall’s central bay was estimated as 6.500 chˇı (2.080 m) according to the timber columns indistinctly showed on the historic photo.
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The three columns placing at the area of Zhacai cellars shall be shelved on the transversal tie-beams (Chu¯anfˇang) rather than plinth on the ground. Roof Style. The roofs of the building were double-pitched according to the survey and local vernacular building examples [2]. The roof of the main hall and two wing buildings were open gable roof and semi-intersected with each other, while the roof of gateway hall was fully intersected with the two wing buildings. Building Elevations and Elements. The building elevations and elements were mainly referred to the survey drawings, compromising with the integral dimensions in Yíngzàochˇı Kùpíngzhì and avoiding contradiction with the reasoning above. For example, the diameters of columns were recorded as 220 mm on the drawings. In this case, it was adjusted to 224 mm in order to ensure the integral dimension of 7 cùn. The historic appearance of Shàngyuàn in 1990s was reasoned as estimated as shown in Fig. 9a. 4.2 Historic Appearance Around 1900 There were three contradictions between the status of Shàngyuàn in 1990s to the style of local vernacular buildings. Firstly, the ridge of the main hall was lower than the two wing buildings, which did not meet the hierarchy of the buildings of a typical Siheyuan. This also led the irregular semi-intersection among the main hall and wing buildings. Secondly, openings at the back elevation of the main hall were not the traditional way of local building. Lastly, the plan and elevation of the gateway hall did not follow the style and function of a traditional gateway hall of a Siheyuan. Apart from the intervention being narrated by oral history about the gateway hall after 1950s, there was no clarified evidence indicating these contradictions to traditional style was either the original style of Shàngyuàn or a result of later alternation. Nevertheless, according to the building hierarchy of Shàngyuàn and the social class of the Qius, it was assumed owing to alternation. These contradictions were therefore removed and corrected into traditional ways for Shàngyuàn status around 1900. Specifically, the ridge of the two wing buildings were first lowered to ensure the correct hierarchy and traditional full roof intersection among the buildings. The ridge of east wing building was moved to the third from front elevation purlin rather than the forth one (Fig. 7a). The transversal size of the west wing building and its number of purlin were respectively decreased to 21 chˇı (6.72 m) and six; its ridge was at the third purlin from the front elevation (Fig. 7b). Secondly, the openings on the back elevation of the main hall were removed and the back elevation was an entire rammed earth wall. Thirdly, the gateway hall was changed into timber structure and open space (Fig. 7c). The partition of internal and external space of the quadrangles was a hollow-spaced brick wall (K¯ongdˇouqiáng), with Mˇacáodˇou bonding of 2 cùn by 4 cùn by 8 cùn traditional grey brick. The entrance of the quadrangles was octagonally retracted, so called as Yànw¯o (literally Bird’s Nest), with a Shícháomén gate, according to local building examples [2] and oral history. Lastly, all of the columns in the gateway hall were placed on the plinths on the ground, as the two Zhacai cellars did not exist around 1900 (Fig. 8). As a result of these correction from reasoned 1990s status, the historic appearance of Shàngyuàn around 1900 shall be as Fig. 9b.
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Fig. 7. Section views of the Shàngyuàn buildings around 1900
Fig. 8. Plan of Shàngyuàn around 1900
(a) Status in 1990s
(b) Status around 1900
Fig. 9. Imagery of Shàngyuàn in 1990s and around 1900
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5 Discussion and Conclusion As a result of this research, the measurement system to construct Shàngyuàn was found. The original architecture of Shàngyuàn around 1900 and in 1990s were reasoned. It was originally built as a typical Shiheyuan quadrangles in Szechuan style. Alternation of design and material was implemented to the building because of the change of ownership and society after the mid-20th century. Shàngyuàn was finally demolished in several phases during the decades around the millennium. The research was an application of existing study and theory about the vernacular buildings in Sichuan Basin and showed a methodology to verify historic building archives for built heritage conservation projects. Errors on the drawings of survey conducted in 1997 were discovered through cross-verification among the archives and information collected. An approach to reason the original building for remained building cluster or archaeology site was drawn. Starting with collecting all available information, the information was cross-verified and accepted based on its credibility. Defining the historic measurement system applied to the building’s construction was a critical step to define the precise dimensions. It can be clarified by comparing existing dimensions on the site with the multiple of basic length in the possible measurement systems. In this case, quarter chˇı was considered as the basic length according to previous studies. By defining these aspects of information, an imagery of original building could be proposed. This proposed imagery would finally be compared with similar building examples to distinguish the effects of later alternation. Particularly for vernacular buildings, this comparison was important for reasoning the origin design because of lacking building codes. The outcomes of this research were completely based on the information collected. As a vernacular building devalued in the past decades, there were only few documents and archives available for Q¯ıuji¯a Zhàcaì Zu¯ofang, especially for the demolished Shàngyuàn. Several aspects of the reasoned imagery were based on single evidences, which were not strong, or estimation. As more information about the site would occur in the future, such as more high-resolution satellite images declassified, the outcomes of this research shall be verified and might require further correction. Acknowledgments. This research was supported by the Ministry of Education of China under 2020 Youth Fund for Humanities and Social Sciences (20YJCZH024, 材料与工艺 演变视角下的我国近现代混凝土建筑保护与修复研究) and the Chongqing Municipal Committee of Science and Technology under 2022 Municipal Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1377, 山地湿热环境下历史建筑混凝土材料病害机理研 究). The authors also appreciate the support and assistance to this research provided by Fuling District Committee of Culture and Tourism, Municipality of Chongqing, China.
References 1. Wu, Y.: Research on Regional Characteristics of Bashu Traditional Building. Chongqing University, Chongqing (2007) 2. Li, X.: Sìchu¯an Mínj¯u. China Architecture and Building Press, Beijing (2009)
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3. Compilation Committee of Chronicles of Fuling City Sichuan Province: Chronicles of Fuling City Sichuan Province. People’s Publisher of Sichuan, Chengdu (1995) 4. Xia, F.: Qi¯uji¯a Dàyuàn - Fúlíng Zhàcài cóng Zhèlˇı Zˇou xiàng Shìjiè. Chóngqìng Zhèngxié Bào 2017-3-21, 3. Chóngqìng Zhèngxié Bàoshè, Chongqing (2017) 5. Li, Z.: Standard-ruler, construction-ruler and Luban-ruler - study on the length unit used for ancient Chinese buildings. Hist. Archit. (01), 15–22 (2009) 6. School of Archaeology and Museology Peking University: Chóngqìngshì Héchu¯anq¯u Diàoyúchéng Fànji¯ayàn Yízhˇı Jiànzhù Fùyuán Yánji¯u Bàogào. Peking University, Beijing (2018) 7. He, L.: The Han Nationality Regions in Sichuan Traditional Dwellings Wooden Construction Characteristic Research. Southwest Jiaotong University, Chengdu (2013) 8. She, H.: A Research on Regional Characteristics of the Timber Frame of the Traditional Architecture in Bashu. Chongqing University, Chongqing (2015)
Management of Urban Areas by Preserving the Historic Roofscapes and Timber Traditional Building Technologies Emanuel I. Tamas1,2(B)
and Alexandra I. Keller2
1 Doctoral School of Urban Planning, “Ion Mincu” University of Architecture and Urban
Planning, Academiei 18-20, 010014 Bucharest, Romania [email protected] 2 Department of Architecture, Faculty of Architecture and Urban Planning, Politehnica University Timisoara, Traian Lalescu 2A, 200223 Timisoara, Romania
Abstract. The urban landscape appears as a synthesis between perspective, recognisable shapes, and repetitive and interpretable details. The connection between urban planning, built heritage, and the preservation of urban landscapes and historical building techniques represents one of the most important components when approaching new urban developments in historic areas and interventions in heritage buildings. Based on this, a study was conducted in Timisoara, Romania, a city with a wide variety of heritage areas. Despite this, there have been a series of difficulties regarding the protection and management of these sites, one of the main causes being aggressive new developments in/close to those sites, leading to the loss of highly valuable buildings, but also complex historic construction techniques. Regardless of these interventions in heritage areas, roof structures in Timisoara tend to be overlooked, leading to intact roofscapes around the city. Therefore, taking into account that the roof, not just as a part of a building but as an element of the urban landscape, the study highlights that all elements are interconnected, and none can be approached without taking the others into consideration when developing proper management plans for heritage buildings and historic urban areas. In addition to this, context-related decisions taken in the past also affect the general layout of the roof structures ultimately influencing the considered joined details. Keywords: Heritage perception assessment · Traditional construction techniques · Roof · Roof structures
1 Introduction To ensure that future urban developments are harmonious and respectful of the existing built environment, a connection must be made between urban planning, built heritage, preservation of urban landscapes and historical building practices [1]. This relationship is crucial when dealing with interventions in historic structures and other places where © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 669–682, 2024. https://doi.org/10.1007/978-3-031-39450-8_55
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the preservation of the built environment is important [2–4]. In many cases, preserving the historical and cultural significance requires maintaining its original architectural components and building materials [5]. Unfortunately, roof structures are frequently disregarded despite the significance of maintaining historic buildings [6, 7]. Roofs are essential components of a structure’s architectural legacy because they enhance the building’s overall aesthetic, spatial quality, and cultural relevance [8–11]. To preserve the integrity of heritage buildings and stop the loss of significant architectural aspects, roof structures—including their materials, forms, and details—must also be preserved. Roofs are frequently overlooked since it is thought that since they are hidden from view, maintaining them is not necessary. However, roof constructions can frequently be seen from the street and add to the city’s overall identity [12]. Losing significant historical elements and changing the building’s overall appearance can happen if roof structures aren’t preserved. The cultural and architectural legacy may suffer as a result. Engineers, urban planners, and architects must approach historic preservation holistically, including the roof structures, to avoid this from happening. This requires a thorough comprehension of the building’s historical and cultural significance, as well as an appreciation for their contribution to the overall aesthetics of the building and the city.
2 Interdisciplinary Assessment of Roofs-Roof Structures and Their Context The assessment will be conducted mostly through an engineering and an urbanistic point of view, taking into consideration aspects that both influence and are influenced by another that will offer us a more detailed understanding of how the built environment can affect a structure from the design process and even regarding the construction details. For the study a series of historic roofs and roof structures from Timisoara were analyzed, first based on the way the roof can be perceived from it’s immediate urban context and secondly by assessing how this context is influencing the shape of the roof, the general layout of the roof structure and ultimately its effect on the chosen timber joint types. 2.1 Historic Urban Development When the Habsburg Empire invaded Timisoara in 1716, the existing Ottoman fortress was destroyed, and a new one was constructed on top of it, closely adhering to the Austrians’ norms. As a result, a fortification of the Vauban type is constructed, inside of which is placed a grid of orthogonal streets and corresponding squares. The old structures were gradually torn down so that the stronghold could continue to be used even while it was being rebuilt. As a result, some buildings constructed later on wind up being different sizes and styles from the original ones, genuinely according to the fashion at the time. The role of the newly constructed buildings, the built urban environment, and, accordingly, the choices of the beneficiaries and the architects, will all have an impact on how they look. It will be easy to see how some interventions are
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meant to draw attention to or conceal particular features of some city buildings in this manner. The fortifications surrounding the stronghold lose significance over time and with the development of military technology, respectively, which ultimately results in their demolition. As a result, modifications start to take place in a number of the citadel’s buildings, some of which grow horizontally and others of which add new storeys vertically. For some of the buildings, this required modifying the roof structure, whilst for other buildings, it merely required raising the roof structure over the levels that had just been constructed. 2.2 Perception of Roofs Roof perception in the urban landscape refers to how people perceive or view the roofs of buildings within the city environment. It plays a significant role in shaping the overall appearance and aesthetics of a city, as well as its functional and practical aspects. The way a roof is perceived can be influenced by a number of different characteristics such as the general shape, use of materials, colour of the materials and surroundings. These factors also determine the general aspect of a building and how it blends into the built environment. Taking all this into consideration, we can determine if a certain building was built before or after the neighbouring buildings, if the roof was designed a certain way just because of aesthetics or also had a functional purpose and also if the constructor needed to upgrade the building techniques in order to obtain the requested image of the building. By analysing these factors we can prove that the urban landscape is shaped by a complex interplay of factors including design, materials, visual impact, and context and a well-designed roof can enhance the visual identity of a city, while also providing functional benefits and contributing to the overall atmosphere. 2.3 Roof Structure Types Taking into account the general layout of the roof structures, five different types were identified which are partially related to the period in which the building was built, but also connected to the position of the building in the city and the way the building can be perceived from the pedestrian area (Fig. 1). • The first type is a roof structure without posts and with the complex system of rafters and inner rafters, placed parallel to the rafters, specific for buildings that were built in the 18th century along the streets of the old fortress of Timisoara and in the main religious buildings. • The second type was mainly identified in 19th century buildings and is a queen post structure with an inclined post place almost perpendicular to the rafters. Therefore, this roof structure generally has a lower slope than all other types. • The third type is a typical queen and king post-roof structure, a typology that appeared and was used mainly due to the increasing width of the buildings and the need to increase the height of the roof related to their context.
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• The fourth type of roof structure was specific for the beginning of the twentieth century, usually placed on residential buildings with a higher wall toward the street, therefore exhibiting different slopes toward the two sides of the building. Due to this fact, the roof structures present a series of adapted queen roof structures, with multiple posts, with asymmetric layouts and unusually placed structural elements. • The fifth type of roof structure is characteristic also for the beginning of the twentieth century but for buildings placed in the main urban square of the city. This type of roof structure is similar to type three and four, but in this case specific structural elements for queen and king post roof structures can be identified, which were adapted for the significant height and width of the roof.
Fig. 1. Types and layouts identified in Timisoara
3 Visual Perception, Roof Types, and Construction Details 3.1 Type 1 As a general rule, this type of roof structure has a steep slope regardless of the context in which it was built. Most of the buildings with this type of roof are placed along the narrow streets of the old fortress area, or inside a building block, making it impossible to perceive these roofs from the pedestrian area. This type of roof structure was found above small-scale residential buildings, large-scale public buildings and important religious structures without major differences (Fig. 2).
Fig. 2. Context and perception of buildings with type 1 roof structures
Despite the different way in which these roofs can be perceived from the eye level and the different importance of the buildings, the structures do not show significant differences, exhibiting the same general layout, similar positions of the structural elements,
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and slightly different cross sections due to different widths of the buildings, highlighting therefore the coherence of construction techniques in the 18th century (Fig. 3). The same can also be observed for the joints used, which are exclusively tenon and mortise joints with wooden pegs (Fig. 4).
Fig. 3. Type 1 roof structures
Fig. 4. Type 1 roof structure timber joints
Concerning the timber load bearing system, the roof structure is a complex solution, built in most cases out of oak wood, composed of rafters, inner rafters, tie and collar beam, presenting only in wide span cases a central post in the areas of the main frames. Due to the placement of main structural elements only close to the rafters, the crosssection of all the timber elements is rather significant – reaching to up to 190 × 200 mm for the tie beam and 190 × 290 for the inner rafter for a 12 m span structure, with even more significant cross-sections for more important buildings. Mainly oak wood, from the nearby forest, was used for these types of structures. This type of roof was used in buildings where the perception of the roof was not an important factor. Thus, buildings with this type of roof are mostly hidden inside the neighbourhood, or the roof does not represent a key element of the building’s aesthetics. With the construction technique as a basis, there were no reasons for the constructive details to be modified, nor can interventions be observed only on certain elements to highlight them. As can be seen from the photos taken, the external perception of the building is not affected by the appearance of the roof in any way, nor has the roof undergone interventions to highlight it and include it in the general image of the street or the
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neighbourhood, it remaining an element with the role of protecting the building and not an element with an aesthetic role. 3.2 Type 2 The second type of roof structure is rather peculiar one in Timisoara and was, until now, found in only two buildings, belonging to the same block, initially placed close to the fortress walls. In both cases, the buildings are corner buildings. In both cases, the roof has a rather low slope, compared to all the other types (Fig. 5).
Fig. 5. Context and perception of buildings with type 2 roof structures
The most peculiar feature of these roof structures in the context of Timisoara is the fact that the posts were not vertical like in all the other cases but inclined, almost perpendicular to the rafters. In the area between the posts, the tie beam, and the rafters, a series of additional horizontal and diagonal elements were placed, which form multiple triangles close to the exterior wall area and ensure in this way the transversal rigidity of the whole structure (Fig. 6). The changes to the structural system and use of the two posts is also slightly influencing the cross-section of the timber elements, decreasing, for example the tie beam cross section to 170 × 200 mm. All cross-sections are about 10% lower than in the previous case. Furthermore, considering the history of the city and the importance of the nearby river as a means of trade, softwood was mainly used for these structures, brought in the city by using rafts from other nearby regions. Since this type of roof structure was used for 19th century buildings, changes can be observed in the joining techniques of the timber elements which present a series of tenon and mortise joints but also lap joints due to the fact that in the exterior sides of the structure the timber elements had to pass each other multiple times and a connection between them had to be ensured. In this case, the wooden pegs are no longer used and were replaced with steel fasteners (Fig. 7). Although the structure used for this type of roof is less common, even in this case we cannot say that the visual perception of this element influenced the chosen structural solution. As with the first type of roof, it is rather hidden from the viewer and becomes visible only from a fairly large distance from the building. On the other hand, compared to the other buildings in the neighborhood, the structure used here supports a roof in 4 bays and not in two bays as it exists on the adjacent buildings. Thus, the changes made seem to be more due to the geometry of the roof than to visual perception.
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Fig. 6. Type 2 roof structures
Fig. 7. Type 2 roof structure timber joints
3.3 Type 3 The third type of roof structure can be found mainly above end of the 19th - beginning of 20th century residential or public buildings, which were built in and close around the fortress area, in the proximity of 18th century buildings. Due to this proximity, roof structures for these buildings tend to have a high slope similar to the first type one, but are placed on buildings with a wider span, leading to combined roof structure types (Fig. 8). The most common type of structure used in this period is a combination of a queen post roof in the lower part and an additional king post placed at the top meant to ensure that the timber structure can cover the whole span. Additionally, passing braces are used, which connect the tie beam to the queen posts, the collar beam, and ultimately to the king post, thus forming a series of triangles in the area of the supporting masonry walls. In this way, the load transfer from the rafters to the main load bearing structure can be ensured (Fig. 9). The roof structures have similar height and span as the type 1 ones, but, due to the structural layout, the timber elements also have a slightly decreased cross-section. Similar to type 2, softwood was mainly used for these roofs. Similar solutions for the timber joints as in the case of the second type of roof structure. The analysis of the considered case studies has highlighted that mainly tenon and mortise joints were used for most of the connection, except the intermediate connections to the passing brace, where lap joints were used. Furthermore, since these roof structures cover much longer and wider buildings, scarf joints were also used in the case, mainly in the area of the rafters and purlins. The structures show exclusive use of steel fasteners (Fig. 10).
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Fig. 8. Context and perception of buildings with type 3 roof structures
Fig. 9. Type 3 roof structures
Fig. 10. Type 3 roof structure timber joints
This type is probably the most common we could find. It is a structure used both in places where the roof is not visible from close range, losing the aesthetic value, but also in buildings where the roof represents an important part of the building by bringing it closer to the general look (mostly hight) of the street or block.
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This type usually has a high slope and it probably represented the basic building technique during that period of time. We could not find any different details to be used on this type of structure, nor other interventions to highlight other parts of the buildings. 3.4 Type 4 The fourth type of roof structures are those that are not only purely load bearing systems, but are strongly influenced by the architecture of the building and the way the roof can be perceived from the pedestrian area. In this category of roof structures, asymmetrical systems were included, structures that include vertical and diagonal posts, multiple layers of collar beams, and in most cases also a king post at the upper part, since the buildings have a significant span width (Fig. 11).
Fig. 11. Context and perception of buildings with type 4 roof structures
Peculiar solutions were found in all identified type 4 case studies, mainly influenced by the architecture of the building or the shape of the roof and the way it can be perceived from the pedestrian area. The solutions vary from structures with curved rafters placed towards the street meant to highlight the shape of the roof to completely adjusted structural systems, influenced by exterior walls which are higher towers on the street side. All these context-related factors ultimately change the position of the structural elements of otherwise typical queen post roof structures and lead to the appearance of highly complex, new ones (Fig. 12). In this case, a wide diversity of element cross-sections was identified, with maximum dimensions reaching up to 180 × 200 in the case of the tie-beam. Even rafters have in this case variable dimensions, researching from 80 × 180 mm in the case of complex roof shapes (Fig. 12) to 150 × 150 mm in the case of simple hip roofs. Exclusively softwood was used in for these structures. This type of roof structure is special, not because of the used timber joints, which are also only tenon and mortise joints„ lap joints and scarf joints, but due to the significant number of joints used for each element (Fig. 13) adapted in order to comply to the general layout of the structure. This type of roof clearly shows the influence of visual perception on the building and the fact that the structure has undergone changes to highlight the geometry of the roof, thus transforming it into an integral part of the facade. The changes made to the shape of the roof show the desire to generate a new visual element above the classic facade, an element that continues the architectural style and enriches it, yet without losing its functional characteristics and, respectively, utility. Thus, with this type of
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Fig. 12. Type 4 roof structures
Fig. 13. Type 4 roof structure timber joints
roofs we can observe interventions made towards the street from where the facade is visible, interventions that in some cases have an aesthetic role as well as a functional role, for example, the generation of a vertical wall in continuation of the main facade, in which skylights can be placed for the bridge, thus generating a continuity of the front of the buildings. With this type of roof, we can observe different interventions on certain elements of the structure, intended to help obtain the desired image. The most obvious changes are related to the shape of the rafters, which in some cases become curved and, respectively, elements intended to strengthen the classic structure and provide increased stability in certain areas. 3.5 Type 5 The last type of historic roof structure is the most spectacular and complex of all the analysed case studies. Built at the beginning of the 20th century, starting with major urban developments on the outskirts of the fortress area, these roofs play an important role in defining urban space and the aesthetics of the building they belong to, while their purely functional role is taking a step back (Fig. 14). Roof structures of this type have an oversized height, in order to highlight the importance of the building and increase their monumentality, representing almost a third of the total height of the building. Additionally, since these buildings are part of the whole perception of the urban space, they have complex shapes in plan with rounded or chamfered corners, with different wings which should be highlighted while others remain in
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Fig. 14. Context and perception of buildings with type 5 roof structures
the background. In addition to this, some of the buildings also have additional decorative elements that also had to be supported by the roof structures. All these factors significantly influence the solutions considered for the timber load bearing structures that are rarely of a single typology. Therefore, the analysis of these roofs has highlighted that mainly queen and king post roof structures were used, which were adapted to answer the formal requirements of the roof. This leads to structures that present queen post structures with two consecutive collar beams, necessary due to the significant length of the post, above which an additional king post structure was still necessary. Rounded corners adapt the same solution by simply rotating the main frame structure, while in the case of shed roofs only half of the structure was kept and the second post was repositioned in the wall area in order to transfer the loads from the top of the rafter. Complex solutions were also considered in the areas where different roof shapes had to be joined (Fig. 15). Despite the significant height of these roofs, the cross-section of the timber elements is similar to the other types, highlighting the structural efficiency of the used layouts. Even the posts with a length of about 8.00 m, have a cross-section of 160 × 160 mm, due to the presence of multiple collar braces, significantly lower than in any of the other types. However, despite being complex, similar solutions were found for all the case studies selected for this type of roof structure, showing a coherent approach to solving the formal requirements of the roofs. Similar to the fourth type of roof structure, the timber joints do not present significant changes (Fig. 16).
Fig. 15. Type 5 roof structures
The last type of roof studied highlights the need to emphasise this element in order to obtain the desired image of the building. In the case of these roofs, it is obvious that
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Fig. 16. Type 5 roof structure timber joints
the urban position of the buildings influences the final image of the roof, first due to the adjacent buildings and secondly due to the dimensions of the public space bordered by these buildings. To have a clearly delimited public space, it is necessary that the buildings that border it be on the same scale as the public space. Therefore, in the case of these buildings, if the roof had been ordinary, its height and shape could not have contributed to the final shape of the building. By raising these roofs, the buildings in question seem to have two or even three floors, in addition, bringing them to the market scale. Without this raised roof, the public space would not have had such a clear delimitation. Of course, this raising of the roof also helps to achieve the desired monumentality for these buildings and, respectively, the urban space. Being located in probably the most important square in the city, these are not ordinary objects. In this way, by bringing these interventions to the roofs, the visual perception of the buildings, but especially of the public space, was the desired one. Of course, these changes became visible in the constructive details of the structure as well.
4 Discussion When comparing the identified roof structure types, it can be observed that architectural and urban planning requirements significantly influencing the height of the roof with spans remaining throughout the analysed period around 10.00–13.00 m. However, the most important changes appear in the use of various structural elements and their position, which evolve significantly over time, leading to the more efficient use of timber as a way of solving the general shape of the roof (Table 1). Therefore, it was observed that the dimension of the tie-beam is remaining rather constant until the beginning of the 20th century, when it shows a significant increase, mainly caused by the general structural layout of the buildings they belong to, with structural walls placed only perpendicular to the frames of the roof. The posts are also presenting important changes in time, being used starting with the 19th century and decreasing their cross-section in time until the beginning of the 20th century despite increasing length. The rafters and compound rafters show only little changes, except for roof structures with highly complex shapes (type 4) where they had to be adapted to comply to the imposed layout of the roof. Despite these significant changes in both structural layout and cross-section of timber elements, the joints used remain rather
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Table 1. Analysis of structural characteristics of identified roof structure types Type 1 Wood species
Type 2
Oak/Softwood Softwood
Type 3
Type 4
Type 5
Softwood
Softwood
Softwood
6.50 m
7,50–8.00 m
10.00 m
General dimensions Height
6.50 m
5.00–5.50 m
Span
12.00 m
12.00–13.00 m 10.00–12.00 m 11.00–13.00 m 12.00–13.00 m
Element cross-section Tie-beam
190 × 200 mm
170 × 200 mm 180 × 180 mm 180 × 200 mm 200 × 240 mm
Collar 190 × 220 beam/brace mm
–
Post
–
150 × 185 mm 180 × 180 mm 180 × 180 mm 160 × 160 mm
Rafter
150 × 175 mm
100 × 155 mm 110 × 170 mm 150 × 150 mm 100 × 120 mm
Compound – rafter
50 × 170 mm
180 × 200 mm 80 × 160 mm
145 × 150 mm 110 × 170 mm 180 × 180 mm 160 × 170 mm
constant during the analysed period, with slight changes caused by the appearance of steel fasteners.
5 Conclusion The study brings forward the link between the urban context, the building - the roof shape - the roof structure, and the details hidden inside the roof, a link that was proven to be very important when addressing historic roofs and roof structures and understanding the considered building techniques. Based on selected case studies, the research highlights that, based on the perception of the roof and the period in which the building was constructed, the importance of the roof is changing, leading to significant changes in the general layout of the roof structures and the continuous evolution of construction techniques. This performed study is highly important and up-to-date in the context of preserving the authenticity of historic urban areas, by acknowledging the way the perception of the historic urban space is influenced by the roofscape and how by preserving its authenticity highly valuable structural details are also automatically kept for future generations. It highlights that the shape of the roof is continuously changing in time, leading to a change of the position of structural elements, ultimately leading to adapted timber joint which comply with the new requirements of these layouts. The research can therefore be a starting point for future more extensive studies which would highlight how construction techniques in the case of historic timber roof structures are evolving rap and how they were adapted a long time in order to comply two exterior
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requirements not related to the simple load transfer from the back rafters towards the main load bearing structure.
References 1. ICOMOS: International Charter for the Conservation and Restoration of Monuments and Sites (The Venice Charter 1964), Venice, Italy (1964) 2. Worthing, D., Bond, S.: Managing Built Heritage: The Role of Cultural Values and Significance. Wiley (2016). https://doi.org/10.1002/9780470697856 3. Colavitti, A.M.: Urban Heritage Management: Planning with History. Springer, Cham (2018) 4. Bandarin, F., van Oers, R.: The Historic Urban Landscape - Managing Heritage in An Urban Century. Wiley-Blackwell (2012). https://doi.org/10.1002/9781119968115 5. ICOMOS: Principles for the Analysis, Conservation and Structural Restoration of Architectural Heritage, Victoria Falls, Zimbabwe (2003) 6. Keller, A.: A complex assessment of historic roof structures (2020) 7. Mosoarca, M., Keller, A.: A complex assessment methodology and procedure for historic roof structures. Int. J. Archit. Herit. 12, 578–598 (2018). https://doi.org/10.1080/15583058. 2018.1442519 8. Keller, A., Mosoarca, M.: A complex assessment of historic roof structures. In: Arun, G. (ed.) Proceedings of the 4th International Conference on Structural Health Assessment of Timber Structures, SHATIS 2017, pp. 157–168 (2017) 9. Andreescu, I., Keller, A., Mosoarca, M.: Complex assessment of roof structures. In: Procedia Engineering, pp. 1204–1210. Elsevier Ltd (2016). https://doi.org/10.1016/j.proeng.2016. 08.542 10. Andreescu, I., Keller, A.: Architecture as “Gesamtkunstwerk” – the role of the roof in defining architecture in the 19th and 20th century in Timisoara. In: Proceedings of the 3rd World Multidisciplinary Civil Engineering - Architecture - Urban Planning Symposium, WMCAUS (2018) 11. Keller, A., Mosoarca, M.: Influence of roof structures on seismic vulnerability of historic buildings. In: Branco, J.M., Sousa, H.S., Poletti, E. (eds.) Proceedings of the 5th International Conference on Structural Health Assessment of Timber Structures, SHATIS 2019, pp. 171– 178 (2019) 12. ICOMOS: Charter for the conservation of historic towns and urban areas (Washington Charter 1987) - Preamble and Definitions, Washington, DC (1987)
Construction of Traditional Stepped Wells in Rajasthan (India)- Learning from the Past to Conserve for the Future Deepika Ghosh Saxena1(B) and Richard Hughes2 1 Ideate Design Studio, New Delhi, India
[email protected] 2 London, UK
Abstract. Many countries are facing a drinking water crisis today, and many governments and NGOs are deriving new sustainable water supplies, ensuring quantity and quality. Aiding this, water infrastructure experts are also exploring the revival of traditional water systems and methods to address scarcity, especially to support societal traditions and cultural resilience. While protection of catchments and sources, recharging water tables and strengthening the role of communitiesensuring access and managing water are emphasised in the current conservation and revival strategies, a water system’s most prominent and tangible component, i.e. access and protection structure itself, requires in-depth study to address present restoration challenges. A lack of understanding of the structure and construction of traditional water storage bodies as a product of multi-layered knowledge of topography, geology, hydrology, soil types, local contexts, etc., coupled with the linear and standardised approach, is yielding undesirable and unsustainable results such as inappropriate restoration of the structure, thus compromising structural and material integrity and heritage value. Hence it becomes critical to address this problem with a multidisciplinary technical understanding of excavation, structural and construction systems that have been used to build these architectural marvels, perhaps beyond the craft skills and knowledge available today. The paper explores how the historic step wells were technically and skilfully designed and constructed, the structural and geotechnical considerations/constraints, response to local hydrology, transformed modes of water extraction and how reuse can serve modern local functional needs while preserving and celebrating the historic character and cultural heritage values. Keywords: Traditional water structure · Structural & geotechnical responsive design · Conservation
1 Background Recently, there has been a focus on traditional water retaining and extraction structures as an alternative source of water supply to tackle the prevalent water crisis in many countries. The argument is that if it has worked in the past, why cannot it work well for R. Hughes—Visiting Professor Historic Building Conservation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 683–697, 2024. https://doi.org/10.1007/978-3-031-39450-8_56
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the future, sensitively supporting water sustainability human needs? In the Indian context, too, there have been efforts to revive traditional/historical water structures for storing and supplying safe and clean water – primarily here for consumption (humans & animals), not for industry or agriculture. The author was involved in the mission to systematically document the traditional water structures for potential revival (documenting typologies, systems, attributes of value and assessing the potential for revival, reuse and tourism.) As part of a water system, much effort is put into the remediation of the degenerated catchment and streams and the physical restoration of the water step well structures. Unlike a building, the primary consideration for a water access structure is to address the underground soil-structure interaction and the hydrology of underground ‘flowing’ water, as the main access structure is deeply sunk below the ground level. Furthermore, in Rajasthan (study area-see below), the designs must be responsive to high wind and air pressures in specific locations and generally experience extreme temperatures that cause water evaporation. Since most water extraction structures are primarily underground, the character of the water table, the size of the exposed water body, the nature of masonry construction, the shape and size of stonework, etc., are determined by the geology, geomorphology, hydrology and the availability of local material in the region. An in-depth understanding of the land, soil type, water and water microbiology are crucial to conserving traditional water structures. Therefore, any conservation works or reconstructions should be guided by understanding the context, subsurface and construction system for holistic interventions. To explain the inherent understanding of the structural system of traditional water bodies, the authors will discuss the case example of Rajasthan, India. It is part of the Thar desert and a water-scarce region. The landscape is dotted with traditional water structures and natural water bodies, which have been the primary source of water supply for all settled and migratory community drinking and agricultural needs. Noted in western Rajasthan (study area) is the absence of perineal rivers, springs and not many natural lakes.
2 Study Area- Rajasthan, India Nearly 60–65% semi-arid – arid desert, Rajasthan state is located in the north-western part of India. Geographically, Rajasthan is divided into four zones: western sandy plains, semi-arid zone, plateau and the Aravali mountains. While the desert area is relatively dry and infertile, the hilly southwestern part of the state receives more rainfall and is more fertile, and the eastern part is a transition zone between the deserts and the plains. Further, the area west of Aravalis, while receiving the lowest rainfall, also has saline groundwater. The presence of water was a critical determinant for the habitation to flourish, and terrain, rainfall, and natural drainage are some factors that shaped settlement patterns and agricultural uses in the region. With control of water came political/tribe power and social influence (Figs. 1 and 2). 2.1 Subterranean Structures in the Region Depending on the ground conditions and the hydrology, the well structures were built to responsibly extract the maximum water that could be reached in an age of no pumping.
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Fig. 1. (a) Varying geographical zones within the state of Rajasthan – study area (b) Rainfall status, (c) State of Ground water
Fig. 2. Mean wind speed
Rainwater, seasonal rivers and groundwater were the three primary sources of supply; less supply came from reservoirs; hence the water tapping structures are either via rainwater harvesting/collecting or those extracting underground water contained in the shallow geological formations. Another rather unusual type of water structure was based on collecting condensed dew droplets, a common phenomenon due to extreme daily temperature and humidity regimes. Aqueducts, tunnels and underground conduits are not found in the study area. The primary considerations for the design of water bodies were to mitigate evaporation, provide a stable and safe environment, provide protection from wild animals, pollution and how best to move the stored water to where needed (Figs. 3, 4, 5 and 6).
Fig. 3. General ground condition- This area mainly has sandy/sandy soil with low humus content and the depth of water level varies from 5 m to 100 m bgl across the study area.
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Fig. 4. Picture depicts two basic methods to hold water 1. Embankment (nada) constructed to hold water from seasonal streams/rivers & 2. Use existing depression near water source for water collection (talaab)
Fig. 5. Unlined tank/Kutcha joda is constructed where ground water table also needs to be recharged or is impervious enough to hold water for a longer duration allowing water to slowly seep in and recharge the water table and shallow wells. One usually finds these together/nearby in the study area.
Fig. 6. In areas with a deep groundwater table, well/stepped well are dug to tap water. Alternately, lined tanks/tanka/pakka johad are constructed to collect and hold rain water/surface runoff. Hard base of a tanks do not allow the water to percolate.
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Historically, the areas where the water table was very high, especially the eastern part of the State (an area well-drained by seasonal rivers and groundwater available at 8–10 ft below ground level), had shallow depressions from where water could be sourced easily. However, the water demand increased as the rainfall patterns changed and the population increased. The villagers would dig informal pits along the course of the river at the beginning of summers, which would fill during monsoons and water was used upon their return for the rest of the year. With time, the pits got slender and deeper and more structured to tap deeper groundwater, responding to a further increase in demand, while the kutcha joda or unlined tanks, collected the surface runoff and rainwater. However, these large unlined tanks could not hold water for long, especially in loose sandy soils. Therefore, many smaller and more engineered clay or dressed stonelined tanks, or pakka jodas, dot the western part of the study area - a region with sandy soil and minimal rainfall. Summarising the typological sequence & variations (Figs. 7, 8, 9 and 10):
Fig. 7. (a) Using low lying areas/depressions for collecting rain water (b) Constructing embankments perpendicular to direction of run off to collect water
Fig. 8. (a) Underground cylindrical shaft collection surface run off. The cover mouth with a small opening ensures minimal evaporation during peak summers. (b) Lined tanks/Johad to hold water in sandy soils. This is one of the more ornate examples of a Johad, it can be a humble rectangular masonry tank as well
There are many variations of the above in terms of shape (circular, rectangular, square), size, the material of construction (mud, brick, lime, cement etc.) and ornamentation and the mode to access water (direct/steps/ramps etc.)
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Fig. 9. Well/Kuan - Underground cylindrical shaft either tap ground water or a natural source available
Fig. 10. Stepped Well/Baoli/Bawri/Jhalra- Underground shaft either tap ground water or a natural source available
3 Stepped Well A stepped well, or baoli, is largely an underground water structure and may have an additional wonderful superstructure, complex in architecture and engineering. Typically, these ‘stepped wells’ comprise two main components, i.e. 1. The well (vertical subterranean shaft) and 2. Levels or passage from the existing ground level leading down to the well. The passage may be an inclined narrow ramp, a series of steps in many possible arrangements, broad platforms at regular intervals with rooms/chambers, or a combination of these (Fig. 11).
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Fig. 11. Typical plan and section of a stepped well/Baoli/Bawri. A flight of steps leads down to the water level with intermediate structural platforms acting like beams/horizontal elements holding the long vertical shafts. There is a well usually at the end from water can be drawn.
3.1 Variety of Stepped Well in the Study Region The now famous monumental-sized and most other smaller stepped wells are of gravity retaining wall construction, mostly having arches and stone beams, thick masonry side walls, and a vertical subterranean shaft. The construction may either be with dressed stone blocks, random rubble or locally available fired bricks. While most structures are utilitarian and devoid of ornamentation, some are adorned with wonderful architectural elements such as pilasters, chattris or pavilions, brackets, complex patterns of steps etc. Rani ki Vav (in Gujrat, outside study area) and water structures part of the Hill Forts of Rajasthan (serial inscription) are UNESCO World Heritage Sites, while others such as Chand Boari in Abhaneri and Toorji ka Jhalra (Jodhpur – within the study area), are popular tourist attractions. As seen below, most of these water structures are architecturally significant and have tourism potential as well (Fig. 12).
Fig. 12. (a) Mertani ji ki baoli, Jhunjhunu/Size 85 m × 22 m(ap.), (b) Lahini baoli, Basantgarh/Size 21 m × 13 m(ap.), (c) Katan baoli, Osian, Size 41 m × 35 m(ap.), (d) Stepped well Khandela, Size 30 m × 12 m(ap.), (e) Stepped well Rewasa, (f) Kanak Baori, Sirohi Size 21 m × 26 m(ap.)
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3.2 Construction of Stepped Wells It is assumed that the processes started with the investigation of the ground conditions and hydrology, this followed by planning the architecture and engineering. It would then have needed the appointment of an expert team of builders/contractors. The making of a stepped well then involved construction of the well/vertical shaft excavated deeply through soil or rock down into the water table of the time (noting that seasonally the phreatic surface fluctuated), and from where water is then drawn, and the structure to access that level from the existing natural ground level. Depending on use, patronage and context, the structure leading to the well may be a singular flight of steps (for more utilitarian structures) or may have multiple landings, with or without rooms/chambers at landing levels. Water was both hand drawn by people and with the help of domesticated animals such as camels or cows (as found in many Middle Eastern countries as well). Traditionally, in Rajasthan, the action of digging is known as kinna, and those digging are called kiniyas. The sirvis (with empowered vision) would first ‘see’ the underground water, and then the kiniyas would start the digging. First, the trench is dug in open cut, from the ground level downwards, marking the landing levels or terraces leading to the well. The short-term stability determines the cutting slope angles as excavation proceeds. The well, too, is dug from top to bottom, stabilising the excavated faces with masonry as the mason goes down in regular stages to prevent soil pressure from caving in the shaft. Shafts are kept relatively of small diameter, so earth pressures force arch around the void. If the depth of the well is not too much and the ground is not very loose, then the mason excavates in one go and starts lining the vertical shaft from the bottom upwards, progressively providing upward stability to the surrounding soil faces. As observed during fieldwork, the type of masonry work in wells depends on the depth of the vertical shaft, soil conditions and locally available construction material, for example: 1). The shaft is not too deep (40–50 ft/12–15 mts) – masonry lining is with bricks or stone, work is done bottom up, 2). Shaft between 50–150 ft (15–45 mts)– level wise digging (6–8 ft/1.8–2.4 mts) and simultaneously lining with masonry, work is done top to bottom. Therefore, a series of masonry rings are usually seen in a typical well Sect. 3). Shafts deeper than 150/200 ft (45–50 mts) – use large blocks of dressed stone in dry masonry and with interlocking (along both axes – horizontal and vertical). The use of stone pegs may also be observed in some structures. Work is done from top to bottom to counter the increasing soil pressures.
Fig. 13. Segmental excavation and lining for relatively loose surfaces
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Further, if the soil and subterranean layers are loose soil formations, not firm enough to hold the pressure from the sides, then the excavation is done in segments and followed by simultaneous lining with masonry to avoid collapse. After digging one quarter, the segment opposite to it is excavated to balance out the pressure, a similar procedure is repeated to the remaining two sides. (Refer Figs. 13 and 14). In some ways, this is an interesting ‘low-tech’ precursor to modern diaphragm walling used for constructing shafts. If the shallow soils were weak, then the lining could be constructed top down in stages, each stage formed of inserted timber rings. One usually finds dry construction for shafts in Rajasthan or minimum use of lime mortar; this allows water to percolate from the shaft sides without creating new water pressures on joints and inhibits base ‘boiling’ and with ingress of soil fines.
Fig. 14. Segmental excavation and lining for relatively loose surfaces
The thickness of structural side walls at the foundation can be as wide as 4–5 ft (1.5 m) and reduces with offsets towards the top. Usually, at the ground level, the thickness is observed to be around 1.5–3 ft (0.45–0.9 m). Hence, this sort of buttressing provides stability against pressure from the sides. (Refer Fig. 14) (Fig. 15).
Fig. 15. Excavation and lining of side walls with masonry offsets to counter pressure
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The plan forms of stepped wells, in our random research sampling through Rajasthan, demonstrate a consistent pattern in the proportions of the structural elements. Usually, the well shaft is square in plan (say X m), and the length of the structure leading down to the well is typically a multiple of X m (refer Fig. 16). The module is repeated as the length of the structure increases; it is intercepted by horizontal members, i.e. cross elements (arches, lintels, cross walls) which tie the structure together (refer Fig. 17) (Figs. 18 and 19).
Fig. 16. Plan form and proportions of various stepped found in study area
Fig. 17. Horizontal tie members as portal which hold the large slender subterranean structure against lateral movement
Further, positioning columns at intermediate levels (portals) aided in load transfer and spanning and tying the structure together. The spanning of columns usually depended on the nature of the material available for construction. Usually commonly used stone blocks of sandstone or local quartzite were used as beams above stone columns; these are typically 8–10 ft in length (2.4–3 m). Inserting columns at intermediate levels ensured even load distribution and prevented buckling and cracking. Additionally, tying the side walls and the intermediate portals mitigated the possibility of deflection due to external soil pressures. Therefore, columns, pilasters, symmetrical construction, use of pavilions on corner junctions, horizontal bracing with portals and arches, low centre of gravity, and broad
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Fig. 18. Flight of steps between levels act as tying elements and earthquake dampeners. Note: Rajasthan lies in low to high earthquake risk zone (II, III & IV)
Fig. 19. Chor Baoli, Ajmer
based buttressing walls all enable these subterranean wells to be self-balancing and able to withstand the pressure of soil, water and wind. Hence, it must be noted that, while certain components mentioned above may appear to have more ornamental value, they are critical to the state of stability. The fact that these wells have survived for so long shows that the designers and builders fully understood the engineering and geotechnical/soil mechanics principles. Also, the well shaft is located in the centre of the shorter side of the stepped well structure, at its deepest end, ensuring that it has a well-balanced, robust foundation and structural support from all sides.
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4 Common Issues with the Conservation of Stepped Well Structures A review of some of the recent conservation and restoration works undertaken in the region reveals there is a rather cosmetic approach towards stepped wells. Most common works include the removal of vegetation, typical small shrubs but even large trees(!) that have taken over the sites, local repair to the bigger dislodged masonry elements and surface improvement using more commonly available cement-based renders or a more compatible lime-based render (Fig. 20).
Fig. 20. (a) Recently repaired stepped well by villagers – debris and garbage removal and surface repairs with cement (b) Recently repaired stepped well by Government of Rajasthan – debris and garbage removal, surface cleaning and security grills
The above two pictures of recently repaired stepped wells in Ajmer district depict a few key problems that are either ignored and, in some cases, aggravated by interventions - these are not based on a thorough understanding of the structure and considering future function. For example: 1. Concept of ‘sealing’ the joints and the choice of material – most of the stepped wells have dry construction with interlocking joints, and the use of mortar (most commonly observed – lime mortar) is minimal, usually in the upper segment of the well and in the superstructure (if present). Dry jointing in stone ashlar masonry and the use of coarse lime mortar with bigger granules allows water to seep in from side walls into the vertical shaft, so releasing active pressures exerted by water on the masonry structures, thus preventing the development of retaining wall deflections, bulging and cracking over time. However, insensitive sealing of joints and plastering surfaces during conservation, with either fine lime or cement-based mortar, defeats the purpose. (refer image 31). Thus render is also prone to ‘sheet’ dislodgement. Overall we note that the conservators are not familiar with local hydrology and hydrological requirements. 2. Lack of regard for existing ground condition – Many water structures either lie in settlement outskirts, amidst forest areas/parks etc. or are packed within the core of the town/city and surrounded by dense development. In all these cases, the additional weight of buildings dumped soil, and dirty environment can add significant new
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pressures and stresses- small strains on side walls, leading to local structural failure as seen in Fig. 32- Nachan baoli is located amidst a city level park, and the levels on all sides have been increased in recent times, imposing new loading on the ground and in turn this leading to additional lateral pressures on the thick masonry retaining walls. Though it was repaired in 2016, a recent picture shows bulging walls. Water pollution also results in such ‘changed’ situations. 3. Disregard for concept/working behind a particular typology while undertaking repairs & conservation– Mostly, a standardised approach/methodology is used for the repair and construction of all water structures, which outrealising the concept behind or the mechanism of how the water structure actually functions. Lately, many johad/tanks are being conserved and revitalised in this area by lining the base and repairing the side walls to avoid seepage so that they can once again hold water. We must also note that the term johad may be interchangeably used with other typology in the region, depending on the area of intervention. Now traditionally, johads were lined tanks in this area, a typology found in areas with loose sandy soil. Hence lining was critical to hold water. However, for ground water recharge, the water should percolate through this lining, noting that the subsurface should be hard/impervious enough to hold water. Also, the water seeping through sandy/loose soil can commonly evaporate before any recharge. At times one finds that understanding how a johad traditionally worked is not considered, especially when conservation measures are undertaken. Hence the system gets quickly broken, reducing these facilities to merely being empty rubbish-holding structures. 4. Coursing in masonry- Due to the lack of easy availability of large stone blocks, the tendency is to use thinner sections, smaller sizes, fixed with mortar, that do not interlock/fit in position and detach in due course of time. In this concern, there is a lack of implementing works that conform to national and international conservation charters and conventions 5. Dealing with microbiological infections in the walls and retained water. Thus, there is growing evidence for developing moulds, slimes and even fungi. There is now a need to solve water pollution infiltrating the surrounding urban landscape. In conclusion, it is essential to stress the need for expert design and supervision of conservation and then the onward management and maintenance of the restored functional facility. This all needs to be addressed in developing and implementing a holistic plan with adequate financial resourcing and sustainable participation of the local community.
5 Learnings and Way Forward The important aspect of conservation and renovation for stepped wells is understanding the built components and how the system functions – architecturally and structurally before undertaking any intervention. It is critical to note that in stepped wells, the stone blocks and architectural elements are of a predetermined-precise size and quality due to their structural role–these are not just for aesthetics. Therefore, care must be taken to replace these with new blocks having the same size and properties to maintain structural and architectural integrity and maintain the stepped well’s self-balancing properties. As
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part of this, more knowledge is needed about the construction of the masonry fabric behind the exposed faces of these subterranean structures, and this can only be achieved by a considerable amount of research and investigation – these being scientific forensic processes. When defects are found in the retaining walls, it is necessary to understand the causes and rectify them; otherwise, deformation will continue. To support technical studies, defects must be mapped and may need to be instrumented to assess movement characteristics. It is fundamentally important that if such wells are to play a new role in the freshwater provision, the ground and hydrological conditions are technically understood from geotechnical investigations. As part of conservation planning, it is essential to determine how the wells will provide water to the community. Thus, it is necessary to engage with them and address the intangible heritage and cultural/social values of wells. Conservation and well reuse should address long-term management and maintenance through the production of a Historic Environment Management Plan. It is possible that the value of historic stepped wells may encourage the construction of new ones, built in a traditional or modern, way altogether supporting craft skills and continuity of local culture and lifestyles. With functionally or redundant historic wells, it is important to consider public and tourist visitor safety, especially if it is conserved and accessible to the public. When cleaning out well sumps, there should be archaeological attendance as there are often preserved artefacts within accumulated natural silts and dumped debris. Cleaning out well sumps needs engineering design as the debris can provide structural support. Should a well shaft need to be sunk deeper to penetrate a now depressed water table, then there is a need to do a structural engineering assessment, possibly utilising computer modelling. The deeper shaft should respect the authenticity and integrity of the historic structure, and here the design and construction can, in return, significantly support the analysis and interpretation of the historic structure. It is most commonly observed that mechanical pumping has been introduced in some of the abandoned/defunct wells. However, putting in mechanical pumping is not to be encouraged, as there may be adverse effects on the well stability and character. Should mechanical pumping be considered, this must include thorough engineering and conservation analysis. Mechanical pumping for substantial modern community water demands needs to be put in the context of local and regional sustainable water provision strategies and use requirements. Lastly, here, it is critical that a technically sound conservation and reuse methodology is adopted for undertaking this conservation/revitalisation/modernization process; this includes: 1. 2. 3. 4. 5. 6.
Metric survey at large scale - as baseline heritage and history documentation Engineering and material documentation Architectural and heritage valuation documentation Geotechnical and hydrological investigations Technical condition assessment – and including archaeological attendance Instrumentation and monitoring for supporting short to long-term conservation and reuse objectives 7. Material, water and hydrological testing 8. Assessment of future water functional demands and put in context of global climate change metrics
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9. Design for modern present-day and future uses and need for modern engineering equipment/secure housing and supportive infrastructure such as electricity for lighting and pumps 10. Production of management, conservation, tourism, and maintenance plans 11. Risk assessment related to external factors, including climate change and change in water demands from community 12. Production of specifications and contracts etc., for conservation; this also needed for regulatory approvals. This also requires there to be the implementation of a Health and Safety plan. Appointed contractors must provide a written scheme of construction/conservation, supporting approval of standards and outputs.
References 1. Mishra, A.: The Radiant Raindrops of Rajasthan. Gandhi Peace Foundation (1995) 2. Bhatnagar, M., Saxena, D.: Traditional Water Structures of Rajasthan, INTACH (2018)
From the Intervention of a Vernacular Heritage Structure in Oña – Ecuador, to the Improvement of the Cultural Landscape M. C. Achig-Balarezo(B) , S. Astudillo Cordero, and G. Barsallo Chávez City Preservation Management Research Group, Faculty of Architecture and Urbanism, University of Cuenca, Av. 12 de Abril s/n. Ciudadela Universitaria, Cuenca, Ecuador {cecilia.achig,sebastian.astudillo, gabriela.barsallo}@ucuenca.edu.ec
Abstract. The San Francisco de Oña neighborhood is in southern Ecuador and is included in the national heritage list. About 20% of the heritage buildings are in an advanced state of deterioration, mostly abandoned and without maintenance. This article shows the intervention in one of these vernacular heritage buildings through a so-called Maintenance Campaign, which is an initiative developed by the University of Cuenca and is based on the recognition of values and the participation of different social and institutional actors through collaborative work, known as “minga” in the Andean world. The research was carried out based on two methodologies: a) the preventive conservation methodology according to ICOMOS 2003 and b) the participatory methodologies according to RedCIMAS (2015), which allow for active interactions and mutual learning among its actors. The University of Cuenca developed twenty maintenance projects in the San Francisco de Oña neighborhood, although due to the Covid pandemic it was only possible to intervene in one building. This case study turned out to be very interesting, because not only was a heritage building rescued utilizing traditional constructive techniques, but also an urban project by the Municipality of Oña was halted, which would have led to the destruction of part of this building by transforming a narrow dirt road into a wide road for heavy traffic. If this project had been carried out, heritage in Oña would have been affected in two ways. First, one of the buildings with the highest heritage value of this neighborhood would have been lost and second, a drastic change would have occurred in the historical cultural landscape of the San Francisco de Oña neighborhood. Keywords: Vernacular Heritage · Cultural Landscape · Minga · Preventive Conservation
1 Introduction The San Francisco neighborhood is located in the canton of San Felipe de Oña, which is settled along an old bridle path and a meandering water canal that irrigates the neighboring planted areas as it passes. It is made up of a set of vernacular buildings built on the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 698–708, 2024. https://doi.org/10.1007/978-3-031-39450-8_57
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basis of adobe, wood and tile roofs (Fig. 1). The landscape is strongly characterized by rural life: the pre-Hispanic road and the ramifications that derive from it, the irrigation canals, the crops, the color, texture and materiality of the buildings and the vegetation add to a strong sense of appropriation of those who live here and even of those who only come to visit it, adding value and significance to the area.
Fig. 1. The San Francisco neighborhood in the Oña canton. Source: Astudillo, 2021
In the year 2021 the idea of building a new road takes hold, which would give continuity to the roads in the areas surrounding the urban center. Unfortunately, the proposal for one of these road extensions would mutilate a heritage building that already was in very poor condition, ignoring its values as part of the built complex. This was the beginning of a wide debate as well as negotiations with several institutions to avoid its demolition. These efforts concluded with a minga, which was led by the University of Cuenca (UC) through the World Heritage City (CPM) research project of the Faculty of Architecture and Urbanism (FAUC), aimed restoring the building as a strategy to maintain not only the building itself but also the structure and urban configuration of the neighborhood as well as the recovery of the sense of appropriation and belonging of its inhabitants. 1.1 Objectives This article shows the process that was developed applying the principles of preventive conservation and activating a participatory process, which concluded with the intervention of a heritage asset in Oña. The stated objectives were: • To carry out documentary research on the neighborhood, emphasizing the aspects that characterize the area as a cultural landscape with a long history. • To carry out documentary research on the property, highlighting the importance of vernacular architecture, mainly to the community of Oña and to the residents of the neighborhood.
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• To make an intervention proposal aimed at rescuing the heritage building in dispute, with the participation of various actors, committing them to a minga through a Maintenance Campaign. • To execute the process of recovery of the building with the contribution of various social actors and citizens, under the direction and coordination of the University of Cuenca, the CPM project, the Municipality of Oña and the National Institute of Cultural Heritage (INPC). 1.2 Background The University of Cuenca, its FAUC with the conservation workshop and the CPM research project previously developed several research processes, such as among others the study of mineral pigments and the study of brick diversification. Several projects that focused on the conservation of heritage in the Oña canton have also been carried out, particularly in the cantonal capital and in the rural parish of Susudel, through Maintenance Campaigns based on so-called mingas. The minga is collaborative work consisting of the sum of efforts of diverse actors in a concerted and consensual manner to achieve community or even family benefits. The first Maintenance Campaign was carried out in Susudel in 2011, contributing to the maintenance of forty-nine peasant buildings of vernacular architecture. Immediately afterwards, in 2013, a second project that lasted five days focused on the recovery of the Susudel Cemetery. After these projects in rural areas the maintenance campaigns moved to an urban environment. They had all the facilities, but also the difficulties of an environment in which participation and social cohesion manifest themselves differently. In 2014 the first urban Maintenance Campaign was carried out in the San Roque neighborhood, a traditional neighborhood in the city of Cuenca, during which twenty-two buildings were intervened. In 2018 the Maintenance Campaign of the Las Herrerías neighborhood, which is another traditional neighborhood of Cuenca, was carried out with the intervention of twenty-one buildings, during which, as in previous campaigns, the minga brought together authorities from the city and the neighborhood, neighbors, the armed forces, social organizations, coordinated by teachers and students of the FAUC. In the San Francisco de Oña neighborhood, the work of the University of Cuenca, the FAUC and the CPM project began in 2007–2008 with the research of its history and the context of the city as well as inventorying valuable heritage buildings. Five complete areas were studied in depth. The process culminated in the elaboration of individual maintenance cards, in which the damages and heritage values were identified through the Nara Matrix [1]. In addition, maintenance and improvement actions were proposed for each of the buildings. These actions, in which the University of Cuenca and the National Institute of Cultural Heritage (INPC) participated, resulted in a technical file that served as support for the declaration in 2013 of the urban center of Oña and the San Francisco neighborhood as assets belonging to the Cultural Heritage of the Country [2]. As a result of the presence since 2007 of the University of Cuenca, studies began for the recovery of the most emblematic building in the neighborhood, called the “Beauty of Paris”, which culminated in its comprehensive restoration, turning it into an intercultural community center with the institutional contribution from the Municipality of Verbeke, Belgium. In 2019, with the objective of contributing to the conservation of the
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architectural and urban heritage of the neighborhood, the participation of various social actors was encouraged through a Maintenance Campaign. The University of Cuenca, as part of an academic exercise, worked on twenty of the fifty-five buildings that make up the neighborhood. The University of Cuenca carried out the registration, survey and maintenance proposal, in addition to a comprehensive project aimed at conserving and promoting the cultural landscape. Due to the Covid-19 pandemic it was only possible to intervene in one building. In July 2021 a Maintenance Campaign was carried out in the building belonging to Mr. Miguel Calle (the “Lara-Espinoza” house), with the aim of saving it from the imminent opening of a new road that would have passed through it. With the new road, not only the vernacular building would have disappeared, but also the integrity and configuration of the neighborhood would have been affected.
2 The San Francisco de Oña Neighborhood and the “Lara-Espinoza” House The San Francisco neighborhood is one of the oldest and most representative settlements in the region. Characterized by concentrating administrative, trade and management activities, it was a very active site where bakeries, shoe stores, soft drink factories and furniture factories were located. It was also the center of communication between various communities that marketed their products [3]. Although the neighborhood did not present major alterations or transformations in the urban-architectural aspect, the state of abandonment and deterioration that most of the buildings presented was notorious. The neighborhood is characterized by its natural, cultural and landscape wealth, in contrast to the fragile socioeconomic condition of the population. In addition, the use of traditional construction techniques such as adobe and wood, typical of the Andean region, are all around, as well as the use of paint based on colored earths found locally, which gives the area a particular and unique character. Despite the construction of the Pan-American Highway and the new Central Plaza, the neighborhood has transcended time and shows the traces of progressive abandonment and the economic precariousness of those who inhabit it, which is why today its buildings present a significant deterioration [4]. In the San Francisco de Oña neighborhood, the presence of the “Lara-Espinoza” house stands out, in which the Maintenance Campaign was carried out. 2.1 Maintenance Campaign in the San Francisco Neighborhood Maintenance Campaigns are innovative processes in the field of preventive conservation of built cultural heritage, based on the recognition of its values and the coordination of various actors involved (academy, community, public institutions, private companies, foundations, etc.), in a work called minga. The term “Minga Multiactors” has been adopted for this collaborative process inspired by a form of organization of the Andean tradition: the minga [5]. To guarantee the optimization of resources, especially for owners who do not have money, as is the case of Mr. Miguel Calle, a Maintenance Campaign
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was developed of his building. This intervention was challenging as it was developed during the COVID 19 pandemic (Fig. 2a-b).
Fig. 2. a-b. State of deterioration of the “Lara-Espinoza” house before its intervention. Source: 2a: Achig, 2019. 2b: Astudillo, 2010
The 2005 Faro Convention on the Value of Cultural Heritage for Society [6], emphasizes, among other aspects, the need for the whole of society to participate in the continuous process of defining and managing cultural heritage. It also recognizes personal and collective responsibility for this heritage, requiring greater synergy between the competencies of public and private agents and institutions, a situation that is close to the process developed in the “minga”, which also contributes to the construction of a peaceful and cohesive society, where collective interests take precedence over individual interests. 2.2 Methodology The present investigation was developed under the consideration of the San Francisco de Oña neighborhood as a cultural landscape. In this context and based on experiences developed by the CPM Project, two methodologies were articulated: a) Preventive conservation, which includes the processes of analysis, diagnosis, therapy and control, proposed by the International Council on Monuments and Sites [7] and b) the participatory research methodology proposed by RedCIMAS [8], through which spaces for interaction and mutual learning between various actors are activated. Participatory methodologies seek to facilitate and promote processes of social transformation through initiatives that encourage the involvement of various actors: neighborhood residents, members of the academy, technicians, officials of public institutions, among others. Each phase is complemented by a documentary research process that is essential to validate and feedback this information with the community and other actors, through participatory activities, obtaining a final result shared among the participants [9]. 2.3 Results and Discussions Phase I Analysis. During this phase information is collected to determine the heritage values. Students and teachers of the ninth semester of the Faculty of Architecture of
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the University of Cuenca combined documentary and field work before and during the confinement due to Covid-19. Subsequently, with the community and other actors they proceeded to validate and interpret the information collected. Among the various analyses, the selection of the buildings to be intervened was based on four criteria: heritage valuation, state of conservation, availability and economic capacity of the owner. To collect this information, the field sheets developed by the CPM project were applied. First, the pre-registration analysis was carried out with a first view of all the buildings in the neighborhood. Then the heritage values, damages and predisposition of the owner to participate in the campaign were assessed. Finally, the socio-economic condition of the owners was determined. Through the analysis of the applied files, it was possible to determine that 19% of the buildings in the neighborhood were in a poor state of conservation and 51% have a high heritage value. With this information the selection of the buildings was made and the architectural and photographic survey of them was carried out [10]. Phase II Diagnosis. In this phase the current state, history and heritage values of both the neighborhood and the buildings were determined. A SWOT analysis was applied to determine the situation of the landscape values of the area and of the social relations. The main strengths of the San Francisco neighborhood turned out to be the privileged views towards the entire Oña Valley, the amount of assets classified as national heritage and the high social cohesion of the neighborhood. Among the main opportunities are the prevalence of the historical memory of the neighborhood of several inhabitants, the tourist and architectural potential as well as the natural potential (waterfalls, lagoons, ditches, forests). The neighborhood presents some weaknesses such as the abandonment of the buildings, the few job opportunities and lack of education for its inhabitants, which leads to migration, little public space and the lack of legal protection for heritage conservation. Repeatedly the inhabitants referred to the inadequate paving of the streets, which makes the accessibility to a good part of the buildings difficult. The identified threats are the lack of attention to the neighborhood by the authorities as well as the abandonment by its inhabitants, in search of opportunities in other sectors of the city itself, with better conditions for commerce and with greater endowment of services and equipment [4]. Phase III Therapy. During this phase the execution of the Maintenance Campaign was planned in twenty buildings with the active participation of all the actors involved. The project aroused the interest of various institutions such as among others the Municipality of Oña, the National Institute of Cultural Heritage and the Prefecture of Azuay. Despite efforts made by the University of Cuenca the situation caused by the Covid-19 pandemic made it difficult to obtain financing for the campaign and the project could not be executed as planned. However, adding efforts and commitments, through the minga multiactors, the intervention of the “Lara-Espinoza” house was carried out. This hundred-year-old building was in an advanced state of deterioration and thanks to the willingness of the owner it could be restored. On June 21, 2022 the preliminary cleaning and removal of the roof began. The pieces of wood and tile in good condition were cleaned and stored for reuse. The group of students joined the Maintenance Campaign between July 2 and 10. The expertise in traditional construction techniques of the owner, Mr. Miguel Calle, was very helpful
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during the execution of the works, for example with the in-situ elaboration of the corbels, transmitting this knowledge to the students. The minga above all focused on the restoration of the roof, which was in a particularly poor condition. The traditional system of the roof is made of wood and to guarantee the proper functioning of its structure, all elements that were in poor condition were replaced. The walls were also repaired (at the lower and upper part) in order to support the roof and in this way the structure of the building was not affected by the added weight of the roof. The plasters were replaced, the balusters of the balconies were fixed, the floor of the house was leveled, and some additions such as a bathroom and a laundry room were demolished. Thanks to another research project that was taking place at the same time, artisanal paint prepared with mineral pigments from the area was donated, which was used to paint the facade of the building [11]. During the final day of the intervention the roof tiles were placed and cleanup work was carried out. Later on, all of the participants were witness of an emotional ceremony with the traditional placement of a cross on the roof. It is worth mentioning that the minga for the maintenance of the “Lara-Espinoza” house motivated other residents of the neighborhood to express their desire to paint their buildings and carry out repairs (Fig. 3).
Fig. 3. a-b. Recovery process of the Lara-Espinoza building through the Minga. Source: Astudillo, 2022.
3 Impact of the Campaign on the Urban Planning of the San Francisco De Oña Neighborhood The intervention made it possible to recover a vernacular building typical of the rural landscape with evident heritage values and to stop an urban project of widening a narrow path into a wide avenue for the passage of cargo transportation (Fig. 4b), due to which this building would have been mutilated (Fig. 4a) and at the same time it would have caused a drastic change in the urban configuration of the neighborhood. The project started considering the San Francisco neighborhood as a cultural landscape that allows us to understand the relationship established over time between human beings and nature. This is achieved through the layering of its values and attributes,
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ultimately constituting part of the identity of the place and therefore a heritage of enormous value. A cultural landscape is created over time, given the dynamic nature of social processes, each with its own dynamics, assuming a vital function as a resource for social and economic development. It supposes a vision of the environment in which people live, where the protection and sustainable management of valuable spaces and natural resources is fundamental, guaranteeing the balanced maintenance of environmental aspects and their identity and character. It is about protecting and managing heritage elements from a holistic and integrating vision, where the assets are as important as their context. According to UNESCO, cultural landscapes are defined as places that combine the work of nature and human beings, and that are illustrative of the evolution of human society and the use of space over time, under the influence of physical limitations and/or opportunities presented by the natural environment and of successive social, economic and cultural forces, both external and internal [12]. This definition goes beyond the traditional derivation between nature and human action, evidencing the synergistic relationship between these two components. Nature and humanity interact and are revealed in space, characterized by a dynamic vision of cultural change. In 2011 the INPC proposed a specific concept for the cultural landscapes of Ecuador, defining them as: a part of the territory that encompasses a coherent, articulated system of natural and human actions and interactions marked and integrated by the geography that forms it and by the historical developed processes; product of which spaces, territories, of singular characteristics with historical, sociocultural, ecological, aesthetic, visual, productive, economic, religious, spiritual and symbolic value of local, parish, cantonal, provincial and/or national recognition are created [13]. On the other hand, the cultural landscape that characterizes the San Francisco neighborhood has been considered, in accordance with what Conti (2015) proposes, as a resource for social and economic development in the broadest sense of the term, making it necessary to promote a sustainable management model that leads to a balance between current and future needs, safeguarding the cultural heritage of the environment [14]. Heritage settlements must be managed with the intention of recovering and preserving heritage buildings and complexes with high socio-cultural value, as a way to strengthen identity, improve social cohesion and promote a sense of belonging, as is the case of the San Francisco neighborhood. Understanding the impact generated by the recovery of the heritage asset and, at the same time, avoiding the opening of a wide avenue, altering the structure of the settlement, involves understanding the concept of integrity, beyond the formal and physical structure, including uses, functions, activities, perceptions, etc. Although the concept of integrity has been linked above all to the permanence of physical and material attributes, in order to escape from this and dialogue with the changing nature of heritage areas, the dynamic aspect of significance must be considered. As expressed by Hobson (2004), heritage cannot only act as a transmitter of stable and evident values, but must allow the renewal and adaptation of values [15]. Jokilehto (2006) suggests three dimensions to assess integrity. Social-functional integrity, that is, the identification of the functions related to the social development of the place. Structural integrity, that is, identification related to physical and material sources. Visual integrity, meaning that is required to
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identify the aesthetic aspects of the place [16]. In this context, the opening of the road and the elimination of the heritage asset would have meant the alteration of these three aspects related to the integrity of the neighborhood. Both the loss of one of the heritage assets and the opening of the road would have meant drastically changing the integrity and continuity of the whole, affecting the section of significant layers and the continuity between past, present and future meanings, without allowing the constant reinterpretation of heritage values [17]. Continuity activities go through evidencing the heritage values and attributes, identifying the extent to which the heritage areas may undergo changes, without considering them as undesirable effects.
B B A A
Fig. 4. a. Image of the building (A) and the road (B). Source: CPM Project 2017 b. Image of the planned road (B) and the effect on the heritage building. (A) Source: Oña Municipal GAD
4 Conclusions Despite the difficult situation caused by the pandemic, a small cooperation network (multi-actor minga) was activated with the encouragement of the owner of the property, the group of University of Cuenca students and various institutions such as the Municipality of Oña and the National Institute of Cultural Heritage, generating the conditions to carry out the Maintenance Campaign. Once the Campaign began, the residents became interested in the process, motivating themselves and asking for collaboration to carry out similar actions in their homes. What happened in other Campaigns is ratified, where it was enough to undertake an initial impulse that detonated similar processes in other buildings. The Campaign contributed to promoting the appreciation of the neighborhood and its reactivation. Previous negotiations with the authorities and the participatory process with the community contributed to raising awareness about the importance of cultural heritage. Both inhabitants and authorities as well as other stakeholders were able to better understand how heritage can become a resource for social and economic development and as such improve the quality of life of its inhabitants. Through this process of collaborative participation -minga- that culminated in the Maintenance Campaign, it was possible to prevent a narrow road from becoming a wide avenue destined to the transport of cargo, which would not only have meant the destruction of the individual heritage asset, but also would have considerably altered the configuration of the area and therefore
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strongly affected the cultural landscape and its values. The intervention was the result of a proper understanding of the heritage values of the “Lara-Espinoza” house and its context. A small but important fraction of the history of the house and the neighborhood was preserved. The in-situ learning process carried out by the University of Cuenca through its CPM research project and its Faculty of Architecture and Urbanism constitutes a living laboratory of experimentation for the benefit of the education of students and community. In fact, the knowledge of traditional construction techniques was transmitted by the owner and members of the community and at the same time maintenance was carried out of one of the most representative heritage buildings of rural vernacular architecture in the San Francisco de Oña neighborhood.
References 1. van Balen, K.: The Nara grid: an evaluation scheme based on the Nara document on authenticity. APT Bull. J. Preserv. Technol. 39(2/3), 39–45 (2008). Nara Document on Authenticity (1994), UNESCO - ICCROM-ICOMOS, Japan. http://whc.unesco.org/archive/nara94.htm. Accessed Mar 2018 2. Astudillo, S., Achig-Balarezo, M.C., Barsallo, G., Cardoso, F.: The university work on the Wolrd Heritage City Project, intervention models for the rescue and preventive conservation of earth-based architecture. Article published in the Proceedings of the Terra Education III 2018 congress, held in Grenoble in June 2018 (2018) 3. Ullauri, G.: “Historia del cantón San Felipe de Oña”. En Historia de los Cantones de la Provincia del Azuay. Manuel Carrasco & María Neira editores, 256–282. Cuenca, Ecuador. Cátedra Abierta de Historia de Cuenca y su Región (2011) 4. Arce, E., et al.: Maintenance project of the vernacular heritage architecture of the San Francisco de Oña neighborhood, vol. 1. University of Cuenca (2019) 5. Tenze, A.: Informe de evaluación de la Campaña de Mantenimiento de las edificaciones patrimoniales de Las Herrerías (2018–2019) (2021). Unpublished document 6. Consejo de Europa: Council of Europe Framework Convention on the Value of Cultural Heritage for Society (2005). Recuperado de https://www.coe.int/en/web/conventions/fulllist/-/conventions/rms/0900001680083746 7. ICOMOS Charter - Principles for the analysis, conservation and structural restoration of architectural heritage (2003) Art. 1.6 Downloaded (http://www.icomos.org/charters/structures_e. pdf. Accessed 01 June 2022) 8. Alberich, et al.: Metodologías participativas, Sociopraxis para la creatividad social. RedCIMAS-Observatorio Internacional de Ciudadanía y Medio Ambiente Sostenible, Madrid, España, DEXTRA (2015) 9. Achig-Balarezo, M.C., Guachichulca, J., Cardoso, F., Tenze, A.: Las Campañas de Mantenimiento del patrimonio vernáculo en tierra: el caso del barrio San Francisco de Oña, Ecuador. In: Terra 2022. 13th World Congress son Earthen Architectural Heritage, San Fe, New México, USA (2022) 10. Achig, M.C., Guachichulca, J., Cardoso, F., Tenze, A.: Las Campañas de Mantenimiento del patrimonio vernáculo en tierra: el caso del barrio San Francisco de Oña, Ecuador (2021) 11. Abril, D., et al.: Proyecto de mantenimiento de la arquitectura patrimonial vernácula del barrio San Francisco de Oña, Tomo 1. Universidad de Cuenca (2021) 12. UNESCO: Directrices prácticas para la implementación de la convención (1992). En Pérez S. y Fernández Víctor: Los paisajes culturales de Unesco desde la perspectiva de América
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M. C. Achig-Balarezo et al. Latina y el Caribe. Conceptualizaciones, situaciones y potencialidades: Revista INVI 30(85), 181–212 (2015) INPC: Guía Metodológica para el Paisaje Cultural Ecuatoriano, Quito (2015). disponible en: https://issuu.com/inpc/docs/ojo-guia_paisaje_cultural Conti, A.L.: La conservación y la gestión de las ciudades históricas desde la perspectiva del Paisaje Urbano Histórico. In: Encuentro Internacional “El Paisaje Urbano Histórico como herramienta del desarrollo urbano sostenible” (Quito, Ecuador, 9 al 11 de septiembre de 2015) (2015) Hobson, J.M., Hobson, J.M.: The Eastern origins of Western Civilization. Cambridge University Press, Cambridge (2004) Jokilehto, J.: World Heritage: defining the outstanding universal value. City Time 2(2), 1–10 (2006) Zancheti, S.: Dynamic integrity as an approach to the conservation of Historic Urban Landscape (HUL): the case of Olinda and Recife. In: International Meeting of Contemporary Architecture on Historic Settings (2013)
The Challenges of the Conservation of Earthen Sites in Seismic Areas Claudia Cancino(B) Department of Buildings and Sites, The Getty Conservation Institute, 1200 Getty Center Drive, Suite 700, Los Angeles, CA 90049, USA [email protected]
Abstract. During the 1990s, the Getty Conservation Institute (GCI) carried out a research and laboratory testing program, the Getty Seismic Adobe Project (GSAP), which investigated the performance of historic adobe structures during earthquakes and developed cost-effective retrofit methods that preserve the authenticity of these buildings. While the GSAP methodology was excellent and effective, it felt its reliance on high-tech materials, equipment and professional expertise was a deterrent to it being more widely implemented. To address this, the GCI initiated in 2009, the Seismic Retrofitting Project (SRP) with the objective of adapting the GSAP approach to better match the equipment, materials, and technical skills available in many countries with earthen sites located in seismic regions. The paper will analyze how the SRP was communicated and bought in by national and international stake holders, how high techniques analysis and low-key testing was combined to better understand the seismic performance of earthen sites, how the knowledge acquired in the process was disseminated among Peruvian and Latin American professionals, how two implementations’ projects were carried out and how a set of guidelines were adopted by Peruvian authorities. Keywords: Seismic retrofitting · Earthen heritage conservation · Conservation engineering
1 The Conservation of Earthen Sites For centuries, humans have constructed buildings using earth. This form of construction is universal and ever-present and can be seen in ancient archaeological sites such as the pre-Colombian city of Caral in Peru and in twentieth-century complexes like New Gourna Village in Egypt, designed by Hassan Fathy. Earth has been used in diverse regions and climates and ranges in scale from vernacular housing to large complexes, such as the almost 4,000 Ksour of Northern Morocco and the Mosque of Djenné in Mali. It has also been beautifully used in the form of decorated surfaces, such as the high reliefs of Huaca de la Luna in Trujillo, Peru, and the earthen plasters of Cliff Palace at Mesa Verde National Park in Colorado, USA (Figs. 1 and 2). While this legacy of earthen building constitutes a rich and vast heritage, earth remains to this day an omnipresent modern construction material and an essential form of shelter. Currently there is a total of 89 earthen sites out of the 897 sites on the World © J. Paul Getty Trust 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 709–723, 2024. https://doi.org/10.1007/978-3-031-39450-8_58
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Fig. 1. Kasbah Taourirt, Ouarzazate, Morocco.
Fig. 2. Huaca de La Luna, Trujillo, Peru.
Heritage List—10%. Of the 52 sites on the list considered endangered, 14 are made of earth—27% [1]. The United Nations has estimated that more than 30% of the global population lives in a house made of earth [2]. In this respect, earthen architecture represents a critical aspect of both social and environmental sustainability as well as a critical element of self-determination in many lesser developed regions of the world. Recyclable and low in energy consumption, earthen construction materials have a minimal carbon footprint. While earthen architecture while well maintained is often undervalued, it is a testament to cultural and technological diversity as well as adaptation to its environment, particularly for the latter, earthen architecture has adapted its techniques to face earthquakes, a major threat for its conservation.
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2 The GCI Vision for the Conservation of Earthen Sites Due to its widespread use and potential as a sustainable form of shelter, the Getty Conservation Institute (GCI) has engaged in a variety of projects and initiatives for over thirty years to advance the field of earthen conservation. These efforts have been founded upon strong collaborations with institutions and professionals from around the world. By working across different cultures and geographical borders, the GCI has aimed to create new knowledge that combines innovative research with traditional techniques. Some of the projects undertaken by the GCI include the Getty Seismic Adobe Project (GSAP), the Terra Project (Terra), and the Earthen Architecture Initiative (EAI). Additionally, the GCI has leveraged its resources to promote collective action and inspire a global network of committed professionals, including engineers, dedicated to the conservation of earthen architecture. The GCI thinks it is time to pause, reflect and design the next projects in a more holistic way, answering the international needs for the advancement of earthen conservation in a very pragmatic approach. The EAI has started the design of its project plan for the next ten years and the inclusion of other professions like conservation engineering will be essential. Additionally, the tackle of climate change and disaster management is a must to further advance the field. The EAI hopes to define and develop projects that could address these important issues soon.
3 Research for the Conservation of Earthen Sites Over the past 30 years, the GCI’s involvement in earthen architecture has greatly expanded. However, the organization’s initial foray into the field was due to a need for scientific research. In the 1980s, a small yet significant project was launched at Fort Selden under the guidance of New Mexico State Monuments (NMSM) and the National Park Service (NPS) Southwest Region. The project aimed to investigate the treatment of earthen archaeological remains through various interventions like chemical consolidation, capping, and protective coatings. In 1987, the GCI joined NMSM and NPS in undertaking Phase II of the research at Fort Selden. This phase focused on investigating chemical consolidants and other treatments for earthen walls, sparking the GCI’s direct engagement with earthen architecture. As a result of this engagement, several articles and reports were published [3]. In 1990, given the prevalence of earthen architecture in earthquake-prone regions of the world, the GSAP was established, in cooperation with Stanford University to develop and test minimally invasive and easily implemented techniques to avoid the collapse of historic earthen structures during a seismic event. This first approach addressing the vulnerability of earthen structures in seismic regions brought together architectural historians, engineers, and architectural conservators to design proper techniques using modern materials and professional expertise. Basing the research on articles 2 and 10 of the Venice Charter [4], the GSAP group provided a series of guidelines to implement the designed techniques for adobe historic buildings in California, USA.
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4 Professional Exchange and Knowledge Sharing on the Conservation of Earthen Sites The Getty Conservation Institute (GCI) values the sharing of knowledge - both its own work and that of others in research and practice - within the professional community. Over the past thirty years, the GCI has provided support for international conferences and colloquia that focus on preserving earthen architecture. Beginning with its participation in the Fifth International Meeting of Experts on the Conservation of Earthen Architecture in Rome in 1987, organized by ICCROM and CRATerre, and building on its previous research at Fort Selden, the GCI, the National Museum of the American Indian, and the National Park Service collaborated with ICCROM and CRATerre-EAG to organize the sixth international conference in Las Cruces, New Mexico - known as Adobe90. At this time, professionals working in the field were primarily architects and scientists with an interest in conserving earthen sites. Adobe90 played an instrumental role in transforming what were initially small, specialized meetings of experts into truly international conferences. This was achieved through a significant expansion of the number and geographic distribution of participants and papers, as well as the production of a substantive publication that helped to legitimize the work being done in the field. As a result of these efforts, Adobe90 set a new standard for conferences within the earthen architecture community and inspired institutions in other regions of the world to take on the sponsorship of similar international conferences. Today, these conferences occur every four years and receive hundreds of abstract proposals. During Adobe90, a section on structural conservation was presented for the first time, although a couple of papers had been presented during previous conferences and colloquia [5]. With the intention of organizing the first conference in Africa, the GCI partnered with the Ministry of Culture of Mali to carry out the 10th Terra conference. Four hundred and fifty participants from sixty-five countries attended the conference in Bamako in 2008 [6]. In June 2022, the GCI-EAI in collaboration with the National Park Service, Vanishing Treasures Program and University of Pennsylvania, Stuart Weitzman School of Design and under the aegis of ICOMOS–ISCEAH, organized the thirteen congress in Santa Fe New Mexico. Hundreds of specialists in the fields of conservation, anthropology, archaeology, architecture and engineering, scientific research, and site management of earthen architectural heritage including regional practitioners from the pueblos, tribes and communities in and around New Mexico engaged in caring for this heritage attended the congress. The four-day program convened a diverse group of professionals from a wide range of geographic regions to share their knowledge and experience on the state of the art of earthen heritage study and conservation through presentations, posters, and videos/digital media (Fig. 3). Up to this point, these international colloquia, conferences, and congresses have strengthened collaboration, created regional networks, generated partnerships, and produced proceedings. Three of these proceedings have been published by the GCI. The GCI is also committed to promoting professional exchange globally through institutional support for professional networks such as ISCEAH, Proterra, and Mediterra. The latter collaborated with the GCI to develop its strategic planning in 2009 [7].
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Fig. 3. Participants of the XIII Terra congress in Santa Fe, New Mexico, United States.
The Getty Conservation Institute (GCI) has organized several international colloquia to address specific issues related to the conservation of earthen sites. In 2001, the GCI organized the Protective Shelters for Archaeological Sites in the Southwest colloquium in Tumacacori, Arizona, USA under the umbrella of Terra. Three years later, another Terra colloquium was organized in Mesa Verde, Colorado in 2004 to address the challenges facing the conservation of decorated surfaces on earthen architecture. Two years later, the GCI organized another colloquium at the Getty Center in Los Angeles, California, under the umbrella of the EAI, to assess the impact and efficacy of the GSAP. As described later in this paper, the Seismic Retrofitting Project (SRP) was created in response to the conclusions and recommendations made during this colloquium [8].
5 Education and Capacity Building While all the Global Citizenship Institute’s efforts in the field of earthen architecture have primarily aimed to promote and exchange knowledge, initiatives targeted towards education have concentrated on cultivating a variety of specialists in this area. Through the Gaia Project, four Preservation of Earthen Architecture (PAT) courses were organized between 1989 and 1994 in Grenoble, France, bringing together professionals from around the world for specialized training in earthen architecture conservation. In late 1994, the GCI joined forces with the Gaia Project to translate the international PAT curriculum into a regional, site-based training program. Hosted at the archaeological site of Chan Chan in Trujillo, Peru, PAT96 and PAT99 integrated site management planning into the more technically oriented curriculum, in response to the needs of the field at large to contextualize conservation within a broader decision-making framework for heritage stewardship. During these two PAT courses, Peruvian engineers with expertise in the conservation of earthen sites participated as instructors. With this training partnership, the Gaia project evolved into Terra, which provided a platform for institutional collaboration in research, education, and professional development. The cumulative PAT experiences helped to further build the network of those practicing and teaching earthen architecture conservation. These experiences also led to the development of the EAI Guidelines for the Teaching of Earthen Conservation, a series of teaching resources adapted from the PAT course materials available at the GCI website. However, the subject of conservation engineering was not properly developed even though the course was using a site located in a seismic region. This had to do with the fact that in these first courses and the development of didactic materials focused on a
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strong need -at that time- to emphasize the importance of management of archaeological sites made of earth. Since then, the institute has conducted workshops and informal training, but there have not been any additional formal courses in earthen architecture. Several institutions, such as CRATerre in France and Dachverband Lehm in Germany, serve the European area, but there are limited professional training opportunities for the regions of North Africa, the Middle East, and Central Asia, which are home to most of the world’s earthen heritage. Additionally, these regions were identified by the GCI as in need of training in the conservation of earthen sites. Because of that, the GCI partnered with the Abu Dhabi Department of Culture and Tourism to organize a course to serve mid-career professionals in the region (primarily heritage managers, architects, conservators, engineers, archaeologists) who work with earthen buildings and archaeological sites. Abu Dhabi was selected as the ideal location for this course because of its rich earthen heritage, professional level facilities, central location near the world’s most important earthen sites, and good partnership opportunity with DCT. To this date, two courses in 2018 and 2022 have been carried out for a total of 44 participants from Morocco, Egypt, Jordan, Palestine, Turkey, Afghanistan, Kingdom of Saudi Arabia, Oman, China, and India, among others. This course also includes a section on conservation engineer of earthen heritage as part of its curricula. The next course will be held also in Abu Dhabi in February 2025 [9] and the institution and its partner is looking into start developing more precise training materials on this topic (Figs. 4 and 5).
Fig. 4. Participants of the 2018 Earthen Architecture Course in Abu Dabhi, UAE.
6 Field Projects on the Conservation of Earthen Architecture Perhaps the first GCI fieldwork related to the conservation of earthen sites was the Fort Selden Phase II project, although it was based on research. Much has evolved since then in the field of earthen conservation, both in general and in the GCI’s approach to implementing fieldwork. After our experience at Fort Selden, the importance of implementing
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Fig. 5. Materials science class. Right: Structural engineer class
discrete interventions has evolved into a more holistic approach to preserving earthen sites while also designing solutions for specific problems with the potential for wider impact. Terra and later the EAI consider planning as a powerful tool for the conservation of earthen sites in a comprehensive way but still realize the need to investigate specific treatments and/or interventions to address other issues jeopardizing earthen sites. In recent decades, special attention has been paid to the complexity of addressing the seismic vulnerability of earthen buildings while preserving their historic fabric. Similarly, adapting historic urban settlements made of earth to safe and modern living conditions has also been identified as a need. In the last five years, the EAI has carried out model projects that intends to improve the way conservation interventions are carried out in two major areas: Seismic retrofitting and rehabilitation of historic earthen buildings. The Conservation and Rehabilitation Plan (CRP) for the earthen ensemble of Taourirt in southern Morocco is another EAI model project which aims to develop a methodology for the conservation and rehabilitation of this traditional earthen ensemble that can be used as a model for similar earthen sites across the Maghreb. The CRP’s objective is to establish a conservation process that demonstrates appropriate re-use of such sites, respects the original building fabric, and preserves technical knowhow [10]. 6.1 The SRP On August 15, 2007, an earthquake of 8.0 Moment Magnitude (Mw) and a maximum local Modified Mercalli Intensity (MMI) of VII–VIII occurred with an epicenter off the coast of Pisco, Peru, resulting in 519 deaths and 1,366 injuries. A total of 650,000 people were affected and 80,000 dwellings damaged. From October 28 to November 2, 2007, a rapid assessment to better understand the failure of fifteen historic earthen sites was performed by a multidisciplinary team of national and international experts convened by the GCI. The assessment, which was organized in response to a request from the former Instituto Nacional de Cultura del Perú (INC, Peruvian National Institute of Culture; now the Ministerio de Cultura del Perú, or Peruvian Ministry of Culture), was also published [11].
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Building upon the GSAP Colloquium conclusions mentioned above, the GCI designed in 2010 a seismic retrofitting research project with the objective of adapting the GSAP guidelines for countries where equipment, materials, and technical skills are not readily available by providing low-tech, cost-effective seismic retrofitting techniques and easy-to implement maintenance programs for historic earthen buildings that could improve their seismic performance while preserving their historic fabric. To accomplish this, the GCI joined with the Ministry of Culture of Peru and the School of Sciences Engineering at Pontificia Universidad Católica del Perú to launch in June 2011 the Seismic Retrofitting Project (SRP). Several schools of engineer joined the project at some points, like the Department of Architecture and Civil Engineering at the University of Bath and the Department of Civil, Environmental and Geomatic Engineering of the University College London in the United Kingdom. Currently the SRP is working with the School of Engineering at the University of Minho in Portugal. The project aims to design and test retrofitting techniques; to provide a methodology of intervention for those responsible for implementation, including conservation professionals, building officials, site managers and local builders; and to work with authorities to gain acceptance of these methods. Peru was selected as the location for the project due to the current and historical knowledge and professional interest in the subject; the existence of potential partners for implementation of these techniques on model conservation projects; and background work already completed by the GCI. The SRP is being carried out in four phases: 1) feasibility; 2) research, including laboratory testing and numerical modeling; 3) dissemination of the methodology and results, and 4) implementation of model projects. As part of the first phase four building typologies were defined and one representative construction was selected from each typology for further study. The definition of the typologies examined the characteristics of historic earthen heritage in South America, considering the constructions for which retrofitting techniques are much needed. Several characteristics were considered including use (residential or religious), location (Pacific coast or Andes region), and construction techniques. The selection process included site visits and evaluation of several criteria; among them, it was preferred that the selected building demonstrated typical modes of failure, so that the designed reinforcing techniques could be widely applied. The four building prototypes are: Hotel El Comercio in Lima and Ica Cathedral in Ica (near the Pacific coast), Casa Arones in Cusco and church of Santiago Apóstol of Kuñotambo (Andes region). The first two prototype buildings, Ica Cathedral and Hotel El Comercio, represent the very early adoption in Peru of anti-seismic measures including thin-walled adobe construction on the ground floor and lightweight quincha (a form of wattle & daub) construction for upper floors and roofs. In contrast, the two prototypes in the Cusco region are constructed with very thick adobe walls throughout and heavy timber truss roofs. These differing construction techniques and uses provided a representational group of earthen architecture typologies in the region. From 2010 to 2011, the SRP studied and analyzed the building prototypes resulting in the publication of the Construction Assessment report. The second phase of the SRP started in 2011 and focused on the experimental and analytical investigations, including laboratory testing and numerical modeling. This phase demanded a close interaction between the construction assessments developed in
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the first phase, the experimental testing, and the numerical analysis. Numerical models for all four building prototypes were developed first at the University of Bath to represent the actual state of each of the building prototypes. The evolution of the models was transferred from Bath to UCL, which has published a series of papers describing UCL partial results of this phase [12]. From 2015 until 2017, the University of Minho used modeling as a method to understand structural behavior of the SRP building prototypes and validate the retrofitting techniques later design for them. The way modeling has been used was quite innovative, advancing the field of structural analysis of structures made of earth. From the second phase, four research reports have been published in English and Spanish: “Testing of Materials and Building Components of Historic Adobe buildings in Peru” [13], “Recommendations for Advance Modeling of Historic Earthen Sites” [14], “Modeling of Prototype Buildings” [15] and “Simplified Calculations for the Structural Analysis of Earthen Historic Sites” [16] (Fig. 6).
Fig. 6. Set of research reports as part of the SRP available on the Getty website
Communication with Local and International Stake Holders. Since its conception of the project GCI staff and consultants have traveled to Peru to study and analyze the buildings at least three times a year. During each visit, GCI staff make the effort to always carried out meetings with MDC authorities as well as owners and managers of each of the four prototype buildings. These meetings have the objective to inform the authorities of the advancement of the work as well as next steps. The project always met with those local actors at the beginning and at the end of each campaign, which normally lasted three weeks. As part of the campaign, GCI staff and consultant met with local communities with an interest in the project. Similarly to the meetings with authorities, the advancement of the project was presented to all community members and discussions about next steps were carried out. It was the enthusiasm of local communities which produced the elaboration of construction documents for the Church of Kuñotambo as well as Ica Cathedral, the retrofitting of the first one as part of the implementation of the conservation project of the Church by the local branch of the MDC in Cusco, and the participation of a representative of the Kuñotambo community at the Terra 2022 congress with the intent to create international relations with similar communities across the globe. The implementation of the Ica Cathedral conservation and retrofitting project is expected to start in 2023.
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The SRP also created a peer review group to meet and review the work done at key moments of the project. The SRP peer review group was composed by professional with expertise in conservation engineering, architectural conservation, and conservation of earthen sites from different countries representing ISCEAH, ISCARSAH, CRATerre, PROTerra, University of Minho, University of Cambridge, Massachusetts Institute of Technology, Fundación Antiplano (Chile), Technical University of Catalonia as well as local institutions like the Pontificia Universidad Católica del Perú and local engineering design studios. The first meeting of the SRP peer review was organized in Lima with a site visit to Hotel El Comercio and Ica Cathedral in July of 2011with the objective of reviewing the project methodology, the publication of the Construction Assessment report and the proposal for the testing and modeling research phase. The second meeting of the SRP peer review group was organized in Cusco with a site visit to Casa Arones and the Church of Kuñotambo in July of 2017 with the objective of reviewing the results of the testing and modeling research phase (Figs. 7 and 8).
Fig. 7. Presentation of Ica Cathedral Construction Documents to authorities in Ica, Peru.
The SRP would have never been successful on implementation if it was not because of the creation of channels of communication at the local and international level. Retrofitting projects are not just technical solutions to a problem. For sites located in seismic regions, the retrofitting of historic sites is a question of life and dead. Communities know the importance of preserving the site but also the need to keep the site safe. Churches should be places where communities go after an earthquake and not a place they run out of when once happens. The sense of feeling safe in a historic site is something that the public only learns once informed. It just not happened when the building is retrofitted. The continuous information and involvement of the community is extremely important, particularly to ensure the regular maintenance of the site once retrofitting is implemented. Similarly, the engagement of the international community
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Fig. 8. Visit of SRP peer review group to Kuñotambo, Cusco, Peru.
enriched the project content and outcomes but gave a push to self-confidence to the community and created pride on their heritage. High Techniques and Low-Key Testing. The Testing publication is a summary and conclusions of the more than 300 experimental tests to characterize the materials and structural components of the four building prototypes, carried out PUCP campus. The performed tests were designed and carried out as part of the SRP, being some of these implemented for the first time on earthen materials, structural components and/or traditional construction techniques, providing valuable information to the field. The tests also provided valuable information to the partial and global models of each of the prototypes later developed by the University of Minho. Partial Results of the testing program have been published in several international conferences. The final report gives a general overview and a deeper understanding of the mechanical behavior of materials and structural components of historic earthen buildings in Peru. To understand the modes of failure of the building protypes under seismic loading and considering those depend on the mechanical properties of units and mortar and on the overall geometric configuration of the building (Varum et al. 2014), the project investigated the main structural analysis methods available, both static and dynamic, as well as the finite element method (FEM). Different modeling techniques or homogenization techniques were also used, including the different constitutive models available in commercial software. The use of high techniques for modeling and low-key testing methods was the perfect alliance to move the project forward. While conducting the testing and modeling a series of workshop regarding the project methodology was delivered to Peruvian professionals as well as an upcoming workshop on the use of the modeling techniques not only for analysis but also monitoring will be delivered this year. Additionally, it was extremely important to use the process layout at the Burra Charter, particularly to understand the values of each site, their significant features and attributes to identify which elements could be modified or intervened to provide the needed level of performance. This exercise generated a dialogue between the different
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professionals and stake holders involved in the project that has continued until today. Trying to find a common methodology that pleases conservation engineers and architectural conservators has been a challenge but a very productive exercise. The ultimate outcome of the SRP will be a series of guidelines to be developed with the Ministry of Culture of Peru. These will include the detail description of the methodology used for the significance of the prototypes, the study of the structural systems, the desired performance level, the tests and modeling performed to understand modes of failures and provide proper retrofitting and repairs techniques. The Importance of Dissemination and Implementation. The activities carried out as part of the implementation phase have been significative for the advancement of the project. For the development of the structural component of Ica Cathedral and Kuñotambo, the GCI worked with engineers Daniel Torrealva and Erica Vicente from the Pontificia Universidad Católica del Perú. For Ica Cathedral, the GCI also worked with consultant conservation architects José García Bryce and Mirna Soto to develop all construction documents, as well as the timber specialist, Mikel Landa. For the Church of Kuñotambo, the architectural and conservation proposal was developed by the MDC branch in Cusco, under the direction of architectural conservator Etel Hania Cruz Moscoso; in collaboration with the GCI [17] (Fig. 9).
Fig. 9. (a) Participants at the Kuñotambo inauguration, (b) Interior of the Church after retrofitting.
Construction work by the MDC branch in Cusco started in September 2016. The worksite supervision by the MDC was crucial to ensure the drawings were carefully executed and the seismic retrofitting works were implemented as expected. Major changes to the structural interventions were tested in the numerical model before their approval. During the worksite, the GCI organized several workshops for the professional staff of the MDC to disseminate the approach to the conservation of the church and to share the findings of the research. The church was inaugurated in June 2019 with a ceremony attended by various international and Peruvian stakeholders and saw the participation of the communities of Kuñotambo and of the nearby villages [18]. The possibility to show the completion of a retrofitting project during the implementation phase was major for the project. Furthermore, the GCI in collaboration with Peruvian partners and local stakeholders has installed a Structural Monitoring system for the church of Kuñotambo, as part of larger Maintenance and Monitoring plan. The
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plan will contribute to extend the life of the site and manage its risks; to verify the results of the interventions with particular attention to the seismic retrofitting of the structure and the conservation of its decorated surfaces; and, to monitor the behavior of the building over time and changes after major events. On May 26, 2022, a few weeks after the implementation of the monitoring system, there was a 6.9 earthquake with the epicenter in Ayavari, Puno but felt in the Cusco region. The site was not damaged, and the monitoring system was able to record the event and send the plots generated by the sensors to the University of Minho. The project hopes to start the implementation phase of Ica Cathedral in 2023 and once finished, the same system will put in place for further monitoring of the site.
7 The Challenges and Opportunities of the Conservation of Earthen Sites in Seismic Areas For the past 30 years, the GCI has been working in the field of earthen conservation addressing a series of issues for archaeological sites and historic buildings. As part of congresses, model project, scientific research and capacity building activities, the GCI has involved a series of professionals expanding the field. The importance of a multidisciplinary team has been crucial to approach the conservation of earthen sites in a holistic manner. The multidisciplinary work required that architects, conservation engineers, conservators and community leaders speak the same language. ICOMOS has created a series of international scientific committees which have developed a series of guidelines and charts that have helped to shape this new language. New advances have been developed to tackle projects in all-inclusive approach and now more structural engineers are able to address the retrofitting of earthen sites and have been training at the post-graduate level to properly implement repair and retrofitting techniques. However, a more specific approach for the conservation of earthen sites in seismic regions need to be further developed. The principles of authenticity should be applied in different ways while dealing with sites threated by earthquakes. The resilience of heritage against earthquakes needs to be studied and preserved, particularly the t traditional approach of conservation, including maintenance. However, if modes of failures have been identified, the possibility of reconstruction and use of modern techniques should be considered; particularly if the site needs to perform at the level to avoid total collapse and secure life. The multidisciplinary approach supports the development of innovative solutions that could address several issues like heritage resilience, sustainability, and adaptation to the environment.
References 1. Cancino, C.: From Visionary Leadership to a Field of Study. Over Fifty Years of Earthen Architecture Conservation. Conservation Perspectives. The GCI Newsletter, Spring 2022. Conservation of Earthen Architecture, pp. 4–12 (2022) 2. United Nations: Table 12: Occupied housing units by type of housing unit, construction material of outer walls and urban/rural location: latest available year, 1995–2010
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3. Oliver, A., Getty Adobe Project, Getty Conservation Institute, and Museum of New Mexico: Fort Selden Adobe Test Wall Project: Phase I: Final Report. Getty Conservation Institute, Los Angeles (2000). http://hdl.handle.net/10020/gci_pubs/fort_selden_project 4. Article 2: The conservation and restoration of monuments must have recourse to all the sciences and techniques which can contribute to the study and safeguarding of the architectural heritage. Article 10: Where traditional techniques prove inadequate, the consolidation of a monument can be achieved by the use of any modern technique for conservation and construction, the efficacy of which has been shown by scientific data and proved by experience. International Charter for the Conservation and Restoration of Monuments and Sites 1965. (The Venice Charter- 1964). IInd International Congress of Architects and Technicians of Historic Monuments, Venice, 1964. Adopted by ICOMOS in 1965. https://www.icomos.org/en/partic iper/179-articles-en-francais/ressources/charters-and-standards/157-thevenice-charter 5. International Council on Monuments and Sites. U.S. Committee, and Getty Conservation Institute: 6th International Conference on the Conservation of Earthen Architecture Adobe 90 Preprints: Las Cruces, New Mexico, U.S.A., 14–19 October, 1990. Getty Conservation Institute, Los Angeles (1990). http://hdl.handle.net/10020/gci_pubs/adobe90 6. Rainer, L.H., Rivera, A.B., Gandreau, D. (eds.) Terra 2008: Proceedings of the 10th International Conference on the Study and Conservation of Earthen Architectural Heritage, Bamako, Mali, 1–5 February 2008. Getty Conservation Institute, Los Angeles (2011). http://hdl.han dle.net/10020/gci_pubs/terra_2008 7. Achenza, M., Cancino, C., Correia, M., Ferron, A., Guillaud, H. (eds.) Experts Workshop on the Study and Conservation of Earthen Architecture and Its Contribution to Sustainable Development in the Mediterranean Region, Final report, 20 August 2009. Villanovaforru, Sardegna, Italy, 17–18 March 2009. https://www.getty.edu/conservation/our_projects/field_ projects/earthen/mediterra_finalreport.pdf 8. Hardy, M., Cancino, C., Ostergren, G. (eds.) Proceedings of the Getty Seismic Adobe Project 2006 Colloquium: Getty Center, Los Angeles, 11–13 April 2006. Getty Conservation Institute, Los Angeles (2009). http://hdl.handle.net/10020/gci_pubs/gsap 9. Getty Conservation Institute: International Course on the Conservation of Earthen Architecture. https://www.getty.edu/conservation/our_projects/field_projects/earthen_arch_course/ 10. Getty Conservation Institute: Conservation and Rehabilitation Plan for the Kasbah of Taourirt (2011–2016). https://www.getty.edu/conservation/our_projects/field_projects/kasbah/ 11. Cancino, C.: Damage Assessment of Historic Earthen Buildings after the August 15, 2007 Pisco, Peru Earthquake. Getty Conservation Institute, Los Angeles (2011). http://hdl.handle. net/10020/gci_pubs/damage_assessment 12. Ferreira, C.F., D’Ayala, D., Fernandez Cabo, J.L., Díez, R.: Numerical modelling of historic vaulted timber structures. Adv. Mater. Res. 778, 517–525 (2013) 13. Torrealva, D., Vicente, E., Michiels, T.: Seismic Retrofitting Project: Testing of Materials and Building Components of Historic Adobe Buildings in Peru. Getty Conservation Institute, Los Angeles (2018). https://hdl.handle.net/10020/gci_pubs/testing_materials 14. Lourenço, P.B., Pereira, J.M.: Seismic Retrofitting Project: Recommendations for Advanced Modeling of Historic Earthen Sites. Getty Conservation Institute, Los Angeles; TecMinho– University of Minho, Guimarães (2018). https://hdl.handle.net/10020/gci_pubs/advanced_ modeling 15. Lourenço, P.B., Greco, F., Barontini, A., Ciocci, M.P., Karanikoloudis, G.: Seismic Retrofitting Project: Modeling of Prototype Buildings. Getty Conservation Institute, Los Angeles; TecMinho – University of Minho, Guimarães (2019). https://hdl.handle.net/10020/ gci_pubs/modeling_prototype_buildings 16. Lourenço, P.B., Pereira, J.M., Torrealva, D.: Seismic retrofitting project: simplified calculations for the structural analysis of earthen historic sites. In: Collaboration with Maria Pia
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Ciocci, Federica Greco, Giorgos Karanikoloudis, and Claudia Cancino. Getty Conservation Institute, Los Angeles (2021). http://hdl.handle.net/10020/gci_pubs_simplified_calculations 17. Cancino, C., Macchioni, E., Marcus, B., Mellado, J.C., Menéndez, J.C.: Seismic retrofitting using local materials and expertise at a church in Kuñotambo, Peru. APT Bull. J. Preserv. Technol. 51(2/3), 23–30 (2020). (8 pages) 18. https://www.getty.edu/news/newly-conserved-church-in-peru-offers-a-model-for-the-preser vation-of-earthen-buildings-at-risk/
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made. The images or other third party material in this chapter are included in the chapter’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Post-Earthquake Assessment and Possibilities for Management of Existing Masonry Buildings Karlo Oži´c(B) , Mislav Stepinac, Luka Luli´c, and Dominik Skokandi´c Faculty of Civil Engineering, University of Zagreb, 10000 Zagreb, Croatia [email protected]
Abstract. 2020 Zagreb earthquake sequence provided unprecedented opportunity to answer many unknowns and uncertainties in the understanding on earthquake performance of masonry buildings and to analyze many concerns affecting the post-earthquake assessment and renovation strategies in Croatia. These decisions are based on the updated knowledge obtained through the assessment. Condition assessment can be done on multiple levels, e.g. basic visual assessment of a structure, assessment with various destructive, non-destructive and semi-destructive testing methods, interpretation of a data from structural health monitoring, various levels of structural modelling and safety verification formats. Procedures mentioned are carried out to collect the data on several significant factors that affect the seismic behavior of buildings. The comprehensive data and overview on the seismic performance and management of masonry buildings after the earthquakes in Croatia can be used to test the effectiveness of existing models and to inform the development of new models for seismic risk assessment and resilience analysis. The condition assessment and renovation process of building of exceptional heritage importance will be presented and discussed. The value of information analysis presented for a case study building shows how additional information and acquired knowledge brings multiple benefits in retrofitting and management process. Keywords: Earthquake · Assessment · Existing buildings · Masonry · Value of information
1 Introduction Earthquakes are rare, destructive events that have significant effects on the built environment, human life, and society. They can cause significant damage to populated areas and often lead to financial crisis due to the cost of rebuilding and recovery. In recorded history, Croatia has been hit by many earthquakes and has significant seismic activity. The city of Zagreb, as the most populated part of Croatia, has rather high seismic risk. The seismic hazard is moderate as seen in Fig. 1, but in combination with dense population and quite vulnerable built environment (age of structures, low maintenance, illegal construction, and numerous reconstructions) it builds up to high seismic risk. While the scientific community has tried to raise awareness and progressed in understanding © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 724–735, 2024. https://doi.org/10.1007/978-3-031-39450-8_59
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earthquakes, there are still many unknowns and uncertainties especially in the case of existing buildings. The worst earthquake in Zagreb up-to-now was 140 years ago and caused severe damage to the city. The magnitude of this earthquake was 6.2 (M L ), while historical records say that it caused great damage to buildings, the fall of almost all chimneys, and the eviction of a large number of people (6000 people, 20% of the population at the time) [1]. Nevertheless, the past is easily forgotten and, even though Zagreb and its surroundings lie in a seismically active area, major earthquakes appear infrequently and the public perception of the disaster they can cause is almost totally neglected. On the 22nd of March 2020, at 6 h and 24 min, the area of the City of Zagreb and its surroundings were hit by an earthquake with magnitude of 5.5 (M L ) (Fig. 1) and intensity VII according to the EMS-98 scale [1]. Afterwards, the City of Zagreb and its surroundings were hit by a series of medium-strong and minor earthquakes. The earthquake caused one casualty, 26 injuries (18 severe), and thousands of displaced people. As Zagreb’s historical urban core is mostly built in masonry, the main earthquake damaged most old town buildings, residential and public. In addition, most of these buildings have exceeded their design working life. In seismic terms the earthquake was of moderate magnitude, it caused (unusually) great material damage. More than 26,000 buildings i.e., 20% of all buildings were damaged in Zagreb and its surroundings, while this number raises to almost 50% in historical urban core. Following this recent earthquake, it is of great importance to have a decisive and effective assessment and maintenance plan with the greatest possible utility (health, safety, monetary, sustainability, functionality). To this purpose, the reduction of epistemic uncertainties can be achieved through various inspection techniques. Visual assessment, destructive, semi-destructive and non-destructive testing (NDT) methods and collecting the data with structural health monitoring (SHM) systems are essential parts of strengthening existing structures [2]. Also, the role of updated knowledge and quantifying the Value of Information (VoI) should be investigated in order to reduce uncertainties in the design of existing buildings in the long term.
Fig. 1. Preliminary Earthquake Intensity Map (a) from the 22nd of March 2020, at 6:24 (CET) (adapted from [3] compared with expected peak ground accelerations (b) for a return period of 475 years [4].
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2 Methods and Methodology There is a strong need for an assessment of existing masonry buildings, in particular for those whose design working life has expired. The most typical reasons, besides expired design working life, are construction built before first earthquake regulations, illegal renovation, change in the use of the building, insufficient maintenance and finally visible damage of the structure because of exceptional incidents or accidental loads. In managing the performance of an existing structure, decision making is strongly associated with the condition assessment, encompassing comprehensive and qualitative measurements and properly collected data in a cost-effective way. The first major step in a post-earthquake assessment is a rapid, preliminary usability assessment [5, 6] of buildings damaged in the earthquake. The idea is to, firstly, take care of citizen’s safety in moments of crisis and decide for each building is it safe to use. For 2020 Zagreb earthquake, this part of work was carried out in extremely difficult conditions, not just due to continuing aftershocks, but also because the country was under a severe lockdown due to the COVID-19 pandemic. In Croatia, this type of assessment consisted of a quick visual inspection of individual elements of the load-bearing structure, stating the appropriate degree of damage and deciding on the classification of the building into one of six possible categories (Fig. 2): U1 Usable without limitations (Green label), U2 Usable with recommendations (Green label), PN1 Temporary unusable—detailed inspection needed (Yellow label), PN2 Temporary unusable—emergency interventions needed (Yellow label), N1 Unusable due to external impacts (Red label) and N2 Unusable due to damage (Red label).
Fig. 2. Six categories of usability divided into three original labels (in Croatian) [7]
2.1 Research Works Assessing the strength and reliability of existing buildings is a complex and challenging task that comes with many limitations and uncertainties regarding the real building behavior as seen in [8–12]. Typically, assessments start with a preliminary inspection based on visual observations and an evaluation of available records. The results of this initial assessment determine whether further in-depth assessments are necessary. In order to reduce epistemic uncertainties to a satisfactory level, structural engineers should try to obtain as much information as possible to still have, in economic terms, optimal construction. However, this is not always feasible, and there is a delicate balance between minimizing costs and minimizing invasiveness. When dealing with cultural heritage structures,
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engineers need to find a middle ground between being too cautious, which can lead to excessive structural interventions, and being too invasive, which can cause harm to the defining elements of the heritage building. The goal is to minimize the cost and invasiveness of any experimental tests performed on the structure which results in two conflicting sides of the conservation principle/minimizing the costs and invasiveness. Research work plays a crucial role in the assessment of heritage masonry buildings because it provides a deeper understanding of the materials, techniques, and construction methods used in the past, as well as the degradation mechanisms that affect these structures over time. In Zagreb scenario, as recommended in EN 1998-3 [13], non-destructive, semi-destructive and destructive tests were conducted to assess mechanical properties of materials. Additionally, in historic urban cores, cultural identity is often connected to the facades of culturally protected goods. To capture 3D data of the facades, point clouds were obtained by laser scanning (Fig. 3) or drone imaging. The mentioned data can also be used to assess existing structures for the creation of a 3D numerical model, as seen in the following papers [14–16]. The main focus of research works is to determine mechanical properties of materials. Most commonly used are semi-destructive tests for in-situ masonry shear strength (Fig. 4a) and test methods using flat jacks (Fig. 4b). In-situ masonry shear strength test is conducted using a small hydraulic jack. Because of its relative simplicity, this fast check can be conducted on several locations in a short amount of time.
Fig. 3. Point clouds from laser scanning.
More complex and time-consuming test method using flat jacks enables a more reliable determination of mechanical properties. This method mostly relates to the determination of vertical stress in the wall and elastic modulus (dependence between stress and strain in compression). Flat jacks compose of two steel plates welded together at the periphery. To increase the pressure in flat jacks, a hydraulic pump is used connected to input and output valves to which the jack is connected. Testing with flat jacks is described in ASTM [17–19] and RILEM recommendations [20, 21]. Biggest disadvantage of this method is the time and equipment needed to conduct the tests. Number of different non-destructive tests (methods) can also be used such as the ultrasonic pulse velocity method [22], Schmidt rebound hammer [23] and the sonic tests and impact echo method [24].
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Fig. 4. Test site: in-situ masonry shear strength test (a), test method using flat jacks (b)
3 Value of Information Analysis In post-earthquake assessment of existing buildings number of epistemic uncertainties is larger than in new buildings design. Even more so, they all add up to aleatory ones. To reduce the number of uncertainties extensive on-site testing campaign is conducted. In EN 1998-3 [13] knowledge levels (KL) are defined as a function of the information obtained to overcome current incomplete knowledge regarding geometry, structural details and material properties. EN 1998-3 [13] defines three knowledge levels KL1, KL2, KL3, where the highest level of knowledge corresponds to KL3. In the assessment and design process, engineer or decision-maker chooses to satisfy a certain KL. To achieve certain level enough information needs to be gathered through visual assessment and methods described in the paragraph above for the on-site testing. Each KL corresponds to a Confidence factor (CF) which is then applied to one particular parameter, assumed to be the most critical in affecting building’s response. When an engineer chooses to be satisfied with a lower KL it produces a more conservative result, which can lead to a more expensive and invasive retrofitting as more interventions could be required even if not strictly necessary. This leads to two conflicting sides of the conservation principle/minimizing the costs and invasiveness. Finally, it is of great importance that the assessment result is as close as possible to the real behavior to satisfy the idea of ‘minimum intervention’. To handle these processes, decision making can be considered as a ‘game’ in which the goal is to maximize expected utility by choosing the best options [25, 26]. The utility is always related to decision makers preferences over the set of possible outcomes. Even though utility includes the benefits from longevity, functionality, cost of maintenance, repair actions, risks of failure, it is typically expressed in monetary costs. To this purpose, Value of Information (VoI) [27] analysis is introduced. It can be defined as quantification of the expected utility or benefit increase due to additional or predicted information. A rational approach to decision making is provided by Bayesian decision analysis. It states that rational behavior can be described as maximizing the expectation of a utility function. It enables the decision maker to quantify the expected benefits of various assessments prior to making a decision on which option to choose and thus put a price tag on them. Thus, the decision maker can decide how much it is worth to pay for different types of assessments. This form of decision analysis is here presented in the form of the
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decision tree. The decision problem can be seen as a game between two players, the decision maker and a player called ‘chance’. The game consists of four moves (Fig. 5): the decision maker chooses an experiment e, chance decides the outcome z, the decision maker chooses an action and finally, chance chooses state θ. The game ends and the decision maker obtain the ‘payoff’ through utility u (e, a, z, θ). The Bayesian analysis developed by Raffa and Schleifer [25] is based on a concept in which prior belief is updated with additional information with support for likely values of that parameter drawn from sampled data. Through Bayes’ theorem the current knowledge combined with these collected data allows decision makers/engineers to predict the level of knowledge after the data is collected. Move no.1 Decision maker selects an e in E
- Choice node
Move no.2 Chance selects a z in Z according to the assigned probability
- Chance node
Move no.3
Move no.4
Decision maker selects an a in A
Chance selects a θ in θ according to the assigned probability
- Utility node
- Non-considered branches
Payoff Decision maker receives u (e, z, a, θ)
- Considered branch
Fig. 5. Decision tree
4 Decision Problem The general aim from owner’s perspective is to extend service life of the structure while optimizing the retrofitting process in economic terms. Certainly, to ensure normal use of the building seismic resistance of the building must be satisfied. In this process, additional investments e.g., SHM tools or advanced calculation can be justified by minimizing costs of operation and maintenance. For this reason, a decision-making process is necessary to maximize the benefits of the structure’s existence and reduce unnecessary costs. The owner’s decision on actions or choices greatly depends on the information gathered about the structure. To gather it he can opt out on visual inspection only, assessment according to present codes, assessment based on NDT results or data gained from SHM, etc. More precise data gathered with advanced inspection and monitoring methods are more useful but rather costly (Fig. 6). The important and often rather difficult question regarding additional data is are they a worthwhile investment. Through a simple case study based on the methodology developed in [28–30] procedure will be explained. It is a residential building located in Zagreb, under cultural protection. It consists of basement, 4 floors and attic. It is an H-shaped building built in unreinforced masonry with wall thickness from 60 to 45 cm, while the floor structures and roof are made of timber. In rapid usability assessment, after 2020 earthquake, it was classified as temporarily unusable.
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Prior to taking a final decision about physical action to alter the current condition, the owner can decide to invest in a condition assessment of the structure to see if the current state of the elements is critical or if it will show satisfying results. In the present study, three possible choices for assessment, i.e., obtaining additional data, were considered for enhanced assessment. Decision alternatives represent different scenarios for which the outcome probabilities and related consequences need to be quantified. In this case study, the decision consists of four main branches. Each branch represents one of the assessment levels explained in Table 1, while e0 represents a referent branch connected to no assessment conducted. Branches divide in subbranches that can result in one of two system states, based on the choice in the action nodes: do nothing a0 or strengthen and/or repair a1 (Table 2). The outcomes are states with related probabilities when a structural failure occurs or does not.
Fig. 6. Case study: drone image (a), characteristic floor plan (b), laser scanning (c)
Finally, every system state described with benefits, in economic terms, that appear in the case of its occurrence. Higher levels of assessment (knowledge) are related to higher additional costs. In Table 1, their characteristics and costs associated with the different levels from 1 to 3 are shown. The costs of the presented advanced assessment procedures in Table 1 are estimated based on the type of structure, the basic characteristics of the structure (dimensions, structural system, etc.) and the level of strengthening required. All the associated costs are taken from the official government documents [31, 32]. The differences between various assessment levels mainly arise from the differences in the
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modelling sophistication, uncertainty consideration and knowledge level [33]. The idea was to highlight how gradually decreasing the uncertainty consideration and knowledge level will affect the expected costs of the assessment. Table 1. Levels of assessment and costs. Costs (e/m2 )
Assessment Level Referent Branch Description Level 0
e0
No assessment
0.00
Level 1
e1
Visual assessment, geometry check
4.00
Level 2
e2
Detailed visual assessment, geometry and building plans, linear dynamic analysis
Level 3
e3
Detailed visual assessment, geometry 13.50 and building plans, research works (NDT, semi-NDT) and nonlinear static (pushover) analysis
10.50
In order to acquire prior probability, statistical data [7] from more than 13,300 buildings in the historic urban core of the city of Zagreb were taken into account. The number of buildings damaged in the previously mentioned earthquake in Zagreb was 2160, from which a conclusion was reached to estimate the prior probability of failure at 16% [7]. Table 2. Cost of two action options. Residential Building
Educational Building
Do Nothing (e/m2 )
Strengthen (e/m2 )
Strengthen (e/m2 )
Safe
0.00
447.00
375.00
Failure
1155.00
1600.00
1762.00
Based on the formulation of the assessment problem from [33] and results from the study, the likelihoods in the pre-posterior analysis are taken according to Eq. (1) and the CF for the acquired knowledge level. An approach is based on ‘variability factors’, which account for the different uncertainties while allowing CF to consider the KL of mechanical properties. Two different ‘variability factors’ are defined, αmod , which takes into account modelling uncertainties as seen in [33] and αLS for the identification of the deterministic threshold for the definition of the ultimate element drift ratios. As both variables are aleatory uncertainties, they do not depend on the acquired level of knowledge. In the proposed approach, CF is taken into consideration as αmat = 1/CFmat , i.e., accounting for the acquired knowledge of mechanical material propertie αtot = αmod · αLS · αmat = 0.794 · 0.925 · αmat = 0.734 · αmat
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Fig. 7. VoI analysis for the case study
The outcomes are states with related probabilities when a structural failure occurs or does not occur, with the maximum allowed probability of failure taken as 5·10 − 5 [34]. Finally, to each system state, benefits that appear in case of its occurrence are added. Results of the analysis shown in Fig. 7 show that assessment level 3 i.e. the highest level of knowledge is the optimal scenario for the assessment of residential masonry building. In terms of utility shown through economic perspective.
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The value of additional knowledge or higher level of assessment is obtained by subtracting prior and posterior utility shown in Fig. 7. It is noticeable, when the assessment level with the greatest reduction in uncertainty is chosen, the utility is maximized. It should also be noted that this option also increases the seismic resistance of the building, comfort of living and future maintenance costs.
5 Conclusion This paper presents useful methodology and experiences from the Zagreb earthquake related to post-earthquake assessment and management of masonry buildings. In this process, as we learned to comprehensively evaluate the problem of reconstruction of masonry building we need to optimize our approach. The paper presents a methodology that shows the importance of additional information and updated knowledge when assessing buildings. Based on the Zagreb earthquake in 2020 expected utility for different strategies was calculated for prior probability levels concerning the sufficiency of the structural condition. Decision makers’ options proposed by the structural engineer are presented together with their costs. It is important to mention, that such decisions should be based on the expected costs while taking into account that the probability of failure is reasonable low, i.e. they should be based on maximum utility. This is shown through a VoI analysis for post-earthquake assessment of a case study residential building located in Zagreb. The results obtained from the analysis show the most cost-effective way to strengthen the building is to gather information regarding the different aspects of the building, as it is also the best long-term solution. These results can also be a great encouragement for the owners of buildings with expired design working life to inspect or even strengthen their buildings. In the future development of the methodology, focus should be on improving the data on the likelihoods, variability factors and historical data. This way a better understanding of how updated knowledge affects the modelling and design of masonry structures can be obtained. Finally, with some adjustments and modifications, a defined framework for VoI could be used to optimize the maintenance strategy for the entire building stock. Funding. This research was funded by the Croatian Science Foundation, grant number UIP-201904-3749 (ARES project—Assessment and rehabilitation of existing structures—development of contemporary methods for masonry and timber structures), project leader: Mislav Stepinac.
References 1. Stepinac, M., et al.: Damage classification of residential buildings in historical downtown after the ML5.5 earthquake in Zagreb, Croatia in 2020. Int. J. Disaster Risk Reduct. 56, 102140 (2021) 2. Stepinac, M., Skokandi´c, D., Oži´c, K., Margareta Zidar, M.V.: Condition assessment and seismic upgrading strategy of RC structures—a case study of a public institution in Croatia. Buildings 12 (2022) 3. Damage, R., Assessment N: Croatia earthquake (2020) 4. http://seizkarta.gfz.hr/
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5. Uroš, M., Šavor Novak, M., Atali´c, J., Sigmund, Z., Baniˇcek, M., Demši´c, M., Hak, S.: Postearthquake damage assessment of buildings – procedure for conducting building inspections 6. Stepinac, M., Rajˇci´c, V., Barbali´c, J.: Inspection and condition assessment of existing timber structures. Gradjevinar 69, 861–873 (2017) 7. The Database of Usability Classification, Croatian Centre of Earthquake Engineering (HCPI Hrvatski centar za potresno inženjerstvo), Faculty of Civil Engineering, University of Zagreb and The City of Zagreb, June 2020 8. Moreti´c, A., Stepinac, M., Lourenço, P.B.: Seismic upgrading of cultural heritage – a case study using an educational building in Croatia from the historicism style. Case Stud. Constr. Mater. (2022). https://doi.org/10.1016/j.cscm.2022.e01183 9. Moreti´c, A., Chieffo, N., Stepinac, M., Lourenço, P.B.: Vulnerability assessment of historical building aggregates in Zagreb: implementation of a macroseismic approach. Bull. Earthq. Eng. (2022). https://doi.org/10.1007/s10518-022-01596-5 10. Hafner, I., Lazarevi´c, D., Kišiˇcek, T., Stepinac, M.: Post-earthquake assessment of a historical masonry building after the Zagreb earthquake-case study. Buildings (2022). https://doi.org/ 10.3390/buildings12030323 11. Funari, M.F., Pulatsu, B., Simon Szabo, P.B.L.: A solution for the frictional resistance in macro-block limit analysis of non-periodic masonry. Structures 43, 847–859 (2022) 12. Uroš, M., Demši´c, M., Baniˇcek, M., Pilipovi´c, A.: Seismic retrofitting of dual structural systems—a case study of an educational building in Croatia. Buildings 13, 292 (2023) 13. Eurocode 8: Design of Structures for Earthquake Resistance—Part 3: Assessment and Retrofitting of Buildings (2005) 14. Stepinac, M., Gašparovi´c, M.: A review of emerging technologies for an assessment of safety and seismic vulnerability and damage detection of existing masonry structures. Appl. Sci. (2020). https://doi.org/10.3390/app10155060 15. Dall’Asta, A., Leoni, G., Meschini, A., Petrucci, E., Zona, A.: Integrated approach for seismic vulnerability analysis of historic massive defensive structures. J. Cult. Herit. (2019). https:// doi.org/10.1016/j.culher.2018.07.004 16. Betti, M., Bonora, V., Galano, L., Pellis, E., Tucci, G., Vignoli, A.: An integrated geometric and material survey for the conservation of heritage masonry structures. Heritage (2021). https://doi.org/10.3390/heritage4020035 17. ASTM C1531-16: Standard Test Methods for In Situ Measurement of Masonry Mortar Joint Shear Strength Index, ASTM International (2016) 18. ASTM C1196-14a: Standard Test Method for In Situ Compressive Stress Within Solid Unit Masonry Estimated Using Flatjack Measurements, ASTM International (2014) 19. ASTM C1197-14a: Standard Test Method for In Situ Measurement of Masonry Deformability Properties Using the Flatjack Method, ASTM International (2014) 20. RILEM TC 177-MDT: Test method recommendations of RILEM TC 177-MDT ‘Masonry durability and on-site testing’ - D.4: In-situ stress tests based on the flat jack. Mater. Struct. 37(271), 491–496 (2004) 21. RILEM TC 177-MDT: Test method recommendations of RILEM TC 177-MDT ‘Masonry durability and on-site testing’ - D.5: In-situ stress - strain behaviour tests based on the flat jack. Mater. Struct. 37(271), 497–501 (2004) 22. Vasanelli, E., Calia, A., Luprano, V., Micelli, F.: Ultrasonic pulse velocity test for nondestructive investigations of historical masonries: an experimental study of the effect of frequency and applied load on the response of a limestone. Mater. Struct. 50(1), 1–11 (2016). https://doi.org/10.1617/s11527-016-0892-7 23. Gorokhovich, Y., Doocy, S., Voustianiouk, A., Small, C.: Assessment of mortar and brick strength in earthquake-affected structures in Peru using a schmidt hammer. J. Perform. Constr. Facil. 24, 634–640 (2010)
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24. Grazzini, A.: Sonic and impact test for structural assessment of historical masonry. Appl. Sci. (2019). https://doi.org/10.3390/app9235148 25. Raiffa, H., Schlaifer, R.: Applied Statistical Decision Theory. Harvard University Press, Boston (1961) 26. Stepinac, M., Rajˇci´c, V., Honfi, D.: Condition assessment of timber structures – quantifying the value of information. In: IABSE Symposium NANTES, 2018 Tomorrow’s Megastructures, pp. S27-9. The International Association for Bridge and Structural Engineering, Nantes, France (2018) 27. Wilson, E.C.F.: A practical guide to value of information analysis. Pharmacoeconomics 33(2), 105–121 (2014). https://doi.org/10.1007/s40273-014-0219-x 28. Skokandi´c, D., Mandi´c Ivankovi´c, A.: Value of additional traffic data in the context of bridge service-life management. Struct. Infrastruct. Eng. 18, 456–475 (2022) 29. Skokandi´c, D.: Probalistic assessment of existing road bridges using B-Wim data. University of Zagreb (2020) 30. Oži´c, K., Skeji´c, D., Lukaˇcevi´c, I., Stepinac, M.: Value of information analysis for the postearthquake assessment of existing masonry structures—case studies. Buildings (2023). https:// doi.org/10.3390/buildings13010144 31. Croatian bureau of Statistics, BUILDING MATERIAL PRICE INDEX AT MANUFACTURERS, 1–4 (2022) 32. Program mjera obnove zgrada ošte´cenih potresom na podruˇcju Grada Zagreba, KrapinskoZagorske županije, Zagrebaˇcke županije, Sisaˇcko-Moslovaˇcke županije i Karlovaˇcke županije (2021) 33. Rota, M., Penna, A., Magenes, G.: A framework for the seismic assessment of existing masonry buildings accounting for different sources of uncertainty. Earthq. Eng. Struct. Dyn. 1045–1066 (2013) 34. CEN/TC250/SC10. prEN1990: Eurocode-Basis of structural design (2018)
The Identity Value of Vernacular Productive Architecture Knowledge, Recovery and Enhancement of the Val D’Agri Water Mills Antonella Guida(B) , Vito Domenico Porcari(B) , Alessandro Lanzolla(B) , and Giuseppe Andrisani Università degli Studi della Basilicata_Dipartimento delle Culture Europee e del Mediterraneo DiCEM, Matera, Italy {antonella.guida,vito.porcari,alessandro.lanzolla, giuseppe.andrisani}@unibas.it
Abstract. The Industrial Heritage (I.H) is made of rests of the industrial culture with its historical, technological, social, architectural and scientific elements – parts of buildings, machinery, laboratories, firms, mines and locations where processing and refining procedures took place, warehouses and shops, energy production and transfer sites. Such electricity is used for transport and all its infrastructure as it occurs for places where social activities take place such as accomodation, training or religion worship facilities [1]. The patrimonialisation process of the I.H. is essential as it recognises a community heritage made of memories and identity. The research is based on the Italian productive and vernacular patrimony, especially in the south of Italy, by taking into consideration the proto-industrial period – from the second half of the17th century to the second half of the 19th century – and analyses the organisation of the industrial system before the real industrialisation Era starting in the19th century. Italy is rich in working places, in fact, in southern Italy agribusiness has a great impact with its range of productive activities connected to agricultural products processing. Indeed, the milling vernacular industry represented an economical development source between the 17th and the first half of 20th century, this is the reason why there are lots of mills and bakeries for bread. The study deeply analyses the economic and social impact of water mills – vernacular and productive architectures of rural areas used to process wheat into flour. The “Val D’Agri” presents a large number of water mills and is located in the south-west part of Basilicata region. Its name comes from the river crossing the area. This analysis considers the functional recovery of watermills with a multidisciplinar criterion. Keywords: Industrial Heritage · water mills · proto-industrial · southern italy · vernacular manufacturing architecture
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 736–744, 2024. https://doi.org/10.1007/978-3-031-39450-8_60
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1 Introduction After 30 years of research, nowadays the I.H. field is still rich in ideas regarding the historical, architectural, documentary and even economical value of industrial sites out of the productive cycle with all its connections with the urban context and the society. Italy is rich in working places, especially in the south of Italy where agribusiness has a great role with all the connected activities regarding the agricultural products processing. As a matter of fact, from the 18th to the first half of the 20th century, the milling industry was essential for economic development since mills, pasta firms and bread shops appeared in order to meet rural communities’ needs to produce flour from wheat for themselves and others. During this period, proto-industrial infrastructures such as hydraulic mills and the “centimolo” – a wheat milling machinery moved by animals – had been disappearing. Consequently, new modern and productive cycles and plants were invented such as mechanical rolling mills. Afterwards, during the Industrial Revolution, larger sites were necessary to use steam engines [2], this lead to urban areas development. Here traditional mills definitely disappeared, they were still used in rural areas in an alternative way- for storage or dwelling [3].
2 The Sustainable Vernacular Industry This research concentrates on Basilicata – in the past known as Lucania – located in the south of Italy and bordering on Campania, Puglia and Calabria regions. Two old districts – Potenza and Matera- split the area into two parts that are well-known for their archaeological human remains dating back to lower Paleolithic Age. Between the 17th and the 18th century some industry processes were developing with the aim to produce tools and food. In this period there were more than 900 hydraulic milling systems were used [4]. In particular, throughout the Potenza and Lagonegro areas, textile industry and particularly linen production had a large impact. Around the year 1876 there were not real industries whereas there was a large number of textile and production facilities such as small familiar bread plants and mills having a local economic key role (Fig. 1). Among them, the mill represents the prototype of modern factory as part of the preindustrial architecture, combined with raw materials production machinery. In fact, it used water to produce energy and start the productive process and obviously could not be moved so far away. This is the reason why parts of facilities, prior steam systems, were found near rivers. The vernacular architecture of mills was changing according to territories since different local materials were used and create a camouflage effect that will disappear with factories. Afterwards, with technological progress and rails there were no more industrial facilities near rivers or other natural energy sources. New plants were built near railways to make raw materials movements easier and cheaper [5].
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Fig. 1. Horizontal wheel mill (image from https://andarpercolli.wordpress.com/2015/06/17/lac qua-della-cessanaa-cosa-e-a-chi-serviva/)
In Basilicata there were both vertical and horizontal-wheeled mills working with a penstock tower known an “arubah”. Its origin dates back to the 4th century AC in barren land in Palestine and, according to drainage conditions, could be from 4 to 14 m high [6]. The horizontal-wheeled mills were largely present on mountains where they represented a simple and cheap method for farmers, since no regular maintenance was necessary. It had a vertical shaft with a horizontal wheel on the top [7]. Water flows in this area varied a lot so that it was not possible to guarantee productive activity for the whole year. While building the horizontal-wheeled mills, designers considered that the power of the torrent had to be used. For this reason, there were 4 phases to carry water: – River bed restriction in order to increase the water flow – Waterfall building – water could go down through an inclined slide reaching the shovels of the wheels – Tight slides construction to increase the power of flow
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– In the end, cylindrical stone tower ending with a small hole in order to obtain a large quantity of energy by using a few water. In conclusion, mills differ according to sites and available materials – there are some made of stones and stone/wooden ones. They were split into two levels- downstairs the was the so called “hell” space where the hydraulic wheel was, instead upstairs there was the milling machinery. On the upper side of the building or, on the same level as the ground on the back, there was the water pipe. The wheel, on the contrary, had to be as low as possible to avoid a load loss. After having crossed the mill and starting the wheel, water goes back to the bed of the river through the plug spillway. The upper level presented a small and simple space for the grinding procedure. Horizontal wheels were different according to assembly and shovels since they were built by considering needs and conditions of water flows. Wood was deeply used at the beginning, later it was replaced by iron that was more resistant and long-lasting. Horizontal-wheeled mills has been used in Basilicata till the beginning of the 19th century. It was later abandoned for the grain tax that led to a relevant community reaction and represented one of the possible reasons that caused the closing and the decay of these factories. This fee was emanated in a difficult period for southern Italy that was suffering from robbery, repression, economic, productive, political and institutional crisis. On September of 1869, in Basilicata, there was a general uproar while 997 mills were still working with proper license, 467 were closed and 112 were not regularly registered. The research elaborates particularly on productive vernaculaar architectures in Val D’agri. This area is located in the south-west part of Basilicata and its name comes from the river crossing the territory. Here so many hydraulic mills were present since economy was mainly based on agriculture and high grinding demand.
3 The Role of Knowledge in Enhancement The target of this article is to define a knowledge methodological approach, recovery and enhancement of I.H. in Basilicata through its existing vernacular sites. In the end of the 1900, the archaeological superintendent supported works regarding industrial artefacts, for this reason there was an increasing interest in this industry aimed to protect such a heritage. In 1990 the Soprintendenza Archeologica al Centro Operativo di Maratea [8] published a catalogue reporting registered locations but a few Basilicata towns were mentioned. By considering its spread and relating difficulties in finding documents, a methodological process started to know and enhance the sector and, at the same time, to improve the catalogue and collect evidence about I.H. in Lucania. This strategy required to revise the industrial archaeological heritage law – 30th November 2017, nr.31- that was enacted just by Basilicata, that was one of the first Italian regions in issuing it. Its goal was to exploit this field by recognising its role in local work and culture and, on the other hand, promoting an industrial tourism that may led people to discover such places.
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4 Mills Heritage in Val D’Agri
Fig. 2. Alta Val d’Agri- communities with water mills – orthophotos – Google Earth
The data collection and cataloguing are preparatory for re-usage and enhancement as they allow to define problems, features and potentialities of each phase. Moreover, they are the result of synergistic and multidisciplinary action of knowledge coming from different specialisations. The next stage deals with documents collection - that is to say data management. In other words, retrieve information about people’s memories, cultural traditions, structural aspects, productive process and the study of each component such as wheels, grinds, hoppers etc… by comparing them. The research concentrates on two guidelines – the mill and and fulling mills belonging to the Romano’s family. They are located at the foot of San Martino D’Agri in Val D’Agri along the Trigella creek rising along the Rapanello Mount, running through the town and flowing into the Agri river. San Martino d’Agri (Fig. 2) is a small village in the south-west part of Basilicata, on the head of Val D’Agri. It is very compact and stands on a hill 682 m above sea-level. This a high seismic and hydrogeological risk area since, from a geological point of view, the territory presents surfacing calcarenites, dark-grey limestones and detritus. The whole village of San Martino d’Agri lies in the middle of the Agri river Lagoon and has two tributaries – the Trigella torrent and the Tufolo ditch. These rivers, especially in the past and before the drainage, have been even more important for the geomorphological development and for their sides stability (Fig. 3).
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Fig. 3. Iolanda Conte_Water mills in San Martino d’Agri
Fig. 4. Iolanda Conte _Water mill photos (milestone, tower of the gualchiera, tower of the mill)
The Romano’s mill name comes from its owners, it is split into two spaces – the mill and the fulling mill. Nowadays there are only the two towers that once fed the hydraulic wheels, the vertical one of the fulling mill and the horizontal one of the mill – remaining parts are ruins. Where the mill was before, there is the stone grinder with its 162-cm long diameter (Fig. 4). Walls are a single body with surfaces – inside and outside – with square, dark-grey limestone ashlars made of calcarenite and sandstone. They are connected by different thickness lime mortar layers that look local since were found near the mills.
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Anyway, there is no evidence its extraction in quarries. Walls are from 50 to 100 cm. Thick, have no foundation and are lean on the rock block that represents the western part of the fulling mill. Middle attics cannot be visible for the growth of spontaneous vegetation and the roof is a wooden flap with baked clay jars that is completely collapsed. The historical reconstruction considered the possibility that the fulling machine and the mill were made of two towers that moved two different wheels with the support of water power- the horizontal one of the mill starting the movement of stone grinders and, consequently, the flour production and, on the other side, the vertical one of the fulling machine by using big wooden mallets allowed the wool fulling (Fig. 5).
Fig. 5. Iolanda Conte_Geometric and material relief of the Romano water mill
The two towers were fed by a river canal diverting the Trigella river to get the right quantity of water to the towers. Water went over the fulling mill tower (Fig. 6) with a vertical pipeline getting thinner from top to bottom – from 54 cm to 20 cm. The vertical wheel was connected to the fulling mill with a woody element – the “Mast”. Inside the mill the hydraulic or horizontal wheel was powered by the power of water that went over the pipeline inside the tower. This inclined conduit gets thinner from the top to the bottom. On the upper side there is a hole measuring 80 cm, at the foot there is another one whose diameter is 34 cm. After having powered both wheels, water went back to the torrent with two plug spillways, one per tower. Some parts of pipelines are still visible despite the dense vegetation (Fig. 7).
5 Recovery and Enhancement Strategies Today vernacular buildings look abandoned and deteriorated, some of them are real remains. Their recovery may have a social, economicable and sustainable impact since they are part of our society and may become places of interest.
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Fig. 6. Iolanda Conte _Original Romano water mill hypothesis
Fig. 7. Project concept, plans and section_Iolanda Conte
This study provides some guidelines about the I.H. and shows some simple strategies to use water as a source of energy by using new economical and environmental procedures. For example, the fuller may work as a hydroelectric micro power station and the vertical wheel may be replaced by a turbine according to sizing and requirement. In terms of combined interventions, it may be useful to add new sustainable wooden and rice straw panels in order to use these sites again and let them become a tourist and cultural attraction as well. Recognising such an importance means to find their real identity as past and future heritage. This should be a priority to plan local development strategies.
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Basilicata needs methodical and organised knowledge about these working places and socio-economic memory to protect and enhance its locations in Italy and abroad. At the same time, the law dated 30th November 2017 nr. 31 should be powered and put into practice. This approach will develop two aspects: – A concrete one - with functional and structural facilities recovery – A social, tourist and cultural one - by recognising the value of these sites Innovation of this research is a result of both and is intended to be as a sort of “continuous workshop” on site based on a constant monitoring of the heritage. The attribution of the authors’ contributions is as follows: conception of the research A.L. A.G.; conception of the manuscript A.L - V.P.; methodology A.L - V.P.; data collection A.L.; data analysis: A.L.; drafting of manuscript: A.L.; drafting and revision of final version: V.P. - A.L.; discussion of results: G.A. - V.P. - A.L.; revision and supervision A.G. - A.L.; research funds: A.G.
References 1. Tognarini, I., Nesti, A.: Archeologia industriale. L’oggetto, i metodi e le figure professionali, Roma, Carrocci (2003) 2. Negri, A., De Seta, C.: Archeologia industriale. Monumenti del lavoro tra XVIII e XX secolo. In: s.l.:Touring Club Italiano (1983) 3. Borsi, F.: In: Introduzione all’Archeologia industriale. s.l.:Officina Edizioni (1978) 4. Petrone, G.: In: Archeologia Industriale nell’Alta Val D’Agri. s.l.:Akiris (2007) 5. Cortese, M.E.: I mulini. In: L’Acqua il Grano il Ferro. Firenze: Edizioni all’insegna Del Giglio (1997) 6. Gugg, G., Petrone, G.: Memorie d’Acqua, I mulini del torrente Alli. s.l.:Akiris (2007) 7. Aucello, T.: La Tassa sul Macinato nel Risorgimento. Rivista di Diritto e Storia Costituzionale del Risorgimento, Issue 2 (2017) 8. Bonaventura, M.G., Covino, R., Fontana, G.L., Monte, A., Novello, E.: a cura di, Archeologia industriale in Italia. Temi, progetti, esperienze, in I Quaderni di Patrimonio industiale, Brescia, AIPAI (2005) 9. Alliegro, E.: Al suono delle campane. I tumulti del pane negli anni postunitari. In: Terraferma. Soveria Mannelli: Rubbettino Editore, pp. 25–50 (2019) 10. Guida, A., Missanelli, R., Sabia, A.: Una nuova scienza per un passato recente, collana Architettura e tutela del territorio, Edizioni Ermes, Italia (2000) 11. Guida, A., Mecca, I., Maggio, A.: La via della lana: la ex-filanda Gaeta di Bella (Pz). In: V coloquio latino-americano e internacional sobre rescate y preservación del patrimonio industrial, 18–20 September 2007 12. Guida, A., Bernardo, G., Margiotta, M.R., Grano, M.C., Porcari, V.D., Conte, I.: Opifici Idraulici: Conversione della Gualchiera in Centrale Idroelettrica, recupero del Rudere Romano e valorizzazione dell’area circostante, tesi di laurea sperimentale in Laboratorio di progettazione V-Architettura ed eredità del costruito, a.a. 2019–2020 13. Guida, A., Picione, M., De Luca, M., Gerardi, M.: The recovery of the industrial site: a sugar refinery in Basilicata (Italy). In: International Conference Heritage of Technology – Gda´nsk Outlook 4, Gda´nsk, 4–7 May 2005
Analysis of Local Mechanical Characteristics and Global Structural Arch Behaviour of Cane (Arundo Donax) Sadhbh Donovan(B)
, Elisa Poletti , and Hélder Sousa
University of Minho, ISISE, ARISE, Department of Civil Engineering, Guimarães, Portugal [email protected]
Abstract. It is necessary to encourage the use of natural materials in construction due to the negative environmental impact of modern construction methods. Cane, or Arundo donax, is a grass reed that grows widespread across the world, in predominantly sub-tropical environments. Environmentally, the plant is invasive in most of the regions that it grows. Agriculturally, many farmers and landowners consider it a hindrance. Architecturally, with suitable skills and appropriate design, the material may be harvested and used to form lightweight, resistant, structural elements, namely catenary arches, for use in temporary, permanent or existing structures. As little research exists on the use of canes in arches, an experimental campaign was proposed. An initial material characterisation was carried out using the ISO22157-1 standard for bamboo, as cane standards do not yet exist and the plants are part of the same family of grasses, possessing similar geometric and growth characteristics. Weekly moisture content values were collected to check their variability over time. Compression parallel to the fibers values were determined and subsequently, the compression modulus. For the structural testing, three catenary arches of the same size were constructed by the “Canyaviva” method, using hands, tools and rope. This was achieved through the organisation of a workshop attended by members of the academic community. Once built, full scale tests were carried out using a steel frame loading apparatus, and the arches were loaded until failure. LVDTs were used to determine the deformation at specific locations and visual imagery was analysed for arch behaviour. Results provided strength capacities and collapse mechanisms of the arches. On a local level, it was concluded that the mid-section of the culm exhibits higher load resistance, and older culms resist load better than those with younger maturity. The material possesses a high moisture content that is dependent on surrounding environmental conditions. On a global level, when formed into an arch with a suitable configuration, the material has the capacity to resist up to seventeen times its weight, while maintaining a lightweight and flexible nature. Keywords: Bioconstruction · Natural materials · Cane · Giant reed · Arch behaviour · Sustainable materials
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 745–759, 2024. https://doi.org/10.1007/978-3-031-39450-8_61
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1 Introduction The modern construction industry plays a major part in contributing to CO2 emissions across the world, mainly in the developed world. Considering the issue that many “green building” ratings omit the “embodied carbon” that a building posseses, modern construction accounts for up to 38% of global emissions [1, 2]. Considering the Sustainable Development Goals, as listed and described by the UN, an urgent call for climate action is encouraged, requiring that cities and communities be sustainable, and that life on land is improved for nonhuman species [3]. Therefore, construction methods, designs and materials currently used are in need of radical change. Alternatively, sustainable building solutions are being researched and examined, categorized by the terms bioconstruction and bioarchitecture. In reality, these terms involve techniques and materials that mimic traditional construction methods which would have been in use up to thousands of years ago, but with the added conscious intention of considering the natural environment. These methods seek to improve and where possible, recover the natural environment. Bioconstruction seeks to encourage the use of renewable, natural materials with a low energy disposal (in terms of transport, manufacture and “as built” emissions), limit the use of heavy machinery, mimic the natural environment in which the structure is located, and where possible reinstate the natural biodiversity of the surrounding area, where it is lost. A viable possibility exists in the cane plant (Arundo donax). Belonging to the same poaceae grass family as bamboo, it holds similar geometric and growth characteristics. The plant grows vigorously and is invasive to the majority of regions where it is found. Therefore, its control and mitigation are encouraged. This work suggests a creative and useful purpose for the removed material. When bundled and tied together, using a technique developed by the founder of the bioarchitecure organization Canyaviva, Jonathan Cory-Wright, catenary arches may be constructed using cane harvested from the locality of Apúlia in the North of Portugal. This study focuses on the structural capacity of these arches, through analysing their local methods of failure and the strength capacity, and includes a material characterization of the individual specimens, developing on the little research that currently exists in order to understand further its composition and behaviour.
2 Historic and Modern Cane Construction As it stands, evidence of cane used as a structural material is found both in vernacular and modern construction, albeit in a limited number of examples. One of the earliest examples is found in a quote written by Vitruvius, in De Arquitectura (27 BC), and interpreted by Hurtado Valdez [4], describing the construction of an arch vault bridge (see Fig. 1); “Once the slats are fixed, they will be held together by a texture of crushed Greek reeds, which will be tied with Hispanic esparto cords, as required by the curvature of the vault” The plant is found in the construction of shelters, huts, warehouses and sacred spaces (Fig. 2), and within building elements such as walls, floors, stairs and barrel vaults.
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Fig. 1. Interpretation of Vitruvius’ description of vault construction- George Rusconi, 1509 [Source: Hurtado Valdez (2009)]
UNESCO defines cultural heritage, which may be implicitly applied to architectural heritage, as monuments or sites with elements or structures of an archaeological nature [5].
Fig. 2. (a) Lake Titaca community, Peru [Source: www.fshoq.com]; (b) Mudhif structure, Iraq [Source: www.zmescience.com]
The inspiration for this study comes from the very recent work carried out by the bioarchitecture organisation Canyaviva, founded by Jonathan Cory-Wright. The innovative construction method was developed as an alternative solution to modern approaches and uses a mostly invasive natural resource. Harvesting the material where it is invasive provides a positive environmental contribution. Cory-Wright based the design of the Canyaviva technique on the natural shape of the plant. The technique involves bundling cane specimens together based on their diameter, length and natural rotation, and forming arches. Arches are connected by a primary rib nerve system, as shown in Fig. 3(a), using the same bundling technique but using cane with a smaller cross-section. A cane covering is stitched and tied to secondary nerve system, which completes the basis of the structural form (see Fig. 3(b)). Rigidity of the structure is provided through the knots tying the nerves to the arches, typically tied with rope [6]. The method has been developed in an empirical and intuitive nature by Cory-Wright since 2007, and since its inception permanent and temporary structures have been built around the world in Spain, Portugal and Chile. Previous studies [7–9], have been carried out involving the structural use of the material and in some cases the Canyaviva technique was used to construct arches, with load tests performed.
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Fig. 3. (a) Cane arches during Canyaviva construction [Source: Canyaviva Workshop attendance, 2020]; (b) Completed Canyaviva structure [Source: www.canyaviva.org]
3 Material Characterisation Arundo donax is a member of the poaceae family of grasses, sharing similar physical and geometrical properties with bamboo and sugar cane. In order to determine specific material characteristics that would assist in understanding the mechanical behavior of the cane, ISO 22157-1 “Bamboo- Determination of physical and mechanical properties” [10] and EN408:1995 “Timber structures- Structural timber and glued laminated timberDetermination of some physical and mechanical properties” [11] were followed for all of the testing procedures as those for cane do not yet exist, and bamboo possesses the characteristics most similar to cane amongst construction materials that have been standardized internationally. The experimental data from this chapter may be useful for any future parametric analysis on the use of cane for structural purposes and may contribute to the formulation of a reliable database of mechanical properties of cane, using and comparing against any similar previous data acquired. 3.1 Moisture Content The moisture content of cane influences the dimensional stability, as well as toughness, density, strength, working properties and durability. The level of moisture can vary in one culm and is influenced by age, the time it is harvested and the species [12]. The time between harvest and construction may contribute to the levels of moisture in the cane and should be taken into consideration when using cane as a structural material. For this reason, it was decided to do a weekly check on the moisture content of the cane over time until testing took place. Test Procedure. Specimens were taken from the base of five cane culms and prepared ensuring consistent volume in each (see Fig. 4(a)). Although thicknesses may vary, it was imperative to ensure the width, height and length of each sample measured 25 mm, according to ISO22157. Samples were weighed to the nearest 0.01g and were dried in an oven at 103°C+/− 2°C for 24 h. Then, samples must be weighed every two hours until the difference does not exceed 0.01g. The final mass is considered the dry mass. To calculate the moisture content, the following formula is used: MC =
m − mo × 100 m
(1)
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where m is the mass of the sample before drying and mo is the dry mass of the sample after drying.
Fig. 4. (a) Example of prepared samples for moisture content test; (b) Variability of moisture content (%) over time
Test Results. Figure 4(b) shows that in many of the samples, the moisture content exceeds 100%. Using research carried out on moisture content levels of bamboo, these values may be explained by the porous nature of cane. Previous studies [12, 13], state that bamboo can have moisture content values between 100–150%. Although comparatively this may explain the values obtained, it should be noted that the authors reference these numbers to fresh cut, green bamboo, whereas in this study, there was some time between harvest and the initial moisture content check. Also, the culms were green to brown without their superficial leaf layer, indicating their maturity was not so young. The high moisture content could be attributed to the coastal location from which the culms were sourced, the high moisture levels present, due to puddling, where the cane was stored at Campus of Azurém, and the weather conditions in Guimarães during the time of testing. Liese [12] specifies that the season has an influence on the moisture content, and that in the rainy season of the year the value is at its maximum. It can be said for just one week (19/04–26/04) that all culms experienced a reduction in moisture content. Said week in Guimarães was not exceptionally dry according to [14], with temperatures reaching a high of 18°C and two days experiencing rain showers. Therefore, the reduction in moisture content cannot be explained by a dried ambience caused by high temperatures and low humidity. There may be some explanation for an incremental pattern due to high temperatures - for example during the week of the 28/03–05/04 temperatures reached 21°C in Guimarães - when four out of five samples experienced a reduction in moisture content. However, the values indicate a necessity to carry out further checks on weekly moisture content levels of cane. Referring to bamboo, Liese [12] states that because it is a hygroscopic material, like cane, it loses and absorbs moisture until it becomes in balance with its external environment. The level of moisture at this point of balance is known as the equilibrium moisture content (EMC), which depends on the relative humidity and temperature of the ambient air. The EMC of cane may be a more useful indicator than the moisture content.
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3.2 Compression Parallel to the Grain Compression values parallel to the grain of singular cane culms were required in order to determine how the mechanical strength varies based on the location along the plants’ length and based on its maturity. Compression values were checked for a number of samples taken from the base, the middle and the top of culms, and of two maturity levels – older and younger. The maturity of the cane is based on: the colour, where older culms are brown/ grey, and younger culms are green; the presence of leaves, with younger culms possessing more leaves than older culms; and the presence of branches, with older culms possessing more branches than younger culms. The compression stress (σult ) and the compression modulus (E) were obtained using the following formulae: a) σult = b) E =
Fult A
l(N2 − N1 ) A(x2 − x1 )
(2) (3)
where F ult is the maximum compression load and A is the cross-sectional area of the culm, l is the length of the sample before testing, (N 2 -N 1 ) is the load increment, and (x 2 -x 1 ) is the displacement increment [11]. Test Procedure. Ten cane culms were checked for each growth phase and specimens taken for each location, therefore a total of sixty specimens were prepared. Using [10] as a guideline, it is recommended that the height of the specimen should be equal to the outer diameter of the section of culm to be tested, and where the diameter is 20 mm or less, the height of the specimen should be twice the diameter. Samples were placed in a Lloyd’s 50kN Materials Testing Machine and loaded at a rate of 0.6 mm/min. Test Results. Table 1 shows that compression parallel to the grain values at the middle of the culm possess a higher resistance to loading. Figure 5 represents the average compressive stress values based on location on the culm and age of the culm. A higher concentration of fibers in the middle of the culm may explain the higher resistance. The compression modulus values show that the base of the culm is more brittle, while the middle and top section compression values show that this part of the plant is more ductile in behaviour. Older culms (more than one year old) exhibit a 65% increase in compression strength and a 67.5% increase in compression modulus compared to culms that are less than one year old. Failure types included longitudinal splitting, local buckling, separation between external and internal walls of sections, as seen in Fig. 6. Table 2 gives a comparison of the values against previous studies carried out by [7, 15, 16], however, it should be noted that in their tests, researchers used different specimen sizing guidelines and mechanical parameters to those used in the current study.
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Table 1. Compression load, stress and modulus values Max Compression Load
Max Compression Stress
Compression Modulus
Units
N
N/mm2
N/mm2
Maturity
Old
New
Old
New
Old
Base
10650.15
5258.86
29.61
16.79
1384.19
929.99
Mid
7638.85
3560.55
34.75
17.46
1836.65
1051.77
Top
2769.17
1616.93
30.33
22.98
2038.57
1158.06
Average
7019.39
3478.78
31.56
19.08
1753.14
1046.61
New
Fig. 5. Average ultimate compressive stress by location and age
Fig. 6. (a) Longitudinal splitting; (b) Local buckling; (c) Separation between external and internal walls
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Table 2. Comparison of compressive stress and compression modulus with other research Compression Stress Ranges
Compression Modulus Ranges
Units
N/mm2
N/mm2
Author
Min
Max
Min
García Ortuño (2003)
52.28
52.30
5918.00
Berjerano et al. (2012)
26.58
51.80
4026.80
8134.90
-
-
4500.00
10500.00
22.98
34.75
3025.40
15561.50
Spatz et al. (1997) Current study
Max 6285.00
4 Experimental Campaign In order to determine the global structural behaviour and subsequent local failures of the arches an experimental campaign was set up. Arches were constructed and their final dimensions recorded. The basis of design of the experimental setup was decided upon empirically as cane standards do not yet exist. The setup was limited by the shape and geometry of the arches, the lab space and equipment available at the scheduled time of the procedure and the predicted locations of hinges. 4.1 Arch Construction The design of the arches is based on that outlined by [17], and follows their recommended guidelines provided during the attendance of a Canyaviva workshop in October 2020 [6]. Cane was harvested at roughly two years of age on the 23rd February, 2022, in the coastal town of Apúlia, Portugal. Approximately 450 cane culms were collected, with 80% measuring 5-6m from base to tip, to be used in the arches, and the rest for material characterization tests. Specimens were then prepared by removing leaves, branches and branch nodes, using a sickle. Following this, cane was classified in order to create an inventory of undamaged, suitably sized cane and to establish the rotation of growth of each culm- clockwise or anticlockwise. A simple classifying tool was used to identify the “key”, or the location near the tip where the diameter should be kept at a maximum value (see Fig. 7(b)). In this design the key value was 15 mm. A minimum of 1m length of cane is required from the key to the tip for an efficient overlap in the arch configuration. As 4m cane specimens were required, each cane was cut 3m from the “key”. Each culm was then classified based on its rotation (see Fig. 7(a)). Due to the natural growth of the cane, in some cases culms may exhibit both forms of rotation. Culms were cut at the point of direction change.
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Fig. 7. (a) Determining the cane rotation; (b) Reference points along culm for construction; (c) Cross-section of the column base
The construction of the arches involves forming two columns, consisting of a total of 33 culms at each base tied together using sisal rope (see Fig. 7 (c)). One column is constructed with anti-clockwise culms and the other with clockwise. These are then connected together to form one singular core with an additional 6 cane added per column, to fill the gaps along the length of the core and to ensure the reduction of the cross-section of the core remains minimal from the base to the “key” area. The core is then bent into shape to form the arch. The straight arch length was proposed as 6m once cores were tied together. It was important throughout the entire construction process to ensure the individual canes at the key location did not possess a diameter larger than 15 mm, and that the condition of the cane 100 mm to the left and the right of this location was in an optimal state. Final Arch Geometries. Figure 8 is an annotated diagram of the final arch design. The dimensions are expressed in Table 3. The weight of each of the arches was measured with the hoist crane in the lab and a weighing scale. The anticlockwise and clockwise columns are highlighted on the sketch. It should be noted that precise symmetry was difficult to achieve for each arch due to the natural nature of the material. In addition to this, there was a number of culms damaged, in the form of split, bent and reduced crosssections, in the sensitive area around the “key”, following the bending of the arches. These damages were marked on each arch using coloured paint.
Fig. 8. Annotated representation of final arch shape with column rotations noted
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S. Donovan et al. Table 3. Final arch dimensions
Arch H(mm) S(mm) VA (mm) VC (mm) tB,A(mm) tB ,C (mm) tV,A (mm) tV,C (mm) tK(mm) W(kg) 1
2300
3590
1820
1500
160.1
156.9
130.5
138.5
111.4
18
2
2310
3560
1300
1350
163
157.9
138.5
136.9
116.2
18.5
3
2380
3620
1450
1350
159.2
167.1
136.9
148
111.4
19
4.2 Experimental Procedure Experimental Setup. Out-of-plane behaviour control was necessary as the arches themselves are typically designed as part of a complete structure, connected to other arches as described in Sect. 2. Stability was ensured using two vertical steel profiles as shown in Fig. 9. Teflon stickers were applied to the profiles at the contact points to the arches to minimise friction and subsequent force transfer.
Fig. 9. (a) Elevation view of experimental setup; (b) Section through experimental setup
Supports were constructed to ensure a vertical embedment depth of 400 mm. A mixture of soil, gravel and clay was used. A base layer of 100 mm was inserted into 500× 650×500 mm boxes and the arches were inserted inside. The mixture was compacted every 100 mm. A rubber protection layer was tied to the arches at the contact points to the boxes to minimise stress concentrations and to minimise any vertical force transfer.
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To obtain the load vs displacement graph a load cell was used and LVDT’s attached to the arches to determine horizontal and vertical displacements as shown in Fig. 10. An elastic relationship was expected until the point of yield, after which load would be continually applied until an ultimate point was reached. The load would then be gradually released in order to observe the recuperated form of the arch.
Fig. 10. LVDT locations
Procedure. Using a 20T hoist, a steel cable, a load cell and a pulley system, the arches could be loaded at 1 point on their geometric center near the point of the key. As this point was assumed to be the weakest along the length of the arch, the experimental campaign therefore provides the load capacity of the arches in their suboptimal state. The steel cable was connected at this point and rubber placed between the cane and steel. The cable was sent through the pulley system and a load cell connected and supported by the hoist hook. The speed at which the cable was pulled was set constant to the lowest speed of the crane command.
4.3 Results Global Deformation and Recuperation of Form. It can be seen from Fig. 11 that the arches exhibit a similar deformed shape with hinges forming in almost the same location, on the clockwise side for Arches 1 and 2, and the anti-clockwise side for Arch 3. Hinges clearly form at the point of loading, or the “key” of the arches, and within the section between the “V” and the key for each of the arches. It is within this length where the curvature becomes more pronounced. It is at these points where the columns become more diagonal and curved and the horizontal thrust from the load is being resisted by the arch. The formation of the hinge occurred at locations where the resistance of the arch reached its maximum due to the applied loading. This location indicates the point where the geometry of the arch cannot resist the thrust. In addition to this, certain factors may influence the hinge formation, such as the non-centricity of the applied load, the lack of symmetry in the geometry of the arches, and the condition of the cane in the final construction. Due to the presence of damaged cane, the capacity of the cross-section of the arches at hinge locations was mechanically compromised. Once the load was
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removed, all arches recuperated their form to a level that exhibits the elasticity of the material.
Fig. 11. Initial, final and recuperated forms of Arches 1, 2 and 3 (a) Arches 1 (b) Arches 2 (c) Arches 3
Ultimate Load Versus Displacement. From Table 4, it is clear that the strongest arch of those tested is Arch 2, obtaining an ultimate load of 3.05 kN. However, each of the arches obtained a comparable ultimate load, indicating similarities in construction and loading patterns. The minimum ultimate load resisted by the arches was in Arch 3 at 2.76 kN. Ratios of the ultimate load against the weights of each of the arches are shown. Arch 2 exhibits the highest load to weight ratio, obtaining almost seventeen times its weight in load. Arch 2 showed the highest resistance to loading out of the three specimens, being able to resist 9% more load than Arch 1 and 10.5% more than Arch 3. Figure 12 shows two representative graphs exhibiting both vertical and horizontal deformations for two LVDTs. It can be seen from the graphs that a bi-linear range exists during the loading. This indicates a slight inelasticity in the arch behaviour. This may be due the reaction of the arch to the inclined load and that as it is incrementally increased the deflections are also incrementally increasing. Also, as the cane are tied together and friction between culms is almost non-existent, some material deformities may be occurring in the cross section on a local level. However, after the ultimate load was reached and the cable was released from the point of application, the arches managed to recuperate some of their original shape, indicating the elasticity in the global behaviour of the arches. As each
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of the arches possessed a number of damaged culms around the “key” area, also the location of loading, the ultimate load reached may not be representative of the potential capacity of the arches without any split or bent culms.
Table 4. Ultimate load and displacement values and Load to Weight ratios Arch Ultimate Load to Displacement (mm) [by LVDT] load (kN) Weight ratio A B C D
E
F
G
1
2.79
15.7
−7.09
52.38 29.72 −192.24 72.07 68.75 −12.35
2
3.05
16.7
−6.92
51.69 29.22 −251.76 86.12 76.88 −24.97
3
2.76
14.7
−17.74 85.27 38.78 −320.44 39.6
84.27 −23.21
Fig. 12. (a) Representative horizontal load versus displacement relationship for each arch; (b) Representative vertical load versus displacement relationship for each arch
5 Conclusions and Recommendations The material characteristics and structural capacity of the cane plant are exhibited in this study. As the standards for bamboo were followed in the material characterisation, further studies are recommended to compare the mechanical and structural behaviours of these two plants. Moisture content tests indicated the extremely hygroscopic nature of the material, with many results providing a value over 100%. This was attributed to certain factors such as the coastal area from which the cane was obtained and the storage conditions. In addition, moisture levels were somewhat dependent on the environmental conditions of the surrounding area, however a consistent pattern was not followed. Further investigation into the variability of moisture content and its values over time is encouraged, and the use of the EMC is recommended as a possible moisture level indicator instead.
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Compression parallel to the grain values indicate that the middle section of the culm possesses the highest resistance to load, explained by the higher concentration of fibers in the cross-section, while the base of the culms exhibit more brittle behaviour than the middle and top sections. Older culms gave an increase in over 60% in both the compression stress and modulus values. Different localised failure types were expressed and discussed. For the structural load tests, it was found that hinges formed in similar locations for all of the arches – where the curvature of the catenary arch increases from the inclined bases towards the most curved central area. Although a bilinear relationship exists between the load and displacement, the material’s elasticity was exhibited after the cable was released from the load application point and the arches recuperated some of their original shape. Arches exhibited a load capacity of up to seventeen times their weight, exhibiting the light material’s resistant nature. Further studies are suggested to improve the knowledge on this construction method and better understand its potential. From the experimental results obtained in this project, it is possible to set a database and benchmark scenario to perform parametric numerical analyses, based on the material properties and capacity of arches obtained. Acknowledgements. This research has been carried out with the support of the Civil Engineering faculty of Univerity of Minho, Guimarães, Portugal, the assistance of João Teixeira throughout the construction process and the guidance of Jonathan Cory-Wright from the works’ inception to completion. This work was partly financed by FCT/MCTES through national funds (PIDDAC) under the R&D Unit Institute for Sustainability and Innovation in Structural Engineering (ISISE), under reference UIDB/04029/2020, and under the Associate Laboratory Advanced Production and Intelligent Systems ARISE under reference LA/P/0112/2020.
References 1. Arnold, W.: “The Institution’s response to the climate emergency”, Climate Emergency Conference 2020: Sustainable design in a climate emergency, IStructE, Recorded 30 October 2020 (2020) 2. Egbu, C.: “Sustainable Construction and Development”, London Southbank University, [Online Course: Attended October 2020] (2020) 3. The 17 Goals, Sustainable Development, United Nations Department of Economic and Social Affairs. https://sdgs.un.org/goals. Accessed 15 May 2023 4. Hurtado Valdez, P.: “Las bóvedas de madera en los tratados de arquitectura”, BIA: Aparejadores de Madrid, ISSN 1131-6470, no 260, pp. 99–114 (2009) 5. United Nations Educational, Scientific And Cultural Organisation Convention Concerning The Protection Of The World Cultural And Natural Heritage. Adopted by the General Conference at its 17th session Paris, 16 November 1972. http://whc.unesco.org/ 6. Cory Wright, J.: “Canyaviva: Complete Natural Construction Course”, Tavira, Portugal, October 2020 7. Bejarano, S.G., Delgado, E.S.: Arundo donax L.: Material de construcción, Universitat Politècnica de Catalunya. Departament de Construccions Arquitectòniques II (2012) 8. Molari, L.: Arising student consciousness regarding structural properties of natural materials with a structural challenge employing Arundo Donax. Creat. Educ. 10, 1155–1162 (2019)
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9. Mujika, I., et al.: Estudio del comportamiento mecánico de arcos de caña “arundo donax” según método Canya Viva, Investigació Canyera, Barcelona (2012) 10. ISO22157-1:2004, “Bamboo- Determination of physical and mechanical properties”, International Standard 11. EN408:1995, “Timber structures- Structural timber and glued laminated timber- Determination of some physical and mechanical properties”, British Standard 12. Liese, W., Tang, T.K.H.: “Properties of the Bamboo Culm”, Bamboo: The Plant and its Uses, Tropical Forestry, vol.10, pp. 227–256 (2015). https://doi.org/10.1007/978-3-319-14133-6_8 13. Wakchaure, M.R., Kute, S.Y.: Effect of moisture content on physical and mechanical properties of bamboo. Asian Journal of Civil Engineering (Building and Housing) 13(6), 753–763 (2012) 14. Past Weather in Guimarães, Braga, Portugal (2022). https://www.timeanddate.com/weather/ portugal/guimaraes/historic?month=4&year=2022. Accessed 28 June 2022 15. Spatz, H.-Ch., Beismann,H., Brüchert, F., Emanns, A., Speck. T.: “Biomechanics of the giant reed Arundo donax”. Phil. Trans. R. Soc. London 352(1349) (1997) 16. García Ortuño, T.: “Caracterización de la caña común (Arundo donax L.) para su uso como material de construcción”, Departamento de Ingeniería, Escuela Politécnica Superior de Orihuela, Universidad Miguel Hernández, Orihuela (2003) 17. Cory-Wright, J.: Document Untitled, Canyaviva, Unpublished. nd
Interdisciplinary Projects and Case Studies
Restoration of Cast Iron and Wrought Iron Structures – Case Study: The Restoration of the Orangery at Hof ter Borght in Westmeerbeek (Belgium) K. Verreydt1,3(B) , M. de Bouw2,3 , B. Dewaele2,3 , K. Brosens1,3,4 , and D. Van Gemert1,3,5 1 Triconsult NV, Lummen, Belgium
[email protected]
2 Buildwise, Division of Energy and Renovation, Brussels, Belgium 3 Erfgoed & Visie Bv, Malle, Belgium 4 UHasselt, Hasselt, Belgium 5 KU Leuven, Leuven, Belgium
Abstract. The structural restoration of the heavily degraded combined wrought iron and cast iron orangery of the castle Hof ter Borght at Westmeerbeek, Belgium, proved to be a challenge. This paper presents the problems encountered and the suggested interventions. The assessment of the condition of the construction was difficult because of the very extensive plant growth in and on the orangery, which had broken nearly all the glass panels of the roof and walls and covered most of the wrought iron and cast iron elements. During the disassembly of the structure, the weakened connections between several elements suffered unavoidable additional damage. Microscopical and chemical analyses indicated wrought iron and cast iron of low quality for several elements, exhibiting impurities and air pockets. The mechanical characteristics of the historical wrought iron and cast iron were determined by tensile and compression testing. A finite element model of the orangery is used to analyse the stresses in the structure, assuming an intact structure at first. Secondly, additional modern steel elements are added to support the weakened structure, along with the strengthening of the connections themselves. Several options for reinforcement of the cast iron connections are suggested and compared, ranging from recasting entire elements to bolted steel overlapping plates. Furthermore, the feasibility of local epoxy polymer filling for column feet anchorage and other epoxy prothesis applications for cast iron connections is assessed. Keywords: Cast iron · Wrought iron · 19th Century · Restoration · Orangery · Mechanical characterization
1 Introduction From the second half of the 18th century, iron was introduced as a new metal construction material in the building industry [1]. The Industrial Revolution ushered in new innovations in manufacturing and production processes [2]. Cast iron became a © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 763–773, 2024. https://doi.org/10.1007/978-3-031-39450-8_62
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useful construction material for various constructions (rails, pipers, beams, columns, etc.). Halfway the 19th century industrially produced rolled iron elements for metallic constructions became economically available [3]. Cast iron was used for columns from around 1790 until the beginning of the 20th century. Cast iron beams were used untill 1870 [4] and were gradually replaced by wrought iron. Wrought iron I-section beams were applied from 1850 until 1890, with the introduction of steel. Steel became the dominant metal construction element by 1900. The presented study covers the restoration options for restoring the more than hundred-year old orangery of the castle “ter Borght” at Westmeerbeek, Belgium (Fig. 1). The orangery, which dates back to 1864, is composed of a combination of wrought iron and cast iron elements and is an example of the constructions during the transition period in the second half of the 19th century.
2 Restoration of the Orangery of Castle “ter Borght” The orangery has a symmetrical build up, with two side wings along a higher central part with an arcade. Cast iron twisted columns support a load bearing cast iron gutter. The glazing bars in the glass facades and roofs are made of wrought iron. Rivets connect the glazing bars to the gutters. The cast iron columns consist of several parts interlocking with each other and held together with bolts or rivets, concealed with cast iron ornaments.
Fig. 1. State of the deteriorated orangery at castle ter Borght, Westmeerbeek, Belgium (situation 2012).
The orangery had been neglected for several years and was in dreadful condition. A lot of glass panels in the roof were broken, resulting in water infiltrations, speeding up the corrosion process. Extensive plant growth in and on the orangery covered most of the wrought iron and cast iron elements. Several elements were heavily corroded and damaged. The objective was to dismantle the construction, treat the wrought iron and cast iron elements and reassemble the components. However, during dismantling, it was noticed that the state of the elements was far worse than initially estimated.
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Ruptures and cracks were present in many of the cast iron segments. Among others, the gutters were severely damaged, as presented in Fig. 2. In the construction of the orangery, the cast iron gutters are a structural part, acting as a supporting beam for the horizontal and vertical forces from the glass roof. These cracks indicate that the (limited) tensile strength of the cast iron is exceeded, which may have been caused by overloading of the element, or it can be the result of weathering and corrosion, weakening the material. Besides internal cracks, several connecting brackets or end plates for bolting elements together were broken or missing. Some of the damage was caused during dismantling due to the brittle behavior of the weathered material.
Fig. 2. Damage at the load bearing cast iron gutter (corner)
Water infiltrations, and consequently corrosion and frost, may as well have had their influence on the observed fissures and other damages, often in combination with local impurities or imperfections in the cast material itself. Due to the complexity of the element shapes, the cast iron itself has a low quality. Defects such as insufficient thickness (Fig. 3), impurities, internal air bubbles, internal corrosion, … were noticed during the detailed inspection of the elements. Figure 4 clearly illustrates air inclusions during the casting process found during the preparation of one of the main columns for material tests.
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Fig. 3. Casting defects resulting in insufficient material in certain areas
Fig. 4. Small and major air holes in the wall of a cast iron column noticed during sample taking due to a low quality production process
3 Analysis of the Wrought Iron and Cast Iron Components of the Orangery Given the poor condition of the structural elements, an analysis of the materials was conducted to determine their quality and composition in order to establish the best options for remediation. The material analysis comprised the identification of three samples (column, gutter and glazing bar), along with determining the weldability and performing tensile and compression tests.
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The material tests are destructive tests, hence, the samples are lost and can’t be reused in the restoration. Therefore, samples were taken from elements that were already significantly damaged. The samples were taken in the least deteriorated zone of the chosen elements to minimize any negative impact on material results. 3.1 Characterization of Wrought Iron and Cast Iron Samples The chemical composition of three samples (column, gutter and glazing bar) was determined by executing a combination of ICP-OES (Inductively Coupled Plasma – Optical Emission Spectrometry), combustion (C + S) and fusion (N + O + H) according to ASTM E351 [5] and ASTM E1019 [6] standards. The results of the chemical analysis are listed in Table 1. Table 1. Chemical composition of glazing bar, column and gutter in % Element
Glazing bar
Column
Gutter
As
0.024
0.021
0.020
Cr
0.0033
0.043
0.042
Cu Mg Mn Mo
0.012 1. The RI i,M trends of the three approaches converge with M = 3 (RI i,3 = 0.43), while when M ≥ 4, RI i,M reaches a plateau where the risk does not significantly vary (i.e., RI i,M drops by less than 5%) as the number of available shelters increases (RI i,4 = 0.36). It is worth noticing that, although the RI i,M values coincide when M > 4, the shelters’ positions are differentiated among the three approaches for the path choice, meaning that for this specific application scenario they can be considered at the same level of risk. This particular outcome can also be helpful for evaluating the number of shelters to be prepared according to their available surfaces [m2 ] and the expected number of pedestrians to accommodate, so as to guarantee an adequate density [pp/m2 ] both at their internal, but also in their immediate proximity (e.g., near the entrances, in the crossroads) to avoid flow problems and collisions between pedestrians who arrive in groups at the shelters.
Fig. 3. RIi,t values depending on the approach for the path choice (shortest, quickest, or cheapest) and the number of shelters available M. “Shortest” and “quickest” trends are overlapped.
Where. The most recurring positions are determined through the percentages of selection of the shelters. Results show that, to reduce the risk, the positioning of the shelters should follow a hierarchy according to the urban layout in all three approaches for the path choice. In fact, referring to the evacuation solutions with M ≤ 4: (1) the most recurring shelter is 28, selected 83% of the time, as it manages to collect the maximum number of pedestrians (i.e., eventually all those positioned in the streets, if M = 1);
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(2) the second most recurring shelter is SE, selected 75% of the times (that is in all the cases with M ≥ 2), as it is the only shelter who manages to collect the pedestrians in the square; (3) shelter 18 is selected 50% of the times, that is in all the cases with M ≥ 3; (4) shelter 10 is selected 25% of the times, that is in all the cases with M ≥ 4.
Fig. 4. Illustration of the shelters position progression with M = 1 → 4, being t the number of available shelters. The colored arrows are matched with the shelters’ position (summarized in the top right table) and indicate the progression of the RIi,j values (bottom right). The green pins indicate the most recurring shelters among the three approaches for the path choice when M ≤ 4 (i.e., 28, SE, 18, and 10).
Figure 4 shows an illustration of the most recurring shelters positions considering the first four solutions (map on the left), including also information about the hierarchical criterion of disposition according to the urban layout (colored arrows and top right table) and the associated RI i,M values (bottom right graphic). In particular: • For M = 1, all the approaches select a shelter displaced in the farthest street parallel to the river (pink arrow), i.e., 28 for the “shortest” and the “quickest” approaches, and 30 for the “cheapest” one. The relative RIi,1 values are higher than 0.80, as highlighted by the pink arrow in the bottom right graphic; • For M = 2, all three approaches confirm the previous positions and add the additional shelter within the square (green arrow), that is SE. These solutions allow decreasing the number Na of pedestrians who cannot complete the evacuation (then the relative RIi,2 , as highlighted by the green arrow in the bottom right graphic), by providing a shelter for the pedestrians positioned in the square, who otherwise would have no chance to survive as the corner of the square turned out to be deadly points (V p = 0 m/s); • For M = 3, the three approaches identify the same shelters’ positions, namely 28, SE, and 18. The latter in particular is displaced in the middle street parallel to the river (yellow arrow), and allows decreasing the risk up to -40% (RI i,3 = 0.43, yellow arrow in the bottom right graphic); • For M = 4, the three approaches add the same additional shelter to the previous solution, that is 10, so as to provide a shelter also in the closest street parallel to the
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river (blue arrow). This configuration allows gaining the plateau behind which the risk does not vary (RI i,4 = 0.36). How and Which. The previous sections highlight how the best evacuation solutions in terms of shelters’ number and position (and relative risk indexes values RI i,4 ) are those with 4 available shelters positioned in 28, SE, 18, and 10. Therefore, the discussion of the best evacuation paths is herein addressed by comparing the three approaches for the path choice (“shortest”, “quickest”, and “cheapest”) in this specific configuration. The evacuation paths to reach the indoor shelters having access from the streets (i.e., 28, 18, and 10) are the same in all the approaches, as pointed out by the solid green links in Fig. 5A. Therefore, following the same hierarchical distribution mentioned before, the typological HUBE can be ideally districted in areas of influence that include (1) the shelters where the pedestrians of the given area should be directed, and (2) the entire evacuation paths to get there (Fig. 5B). This type of zoning can ease solving logistic issues such as how rescuers’ operations might be addressed (i.e., by assigning each area of influence to a squad composed of a certain number of rescuers, especially in the unwalkable areas), or how pedestrians could be redirected in the case that one of the shelters becomes unusable. For instance, for what concerns the latter, Fig. 5A shows how pedestrians initially expected in shelter 10 could be redirected in 18 by only traveling the dashed green link (which is equivalent to connecting the blue area to the orange area in Fig. 5B).
Fig. 5. Panel A) Graphical illustration of the evacuation paths to reach the shelters in the case of M = 4: the solid green links indicate the paths in common with the three approaches, the brown links indicate the paths in common between the “shortest” and the “quickest” approaches, the magenta links indicate the paths for the “cheapest” approach. In the case of M = 3, pedestrians collected in 10 should reach 18 by traveling the dashed green link. Red nodes are shelters, isolated blue nodes are deadly points. Panel B) Areas of influence with M = 4 (while if M = 3, the blue area is merged with the orange one).
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However, the almost absolute concordance between the three approaches for the path choice could be probably brought back to the use of an application scenario in which the street network does not consider factors such as the possible differences in the paving and/or in the sewer system, besides of the simple geometry (i.e., there are no changes of width, slope, and direction of the streets). In fact, even considering a slightly more complex portion of the graph like that representing the square, the approaches are differentiated and provide two possible evacuation paths (characterized by the same level of risk RI i,4 = 0.36) connecting the up-left starting node to the outdoor shelter SE, that is traveling the brown links (following the “shortest” or the “quickest” approach), or the magenta links (following the “cheapest” approach) in Fig. 5A.
4 Discussion The best evacuation solution is unanimously identified by all the tested approaches for the path choice, and it consists of (a) 4 shelters, that is the threshold beyond which the risk does not improve as the number of shelters increases; (b) selecting the nodes SE, 28, 18, and 10, so as to cover four main areas of the HUBE, that are the square and the three streets parallel to the river; (c) traveling the evacuation paths pointed out in previous Fig. 5A, as they turned out to be at the same time the shortest, the quickest, and the less effortful ones. It is worth noticing that due to the hydrodynamic conditions established within the HUBE, there are no approaches able to nullify the number Na of pedestrians who cannot complete the evacuation, that are those placed in the most downstream street perpendicular to the river (the “northernmost” with reference to the map in previous Fig. 4), and any of those placed in the square (the critical nodes are in the corners of the square, and close to the river). Therefore, the only way to improve such outcome is executing the evacuation before the event reach its peak time. Despite the low complexity of the application scenario, further precious information can be obtained from the analysis of the evacuation solution. In particular, the application of the methodology can be helpful for subdividing the HUBE into areas of influence within which the evacuation can be entirely developed since they include both the shelters and the evacuation paths to get there. This type of result can be helpful, for instance, to plan the number of squads necessaire for the rescue operations and the implementation of wayfinding systems (including communication through portable devices) and road signs to direct pedestrians toward the same shelter also in pre-disaster conditions. In addition to this, the methodology could also be exploited to optimize for instance the design costs as a function of the shelters’ number (e.g., in the application scenario, providing more than four shelters does not decrease the risk) and position (e.g., in presence of constraints such as cultural heritage where it would be impossible implementing shelters). Finally, the analysis of the evacuation paths could provide information on the areas that necessitate the implementation of urban furniture (e.g., handrails, raised platforms/sidewalks) to ease the pedestrians’ motion (i.e., speed and stability), which are basically those with the highest number of pedestrians who cannot complete the evacuation (e.g., in this application scenario, the isolated blue nodes in Fig. 5A).
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5 Conclusions In case of flood in historic urban built environments (HUBEs), pedestrians can experience difficulty in choosing or performing the right approach for the path choice to minimize their risk. Therefore, operational decisions and procedures should be evaluated before a disaster actually occurs. In this work, a novel methodology is proposed in order to evaluate the effectiveness of evacuation plans to cope with the emergency in the phase of preparation for the disaster. In particular, starting from a case study already tested in previous works, the application scenario chosen for testing the methodology consists of a typological HUBE representative of the most recurring geometrical features of flood-prone Italian historic centers, in which a real-world event has been simulated. The subsequent hydrodynamic conditions established within the HUBE have been used to determine the pedestrians’ motion conditions thanks to experimental laws that relate the water depth and speed to the human speed and stability. Different evacuation solutions have been investigated at varying (1) the approach for the path choice, by changing the paths selection criteria between the shortest, the quickest, and the less effortful path, and (2) the number of available shelters in the HUBE, ranging from a minimum of one to a maximum of twelve (that is in each dry or quasi-dry are of the application scenario). In particular, the optimal evacuation solutions are computed by solving an Integer Linear Program (ILP) that in turn minimizes the length, the time, and the effort to travel the evacuation paths, together with the number of pedestrians who cannot complete the evacuation. In this process, the group dynamics are favored rather than those of the single pedestrian (i.e., ILP minimizes the evacuation paths with the respect to the total number of initial pedestrians). Since holistic, systematic approaches are required to deal with disaster management, the proposed methodology finally estimates the risk associated with each optimal solution through a synthetic index RI that takes advantage of Key Performance Indicators that jointly consider aspects inherent in the urban layout, the event intensity, and the human factor. Accordingly, 3 sets of solutions are compared (distinguishing the approach for the path choice) so as to determine the optimal number and position of the shelters (how many and where), together with the evacuation paths (how and which) to be provided to guarantee the pedestrians’ safety. In the application scenario, the best evacuation solutions are unanimously identified by the three tested approaches, meaning the shortest path, the quickest path, and the less effortful path coincide (in reference to all 240 pedestrians rather than the least favored one). Results obtained offer also precious insights about possible zonings of the HUBE by identifying areas of influence within which the evacuation process can be entirely developed (i.e., those areas include the starting points, the evacuation paths, and the shelters) so as to ease logistic and operational assessments. Promising results encourage future applications to more complex scenarios as well as real-world case studies by also including non-geometrical features that can affect the event progression (i.e., the presence of sewer systems, the differences in the paving, the presence of green areas) and/or logistic constraints such as the optimization considering also the budget granted by the administrations, the rescuers’ intervention, the presence of cultural heritages unsuitable to be used as shelters or that can obstruct safety
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operations. Furthermore, the proposed Risk Index could be refined by considering the aforementioned issues with the help of multicriteria decision-making techniques like the Analytic Hierarchy Process, that allow assigning priorities and evaluating the impact of each parameter by assigning them different weights. Finally, further efforts can be also addressed at improving the proposed solving algorithm, for instance by including factors that consider also the interaction between pedestrians also in view of possible future applications for computational modelling on evacuation simulation software.
Appendix A See Tables 3 and 4. Table 3. ILP model: parameters and variables description PARAMETERS
MEANING
V = {1, . . . , |V |}
set of nodes, being t the dummy nodes for “alive” pedestrians, and z the dummy nodes for pedestrians who cannot complete the evacuation
E = {1, . . . , |E|}
set of links
I = {1, . . . , |P|}
=1 k pu =0
set of pedestrians, being P the total number of pedestrians if the pedestrian k starts the evacuation from the node u otherwise
cuv
cost of the link (u,v), being u and v, respectively, the two node of a link
M
Maximum number of evacuation points
VARIABLES
=1 k xuv =0
=1 yu =0
MEANING if the pedestrian k travels the link (u,v) otherwise if the potential shelter u is chosen otherwise
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CONSTRAINTS k min cuv xuv
MEANING Objective function
(u,v)∈E
(u,v)∈E
k − pk = xuv u
k xuv ≤ Pyu
(v,u)∈E
k xvu
k ∈ I, u ∈ V \{t}
Flow balance on each node of the graph
u ∈ V \{z}
Nodes crossed by the flow
u ∈ V \{z}
Maximum number of available shelters
k∈I
yu ≤ M
u:(u.t)∈E
References 1. Polaris. http://polaris.irpi.cnr.it/report/. Accessed 15 Oct 2022 2. UNDRR. https://www.undrr.org/terminology. Accessed 15 Oct 2022 3. Ahmadi, M., et al.: A humanitarian logistics model for disaster relief operation considering network failure and standard relief time: a case study on San Francisco district. Transp. Res. Part E 75, 145–163 (2015) 4. Arrighi, C., et al.: Flood risk assessment in art cities: the exemplary case of Florence (Italy). J. Flood Risk Manag. 11(S2), S616–S631 (2018) 5. Hassan, W., et al.: Efficiency assessment of tsunami evacuation routes in Viña Del Mar, Chile. In: 11th U.S. National Conference on Earthquake Engineering (2018) 6. Quagliarini, E., Romano, G., Bernardini, G., D’Orazio, M.: Leaving or sheltering? A simulation-based comparison of flood evacuation strategies in urban built environments. In: Littlewood, J.R., Howlett, R.J., Jain, L.C. (eds.) Sustainability in Energy and Buildings 2021. SIST, vol. 263, pp. 113–123. Springer, Singapore (2022). https://doi.org/10.1007/978-98116-6269-0_10 7. Haynes, K., et al.: ‘Shelter-in-place’ vs. evacuation in flash floods. Environ. Hazards 8(4), 291–303 (2009) 8. Chow, V.T.: Open-Channel Hydraulics. McGraw-Hill, New York (1959) 9. Bernardini, G., et al.: How urban layout and pedestrian evacuation behaviours can influence flood risk assessment in riverine historic built environments. Sustain. Cities Soc. 70 (2021) 10. Bernardini, G., Postacchini, M., Quagliarini, E., D’Orazio, M., Brocchini, M.: Flooding pedestrians’ evacuation in historical urban scenario: a tool for risk assessment including human behaviors. In: Aguilar, R., Torrealva, D., Moreira, S., Pando, M.A., Ramos, L.F. (eds.) Structural Analysis of Historical Constructions. RILEM Bookseries, vol. 18, pp. 1152–1161 (2019). Springer, Cham. https://doi.org/10.1007/978-3-319-99441-3_124 11. Bernardini, G., et al.: Investigating exposure in historical scenarios: how people behave in fires, earthquakes and floods. In: RILEM Bookseries (2019) 12. Salvati, P., et al.: Gender, age and circumstances analysis of flood and landslide fatalities in Italy. Sci. Total Environ. 610–611, 867–879 (2018) 13. Bernardini, G., et al.: A preliminary combined simulation tool for the risk assessment of pedestrians’ flood-induced evacuation. Environ. Model. Softw. (2017) 14. Cox, R.J., et al.: Australian rainfall & runoff revision project 10: appropriate safety criteria for people, April 2010
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15. Ibri, S.: An ILP for joint districting and evacuation. In: Arai, K. (ed.) FTC 2021. LNNS, vol. 359, pp. 540–549. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-89880-9_40 16. Yuan, Y., Wang, D.: Path selection model and algorithm for emergency logistics management. Comput. Ind. Eng. 56(3), 1081–1094 (2009) 17. European Civil Protection and Humanitarian Aid Operations. https://civil-protection-humani tarian-aid.ec.europa.eu/what/humanitarian-aid/shelter-and-settlements_en. Accessed 21 Nov 2022 18. Velasquez, W., Alvarez-Alvarado, M.S.: Outdoors evacuation routes algorithm using cellular automata and graph theory for uphills and downhills. Sustainability 13(9), 4731 (2021) 19. Xie, A., et al.: Risk minimization routing against geographically correlated failures. IEEE Access 7, 62920–62929 (2019) 20. Bernardini, G., et al.: Dynamic guidance tool for a safer earthquake pedestrian evacuation in urban systems. Comput. Environ. Urban Syst. 65, 150–161 (2017) 21. Mu, A., Yu, S.: Calculation of optimal path in post-earthquake emergency period. World Earthq. Eng. 34(1), 113–120 (2018) 22. Guo, P., et al.: Selection of optimal escape routes in a flood-prone area based on 2D hydrodynamic modelling. J. Hydroinform., 1310–1322 (2018) 23. Péroche, M., et al.: An accessibility graph-based model to optimize tsunami evacuation sites and routes in Martinique, France. Adv. Geosci., 1–8 (2014). https://doi.org/10.5194/adgeo38-1-2014 24. Zhu, Y., et al.: Optimal evacuation route planning of urban personnel at different risk levels of flood disasters based on the improved 3D Dijkstra’ s algorithm. Sustainability (2022) 25. https://www.ibm.com/it-it/analytics/cplex-optimizer. Accessed 03 Jan 2022
Challenges in the Preventive Maintenance of Early 20th-Century Reinforced Concrete Architectural Sculptures Esmeralda Paupério1(B) , Xavier Romão2 , Rui Silva1 , and Susana Moreira2 1 Construct – LESE - Instituto da Construção da Faculdade de Engenharia da Universidade do
Porto, Porto, Portugal [email protected] 2 Construct – LESE - Faculdade de Engenharia da Universidade do Porto, Porto, Portugal
Abstract. “Twentieth-century building materials and construction techniques may often differ from traditional materials and methods of the past. There is a need to research and develop specific repair methods appropriate to unique types of construction.” Approaches for the Conservation of Twentieth-Century Architectural Heritage, Madrid Document 2011, ICOMOS. Natural deterioration caused by the ageing of the materials and their exposure to severe environmental conditions leads to a significant increase in the vulnerability of constructions. The conservation of reinforced concrete structures of the early 20th century brings challenges due to the specific characteristics of their construction processes. If at the structural level these processes are already somehow identified and linked to the systems of construction engineers such as Hennebique, Coignet, etc., at the level of decorative elements like ornaments, sculptures or others, their conservation deals with unknown techniques and requires greater care to maintain their authenticity and integrity. Reinforced concrete, which is made of cement and steel, forms a material with a reduced lifespan when compared to natural and traditional construction materials such as stone or timber. Among other sources, the degradation of reinforced concrete is often caused by the corrosion of embedded steel, responsible for important losses of material which become particularly critical in sculptural elements. When facing the need to make conservation interventions to preserve, rehabilitate, or restore degraded cultural heritage elements, several restrictions must be dealt with. Such restrictions are related to the safeguarding of the heritage’s cultural value and significance that must be weighed against safety and durability needs, as well as against the duration and budget constraints of the intervention. To assist the decision-making process about the type of interventions that can be carried out, an adequate balance of the several constraints must be sought. Therefore, in this paper, a two-step approach that can be integrated within the maintenance plan is proposed. The first step consists of a method to determine a case-by-case intervention index that gauges the referred criteria influencing the type of intervention. The referred index weighs the influence of several qualitative and quantitative criteria which are graded according to the characteristics of the cultural heritage element under analysis. The second step focuses on the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1242–1255, 2024. https://doi.org/10.1007/978-3-031-39450-8_101
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development of maintenance indicators that can be used to assess the performance of the interventions that are carried out. This procedure was developed and implemented in the decision-making process related to the conservation of the decorative elements of a 20th-century building theatre in Portugal. A detailed analysis of the selected criteria for the intervention index and maintenance indicators is presented, as well as the advantages that might come from implementing the proposed procedure for the development of a sustainable conservation plan. A preliminary assessment of the maintenance indicators confirms that preventive measures decrease the number of repairs that are needed over time, meaning that the intervention index is correctly assessing the level of intervention required for a given decorative or sculptural element. Keywords: Decision-making process · conservation · cultural heritage · management of interventions · intervention index · maintenance indicator
1 Introduction The conservation of the built heritage in reinforced concrete from the beginning of the 20th century faces new challenges associated with the need for its consolidation, conservation, and repair. Natural deterioration, caused by the inevitable ageing of reinforced concrete and its exposure to atmospheric agents, has led to a considerable increase in the vulnerability of this type of structure. However, other degradation agents threaten these structures, such as inappropriate repair interventions, lack of maintenance or abandonment. The concern with the conservation of reinforced concrete buildings from the beginning of the 20th century has been growing over recent years, particularly on how it would be carried out since its specificities are diverse from the ones regarding masonry and timber buildings. The main obstacles are related to the lack of specific know-how to intervene and limited data regarding the compatibility of materials and assessment of the impact of interventions over long periods. These aspects are crucial when it comes to the rehabilitation of architectural sculptures executed in reinforced concrete (or cement) in which the artist’s hand is a factor of authenticity. Under the scope of the maintenance plan, a two-step approach is proposed in this paper. The first step focuses on supporting the decision-making process regarding what type of intervention on reinforced concrete architectural sculptures is appropriate. This was achieved through an intervention index, I TI , which weighs the influence of several qualitative and quantitative criteria, classifying them according to the characteristics of the sculptural element under analysis. The second step concerns the development of indicators that can support the assessment of the implementation of the maintenance plan. These indicators enable the classification of the importance of facades, which is crucial for the prioritization of actions, and for analysing the evolution of interventions according to their level of complexity/intensity.
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The two-step procedure was applied to the architectural sculptures of the façades of the São João National Theatre, which is a national monument located in the city centre of Porto, built at the beginning of the 20th century. It should be noted that the I TI was initially developed aiming at the 2013 interventions carried out on the facades of São João National Theatre, since the degradation was severe. It continued to be applied in the following inspections in support of the decision, which is briefly presented here, since the focus of the discussion is on the evaluation of the effectiveness of the implementation of the maintenance plan.
2 Concrete Degradation and Other Factors to Ponder in Conservation Interventions in Architectural Sculptures Reinforced concrete, which is made of cement and steel, forms a material with a reduced lifespan when compared to natural and traditional construction materials such as stone or timber. Among other sources of decay, reinforced concrete deterioration is often caused by the corrosion of reinforcement steel [1]. Since the origin of this deterioration usually starts from within the concrete element, available repair approaches are seen as considerably intrusive. Therefore, this source of decay is especially difficult to address when dealing with the repair of reinforced concrete decorative elements or sculptures, where conservation operations could destroy their authenticity (Fig. 1). Normally, the reinforcement steel is protected against corrosion by being embedded in the concrete and its high alkalinity. This protection, however, can be destroyed in two major ways [2]. The first is carbonation, which occurs when carbon dioxide in the air reacts chemically with the cement paste at the surface and reduces the alkalinity of the concrete. The second is through chloride ions from salts which combined with moisture produce an electrolyte that effectively corrodes the reinforcement bars. Chlorides may come from seawater additives in the original mix, or from prolonged contact with salt spray or de-icing salts. Regardless of the cause, corrosion of reinforcement bars increases their volume and causes expansive forces within the concrete [3, 4]. Cracking and spalling of the concrete are frequent results of this expansion phenomenon. Rust stains on the surface of the concrete are another indication that internal corrosion is taking place.
Fig. 1. Architectural sculptures in reinforced concrete with material degradation resulting from corrosion of the reinforcement.
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To sum up, 20th-century constructions may present two types of problems associated with reinforced concrete degradation: • Problems related to the structural stability of the building. • Problems related to the conservation of architectural sculptures. The problems related to the structural stability of constructions are the result of a reduction in the load-carrying capacity of reinforced concrete elements due to the loss of concrete, the loss of bond between steel and concrete, and due to the decrease in thickness of the reinforcing bars themselves. The problems related to the conservation of decorative elements raise important questions associated with the safeguarding of the heritage cultural value and significance that have to be weighed against safety and durability needs. During the decision-making process about what intervention has to be carried out to preserve, rehabilitate, or restore degraded cultural heritage elements, an adequate balance of these constraints must be found. To assist in this decision-making process, the proposed methodology will enable the development of an intervention index that weighs the influence of several qualitative and quantitative criteria associated with the state of conservation and characteristics of the cultural heritage element under analysis. 2.1 The Proposed Intervention Index I TI The proposed index [5] was developed such as to establish a quantitative measure that would recommend either the in situ repair or the replacement of the element under analysis. This index weighs the influence of several qualitative and quantitative criteria which are graded according to the characteristics and the level of degradation of the element being analysed. This index was developed such as to account for several restrictions that may control the type of admissible intervention. Some of these restrictions are related to the safeguarding of the heritage’s cultural value and significance that have to be weighed against restrictions related to safety and durability requirements, as well as duration and budget constraints. The proposed intervention index is quantified for each decorative element and reflects the weighted combination of seven criteria (C1 to C7) according to: 7 Ci × wi (1) ITI = i=1 7 i=1 wi where C i corresponds to the grade assigned to the ith criterion and wi is the weight factor of the ith criterion. Some of the selected criteria are graded directly while others depend on the value of auxiliary parameters (P1 to P9). A description of the selected criteria, the information, and parameters considered for their quantification, and of their weight factors is presented in the following: • C1 – Durability of the decorative element: the grading of this criterion combines information about the level of cracking of the element (P1), the existence and location of the reinforcement (P2), the level of corrosion of the reinforcement (P7), and the amount of repair required by the element (P8). The weight factor w1 is considered to be 5.
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• C2 – Meeting the deadline for the project completion: the grading of this criterion combines information about the size of the element (P3), the difficulty to make a cast of the element to replicate it (P4), the difficulty of fixing this replica to the façade (P5), and the amount of repair required by the element (P8). The weight factor w2 is considered to be 5. • C3 – Risk associated with the fall of the decorative element: the grading of this criterion depends on the life-threatening hazard due to the fall of a decorative element and on the possibility of observing the state of conservation of that element from the ground. The weight factor w3 is considered to be 5. • C4 – Authenticity of the decorative element: the grading of this criterion depends on the decorative element being authentic or not (i.e. the decorative element is a replica or it has been previously repaired). The weight factor w4 is considered to be 4. • C5 – Repetitiveness of the decorative element: the grading of this criterion depends on the number of times a given decorative element is repeated on the façades (P6). The weight factor w5 is considered to be 3. • C6 – Evolution of the state of degradation of the decorative element since 1995: the grading of this criterion reflects the evolution of the state of degradation of the element based on its condition in 1995 when the state of conservation of the façades was surveyed and conservation interventions were carried out in some parts of the building. The weight factor w6 is considered to be 1. • C7 – Replacement potential of the decorative element: this criterion depends on information about the level of cracking of the element (P1), the level of corrosion of the reinforcement (P7), and the amount of repair required by the element (P8), and its grading combines data about the size of the element (P3), the difficulty of making a cast of the element to replicate it (P4), the difficulty of fixing this replica to the façade (P5), and the level of cracking of the element (P1). The weight factor w7 is considered to be 5. By combining the grading of the several criteria using Eq. (1), the intervention index ITI is then obtained. The index ranges between 0 and 3 and if a value lower than 2 is obtained, the decorative element under analysis is recommended to be repaired and consolidated. Otherwise, the replacement of the element with a replica is suggested. With respect to C2, it is noted that, when it comes to interventions in cultural heritage, it is not uncommon for there to be a lack of prior inspection and diagnosis actions. Even when such actions are taken, they may not always provide a conclusive assessment due to various observational challenges. Unfortunately, this can result in a planning of prices and work schedules that may not be in line with the requirements of the necessary conservation works. As a result, it might be necessary, in some cases, to adjust the conservation approach by either rescheduling certain tasks or prioritizing the most crucial elements that may be addressed within the allotted time for the works.
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2.2 Maintenance Plan Indicators After the major conservation intervention in 2013/2014, and since the continuous degradation of the reinforced concrete decorative elements was expected, a periodic maintenance plan was defined for the facades. This maintenance plan includes regular inspections followed by targeted conservation actions on the façades to repair damaged elements. Between 2014 and 2022, three inspections and two conservation actions were carried out, with the first and second inspections corresponding to a conservation action in 2019, and the third inspection in 2022 corresponding to a subsequent conservation action to optimize means and efforts. The parameters recorded in each action were the number of damages per façade detected in the inspection, the intensity level of the intervention need to address each observed damage, and the location of the damage. The importance level of each façade was defined based on the percentage of decorative elements and the percentage of unique decorative elements. The maintenance plan is rooted in prevention rather than repair, therefore preventive actions should always be the majority of actions. In addition, to correctly implement the maintenance plan, it is necessary to balance the level of interventions with the importance of the façade. Hence, the proposed indicators aims to account for both issues. The classification of the importance of the façade enables the prioritization of interventions, which is critical for implementing the maintenance plan. It is based on the distribution of decorative elements and sculptures across a façade and on which of these elements are unique, meaning elements that are not repeated throughout the façade may require a specific cast of single-use. The presence of decorative elements and sculptures on the façade, and the fact that they might be unique, increase the cultural value of each façade. The importance of each façade was determined using the relation between the total area of the façade and the area of decorative elements and sculptures, also weighing the uniqueness or the repetitiveness of the decorative elements and sculptures of the façade. The following three types of interventions were defined based on purpose and complexity (increased level of action from Type I1 to Type I3): Type I1 – preventive action, which encompasses the repair of fine cracks with mortar or replacement of the protective and/or water-repellent layer (Fig. 2); Type I2 – remedial action, which encompasses repair of cracks or fractures with stabilization of metallic components (e.g., steel reinforcements) and/or restoration of the previous form (Fig. 3); and finally, Type I3 – remedial action, which encompasses repair of fractures or missing parts, with the removal of the metallic component and grout injection, stitching or restoration of the previous form (Fig. 4). Therefore, each intervention that is planned should be classified with one of these levels of intensity, whenever they take place. Consequently, it will be possible to have a track record of the interventions being performed and assess their effectiveness over time.
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Fig. 2. Example of intervention type I1
Fig. 3. Example of intervention type I2
Fig. 4. Example of intervention type I3
3 Case Study: The São João National Theatre The São João National Theatre is a National Monument located in the city of Porto, Portugal. The construction of the current theatre started in 1910 under the direction of architect Marques da Silva, the most important architect of Porto at the time, after the original building was destroyed by a fire in 1908. The style of L’Ecole des Beaux-Arts in Paris, where Marques da Silva studied, is found in the São João theatre’s architecture. The Beaux-Arts architecture expresses a neoclassical architectural style that involved sculptural decoration along conservative modern lines and employed French and Italian Baroque and Rococo formulas combined with an impressionistic finish and realism. An abundance of balustrades, statues, columns, garlands, pilasters between doors and windows, and grand staircases is typical of this architectural style. In the case of the São João National Theatre, these decorative elements exist in all the façades (with a total area of approximately 4800 m2 ) and are made of reinforced concrete (Fig. 5 e Fig. 6). Some of the decorative elements having vegetal and geometrical patterns are seen to be repeated throughout the façades.
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Fig. 5. Façade of the São João National Theatre
Fig. 6. Reinforced concrete architectural sculptures of the São João National Theatre
In 2006, the façades of the São João National Theatre began to exhibit severe signs of deterioration due to the long-term weathering of the concrete surfaces, the corrosion of steel reinforcement and the fall of pieces of mortar (the latter enforced the need to install façade nets to prevent such pieces to fall over the pedestrians). The development of a conservation project for the façades was therefore needed with some urgency. Considering the previously referred degradation issues related to steel corrosion and concrete spalling, the conservation and preservation of such a rich and dense array of decorative elements and sculptures presented numerous issues and several intervention options not easy to choose from. Besides the severe cracking and spalling levels found in the concrete due to corrosion of the reinforcement, significant damages were also found to be related to bird-dropping deposits and the presence of black crusts. To illustrate the state of degradation of some of the reinforced concrete elements of the theatre façades, Fig. 7 presents some examples of damaged reinforced concrete decorative elements of the façades of the São João National Theatre. To adequately plan and prepare these interventions that occurred in 2013/2014, a survey of the damages and degradation levels found on the façades and their decorative elements and sculptures was needed. A first assessment of their state of degradation was carried out before the cleaning operations of the façades took place, which resulted in an incomplete characterization of the elements’ condition. A reliable assessment was only possible after the cleaning operations (Fig. 8). In addition to the damage survey,
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several concrete samples were taken from the façades for laboratory analysis and testing to determine the components and mix proportions of the original concrete, thus enabling the development of a repair mix with properties compatible with the original concrete.
Fig. 7. Examples of damaged reinforced concrete decorative elements of the façades of the São João National Theatre.
The cleaning operations also revealed that a conservation intervention had been previously carried out on the façades in the mid-20th century because some decorative elements exhibited additional layers of mortar over the original ones which altered their original volumetric proportions. In other cases, by visual observation and by comparing the several types of mortars, it was possible to conclude that some of the original decorative elements were replaced during that intervention. Given these aspects, the current intervention project foresees the possibility of making casts of original elements to replace similar ones previously intervened in the mid-20th century. These replaceable elements are those exhibiting a current state of degradation that implies a level of repair incompatible with the simultaneous upholding of their authenticity and of their safety against falling. Even though the fundamental purpose of the intervention is to replace as few elements as possible, the main objective of the proposed index is thus to identify which elements exhibit the need for a more severe repair intervention along with a higher potential for replacement.
(a)
(b)
( c)
(d)
Fig. 8. Cleaning operations: (a) Cleaning operation to remove limewash, (b) cleaning operation by micro-abrasion, (c) example of a decorative element before cleaning; (b) after cleaning.
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3.1 Application of the ITI to São João National Theatre To apply the proposed methodology the identification of each element was not a simple operation due to the high level of interconnection between consecutive decorative forms (Fig. 9). In these cases, individual elements were selected based on symmetry and repetitiveness criteria.
Fig. 9. Example of the considerable interconnection of architectural sculptures.
Although the proposed index establishes a set of objective criteria to characterize a given element, the grading of some aspects sometimes involves a certain degree of subjectivity. Grading the difficulty of making a cast of the element to replicate it (P4) or defining with absolute certainty the authenticity of a decorative element (C4) are examples of factors that may involve some degree of subjectivity. The cleaning operations of the façades are also decisive in the results of the index. As previously mentioned, a reliable assessment of the state of degradation of the decorative elements is not possible before such operations expose the true state of the elements which is, many times, hidden below several layers of dirt, black crusts, or paint. To illustrate some of the results obtained when applying the proposed methodology to the São João National Theatre, Fig. 10 presents the value of the obtained I TI for seven reinforced concrete decorative elements or sculptures from West facade. As can be seen, the replacement of elements 3, 6 and 7 is suggested by the results. For the case of element 6, and comparing with the result obtained for element 5 which is similar to element 6, the “replacement” result given the index is because this element exhibits a high level of degradation with severe steel corrosion and concrete spalling, and more than 75% of its volume requiring consolidation. On the other hand, element 5 presents no steel corrosion, no spalling, and less than 25% of its volume requires consolidation. Concerning element 7, the decisive characteristics for the “replacement” result are its level of steel corrosion and concrete cracking, the fact that it requires the consolidation of more than 50% of its volume and the fact that it is not an original element. In terms of
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element 3, aside from its high level of cracking and needed consolidation, the fact that it is a small element easy to replicate is also a decisive factor to obtain a “replacement” result.
Fig. 10. Sample results obtained by the proposed intervention index when grading different types of reinforced concrete decorative elements of the São João National Theatre.
3.2 Assessment of the Maintenance Plan Indicators Following the interventions carried out in 2014, the National Theatre São João was subjected to maintenance interventions in 2019 and 2022, so it was possible to implement the maintenance indicators in both years and analyse the evolution. According to what was established in Sect. 2.2, one of the first steps is to determine the importance of each façade. This was accomplished by quantifying the total area of decorative elements and sculptures and the total area of unique decorative elements and sculptures on each facade. As shown in Fig. 11, the North façade, where the main entrance of the theatre is located, is the one with the highest density of decorative elements and sculptures, as well as unique elements, which leads to the classification of high importance. On the opposite side, the South façade clearly has less importance in terms of architectural sculptures, and the East and West facades have equal importance probably due to their symmetry (Fig. 11).
10%
2%
21%
10%
West
37%
12%
West
South
South
East
East
North
North 65%
(a)
21%
(b)
Fig. 11. Determination of elements’ density per facade: (a) Density of the total amount of decorative elements and sculptures per façade; (b) Density of unique decorative elements and sculptures per total of elements and façade.
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The next step concerns the analysis of the types of interventions carried out during the implementation of the maintenance plan and their evolution between 2019 and 2022. First, the interventions of 2019 and 2022 were classified using the levels presented in Sect. 2.2, as shown in Fig. 12. Then, a verification was performed to determine if interventions carried out in 2022 occurred in the same location of the same element of 2019. The total numbers of 170 and 193 interventions were carried out in 2019 and 2022, respectively. The increased number in 2022 is justified by the larger number of Type I1 interventions (preventive interventions) carried out (Fig. 13). Type I1 interventions carried out in 2022 had a higher weight on the total number of interventions when compared with the ones carried out in 2022. One considers that this might be due to the confirmed effectiveness of interventions carried out in 2019, which reduced the number of Type I2 and Type I3 interventions. This it is also related to the fact that each façade was scheduled for intervention in pre-allocated time intervals, and during those intervals, technicians would execute interventions from Type I3 to Type I1 and if additional time was left, they would carry out preventive Type I1 actions that were not detected during the inspection or did not qualify as mandatory. From 2019 to 2022, the weight of Type I2 and Type I3 interventions decreased, except for the Type I2 interventions on the East façade, while Type I1 actions increased in all facades. It is necessary to clarify that the interventions were executed during a specific interval of time and not sporadically throughout the year, due to the cost associated with resource mobilization. I1
I1
I1
I1
A L S.JOÃO I1
I2 I1 I1
I1
I1
I1
I1 I1
I1 I1 I1
I3
I1
I1 I1
I1 I2
I1 I1
I1
I1
Interventions Type I1 2019
I2
Interventions Type I2 2019
I3
Interventions Type I3 2019
I1
Interventions Type I1 2022
I2
Interventions Type I2 2022
I3
Interventions Type I3 2022
I1
Fig. 12. Classification of type of intervention relative to one part of the North façade.
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2019 Type 2
2022 Type 1
2019 Type 3
19%
90% 80% 70%
34% 37%
60%
10% 24%
50% 40%
21%
30% 20% 10%
34%
51%
56%
44%
42%
28%
0% West
(a)
South
Facade
East
90% 80% 70%
20%
(b)
2022 Type 3
7% 4%
7% 14%
14%
60% 50% 40% 30%
100%
89%
79%
67%
20% 10% 0% West
North
2022 Type 2
0%
100%
Type of intervention per total (%)
Type of interventions per total (%)
100%
South
East
North
Facade
Fig. 13. Type of interventions on decorative elements and sculptures: (a) in 2019; (b) in 2022.
From Fig. 14, one can understand the evolution of the type of interventions in the same location of the same element, considering the interventions performed in 2019 and 2022. Interventions in coincident locations of the same element did not worsen since no cases are reporting an increase in severity (first two columns). In the West façade, there are two elements with the same type of intervention in 2019 and 2022 (I3-I3), which indicates that the previous intervention in 2019 did not result in an improvement in the situation. Taking into consideration, the level of importance of each façade and the discussion performed regarding all interventions and interventions carried out on the same location of the same element, the North and West facades are the ones that require more attentive action and detailed analysis within the maintenance plan.
Fig. 14. Evolution of the type of interventions in the same location of the same element, from 2019 to 2022.
4 Conclusions The conservation practice of reinforced concrete heritage from the late 19th and early 20th centuries has its specificities when compared to other historic constructions. The lack of professional experience and know-how in their repair is particularly important,
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namely when dealing with decorative elements in reinforced concrete. The fundamental purpose of an intervention is to maintain as many of the elements as possible, involving repair and consolidation operations that will safeguard as much as possible the elements’ authenticity. Aside from the need to safeguard the cultural value and significance of the heritage, other important issues must also be weighed, namely those related to safety and durability, as well as to the intervention’s duration and budget constraints. Given the difficulty of balancing all the factors that influence the type of intervention to be carried out in each element under analysis, an intervention index was developed to help in this decision-making process. Although the proposed index involves a set of objective criteria to characterize a given element, the grading of some aspects is sometimes subjective. Furthermore, a reliable assessment of the state of degradation of the decorative elements is not possible before cleaning operations expose the true state of the elements which is, many times, hidden below several layers of dirt, black crusts, or paint. A preliminary analysis of the maintenance indicators confirms the adequacy of the interventions carried out in 2019, with a clear decrease in Type I2 and Type I3 interventions in 2022. Particularly, when analysing interventions in the same location of the same element, one can verify that the intensity of the interventions did not escalate. The North and West facades are the ones that require more attentive action and detailed analysis within the maintenance plan. Acknowledgements. The authors would like to acknowledge the financial support by Base Funding - UIDB/04708/2020 of CONSTRUCT - Instituto de I&D em Estruturas e Construções, funded by national funds through FCT/MCTES (PIDDAC).
References 1. Gaudette, P., Slaton, D.: Preservation briefs 15: preservation of historic concrete. Technical preservation services division, National Park Service, US Department of the Interior, Washington, DC (2007) 2. Bertolini, L., Elsener, B., Pedeferri, P., Polder, R.: Corrosion of Steel in Concrete: Prevention, Diagnosis and Repair. Wiley-VCH Verlag GmbH & Co. KGaA, Berlin (2004). ISBN: 3527308008 3. Mailvaganam, N.: Repair and Protection of Concrete Structures. CRC Press, Boca Raton, Florida (1992). ISBN-13: 978-0849349935 4. Page, C.: Degradation of reinforced concrete: some lessons from research and practice. Mater. Corros. 63(12), 1052–1058 (2012) 5. Paupério, E., Romão, X., Vila Pouca, N.: Elementos decorativos das fachadas do Teatro Nacional São João. Como se construiram, porque se degradam. Teatro Nacional de São João e Instituto da Construção-Faculdade de Engenharia da Universidade do Porto, pp. 121–147 (2020). ISBN 978-989-54947-0-5
Vulnerability Assessment: Comparison of Empirical and Analytical Approach – A Case Study in Zagreb, Croatia Antonela Moreti´c1(B) , Mislav Stepinac1 , Nicola Chieffo2 and Paulo B. Lourenço2
,
1 Faculty of Civil Engineering, University of Zagreb, Kaˇci´ceva 26, 10 000 Zagreb, Croatia
[email protected] 2 Department of Civil Engineering, University of Minho, Braga, Portugal
Abstract. In March 2020, the capital of Croatia was hit by two earthquakes of moderate magnitudes. The earthquakes caused high economic losses, due to damage that occurred in the city centre. The city centre is mostly made up of historical masonry structures that have proven to be extremely vulnerable in the case of an earthquake. The paper represents two approaches to estimating vulnerability: an empirical and an analytical approach, respectively. The case studies building aggregates are in the city centre, Lower Town. The application of the empirical approach requires data about previous earthquakes and the damage that occurred. Firstly, the macroseismic approach, which is an indexbased method, is being used. Structures were categorized into typological classes. The results were calibrated according to data from the earthquake that occurred in 2020 and are presented in terms of vulnerability and fragility curves as well. Next, the analytical approach was considered, by performing a non-linear static analysis on the selected structural unit as a representative of the predominant structural typology present in the study area. The selected structural unit was modelled in software 3Muri, using the macro-element approach. The impact of structural interaction was considered by adopting a simplified numerical procedure. Moreover, fragility curves were derived from pushover curves. The main aim of the research was to compare the empirical and analytical approaches to validate the empirical approach. While the analytical approach is more precise, due to more input information, the macroseismic method is simpler to use and it provides results on a wider scale which is useful when developing risk mitigation strategies. Keywords: Vulnerability · Earthquake · Empirical Approach · Analytical Approach · Masonry aggregates · Fragility curves
1 Introduction Earthquakes are extreme phenomena that produce ground shaking because of a massive quantity of energy being released, suddenly producing the highest horizontal forces on engineering structures. Seismic risk is defined according to seismic hazard, exposure, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1256–1267, 2024. https://doi.org/10.1007/978-3-031-39450-8_102
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and vulnerability. Compared to hazard and exposure, vulnerability is the easiest parameter to influence. Vulnerability is the susceptibility of the structure to the effects of an earthquake. Methods to assess vulnerability are classified as empirical, analytical, expertbased or hybrid methods [1]. Empirical methods are based on statistical data collected from post-earthquake inspections, whereas the analytical methods rely on numerical models and simulations of structural seismic response [2]. Expert-based methods imply vulnerability assessment based on the knowledge and experience of experts. Finally, hybrid methods are a combination of previous methods. Until recent earthquakes struck Croatia in 2020, the analytical approach was more appropriate to assess the vulnerability because the database concerning the historical damages detected by the previous earthquakes was non-existent [3]. In 2020, postearthquake assessments were carried out under the guidance of the Faculty of Civil Engineering [4, 5]. As a result, the damage database was created, which enabled the application of empirical methods. The paper presents a brief overview of empirical and analytical approach and their implementation in the Croatian capital. The methods were applied to traditional masonry structures erected in aggregate conditions. Masonry structures represent a large portion of the European building stock and are characterised by their low resistance to horizontal forces [6, 7]. Additionally, if the structures are grouped in aggregates, the complexity of the structural response increases. Also, the structures are mainly residential buildings which implies a high number of users, meaning higher exposure. The service life of these traditional structures has exceeded, and they were poorly maintained which has an impact on the vulnerability of the structures. The structures are in Zagreb’s Lower Town, the city’s historical centre, and are preserved as heritage. The latter is the primary cause of highly estimated economic losses [8].
2 Empirical Approach Empirical methods are applicable if the information about the damage from previous earthquakes exists. The approach is based on statistical data processing. The macroseismic method is an empirical method in which the damage is described by the macroseismic intensity scale, in this case - the European macroseismic scale, EMS98 (Table 1) [9]. The method is suitable for application on larger-scale investigations [5, 6]. The results are usually achieved for typological classes, which are defined based on the structural systems, construction material, construction year, number of floors etc. [12]. The more elaborate classification implies more precise results, but it must be emphasized that the method provides useful results despite limited databases and numerous assumptions. In March 2020, earthquakes with magnitudes MW = 5.3 and MW = 5.0, and intensity VII (according to EMS-98) hit Croatia [13]. After the earthquake, civil engineers conducted post-earthquake assessments. All the data was gathered into a database by the newly formed Croatian Centre for Earthquake Engineering. Three aggregates, consisting of 66 structural units (SUs), were chosen as a case study (Fig. 1a). The aggregates are in Lower Town, in the heritage-protected area. Visual inspections were performed, the documentation from archives was collected, and the access to results of post-earthquake assessments was provided by Croatian Centre for Earthquake Engineering (Fig. 1b).
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(a)
(b)
Fig. 1. Case study located in Zagreb, Croatia a) aerial view [14] and b) post-earthquake assessment results [15].
Three typological classes among observed structures are defined: M1 – masonry structures with deformable floors, M2 – masonry structures with rigid floors and RC – reinforced concrete structures (Fig. 2). Since structural units classified as M1 predominate and are considered to be the most vulnerable among these typology classes, a vulnerability assessment of typology class M1 was conducted [16].
(a)
(c)
(b)
(d)
Fig. 2. Classification of structures according to a) construction material b) number of storeys c) construction year d) plan area.
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Table 1. Damage grade provided by the European macroseismic scale – EMS 98 [9]. Damage state
Damage score k
Damage description
D0
0
No damage
D1
1
Negligible to slight damage (no structural damage, slight non-structural damage)
D2
2
Moderate damage (slight structural damage, moderate non–structural damage)
D3
3
Substantial to heavy damage (moderate structural damage, heavy non–structural damage)
D4
4
Substantial to heavy damage (moderate structural damage, heavy non–structural damage)
D5
5
Destruction (very heavy structural damage)
The results of the method are mainly presented in terms of vulnerability and fragility curves. Vulnerability curves depict the correlations between intensity and mean damage grade. The correlation depends on the vulnerability index (VI ), ductility factor (Q) and intensity (I) as widely explained in the study proposed by [17]. Various index-based methods to calculate the vulnerability index have been proposed. They differ by influencing vulnerability parameters. The index-based method proposed in [18] suggests that structural vulnerability depends on 10 parameters. The method was adapted by adding five more parameters to consider the aggregate effect since the original 10 parameters refer to isolated structures only [19]. The value 2.3 representing the ductility factor, Q, for masonry structures has been adopted [20]. The vulnerability curve was derived according to the formulation proposed in [17] and calibrated based on the damage that was caused by the earthquake that occurred in the study area (Eq. (1)). I + 8,1 · VI − 10,75 (1) μD = 2,5 · 1 + tanh Q In Fig. 3 the comparison between the calibrated typological vulnerability curve and the corresponding literature one has been presented. Subsequently, the fragility curves (Fig. 4) have been derived according to the intensity-acceleration conversion law (I-PGA) as suggested in [21] and they show the probabilities of exceeding a certain damage level conditioned to a given peak ground acceleration.
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Fig. 3. Macroseismic method – vulnerability curves comparison [16, 17].
Fig. 4. Macroseismic method – calibrated fragility curves for the M1 typological class.
3 Analytical Approach Analytical methods can be performed regardless of data about previous earthquakes. They are based on the simulation of a seismic event and structural response. Simulation of seismic events is performed by linear static, linear dynamic, non-linear static or nonlinear dynamic method. Damage states are expressed according to displacement, rotation, drift etc. The description of damage states concerning displacement was adopted in this instance (Table 2).
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Table 2. Damage threshold evaluated in terms of displacement capacity of SDoF system [22]. Damage state
Damage description
Displacement
D1
Slight
0,7‧Dy
D2
Moderate
Dy
D3
Near collapse
Dy + 0,5‧(Du - Dy)
D4-D5
Collapse
Du
For practical reasons and precision, a non-linear static method was conducted. To create an adequate structural model, it is necessary to have a detailed insight into detailed project documentation. Therefore, the analytical approach was implemented referring to one structural unit (S.U.1 - intermediate), as previously classified as M1 typology (Fig. 5).
Fig. 5. Case study aggregate consisting of 3 SUs [23].
The plans, results of post-earthquake assessments, both preliminary and detailed inspections are available. The pushover analysis was performed in 3Muri software [24], by applying two different modelling techniques, e.g. the structural unit was modelled in isolated and aggregate configuration, respectively (Fig. 6). The software operates by adding macro-elements that are then discretized into deformable elements such as piers and spandrels that are connected by non-deformable rigid nodes.
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Table 3. Material characteristics
Value
Modulus of elasticity
800 N/mm2
Shear modulus
270 N/mm2
Specific weight
18 kN/m3
Mean compressive strength of masonry
4,1 N/mm2
Partial safety factor for material
1.5
Shear drift
0.004
Bending drift
0.008
Final creep coefficient
0.5
(a)
(b)
Fig. 6. Structural model obtained in 3Muri software a) isolated configuration b) aggregate configuration.
The pushover was performed in X and Y directions, using two different distributions of horizontal load - uniform and proportionate to the static forces. According to the uniform distribution, forces are proportional to the mass of the corresponding floor. The distribution proportional to static forces is also affected by floor heights. 3Muri software shows the results of the analysis also in terms of pushover curves and risk indices α. Pushover curves show the correlation between base shear and control displacement. The risk index is the ratio between capacity acceleration and demand peak ground acceleration. The most critical analyses were considered, both in X and Y direction, meaning the ones with the lowest risk index. Figure 7 displays the capacity pushover curves, the stiffness is enhanced in aggregate configurations in both directions, but the stiffness is higher overall in the Y direction. The ductility coefficient was calculated as the ratio of ultimate and yielding displacement. It is 82% higher in the aggregate configuration for the X direction, while it remains the same in the Y direction.
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Fig. 7. Capacity curves a) X b) Y direction.
Furthermore, fragility curves are defined according to Eq. (2) 1 PGA P[DK |PGA ] = φ · β PGADK
(2)
where: represents the cumulative distribution function, while PGADK is the median acceleration value related to the damage threshold (D0 … D4-D5). The parameter β is the standard deviation of the log-normal distribution, it is a function of the ductility of the structural system, μ. However, in this research work, the proposed fragility functions are derived according to Eq. (3) [21] Sa,e = ω · Sd ,e = 2
2π T
2 · SDK
(3)
whereas: Sa,e is spectral acceleration, T is the vibration period of the structure and SDK is the displacement correlated to the damage threshold. Fragility curves are depicted in Fig. 8, where solid lines represent the probability response of the aggregate configuration, while the dashed ones stand for isolated configuration. It is noticeable that in X direction, the aggregate has a beneficial impact. Meaning, for the same value of PGA, the probabilities of exceeding more serious damage states are higher for isolated structures. On the other hand, considering Y direction, it is observed that interaction between units increases the vulnerability of the monitored SU. This may be justified, as the aggregate configuration implies higher mass while the stiffness and ductility increments are much higher in X direction than in Y direction, where stiffness increased, but ductility remained the same, as can be seen from Fig. 7.
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(a)
(b)
Fig. 8. Analytical method – fragility curves a) X direction b) Y direction.
4 Discussion and Conclusion A vulnerability assessment is a necessary step to assess seismic risk. This paper focuses on the macroseismic method (empirical approach) and analytical method by applying the pushover method. Three aggregates located in the historical centre of Zagreb were the subject of the research. Due to exceeded service life, poor maintenance, many users and high seismic hazard, these traditional structures imposed themselves as a case study. The macroseismic, index-based method relies on the application of statistics. Based on the statistical processing of damage data from previous earthquakes, it is possible to express damage scenarios for each earthquake intensity or PGA if there is a valid correlation between intensity and PGA. Its simplicity, speed of application and the amount of uncertainty it successfully tolerates make it a practical tool for assessing the vulnerability of many buildings (at the local, urban, and regional levels). Even with a limited database and numerous assumptions, it provides useful results. However, its application requires data on damage to buildings during previous earthquakes. Its results are displayed in terms of vulnerability or fragility curves, but usually not for a single structure but a group of structures. Therefore, it is necessary to classify the structures into typological classes, otherwise, the averaged results are meaningless. On the other hand, the analytical method applies to a smaller number of structures. This is conditioned by two main reasons, firstly it is time-consuming and secondly, the necessary information such as material and geometry characteristics is often unavailable. Still, if it is possible to implement, it provides more detailed results in opposition to the macroseismic approach. In the case of the application of the pushover method, it is possible to obtain fragility curves, but also information about base shear, displacement, rotation, story drift, ductility, periods etc. Since the fragility curves derived by the analytical approach are in this case, depicted in terms of spectral acceleration which is a function of the structural period it is not possible to directly compare the results with the fragility curves obtained by the macroseismic method. For that reason, from the results of the analytical method, the vulnerability indices and ductility coefficients were calculated and applied to the Eq. (1). Hence, the vulnerability curves have been derived. According to the macroseismic method, the aggregate effect is beneficial, and this resonates with observations from other authors [25]. The analytical method, unlike the macroseismic, provides results, distinctly for both X and Y directions. It implies higher
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vulnerability in case of an isolated configuration in X direction. In Y direction, the vulnerability is increased due to aggregate conditions. Table 3 shows the differences between probabilities of reaching certain damage states, obtained by macroseismic and analytical methods, both for aggregate configuration. For example, according to the macroseismic method, if X direction is observed, there is a 13,9% higher probability that damage state D1 will be reached if subjected to the earthquake with an intensity of VII. For damage states D1, D2 and D3, the average deviation is minimal, less than 5%. The difference is much higher for damage states D4 (the average difference is 10,5%) and D5 (the average difference is 16,5%). The deviations are lower for Y direction (the average deviation is 3,9). Overall, the macroseismic method provides more conservative results (Table 4). Table 4. Differences between probabilities obtained by macroseismic and analytical method, aggregate configuration. Intensity
V
VI
VII
VIII
IX
X
XI
−2,4
−1,8
−0,6
−0,1
XII
X direction D1 (%)
3,6
D2 (%)
−19,9
−5,5
3,1
−5,3
−7,9
−4,5
−1,9
−0,7
D3 (%)
−13,0
−13,7
−3,0
−2,3
−13,3
−15,6
−11,0
−6,3
D4 (%)
−3,3
−6,8
−4,6
5,3
1,9
−13,6
−23,6
−24,8
D5 (%)
−0,3
−1,1
−1,6
5,0
21,2
34,3
36,7
31,8
0,0
13,9
4,6
0,0
Y direction D1 (%)
−13,7
−2,0
0,1
0,0
0,0
0,0
D2 (%)
10,4
16,9
−1,0
−4,3
0,8
0,3
0,0
0,0
D3 (%)
1,9
9,2
11,9
−2,0
2,5
2,5
0,8
0,2
19,4
D4 (%)
0,2
2,0
8,8
4,4
1,4
7,9
7,5
D5 (%)
0,0
0,2
−2,0
4,3
−4,8
−10,7
−8,3
4,5 −4,6
The macroseismic method is a more favourable solution in case of vulnerability assessments at larger scales, it can be a useful tool in planning risk mitigation strategies [26] at a state or city level, as it highlights the critical parts of the building stock. Implementation of the analytical method on an urban scale is not realistic, given that it includes seismic analysis. It is a more practical tool in the case of seismic retrofitting [27, 28], as it highlights critical elements of the individual structure. Funding. This research is funded by the Croatian Science Foundation, grant number UIP-2019– 04-3749 (ARES project—assessment and rehabilitation of existing structures—development of contemporary methods for masonry and timber structures), project leader: Mislav Stepinac.
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References 1. Moufid, M., Mohamed, F., Noroozinejad. E.: The seismic vulnerability assessment methodologies: a state-of-the-art review. Ain Shams Eng. J. 11, 849–864 (2020). https://doi.org/10. 1016/j.asej.2020.04.001 2. Formisano, A., Massimilla, A.: A novel procedure for simplified nonlinear numerical modeling of structural units in masonry aggregates. Int. J. Archit. Herit. 12, 1162–1170 (2018). https://doi.org/10.1080/15583058.2018.1503365 3. Atali´c, J., Šavor Novak, M., Uroš, M.: Seismic risk for Croatia: overview of research activities and present assessments with guidelines for the future. Gradevinar, 923–947 (2019) 4. Uroš, M., et al.: Post-earthquake damage assessment of buildings - procedure for conducting building inspections. Gradevinar 72, 1089–1115 (2021) 5. Novak, M.Š., et al.: Zagreb earthquake of 22 March 2020 – preliminary report on seismologic aspects and damage to buildings. Gradevinar 72, 843–867 (2020) 6. Kišiˇcek, T., Stepinac, M., Reni´c, T., Hafner, I., Luli´c, L.: Strengthening of masonry walls with FRP or TRM. Gradevinar, 937–953 (2020) 7. Hafner, I., Lazarevi´c, D., Kišiˇcek, T., Stepinac, M.: Post-earthquake assessment of a historical masonry building after the Zagreb earthquake–case study. Buildings 12 (2022) 8. Government of the Republic of Croatia, The World Bank. CROATIA EARTHQUAKE Rapid Damage and Needs Assessment (2020) 9. Borg, R.P., Indirli, M., Rossetto, T., Kouris, L.A.: L’Aquila earthquake April 6th, 2009: the damage assessment methodologies. In: COST ACTION C26 Urban Habitat Constructions Under Catastrophic Events - Proceedings of the Final Conference, pp. 557–564 (2010) 10. Julià, P.B., Ferreira, T.M.: From single- to multi-hazard vulnerability and risk in historic urban areas: a literature review. Nat. Hazards 108(1), 93–128 (2021). https://doi.org/10.1007/s11 069-021-04734-5 11. Formisano, A., et al.: Seismic vulnerability analysis of historical centres: a GIS application in Torre del Greco. In: COST ACTION C26 Urban Habitat Constructions Under Catastrophic Events - Proceedings of the Final Conference, pp. 583–588 (2010) 12. Chieffo, N., Formisano, A.: Induced seismic-site effects on the vulnerability assessment of a historical centre in the molise region of Italy: analysis method and real behaviour calibration based on 2002 earthquake. Geosciences 10 (2020) 13. Stepinac, M., et al.: Damage classification of residential buildings in historical downtown after the ML5.5 earthquake in Zagreb, Croatia in 2020. Int. J. Disaster Risk Reduct. 56 (2021) 14. Google Earth. https://earth.google.com/web/ 15. Croatian Centre for Earthquake Engineering. https://www.hcpi.hr/ 16. Moreti´c, A., Chieffo, N., Stepinac, M., Lourenço, P.B.: Vulnerability assessment of historical building aggregates in Zagreb: implementation of a macroseismic approach. Bull Earthq. Eng. (2022). https://doi.org/10.1007/s10518-022-01596-5 17. Lagomarsino, S., Cattari, S., Ottonelli, D.: The heuristic vulnerability model: fragility curves for masonry buildings. Bull. Earthq. Eng. 19(8), 3129–3163 (2021). https://doi.org/10.1007/ s10518-021-01063-7 18. Petrini, V., Benedetti, D.: A method for evaluating the seismic vulnerability of masonry buildings (1984) 19. Formisano, A., Mazzolani, L.F., Landolfo, R., Florio, G.: A quick methodology for seismic vulnerability assessment of historical masonry aggregates (2010) 20. Lagomarsino, S.: On the vulnerability assessment of monumental buildings. Bull. Earthq. Eng. 4, 445–463 (2006) 21. Margottini, C., Molin, D., Serva, L.: Intensity versus ground motion: a new approach using Italian data. Eng. Geol. 33, 45–58 (1992)
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22. Formisano, A., Mochi, G., Chieffo, N.: Empirical and mechanical analysis methods for seismic vulnerability assessment of clustered buildings of historical centres: a case study. In: 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Institute of Structural Analysis and Antiseismic Research National Technical University of Athens, COMPDYN 2021, vol. 1, pp. 331–337 (2021) 23. State archives in Zagreb. http://daz.hr/en/ 24. S.T.A. DATA, 3Muri Program 12.5.0.2. http://www.stadata.com/. Accessed 14 Dec 2021 25. Ramos, L.F., Lourenço, P.B.: Modeling and vulnerability of historical city centers in seismic areas: a case study in Lisbon. Eng. Struct. 26, 1295–1310 (2004) 26. Oži´c, K., Skeji´c, D., Lukaˇcevi´c, I., Stepinac, M.: Value of information analysis for the post earthquake assessment of existing masonry structures — case studies (2023) 27. Moreti´c, A., Stepinac, M., Lourenço, P.B.: Seismic upgrading of cultural heritage – a case study using an educational building in Croatia from the historicism style. Case Stud. Constr. Mater. 17, e01183 (2022) 28. Stepinac, M., Skokandi´c, D., Oži´c, K.: Condition assessment and seismic upgrading strategy of RC structures — a case study of a public institution in Croatia. Buildings, 1–28 (2022) 29. Author, F., Author, S.: Title of a proceedings paper. In: Editor, F., Editor, S. (eds.) CONFERENCE 2016, LNCS, vol. 9999, pp. 1–13. Springer, Heidelberg (2016) 30. Author, F., Author, S., Author, T.: Book Title, 2nd edn. Publisher, Location (1999) 31. Author, F.: Contribution title. In: 9th International Proceedings on Proceedings, pp. 1–2. Publisher, Location (2010) 32. LNCS. http://www.springer.com/lncs. Accessed 21 Nov 2016
Deep Learning Modelling of Earthquake Damage Data for Identification of Patterns of Damage in Heritage Structures Satwant Rihal1(B) , Hisham Assal2 , and Fernando Peña3 1 College of Architecture and Environmental Design, Cal Poly State University, San Luis
Obispo, CA, U.S.A. [email protected] 2 Department of Computer Science and Software Engineering, Cal Poly State University, San Luis Obispo, CA, U.S.A. [email protected] 3 Instituto de Ingeniería, Universidad Nacional Autónoma de México (UNAM), Mexico City, Mexico [email protected]
Abstract. The September 2017 Puebla, Mexico earthquakes caused unprecedented devastation, loss of lives and widespread damage of historical churches in Puebla, Morelos and Oaxaca. Chavez et. al. (2021) and Pena et. al. (2021) present an analysis of observed earthquake damage data, including images, which was collected within three months of the earthquake event. The analysis focuses on the type of damage to each building element (e.g. Facades and bell towers, roofing systems - vaults and domes, side walls,), and the intensity of damage (minor, moderate, severe). A database was built to manage the collected data and present it to users based on built-in queries. Access to this database has been provided to the authors of this paper. The collected data and the analysis provided in those papers form the basis for a machine learning model to automatically identify types of damage and their intensity in similar earthquake events. The machine learning model will follow the development steps outlined in Rihal and Assal (2022) and will generalize some of the data elements, such as the building type, construction method, and material. It will also consider data about the earthquake event, such as the intensity and the epicenter and data about the location of each structure and its distance from the epicenter. The model will be trained and tested on the provided data. It can also be retrained with data from other events as they become available. Keywords: Mexico colonial churches · Puebla-Morelos Mexico 2017 earthquakes · Observed earthquake damage data · Domes and vaults · Bell Towers · Historic Facades · Deep Learning Systems · Ontology · Feature engineering
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1268–1279, 2024. https://doi.org/10.1007/978-3-031-39450-8_103
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1 Introduction The world has witnessed unprecedented devastation from the impact of catastrophic earthquakes especially during the past twenty-five years. Mexico is blessed with a very rich, deep and widespread, architectural heritage with more than 50,000 archaeological sites and over 100,000 heritage buildings built between 16th 19th Century AD, including 35 UNESCO world heritage sites, as presented by [1]. The beautiful and rich architecture of the historical churches in Mexico, Peru, Ecuador, Colombia and Chile among others, has evolved over centuries using local building materials, craftsmanship and construction techniques. The vast majority of religious heritage architecture located in seismic zones, not only in South America but around the world [3], is constructed of unreinforced masonry, stone, brick and adobe like materials. Such historical construction of the heritage churches in Mexico has been found to be very vulnerable to the effects of the devastating earthquakes that have struck along the active seismic zones in Mexico time and again over the past decades. The restoration and preservation of historical churches in developing countries such as Mexico, Peru and Ecuador among others is extremely important, as the residents rely on the historical churches - places of worship - and power of prayer to cope up with the economic, psychological and traumatic consequences of the earthquake devastation and its impact on their lives. Extensive data from the surveys and reconnaissance of historical churches that suffered damage and collapse during the September 2017 earthquakes in Puebla, Oaxaca & Morelos, provides a rich resource for extraction of lessons for prevention of such damage to historical churches in future earthquakes, including development of restoration and strengthening plans and procedures for protection of the beautiful heritage religious structures in Mexico.
2 The Data A machine learning system relies heavily on data and its quality and labeling. The more data collected for each class of objects or events the better the identification accuracy will be. Data will have to be prepared for the learning system through a number of preprocessing operations. Image sizes will need to be standardized, missing fields will need to be filled, etc. Understanding of data elements and interrelationships contributes to building a viable model, which will lead to a successful learning experience [11, 12]. 2.1 The September 2017 Earthquakes South and Central Mexico was hit by two catastrophic earthquakes in September 2017, the first one on September 7 (Mw = 8.2) and the second on September 19 (Mw = 7.1). According to official records, 2340 heritage buildings, amounting to about 6% of all the heritage buildings in the areas affected by the two devastating earthquakes were damaged [6]. These two devastating 2017 Mexico earthquakes have been extensively studied, and their impacts on the affected cities and communities have been documented [2, 5–10, 18].
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The MMI Intensity of shaking maps for these two 2017 Mexico earthquakes are presented in Fig. 1. These shaking maps show the earthquake shaking intensities in the areas affected by these devastating earthquakes. The event of September 7 was cataloged as normal failure and is the largest recorded in the country. The maximum accelerations recorded in the field were higher than 228 Gal; while the event of September 19 was an intraplate earthquake of normal failure with peak ground acceleration greater than 220 Gal, recorded in the epicentral zone [6].
(a)
(b)
Fig. 1. Shaking maps of 2017 earthquakes: a) September 7 (modify from SSN, 2017a), b) September 19 (modify from SSN, 2017b)
2.2 Observed Earthquake Damage of Historical Churches in Mexico – II-UNAM Database. Outstanding work on surveys, reconnaissance and documentation of historical colonial churches damaged during the September 2017 earthquakes has been carried out by the teams at UNAM, INAH, EERI, GEER, local universities, local church organizations, among others. The results of using advanced technology e.g. aerial photography, photogrammetry, UAV, drones, in capturing earthquake damage and devastation caused by the September 2017 Puebla earthquakes are presented by [1, 4], among others. After the occurrence of the two seismic events, a team of Institute of Engineering at UNAM (II-UNAM) performed a campaign of reconnaissance of damages to assess the damage in historical temples in the affected areas. A total of 58 temples were visited: 22 in Oaxaca, around the Mixteca Alta and Tehuantepec regions; 11 inside the Mixteca region, Puebla; 15 in Morelos, along the route called Ruta de los Conventos (Convents Route) and 10 in Mexico City. Some of these temples are included in the World Heritage List of UNESCO. The damage observed is described according to the type of structural elements of the church. For this purpose, the temples were divided into facades and bell towers; domes and vaults; and side walls and apse. The damages observed in the facades were produced mainly because of higher levels of shear stresses in the plane of these elements. These damages were displayed with the formation of diagonal cracks and/or with the separation of the main body of the façade or the separation of the sidewalls. However, some damages were associated with an out-ofplane behavior, mainly due to the overturning of the frontispiece and belfries. The bell towers were one of the most damaged elements. In most cases, a partial or total collapse
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of the belfries was observed. Few facades were damaged because of the presence of the out-of-plane behavior; since the façade was separated from the vault because of a deficient anchoring of the roof to the façade wall. Likewise, the frontispiece collapsed due to the out-of-plane motion. Some typical examples are shown in Fig. 2 [5]. Domes and vaults are the most common roof structural system. Many cases of damages were observed, from longitudinal and transversal cracks up to a partial or total collapse. Usually one or more cracks appear at the top of the vault, in the intrados and extrados, severely damaging the infills that commonly cover the haunches of the vault in the extrados. Typical damages were observed in domes: radial cracks at the base of the dome and meridian cracks on the body of the element. In some cases, the damage was located only in the drum. In others, the dome collapsed and the drum remained standing, apparently undamaged. Figure 3 shows typical damages [5]. Walls are usually robust and can resist collapse wall. However, damage may occur mainly by shear forces that the masonry cannot resist. In some cases, the sidewalls have horizontal cracks that cross the thickness of the wall and generally are located below the windows. This type of cracking is due to bending moments out of the plane of the wall, which occur mainly in churches that have other small structures attached to the sidewalls, such as convents, chapels or parish offices. Figure 4 shows typical damages [5].
Fig. 2. Typical damages in facades and bell towers
Fig. 3. Typical damages in vaults and domes
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Fig. 4. Typical damages in sidewalls
2.3 II-UNAM Database Due to the large amount of information collected during the damage recognition campaign, it was compiled in a database for a better management [16, 17]. The database was developed by using the Microsoft software Access. The database is organized in such a way that it can be searched in three different ways: state or location, type of roof system and shape of the nave (see Fig. 5). Once the search is selected, the list of churches that match the search criteria is displayed. Clicking on the name of the selected church, the record of each church is accessed. This record is divided in five sections. In the first one, the name of the church and its location is displayed. The second section is about the photos of the building available in the database. For each record, there are photos of the state of the structure before the 2017 earthquakes, of the damage observed by these earthquakes and of the rehabilitation project (in case there is information about it). In the third section, complementary files, as documents, videos or draws, can be found. The fourth section give information about the characteristics of the church, as well as the damages reported for each microelement: façade, nave, transept, apse and dome. Finally, the record ends with a brief overview of the damage observed in the building, as well as the reinforcing actions implemented (in case there is information about it).
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Fig. 5. Main screen of the database
3 Information Types For the purposes of building a machine learning system, from the information in the database, it can be summarized in the table below. The table shows the essential attributes, from which the system will learn to identify the damage in new pictures. The learning objective of the initial system will be the classes of damage, which are described in the column ‘structural damage pattern.’ All the other attributes in the table will be used to label the data for the training and validation steps (Table 1). 3.1 Emergency Shoring and Restoration Techniques Documentation of the inadequate interventions, emergency shoring and stabilizing techniques, and suitable retrofitting strategies for the historical colonial churches severely damaged by the September 2017 earthquakes has been presented by [6] and [10]. The shoring system is a temporary system that must be removed when the intervention works are finished. Wood is the most common material used for shoring system due its versatility, manageability, ease of construction and cheap; where wooden truss supports are common used. In other cases, especially when the height of the building is considerable, as in churches, a steel shoring system or mixed system of steel and wood are used [6].
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Features
Materials
Structural Damage Pattern
Description
Vaults/Arches
Stone masonry or brick masonry
Cracks in vaulted ceilings/roofs
Tensile cracks Collapse in of vaults/arches Domes, vaults and arches
Domes
Stone masonry/brick masonry/concrete
Severe damage in domes
Radial and meridian cracks
Drum
Stone masonry/concrete
Severe damages
Shear cracks
Facades
Stone masonry
Diagonal Cracks
Bell Towers
Stone masonry
Failures
Cause of Damage Vertical vibration of the roof system
Cracks, collapse Higher levels of shear stresses, openings Higher levels of shear stresses
Separation between Façade and side walls
Vertical Tensile cracks in joint cracks
Deficient connection between façade and sidewalls
Out-of-plane behaviour
Horizontal or vertical cracks in the joint between elements (vaults and façade)
Deficient anchoring of the roof system to the facade
Most Damaged elements
Diagonal Partial or Lack of shear damage total structural in belfries collapse integrity
Tensile cracks
Irregularities Large openings
4 Objectives In [13–15] a general description for the information needs to build a deep machine learning system for the identification of damage in earthen heritage structures was presented. The system description was based on data collected from the Mexico earthquake of
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2017. In this paper we expand the objective of this work to include building an ontology to represent different types of structures, starting with religious heritage structures (churches) and expanding to include all types of modern structures. The ontology also includes representation of natural hazard events such as earthquakes, hurricanes, floods, and fires. This ontology will include rules that describe how hazard events affect elements of buildings and cause different types of damage. The rules along with the ontology will allow us to automatically extract relevant features for a desired learning system. 4.1 Benefits Of ML for Earthquake Data Analysis Deep learning systems can process large volumes of data in many formats (numerical, images, video, etc.) and extract patterns for the identification, classification and prediction of types of damage to buildings, related to an earthquake event, or any other hazard event. The amounts of data that can be collected today is beyond the ability of human engineers to process without the help of sophisticated tools. Machine learning systems can help identify the types and extents of damage to structures from a set of pictures, which may be taken by drones/UAV flying over an affected area. They can also help with search and rescue efforts immediately after an earthquake by identifying patterns of damage from pictures or videos, which may point to the need for a closer look for survivors.
5 Methodology In [13] we presented a general design for an ontology to support work with heritage structure documentation. In this paper we develop this ontology further with more specific data from the Puebla, Mexico earthquakes of 2017. The work presented in [1] and [6] describes the information collected from these earthquakes and the database, which houses this information. The Ontology development relies on the structure of the Puebla earthquake database to represent the important aspects of heritage structures and the types of damage that was caused by the earthquake. The ontology has four main areas: buildings, hazard events, sites and regulations. It represents all the available information about structures in earthquake zones, related to earthquake events and the damage that may have been caused by it. The regulations component of the ontology reflects the cultural value of structures through the requirements of preservation and repair efforts that must be performed on damaged structures. The cultural value can be separated into its own section of the ontology to reflect values that may be designated by non-governmental organizations. A set of mapping tools contain rules that describe the attributes of the ontology that contribute to a given learning objective. For example, if the learning objective is to identify structural damage in buildings from pictures, the rules in the mapping tool set will describe the attributes in an image that refer to structural damage. This may be done in a set of rules to describe each type of damage in more details. The rule sets help in the area of feature engineering for machine learning systems. Once of features for a learning objective are identified from the ontology, a machine learning model can be constructed automatically, and data sets that are needed for the training and validation
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processes can be selected from the data base and labelled with the appropriate labels. The labelling process can also be done automatically, since all the information needed for that will be stored in the database. A machine learning platform can be built to support developing a variety of learning systems and run the development workflow, which includes training the network, validating results, adjusting the network parameters as needed until the desired accuracy is achieved. The platform is built on existing open source libraries to support the basic operations of building, training, validating and testing neural networks for machine learning systems, as well as using the trained network for making predictions, classification or generating recommendations (Fig. 6).
Fig. 6. Architecture of the proposed system
5.1 Data Modelling All the data that will be used in a deep learning system will need to be modelled in a uniform way to be input to the system. The model for each learning system will focus on the required output classes. All the features in the model will have to be converted into numerical values. For example, in Table 2, the damage types can be represented by sequential numbers, while the damage extent can be represented as a percentage (or a value between 0.0 and 1.0). Elements will need to be identified with a unique identifier, which is also a numeric value, and related to the image file that shows damage to that element.
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Table 2. Examples of modelling information types into numeric values Damage Type Structural Damage Element Extent
Distortion/ Displacement
Crack Opening
Label
1 (small)
Image File name
3
1.2
0.70 (70%) 2 (rotation)
2
4.1
0.40 (40%) 1 (displacement) 2 (medium)
6
2.3
0.65 (65%) 3 ()
Image File name
0 (no cracks) Image File name
6 Results and Outcomes The product of this work will be the ontology and a toolset to help with the development of machine learning models. The ontology is based on the information that is available in the database and will be augmented with information from other sources of as outlined in [13]. The hazard event component of the ontology will include earthquake information from other events, especially those where heritage structures were affected around the world. The toolset will include mapping tools to extract model features based on a set of requirements for a learning system. For example, a learning system that can predict the type of damage for a given structure can be developed based on the type of structure and assumptions about a possible earthquake nearby. The specific learning system will serve as an example and blueprint for developing other learning systems based on the same methodology. This can expedite the development process and produce a variety of both practical and experimental systems.
7 Conclusions Deep learning systems provide great opportunities to process large volumes of data for the purposes of identifying patterns as well as predicting future outcome of similar events with greater precision. The main hurdle that deep learning systems have to overcome is the data. The amount of data, its quality, completeness and annotations describing the content of this data are all important elements for developing successful learning systems. The database for the damage information caused by the 2017 Mexico earthquake offer a considerable opportunity to build a deep learning system for identifying types of damage to structural elements in heritage buildings from pictures, which can be collected in large amounts using modern technology, such as drones and UAVs. The opportunity goes beyond a single deep learning system. Development of many systems for a variety of purposes can be done with the same data. To facilitate this objective, we presented a framework for speeding up the process of extracting models for machine learning from a common ontology, which can be developed from the vast amount of information that is collected from many earthquake events and the damage they cause to many types of buildings. The focus on heritage buildings is justified by the high cultural value they hold and the need to perform preservation and restoration work on them.
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References 1. Chavez, M., Peña, F., Garcia, N., Duran, D.: Damage patterns in historical temples of puebla, morelos and oaxaca after september 2017 mexico earthquakes. In: 12th . International Conference on Structural Analysis of Historical Constructions, SAHC2020, Barcelona, Spain Oct. 2021. Roca, V., et al. (eds.) 2. Diaz, D., Baquedano, P., D’Amato, M., Laterza, M.: Preliminary seismic damage assessment of mexican churches after september 2017 earthquakes. International Journal of Architectural Heritage (2019) 3. Ferracuti, B., Imperatore, S., Zucconi, M., Colonna, S.: Damage to churches after the 2016 central Italy seismic sequence. Geosciences 12, 122 (2022) 4. Hutchinson, T., Franke, K., Mayoral, V., Juan, M.: Geotechnical engineering reconnaissance of the 19 september 2017 Mw 7.1 Puebla-Mexico City earthquake. GEER Report Version 2.0 (2020). (www.geerassociation.org) 5. Peña, F., Chavez, M., García, N.: Mexican colonial churches: structural assessment and seismic behaviour. Chapter 12, in Masonry construction in active seismic regions. Rupakhety, R., Gautam, D.(eds.) Elsevier (2021) 6. Peña, F., Chavez, M.: Inadequate cases of intervention in architectural heritage buildings in Mexico after the september 2017 earthquakes. In: 12th . International Conference on Structural Analysis of Historical Constructions, SAHC2020, Barcelona, Spain Oct. 2021. Roca, P., et al. (eds.) 7. Peña, F., Chavez, M.: Seismic behavior of Mexican colonial churches. Int. J. Architectural Heritage 10(2–3), 332–345 (2016) 8. Peña, F., et al.: Damage Observed in Ancient Churches due to the Earthquakes of September 7th. and 19th., 2017 in Mexico. Abstract, REHABEND 2020 Congress 9. Preciado, A., Peña, F., Fonseca, F., Silva, C.: Damage description and schematic crack propagation in Colonial Churches and old masonry buildings by the 2017 Puebla-Morelos earthquakes (Mw =8.2 and 7.1). Engineering Failure Analysis 141 (2022) 10. Preciado, A., Santos, J., Silva, C., Ramirez-Gaytan, A., Falcón, J.: Seismic damage and retrofitting identification in unreinforced masonry Churches and bell towers by the September 19, 2017 (Mw=7.1) Puebla-Morelos Earthquake. Engineering Failure Analysis, 118 (2020) 11. Rihal, S., Assal, H.: A database integration approach to support earthquake hazard assessment and seismic retrofit of buildings. In: Proceedings, 15th World Conference on Earthquake Engineering, Lisbon, Portugal (2012) 12. Rihal, S., Assal, H.: An intelligent framework to support the seismic hazard mitigation of heritage structures in New Delhi. In: Proceedings, International Conference on Urban Risks (iCUR), Lisbon, Portugal (2016) 13. Rihal, S., Assal, H., Badillo, H., Lagunes, M.M.S.: A deep learning system for the assessment and restoration of heritage structures: case study of the 2017 Puebla, Mexico Earthquake. ICOMOS GA 2020 6-ISCs Joint Meeting: Advancing Risk Management for the Shared Future. Live Webinar, 2022 (2020) 14. Rihal, S., Assal, H.: Information needs for a deep learning system for the assessment and restoration of earthen heritage structures: case study of the 2017 Puebla, Mexico, Earthquakes. Terra 2022, 13th World Congress on Earthen Architectural Heritage, Proceedings, Los Angeles, California, Getty Publications, forthcoming (2022) 15. Rihal, S., Assal, H.: “Machine learning for the documentation, prediction, and augmentation of heritage structure data. Proceedings, CIPA 2023 (in preparation) (2023) 16. SSN, “Reporte Especial del sismo de Tehuantepec (2017–09–07 23:49 M 8.2)”, Servicio Sismológico Nacional (2017ª)
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17. SSN, “Reporte Especial del sismo del día 19 de Septiembre de 2017, Puebla-Morelos (M 7.1)”, Servicio Sismológico Nacional (2017b) 18. Weiser, D., Hunt, J., Jampole, E., Gobbato, M.: M7.1 Puebla, Mexico Earthquake on September 19, 2017. EERI Earthquake Reconnaissance Team Report, Earthquake Engineering Research Institute, February (2018)
Seismic Vulnerability Assessment of Churches Through an Expeditive Evaluation Form: Application to a Representative Sample from Central Italy Giorgia Cianchino, Maria Giovanna Masciotta, and Giuseppe Brando(B) Department of Engineering and Geology, University “G. d’Annunzio” of Chieti Pescara, 65127 Pescara, Italy {giorgia.cianchino,g.masciotta,giuseppe.brando}@unich.it
Abstract. This paper addresses the seismic vulnerability assessment of churches in Central Italy and discusses the main outcomes of the in-situ survey activities carried out within the cooperation agreement between the Italian Network of University Laboratories of Seismic and Structural Engineering (ReLuis) and the Ministry of Cultural Heritage (MIC), aimed at collecting structural and damage information of existing churches. The seismic vulnerability assessment is performed on the basis of an empirical methodology applied through the use of the MaCHRO evaluation form. A predictive model, already calibrated for churches of the inner Abruzzi, is here extended to the Central area of Italy where, due to the high seismicity, cultural heritage features major alterations occurred over time. In the first part of the paper, the analyzed sample of churches is presented. A wide description of the anti-seismic devices and fragility indicators recurrent in the ancient masonry buildings of the territory is provided, highlighting their fundamental role in preventing (or promoting) specific local failure mechanisms. Statistics regarding all information of interest from a seismic viewpoint are given for the entire sample. In the second part of the work, the vulnerability of each church is assessed in terms of vulnerability indices (IV s), evaluated according to the procedure given by Italian Guidelines of Cultural Heritage. These indices account for both the sources of fragility and the existence of possible protection devices for each macro-element. Finally, based on the obtained IV s, fragility curves for predicting the extent of probable earthquake-induced damage in the analyzed churches are estimated. The results are proven to be useful for seismic risk mitigation purposes, allowing to define priorities of intervention on a large scale. Keywords: Masonry Churches · Cultural Heritage · Vulnerability model
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1280–1292, 2024. https://doi.org/10.1007/978-3-031-39450-8_104
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1 Introduction The protection of cultural heritage is a theme of huge significance in Italy due to the existence of a wide number of historical buildings with non-negligible cultural value throughout the territory. The maintenance of high safety standards in these structures is essential to guarantee acceptable performance levels and long-term preservation. It is widely known that historical buildings were not designed according to codified rules but following an empirical approach, handed down from generation to generation, which allowed the manufacturers to intuitively understand their structural behavior and to adopt the most suitable solutions. Such an approach brought over time to the development of local construction techniques strictly connected to the structural and architectural features of each building typology [1]. For instance, in earthquake-prone areas, particular block arrangements were generally used to avoid – or at least reduce – seismic damage in masonry structures. Though, the structural benefits associated with these construction techniques were progressively forgotten given the discontinuity of seismic events [2]. Another important example of historical anti-seismic devices for masonry buildings was represented by the use of wooden beams with the function of ties. Their presence was indeed observed in several structures during the surveys carried out after L’Aquila (2009) and Central Italy (2016) earthquakes [3]. Knowing the layered historical evolution of the built cultural heritage, including ancient local construction techniques, building materials, historical anti-seismic devices, ex post alterations, is essential to obtain a reliable evaluation of the actual structural behavior of masonry buildings and to provide effective seismic improvements, avoiding inadequate interventions and incompatible techniques. In this context, the development of viable and expeditive tools for large-scale seismic vulnerability assessment acquires great significance, especially in what concerns the planning of preventive measures for risk mitigation (event preparedness) and the definition of post-emergency intervention priorities (event response). Such tools are usually based on the observation of damage induced in the buildings by seismic events as well as on the survey of the structural and geometrical characteristics of such buildings. These activities can be very time consuming and the employment of automatic survey forms aimed at the reconnaissance of the main sources of vulnerability for masonry structures and at the estimation of their incidence on the overall seismic performance can be of great help. Based on these premises, the main aim of this paper is to provide an expeditive method for assessing the most important fragilities of masonry churches in Central Italy, starting with the analysis of the earthquake-induced damage on a representative sample of 87 churches [4] through the application of the MaCHRO form, described in Sect. 2, and then applying a large-scale seismic vulnerability assessment (Sect. 3) to predict the most probable damage scenarios that these structures would undergo for earthquakes of different intensities (Sect. 4). The results, expressed in terms of fragility curves, can be exploited to improve cultural heritage preparedness to future earthquakes as well as to drive cost-effective retrofitting measures, fostering a better allocation of national resources.
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2 Structure of the Machro Form A first type of form that consider expert judgment was proposed by GNDT [5], which was conceived by Benedetti and Petrini [6] and tested following the 1997 Umbria and Marche earthquakes. The module was based on the decomposition of the churches into homogeneous and “autonomous” parts, called macro-elements, and on the identification of recurrent damage mechanisms associated with the identified macro-elements. Updates were finally proposed to define the current form based on the assessment of 28 possible collapse mechanisms [7]. The MaCHRO Form (Masonry CHurches Reconnaissance Operational Form), developed by De Matteis et al. [8] and employed in this study, draws inspiration from this previous format, but it is appropriately modified with the aim of reducing the intrinsic sources of uncertainty and subjectivity of judgment when ranking the indicators of vulnerability and protection that may influence the seismic behavior of the considered structures. Using the MaCHRO form, the technical compiler, even if non-specialist, has only the task to describe the asset through simple basic information. This information is then processed by means of an automatic calculation tool connected to the form, allowing to provide in real time a Vulnerability Index (IV ) for the investigated structure. In fact, the scores attributed to the different parameters coming into play for the vulnerability assessment of masonry churches are pre-assigned by the Authors according to their engineering experience, result of years of in-depth studies on the structural behavior of this type of artefacts under earthquake actions. Particular attention is given to those arrangements and devices that play a fundamental role for the seismic performance of the considered churches, thus establishing different weighs and ranking criteria based on their incidence on the overall structural vulnerability. The MaCHRO form is spreadsheet consisting of several sections useful for the complete description of the masonry churches, from their identification in the context in which they are inserted, to the analysis of their specific stylistic characteristics and, finally, the survey of their construction details. With reference to the latter, the required information must always be interpreted according to a dual approach: the analysis of the devices that reduce the vulnerability of the structure (i.e., good masonry quality, connections between orthogonal walls, chains, etc.), and the analysis of the sources of vulnerability that may adversely affect the local or global behavior of the structure (e.g., slender walls, vaults, pushing elements, and the like). The Italian Guidelines for evaluation and mitigation of seismic risk to cultural heritage use this method to analyze masonry churches. As mentioned above, the scores attributed to the different building parameters coming into play for the vulnerability assessment of the churches are pre-assigned, turning the form into an automatic tool and greatly reducing the subjectivity of judgment during the survey. According to the proposed MaCHRO-based procedure, the operator is only in charge of describing the considered church by filling in the form with basic information deduced from observation; afterwards, the data are properly re-elaborated to return the specific value of vulnerability index (Iv ) associated with the analyzed structure.
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Below is the list of the sections that compose the form: SECTIONS 1–5: GENERAL ANALYSIS. • • • • •
Architectural features Intended use Relation with the context Historical information Output from photographic and technical surveys
SECTIONS 6–8: ANTI-SEISMIC DEVICES, GOOD CONSTRUCTIVE PRACTICES AND FRAGILITY INDICATORS. • Presence/absence of anti-seismic devices • Presence/absence of good constructive practices • Presence/absence of fragility indicators SECTIONS 9–19: MACRO ELEMENTS ANALYSIS. • • • •
Presence/absence of macro-elements Architectural/structural features Effectiveness of anti-seismic devices Influence of fragility indicators
Each section is pivotal in the definition of the Vulnerability Index (IV ), as better described in the next section.
3 Methodology for Large-Scale Vulnerability Assessment The information collected via the MaCHRO form is processed through an automatic calculation tool, which ultimately provides a measure of the church vulnerability [9]. The obtained Vulnerability Index Iv , varying in the range [0–1], is computed according to the following expression: 28 1 1 k=1 ρk,i · vk,i − vk,p (1) Iv = · + 28 6 2 ρ k=1 k,i In Eq. (1), for the generic macro-element k (k = 1, 2, …, 28) experiencing a mode I (out-of-plane) or mode II (in-plane) mechanism, vk,i and vk,p are values assigned through Eq. (2) and Eq. (3) based on the presence (zk ), importance (wk ) and effectiveness of fragility indicators ( f k ) and anti-seismic devices (ηk ), respectively, in influencing or worsening the considered macro-element’s mechanism k; whereas, ρ k is a factor that weights the mechanism k according to its importance on the global stability of the church (Table 1). The wk values related to the importance of the protection device(s) or of the vulnerability indicator(s) are pre-defined in the range [0 – 2] and not editable. They have been calibrated by the Authors after years of in-depth studies on the structural behavior of churches during earthquakes. The coefficient zk is a Boolean coefficient equal to 0 when the kinematic mechanism is absent, or to 1 when it is present; zk is automatically defined through the compilation of Sects. 6–8. Finally, factors f k and ηk measure respectively the
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severity of fragility indicators and the efficiency of anti-seismic devices, and vary from 0, meaning no fragility or effectiveness, to 1, i.e. maximum fragility or effectiveness. These values are defined by filling in Sects. 9–19. For example, considering the presence of tie-rods in the façade, a maximum (ηk = 1.5) or minimum (ηk = 0) value can be assigned for the effectiveness of these anti-seismic devices depending on the number of tie-rods and the type of anti-pull systems. vk,i = zk · wk · fk
(2)
vk,p = zk · wk · ηk
(3)
It is stressed that the difference between vk,i and vk,p allows estimating a specific score of vulnerability V M in the range [−3, 3] for each identified mechanism, where 3 indicates high vulnerability (i.e. presence of fragilities/absence of effective anti-seismic devices) and −3 means low vulnerability (i.e. presence of effective anti-seismic devices/absence of fragilities). The definition of this score enables the immediate identification of the most vulnerable mechanism in each considered building, that is where seismic improvement strategies should be addressed first. Figure 1 exemplifies the estimation of V M for the overturning mechanisms of façade and apse of San Leucio church in Pietracamela (Teramo province). As it can be observed, the apse overturning is more vulnerable than the façade overturning in this structure, since the presence of all fragility indicators that lead the activation of such a mechanism. The reduction of this value could be achieved through the introduction of specific devices such as ties, retaining elements or connections between walls. As can be seen above, the automatic form is a useful tool for defining possible improvement strategies for each of the church’s macro-elements After defining the mean Vulnerability Index (I v ) of the entire sample, it is possible to estimate the mean damage grade μD as given in Eq. (4), where the earthquake intensity (I) is expressed according to the Mercalli-Cancani-Sieberg (MCS) scale, with values ranging from 1 (lowest intensity) to 12 (highest intensity). Although originally proposed for threenave churches [9], the formulation in Eq. (4) is deemed reliable enough to be applied to the sample of churches analyzed in the present study. The mean damage grade is exploited to determine the damage probability pk associated with the investigated sample of churches by resorting to the Binomial Probability Distribution Function (BPDF) shown in Eq. (5): I + 6.20Iv − 11 (4) μD = 2.5 · 1 + tanh · 3 μ j 5! μD 5−j D pj = · · 1− (5) j! · (5 − j)! 5 5 where j represents a damage score ranging from 1 to 5, according to the damage classification proposed by Grünthal [10]. Based on the BPDF it is possible to draw fragility curves, which represent the probability of exceeding a pre-established damage grade for different earthquake intensity measures (P[D > Dk ] = 51 pj ). Fragility curves are a convenient way to describe seismic vulnerability, particularly for large-scale assessments.
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Table 1. Weighting factors attributed to the 28 collapse mechanisms identified for churches. Kinematic mechanisms for religious buildings
ρk
1
Façade overturning
1,00
2
Mechanism on the top of the façade
1,00
3
Mechanism in the plane of the façade
0,50
4
Narthex
0,25
5
Transversal response of the main body
1,00
6
Shear mechanisms at the lateral walls
1,00
7
Longitudinal response of the columns
1,00
8
Central nave vault
1,00
9
Lateral aisles vaults
0,75
10
Transept main wall overturning
0,75
11
Shear mechanism at the transept lateral wall
0,50
12
Transept vaults
0,50
13
Triumphal arches
1,00
14
Dome
0,75
15
Lantern
0,25
16
Apse overturning
0,75
17
Shear mechanism at the apse and presbytery
0,50
18
Presbytery and apse vaults
0,75
19
Mechanism due to the riddle in the lateral walls
0,50
20
Mechanism at the top of the transept
0,50
21
Mechanism at the top of the presbytery and of the apse
0,50
22
Chapel overturning
0,25
23
Shear mechanism in chapel walls
0,25
24
Chapels vaults
0,50
25
Plan – Height irregularity
1,00
26
Architectural details
0,25
27
Bell tower
1,00
28
Bell cell
0,50
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Fig. 1. Extract from MaCHRO form for two different overturning mechanisms (façade and apse).
4 Analyzed Sample of Churches The sample of 87 churches herein analyzed (Fig. 2) was surveyed through the application of the so-called “A-DC” form [11] during the inspections conducted by the Authors after the Central Italy earthquake, together with the technicians of the Civil Protection Department and of the Ministry of Cultural Heritage. The A-DC form was used for postevent emergency management in order to evaluate the accessibility of damaged cultural heritage buildings. The inspections allowed to i) collect structural/typological data, ii) catalogue photos, iii) conduct geometric surveys. Details about the gathered information can be found in [4]. In this work, the focus will be describing the fragilities and protection devices observed in the different churches in order to estimate their seismic vulnerability at the large scale in a straightforward manner, i.e. through the use of the MaCHRO form.
Fig. 2. The 87 surveyed churches in Central Italy.
4.1 Anti-Seismic Devices Anti-seismic devices are conceived with the aim to improve the structural response of the building to a seismic action, thus avoiding or, at least, reducing earthquake-induced
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damage. The most common anti-seismic devices are metallic tie rods (or ring ties) (Fig. 3a), corner connections (Fig. 3b) and retaining elements (Fig. 3c). They are mainly employed to counteract overturning mechanisms. The major or minor diffusion of this kind of devices is strictly connected to the seismic hazard associated with a particular area, resulting indeed more widespread in territories frequently struck by strong earthquakes. In Central Italy, the use of anti-seismic devices significantly increased during the 18th century, following the seismic events that stroke Valnerina and L’Aquila in 1703 [12]. For completeness, Fig. 4 shows all the main earthquakes (Mw > 4) occurred in Central Italy between the 17th and 19th centuries, extrapolated from the Parametric Catalogue of Italian Earthquakes. All these events contributed to raising awareness about the necessity to adopt adequate building techniques and devices to mitigate the seismic damage. Though, the absence of analogous events during the 19th century led to a progressive loss of awareness and attention towards the adoption of preventive measures [13].
(a)
(b)
(c)
Fig. 3. Common anti-seismic devices of Abruzzi churches: a) Ties in the lateral wall of Santa Maria della Neve church in Castelli (Teramo province); b) corner connection in the façade of San Rocco (SR) church in Castelli (Teramo province); c) contrast elements in the lateral walls of San Giovanni ad Insulam church in Isola del Gran Sasso (Teramo province).
(a)
(b)
Fig. 4. Location (a) and magnitude (b) of the major earthquakes occurred in Central Italy between the 17th and 19th centuries. The most severe earthquake (Valnerina, Umbria) is highlighted in red. (Data retrieved from Parametric Catalogue of Italian Earthquakes (CPTI15)) [12].
With regard to the sample of churches analyzed in the present study, a visual insight into the most frequently observed anti-seismic devices is provided in Fig. 5. The different types of ties are distinguished not only according to their direction or involved macroelement, but also based on their deployment level: for instance, I order ties refer to
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ties placed at the arch impost, whereas II order ties indicate ties placed at the roof level. Looking at the percentage frequencies of occurrence of tie rods, it is found that the highest frequencies occur with transverse tie-rods at the facade (38%) and transverse tie-rods at the roof level (25%). Conversely, ring ties are less frequent and mainly observed in the bell tower (13%) and bell cell (13%) of the considered churches. As for the contrast elements (e.g. buttresses), they are generally found in correspondence of the church façades (38%) and apse (nearly 20%). Altogether, corner connections are among the most widespread anti-seismic devices for the façades (56%), but they result far less frequent in other macro-elements.
Fig. 5. Frequency of occurrence of ties, contrast elements and corner connections in the analyzed sample of churches.
4.2 Fragility Indicators Fragility indicators are structural or architectural elements which increase the seismic vulnerability of the buildings. The most common fragility indicators identified in the analyzed sample of churches are heavy vaults (Fig. 6a), unconstrained façade head gables (Fig. 6b) and large wall openings (Fig. 6c). Analyzing the presence/absence of these sources of vulnerability across the entire sample, in Fig. 7 the results show that: 47% of the churches have a gabled façade not properly connected to the rear of the structure; 42% of the churches feature a central nave with heavy vaults; and a remarkable percentage of churches has large openings, either in the plane (63%) and/or at the top of the façade (73%). The presence of these elements can remarkably affect the structural behavior of the churches under seismic actions at both global and local levels. 4.3 Seismic Vulnerability Assessment: from the Building Scale to the Macro-Regional Scale Assembling all the collected information through the compilation of the MaCHRO form, it was possible to estimate the seismic vulnerability of each church following the methodology outlined in Sect. 3. The average value of vulnerability index derived for the considered stock of churches is 0,51. The lowest value is found for the church of San Vincenzo sited in the municipality of Isola del Gran Sasso (iv = 0.41). This is a church built in the 19th century with a simple nave footprint, without apse nor transept. Transversal ties
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(b)
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(c)
Fig. 6. Sources of vulnerability of Abruzzi churches: a) vaults in San Bartolomeo Church in Sant’Eufemia a Majella (Pescara province); b) unconstrained Gable in San Rocco Church in Castelli (Teramo province); c) Large opening in San Martino Church in Cortino (Teramo province).
Fig. 7. Frequency of occurrence of the major fragility indicators in the analyzed sample of churches.
were included afterwards, during the 20th century interventions (Fig. 8a). The highest vulnerability is observed in Santa Giusta church in Cortino (iv = 0.68) whose fragility is mainly related to the presence of a heavy concrete roof (Fig. 8b) and a poor masonry quality (Fig. 8c).
(a)
(b)
(c)
Fig. 8. Exterior views of a) San Vincenzo church in Isola del Gran Sasso (Teramo province); b) and c) Santa Giusta church in Cortino (Teramo province).
Based on the mean vulnerability index of the examined churches, the mean damage µD was calculated for different earthquake intensities, i.e., from 1 to 12 according to
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the Mercalli-Cancani-Sieberg (MCS) scale (Fig. 9a). For each value of µD , the binomial distribution given in Eq. (5) was used to plot the Damage Probability Matrices (DPMs) shown in Fig. 9b.
(a)
(b)
Fig. 9. Vulnerability of the analyzed churches: a) mean damage levels for different earthquake intensities and b) damage probability matrices.
The results obtained through the DPMs were cumulated to obtain – through the relation proposed by Margottini et al. [14] – potential damage scenarios in the form of fragility curves. These curves, which are extremely useful for large-scale assessments, provide the probability P(D > Dk ) of the structures to exceed a certain damage grade Dk for earthquakes of increasing seismic intensity. They can be estimated both as a function of the macro-seismic intensity (IMCS ) and as a function of the peak ground acceleration (PGA). The fragility curves resulting from the analysis of the investigated sample of churches, characterized by a mean vulnerability index of 0.51, are shown in Fig. 10a-b. The outcome of the analyses corroborates that the seismic vulnerability of Abruzzo masonry churches is mainly related to three sources: i) intrinsic features of the structure, i.e. quality of materials and construction techniques, ii) presence/absence of fragility indicators; iii) effectiveness of anti-seismic devices.
(a)
(b)
Fig. 10. Expected probability of the analyzed churches to exceed a certain damage level (from D1 to D5) as a function of increasing a) macro-seismic intensities (IMCS) and b) peak ground accelerations (PGA).
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5 Conclusions This paper focused on the seismic vulnerability assessment of a sample of 87 churches in Central Italy. The vulnerability was evaluated by applying an empirical method which considers 28 possible kinematic mechanisms, according to the Italian Guidelines, and resorting to a semi-automatic in-house form conceived to turn the assessment procedure into a task as objective and expeditive as possible. The results were used to derive the fragility curves associated with the analyzed sample of churches, allowing to predict the probability of exceeding pre-established damage levels for different seismic intensities. The most important conclusions drawn from the work are summarized below: – The MaCHRO form is an effective tool that allows collecting in a straightforward and objective manner all the information needed to measure the vulnerability of churches and provide reliable input data to forecast potential damage scenarios at the building, regional and territorial scales; – The predicted damage scenarios, expressed as percentage of buildings that are likely to experience predefined damage levels for given earthquake intensities, can be used to drive preventive measures for risk mitigation as well as define post-emergency intervention priorities at different scales. – Considering and grading both the presence and effectiveness of anti-seismic devices as well as the presence or absence of different sources of vulnerabilities is of utmost importance to identify the most vulnerable macro-elements of masonry churches in order to address targeted interventions and optimize the allocation of resources to invest in seismic risk mitigation strategies.
References 1. Varagnoli, C., Angelillo, C.R., et al.: La costruzione tradizionale in Abruzzo: fonti materiali e tecniche costruttive dalla fine del Medioevo all’Ottocento. Roma: Gangemi (2008) 2. D’Antonio, M.: Ita terraemotus damna impedire. Note sulle tecniche antisismiche storiche in Abruzzo. EAN: 9788850103195 Ed. Carsa, Pescara, 24 p., ill., Brossura (2013) 3. Cianchino, G., Masciotta, M.G., Verazzo, C., Brando, G.: An overview of the historical retrofitting interventions on churches in central Italy. Appl. Sci. 13, 40 (2023). https://doi.org/ 10.3390/app13010040 4. Cianchino, G., De Matteis, G., Brando, G.: Typological classification and observed damage patterns of masonry churches after the 2016 Central Italy Earthquake. In: Proceedings of 12th International Conference on Structural Analysis of Historical Constructions (SAHC2020), 2021, Vol. Vulnerability and risk analysis 2021 (2021). https://doi.org/10.23967/sahc.202 1.311 5. GNDT-SSN: Scheda di Esposizione e Vulnerabilità e di Rilevamento Danni di Primo e Secondo Livello (Murata e Cemento Armato). Rome, Italy (1994) 6. Benedetti, D., Petrini, V.: On seismic vulnerability of masonry buildings: proposal of an evaluation procedure. L’industria delle Costruzioni 18, 66–78 (1984) 7. Minister of Heritage and Cultural Activities, Circular n.26, Italian Code for protection of cultural heritage. Linee Guida per la valutazione e la riduzione del rischio Sismico del patrimonio culturale con riferimento alle norme tecniche per le costruzioni. Prot 10953 of 02/12/2010
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8. De Matteis, G., Brando, G., Cianchino, G., Corlito, V., Criber, E.: The MaChro form: a new automatic tool for the survey and seismic vulnerability assessment of churches. In: Proceedings of Atti del XVIII Convegno ANIDIS L’ingegneria Sismica in Italia. Postoia, 17–21 settembre 2017 (2017) 9. De Matteis, G., Brando, G., Corlito, V.: Predictive model for seismic vulnerability assessment of churches based on the 2009 L’Aquila earthquake. Bull. Earthq. Eng. 17(9), 4909–4936 (2019). https://doi.org/10.1007/s10518-019-00656-7 10. Grunthal, G.: European Macroseismic Scale, Centre Européen de Géodynamique et de Séismologie, Luxembourg 1998; vol 15 (1998) 11. DPC. Survey form of the cultural heritage—Damage of the churches (in Italian). Department of Civil Protection. https://egeos.eucentre.it/danno_osservato/web/danno_osservato? lang=EN 12. Rovida, A., Locati, M., Camassi, R., Lolli, B., Gasperini, P.: The Italian earthquake catalogue CPTI15. Bull. Earthq. Eng. 18(7), 2953–2984 (2020). https://doi.org/10.1007/s10518-02000818-y 13. D’Antonio, M.: Ita Terraemotus Damna Impedire, Note Sulle Tecniche Antisismiche Storiche in Abruzzo, 2nd ed.; Carsi Edizioni, Pescara, Italy (2013). ISBN: 978–88–501–0356–0 14. Margottini, C., Molin, D., Narcisi, B., Serva, L.: Intensity vs acceleration: Italian data. In: Proceedings Work Hist Seism Cent Mediterr Reg, pp. 213–226 (1987)
Vulnerability Assessment of Masonry Constructions Towards Rockfall Hazard Anne-Sophie Colas1(B) , Marion Bost1 , Franck Bourrier2 , and Isabelle Ousset2 1 University of Gustave Eiffel, Univ Lyon, GERS-RRO, 69675 Lyon, France
[email protected] 2 University of Grenoble Alpes, INRAE, ETNA, 38000 Grenoble, France
Abstract. Impact tests on full-scale masonry panels are undertaken in order to explore the vulnerability of vernacular construction to rockfall hazards in mountainous areas. Seven 2.5 m high walls made of bricks subjected to a static gravity overload are subjected to a dynamic impact load on their centre, provided by ETAG concrete blocks launched at different energies (from 5 to 15 kJ). This experimental campaign is analysed through numerical simulations. Two different approaches have been explored: a micro-modelling based on the discrete element method (DEM) using the free software Siconos from Inria and a macro-modelling based on the finite element method (FEM) using Abaqus. Models have been adapted to the specificity of masonry structures under dynamic stress by hard shock. They show the strong influence of the overload on the resistance of the wall. The present work aims at assessing the damage generated by an impact on a masonry structure in real conditions. It also leads to question the failure characterisation of the structure after impact. On a long-term perspective, this work is intended to provide damage curves for masonry buildings and thus contribute to the development of normative prescriptions for natural hazard prevention. Keywords: masonry constructions · rockfall hazard · full-scale experiments · FEM · DEM
1 Introduction The vulnerability of masonry buildings towards dynamic impacts is at stake in mountainous areas where this type of construction is widespread and the rockfall risk is high. Indeed, although protective structures (e.g. rockfall net fences) are set up, a hazard downstream can still occur. Therefore, it is important to better understand the behaviour of constructions subjected to residual rockfall hazard, in order to edict construction requirements. Literature on the vulnerability of existing buildings to rockfalls is quite scarce. In Switzerland, the Association of Cantonal Fire Insurance Companies (AEAI), for example, bases its building design requirements on unpublished work. Bost et al. [4] investigated failure mechanisms and impact strength of reinforced concrete walls during a fullscale test campaign. Two failure modes have been highlighted: punching and bending, depending on the impact characteristics (mass and energy). © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1293–1302, 2024. https://doi.org/10.1007/978-3-031-39450-8_105
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Regarding masonry structures, only little data is available concerning the damage generated by the impact of boulders [15]. Although many studies have been dedicated to the dynamic behaviour of masonry structures in the framework of seismic risk assessment [1, 6], they cannot be extended to boulder impact as seismic loading is much faster, with a global effect on the structure, leading to different failure mechanisms. Work can also be found on the effect the impact of vehicles on masonry bridge parapet [10]. In this case, the loading speeds are of the same order of magnitude (between 10 m/s and 30 m/s, i.e. 36 km/h and 108 km/h), the difference coming from the deformation of the impacting vehicle during the loading. The soft shock results in a systematic partial energy dissipation. Thus, these studies on the dynamic behaviour of masonry structures cannot be directly extended to boulder impact considering the differences on the characteristics of the loading mode. A few experimental works can be found on the impact of a rigid block on a masonry wall [5, 9]. Gilbert et al. [9] investigate the resistance of a metric scale brick or concrete block masonry wall, with or without mortar, but without overload, when subjected to a hard shock of a few tens of kJ. Bui et al. [5] study the impact behaviour of 1/2 scale masonry walls loaded by an impact of a few kJ. The reduced scale of the structure and the low energy level of the impact make it difficult to draw comparisons with real conditions. Some authors have investigated the behaviour of the constitutive materials of masonry when subjected to an impact [3, 12]. Beattie et al. [3] show that depending on the loading speed and the boundary conditions, the mortar joint presents two different failure modes, by shear or tension. Lourenco et al. [11] develop dynamic behaviour laws for brick, mortar joints and masonry, with strength characteristics increasing with the loading speed. A few attempts have been made to develop a model of a masonry structure subjected to a localised hard shock. Gilbert et al. [9] propose an analytical model based on a single failure mode. Bui et al. [5] complete their reduced scale experimental campaign with a modal analysis. Burnett et al. [7] use the finite element method to simulate the tests performed by [9], showing that the model is sensitive to the masonry characteristics, in particular the joint dilatancy; this work has been latter on extended to introduce an overload at the top of the wall [2]. This model relies on 21 parameters, with the dynamic properties of the material remaining difficult to characterise, in particular at the joint interface. Li et al. [11] develop a DEM model, where the contacts between blocks have to be defined. Mavrouli et al. [13] resort to PFEM to establish a load equivalent to the impact; this equivalent load is then applied in a FEM simulation considering a macro-model for the masonry structure to determine the damage to the structure. Finally, some models taking into account the dynamic behaviour of the components [12, 15] are relevant for higher stress velocities than in the case of a rock boulder impact. Reliability analyses have also been performed in order to assess masonry structure behaviour loaded by a boulder impact [8, 16]. These approaches rely on the definition of the failure modes and criteria which, in the current state of the knowledge, struggle to reflect the complexity of the structure behaviour. As a conclusion, the works presented in the literature do not make it possible to define curves characterising the damage of masonry walls subjected to the impact of a rock
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boulder. Moreover, experimental results are too few to have a critical and constructive approach to the models already developed. The present work aims at providing supplementary experimental data in order to enhance the simulations of masonry construction exposed to rockfall.
2 Experimental Design A full-scale experimental campaign is undertaken to assess the vulnerability of masonry panels subjected to a boulder impact at University Gustave Eiffel test site in Montagnole near Chambéry (France). Walls of height H = 2.50 m and length L = 3.00 m have been built and tested. They are made up 10 layers of 7 single-wall bricks with dimensions of 0.425 × 0.282 × 0.249 m and density ρ m = 0.795 (Table 1), laid dry or jointed with a specific mortar designed for these bricks. The coefficient of friction φ m between the blocks was estimated at 0.75 and the tensile strength of the mortar at 0.072 MPa. The geometrical and physical characteristics of the experimental walls are given in Table 1. Table 1. Geometrical and physical characteristics of the experimental walls. Brick
Length l (m)
0.425
Width w (m)
0.282
Height h (m)
0.249
Density ρ Compressive strength f (MPa)
0.795 10
Friction coefficient ϕ
0.75
Mortar
Tensile strength (MPa)
0.072
Wall
Length L (m)
3.000
Width W (m)
0.282
Height H (m)
2.500
The first bed of each wall is blocked, to simulate a rock foundation of the same nature as the blocks of the wall. On the edges, two limit conditions are explored: the wall is either constrained in a metallic frame, in order to simulate the presence of shear walls, or left free. Finally, a static overload of 20 kPa, simulating the effect of an upper floor and/or a roof, is applied at the top of the wall. The test consists in impacting the centre of the wall with a block launched normally to its front face. Impacting blocks conform to ETAG (European Technical Approval Guidelines) recommendations: they are polyhedral (rhombicuboctahedron) reinforced concrete blocks of two different specific lengths (Fig. 1), leading to two different masses of the impacting block (100 and 277 kg). Blocks are launched at two different heights using the pendulum system of the test site, thus corresponding to two different expected energy levels (5 and 15 kJ).
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Fig. 1. Rhombicuboctahedron reinforced concrete impacting block of specific length L ext conforming to ETAG 027.
The instrumentation comprises an accelerometer within the impacting block, two high-speed cameras, one at the front and one at the back of the wall, and a camcorder, in order to identify the characteristics of the impact (speed and position) as well as the wall behaviour. A total amount of seven walls have been tested, with varying conditions in terms of masonry joint, lateral limit conditions, and impacting conditions (mass and energy). The experimental design is detailed in Table 2. Table 2. Experimental design for full-scale impact tests on masonry panels. Test
Masonry
Limit conditions
Impacting conditions Mass (kg)
Energy (kJ)
#1
Dry joint
Constrained
100
5
#2
Dry joint
Constrained
277
5
#3
Dry joint
Constrained
277
15
#4
Dry joint
Free
100
5
#5
Dry joint
Free
277
5
#6
Dry joint
Free
277
15
#7
Mortar joint
Free
277
15
3 Full-Scale Test Results and Discussion The different tests have been analysed with the same protocol. This will be illustrated in this paper on test #2 (Fig. 2). Test wall #2 is a dry joint wall, which edges displacements have been constrained by a metallic frame (Fig. 2a). It has been tested by launching a 277 kg block on the centre of the panel normally to its front face at an expected energy of 5 kJ. The accelerometer enables to identify the different phases of the impacting block trajectory (Fig. 3a), from the release of the impacting block at t = 0 s to the impact of
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(b)
Fig. 2. Full-scale experimental wall #2 prior (a) and after (b) impact.
Acceleration (g)
the wall, around t = 3 s. The high-speed cameras records are exploited using Tracker video analysis (Fig. 3b), revealing that the impacting block is entering in contact with the front face of the wall at a speed of 22.3 km/h, corresponding to an energy of 5.3 kJ, which is consistent with the expected value of 5 kJ.
X Y Z
Time (s) (a)
(b)
Fig. 3. Accelerometer measurement (a) and video speed analysis (b) of the impacting block for test #2.
When analysing the wall after impact (Fig. 2b), it can be noted that the wall did not succeed in stopping the block. The test led to the destruction of 5 to 8 blocks around the impact area, with a more failure important surface at the back than at the front of the wall. Nevertheless, the test did not lead to the collapse of the wall. Similar analyses can be made on the other tests. In all the configurations explored, the impacting block was not stopped by the wall. Yet, the impact did not lead to the collapse of the structure but to the complete or partial destruction of the masonry bricks located around the impact area (between 5 to 10 equivalent blocks), close to the punching behaviour observed on reinforced concrete panels tests [4]. Nevertheless, contrary to what have been observed on concrete structures, the failure mode was similar for all tests, and did not depend on the mass or energy of the impact.
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4 Numerical Simulations and Preliminary Validations The experimental campaign has been completed by numerical simulations. These simulations aim at reproducing the specific behaviour of masonry structures when exposed to a hard shock. They will be validated using the experimental results presented in Sect. 3, and then used to perform parametric analyses. In this work, two modelling approaches have been explored: a micro-modelling using DEM (Fig. 4a) and a macro-modelling using FEM (Fig. 4b).
(a)
(b)
Fig. 4. Numerical simulations of the experimental tests by discrete element method using Siconos (a) and finite element method using Abaqus (b)
4.1 Discrete DEM Approach The micro-modelling approach (Fig. 4a) is performed using the DEM software Siconos. Siconos is an open-source scientific software developed at Inria Grenoble for the simulation of non-smooth dynamic systems. It has already been used to simulate the behaviour of masonry structures under static loads and the trajectory of rockfall. This study aims at evaluating the capacities of the software to simulate the behaviour of masonry structures under the impact of a boulder. Masonry is modelled as rigid parallelepipedal blocks interacting at their contact surfaces following a purely frictional contact law of normal restitution em and friction angle ϕ m . The masonry panel is founded on a rigid support. The interface law between the base of the wall and the support is identical to the interface law between the constituent elements of the structure, as in the experimental campaign. A rigid block of the same length and thickness as the wall is placed at the top of the wall to simulate the overload due to the upper floor or the roof. Two lateral boundary conditions have been explored: blocking all the degrees of freedom, except the translation along the vertical axis (named Fix[x,y,X,Y,Z]), or blocking the horizontal displacement according to the direction of impact (named Fix[x]). In order to allow masonry block displacements, a horizontal gap of 5 mm between blocks is integrated in the model. The impacting block is simulated as a rigid rhombicuboctahedron interacting with the constituent elements of the masonry structure, also using a frictional contact law of
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normal restitution eb and friction angle ϕ b . In addition to the initial mass of the impacting block and its shape, it is necessary to define its location and initial speed. The impact of the boulder on the structure is modelled as an iterative process in time. The occurrence of an interaction between the different rigid bodies is checked at each time step. In the case of an interaction, an impulse is applied to the rigid bodies in interaction. Displacements of the rigid bodies during impact are calculated using the fundamental principle of dynamics. 4.2 Continuous FEM Approach The macro-modelling approach (Fig. 4b) relies on Abaqus FEM software. The masonry panel is constituted of a homogenised material which properties are based on Eurocode 6, with compressive strength ranging from 1.0 to 2.5 MPa, tensile strength from 0.035 to 0.09 MPa, and Young’s modulus from 400 to 1670 MPa. The homogenised masonry follows the Concrete Damaged Plasticity (CDP) behaviour law as implemented in Abaqus. This behaviour law includes first a linear elastic part, then a parabolic hardening-softening part, and finally a linear softening part. The behaviour in tension is described by a linear elastic part followed by a softening part. For simplicity reason, the behaviour of the masonry is considered as isotropic, and shear behaviour is not taken into account. The panel is simulated in 3D using explicit deformable solid finite elements of the quadrilateral type linear with 8 nodes (C3D8R elements). The impacting element is modelled using explicit rigid discrete finite elements of type bi-linear quadrilaterals with 4 nodes (R3D4 elements). The mesh size varies from 2.5 (in the impact zone) to 20 cm for the wall, and is of 2.5 cm for the block. The wall is embedded at the base and displacement in the direction normal to the wall are blocked on the edges at the back of the wall to simulate the effect of unmodeled shear walls. A vertical pressure field is applied at the top of wall to simulate the action of an upper floor or a roof. The contact between the impacting block and the wall is created by a general contact type interaction with a tangential friction coefficient ϕ b = 0.75. 4.3 Preliminary Validations and Failure Mode Characterisation For numerical simulations, three levels characterising the damage of the structure postimpact have been introduced: – masonry block displacements without collapse, named D1; – collapse of one or several masonry blocks around the impact area, named D2; – collapse of one or several masonry blocks at the top of the wall, named D3. This damage level can be completed by the maximal displacement registered for the wall X + , and the number of collapsing blocks N + for D2 and D3. The continuous model can also supply complementary global information as stress or strain fields, and plastic damage.
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Table 3. Damage characterisation of the impacted walls for DEM and FEM simulations. Impacting conditions M ass (kg) Energy (kJ) 5
100
15
50
5
277
15
50
5
800
15
50
Simulation DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x] DEM /Fix[x,y,X,Y,Z] DEM /Fix[x] FEM /Fix[x]
Damage level D1 D1 D1 D1 D2 D2 D2 D2 D2 D2 D1 D1 D2 D2 D2 D2 D3 D2 D1 D1 D1 D2 D2 D2 D3 D3 D2
M ax. displacement X+ (cm) 10.6 10.7 12.3 19.2 24.3 / 33.1 59.7 / 33.1 35.9 11.1 37.4 34.2 / 29.4 46.0 / 29.4 34.9 11.2 23.1 59.2 / 41.5 45.5 /
Collapsing blocks
N+ − − − − 1 3 1 12 7 1 − − 1 5 4 12 24 7 − − − − 9 6 24 26 10
Impacting block stop Yes Yes Yes Yes Yes No Yes No No Yes Yes Yes Yes Yes No Yes No No Yes Yes Yes Yes Yes No Yes No No
Modelling have been carried out on 9 different impact conditions corresponding to 3 different impacting block masses from 100 to 800 kg, and 4 different level of energy from 5 to 50 kJ. Results are presented in Table 3. Simulations show that for the same range of impact conditions as the experimental ones (masses from 100 kg to 277 kg and energy from 5 to 15 kJ, in light grey in Table 3), modelled walls succeed in stopping the impacting block in almost all the cases, except for the continuous model with the 277 kg block at 15 kJ. This difference between simulations and experiments can be explained by the low strength of the experimental bricks; complementary tests using stone blocks or complementary simulations integrating masonry block crushing should be performed in order to confirm this hypothesis. Complementary simulations have been performed in order to undertake a parametric analysis. These tests have led to a reflection on the characterization and quantification of the failure mode of masonry constructions under a boulder impact and the vulnerability of a structure towards rockfall hazards.
5 Conclusion This study deals with the vulnerability of masonry constructions to rockfall hazards. This issue is at stake in the context of the protection of buildings in mountainous areas. The literature has shown that the subject has been little explored. Although the static or seismic behaviour of masonry structures has been the subject of a large number of
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publications, their response to a hard shock has been very little explored, both from simulation and experimentation points of view. Indeed, experiments have been confined to reduced scales and low energy levels. This work aims at developing a better understanding of the behaviour of masonry constructions under dynamic stress caused by hard shock. A full-scale experimental campaign has been carried out in order to identify the damage generated by an impact on a masonry structure in real conditions, and to calibrate numerical simulations. For the different experimental configurations explored, only one failure mode by punching has been identified. This can be due to the low strength of the masonry blocks used in the experiment; new tests with stone block could confirm this hypothesis. In addition, numerical simulations adapted to the specificity of the masonry structures under hard shock dynamic loading have been developed. Two numerical models have thus been proposed: a discrete model based on the free software Siconos from Inria, and a continuous model using Abaqus. Simulations make it possible to explore the capacities of the two approaches to describe the behaviour masonry structures under impact. They prove the strong influence of the limit conditions. Finally, they have led to a reflection on the question of the failure mode of the structure and on the definition of indicators to characterise the level of damage to the structure after impact. As a long-term perspective, this action aims at defining damage curves for masonry buildings, and thus contribute to the prescription of normative requirements for building construction in mountainous areas.
References 1. Ahmed, H.A., Shahzada, K.: Numerical modeling of confined brick masonry structures with parametric analysis and energy absorption calculation. Int. J. Protective Struct. 12, 129–152 (2021) 2. Asad, M., Dhanasekar, M., Zahra, T., Thambiratnam, D.: Failure analysis of masonry walls subjected to low velocity impacts. Eng. Fail. Anal. 116, 104706 (2020). https://doi.org/10. 1016/j.engfailanal.2020.104706 3. Beattie, G., Molyneaux, T., Gilbert, M., Burnett, S.: Masonry shear strength under impact loading. In: Proceedings of the 9th Canadian Masonry Symposium (2001) 4. Bost, M., Limam, A., Joffrin, P., Pruvost, C.: Failure mechanisms within unreinforced concrete wall under rockfall impact loading. In: 4th RSS – Rock Slope Stability Symposium (2018) 5. Bui, T.T., Limam, A., Bui, Q.B.: Characterisation of vibration and damage in masonry structures: experimental and numerical analysis. Eur. J. Environ. Civ. Eng. 18, 1118–1129 (2014) 6. Bui, T.T., Limam, A., Sarhosis, V., Hjiaj, M.: Discrete element modelling of the in-plane and out-of-plane behaviour of dry-joint masonry wall constructions. Eng. Struct. 136, 277–294 (2017). https://doi.org/10.1016/j.engstruct.2017.01.020 7. Burnett, S., Gilbert, M., Molyneaux, T., Beattie, G., Hobbs, B.: The performance of unreinforced masonry walls subjected to low-velocity impacts: finite element analysis. Int. J. Impact Eng. 34, 1433–1450 (2007) 8. De Biagi, V., Napoli, M.L., Barbero, M.: A quantitative approach for the evaluation of rockfall risk on buildings. Nat. Hazards 88(2), 1059–1086 (2017). https://doi.org/10.1007/s11069017-2906-3
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9. Gilbert, M., Hobbs, B., Molyneaux, T.: The performance of unreinforced masonry walls subjected to low-velocity impacts: experiments. Int. J. Impact Eng. 27, 231–251 (2002) 10. Hobbs, B., Gilbert, M., Molyneaux, T., Newton, P., Beattie, G., Burnett, S.: Improving the impact resistance of masonry parapet walls. Proc. Inst. Civ. Eng. Struct. Buildings 162(1), 57–67 (2009). https://doi.org/10.1680/stbu.2009.162.1.57 11. Li, Z., et al.: Simulating the damage extent of unreinforced brick masonry buildings under boulder impact using three-dimensional discontinuous deformation analysis (3-D DDA). Eng. Fail. Anal. 93, 122–143 (2018) 12. Lourenço, P.B., Hashemi, S., Pereira, J.M.: A constitutive three-dimensional interface model for masonry walls subjected to high strain rates. In: Civil-Comp Proceedings. Civil-Comp Press (2014) 13. Mavrouli, O., Giannopoulos, P.G., Carbonell, J.M., Syrmakezis, C.: Damage analysis of masonry structures subjected to rockfalls. Landslides 14(3), 891–904 (2016). https://doi.org/ 10.1007/s10346-016-0765-8 14. Rafsanjani, S., Lourenço, P.B., Peixinho, N.: Analysis of masonry walls subjected to high strain rate out-of-plane loads with a rate dependent interface model. In: 9th International Masonry Conference, Guimarães, Portugal (2014) 15. Scavia, C., et al.: Evaluating rockfall risk: some critical aspects. Geosciences 10(3), 98 (2020) 16. Vallero, G., De Biagi, V., Barbero, M., Castelli, M., Napoli, M.L.: A method to quantitatively assess the vulnerability of masonry structures subjected to rockfalls. Nat. Hazards 103(1), 1307–1325 (2020). https://doi.org/10.1007/s11069-020-04036-2
Simplified Vulnerability Assessment of Masonry Bell Towers Corrado Chisari, Mattia Zizi, Francesco Roselli, and Gianfranco De Matteis(B) Department of Architecture, and Industrial Design, University of Campania “Luigi Vanvitelli”, San Lorenzo Abbey, 81031 Aversa, CE, Italy [email protected]
Abstract. Masonry bell towers represent some of the most iconic historical assets of European heritage. However, the typical poor mechanical characteristics of masonry, lack of maintenance and conservation interventions as well as their high slenderness could lead to significant vulnerability against natural actions, such as earthquakes. Given their widespread diffusion in the European and, especially, Italian territories, the seismic vulnerability assessment of such buildings at territorial level can benefit from simplified large-scale methods based on a low amount of input data. Such methodologies, combined with hazard and exposure quantification, are thus adopted for simplified risk analyses leading to the definition of prioritisation rankings aimed at planning intervention activities. In this paper, a novel methodology for fast seismic vulnerability assessment developed by the authors is described. This is formulated as a simplification based on parameter reduction of an existing analytical approach providing a force-based estimation of the structural capacity under horizontal loading. The capacity is then turned into a suitable vulnerability index ranging from zero to one. The methodology is applied to a sample of about 25 bell towers of Naples to perform a preliminary seismic risk analysis by means of purposedly developed fragility curves. Keywords: Vulnerability index · Fragility curve · Risk scenario · Simplified assessment methodologies
1 Introduction The recent seismic events occurred in Italy (i.e. L’Aquila 2009, Emilia 2012 and Central Italy 2016–17) clearly showed that masonry bell towers are prone to suffer severe damage when subjected to earthquake excitations [1, 2]. In the context of seismic risk mitigation of the existing cultural heritage, in recent times research and practitioners’ communities have been moving towards the adoption of large-scale methods, which can represent an effective tool for preliminary seismic vulnerability and risk assessments, as well as definition of intervention priorities [3, 4].
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1303–1312, 2024. https://doi.org/10.1007/978-3-031-39450-8_106
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As far as ancient masonry bell towers are concerned, the seismic vulnerability assessment can be performed, similarly to masonry churches, at different Evaluation Levels (ELs), including [5]: • EL0: large scale methods based few typological information aimed at providing simplified risk assessment of investigated structures (e.g. by means of fragility curves); • EL1: simplified mechanical and statistical models; • EL2: analytical models aimed at studying local collapse mechanisms (e.g. limit analysis through static and/or kinematic approaches); • EL3: accurate global seismic assessment. Whilst EL1, EL2 and EL3 consist of methodologies usually defined at national level to provide an increasingly-accurate capacity-to-demand measure at structural scale [6], EL0 methods are more suited to large-scale analyses [7]. In particular, they are aimed at constructing fragility curves at territorial scale, by means of which it is possible to simulate risk scenarios relating the probability of reaching a certain damage level (or limit state) to the seismic input. One of the first applications of fragility curves for damage analyses dates to 1982, when Braga et al. [8] proposed the adoption of binomial distribution probability functions for interpreting the damage surveyed in the aftermath of Irpinia earthquake (1980) for ordinary buildings. After this pioneering application, countless examples of empirical or parametric fragility curve proposals for different structural types can be found in the literature [9, 10] and to date, the cumulative lognormal distribution is considered as one of the most appropriate formulations for fitting observed damage. Fragility curves, as an estimate of probability of collapse at territorial scale, are based on the combination of a vulnerability measure of the investigated buildings with the demand usually parameterised by intensity or Peak Ground Acceleration (PGA). Among the EL0 methodologies developed for vulnerability assessment of masonry bell towers available in the literature (e.g. [11, 12]), in this paper the procedure recently proposed by the authors [13] is applied to a sample of 25 bell towers of the historical centre of Naples. Such a procedure allows for defining a vulnerability index ˜iv in the range 0–1, measuring the susceptibility to seismic damage of each investigated structure. In particular, this is a force-based measure of capacity at the Ultimate Limit State (ULS) in terms of spectral acceleration; for this reason, preliminary fragility curves at ULS representative of the investigated sample of the Neapolitan bell towers have been derived combining capacity and demand, and considering the ductility of the structural system according to the collapse mechanism.
2 The Vulnerability Assessment Method for Masonry Bell Towers The EL0 seismic vulnerability assessment method developed in [13] and applied in this paper is based on a sensitivity-informed parameter reduction of an enhancement of the EL1 method proposed by Italian Code [6]. The tower is represented as a variable-section cantilever beam subjected to a linear acceleration profile depending on the effective height of the structure, i.e., the height of the part of the tower which is not restrained by surrounding buildings (Fig. 1).
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Fig. 1. Scheme of the bell towers according to the method proposed by [6] (from [13]).
Unlikely [6], in which a simple check to eccentric axial force is performed to any cross-section, in [13] three different collapse types are considered for the cross-section: full cross-section bending failure (Fig. 2a), belfry failure (Fig. 2b), shear failure (Fig. 2c). For any of them, the ultimate resisting moment Mu,i of the i-th cross-section of the tower may be evaluated.
(a)
(b)
(c)
Fig. 2. Failure types for a masonry bell tower (from [13]).
Given the assumption of linear acceleration profile equivalent to the seismic ground i provoking an acting moment equal to Mu,i in motion, the spectral acceleration Se,ULS
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the i-th cross-section can be evaluated as: qgMu,i nk=1 zk Wk i n 2 = Se,ULS n 0.85W k=i zk Wk − zi∗ k=i zk Wk FC
(1)
where: • q is the behaviour factor; • zk and Wk are the centroid height and the weight of the k-th sector, defined as part of the tower having constant cross-section; • zi∗ is the height of the i-th cross-section; • W is the total weight of the tower; • FC is the confidence factor, which, given the level of detail of the analysis, is equal to 1.35, maximum value assumed by the code. i The minimum among Se,ULS evaluated over the n cross-sections by which the tower has been discretised represents the spectral acceleration at Ultimate Limit State. A vulnerability index can be established on the force-based measure of capacity Se,ULS as: 1 Se,ULS (2) iv = 1 − k q
where k represents the conventional value of Se,ULS /q for which iv =0.0, and is herein assumed equal to k = 0.25g. This value represents an upper bound for Se,ULS /q evaluated in the samples analysed in [13], but its selection is arbitrary as it only governs the intersection of iv Se,ULS with the iv = 0 axis. The application of the method, which can be classified as Evaluation Level 1 as it requires a mildly accurate geometrical survey and limited mechanical characterization, is straightforward as it is based on closed-form formulations. However, it is not always easily applicable on a large scale given the level of detail required at least in the geometrical representation. In [13] it is shown that it is possible to construct a simplified representation, i.e., EL0, of the tower by means of a limited set of quantitative parameters in which the remaining unknown parameters are assigned typical values based on preliminary survey of the sample. By increasing the number of parameters of which information is available, it is possible to control the degree of accuracy of the prediction. Based on a large-scale analysis of numerically generated bell towers, the authors established a set of parameters providing a good compromise between accuracy in the vulnerability estimation and feasibility of use at territorial scale. These are: • • • • • •
Htot Lmin , slenderness of the tower; Lb,open Lmin , opening width ratio at belfry; t0 Htot , dimensionless wall thickness at basement; Htot , total height of the tower; Hi , average height of the floors; ol , location of openings with respect to the motion
direction (0 = no openings; 1 = on the sides orthogonal to motion; 2 = on the sides parallel to motion; 3 = on all sides).
In Fig. 3 the evolution of the distribution of accuracy = ˜iv /iv , as ratio between the vulnerability index ˜iv evaluated on the EL0 model and the exact (EL1) iv where all
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the parameters are set at their real value is shown. It can be observed that the use of the 6-parameter model is able to achieve a significant reduction of the accuracy dispersion compared to the non-informative model based on the average values of all parameters.
(a)
(b)
(c )
Fig. 3. Distribution of accuracy index at increasing complication of the model: (a) by using average values for all input, (b) by using 6 parameters, (c) by using 15 parameters (from [13]).
3 Empirical Fragility Curves Given the capacity of the bell tower in terms of strength, summarised by its vulnerability index, the construction of the empirical fragility curves at ULS of a sample of bell towers may be performed by including some information about the demand (site) and completing the description of the single structural response by defining the structure fundamental period, i.e., the stiffness, and behaviour factor, i.e., the ductility. This allows for the implicit definition of the simplified bilinear capacity curve of the structure and for performing the seismic check at Ultimate Limit State (ULS) by using a simplification of the N2 method. The fundamental period T 1 of the tower may be evaluated according to the empirical formulation calibrated in [14]. It reads T1 = f11 , where: −0.341 −0.216 f1 = 14.61L−0.254 Heff Htot min
(3)
−1.73 f1 = 208.54L−0.55 min Htot
(4)
for bounded towers, and:
for isolated towers. In case of assessment at Ultimate Limit States, [6] suggests increasing the elastic period by means of a factor T f ranging from 1.4 to 1.75. In this work a median value equal to T f = 1.575 has been adopted. The behaviour factor of a bell tower should be based on the results of a static or dynamic nonlinear analysis. Within a simplified framework as that described in this paper, the Italian code [6] suggests values ranging between 2.8 for towers with abrupt changes in stiffness along the height or for bounded towers, to 3.6 for structure which are regular in elevation. Whereas these values are based on those for buildings, some authors
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have highlighted the possible overestimation due to the lack of structural redundancy of the bell tower static scheme [15, 16]. In this work, the behaviour factor has been defined based on the type of failure, determined as per Sect. 2: ⎧ ⎨ 1.5 belfry failure q = 2.25 shear failure (5) ⎩ 3.0 bending failure The demand is represented by a 5%-damped ULS elastic design spectrum, which according to the Italian code is defined by parameters ag (Peak Ground Acceleration), S ·F0 (spectral amplification factor) and TC (starting period of constant velocity branch), characteristics of the site. This reference spectrum is also function of sub-soil and topography category. It is thus possible to find the peak ground acceleration at bedrock leading to ULS the bell tower by means of the formulas: S e,ULS TB ≤ T 1 < TC SF0 (6) aULS = Se,ULS T1 SF0 TC TC ≤ T 1 < TD where Se,ULS is evaluated by inverting Eq. (2): Se,ULS = kq(1 − iv )
(7)
The safety index fa = aULS /ag defines thus the occurrence (or not) of collapse for an earthquake of a given return period, characterised by ag . By repeating the procedure for all bell towers and several return periods it is possible to construct empirical fragility curves for the sample of bell towers.
4 Application to Neapolitan Bell Towers 4.1 Description of the Samples A sample of 25 masonry bell towers in the Neapolitan historical centre and its surrounding was surveyed with the aim of defining fragility curves (Fig. 4). The construction period of the bell towers, 23 of which are connected to adjacent buildings (usually a church) and 2 are isolated, ranged from 12th to 18th century. The main data collected to estimate the vulnerability index are the total height (H tot ), the slenderness (H tot /L min ), the opening ratio in the belfry (L b,open /L min ), the slenderness ratio of the wall in elevation (t 0 /H tot ), the average height of the sectors (H i ), and the position of the openings at the base with respect to the direction of seismic forces (ol ). Additional data were collected in order to apply the framework described in Sect. 3: the subsoil category and the topographic category, affecting the demand, and the effective height (H eff ) of the bell tower, for the estimation of the fundamental period. Some statistical information about the bell tower sample is reported in Fig. 5. The average total height of the bell towers is 32 m, with the lowest bell tower being S. Maria Stella Maris, which measures 15 m, and the tallest bell tower S. Maria del Carmine Maggiore, with an elevation of 75 m. The slenderness ratio is distributed from 3 and 9, with most samples being in the range 4–6.
Simplified Vulnerability Assessment of Masonry Bell Towers
1309
(a)
10 9 8 7 6 5 4 3 2 1 0
# of samples
# of samples
Fig. 4. Location of the analysed bell towers in Naples.
Htot [m]
(b)
10 9 8 7 6 5 4 3 2 1 0
Htot/Lmin [m]
Fig. 5. Distribution of (a) total height, and (b) slenderness in the bell tower sample.
Subsoil categories were identified through the use of the national geological map [17]. The data showed that the subsoil categories are predominantly zone C, and only one tower (S. Eligio Maggiore) is in zone B, according to the classification of NTC2018 [18]. The topographic categories, which were surveyed through the use of Google Earth Pro’s “show elevation profile” tool [19], are all T1, i.e., flat surfaces, slopes and isolated reliefs with average slope i ≤ 15°. The bell tower of S. Luigi Gonzaga, on the other hand, is in topographic category T2 (slopes with i > 15°). The average effective height is 17 m. The lowest height is observed for Pappacoda Chapel, which measures 3 m, while the highest effective height is that of S. Maria del Carmine, which measures 58 m. It is interesting to note that many of the parameters needed to estimate the vulnerability index can be retrieved from publicly available tools, i.e., Google Earth, while the need of a survey or documentation analysis is limited to the parameters related to the internal spaces, i.e., t 0 /H tot , H i , and, in some cases, ol .
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4.2 Construction of the Empirical and Parametric Fragility Curves The procedure described in Sect. 3 has been applied to the considered sample of 25 bell towers in order to derive preliminary fragility curves at ULS. The demand spectra have been constructed by considering different return periods TR and the values of the independent parameters (i.e. ag , F0 and TC∗ ) provided by Annex B of Italian Standards of 2018 [18] for the site of Naples and reported in Table 1. Table 1. Values of the basic spectrum parameters assumed for each return period (in years). Parameter
TR = 30
TR = 50
TR = 72
TR = 101
TR = 140
TR = 201
TR = 475
TR = 975
TR = 2475
ag [g]
0.045
0.06
0.073
0.086
0.101
0.12
0.168
0.213
0.28
F0 [-]
2.341
2.338
2.325
2.329
2.324
2.318
2.378
2.447
2.574
TC * [s]
0.284
0.312
0.322
0.328
0.332
0.335
0.34
0.343
0.344
Once the demands have been defined, they have been compared with the capacity according to the procedure described in Sect. 3 to establish the number of collapsed towers for each considered return period, i.e., each level of ag . The number of collapses has then been normalised with respect to the total number of the sample to obtain the frequencies of collapse at the Ultimate Limit State. The obtained empirical curve, shown in Fig. 6, has been also fitted by means of a lognormal cumulative distribution:
ln(x/μ) (8) P ag ≥ aULS |ag = x = Φ β where P ag ≥ aULS |ag = x is the probability of exceedance the ultimate limit state capacity as a function of a given intensity measure ag = x, Φ is the standard normal cumulative distribution and μ and β denote the median value and the logarithmic standard deviation, respectively. Given that the adopted methodology is directly based on the frequency of exceedance, function of the different considered return periods, it was not possible to analytically define the mean and standard deviation values better fitting the obtained results. Thus, an optimisation procedure based on the Ordinary Least Squares (OLS) technique [19] has been adopted aimed at finding the couple of values μ and β minimizing the sum of the squares of the residuals (i.e. the difference between the obtained and the fitted values provided by the lognormal cumulative distribution). The OLS optimization procedure led to a fragility curve related to the Ultimate Limit State as per Eq. (8) with the following parameters: μ=0.161 g and β=0.52. The comparison between the empirical and parametric fragility curves provided in Fig. 6 shows the satisfying level of fitting given by the lognormal formulation.
Simplified Vulnerability Assessment of Masonry Bell Towers
P(ag≥aULS)
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
1311
Empirical Lognormal 0
0.1
0.2
ag [g]
0.3
0.4
0.5
Fig. 6. Probability of exceedance of Ultimate Limit State: empirical and fitted lognormal fragility curves.
5 Conclusions In this paper, a recently developed EL0 seismic vulnerability formulation for masonry bell towers is applied to a sample of 25 structures in Naples. The procedure is then enriched by the definition of the demand at several return periods in order to determine empirical fragility curves at ULS for the samples. The empirical curve is then fitted by a parametric lognormal curve, showing a good match and confirming the suitability of this formulation. Future work will expand the definition of the fragility curves to other Limit States by exploiting the simplified formulation of the bilinear capacity curve. Development of a probabilistic formulation for vulnerability, accounting for the uncertainty in the shift from EL1 to EL0, will also be investigated.
References 1. De Matteis, G., Zizi, M.: Seismic damage prediction of masonry churches by a PGA-based approach. Int. J. Architect. Heritage 13(7), 1165–1179 (2019) 2. Acito, M., Bocciarelli, M., Chesi, C., Milani, G.: Collapse of the clock tower in Finale Emilia after the May 2012 Emilia Romagna earthquake sequence: numerical insight. Eng. Struct. 72, 70–91 (2014) 3. Lagomarsino, S., Cattari, S., Ottonelli, D.: The heuristic vulnerability model: fragility curves for masonry buildings. Bull. Earthq. Eng. 19(8), 3129–3163 (2021). https://doi.org/10.1007/ s10518-021-01063-7 4. Masi, A., Lagomarsino, S., Dolce, M., Manfredi, V., Ottonelli, D.: Towards the updated Italian seismic risk assessment: exposure and vulnerability modelling. Bull. Earthq. Eng. 19(8), 3253–3286 (2021). https://doi.org/10.1007/s10518-021-01065-5 5. Zizi, M., Rouhi, J., Chisari, C., Cacace, D., De Matteis, G.: Seismic vulnerability assessment for Masonry Churches: an overview on existing methodologies. Buildings 11, 588 (2021) 6. Ministero dei Beni e le Attività Culturali, Linee Guida per la valutazione e riduzione del rischio sismico del patrimonio culturale allineate alle nuove Norme tecniche per le costruzioni. Circolare 26/2010, Roma (2010)
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7. Calvi, G.M., Pinho, R., Magenes, G., Bommer, J., Restrepo-Vélez, L., Crowley, H.: Development of seismic vulnerability assessment methodologies over the past 30 years. ISET J. Earthq. Technol. 43(30), 75–104 (2006) 8. Braga, F., Dolce, M., Liberatore, D.: A statistical study on damaged buildings and an ensuing review of the MSK-76 scale. In: Proceedings of the Seventh European Conference on Earthquake Engineering, 20–25 September, pp. 431–450, Athens, Greece (1982) 9. Hofer, L., Zampieri, P., Zanini, M.A., Faleschini, F., Pellegrino, C.: Seismic damage survey and empirical fragility curves for churches after the August 24, 2016 Central Italy earthquake. Soil Dyn. Earthq. Eng. 111, 98–109 (2018) 10. Cescatti, E., Salzano, P., Casapulla, C., Ceroni, F., da Porto, F., Prota, A.: Damages to masonry churches after 2016–2017 central Italy seismic sequence and definition of fragility curves. Bull. Earthq. Eng. 18(1), 297–329 (2019). https://doi.org/10.1007/s10518-019-00729-7 11. Shakya, M., Varum, H., Vicente, R., Costa, A.: Seismic vulnerability assessment methodology for slender masonry structures. Int. J. Architect. Heritage 12(7–8), 1297–1326 (2018) 12. Sepe, V., Speranza, E.V.A.: A method for large-scale vulnerability assessment of historic towers. Struct. Control Health Monit. 15, 389–415 (2008) 13. Chisari, C., Cacace, D., De Matteis, G.: A mechanics-based model for simplified seismic vulnerability assessment of masonry bell towers. Eng. Struct. 270, 114876 (2022) 14. Diaferio, M., Foti, D., Potenza, F.: Prediction of the fundamental frequencies and modal shapes of historic masonry towers by empirical equations based on experimental data. Eng. Struct. 156, 433–442 (2018) 15. D’Ambrisi, A., Mariani, V., Mezzi, M.: Seismic assessment of a historical masonry tower with nonlinear static and dynamic analyses tuned on ambient vibration tests. Eng. Struct. 36, 210–219 (2012). https://doi.org/10.1016/j.engstruct.2011.12.009 16. Ceroni, F., Pecce, M., Manfredi, G.: Seismic assessment of the bell tower of Santa Maria Del Carmine: problems and solutions. J. Earthquake Eng. 14(1), 30–56 (2009) 17. Geological Map of Italy: Excerpt of the Geological Map of the City of Naples, 1: 50,000 Sheet 447. https://www.isprambiente.gov.it/Media/carg/447_NAPOLI/Foglio.html. Accessed 15 Feb 2023 18. MIT: Norme Tecniche per le Costruzioni - Decreto Ministeriale 17 Gennaio 2018. Ministero delle Infrastrutture e dei Trasporti, Rome (2018) 19. Google LLC: Google Earth Pro (7.3) (2022). https://www.google.com/intl/it/earth/about/ver sions/. Accessed 15 Feb 2023 20. Zdaniuk, B.: Ordinary least-squares (OLS) model. In: Michalos, A.C. (ed.) Encyclopedia of Quality of Life and Well-Being Research, pp. 4515–4517. Netherlands, Springer, Dordrecht (2014)
Author Index
A Achig-Balarezo, M. C. 698 Addessi, Daniela 421, 433 Adhikari, Omkar S. 387 AlShawa, O. 278 Andrisani, Giuseppe 736 Arce, Andres 849 Armando, La Scala 543 Assal, Hisham 1268 Astudillo Cordero, S. 698 B Baik, Ahmad 407 Bal, Ihsan E. 1159 Barsallo Chávez, G. 698 Battini, Carlo 352 Battisti, Andrea 421 Bellin, Sonia 472 Bernardini, Gabriele 1212, 1227 Beyer, Katrin 400, 591 Bianconi, Francesca 484 Bilotta, Emilio 312 Bondi, Andrea 935 Boostani, A. 505 Bost, M. 374 Bost, Marion 1293 Bourrier, Franck 1293 Božuli´c, Ivana 400 Brando, Giuseppe 1280 Brosens, K. 763 Burgetová, Eva 785 Burzic, Emina 445 C Caicedo, B. 1009 Calderini, Chiara 339, 352 Caliò, Ivo 566 Cancino, Claudia 709 Cao, Yongkang 655 Cappi, Leonardo 935 Casarin, Filippo 472, 935
Chang, Chia-Ming 1106 Chieffo, Nicola 1256 Chisari, Corrado 1303 Choi, Il Kyu 195 Choquemaqui, Susan 532 Chuang, Yi-Ji 1106 Chun, Qing 1134 Cianchino, Giorgia 1280 Clarke, Nicholas J. 858 Clementi, Francesco 484 Cointe, Alain 458 Coïsson, Eva 1169 Colas, A.-S. 374 Colas, Anne-Sophie 1293 Conte, Raoul Paolo 312 Cornadó, Còssima 1031 Coureau, Jean-Luc 458 Cusmano, Valeria 566
D D’Altri, A. M. 366 D’Amato, Michele 1146 D’Orazio, Marco 1212 Daudon, Dominique 494 Daugeviˇcius, Mykolas 1204 Davis, Lucy 217 de Bouw, M. 763 De Matteis, Gianfranco 1303 de Miranda, S. 366 de Oliveira, Benedito Tadeu 799 DeJong, M. 913 Del Cueto-Ruíz Funes, J. 950 Destro Bisol, Giacomo 278, 913 Dewaele, B. 763 Dokku, Prathyusha 985 Domenech, Marta 1031 Donovan, Sadhbh 745 dos Santos, Ketson Roberto Maximiano Du, Qian 655 Duncan, Neil A. 445
© RILEM 2024 Y. Endo and T. Hanazato (Eds.): SAHC 2023, RILEM Bookseries 46, pp. 1313–1317, 2024. https://doi.org/10.1007/978-3-031-39450-8
591
1314
E Egiluz, Ziortza 1093 Eleni, Tsangouri 1021 Endo, Yohei 125 F Farrell, David 899 Ferrero, Chiara 339, 352 Ferrero, Marco 352 Ferretti, Daniele 1169 Ferretti, Francesca 578 Figueiredo, Rui 1117 Flora, Alessandro 312 Fofiu, Mihai 1146 Formisano, Antonio 1146 Foti, Dora 543 Fratini, F. 505 Friedman, Donald 810 Fujita, Yasuhito 63 Fukuda, M. 41 Fukuda, Mitsuharu 12
Author Index
Holschemacher, Klaus 1192 Hughes, Moriah G. 1181 Hughes, Richard 683 I Ikegami, Shigeyasu 83 Ishizuka, Mitsumasa 12 Iskander, George 445 Ita, Paola 494 Italia, Raffaele 472 Ivorra, Salvador 543 Iwasaki, Y. 41 Iwasaki, Yoshinori 12 J Javier Torrijo Echarri, F. 1067 Jin, Chi 655 Jing, Tingyun 125 Jingyao, Zhang 75 Jocelyn, Travasso 1021 Jok¯ubaitis, Aidas 1204
G Galimard, Philippe 458 Gao, Xiaoyue 1134 García-Rubalcava, José Luis 996 Garmendia, Leire 1093 Gatti, Loic 1021 Gilbert, Matthew 626 Giordano, Ersilia 484 Glisic, B. 366 Gliši´c, Branko 1181 Goncalves, Ana Paula Arato 899 Grazzini, R. 505 Grillanda, Nicola 1146 Guida, Antonella 736 Guillén-Guillén, C. 950
K Kakehashi, Naoki 51 Kamalakar, Vrushali 985 Kamatoko, Miyako 51 Kapsalis, Panagiotis 849 Kauffmann, Lawrence 458 Keller, Alexandra I. 268, 669 Kirizsán, Imola 884, 959 Kita, Shigenori 26 Korff, Mandy 232 Korswagen, Paul A. 232 Koyama, T. 41 Krajewski, Piotr 873 Kunecký, Jiˇrí 259, 617 Kwiecie´n, Arkadiusz 858, 873
H Han, Yidan 1134 Hanazato, T. 101 Hanazato, Toshikazu 26, 125 Hashimoto, R. 41 Hataj, Martin 259 Hayasaki, Yoichi 112 Herrera-León, William Herbe 996 Hinz, Elisabeth 824 Hochreiner, Georg 259 Hojdys, Łukasz 873
L Lacanna, G. 505 Lai, Chi-Ming 1059 Lam, Chi Chiu 556 Lanzolla, Alessandro 736 Lauder, Nicola 899 Lee, Chan Hee 184, 195 Lee, Gwan Su 184 Lenticchia, Erica 1169 Levi, Aharon 472 Liberatore, D. 913
Author Index
Liberatore, Domenico 421, 433 Liew, Andrew 626 Lin, Yi-Pin 1059 Liu, Ke 301 Longo, Michele 232 Lopez-Garcia, Diego 517 Lourenço, Paulo B. 143, 1256 Luli´c, Luka 724 Ly, Vanna 12 M Malomo, Daniele 217 Marinelli, Fabrizio 1227 Masciotta, Maria Giovanna 1280 Massafra, A. 156 Mazzotti, Claudio 578 McCarthy, Robert 12 Medzvieckas, Jurgis 1204 Mehrotra, Anjali 287 Menil, A. 374 Messali, Francesco 287 Miku, Hamaoka 75 Milani, Gabriele 170 Mileto, Camilla 1067 Mishra, Chhabi 125 Misseri, G. 505 Mitsji, K. 101 Mitsuhiro, Miyamoto 75 Miyoshi, Kimiko 112 Mocellini, Marco 472 Möller, Eberhard 924 Monaco, Anna Lo 1146 Monteferrante, Chiara 578 Montesinos, Mijail 532 Montoya, T. 641 Moreira, Susana 1242 Moreti´c, Antonela 1256 Morikawa, Hitoshi 63 Mosoarca, A. 838 Mosoarca, Marius 268, 1146 Motoyui, Shojiro 63 Muciño-Vélez, A. 950 Mutoh, Atsushi 63 N Nakagawa, Takeshi 12 Nanayakkara, Isuru 626 Niitsu, Y. 101 Noriyuki, Takahashi 75
1315
O Ohashi, Yoshimitsu 112 Oktiovan, Yopi 287 Onescu, I. 838 Onescu, Iasmina 1146 Orenday-Tapia, Edith Estefanía 996 Ousset, Isabelle 1293 Oži´c, Karlo 724 P Pacheco-Martínez, Jesús 996 Padilla-Ceniceros, Raudel 996 Pantò, Bartolomeo 566 Paoloni, Alessandra 433 Papanicolaou, Catherine G. 849 Pari, Manimaran 603 Park, Jun Hyoung 184 Park, Seok Tae 184 Passante, Giulia 935 Paupério, Esmeralda 1080, 1242 Paxinou, Katerina 1159 Peña, Fernando 1268 Pereira, João M. 143, 387 Pereira, M. 366 Pereiro-Barceló, Javier 543 Perucchio, Renato 170 Piñero, Ignacio 1093 Poletti, Elisa 745 Porcari, Vito Domenico 736 Prajapati, S. 278 Prati, D. 156 Prosperi, Alfonso 232 Putz, Andreas W. 824 Q Qiu, Bowen 655 Quagliarini, Enrico 1212, 1227 Quapp, Ulrike 1192 Quesada-Ganuza, Laura 1093 R R. Gulli, 156 Rapicavoli, Davide 566 Rastenis, Justinas 1204 Ravetllat, Pere-Joan 1031 Regan, O. Moreno 323 ˇ Rehák, Jakub 785 ˇ Rehák, Josef 785 Remus, Anna 170
1316
Riccio, Cristiana 170 Rihal, Satwant 1268 Riho, Hayashi 75 Roca, Pere 339 Rojas-Bravo, Julio 532 Roji, Eduardo 1093 Romano, Guido 1227 Romão, Xavier 1080, 1117, 1242 Romstedt, Friedrich 203 Ronen, Meir 472 Roselli, Francesco 1303 Rots, Jan G. 232 Rots, Jan 287, 603 Rovero, L. 505 S Sacco, Giulio Lucio Sergio 352 Salazar, L. Gerardo F. 1117 Salvalaggio, Matteo 472 Sandoval, Cristián 517 Santa-Cruz, Sandra 494 Saretta, Ylenia 245 Sasano, Shiro 63 Saxena, Deepika Ghosh 683 Sbrogiò, Luca 245 Scaletti, A. 641 Schaffer, Yaacov 472 Schiavoni, Mattia 484 Schmid, Benjamin 924 Sebera, Václav 617 Shakya, Manjip 125 Shimoda, Ichita 12 Shrestha, Kshitij C. 75 Shrive, Nigel G. 445 Siedler, Gunnar 203 Silva, Luis C. 170 Silva, Rui 1242 Skokandi´c, Dominik 724 Skuodis, Šar¯unas 1204 Smyrou, Eleni 1159 Šneideris, Arnoldas 1204 Somma, Fausto 312 Sorrentino, L. 278, 913 Sousa, Hélder 745 Standoli, Gianluca 484 Stepinac, Mislav 724, 1256 Su, Hung-Chi 1059 Subrin, D. 374 Suzuki, Hayato 26 Suzuki, Tomoaki 26
Author Index
Syojo, Naoya 112 Szkuta, Tomasz 970 T Tahuiton-Mora, A. 950 Takahashi, Hideaki 26 Takayoshi, Aoki 75 Takeda, Akisumi 3 Tamas, Emanuel I. 669 Tarque, Nicola 494 Tekieli, Marcin 873 Tenzin, Kunzang 75 Terao Voskova, Katarina 1042 Tezcan, Selman 170 Tikhonova, Olha 774, 1080 Torres, Wilson 517 Triantafillou, Thanasis C. 849 Trizio, Francesca 1067 Tse, Demiana 143 Tsumura, Shohei 51 Tudoreanu-Cris, an, Adrian 884, 959 Tung, Shu-Fen 1059 Tzeng, C. T. 1059 U Urland, Andrea
1042
V Valenzuela, María I. 517 Valer, Matt 532 Valivonis, Juozas 1204 Valluzzi, Maria Rosa 245, 472 Van Gemert, D. 763 Vanin, Francesco 400 Varela, Ainhoa 1031 Vegas, Fernando 1067 Verreydt, K. 763 Vetter, Sebastian 203 Villacreses, J. 1009 Villaverde, Ane 1093 Vima-Grau, Sara 1031 W Wan, Hoi Lon 556 Wang, Qianqing 591 Weber, Christiane 924 Wenzel, Baris 924 Wieser, M. 641 Wilkie, Simeon 899
Author Index
X Xu, Lingyan
1317
655
Y Yamada, S. 41 Yamaguchi, Kentaro 125 Yang, Hye Ri 195 Yang, Qingshan 301
Yépez, F. 1009 Yu, Pan 301 Z Zanazzi, Elena 1169 Zanni, Tatiana 245 Zhang, Zinan 217 Zizi, Mattia 1303