Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3) 9819915783, 9789819915781
This book presents select proceedings of the 17th Symposium on Earthquake Engineering organized by the Department of Ear
323 90 51MB
English Pages 762 [763] Year 2023
Contents
About the Editors
Investigation on Influence of Embedment Depth of Shallow Foundation on Seismic Response of Building Considering Soil–Structure Interaction
1 Introduction
2 Experimental Study
2.1 Prototype and Shake Table Characteristics
2.2 Scaling Ratio and Model
2.3 Input Ground Motions
2.4 Instrumentation
2.5 Testing Procedure
3 Results and Discussion
4 Summary and Conclusions
References
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand Through Bender Element Test
1 Introduction
2 Materials and Methods
3 Microbial Culture
4 Methodology
4.1 Preparation of Bio-Cemented Sand Specimens
4.2 Determination of Percentage of Calcium Carbonate
4.3 Details of Bender Element Test
5 Results and Discussions
5.1 Microstructure Analysis
5.2 Variation of Dry Density and CaCO3
5.3 Low-Strain Shear Wave Velocity of Bio-Cemented Sand
6 Summary and Conclusions
References
Seismic Site Characterization and Ground Response Analysis of Railway Line on Eastern Dedicated Freight Corridor
1 Introduction
2 Study Area Details
3 Correlation Between SPT-N and VS
4 Seismic Site Characterization
5 Ground Response Analysis
6 Conclusions
References
Earthquake-Induced Damage Assessment of Coal Mine Overburden Dump Slope Using Extended Finite Element Method Coupled with Voronoi Tessellation Scheme
1 Introduction
2 Theoretical Background of XFEM
3 Material Properties of the OB Dump Model
4 Coal Mine OB Dump Model Based on XFEM-Coupled Voronoi Tessellation Scheme
5 Results and Discussions
5.1 Amplification Ratio at Key Points of the OB Dump
5.2 Permanent Deformation at Key Points of the OB Dump Slope
6 Conclusions
References
Preliminary Studies on Developing a Physics-Based Smoothed Particle Hydrodynamics Model for Landslides
1 Introduction
2 Smoothed Particle Hydrodynamics: Concept and Formulations
2.1 Soil Constitutive Model
3 Problem Statement
3.1 Ground Motion
3.2 Soil Data for Daguangbao Site (Taken from Zhang et al. [20])
3.3 Methodology
4 Results and Discussions
4.1 Validation
4.2 Propagation of Daguangbao Landslide
5 Summary
References
Optimization of Single-Track PSC I-Girder for Metro Viaduct
1 Introduction
2 Methodology
2.1 Finite Element Analysis and Design of I-Girder
3 Result and Discussion
3.1 Cost of I-Girder for 20, 30 and 40 m Spans
3.2 Cost of 120 m Elevated Viaduct
4 Conclusion
References
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation
1 Introduction
2 Governing Equations
3 Nerical Modeling
3.1 Model Description
4 Results and Discussion
4.1 Verification
4.2 Dry and Wet Models’ Comparison in a 1D Soil Column
4.3 2D Idealized Embankment Geometry
5 Conclusions
References
Formulation of Response Reduction Factor for Wall-Type Bridge Piers
1 Introduction
2 Components of Response Reduction Factor
2.1 Over-Strength Factor (RS)
2.2 Ductility Reduction Factor (Rµ)
2.3 Redundancy Factor (RR)
3 Methodology
4 Numerical Study
5 Result and Discussions
6 Conclusions
References
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet Pile Driving
1 Introduction
2 Displacement Gradient Along the Ground Surface
3 Field Study—Preconstruction Survey
3.1 Site Location and Neighboring Structures
3.2 Geological Profile
3.3 Piling Details and Source of Vibration
3.4 Vibration Monitoring Instrument
4 Measurement of Ground Motion Data During Z Section Sheet Pile Driving
5 Dispersion Analysis
5.1 Rayleigh Wave Velocity or Phase Velocity (V2R or Vph)
5.2 Wave Propagation Time or Time Lag (tph ( fn ))
5.3 Phase Angle or Phase Difference (Δ2XY ( fn ))
5.4 Determination of Rayleigh Wave Velocity or Phase Velocity (m/s)
6 Results and Discussion
6.1 Peak Particle Velocity (mm/s) Versus Radial Distance (m)
6.2 Peak Particle Velocity (mm/s) Versus Pile Driving Depth (m)
6.3 Estimation of Shear Strain Magnitude (%)
7 Summary and Conclusion
References
Simulation of Interaction Properties in Confined Masonry Walls at Wall-to-Tie-Column Interface
1 Introduction
2 Interaction Models
3 Determination of Interaction Properties
3.1 Tension Bond Test (Normal Direction)
3.2 Triplet Shear Test (Tangential Direction)
3.3 Experimental Results
4 Finite Element Modeling and Analysis
4.1 Material Model
5 Calibration of Interaction Properties
5.1 Tension Bond Properties
5.2 Triplet Shear Test
6 Validation of Interaction Properties
7 Conclusions
References
Seismic Design of Periphery RC Beams in Buildings with Large Plan Aspect Ratio
1 Introduction
2 Numerical Study
3 Results and Discussion
3.1 Lateral In-Plane Deformation of Diaphragm
3.2 Axial Tensile Force
3.3 Increase in Area of Longitudinal Reinforcement in Periphery Beams
3.4 Increase in Transverse Reinforcement in Periphery Beams
4 Conclusion
References
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund Fault
1 Introduction
1.1 Objective of the Study
2 Methodology
2.1 General PSHA Formulation
2.2 PSHA Formulation for Permanent Ground Displacement
3 Case Study of Real Fault—Allah Bund Fault
3.1 Allah Bund Fault
3.2 Results and Discussions
4 Summary and Conclusions
References
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based Method
1 Introduction
2 PEER Framework
3 Proposed Framework for Risk-Targeted Importance Factors
3.1 Formulation of Risk-Targeted Importance Factor
3.2 Framework for Determination of Generalized Risk-Targeted Importance Factor
4 Example Assessment of Risk-Targeted Importance Factor
4.1 Analytical Models
4.2 Ground Motion Selection
4.3 Fragility Assessment
5 Results
5.1 Generalized Risk-Targeted Importance Factor for Example Buildings
5.2 Risk Margin Important and Critical Buildings as Per IS 1893–2016
6 Summary and Conclusions
References
Study of Liquefaction Potential at Jaigarh Port Using Standard Penetration Test Data and Consequences: A Case Study
1 Introduction
2 Study of Subsoil
3 Stratigraphy of the Region
4 Recorded Past Earthquake
5 Semi-Empirical Correlations with SPT (N)
6 Calculations, Results and Findings
6.1 Chinese Criteria [11]
7 Conclusion
References
Seismic Assessment of Tunnels in Near Fault Ground Motion
1 Introduction
2 Numerical Simulation
2.1 Two-Dimension Model Description
2.2 Three-Dimensional Model Description
3 Results and Discussion
4 Conclusion
References
Effect of Reinforced Soil Interaction with Other Components on Static and Dynamic Performance of MSE Wall
1 Introduction
2 Model Development
2.1 Backfill: Reinforced and Retained
2.2 Wall Facing
2.3 Reinforcements
2.4 Interfaces
2.5 Reinforcement–Wall Connections
3 Dynamic Analysis
3.1 Modal Analysis
3.2 Input Motion
3.3 Damping
4 Results
4.1 Lateral Deformation
4.2 Acceleration Amplification
4.3 Reinforcement Strains
5 Conclusions and Future Scope
References
Numerical Solution for 1-D Consolidation of Partially Saturated Soil Under Cyclic Loading
1 Introduction
2 Methodology
2.1 Governing Equation for Water Phase Based on Darcy’s Law [4, 5]
2.2 Governing Equation for Air Phase Based on Conservation of Mass [4, 5]
3 Problem Statement
4 Validation
5 Parametric Study
5.1 Effect of Ka/Kw
5.2 Effect of Loading
6 Conclusion
References
13 August 2021 Chenab River Coalescent Disaster: A Geo-informatics-Based Investigation
1 Introduction
2 Study Area
3 Data and Methodology
3.1 Datasets and Tools
3.2 Methodology
4 Results and Discussions
5 Conclusions
References
Numerical Simulation of Special Moment Resisting Frame with Reduced Beam Section Under Cyclic Load
1 Introduction
2 Building Archetype and Design
3 Numerical Modeling
3.1 Simulation for Validation of the Modeling Approach
3.2 Finite Element Modeling of Present Beam-Column Connection
4 Nonlinear Static Analysis
4.1 Modeling of Nonlinear Plastic Hinges
4.2 Pushover Analysis of Sample Steel SMRF with and Without RBS
5 Summary and Conclusions
References
Seismic Stability Analysis of Partially Saturated Slope Reinforced with Pervious Anti-slide Piles Subjected to Repeated Shaking Using Shaking Table Tests
1 Introduction
2 Material Used
2.1 Debris Soil
2.2 Model Development Methodology
3 Experimental Program
3.1 Slope Preparation and Instrumentation Scheme
3.2 Testing Conditions
4 Results and Discussion
4.1 Displacement of Slope
4.2 Acceleration Response of Slope
4.3 Porewater Pressure (PWP) Response
4.4 Structural Response During Repeated Shaking Events
5 Conclusion
References
Investigations on Rubber-Sand Mixture Reinforced with Geogrid as a Low-Cost Geotechnical Seismic Base Isolation Technique
1 Introduction
2 Building Details
3 Numerical Modeling
3.1 Validation of Model
4 Results and Discussions
4.1 Seismic Response Reduction by RSM
4.2 Seismically Induced Settlement Due to RSM
4.3 Effect of Earthquake Input Motion
5 Conclusions
References
Performance Evaluation of Partially Saturated Slope Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments
1 Introduction
2 Experimental Set-Up
2.1 Shake Table
2.2 Sample Preparation
2.3 2D-DIC Setup
3 Testing Condition
4 Numerical Modelling
5 Results and Discussion
5.1 Slope Settlement Using 2D-DIC
5.2 Acceleration Response on the Slope
5.3 Structure Response During Repeated Shaking Events
5.4 Pore Pressure Response
5.5 Numerical Modelling
6 Conclusion
References
Numerical Study on One-Dimensional Aperiodic Foundations for Seismic Isolation of Structures
1 Introduction
2 Proposed Aperiodic Foundation
3 Aperiodic Arrangements and Attenuation Results
4 Summary and Conclusion
5 Future Scope
References
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: An Analytical Approach for Natural Frequency Estimation
1 Introduction
2 Mathematical Model of Offshore Wind Turbine
2.1 Development of Governing Equations
2.2 Solutions for Governing Differential Equations
2.3 Formulation of Transfer Matrix
2.4 Boundary Conditions
3 Results and Discussions
3.1 Eigen Value Extraction
3.2 Validation Study
3.3 Mesh Convergence
4 Conclusions
References
Seismic Performance Assessment of Reinforced Concrete Moment Resisting Frame Designed by Force-Based Design Method and the Performance-Based Plastic Design Method
1 Introduction
2 Description of the Study Frame
3 Earthquake Forces
3.1 Earthquake Forces and Its Distribution in FBD Frames
3.2 Earthquake Forces and Its Distribution in PBPD Frames
4 Design of Sections
5 Seismic Performance Evaluation
6 Conclusion
References
Influence of Existing Tunnel—Surface Structure Interaction Under Repeated Dynamic Loading Conditions
1 Introduction
2 Experimental Programme
2.1 Uni-Axial Shaking Table Setup
2.2 Development of Scaled-Down Model Structures
2.3 Experimental Preparation
3 Results and Discussion
3.1 Acceleration Response of Interaction System
3.2 Effect of Settlement Response of Interaction System
3.3 Structural Deformations During Repeated Input Motion
3.4 Influence of Pore Water Pressures
4 Conclusion
References
Similitude Characteristics Between Small-Scale Model and Full-Scale Piles Under Dynamic Excitations
1 Introduction
1.1 Brief Review of the Scaling Law
2 Soil Properties and Small-Scale Model Preparation
2.1 Test Results
3 Scaling to Prototype
4 Conclusions
References
Numerical Simulations and Validation of a Rocking Foundation Model for Seismic Loading
1 Introduction
2 Performance Parameters of Rocking Foundations
3 Development and Validation of Numerical Model
4 Comparisons of Numerical Model Predictions for Performance Parameters with Experimental Results
5 Summary and Conclusions
References
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated Ground Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments
1 Introduction
2 Methodology
2.1 Uni-Axial Shaking Table
2.2 Soil Selected for the Experimental Study
2.3 Sample Preparation for Experimental Testing
2.4 Scaling Laws
2.5 Instrumentation
2.6 2D Digital Image Correlation Technique
3 Results and Discussions
3.1 Acceleration Response of Soil
3.2 Development of Pore Water Pressures in the Soil
3.3 Dynamic Earth Pressure
3.4 Effect of Displacement of Soil
3.5 Displacement and Strains Developed on the Tunnel
4 Conclusions
References
Assessment of Liquefaction Potential of Allahabad, India: A Future Smart City
1 Introduction
2 About Allahabad City and Its Development
3 Geology and Seismotectonic Setup
4 Standard Penetration Test Data
5 Determination of Peak Ground Acceleration for Allahabad
6 Methodology
7 Semi-Empirical Approach
8 Liquefaction Potential Index
9 Results and Discussions
10 Conclusions
References
Seismic Evaluation of Assam-Type Building Using ABAQUS®
1 Introduction
1.1 Region: Assam
1.2 History
1.3 Climate of the Region
1.4 Disasters
2 Methodology
3 Description of the Structure
3.1 Overview
3.2 Assam-Type House
4 Seismic Analysis of Assam-Type Building
4.1 Finite Element Software ABAQUS®
4.2 Finite Element Modelling
4.3 Plan of the House to Be Modelled in ABAQUS®
4.4 Structural Modelling in ABAQUS®
4.5 Response Spectrum Analysis
5 Conclusions
References
Suitability of Foam Concrete and Confined Masonry for Retaining Walls Application in Seismically Active Regions: A Review
1 Introduction
2 Potential of the Use of Confined Masonry in Retaining Walls
3 Potential of Interlocking Blocks for Use in Seismic Resistant Retaining Walls
4 Potential of Use of Foam Concrete in Seismic Resistant Confined Masonry Retaining Wall
5 Summary
References
Role of Hydrodynamic Forces on the Seismic Response of a Dam
1 Introduction
2 Methodology
2.1 Modeling of the Dam
2.2 Load Conditions
2.3 Frequency Analysis
2.4 Time History Analysis
3 Results and Discussion
3.1 Static Analysis
3.2 Seismic Analysis
4 Summary and Conclusions
References
2020 Tuipuiral Earthquake Review
1 Introduction
2 Seismotectonic of the Mizoram Region
3 Common Construction Practices
3.1 Traditional Timber Building Construction
3.2 Semi-Pucca Building Construction
3.3 Reinforced Concrete Construction
4 Field Observations and Observed Damages
4.1 Serchhip District
4.2 Ruantlang Rural Development Block
4.3 Khawbung RD Block
4.4 Zokhawthar
5 Other Effects
6 Isoseismal Map
7 Lesson Learnt and Remedial Measures
8 Conclusions
References
Experimental Investigations on the Pervious Concrete Piles in Saturated Ground Under Repeated Shaking Conditions
1 Introduction
2 Materials Characterization
2.1 Soil Characterization
2.2 The Pervious Concrete Development and Characterization
3 Experimental Methodology
3.1 Experimental Setup, Sand Bed Preparation
3.2 PCP Design and Installation
3.3 Testing Conditions
4 Results and Discussion
4.1 Influence of Excess Pore Water Pressure Ratio on Unreinforced and PCP Treated Ground
4.2 Effect of Incremental Acceleration on Ground Displacement and Foundation Settlement
5 Conclusion
References
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties of Gravel-Rubber Mixtures
1 Introduction
2 Test Materials and Procedure
3 Results and Discussion
3.1 Bender Element Tests
3.2 Small-Strain Cyclic Triaxial Tests
3.3 Analytical Hyperbolic Model
4 Conclusion
References
Numerical Evaluation of the Seismic Performance of GSI Foundation Systems for Buildings Using Gravel-Rubber Mixtures
1 Introduction
2 Finite Element GSI Model
3 Simulation Results and Discussion
4 Conclusion
References
A Critical Review on Soil Reliquefaction Resistance Using Physical Modelling Experiments
1 Introduction
2 Reliquefaction Studies
3 Factors Influencing Reliquefaction Resistance
3.1 Sample Preparation
3.2 Relative Density
3.3 Input Motion Characteristics
3.4 Preshaking History
4 Reliquefaction Resistance
5 Conclusions
References
Inclusion of Fatigue Checks in Current IS Codes for Monopole and Stack Structures
1 Introduction
1.1 General
1.2 Wind-Induced Fatigue Analysis
1.3 Factors Affecting Fatigue Life
2 Numerical Models
2.1 Case Study
3 Methodology
3.1 Past Literature and Country Standards
3.2 Adopted/Proposed Methodology
4 Numerical Example
4.1 Data Adopted
4.2 Solution
5 Conclusions
References
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil for Gulf of Khambhat Region
1 Introduction
2 Finite Element Modelling
3 Soil Model
4 Data Processing
5 Results and Discussion
6 Conclusions
References
Linear Spring Constants of Soil for Pile Groups for the Nuclear Power Plants
1 Introduction
2 Description of Single Pile and Pile Group
3 Verification of Single Pile Model
4 Verification of Pile Group Model
5 Conclusions
References
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static Seismic Load
1 Introduction
2 Numerical Study
3 FE Modeling and Analysis
4 Results and Discussion
5 Conclusions
References
Strength of Masonry Infill RC Frame Influenced by Weak and Strong Type RC Frames
1 Introduction
2 Finite Element Modelling
3 Validation of the Modelling Approach
4 Results and Discussion
5 Conclusions
References
Drained and Undrained Response of Fully Saturated Specimen in Resonant Column Tests Subjected to Large Number of Torsional Vibrations
1 Background
2 Sand Properties and Test Procedure
3 Results and Discussion
4 Summary and Conclusions
References
Development of Application Software for Lateral and Vertical Load Carrying Capacity of Piles
1 Introduction
2 General Formula for Calculation of Ultimate Load (Qu)
2.1 Piles in Cohesive Soils
2.2 Piles in Cohesionless Soils
2.3 Deflection and End Moment Under Lateral Loading
2.4 Determination of Pile Head Deflection Y, Moment M, Slope S and Soil Reaction P (Reese and Matlock)
3 Validation
3.1 Validation of Bearing Capacity of Single Vertical Pile in Single Layer Sand, Loaded Axially
3.2 Validation of Bearing Capacity of Single Vertical Pile in Multi-Layer Sand, Loaded Axially
3.3 Validation of Bearing Capacity of Vertical Pile in Single Layer Clay, Loaded Axially
3.4 Validation of Bearing Capacity of Vertical Pile in Multi-Layer Clay, Loaded Axially
3.5 Validation of Deflection, Moment, Slope, Soil Reaction of Vertical Pile, Loaded Laterally. (Reese and Matlock Method)
4 Development of Application Software CAP
5 Results and Discussion
6 Conclusion
References
Numerical Analysis of a Rigid Wall Retaining Soil Reinforced with C&D Waste
1 Introduction
2 Methodology
2.1 Material
2.2 Material Characterization/Properties
2.3 Numerical Modelling
3 Results and Discussion
4 Conclusions
References
Seismic Analysis of Railway Track
1 Introduction
2 Validation of FE Model of Railway Track
2.1 Beam on Elastic Foundation Model (BEF)
2.2 Finite Element Model
3 Various FE Models of Railway Track
3.1 Beam on Elastic Foundation (BEF) Model with Composite Beam (Model 1)
3.2 Track Model with Discrete Rails and Sleepers (Model 2)
3.3 Model with Rails, Sleepers, and Discrete Ballast (Model 3)
3.4 Comparison of Responses of the Three Models of Railway Track
4 Seismic Excitation Over Partial Length of Track
4.1 SAP2000 and ABAQUS® Results Comparison
4.2 FE Model Subjected to Seismic Excitation on Partial Length
4.3 Effect of Length Subjected to Seismic Excitation
5 Discussions and Conclusions
References
Time Series Analyses of Bhatwari Landslide Triggered by the 1991 Uttarkashi Earthquake
1 Introduction
2 Site Geology and Slope Profiles
3 Material Properties
4 Methodology and Analyses
5 Results and Discussions
6 Concluding Remarks
References
Importance of Multiple Geophysical Tests for Effective Subsurface Profiling
1 Introduction
2 Location of Study Area
3 Methods of Investigation
3.1 MHVSR
3.2 Multichannel Analysis of Surface Waves (MASW)
3.3 Seismic Crosshole Test
3.4 Seismic Downhole Test
4 Result and Discussion
5 Summary and Conclusions
References
Dynamic Characterization and Ground Response Analysis of Clay Soil Profiles
1 Introduction
2 Experimental Investigation
2.1 Materials
2.2 Geotechnical Properties
2.3 Bender Element Technique
3 Results and Discussions
3.1 Degree of Saturation and Confining Pressure
3.2 Density, Plasticity Index, and Cohesion
3.3 Ground Response Analysis
4 Conclusions
References
Effect of Vibration Induced by Dynamic Tests on an Adjacent Building—Finite Element Investigations
1 Introduction
2 Experimental Investigation
2.1 Measurements on the Pile Groups
2.2 Measurements at Different Levels of the Building
3 Integrated 2D FE Modelling
3.1 General Assumptions
3.2 Constitutive Model
3.3 Lateral Boundary Condition
3.4 Mesh Size and Element Type
3.5 Foundation Soil Interface
3.6 Loading
3.7 Response
4 Discussions and Conclusions
References
Liquefaction Susceptibility of Bottom Ash Under Cyclic Loading
1 Introduction
2 Experimental Investigation
2.1 Description of Material
2.2 Preparation of BA Samples
2.3 Test Procedure
3 Results and Discussions
3.1 Stress–Strain Response
3.2 Effect of Cyclic Axial Strain (εa) on the Excess PWP Generation in BA
3.3 Effect of Cyclic Axial Strain (εa) on Dynamic Shear Modulus (G) of BA
3.4 Effect of Cyclic Axial Strain (εa) on Damping Ratio (D) of BA
4 Conclusions
References
Soil-Structure Interaction Effect on a Multi-storied Building with Pile Foundation Considering Linear Approach
1 Introduction
2 Geometric Modelling
3 Material Properties
4 Characterization and Simulation of Earthquake Data
5 Results and Discussion
5.1 Evaluation of SSI Effects on Natural Frequency for Different Soil Models
5.2 Evaluation of SSI Effects on Displacement Values for Different Soil Models
5.3 Evaluation of SSI Effects on Storey Shear Distribution by Considering Soil as a Linear Spring
6 Conclusions
References
Geotechnical Characterization of Natural Sub-Base and Subgrade Material for Pavements
1 Introduction
2 Site Investigation and Location of Study Area
2.1 Surface Mining: An Overview
2.2 Site Location
3 Laboratory Testing
3.1 Natural Moisture Content
3.2 Grain Size Analysis
3.3 Atterberg Limits
3.4 Specific Gravity
3.5 Compaction Test
3.6 Large-Scale Direct Shear Test
3.7 California Bearing Ratio
4 Result and Discussion
5 Conclusion
References
Response of a Nuclear Containment with Soil Underneath Under Earthquake Excitation
1 Introduction
2 Methodology and Material
2.1 Loading and Boundary Conditions
3 Results and Validation
3.1 Frequency Analysis
3.2 Elastic Dynamic Response
3.3 Nonlinear Dynamic Response
3.4 Stress Analysis
4 Conclusions
References
Numerical Simulation of a Laminar Soil Box to Study Seismic SSI Effects of Nuclear Facilities
1 Introduction
2 Calibration of Model Parameters for Numerical Simulation
2.1 Calibration Using Static Triaxial Test of Sands
3 Selection of Input Motion and Estimation of Base Shear from 1D Analysis of Laminar Box
3.1 Estimation of Surface Acceleration and Base Shear from 1D Numerical Model of Laminar Box
4 2D FE Nonlinear Simulation of Laminar Box with Soil
5 Conclusions
References
Numerical Derivation of Pressure-Impulse Diagrams for a Fixed-End RC Beam Subjected to Blast Loads
1 Introduction
2 Analysis Models for RC Beam
2.1 SDOF Analysis
2.2 Finite Element Analysis
2.3 Development of P-I Diagrams and Possible Failure Modes
3 Results and Discussion
4 Conclusions
References
Seismic Evaluation of Building Having Steel-Concrete Composite Columns and RC Beams
1 Introduction
1.1 Outline of the Research
2 General Specifications for the Steel-Concrete Composite Section and Selected Building
2.1 Selection of the Steel-Concrete Composite Column Section
2.2 Specifications of the Selected Building
3 Nonlinear Seismic Evaluation of the Buildings
4 Results from Nonlinear Dynamic Analysis
4.1 Nonlinear Dynamic Analysis
5 Conclusion
References
Chaos Game Representation of Indian Plate Seismicity
1 Introduction
1.1 Iterated Function Systems
2 Method of Chaos Game Representation
3 Data
4 CGR of Earthquake Epicenters
5 Conclusions
References
A Fast Staggered Grid Finite Difference Modelling of Rayleigh Wave
1 Introduction
2 Methodology
3 Numerical Examples
3.1 Profile-A (Homogeneous Half-Space)
3.2 Profile B (Single Layer Overlaying Half-Space)
3.3 Profile-C (Six-Layer Model)
4 Conclusion
References
Calibration of UBC3D-PLM Constitutive Model to Simulate the Dynamic Response of Earthen Embankment Resting on Liquefiable Soil
1 Introduction
2 Computational Program
3 Fundamentals of the UBC3D-PLM Material Model's Constitutive Behaviour
4 Calibration of UBC3D-PLM Constitutive Model
5 Earth Embankment Resting on Liquefiable Ground: A Centrifuge Study
6 Conclusions
References
Recommend Papers
![Proceedings of the 17th annual ACM-SIAM symposium on discrete algorithms [SIAM ed.]
0898716055, 9780898716054](https://ebin.pub/img/200x200/proceedings-of-the-17th-annual-acm-siam-symposium-on-discrete-algorithms-siamnbsped-0898716055-9780898716054.jpg)
![Proceedings of the 4th International Conference on Performance Based Design in Earthquake Geotechnical Engineering (Beijing 2022) (Geotechnical, Geological and Earthquake Engineering, 52) [1st ed. 2022]
3031118979, 9783031118975, 9783031118982](https://ebin.pub/img/200x200/proceedings-of-the-4th-international-conference-on-performance-based-design-in-earthquake-geotechnical-engineering-beijing-2022-geotechnical-geological-and-earthquake-engineering-52-1st-ed-2022-3031118979-9783031118975-9783031118982.jpg)
![Evolution of Marine Coastal Ecosystems under the Pressure of Global Changes: Proceedings of Coast Bordeaux Symposium and of the 17th French-Japanese Oceanography Symposium [1st ed.]
9783030434830, 9783030434847](https://ebin.pub/img/200x200/evolution-of-marine-coastal-ecosystems-under-the-pressure-of-global-changes-proceedings-of-coast-bordeaux-symposium-and-of-the-17th-french-japanese-oceanography-symposium-1st-ed-9783030434830-9783030434847.jpg)
- Author / Uploaded
- Manish Shrikhande
- Pankaj Agarwal
- P. C. Ashwin Kumar
- Similar Topics
- Science (general)
- International Conferences and Symposiums
File loading please wait...
Citation preview
Lecture Notes in Civil Engineering
Manish Shrikhande Pankaj Agarwal P. C. Ashwin Kumar Editors
Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3)
Lecture Notes in Civil Engineering Volume 331
Series Editors Marco di Prisco, Politecnico di Milano, Milano, Italy Sheng-Hong Chen, School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China Ioannis Vayas, Institute of Steel Structures, National Technical University of Athens, Athens, Greece Sanjay Kumar Shukla, School of Engineering, Edith Cowan University, Joondalup, WA, Australia Anuj Sharma, Iowa State University, Ames, IA, USA Nagesh Kumar, Department of Civil Engineering, Indian Institute of Science Bangalore, Bengaluru, Karnataka, India Chien Ming Wang, School of Civil Engineering, The University of Queensland, Brisbane, QLD, Australia
Lecture Notes in Civil Engineering (LNCE) publishes the latest developments in Civil Engineering—quickly, informally and in top quality. Though original research reported in proceedings and post-proceedings represents the core of LNCE, edited volumes of exceptionally high quality and interest may also be considered for publication. Volumes published in LNCE embrace all aspects and subfields of, as well as new challenges in, Civil Engineering. Topics in the series include: • • • • • • • • • • • • • • •
Construction and Structural Mechanics Building Materials Concrete, Steel and Timber Structures Geotechnical Engineering Earthquake Engineering Coastal Engineering Ocean and Offshore Engineering; Ships and Floating Structures Hydraulics, Hydrology and Water Resources Engineering Environmental Engineering and Sustainability Structural Health and Monitoring Surveying and Geographical Information Systems Indoor Environments Transportation and Traffic Risk Analysis Safety and Security
To submit a proposal or request further information, please contact the appropriate Springer Editor: – Pierpaolo Riva at [email protected] (Europe and Americas); – Swati Meherishi at [email protected] (Asia—except China, Australia, and New Zealand); – Wayne Hu at [email protected] (China). All books in the series now indexed by Scopus and EI Compendex database!
Manish Shrikhande · Pankaj Agarwal · P. C. Ashwin Kumar Editors
Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3)
Editors Manish Shrikhande Department of Earthquake Engineering Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India
Pankaj Agarwal Department of Earthquake Engineering Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India
P. C. Ashwin Kumar Department of Earthquake Engineering Indian Institute of Technology Roorkee Roorkee, Uttarakhand, India
ISSN 2366-2557 ISSN 2366-2565 (electronic) Lecture Notes in Civil Engineering ISBN 978-981-99-1578-1 ISBN 978-981-99-1579-8 (eBook) https://doi.org/10.1007/978-981-99-1579-8 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Contents
Investigation on Influence of Embedment Depth of Shallow Foundation on Seismic Response of Building Considering Soil–Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vaibhav Mittal and Manojit Samanta
1
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand Through Bender Element Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nilanjana Banik and Rajib Sarkar
15
Seismic Site Characterization and Ground Response Analysis of Railway Line on Eastern Dedicated Freight Corridor . . . . . . . . . . . . . . . Sandhya Joshi and Aakash Kumar
27
Earthquake-Induced Damage Assessment of Coal Mine Overburden Dump Slope Using Extended Finite Element Method Coupled with Voronoi Tessellation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . Madhumita Mohanty, Rajib Sarkar, and Sarat Kumar Das Preliminary Studies on Developing a Physics-Based Smoothed Particle Hydrodynamics Model for Landslides . . . . . . . . . . . . . . . . . . . . . . . Nadia Mubarak and Ritesh Kumar Optimization of Single-Track PSC I-Girder for Metro Viaduct . . . . . . . . . A. S. Kidwai, I. Rahman, and Md. I. Ansari
39
51 65
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. M. George and S. Veeraraghavan
77
Formulation of Response Reduction Factor for Wall-Type Bridge Piers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Debaraj Bailung Sonowal and Jayanta Pathak
89
v
vi
Contents
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet Pile Driving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Vinoth and Ambarish Ghosh
99
Simulation of Interaction Properties in Confined Masonry Walls at Wall-to-Tie-Column Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Vaibhav Singhal, Amit K. Singh, and K. K. Fayaz Ahmed Seismic Design of Periphery RC Beams in Buildings with Large Plan Aspect Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 P. Bansode and R. Goswami Probabilistic Mapping of Ground Displacement Hazard for Allah Bund Fault . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 Phibe Khalkho and I. D. Gupta Risk-Targeted Seismic Design of Critical Buildings Using Force-Based Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Prakash Singh Badal and Ravi Sinha Study of Liquefaction Potential at Jaigarh Port Using Standard Penetration Test Data and Consequences: A Case Study . . . . . . . . . . . . . . . 171 Supratim Chanda, M. Kumar, Neeraj Kumar, and R. P. Shukla Seismic Assessment of Tunnels in Near Fault Ground Motion . . . . . . . . . . 185 Bhavesh Banjare and Swetha Veeraraghavan Effect of Reinforced Soil Interaction with Other Components on Static and Dynamic Performance of MSE Wall . . . . . . . . . . . . . . . . . . . . 199 Sajan Malviya and Prishati Raychowdhury Numerical Solution for 1-D Consolidation of Partially Saturated Soil Under Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 D. K. Singh, S. Mehndiratta, and R. J. Vishwakarma 13 August 2021 Chenab River Coalescent Disaster: A Geo-informatics-Based Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 D. K. Dwivedi, A. K. Saraf, and J. D. Das Numerical Simulation of Special Moment Resisting Frame with Reduced Beam Section Under Cyclic Load . . . . . . . . . . . . . . . . . . . . . . 231 A. H. Rangoonwala, S. Paul, and S. K. Deb Seismic Stability Analysis of Partially Saturated Slope Reinforced with Pervious Anti-slide Piles Subjected to Repeated Shaking Using Shaking Table Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 R. Ram Kumar, S. K. Jeeva, P. Madhiyarasu, and S. Ganesh Kumar Investigations on Rubber-Sand Mixture Reinforced with Geogrid as a Low-Cost Geotechnical Seismic Base Isolation Technique . . . . . . . . . 257 T. Suyal and R. M. Varghese
Contents
vii
Performance Evaluation of Partially Saturated Slope Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments . . . . . 269 S. K. Jeeva, M. D. Godson, and S. Ganesh Kumar Numerical Study on One-Dimensional Aperiodic Foundations for Seismic Isolation of Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Sanjay R. Kumawat, Sumiran Pujari, Manish Kumar, and Arghadeep Laskar Fluid-Soil-Structure Interaction of Offshore Wind Turbine: An Analytical Approach for Natural Frequency Estimation . . . . . . . . . . . 295 Somya Ranjan Patro, Arnab Banerjee, and G. V. Ramana Seismic Performance Assessment of Reinforced Concrete Moment Resisting Frame Designed by Force-Based Design Method and the Performance-Based Plastic Design Method . . . . . . . . . . . . . . . . . . . 307 R. Vyas and A. I. Shirkol Influence of Existing Tunnel—Surface Structure Interaction Under Repeated Dynamic Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . 329 M. D. Godson, S. Ganesh Kumar, and J. Visuvasam Similitude Characteristics Between Small-Scale Model and Full-Scale Piles Under Dynamic Excitations . . . . . . . . . . . . . . . . . . . . . . 345 Shiva Shankar Choudhary, Sanjit Biswas, and Bappaditya Manna Numerical Simulations and Validation of a Rocking Foundation Model for Seismic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 S. Soundararajan, S. Gajan, and P. Raychowdhury Experimental Studies on Tunnel-Soil Interaction in Partially Saturated Ground Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 K. S. Amith, S. Ganesh Kumar, and M. D. Godson Assessment of Liquefaction Potential of Allahabad, India: A Future Smart City . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 Keshav Kumar Sharma, Kumar Pallav, Manjari Singh, Ashhad Imam, and Alvin Harrison Seismic Evaluation of Assam-Type Building Using ABAQUS® . . . . . . . . . 397 P. Boruah and A. K. Dutta Suitability of Foam Concrete and Confined Masonry for Retaining Walls Application in Seismically Active Regions: A Review . . . . . . . . . . . . 413 Abhishek Kamisetty, Abhishek Kumar, and Indu Siva Ranjani Gandhi Role of Hydrodynamic Forces on the Seismic Response of a Dam . . . . . . 423 Dhananjay Vyas, Jithin P. Zachariah, Alla Kranthi Kumar, and Ravi S. Jakka
viii
Contents
2020 Tuipuiral Earthquake Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 R. Ramhmachhuani, C. Lallawmawma, H. Laldintluanga, M. L. Sharma, K. Seshagiri Rao, A. K. Jain, and Laldinpuia Experimental Investigations on the Pervious Concrete Piles in Saturated Ground Under Repeated Shaking Conditions . . . . . . . . . . . . 453 R. V. Yogesh, S. Ganesh Kumar, and G. Santha Kumar Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties of Gravel-Rubber Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Gabriele Chiaro, Ali Tasalloti, Alessandro Palermo, and Laura Banasiak Numerical Evaluation of the Seismic Performance of GSI Foundation Systems for Buildings Using Gravel-Rubber Mixtures . . . . . 479 Davide Forcellini, Gabriele Chiaro, Alessandro Palermo, and Laura Banasiak A Critical Review on Soil Reliquefaction Resistance Using Physical Modelling Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 Gowtham Padmanabhan and B. K. Maheshwari Inclusion of Fatigue Checks in Current IS Codes for Monopole and Stack Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 K. A. Sahakari, S. U. Talankar, and Y. K. Gaude Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil for Gulf of Khambhat Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 R. Singh Sujawat and R. Kumar Linear Spring Constants of Soil for Pile Groups for the Nuclear Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Mohd Firoj and B. K. Maheshwari Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static Seismic Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 V. Sharma, D. Raj, and R. Gupta Strength of Masonry Infill RC Frame Influenced by Weak and Strong Type RC Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Kaushal P. Patel and R. N. Dubey Drained and Undrained Response of Fully Saturated Specimen in Resonant Column Tests Subjected to Large Number of Torsional Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 Ninad Sanjeev Shinde and Jyant Kumar Development of Application Software for Lateral and Vertical Load Carrying Capacity of Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 Aditya Patil and Shrabony Adhikary
Contents
ix
Numerical Analysis of a Rigid Wall Retaining Soil Reinforced with C&D Waste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 A. R. Prajapati and H. M. Rangwala Seismic Analysis of Railway Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 A. S. Ghogre, H. D. Phadke, and O. R. Jaiswal Time Series Analyses of Bhatwari Landslide Triggered by the 1991 Uttarkashi Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609 Neha Gupta, Josodhir Das, and D. P. Kanungo Importance of Multiple Geophysical Tests for Effective Subsurface Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619 Ravinesh Kumar, P. Anbazhagan, and Ayush Kumar Dynamic Characterization and Ground Response Analysis of Clay Soil Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 K. Rangaswamy Effect of Vibration Induced by Dynamic Tests on an Adjacent Building—Finite Element Investigations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 M. Bharathi, Dhiraj Raj, and R. N. Dubey Liquefaction Susceptibility of Bottom Ash Under Cyclic Loading . . . . . . 655 L. Abhijith, K. Rangaswamy, and Renjitha Mary Varghese Soil-Structure Interaction Effect on a Multi-storied Building with Pile Foundation Considering Linear Approach . . . . . . . . . . . . . . . . . . 667 S. Banerjee and K. Bhattacharya Geotechnical Characterization of Natural Sub-Base and Subgrade Material for Pavements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681 A. Kumar, S. K. Kumawat, M. Jain, S. Dangayach, D. Raj, and H. K. Sharma Response of a Nuclear Containment with Soil Underneath Under Earthquake Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 Charity Marbaniang and Kamal Bhattacharya Numerical Simulation of a Laminar Soil Box to Study Seismic SSI Effects of Nuclear Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 R. Banerjee, S. Bandyopadhyay, Y. M. Parulekar, and J. Chattopadhyay Numerical Derivation of Pressure-Impulse Diagrams for a Fixed-End RC Beam Subjected to Blast Loads . . . . . . . . . . . . . . . . . . 723 Ravi Mudragada, Ankit Agrawal, and Pradeep Bhargava Seismic Evaluation of Building Having Steel-Concrete Composite Columns and RC Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735 R. C. Mukhedkar and A. P. Khatri
x
Contents
Chaos Game Representation of Indian Plate Seismicity . . . . . . . . . . . . . . . 747 Cyril Shaju and Kamal Kamal A Fast Staggered Grid Finite Difference Modelling of Rayleigh Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757 Mrinal Bhaumik and Tarun Naskar Calibration of UBC3D-PLM Constitutive Model to Simulate the Dynamic Response of Earthen Embankment Resting on Liquefiable Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771 Abhijit Chakraborty and V. A. Sawant
About the Editors
Dr. Manish Shrikhande is Professor and Head of the Department of Earthquake Engineering at Indian Institute of Technology Roorkee. His current research interests are vibration monitoring and control, seismic risk and mitigation, and computational mechanics. Dr. Pankaj Agarwal is Professor at the Department of Earthquake Engineering, Indian Institute of Technology Roorkee. His research interests are earthquakeresistant design of masonry and RC structures, post-damage assessment survey of earthquake-affected areas, risk assessment, cyclic testing of structures, seismic instrumentation in multi-storied buildings, health monitoring, and damage detection in buildings. He is continuously engaged in research on structurally sound and seismically efficient construction and has published several research papers in national and international journals and conferences/seminars/symposia. Dr. P. C. Ashwin Kumar is Assistant Professor at the Department of Earthquake Engineering, Indian Institute of Technology Roorkee. He has been engaged in teaching and research in earthquake-resistant design of steel structures, development of passive devices for seismic protection, vulnerability assessment, and retrofitting of structures.
xi
Investigation on Influence of Embedment Depth of Shallow Foundation on Seismic Response of Building Considering Soil–Structure Interaction Vaibhav Mittal
and Manojit Samanta
Abstract Embedment depth of foundation plays significant role on the seismic response of the superstructures. The present study investigates the effect of embedment depth of shallow foundation on the seismic response of building through the scaled-down test. A scaled-down model of five-storey and shallow foundations of different embedment depths (75, 150, 300, and 600 mm) has been used in the present study. All the model tests are conducted through shake table testing in laminar shear box. The model is subjected to scaled-down earthquake motions. The seismic response of the building has been estimated and expressed in terms of amplification ratio, maximum lateral displacement, interstorey drift, and rocking of the foundation. The test results indicate that the change in embedment depth of the foundation has a significant effect on lateral displacement, interstorey drift, and rocking of the foundation. It is found that lateral displacement, interstorey drift, and rocking of the foundation for the maximum embedment depth (600 mm) are reduced by 70%, 74%, and 41%, respectively, when compared with smallest embedment depth of foundation (75 mm). Keywords Shake table · Model · Shallow foundation · Earthquake · Seismic amplification
1 Introduction The overall performance of a building during any seismic excitation is characterized by the interaction between the foundation and the structure. Generally, the structures V. Mittal · M. Samanta (B) GEGH Group, CSIR—Central Building Research Institute (CSIR—CBRI), Roorkee, India e-mail: [email protected] V. Mittal e-mail: [email protected] Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_1
1
2
V. Mittal and M. Samanta
are founded on stiff soil or rock and designed as fixed base with ignorance of soil– foundation–structure interaction (SFSI) effects [15]. However, ignorance of these effects may cause permanent displacement, distortion, or distress to the soil–structure system during any seismic excitations. Past earthquakes such as Bihar-Nepal Earthquake 1934, Alaska and Niigata Earthquake 1964 show the damage in approximately 340 reinforced concrete (RCC) building, founded on shallow foundation, supported by uniform fine sand [2, 17, 20]. A settlement of approx. 0.25–2.5 m has been observed in the damaged building. Tokimatsu et al. [22] reported significant settlement in most of the buildings among 120 damaged RCC buildings resting on shallow foundations in Dagupan City. Hokmabadi et al. [12] studied the influence of shallow foundation and floating pile foundation on the seismic response of mid-rise buildings. The results show that the lateral displacement of the building supporting shallow foundation is more in comparison to the floating pile foundation. Pavan et al. [18] studied the influence of soil–structure interaction for framed structures supported on shallow foundation and found that foundation with lower subgrade reactions leads to larger amplification. Storie et al. [21] studied the effect of the sizes of shallow foundation on seismic response of buildings and found that the larger size foundation provides less amplification. Bagheri et al. [3] compare the response of shallow foundation and pile foundation supporting mid-rise and high-rise steel buildings through numerical investigation. The result shows that the building supported on shallow foundation exceeds the life-safe limit for the performance-based seismic design. The above literature shows that the seismic response of structures depends on a number of factors, such as embedment depth of the foundation, position of water table, geometry of the building, ground motion characteristics with different fault mechanisms, and existing soil conditions. Studies on buildings on the shallow foundations in the recent earthquake show that during large earthquake shaking, uplift of shallow foundation and plastic deformation of the existing soil controls the performance of the building. However, studies on influence of embedment depth and amount of rotation of the foundation caused due to large shaking are not well explored. The present study investigates the influence of embedment depth on the seismic response of regular structure considering soil–foundation–structure interaction through shaking table tests.
2 Experimental Study 2.1 Prototype and Shake Table Characteristics A five-storey prototype building, 15 m high and 4 m wide with one span in each direction, is selected. The sizes of the column and beam obtained are 990 × 990 mm. Slabs of thickness 150 mm have been used in the prototype structure. The prototype is made of reinforced concrete structure. The building is supported on
Investigation on Influence of Embedment Depth of Shallow Foundation …
3
shallow foundation of size 2 × 2 m, having an embedment depth of 1.5 m, giving D/B ratio of 0.75. However, in order to perform parametric analysis, several larger embedment depths have been used in the present study. The geometric and material characteristics of the components of the prototype structure are found to be safe against different load combinations, as per [14]. The time period of the prototype building is 0.19 s. The soil medium beneath the structure is sandy soil, having a unit weight of 15.4 kN/m3 and a shear wave velocity of 246.63 m/s. Sieve analysis, Pycnometer test, Vibrating table test, Constant head test, and Monotonic shear test have been performed to estimate the index and engineering properties of the soil. Figure 1 shows the particle-size distribution of the soil used. Minimum and maximum dry unit weights of the sand are 14.06 and 16.45 kN/m3 , respectively. The soil sample is classified as poorly graded sand or SP (coefficient of curvature, C c = 0.80; coefficient of uniformity, C u = 1.87) [5]. Table 1 represents the properties of the soil. The experimental investigation has been conducted using the uniaxial shaking table available at the geotechnical laboratory of CSIR–CBRI, Roorkee. The size of the shaking table is 2 × 2 m, with a stroke length of ± 160 mm and maximum payload of 35 kN. The testing frequency range of the shaking table is 0.1–100 Hz and maximum acceleration of 10 g with no payload and 0.005 g with 35 kN of payload. Fig. 1 Particle size distribution curve
Table 1 Properties of soil
Properties
Values
Sand (%)
97.00
Fines (%)
3.00
Cohesion (kPa) @ 45% RD
11
Cohesion (kPa) @ 65% RD
2
Friction angle (º) @ 45% RD
36
Friction angle (º) @ 65% RD
40
4
V. Mittal and M. Samanta
2.2 Scaling Ratio and Model Model tests offer the benefit of simulating complex systems under controlled conditions, helping to understand the realistic behavior/mechanism of the soil–structure system. Shaking table tests are considered as 1 g modeling, in which the acceleration of the scaled-down model and prototype remains same. A dynamic similitude relationship between the scaled-down model and prototype has been used, as shown in Table 2 [24]. A geometric scaling factor (N) of 1:20 is selected based on the specifications of the available shaking table. According to Table 2, the required time period for the scaled-down model should be 0.0424 s. Also, the shear wave velocity and unit weight for the scaled-down soil medium should be 55.15 m/s and 15.04 kN/m3 , respectively. Based on the scaling relationships, the length, width, and height of the scaleddown structure are found to be 200 mm, 200 mm, and 750 mm, respectively, as shown in Fig. 2. Angle sections (25 × 25 × 3 mm) of aluminum (E = 76 GPa) are used for the fabrications of beams and columns of the scaled-down building, while the floor consists of 200 × 200 × 3 mm aluminum plates. Metal screw is used to rigidly connect the floors, columns, and beams. The total weight of the modeled structure is found to be 37.96 N. Each column of the building is supported on a shallow foundation [made of mild steel (MS)] of size 100 mm × 100 mm and varying depths of embedment (ED). Four different embedment depths, i.e., 75, 150, 300, and 600 mm, have been used in this study, as shown in Figs. 2 and 3. MS bolts are used to connect the foundation with the scaled-down building rigidly. The laminar shear box used during the test is an aluminum tank of dimension 1200 mm × 800 mm × 1200 mm. The shear box consists of 24 rectangular laminas placed at equal spacing, supported over rollers in direction of shaking, which are stiffened over an iron stand on both sides, as shown in Fig. 3b. This allows the tank to move freely in the direction of shaking. However, the tank has the rigid boundaries on the other two sides, while the bottom of tank is rested over a base plate of mild steel (MS), which is fixed over the shaking table using six bolts. A 2-mm thick polystyrene (PS) sheet has been provided inside the container, to maintain uniformity and avoid spillage of soil from the container. Also, the side walls of the laminas, parallel to the shaking direction, are lubricated properly to avoid the generation of shear stress Table 2 Scaling relationship in terms of scaling factor (N)
Parameter
Scaling relationship
Density
1
Acceleration
1
Length
N
Stress
N
Frequency
N −1/2
Time
N 1/2
Flexural rigidity
N5
Investigation on Influence of Embedment Depth of Shallow Foundation …
5
Fig. 2 Cross-sectional details of the scaled-down model
Fig. 3 Details of experimental study a fixed-base study, b complete setup with shallow foundation
between the laminas and rollers. The lateral dimension (1200 mm) of the tank is approx. 6 times the total area of the scaled-down model. Therefore, the effect of artificial boundaries on the seismic behavior of the building is insignificant [11]. Figure 3b shows the complete experimental setup used in this study. A free-field response analysis for the prototype has been performed and found that the variation of lateral displacement along the height of the container under empty and filled conditions shows a good match with the free-field response. Hence, the developed model minimizes the boundary and side wall effects due to the reflection of seismic waves.
6
V. Mittal and M. Samanta
Table 3 Characteristics of input ground motion Parameter
Magnitude (Mw)
PGA (g)
Hypocentral distance (km)
Type
Arias intensity (m/s)
El Centro 1940
7.65
0.281
8.8
Near Field
1.556
Fig. 4 Details of input ground motion a scaled El Centro Earthquake (1940), b frequency domain
2.3 Input Ground Motions The ground motions used in this study are real-time earthquakes recorded at the bedrock level. All models are subjected to a near-field El Centro (1940) earthquake, obtained from Pacific Earthquake Engineering Research (PEER) ground motion database [20]. Table 3 provides the characteristics of recorded ground motion used in this study. Considering the scaling laws, the imposed earthquake excitation has also been scaled down, reducing the time interval by a factor of 4.47 (N 1/2 , N = 1/20), though the magnitude of earthquake remains same. Figure 4a shows the acceleration time record of the scaled El Centro earthquake. The dominant frequency of the scaled-down earthquake obtained by Fast Fourier Transformation is 6.58 Hz, as shown in Fig. 4b.
2.4 Instrumentation Five laser displacement sensors (LDSs), six accelerometer transducers (ATs), and a 32-channel data acquisition system (DAS) have been used during the test. The LDS operates with a semiconductor laser with a wavelength of 670 nm, which works on the principle of optical triangulation, i.e., a visible, modulated point of light is projected onto the target surface. The measuring range of the LDS used is 200 mm. The AT is an oil damping-type waterproof transducer, having a measuring range equal to 5 g. Four ATs are initially installed in the laminar shear box at vertical intervals of 400 mm to measure the variation of acceleration, as shown in Fig. 5a. However, when scaleddown foundation–building model is placed inside the laminar box at required depth
Investigation on Influence of Embedment Depth of Shallow Foundation …
7
Fig. 5 Schematic representation of sensors a container with soil, b complete setup
of embedment, the arrangement of sensors/transducers has been done at different positions, as shown in Fig. 5b. Further, AT is used to measure the acceleration at the two locations within the soil, base of footing, plinth level, and different floor levels (first and fifth), whereas LDS is used to measure the lateral displacement of the building at each floor level, as shown in Fig. 5b. The DAS consists of a data logger, display unit, and communication ports/channels. The communication ports connect the data logger to the display unit, which records the data and helps the user to interpret the required information. The logging frequency of 1.2 kHz is used to record and store the data.
2.5 Testing Procedure The shaking table tests are carried out for two cases: initially, the scaled-down model is fixed on the top of the table to simulate the fixed base (FB) conditions, as shown in Fig. 3a. Two accelerometers and five laser displacement sensors (at each floor level) are used to estimate the dynamic response of the structure, as shown in Fig. 3a. A sine sweep test is performed to determine the time period of the system and is found to be 0.046 s, which is in good agreement with desired time period of the structural model (0.0424 s). The natural frequency of the structure obtained is less than the dominant frequency of the earthquake (6.58 Hz); hence, the effects of resonance have not been considered in this study. A free vibration test has also been performed to determine the structural damping and is found to be 0.42% obtained using Taylor series expansion [8]. Subsequently, a time history analysis has been performed by applying the scaleddown earthquake on the table, and variation in lateral displacement at each floor level is estimated.
8
V. Mittal and M. Samanta
The second case of the experimental investigation is to study the influence of embedment depth of shallow foundation under the seismic excitation. After installing the laminar soil container on the shaking table, sand is filled in the laminar shear box in a series of 50 mm lifts. The quantity of soil essential for every lift to achieve the relative density is measured. The required amount of soil has been poured, and the in-situ density has been estimated at the four corners of the box by sand replacement method [6]. The entire filling of the soil in the container is completed in one day and has been left for 24 h to achieve a static equilibrium condition. Four accelerometers are installed inside the soil at an equal interval of 400 mm, to determine the variation of acceleration within the soil, as shown in Fig. 5a. A sine sweep test has been performed on empty and filled laminar box to obtain the natural frequency and is found to be 11.64, and 11.54 Hz, which is in good agreement with the predicted value (11.49 Hz). Five LDSs and six ATs are installed at different locations to measure the response of the foundation–building model, as shown in Fig. 5b.
3 Results and Discussion The following section describes the variation in acceleration at different locations inside the soil medium only, the variation in peak ground acceleration (PGA) amplification factor, lateral displacement and interstorey drift of the building, and rocking of the foundation obtained from the experimental investigation for different embedment depths of shallow foundation. The PGA amplification factor has been calculated as the ratio of PGA at the ground level of the building to the PGA at the base of the laminar shear box. The lateral displacement at each floor level is obtained by subtracting the displacement of the table, i.e., all the displacements are relative to base motions. The interstorey drift has been calculated using the following relationship: Drift(%) =
(LDi+1 −LDi ) × 100, h
(1)
where LDi+1 and LDi = lateral displacement at i + 1 and ith level, respectively, and h = height of the storey. Figure 6a shows the typical variation of acceleration across the soil depth. With regards to the influence of effects of SSSI, the ground amplification of the input motion, also known as site amplification, plays a significant role in influencing the response of the structures. Heidebrecht et al. [10] studied the influence of local site effects at Mexico City during 1985 earthquake and found that site amplification has led to severe damage to the buildings. They reported several factors such as high moisture content, plasticity index, low shear modulus and damping, and lesser intensity of excitation at rock level which have led to site amplification. Meli et al. [16] studied the variation of amplification at different levels of a building in Mexico, located on clayey bed, and found that the amplification of the motion at the ground level is almost 2.6 times the motion at the base of the deposits. They found that
Investigation on Influence of Embedment Depth of Shallow Foundation …
9
as the seismic wave travels across the soil medium, the acceleration of the wave gets amplified, depending on the frequency content of the earthquake. Generally, seismic waves travel faster through hard rocks than sediments and soils. Due to the absorption of seismic energy through sediments/soil deposits, the amplitude of the waves increases. The PGA at the base of the table is 0.281 g. The test results indicate that when the seismic wave reaches the top of the soil, the PGA increases by approx. 28%, as shown in Fig. 6a. However, on increasing the density of the sand (65% RD), the PGA at the top reduces by approx. 6% when compared with 45% RD. The amplification is influenced by the presence of the structures also. Guéguen and Bard [9], Meli et al. [16] studied the influence of presence of structure on amplification of input ground motions and found that the motion at the plinth and roof level is almost 2.6 and 3 times the input motion at the base of deposit and plinth level, respectively. In the present study, the variation in PGA amplification factor has been calculated as the ratio of PGA at the plinth level to the PGA at the base of the table, as shown in Fig. 6b. The test results show that with change in embedment depth (ED) of foundation from 75 to 150, 300, and 600 mm, the corresponding PGA at the plinth level is 0.36 g, 0.33 g, 0.32 g, and 0.31 g, respectively. The test results also indicate that the amplification at the plinth level for larger embedment depth of foundation (ED = 600 mm) is reduced by 13.34% in comparison to smaller embedment depth of foundation (ED = 75 mm). The reduction in PGA for larger embedment depth has occurred due to the greater resistance offered by surrounding soil, which reduces Fig. 6 a Variation of site amplification at 45% RD, b variation of PGA amplification factor
10
V. Mittal and M. Samanta
the amount of seismic energy absorbed. This leads to decrease in amplification of the building supported on larger embedment depth of foundation. Figure 7a shows the comparison between the peak storey displacements at each floor level for 45% RD. The maximum lateral deflection of the fixed-base building is 1.48 mm. The test results indicate that with change in the embedment depth (ED) from 75 to 150, 300, and 600 mm, the corresponding maximum lateral displacement is 9.53 mm, 7.63 mm, 4.92 mm, and 2.93 mm, respectively. The lateral displacement of the building supported on larger embedment depth of foundation (ED = 600 mm) reduces by approx. 70%, in comparison with the smaller embedment depth (ED = 75 mm). The decrement in lateral displacement has occurred due to increase in the resistance offered by the surrounding soil for larger embedment depth. Wolf [23] studied the influence of relative density of soil on response of the building and found that the lateral displacement/drift reduces with increase in relative density. A similar observation has been made by Hwang et al. [13], who measured the influence of variation in relative densities on the response of urban sites and structures. The test results indicate that on increasing the denseness of the soil, the lateral displacement of the building has decreased substantially. The maximum lateral displacement is observed to decrease almost by 24.99%, 21.96%, 13.12%, and 4.07% for embedment depth of 75, 150, 300, and 600 mm, respectively, for 65% RD in comparison to 45% RD as shown in Fig. 7b. Figure 8a shows the typical variation of interstorey drift at each floor level for fixed-base and shallow foundation of different embedment depths. The maximum interstorey drift for the fixed-base building is 0.26%. The test results indicate that with change in the embedment depth (ED) from 75 to 150, 300, and 600 mm, the corresponding maximum interstorey drift is 1.75%, 1.58%, 0.92%, and 0.46%, respectively. The maximum interstorey drift of the building supported on different embedment depths has increased on an average by 71% with respect to fixed-base structures. However, on increasing the density of the soil, the maximum interstorey drift is observed to decrease significantly. The maximum interstorey drift is observed to decrease by 34%, 30%, 18%, and 15% for embedment depth of 75, 150, 300, and 600 mm, respectively, for 65% RD in comparison to 45% RD as shown in Fig. 8b.
Fig. 7 a Typical variation of lateral displacement at 45% RD, b variation of maximum lateral displacement
Investigation on Influence of Embedment Depth of Shallow Foundation …
11
Fig. 8 a Typical variation of interstorey drift at 45% RD, b variation in maximum interstorey drift
This parameter also helps in governing the performance level of the building. To ensure the safety of the building, different seismic design standards provide a limiting value for the performance level of the building based on interstorey drift. For instance, FEMA 243/273 [4] describes the performance level of any building as fully operational (< 0.2%), operational (< 0.5%), life safe (< 1.5%), near collapse (< 2.5%), or collapse (> 2.5%), on the basis of quantitative estimation of the interstorey drift. The Indian standard limits the interstorey drift to 0.4% of the floor height [14]. Similarly, ASCE 7-22 [1] limits the total storey drift to 1.5–2.5% depending on the occupancy category for the moment-resisting framed buildings. The vertical and horizontal lines (purple color) show the permissible limit for the range of interstorey drift according to different design standards in Fig. 8. The test results for 45 and 65% RDs indicate that the interstorey drift for the buildings supported on shallow foundation with embedment depth 75, 150, and 300 mm exceeds the life-safe limit. The performance level of the structure may shift the performance of the building from life-safe limit to collapse or nearly collapse conditions. However, the structure supported on shallow foundation with 600 mm embedment comes under the category of operational, when the RD of the soil is increased to 65%. Hence, it may be concluded that the performance level of soil–structure system should be considered to obtain the actual deformability of the structure. The rocking component of the foundation is one of the major factors in estimating the lateral displacement of the structure. The structural lateral displacement during any seismic excitation generally consists of two components, namely rocking and translation components. Celebi and Safak [7] studied the seismic response of Transamerica building at San Francisco during Loma Prieta Earthquake (1989) and reported that rocking of foundation has significantly influenced the motions at the basement and ground, although the magnitude of rocking is very small. Figure 9 shows the variation in rocking angle of the shallow foundation for different embedment depths and relative densities of the soil. The results indicate that on average 36.03% of the maximum lateral deflection recorded is a result of rocking component, while 63.97% has occurred due to translation component. The rocking in shallow foundation occurs due to the generation of inertial forces in superstructure, which causes compression/settlement on one side and tension/uplift on the other side. The
12
V. Mittal and M. Samanta
Fig. 9 Variation in rocking of foundation
test results indicate that with change in the embedment depth (ED) from 75 to 150, 300, and 600 mm, the corresponding maximum rocking of foundation is found to be 0.2°, 0.17°, 0.14°, and 0.12°, respectively. The maximum rocking of foundation for larger embedment depth (ED = 600 mm) reduces 41%, in comparison with the smaller embedment depth (ED = 75 mm). Due to higher contact surface area with the surrounding soil, the larger embedment depth experiences more friction and passive resistance in comparison to smaller embedment depth. Hence, on increasing the embedment depth of foundation, the rocking of the foundation has reduced substantially. Similarly, on increasing the relative density of the soil, rocking of the foundation has reduced substantially, as shown in Fig. 9. The maximum rocking of foundation is observed to decrease by 27%, 26%, 19%, and 17% for embedment depth of 75, 150, 300, and 600 mm, respectively, for 65% RD in comparison to 45% RD as shown in Fig. 9.
4 Summary and Conclusions This study aims at evaluating the influence of different embedment depths of shallow foundation on seismic response of building considering soil–structure interaction. The experimental tests have been conducted on uniaxial shaking table. Based on the adopted study and parameters considered, the following conclusions are drawn: . The study on the influence of embedment depth of shallow foundation shows that the acceleration amplification factor for larger embedment depth (600 mm) is observed to reduce by 13.34%, compared with smaller depth of embedment (75 mm). This study shows that shallow foundation with larger embedment depth experiences larger resistance from the surrounding soil and hence leads to reduction in acceleration amplification factor. . The lateral displacement of the building consists of two components: foundation rocking and translation. The present study shows that the maximum rocking of foundation for larger embedment depth of foundation (ED = 600 mm) reduces by 41%, in comparison with the smaller embedment depth (ED = 75 mm). The
Investigation on Influence of Embedment Depth of Shallow Foundation …
13
reduction in rocking has occurred due to higher frictional and passive resistance offered by the surrounding soil to the foundation with larger embedment depth. . The results also show that the structure supported on shallow foundation with 600 mm embedment, resting over sandy stratum with 65% RD, only satisfies the permissible limit for the performance-based seismic design. However, the results obtained for all other cases show that embedment depth of foundation affects the performance level of building which exceeds life-safe limit. Acknowledgements VM [IF190173] acknowledges the financial support from DST under a unique scheme “INSPIRE” during the present work. The authors are grateful to the Director, CSIR–CBRI, for providing the experimental facilities to complete this study. The authors are also grateful to Mr. Abishek RR for the assistance provided during the work.
References 1. ASCE: Minimum Design Loads for Buildings and Other Structures. ASCE/SEI 7-22. American Society of Civil Engineers, Virginia (2022) 2. Auden, J.B., Dunn, J.A., Ghosh, A.M.N., Wadia, D.N., Roy, S.C.: The Bihar-Nepal earthquake of 1934. Memoirs Geol. Surv. India 73, 1–391 (1939) 3. Bagheri, M., Jamkhaneh, M.E., Samali, B.: Effect of seismic soil–pile–structure interaction on mid-and high-rise steel buildings resting on a group of pile foundations. Int. J. Geomech. 18(9), 04018103 (2018) 4. BSSC (Building Seismic Safety Council): NEHRP Guidelines for the Seismic Rehabilitation of Buildings. FEMA, Washington, DC (1997) 5. Bureau of Indian Standards: Classification and Identification of Soils for General Engineering Purposes. Indian Standard IS 1498. Bureau of Indian Standards (2007) 6. Bureau of Indian Standards: Determination of Dry Density of Soils In-Place, by the Sand Replacement Methods. Indian Standard IS 2720, Part 28, 1974. Bureau of Indian Standards (2020) 7. Celebi, M., Safak, E.: Seismic response of Transamerica building. I: data and preliminary analysis. J. Struct. Eng. 117(8), 2389–2404 (1991) 8. Craig, R.R.J., Kurdila, A.J.: Fundamentals of Structural Dynamics. Wiley, Hoboken (2006) 9. Guéguen, P., Bard, P.-Y.: Soil–structure and soil–structure–soil interaction: experimental evidence at the Volvi test site. J. Earthq. Eng. 9(05), 657–693 (2005) 10. Heidebrecht, A., Henderson, P., Naumoski, N., Pappin, J.: Seismic response and design for structures located on soft clay sites. Can. Geotech. J. 27(3), 330–341 (1990) 11. Hokmabadi, A.S., Fatahi, B., Samali, B.: Physical modeling of seismic soil-pile-structure interaction for buildings on soft soils. Int. J. Geom. 15(2), 04014046 (2014) 12. Hokmabadi, A.S., Fatahi, B., Samali, B.: Assessment of soil–pile–structure interaction influencing seismic response of mid-rise buildings sitting on floating pile foundations. Comput. Geotech. 55, 172–186 (2014) 13. Hwang, Y.W., Dashti, S., Kirkwood, P.: Impact of ground densification on the response of urban liquefiable sites and structures. J. Geotech. Geoenviron. Eng. 148(1), 0402117 (2022) 14. IS 1893-1: Criteria for Earthquake Resistant Design of Structures—Part 1: General Provisions and Buildings. Bureau of Indian Standards, New Delhi (2016) 15. Kramer, S.L.: Geotechnical Earthquake Engineering. Pearson Education India (1996) 16. Meli, R., Faccioli, E., Murià-Vila, D., Quaas, R., Paolucci, R.: A study of site effects and seismic response of an instrumented building in Mexico City. J. Earthq. Eng. 2(01), 89–111 (1998)
14
V. Mittal and M. Samanta
17. Ohsaki, Y.: Niigata earthquakes, 1964 building damage and soil condition. J. Soil Mechan. Found. 6(2), 14–37 (1966) 18. Pavan, R.C., Costella, M.F., Guarnieri, G.: Soil-structure interaction for frame structures on shallow foundations. Revista IBRACON de Estruturas e Materiais 7, 273–285 (2014) 19. Pacific Earthquake Engineering Research Center (PEER): PEER Ground Motion Database. University of California, Berkeley, CA (2012) 20. Seed, H.B., Idriss, I.M.: Analysis of soil liquefaction: Niigata earthquake. J. Soil Mechan. Found. ASCE 93(3), 83–108 (1967) 21. Storie, L.B., Pender, M.J., Clifton, G.C., Wotherspoon, L.M.: Soil-foundation-structure interaction for buildings on shallow foundations in the Christchurch earthquake. In: Proceedings 10NCEE, Anchorage, Alaska. 2014 July 21 22. Tokimatsu, K., Midorikaw, S., Tamura, S., Kuwayama, S., Abe, A.: Preliminary report on the geotechnical aspects of the Philippine earthquake of July 16, 1990. Proc. ICRAGEE 1, 357–364 (1991) 23. Wolf, J.: Dynamic Soil-Structure Interaction. Prentice-Hall International Series in Civil Engineering and Engineering Mechanics (1985) 24. Wood, D.M.: Geotechnical Modelling. CRC Press (2017)
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand Through Bender Element Test Nilanjana Banik
and Rajib Sarkar
Abstract Bio-geotechnical method for mitigation of liquefaction of saturated cohesionless soils is one of the emerging methods owing to its lesser carbonintensive, economic, and environmental friendly propositions. Among the various bio-geotechnical methods, Microbially Induced Calcite Precipitation (MICP) technique is one of the popular choices of ground improvement for its easy implementation. In this study, poorly graded standard Ennore sand is treated with MICP technique through the urease-producing bacteria for improving its behavior against liquefaction. The morphological and chemical compositions of the bio-cemented sand are investigated through Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD) tests, respectively. Bender element testing has been carried out to investigate the improvement in low-strain stiffness indicated by shear wave velocity of bio-cemented sand. Results indicate significant enhancement in the stiffness of the bio-cemented sand. Therefore, the study may be helpful for the practicing researchers and engineers in understanding the efficacy of MICP treatment for dynamic/cyclic behavior of Ennore sand. Keywords Standard Ennore sand · MICP treatment · Bender element test
1 Introduction In recent years, Microbially Induced Calcite Precipitation (MICP) technique has emerged as one of the environmentally friendly techniques in the area of geotechnical engineering. This technique is adopted to improve the bonding between the soil particles of weaker soils. As a result, the mechanical properties of the soil get improved. Several studies have been conducted to investigate the engineering properties of bio-treated geomaterials [1, 2]. In this technique, stabilization of loose sand is generally done through ureolysis in presence of calcium chloride to induce calcite N. Banik · R. Sarkar (B) Department of Civil Engineering, IIT(ISM) Dhanbad, Jharkhand 826004, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_2
15
16
N. Banik and R. Sarkar
precipitation. Calcite precipitation held the loose sand particles together, and as a result, strong bonding occurs between the sand particles. There are two mechanisms of calcite precipitation. First is the attachment of bacterial cells to the nucleation site for the precipitation of calcium carbonate (CaCO3 ) and second is the hydrolysis of urea which increases the pH value by producing carbonate ions around the cells [3, 4]. In this study, microstructural characteristics and chemical composition of biotreated sand have been investigated through Scanning Electron Microscope (SEM) and X-Ray Diffraction (XRD) analyses. Stiffness properties have been investigated through advanced bender element tests. For microbial calcite precipitation, ureaseproducing bacteria S. pasteurii was used. Cementation solution was varied by Pore Volumes (1, 0.5 PV) considering the treatment period and frequency of treatment cycles.
2 Materials and Methods Standard Ennore sand collected from Chennai, India, is used in this study, and the sand conforms to Grading Zone-III sand following Indian standard [5]. Moreover, the sand is classified as poorly graded sand as per Indian standard [6], implying that the sand may be liquefiable under saturated condition. Various geotechnical and chemical properties of the sand are listed in Table 1. The particle size distribution curve of the sand is represented in Fig. 1. Table 1 Properties of Ennore sand
Geotechnical properties Coefficient of uniformity, C u
1.711
Coefficient of curvature, C c
0.837
Diameter corresponding to 10% finer D10 (mm)
0.445
Specific gravity, Gs
2.65
Maximum void ratio, emax
0.74
Minimum void ratio, emin
0.56
Chemical properties Silicon dioxide (SiO2 ) (%)
99.30
Aluminum oxide (Al2 O3 )
–
Ferric oxide (Fe2 O3 ) (%)
0.10
Calcium oxide (CaO)
–
Loss on extraction with hot HCl (%)
0.11
Loss on ignition
–
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand …
17
Percentage Finer (%)
100 80 60 40 20 0 0.0
0.1 1.0 Sieve Opening Size (mm)
10.0
Fig. 1 Particle size distribution curve of standard Ennore sand
3 Microbial Culture Bacillus sp. also known as S. pasteurii (NCIM 2477) is collected from NCIM, Pune (National Collection of Industrial Microorganisms). The bacterial strain is stored at − 20 °C. Bacterial culture is prepared in nutrient broth solution under laminar airflow condition. The bacterial strain is placed in orbital shaking incubator for 24 h at a rotating speed of 120 rpm at 30 °C. The optical density (OD) is measured using spectrophotometer at 580 nm. OD is measured to be approximately 1.0.
4 Methodology 4.1 Preparation of Bio-Cemented Sand Specimens Ennore standard sand was oven dried at 105 °C for 24 h before the test. Sand samples were prepared at a relative density of 40%. Plastic spray bottles of size 50 mm diameter and 100 mm height are taken to prepare triaxial samples of bio-cemented sand. Bottle caps were used as a nozzle to control the drainage of the arrangement. Sand samples were poured in the moulds using funnel to achieve relative density of 40% through pluviation technique. About 325 g of sand samples were poured in five layers. Bacterial solution was sprayed in the sand sample uniformly. 1.0 pore volume (PV), 0.5 PV of bacterial solution was sprayed at sand samples at an interval of 12 h and 24 h, respectively. Bacterial solution was held for 15 h since most of the bacterial growth was during this phase. After 15 h of attachment period without draining the bacterial solution, cementation solution was sprayed in the sand samples. Cementation solution was sprayed without calcium chloride dihydrate and
18
N. Banik and R. Sarkar
Table 2 Composition of the cementation solution (1:1) used in the study [8, 9] Material
Mass (gm/ml)
Urea
30.03
Cacl2 .2H2 O
73.5
NH4 Cl
10.0
NaHCO3
2.12
Nutrient broth
3.0
Table 3 Sample prepared for evaluation of bender element test Sample designation (treatment period in days)
Cementation concentration
Pore volumes (PVs)
Treatment interval (in h)
B1 (7 days)
1:1
1.0
12
B2 (7 days)
1:1
0.5
24
B3 (7 days)
1:1
0.5
12
B4 (7 days)
1:1
1.0
24
kept for 24 h, so that urea hydrolysis takes place. This period is commonly known as stimulation period [7]. After this stimulation period, the cementation solution was drained and fresh cementation solution was provided with calcium chloride dihydrate to observe calcite precipitation for 7 days at an interval of 12 h and 24 h, respectively. Figure 1 shows the bacterial strain utilized in the study, inoculated bacterium in orbital shaking incubator, and culture of bacterium in nutrient broth. The composition of the cementation solution is presented in Table 2, and it may be mentioned that nutrient broth was not autoclaved. Table 3 presents the samples prepared for testing with different treatment periods and treatment intervals (Fig. 2).
4.2 Determination of Percentage of Calcium Carbonate Percentage of calcite precipitation is determined by gravimetric analysis. This technique is also known as acid treatment weight loss technique. 20 g of dry sample is crushed into fine powder for the analysis. Effervescence shows the presence of carbon dioxide produced due to the reaction between two molar hydrochloric acid and carbonate present in the treated sample. The residue left is collected by using a filter paper and oven dried at a temperature of 105 °C. Measured weight loss of the sample helps to determine the percentage of calcium carbonate in the treated sample [10]. Percentage of calcium carbonate may be calculated as: (M 1 − M 2 )/M 1 , where M 1 = initial mass of the sample; M 2 = mass of the sample after acid treatment.
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand …
19
Fig. 2 a Bacterial strain bacillus sp. (NCIM 2477), b inoculated bacterium in orbital shaking incubator, c culture of bacterium in nutrient broth
4.3 Details of Bender Element Test In this study, bender element testing has been carried out on MICP-treated sand for evaluation of the low-strain shear wave velocity values. A bender element test setup consists of transmitter and receiver piezoelectric bender elements for transmitting and receiving signals. The setup is attached with a function generator for generation of input waves with variables such as frequency, amplitude, and waveform. The tests were conducted under dry condition. It may be noted here that maximum shear modulus value of saturated sand can be lower than that of dry sand [11]. Since the tests were conducted under dry conditions, then the saturation phase is avoided in the bender element testing. The input and output waves are monitored through the oscilloscope. In this study, the excitation voltage 20 V (peak to peak, i.e., 20 V pp ) with frequency of 1 kHz is used as input wave through the transmitting bender element. The prepared samples were then mounted on bender element apparatus
20
N. Banik and R. Sarkar
for further testing. A porous stone and a filter paper were placed on the bottom of pedestal. The treated samples were placed on the filter paper and rubber membrane is stretched by connecting to a vacuum pump. The treated sample is crushed same as untreated sand for testing particles of same size. Another filter paper and a porous stone were placed on the top of sample. The tests were carried considering different confining pressures with dry samples. The photographs of bender element test setup of IIT(ISM) Dhanbad are shown in Fig. 3. (a)
(b)
Function Generator Receiver Transmitter Oscilloscope
(c)
Fig. 3 a Bender element setup at IIT (ISM) Dhanbad, b function generator and oscilloscope of the setup, c prepared sample for testing
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand …
21
5 Results and Discussions 5.1 Microstructure Analysis Microscopic analyses have been carried out to investigate the change in the microstructure of the sand which is responsible for the improvement in dynamic properties of the sand. It helps in ascertaining the formation of CaCO3 precipitation and to determine the bonding between the grain hosts and bonding agents. Scanning Electron Microscopy (SEM) investigation was performed to analyze the microstructure of the treated and untreated samples. It may be noted that SEM is a type of microscope that produces images of a sample by scanning the surface with a focused beam of electrons [12]. Irregular, discrete and bigger size of particles was observed in untreated sand, whereas the size of the particles was smaller and agglomeration of particles has been observed in treated samples. Small crystals of calcite precipitation were also observed after 7 days of treatment, and the voids were significantly lower than the untreated silica sand. Figure 4a, b depict the SEM images of treated and untreated samples. Additionally, chemical composition of the treated and untreated samples has been investigated through X-Ray Diffraction (XRD) investigation. From the XRD analyses, it was evaluated that the untreated sand consists of only silica and the treated samples showed calcium composition along with silica showing precipitation of calcium carbonate after MICP treatment. Figure 4c presents the XRD analyses’ results of treated sand with 1:1 cementation solution.
5.2 Variation of Dry Density and CaCO3 The carbonate contents of the 7 days’ treated sample were observed to be varying between 8 and 15%. The results are quite satisfactory with reference to the past studies where calcite precipitation was observed to be maximum of 16% after treating with S. pasteurii for 12 h [13]. Samples treated with frequent cementation solution and with more pore volume showed higher calcite precipitation. Cementation was observed to be uniform throughout the sample. Figure 5 shows the change in variation of dry density and calcite content after treatment period. The dry density is measured by the ratio of weight of the oven-dried sample ejected after treatment and the volume of the sample.
5.3 Low-Strain Shear Wave Velocity of Bio-Cemented Sand In this section, the shear wave velocity of the bio-cemented sand for different treatment periods is reported through bender element tests. Figure 6 shows the typical waveform of a treated sand where the travel time is clearly indicated. The travel
22
N. Banik and R. Sarkar
Fig. 4 a SEM image of untreated sand, b SEM image of treated sand with 1:1 cementation solution, c XRD analyses’ results for treated sand with 1:1 cementation solution
time difference is 380 µs. For the calculation of shear wave velocity, the distance is taken as length of the sample, i.e., 100 mm. The shear wave velocity of biocemented sand is determined for wide range of confining pressure varying from 0.5 to 3.0 kg/cm2 . Figure 7a presents the shear wave velocity of bio-cemented sand for 7 days of treatment for different levels of confining pressure. It is observed that the shear wave velocity increases due to bio-cementation of the sand. For 7 days of treatment, bender element testing shows that the shear wave velocity of bio-cemented sand varies from 200 m/s to about 400 m/s for different confining pressures. It may be noted that the shear wave velocity of the untreated standard sand was observed to be varying between 86 and 102 m/s for confining pressure 0.5–3.0 kg/cm2 . Based on this range of value of shear wave velocity, standard sand may be classified as soft soil as per NEHRP (2003) guideline indicating lesser low-strain stiffness and need
23
1.80
16
1.78
14 12
1.76
10 1.74 8 1.72 6 1.70
4
1.68
Calcium Carbonate (%)
Dry Density (gm/cc)
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand …
2 0
1.66 Sample B1
Sample B2 Dry Density
Sample B3
Sample B4
Calcium Carbonate
Fig. 5 Dry density and percentage of calcite precipitation for 1:1 cementation solution
for improvement for better dynamic performance. Further, this study results indicate that the bio-cementation enhances the shear wave velocity significantly ranging from 200 to 400 m/s. It highlights the significance of bio-cementation in improving the low-strain stiffness values of the sand. For quantification, improvement ratio of the shear wave velocity of the bio-cemented sand to that of untreated sand (Rbu ) was determined and presented in Fig. 7b. This indicates that the minimum improvement in case of bio-cemented sand is more than 2.0 and maximum improvement for 3.0 kg/cm2 confining pressure is about 4.0. Figure 7c shows the variation of shear modulus with effective confining pressure. Additionally, it may be highlighted here that the bacterial activity does not stop even after the treatment period [14].
Fig. 6 Typical waveform obtained from bender element test for a treated sample
24
N. Banik and R. Sarkar
(a)
450 B1
Shear Wave Velocity (m/s)
400
B2
B3
B4
350 300 250 200 150 100 50 0 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00
Confining Pressure (kg/cm2)
(b) 4.50 B1
B4
B3
B2
4.00
Rbu
3.50
3.00
2.50
2.00 0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Confining Pressure (kg/cm2)
(c) 3500000 B1
Shear Modulus,Gmax (kPa)
3000000
B4
B3
B2
2500000 2000000 1500000 1000000 500000 0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
Confining Pressure (kg/cm2)
Fig. 7 a Variation of shear wave velocity of bio-cemented sand, b ratio of shear wave velocity of bio-cemented sand with untreated sand (Rbu ) for different confining pressures considering 7 days of treatment, c variation of maximum shear modulus with confining pressure for 7 days’ treatment
Evaluation of Dynamic Properties of MICP-Treated Ennore Sand …
25
This may be the reason of having higher shear wave velocity for samples with 24 h’ interval of treatment. Sample B2 showed little higher velocity as compared to other samples. This sample receives 0.5 PV of cementation solution and a total of 3.5 PV of cementation solution for 7 days, whereas the sample B1 received a total of 14 PV cementation solution for 7 days. This may be due to the early completion of biochemical reaction or may be due to time lag in treatment frequency [15, 16]. It may be highlighted that the improvement in shear wave velocity of the sand through biocementation may consider to be improvement against liquefaction of the particular sand [17].
6 Summary and Conclusions The present study on stiffness enhancement of bio-cemented sand may be summarized as following: (a) More or less uniform calcite precipitation was observed for all the samples. Effectiveness in the attachment of bacteria can be observed from the uniformity in calcite precipitation and inoculation technique of bacterial attachment in the sand sample. (b) From the microscopic investigation, it was clear that the uniform calcite precipitation leads to significant agglomeration of sand particles at different levels of the triaxial sample. (c) Shear wave velocity evaluated through bender element testing indicates that the bio-cemented sand transforms into dense soil or stiff soil condition as per NEHRP (2003) guidelines. The improvement of 2.0–4.0 times was observed for shear wave velocity values of bio-cemented sand in comparison to the untreated sand considering different confining pressures. (d) The increase in treatment cycle results in large crystal formation between the sand grains which significantly increases the stiffness of the sand.
References 1. Harkes, M.P., Van Paassen, L.A., Booster, J.L., Whiffin, V.S., Van Loosdrecht, M.C.M.: Fixation and distribution of bacterial activity in sand to induce carbonate precipitation for ground reinforcement. Ecol. Eng. 36(2), 112–117 (2010) 2. Van Paassen, L.A.: Biogrout, Ground Improvement by Microbial Induced Carbonate Precipitation. Doctoral Dissertation, Delft University of Technology, TU Delft, South Holland (2009) 3. Dejong, J.T., Fritzges, M.B., Nüsslein, K.: Microbially induced cementation to control sand response to undrained shear. J. Geotech. Geoenviron. Eng. 132(11), 1381–1392 (2006) 4. Stocks-Fischer, S., Galinat, J.K., Bang, S.S.: Microbiological precipitation of CaCO3 . Soil Biol. Biochem. 31(11), 1563–1571 (1999)
26
N. Banik and R. Sarkar
5. IS 383: Indian Standard Specification for Coarse and Fine Aggregates from Natural Sources for Concrete, 1–19. Bureau Indian Standard. New Delhi (1970) 6. IS 2720-Part 4: Indian Standard: Methods of Test for Soils, Part 4: Grain Size Analysis, 1–39. Bureau Indian Standard. New Delhi (1985) 7. Cheng, L., Shahin, M.A., Mujah, D.: Influence of key environmental conditions on microbially induced cementation for soil stabilization. J. Geotech. Geoenv. Engg. 143(1) (2016) 8. Whiffin, V.S., Van Paassen, L.A., Harkes, M.P.: Microbial carbonate precipitation as a soil improvement technique. J. Geomicrobiol. 24, 417–423 (2007) 9. Sharma, M., Satyam, N.: Strength and durability of bio-cemented sands: wetting-drying cycles, ageing effects and liquefaction resistance. J. Geoderma. 402, 115359 (2021) 10. Soon, N.W., Lee, L.M., Khun, T.C., Ling, H.S.: Improvements in engineering properties of soil through microbial induced calcite precipitation. J. KSCE 17(4), 718–728 (2013) 11. Gu, X., Yang, Z., Huang, M., Gao, G.: Bender element tests in dry and saturated sands: signal interpretation and result comparison. J. Soils Found. 55(5), 951–962 (2015) 12. Kalantary, F., Govanjik, D.A., Gonbad, M.S.S.: Stimulation of native microorganisms for improving loose salty sand. J. Geomicrobiol. ISSN: 0149-0451 (2019) 13. Sharma, M., Satyam, N., Reddy, K.R.: Rock-like behaviour of bio-cemented sand treated under non-sterile environment and various treatment conditions. J. Rock Mechan. Geotech. Eng. 13, 705–716 (2021) 14. Mitchell, J.K., Solymar, Z.V.: Time-dependent strength gain in freshly deposited or densified sand. J. Geotech. Eng. 110, 1559–1576 (1984) 15. Liu, L., Liu, H., Stuedlin, A.W., Evans, T.M., Xiao, Y.: Strength, stiffness and microstructure characteristics of bio-cemented calcareous sand. Can. Geotech. J. 56(10), 1502–1513 (2019) 16. Mahawish, A., Bouazza, A., Gates, W.P.: Improvement of coarse sand engineering properties by microbially induced calcite precipitation. J. Geomicrobiol. 35(10), 887–897 (2018) 17. Saxena, S.K., Reddy, K.R., Avramidis, A.S.: Liquefaction resistance of artificially cemented sand. J. Geotech. Eng. 114(12), 1395–1413
Seismic Site Characterization and Ground Response Analysis of Railway Line on Eastern Dedicated Freight Corridor Sandhya Joshi
and Aakash Kumar
Abstract Response of local soil during seismic events influences the response of the motion of the structure. Therefore, it is important to consider the local site characteristics while designing the structure for seismic design. In the present work, seismic site characterization and ground response analysis (GRA) have been performed for the proposed railway line between New Karchana Station and New Bhaupur (Kanpur) railway station, India. Total of 27 borehole data has been collected from the site. Further, seismic site characterization has been performed by adopting the US National Earthquake Hazard Reduction Program (NEHRP) guidelines. A power method of nonlinear regression analysis has been used to propose an empirical correlation between SPT blow count (SPT-N) and shear wave velocity (V S ) for the study site to estimate the V S profile. All the borehole locations have been characterized as class D as per 30 m average V S and SPT-N. In addition, a 1D equivalent linear approach has been used for the seismic GRA for six borehole locations by using DEEPSOIL v7.0 software. Total of three ground motions have been considered for GRA. Significant amplification has been observed at the site. Maximum displacement at the surface layer, Fourier amplification ratio, amplification factor, amplified PGA at surface level, effective stress, and maximum stress ratio have been also estimated for all the locations. Average response spectra have been estimated for the site. With the help of the above findings, liquefaction studies, seismic hazards analysis, and existing structures could be retrofitted with seismic protection. Keywords Correlation · Seismic site characterization · Ground response analysis
S. Joshi DIT University, Dehradun 248009, India A. Kumar (B) National Institute of Technology, Meghalaya, Shillong 793003, India e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_3
27
28
S. Joshi and A. Kumar
1 Introduction Indian Railway plays a major role in integrating markets and increasing trade along with providing conveyance of people and goods in India. Considering the significance of the railway line in the present era, it is obvious that extended loss due to the non-function of a major railway line for any reason could have significant regional, national, and even global financial impacts. One of the critical phases of seismic microzonation is the assessment of seismic site characterization and estimation of site response during earthquakes, which includes ground shaking intensity and amplification of ground motion. The purpose of seismic site characterization is to determine the basic index properties as well as engineering properties of soil. The potential of hazard can only be understand by analyzing the in-depth investigation [1]. Ground response analysis (GRA) is used to evaluate the liquefaction potential, predict site natural periods, assess seismic ground motion amplification, determine forces induced by a seismic event that may result in instability of the earth and earth slopes, and provide ground motions for the development of design response spectra. The behavior of the soil supporting the foundation also affects seismic risk in addition to strong ground motions [3]. Seismic shaking at a particular site can vary in intensity, magnitude, and duration depending on the various factors like seismotectonic of the site, source parameter, path parameter, and other site-specific characteristics [6]. In the present work, seismic site characterization has been done for the site using the US National Earthquake Hazard Reduction Program (NEHRP) guidelines using 30 m average VS and SPT-N [11]. For the estimation of site-specific shear wave velocity (V S ), an empirical correlation has been developed for all soils between SPT-N and V S using power method of nonlinear regression analysis [2, 14]. Various computer programs available for the seismic ground response analysis are EERA, ProShake, DEEPSOIL, SHAKE, and D-MOD2000 [8, 10]. A 1D equivalent linear GRA has been performed for the Railway Line on Eastern Dedicated Freight Corridor (EDFC) of India using DEEPSOIL v.7.0 to investigate the effects of local site conditions on the seismic ground motions [5]. The findings of this study will help designers to evaluate the safety of designing structures against seismic forces in the Eastern Dedicated Freight Corridor, especially in the absence of site-specific geophysical data.
2 Study Area Details In this study, the proposed railway line of EDFC is between New Karchana Station and New Bhaupur (Kanpur) railway station (241 km), India, as shown in Fig. 1. This area falls in the seismic zone III, with a zone factor of 0.16, indicating a moderate seismic alert zone. Total of 27 borehole data has been collected at Major Bridges/RUBs along the proposed EDFC alignment. The deposits encountered within the depths investigated for this study are alluvial. In this area, the younger alluvium of the Recent Age is underlain by the older alluvium of the Upper Pleistocene Age.
Seismic Site Characterization and Ground Response Analysis …
29
Fig. 1 Eastern dedicated freight corridor (EDFC) between Karchana and Bhaupur
The natural soil at the site consists of sandy silt/clayey silt to about 10–15 m depth. Below this, silty fine sand is found at a depth of about 21–30 m. However, variations in the stratigraphy are observed in the boreholes along the alignment. At the time of the field inquiry, groundwater was encountered at a depth of roughly 1.5–14.2 m.
3 Correlation Between SPT-N and V S In the present work, due to the absence of geophysical test data, an empirical correlation between SPT-N and V S has been proposed for all soil types [9, 10, 12]. To estimate the V S at various layers for all soils in the proposed site, worldwide acceptable correlations have been considered initially [4]. Average V S values are further used for the development of correlation equation. Then, power model of nonlinear regression analysis has been applied using the obtained SPT-N values with average V s for all soil types obtained from 27 boreholes [2, 7, 8, 14]. Proposed correlation has been presented in Fig. 2 with ± 10% of error bars, which gives a visual sense of the best fit of correlation equation. The R2 value is obtained as 0.9993 for the proposed correlation. Proposed correlation equation is presented in Eq. 1. VS = 70.797N 0.403 .
(1)
In Fig. 3, the proposed correlation is compared with the existing correlations for all soils that are currently available for various regions of India. Variation of SPT-N and V s obtained from proposed correlation with depth has been depicted in Fig. 4.
30
S. Joshi and A. Kumar
Fig. 2 Empirical correlation between SPT-N and V S for all soils
Fig. 3 Comparison of proposed correlation with correlation available for various parts of India
4 Seismic Site Characterization Site characterization is the process of characterizing a site or region based on the typical subsurface material properties. Individual site characterization based on properties is a more direct indicator of local site effects [7]. In engineering site investigation, a standard depth for soil exploration as well as seismic site characterizations is 30 m. As a result, the majority of site-effect investigations in seismic ground motions are based on properties in the upper 30 m. SPT-N data obtained from bore logs collected in the EDFC site are analyzed in detail. A 30-m average SPT blow
Seismic Site Characterization and Ground Response Analysis …
31
Fig. 4 Bore log profiles for BH-1 along with variation of SPT-N and V s with depth
Table 1 Seismic site classification guidelines as per NEHRP guidelines [11]
Site class
Generalized description
N 30
V S30 (m/s)
A
Hard rock
–
> 1500
B
Rock
–
760–1500
C
Very dense soil and soft rock
> 50
360–760
D
Stiff soil
15–50
180–360
E
Soft soil
< 15
< 180
count (N 30 ) and average shear wave velocity (V S30 ) approach have been used in this study as per NEHRP guidelines [11]. Estimation of N 30 and V S30 has been done by Eq. 2. The site shall be characterized as site class A, B, C, D, or E based on the site soil property following NEHRP guidelines. A detailed description of NEHRP guidelines for seismic site characterization has been displayed in Table 1. Σn di N 30 = VS30 = Σn i=1 di
.
(2)
i=1 Ni or VSi
The estimated value of N 30 and V S30 for each borehole location with site class has been displayed in Table 2. All the borehole locations fall in site class D.
5 Ground Response Analysis Soft sediments allow ground motion to be amplified as seismic waves travel from the bedrock to the surface. This happens as a result of the seismic waves being trapped, which causes a variation in impedance between the soil sediments and the
32
S. Joshi and A. Kumar
Table 2 Seismic site classification of the proposed site Borehole
Chainage
N 30
V S30
Site class
BH-1
464,658
20.66
251.88
D
BH-2
464,658
26.99
281.93
D
BH-3
472,071
25.97
279.86
D
BH-4
472,071
24.77
267.72
D
BH-5
475,017
29.85
289.63
D
BH-6
475,017
32.05
307.02
D
BH-7
475,799
30.10
295.17
D
BH-8
475,799
27.95
281.95
D
BH-9
478,994
24.11
268.67
D
BH-10
478,994
23.68
267.92
D
BH-11
478,994
19.73
252.43
D
BH-12
479,931
19.32
265.10
D
BH-13
479,931
36.29
314.08
D
BH-14
481,834
19.75
265.47
D
BH-15
481,834
24.02
273.11
D
BH-16
481,834
18.14
248.67
D
BH-17
488,764
20.12
247.58
D
BH-18
497,358
22.53
275.22
D
BH-19
497,358
26.77
286.09
D
BH-20
497,358
26.63
291.82
D
BH-21
498,807
21.68
267.84
D
BH-22
498,807
30.73
299.31
D
BH-23
498,807
27.10
281.75
D
BH-24
503,153
30.44
305.64
D
BH-25
503,153
23.53
271.20
D
BH-26
504,185
21.01
269.70
D
BH-27
504,185
23.00
273.16
D
bedrock beneath. Resonance patterns are created as a result of these trapped waves interacting with one another. Thus, as seismic waves travel through the soil deposits, their frequency content and amplitude are altered. Amplification of ground motion refers to the complete process wherein local soil significantly alters the strong motion characteristics of an earthquake. [15]. The main objective of the GRA is to determine how local soils affect seismic waves by amplification or de-amplification and to estimate surface motion and seismic response spectra so that they can be utilized in the further design of the structure. In this study, 1D equivalent linear GRA has been performed for the six borehole locations of the proposed EDFC site at regular interval (BH-1, BH-5, BH-10, BH-15, BH-20, and BH-25) using DEEPSOIL v.7.0
Seismic Site Characterization and Ground Response Analysis …
33
Fig. 5 a 2001-Bhuj earthquake, b 1991-Uttarkashi earthquake, and c 1999-Chi-Chi earthquake ground motion considered for the study
software. For this analysis, total three ground motions (a) 2001-Bhuj earthquake, (b) 1991-Uttarkashi earthquake, and (c) 1999-Chi-Chi earthquake ground motions have been considered and shown in Fig. 5. In this analysis, the iterative approach has been used to estimate the linear damping ratio (ξ ) and equivalent linear shear secant modulus (G) to approximate the nonlinear hysteretic stress–strain property of the critically loaded soils. The inbuilt model of G/Gmax and damping curves have been considered for this analysis [13, 16]. These curves have been shown in Fig. 6, representing the variation of G and ξ with shear strain (%). Soil level with SPT-N of more than 100 is considered a rigid bedrock level. Surface level acceleration time history with bedrock motion of 2001-Bhuj earthquake for BH-1 has been depicted in Fig. 7. Maximum surface PGA is observed as 0.330 g at BH-20 and minimum as 0.212 g at BH-1 against the bedrock PGA of 0.11 g. Five % damped response spectra at surface level with their average have been depicted in Fig. 8. Maximum amplification factor is obtained as 5.98 at BH-20 and minimum as 3.49 at BH-1, which indicates significant amplification of ground motion. Fourier amplification ratio with frequency curve has been shown in Fig. 9 for all 6 borehole locations. Variation of PGA (g) along the depth is depicted in Fig. 10 for all six borehole locations.
34
S. Joshi and A. Kumar
Fig. 6 Shear modulus and damping curves for a cohesive soil [16], b cohesionless soil [13]
Fig. 7 Effect of local soil on the ground response with bedrock motion for BH-1
Variation of displacement along the depth of all six boreholes has been illustrated in Fig. 11. Maximum surface displacement is observed as 0.0268 m at BH-5 and minimum as 0.0096 m at BH-15. Maximum effective stress is obtained as 404.962 kPa at BH-5 and minimum as 266.347 kPa at BH-15. Maximum stress ratio is observed as 0.676 at BH-20 and minimum as 0.456 at BH-1. Because of directivity and fling step effects, it has been found that near-field ground motions can produce different ground motion characteristics that are in the far-field.
Seismic Site Characterization and Ground Response Analysis …
35
Fig. 8 Five % damped response spectra at surface layer for each borehole location
Fig. 9 Fourier amplification ratio with frequency curve
6 Conclusions The local site condition is always crucial in amplifying ground motion as it propagates through a soil layer. As a result, it is essential to investigate the dynamic behavior of local site conditions to assess site-specific seismic hazards while designing
36
S. Joshi and A. Kumar
Fig. 10 Variation of PGA (g) along the depth
Fig. 11 Variation of displacement along depth
earthquake-resistant structures for better performance over their design life. This study has been performed for the proposed Railway Line on EDFC site between New Karchana Station and New Bhaupur Station, India. An empirical correlation between SPT-N and V S has been proposed for the estimation of V S . Seismic site characterization has been performed for each borehole location. The results showed that the site has N 30 values between 15 and 50 and V S30 values between 180 and
Seismic Site Characterization and Ground Response Analysis …
37
Table 3 Summary of results obtained from ground response analysis (Maximum values are highlighted in bold font) Borehole location
Deflection at top (m)
Effective stress (kPa)
Maximum PGA (g)
Amplification factor
Maximum stress ratio
BH-1
0.0215
288.457
0.212
3.49
0.456
BH-5
0.0268
404.962
0.241
4.41
0.512
BH-10
0.0214
276.165
0.309
4.87
0.668
BH-15
0.0096
266.347
0.246
4.86
0.526
BH-20
0.0227
322.567
0.330
5.98
0.676
BH-25
0.0203
286.867
0.276
3.84
0.587
360 m/s, indicating that the study site falls under site class D type as per NEHRP guidelines. Further, 1D equivalent linear GRA has been performed for the six borehole locations at regular interval (BH-1, BH-5, BH-10, BH-15, BH-20, and BH-25) using the computer program DEEPSOIL v7.0. Significant amplification of bedrock motion has been observed at the site. For each location, maximum displacement, effective stress, maximum PGA, amplification factor, and maximum stress ratio are listed in Table 3.
References 1. Anbazhagan, P., Kumar, A., Sitharam, T.G.: Seismic site classification and correlation between standard penetration test N value and shear wave velocity for Lucknow City in Indo-Gangetic Basin. Pure Appl. Geophys. 170(3), 299–318 (2013) 2. Chatterjee, K., Choudhury, D.: Variations in shear wave velocity and soil site class in Kolkata city using regression and sensitivity analysis. Nat. Hazards 69(3), 2057–2082 (2013) 3. Das, S., Sil, A., Naveen, B.P.: Effects of soil–structure interaction on seismic fragility of railway concrete bridge, in India. Iran. J. Sci. Technol. Trans. Civ. Eng. 1–20 (2022) 4. Hanumantharao, C., Ramana, G.V.: Dynamic soil properties for microzonation of Delhi, India. J. Earth Syst. Sci. 117(2), 719–730 (2008) 5. Hashash, Y.M.A., Musgrove, M.I., Harmon, J.A., Ilhan, O., Xing, G., Numanoglu, O., Groholski, D.R., Phillips, C.A., Park, D.: DEEPSOIL 7.0, User Manual. Urbana, IL, Board of Trustees of University of Illinois at Urbana-Champaign (2020) 6. Kumar A., Debnath N.: Seismic behaviour of a typical rail bridge using North-East India specific synthetic ground motions under multi-support excitation. In: Das B., Barbhuiya S., Gupta R., Saha P. (eds.) Recent Developments in Sustainable Infrastructure. Lecture Notes in Civil Engineering, vol. 75, pp. 291–300. Springer, Singapore (2021) 7. Kumar, A., Harinarayan, N.H., Verma, V., Anand, S., Borah, U., Bania, M.: Seismic site classification and empirical correlation between standard penetration test n value and shear wave velocity for Guwahati based on thorough subsoil investigation data. Pure Appl. Geophys. 175(8), 2721–2738 (2018) 8. Kumar, A., Satyannarayana, R., Rajesh, B.G.: Correlation between SPT-N and shear wave velocity (VS) and seismic site classification for Amaravati city, India. J. Appl. Geophys. 205, 104757 (2022)
38
S. Joshi and A. Kumar
9. Maheswari, R.U., Boominathan, A., Dodagoudar, G.R.: Use of surface waves in statistical correlations of shear wave velocity and penetration resistance of Chennai soils. Geotech. Geol. Eng. 28(2), 119–137 (2010) 10. Naik, N.P., Choudhury, D.: Comparative study of seismic ground responses using DEEPSOIL, SHAKE, and D-MOD for soils of Goa, India. In: Geo-Congress 2014: Geo Characterization and Modeling for Sustainability, pp. 1101–1110 (2014) 11. NEHRP: NEHRP recommended provisions for seismic regulations for new buildings and other structures. FEMA (2003) 12. Rao, V.D., Choudhury, D.: Estimation of shear wave velocity and seismic site characterization for new nuclear power plant region, India. Nat. Hazards Rev. 21(4), 06020004 (2020) 13. Seed, H.B., Idriss, I.M.: Soil moduli and damping factors for dynamic response analyses. In: EERC Reports (EERC 70-10), 1–15 (1970) 14. Sil, A., Haloi, J.: Empirical correlations with standard penetration test (SPT)-N for estimating shear wave velocity applicable to any region. Int. J. Geosynth. Ground Eng. 3(3), 1–13 (2017) 15. Sil, A., Haloi, J.: Site-specific ground response analysis of a proposed bridge site over Barak River along Silchar Bypass Road, India. Innov. Infrastruct. Solut. 3(1), 1–19 (2018) 16. Vucetic, M., Dobry, R.: Effect of soil plasticity on cyclic response. J. Geotechn. Eng. 117(1), 89–107 (1991)
Earthquake-Induced Damage Assessment of Coal Mine Overburden Dump Slope Using Extended Finite Element Method Coupled with Voronoi Tessellation Scheme Madhumita Mohanty , Rajib Sarkar , and Sarat Kumar Das Abstract Seismotectonic activity in the coal mining areas is a threat to the stability of overburden (OB) dump slopes. The consequent dump failures cause the loss of innocent lives, hamper the mining infrastructure, and disturb the mining activities. Thus, there is an undesirable delay in the production of coal. The challenges in obtaining the material properties of the OB dump and the heterogeneous nature of its particles forbid the assessment of earthquake-induced damage in an appropriate manner. The present study utilizes multi-channel analysis of surface waves (MASW) test-based material properties of an OB dump slope situated at an Indian opencast coal mine located in Jambad. The representation of heterogeneity in size and shape of the dump particles was done by coupling extended finite element method (XFEM) with Voronoi tessellation scheme through RS2 software. The earthquakes, Coyote (1979) and Kobe (1995), were used to perform the dynamic analysis of a coal mine OB dump consisting of two benches. Finally, the effect of peak ground acceleration (PGA) on amplification ratio and permanent deformation at different key locations of the OB dump was investigated after ten seconds of the cease of the input seismic motion. In the absence of guidelines regarding the threshold of damage due to seismic forces on the coal mine OB dump, this work would prove beneficial for the mining authorities in the preparation of guidelines for ensuring the safety of coal mine OB dumps in earthquake prone areas. Keywords Coal mine overburden dump slope · Extended finite element method (XFEM) · Voronoi tessellation scheme · Amplification ratio · Permanent deformation
M. Mohanty · R. Sarkar (B) · S. K. Das Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, Jharkhand, India e-mail: [email protected] M. Mohanty e-mail: [email protected] S. K. Das e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_4
39
40
M. Mohanty et al.
1 Introduction Open-pit mining is a popularly used surface mining method for the extraction of coal. It is beneficial when the coal deposits are located closer to the surface of the earth. The removal of the waste material existing over the coal seams is carried out to reach the coal seams. The structure formed on storing these heterogeneous waste materials [1] in the vicinity of the coal mine is termed as the coal mine overburden (OB) dump. With the increase in depth of the open-pit mines, there is a simultaneous increase in the height of the OB dump due to which the operators of the coal mines suffer from serious environmental, economic, and social liabilities. Furthermore, the lack of dumping space forces the authorities of the coal mines to accommodate the OB dump in such a manner that it acquires minimum area; consequently, it becomes steeper with rise in its height. The frequency of accidents on account of the OB dump failures has been increasing rapidly [2]. The occurrence of various problems on account of the coal mine OB dumps has been summarized in Table 1. Various factors are responsible for the OB dump failures, and earthquake is one among them. It is worthwhile to mention here that the seismic energy evolved during the phenomena of earthquake is uncontrollable and thus very devastating; still, there are no regulations in the Indian guidelines regarding the permissible damage due to their occurrence. The seismic slope stability assessment of the OB dump considering its heterogeneous nature is a challenging issue. OB dump is a heterogeneous mass with numerous discontinuities, which can be well represented using the scheme of Voronoi tessellation. In the presence of innumerable discontinuities, extended finite element method (XFEM) is advantageous as it overcomes the difficulties in meshing which is faced while using finite element method (FEM). Thus, the present study investigates the damaging influence of seismic forces by coupling the XFEM and Voronoi tessellation scheme with the implementation of the commercial software package, RS2 v11.013 2021 [7]. The assessment of the earthquake-induced damage was performed by considering Coyote (1979) [8] and Kobe (1995) [8] with peak ground acceleration (PGA) values of 0.12 g and 0.82 g, respectively. Further, the predominant frequency, bracketed duration, and Arias intensity of the Coyote (1979) are 2.40 Hz, 2.89 s, and 0.12 m/s, respectively, whereas that for the Kobe (1995) these parameters are widely different Table 1 Various problems due to coal mine OB dumps based on literature Problems arising due to coal mine OB dumps
Literature
Depletion of precious land and replacement of existing ecosystems with coal mine OB dumps
[3]
Environmental hazards
[4]
OB dump failure causing burial of several houses and seven persons
[5]
Interruption in mining operation, environmental Issues, and a huge price of remediation
[6]
Earthquake-Induced Damage Assessment of Coal Mine Overburden …
41
and are 1.45 Hz, 21.40 s, and 8.39 m/s, respectively. These two earthquake time histories were selected for investigation on the performance of the OB dump slope under widely varying strong motion parameters. Finally, the estimation of earthquakeinduced damage was performed in terms of amplification ratio [9] and permanent deformation at four key locations along the slope. Negligible literature is available based on the assessment of damage faced by the heterogeneous OB dumps due to earthquakes. Therefore, the present work would be favorable in the preparation of design guidelines for coal mine OB dumps in areas prone to earthquakes.
2 Theoretical Background of XFEM When the problem domain is moderately jointed, meshing can be done appreciably by using FEM, but if it is heavily jointed, meshing becomes difficult in FEM. This potential of the conventional FEM in modeling numerous joints can be enhanced by means of XFEM. XFEM is based on the generalized finite element method and the partition of unity method and has been successfully applied in several fields [10]. It is capable of modeling numerous joints without conforming the mesh [11–13]. When joints cross the element, their influence is considered in an implicit manner [14]. The enrichment of nodes of a problem domain having three sets of joints is shown in Fig. 1. To model the complicated geometry of a domain in XFEM, extra degrees of freedom are utilized for the enrichment of a node when the element is intersected by a joint. For the consideration of discontinuity in the element, Heaviside function, H(x), is used. The local coordinates of the joint (x, y) are needed to represent the location of a point. The above-mentioned function is expressed as follows [12]:
Fig. 1 Enrichment of nodes in a problem domain intersected by three joints (adopted from Moallemi et al. 2018 [14])
42
M. Mohanty et al.
⎧ ⎨ +1 y > 0 H (x) = 0 y = 0 ⎩ −1 y < 0
(1)
The displacement, u(x), can be expressed as follows [10]: u(x) =
Σ i∈I
Ni (x)u i +
Σ
( ) N j (x) H (x) − H (x j ) u j . Λ
(2)
j∈J
In this equation, N i is the shape function for the ith node, I is the set of all nodes in the domain, J is the set of enriched nodes, u i is the set of standard DOFs, and u j is the set of enriched DOFs. The Voronoi tessellation scheme is devised by means of randomly shaped Voronoi blocks (varying in their size) with Voronoi contacts existing in between them. The density of the Voronoi joints is specified by providing the average length (1 m in this study) of the sides of Voronoi polygons. To obtain a random network of polygons, the regularity of the polygon shape was specified as “irregular”. The randomness thus generated was kept constant throughout the study. The mesh formed in FEM while incorporating Voronoi blocks and Voronoi contacts has been illustrated in Fig. 2a, whereas the XFEM mesh developed for the same condition is shown in Fig. 2b. It may be mentioned here that while incorporating Voronoi blocks and Voronoi contacts in FEM, the developed mesh should necessarily be aligned with the joints, whereas the XFEM mesh developed for the same condition is independent of the joint network. Λ
Fig. 2 Meshing with a FEM approach and b XFEM approach with the Voronoi blocks and Voronoi contacts
Earthquake-Induced Damage Assessment of Coal Mine Overburden …
43
Table 2 Properties of the Voronoi block in the OB dump Property
Unit weight
Elastic modulus
Poisson’s ratio
Cohesion
Friction angle
Tensile strength
Unit
(kN/m3 )
(kPa)
_
(MPa)
(°)
(MPa)
Value
14.5
304,850
0.35
0
33.32
0
Table 3 Properties of the Voronoi contact in the OB dump Property
Normal stiffness
Shear stiffness
Cohesion of joint
Friction angle of joint
Unit
(kPa/m)
(kPa/m)
(MPa)
(°)
Value
430,000
70,000
0
30.02
3 Material Properties of the OB Dump Model The properties of the Voronoi blocks and Voronoi contacts are based on multi-channel analysis of surface waves (MASW) test performed on the OB dump of Jambad opencast coal mine (India) and utilizing several correlations [15–18]. The mean values of the required material properties (considering log-normal distribution) found from the obtained datasets of MASW testing were assigned to the Voronoi blocks. The Mohr–Coulomb constitutive model was applied throughout the numerical model of the OB dump. The OB dump was considered to be comprised of cohesionless materials, and thus, the cohesion of the joint was taken as zero. The details regarding the procedure of obtaining normal and shear stiffness values for the Voronoi joint can be found in Tan et al. [18]. The range of values for friction angle of the joint used was 26°–33° [16] and it was assumed to follow a log-normal distribution; thus, a mean value of 30.02° was considered in this study. The properties of Voronoi blocks and Voronoi contacts have been elucidated in Tables 2 and 3, respectively.
4 Coal Mine OB Dump Model Based on XFEM-Coupled Voronoi Tessellation Scheme The geometrical configuration of the OB dump model confirming to the regulations stated in Coal Mines Regulation 2017 [19] is illustrated in Fig. 3 along with the boundary conditions and four key points [(i) toe of lower bench, (ii) crest of lower bench, (iii) toe of upper bench, and (iv) crest of upper bench]. The average Voronoi joint length was assigned as 1 m. Along the vertical lateral boundary of the model, transmitting boundary condition was assigned, and along the bottom of the model, absorbing boundary condition was provided for preventing reflections of the input seismic wave. Remaining surfaces were kept free. The final mesh as shown in Fig. 3 was derived based on the following: (i) the maximum size of the element was considered to be less than one-tenth of the wavelength associated with
44
M. Mohanty et al.
the highest frequency of the input wave according to Kuhlemeyer and Lysmer [20] and (ii) mesh sensitivity analyses were carried out with the models developed with three-node triangular elements. Rayleigh damping of three percentage was applied in the study considering the applicable range of damping for sandstone materials [21]. Finally, Coyote (1979) [8] and Kobe (1995) [8] earthquakes were applied as seismic inputs. Initially, the input earthquake motion was applied at the base of the OB dump model as velocity history. The model base has absorbing boundary condition; thus, the velocity record had to be transformed to a stress record using the compliant base condition. The input wave thus obtained then propagates upward through the OB dump base. Earthquake-induced effects can be captured through several parameters [such as Arias intensity and cumulative absolute velocity (CAV)]. However, since the OB dump materials are loosely packed and compacted and may dominantly experience sliding displacement due to earthquake motions, amplification ratio and permanent deformation were considered to be indicative of the earthquake-induced damage. The amplification ratio and permanent deformation at the four key locations were evaluated after ten seconds of the cease of the earthquake [22] for assessment of permanent damage induced in the system.
Fig. 3 Geometrical configuration and boundary conditions of the XFEM-coupled Voronoitessellated OB dump model for seismic slope stability analysis
Earthquake-Induced Damage Assessment of Coal Mine Overburden …
45
5 Results and Discussions As mentioned earlier, for the dynamic analyses, two earthquakes with a wide difference in their strong motion parameters were adopted: (i) Coyote (1979) and (ii) Kobe (1995). Earthquake-induced damage was quantified in terms of: (i) amplification ratio (ratio between the PGA at the key point of the OB dump and the PGA of the applied seismic input motion) and (ii) permanent deformation. The heterogeneous model was generated by coupling XFEM with the Voronoi tessellation scheme (as explained in the previous sections), and a homogeneous model was generated with identical external geometry, boundary conditions, and material properties. A comparative study was conducted to differentiate the damages observed in heterogeneous and homogeneous OB dumps. The results have been detailed in the upcoming sections.
5.1 Amplification Ratio at Key Points of the OB Dump The pictorial representation showing variation of amplification ratio for the earthquake motions considered in the present study for the lower and upper benches of the OB dump slope has been provided in Figs. 4 and 5, respectively. On considering toe of the lower bench for both the time histories, it was seen that the amplification ratios are almost the same and nearly unity for the heterogeneous and homogeneous OB dump slopes since this point lies on the plane where the earthquake time histories were applied (Fig. 4a). For both the earthquake time histories, crest of the lower bench experiences greater amplification for the heterogeneous model of the OB dump slope (Fig. 4b). Moreover, it may be noted that the extent of amplification for Coyote earthquake is greater than the Kobe earthquake. This observation may be related with strong motion parameter of the earthquake time histories considered. It may be due to the closeness of the predominant frequency (2.40 Hz) of the Coyote earthquake with the fundamental frequency of the system (varying approximately between 4 and 5 Hz for various conditions). Similar observation was made for the upper bench as well and is shown in Fig. 5. From Fig. 5a, it is evident that the toe of the upper bench of the heterogeneous OB dump experiences more amplification ratio in comparison to the homogenous one. Further, reflection of waves at the crest level may induce higher amplification at the toe of the upper bench. Moreover, Coyote earthquake shows comparatively higher amplification in comparison to the Kobe earthquake. Further, the crest of the upper bench of the heterogeneous OB dump slope indicates quite insignificant amplification ratio when compared with the OB dump considering homogeneity (Fig. 5b). This may be due to the lesser continuity of the system at the bench for the propagation of wave, the induced higher damping, and discontinuity of the materials in the heterogeneous slope model for propagation of wave to the top. Further, it may be highlighted that in case of heterogeneous OB dump slope, the dynamic response of the system is highly dependent on several factors such as: (i) material properties of the Voronoi blocks and (ii) properties of the Voronoi
46
(a) 1.8 Amplification Ratio
Fig. 4 Variation of amplification ratio for the earthquake motions considered in the present study at: a toe and b crest of lower bench of the OB dump slope
M. Mohanty et al.
1.2 0.6 0
(b) 1.8
Amplification Ratio
Heterogeneous OB dump Homogeneous OB dump
Coyote (0.12 g) Kobe (0.82 g) Earthquake (PGA g) Heterogeneous OB dump Homogeneous OB dump
1.2 0.6 0
Coyote (0.12 g) Kobe (0.82 g) Earthquake (PGA g)
contacts, whereas in case of the homogeneous one, the properties of the contacts are not considered.
5.2 Permanent Deformation at Key Points of the OB Dump Slope The graphical representation of the changes in permanent deformations at the various key points due to Coyote (1979) and Kobe (1995) is given in Figs. 6 and 7, respectively. It can be seen from Figs. 6 and 7 that for both the earthquake time histories, the permanent deformations at various key points of the heterogeneous OB dump slope were greater than that of the corresponding ones of the homogeneous OB dump slope, and the permanent deformation may reach more than 500 mm at the crest of the two-benched slope indicating high damage of the slope in all practical situations. As expected, irrespective of the consideration of heterogeneity, there was rise in permanent deformation from base to top of the OB dump (i.e., from toe of the lower bench to the crest of the upper bench). The deformation gets escalated noticeably at the crest of the upper bench of the heterogeneous OB dump as can be seen in Fig. 6. In case of permanent deformation, it was observed that Kobe (1995) earthquake induces higher deformation on all the monitoring points of the OB dump slope than the Coyote (1979). This may be due to the hugely varying PGA of the two histories considered. It may be noted that Kobe (1995) earthquake time history used
Earthquake-Induced Damage Assessment of Coal Mine Overburden …
(a) 1.8
Amplification Ratio
Fig. 5 Variation of amplification ratio for the earthquake motions considered in the present study at: a toe and b crest of upper bench of the OB dump slope
Heterogeneous OB dump Homogeneous OB dump
1.2 0.6 0
(b) 1.2
Amplification Ratio
47
Coyote (0.12 g) Kobe (0.82 g) Earthquake (PGA g) Heterogeneous OB dump Homogeneous OB dump
0.8 0.4 0
Coyote (0.12 g)
Kobe (0.82 g)
Earthquake (PGA g)
Upper bench_crest Upper bench_toe Lower bench_crest Homogeneous-Coyote Lower bench_toe
Heterogeneous-Coyote 0
200 400 600 Permanent Deformation (mm)
800
Fig. 6 Permanent deformations at key points of OB dump slope for Coyote (1979) earthquake
in this study has PGA of 0.82 g, whereas Coyote (1979) has 0.12 g PGA. The increased deformation for Kobe earthquake may be due to the plasticity induced in the system for the higher PGA value. This may also cause differential movement of the discretely attached particles of the OB dump slope simulated through the XFEM. This differential movement of the particles causes higher permanent deformation in the OB dump slope for the Kobe earthquake time history. Further, it may be noticed that the other strong motion parameters (such as Arias intensity and bracketed duration) of Kobe earthquake time history are significantly higher indicating the higher input energy of the earthquake time history.
48
M. Mohanty et al.
Upper bench_crest Upper bench_toe Lower bench_crest Homogeneous-Kobe
Lower bench_toe
Heterogeneous-Kobe 0
200 400 600 800 Permanent Deformation (mm)
1000
Fig. 7 Permanent deformations at key points of OB dump slope for Kobe (1995) earthquake
6 Conclusions The dynamic analysis of the XFEM-coupled Voronoi-tessellated OB dump model was carried out by utilizing Coyote (1979) and Kobe (1995) as the seismic inputs. The consideration of heterogeneity is useful in the appropriate evaluation of the amplification ratio. At a particular key point, irrespective of the type of OB dump, the permanent deformation experienced due to Kobe (1995) was much higher than that due to Coyote (1979). The novel concept of incorporating the Voronoi tessellation scheme in the XFEM framework was successful in the representation of the heavily jointed and heterogeneous OB dump and thus assessing the earthquake-induced damage.
References 1. Nayak, P.K., Dash, A., Dewangan, P.: Design considerations for waste dumps in Indian opencast coal mines - a critical appraisal. In: Proceedings of 2nd International Conference on Opencast Mining Technology and Sustainability, pp. 19–31 (2020) 2. Director General of Mines Safety (DGMS): Design, Control and Monitoring of Pit and Dump Slopes in Opencast Mines. Director General of Mines Safety, Circular No. 02, Dhanbad, India (2010). 3. Tripathi, N., Singh, R.S., Chaulya, S.K.: Dump stability and soil fertility of a coal mine spoil in Indian dry tropical environment: a long-term study. Environ. Manage. 50(4), 695–706 (2012) 4. Adibee, N., Osanloo, M., Rahmanpour, M.: Adverse effects of coal mine waste dumps on the environment and their management. Environ. Earth Sci. 70, 1581–1592 (2013) 5. Duc, D.M., Hieu, N.M., Sassa, K., Hamasaki, E., Khang, D.Q., Miyagi, T.: Analysis of a deep-seated landslide in the Phan Me coal mining dump site, Thai Nguyen Province, Vietnam. Proceedings of world landslide forum 3, 2–6 June 2014, Beijing, 1. In: Sassa K., Canuti P., Yin Y. (eds.) Landslide Science for a Safer Geoenvironment, pp. 373–377. Springer, Cham (2014) 6. Wang, J., Chen, C.: Stability analysis of slope at a disused waste dump by two-wedge model. Int. J. Min. Reclam. Environ. 31(8), 575–588 (2017)
Earthquake-Induced Damage Assessment of Coal Mine Overburden …
49
7. RS2 v11.013: 2D Finite Element Based Software. Rocscience Inc., Toronto, Ontario, Canada (2021) 8. Pacific Earthquake Engineering Research Center (PEER) Ground Motion Database Web Application, PEER. http://peer.berkeley.edu/smcat/ (2010) 9. Bottari, C., Albano, M., Capizzi, P., Alessandro, A.D’, Doumaz, F., Martorana, R., Moro, M., Saroli, M.: Recognition of earthquake-induced damage in the Abakainon Necropolis (NE Sicily): results from geomorphological, geophysical and numerical analyses. Pure Appl. Geophys. 175, 133–148 (2018) 10. Fries, T.P., Belytschko, T.: The extended/generalized finite element method: an overview of the method and its applications. Int. J. Numer. Meth. Eng. 84, 253–304 (2010) 11. Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Meth. Eng. 45(5), 601–620 (1999) 12. Moës, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46(1), 131–150 (1999) 13. Moës, N., Belytschko, T.: Extended finite element method for cohesive crack growth. Eng. Fract. Mech. 69(7), 813–833 (2002) 14. Moallemi, S., Curran, J.H., Yacoub, T.: On modeling rock slope stability problems using XFEM. Paper presented at the 2nd International Discrete Fracture Network Engineering Conference, Seattle, Washington, USA, June 2018, pp. 1–9 (2018) 15. Anbazhagan, P., Uday, A., Moustafa, S.S.R., Al-Arifi, N.S.N.: Correlation of densities with shear wave velocities and SPT N values. J. Geophys. Eng. 13, 320–341 (2016) 16. Barton, N.: The shear strength of rock and rock joints. Int. J. Rock Mechan. Mining Sci. Geomechan. Abstr. 13(9), 255–279 (1976) 17. Kumar, R., Bhargava, K., Choudhury, D.: Estimation of engineering properties of soils from field SPT using random number generation. INAE Lett. 1, 77–84 (2016) 18. Tan, X., Zhao, M., Zhu, Z., Jin, Y.: Elastic properties calibration approach for discrete element method model based on Voronoi tessellation method. Geotech. Geol. Eng. 37(3), 2227–2236 (2019) 19. Director General of Mines Safety (DGMS): Coal Mines Regulations, Notification, New Delhi, 27.11.2017. Ministry of Labor and Employment, Directorate General of Mines Safety (2017) 20. Kuhlemeyer, R.L., Lysmer, J.: Finite element method accuracy for wave propagation problems. J. Soil Dyn. Div. 99, 421–427 (1973) 21. Shahnazari, H., Esmaeili, M., Ranjbar, H.: Simulating the effects of projectile explosion on a jointed rock mass using 2D DEM: a case study of Ardebil-Mianeh railway tunnel. Int. J. Civ. Eng. 8, 125–133 (2010) 22. Bottari, C., Albano, M., Capizzi, P., D’Alessandro, A., Doumaz, F., Martorana, R., Moro, M., Saroli, M.: Recognition of earthquake-induced damage in the Abakainon necropolis (NE Sicily): results from geomorphological, geophysical and numerical analyses. Pure Appl. Geophys. 175(1), 133–148 (2018)
Preliminary Studies on Developing a Physics-Based Smoothed Particle Hydrodynamics Model for Landslides Nadia Mubarak and Ritesh Kumar
Abstract Landslides triggered by earthquakes pose a major threat worldwide, in terms of economic loss and causalities. In order to effectively mitigate this hazard, it is requisite to carry out Quantitative Risk Assessment (QRA) of landslides wherein the probability of landslide occurrence and the post-failure scenario both can be studied in detail. The devastating effects of any landslide can be attributed to its post-failure phase which involves large deformations, and due to the complex nature of these deformations, it is difficult to model them using slope stability methods like the Limit Equilibrium or the Finite Element Method (FEM). The presented work aims at studying the behavior of landslides triggered by seismic action and exploring the applicability of the mesh-free computational method, Smoothed Particle Hydrodynamics (SPH) in predicting the size of landslides, in terms of volume and run-out distance. To achieve the said objective, slopes in vulnerable areas shall be analyzed using SPH; a threshold value for sliding mass volume and runout distance shall be chosen based on some prominent works to decide on the stability of a given slope. Hence, the objective of getting an insight into the entire process of landslides, right from the initiation phase to the final consequences, shall be achieved. This particular article includes a preliminary study carried out to assess the applicability of our initial model and to gauge its performance when applied to the real-life scenario. For that purpose, the famous Daguangbao landslide triggered by the 2008 Wenchuan earthquake has been modeled, and the results have been found to be in good agreement with the field data. Keywords SPH · Landslides · Volume · Runout distance · Earthquake
N. Mubarak (B) · R. Kumar Department of Earthquake Engineering, IIT Roorkee, Roorkee, India e-mail: [email protected] R. Kumar e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_5
51
52
N. Mubarak and R. Kumar
1 Introduction Landslides are a very common phenomena and various agencies have defined them differently. One of the most commonly accepted definitions of landslides is the one provided by the US Geological Survey, according to which, “a landslide is the movement of a mass of rock, debris, or earth down a slope. Landslides are a type of mass wasting, which denotes any down-slope movement of soil and rock under the direct influence of gravity”. As for the causes, there are numerous factors that may trigger a landslide occurrence, for example, rainfall, tectonic activities, snowmelt, changes in water level, stream erosion, and human activities. The most common of these all is being rainfall and earthquakes. The threat posed by landslides is not limited to a piece of earth or a specific domain of existence, rather its impacts are diverse. According to a report by the WHO, during the period between 1998 and 2017, the number of deaths caused by landslides is near about 18,000. For countries like Japan, USA, and India, economic loss caused by landslides is around 1 billion for each country on a yearly basis. As far as India is concerned, the land area that is landslide prone is about 4.2 M km2 . Even when the risk posed by landslides is highly acknowledged, there is not much that can be done to stop them. Hence, focus should be more on developing ideas on how the effect of landslides, on people and resources, can be reduced. The motivation for this work comes from the idea that predicting the size of the landslide beforehand can reduce the consequences to some extent. As for any general problem in life, the consequences are directly proportional to the size of the problem, landslides are not different. Hence, bigger the landslide, more will be the damage caused to life and property. So, if it can be predicted with precision how big the landslide in a particular location owing to certain factors is going to be, the after-effects can be reduced by a considerable margin. The size of a landslide is measured in terms of the volume of sliding mass (m3 ) and the run-out distance (m). The modeling of slope behavior has evolved a lot over the past years. It was not until recently that the post-failure phase of landslides could be simulated. Wide range of approaches have made it possible to consider the complexities that increase as we tend to get closer to modeling the actual site behavior. Earlier, with the simple classical methods of slope stability analysis, the failure surface would be pre-determined and the spatial variability of geotechnical properties was ignored. Until when researches like [8, 13] started to combine nonlinear finite element methods with random field generation techniques that could fully account for spatial correlation and local averaging. It proved to be a powerful slope stability analysis tool that did not require a prior assumption related to the shape or location of the failure mechanism. To put such methods into practical use, [6] then developed a Random Finite Element Method (RFEM) to determine the probability of failure of a cohesive slope and compared it with results from the traditional approach on the same slope which was found to produce a non-conservational estimate of probability of failure. This code developed by the writers enabled a random field of shear strength values to be generated and mapped on to the finite element mesh taking into full account the element size in the
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
53
local averaging process. The analyses involved the application of gravity loading and the monitoring of stress at all Gauss points. Slope stability analysis was carried out by choosing a suitable soil constitutive model. This was an iterative process which would continue until the soil constitutive model and global equilibrium were satisfied at all points within the mesh. However, the method suffered from the drawback that it could not model large deformations. Hence, the researchers kept looking for alternatives to model the post-failure scenario. Later, the concept of SPH was introduced to model the post-failure behavior of landslides [4, 10, 11, 15, 20]. SPH has been used previously for simple slope stability analysis as well [3, 4] which does not necessitate using separate methods for stability analysis and for modeling of post-deformation scenario. If compared to other particle-based methods such as the Material Point Method (MPM) [13], SPH was found to be efficient in a way that it was not affected by size and orientation of background grid, as was the case in MPM. The choice of iteration ceiling was also subjective [5].
2 Smoothed Particle Hydrodynamics: Concept and Formulations SPH is a mesh-free, particle, computational method based on Lagrangian continuum theory. Originally developed for the problems of astrophysics [5, 15] this method has now found application in various other fields like Solid Mechanics, Geomechanics, and Hydrodynamics. The attributes of this method that have been particularly advantageous to our work are its ability to consider the behavior of moving boundaries and interface problems and model complex geometries and large deformations. Although it suffers from certain disadvantages as well, like, tensile instability (not serious in soils, unless we want to model tensile cracking), more computational expense as compared to grid-based methods, difficulty in implementing boundary condition, still this method suits our problem well and has proven to produce good results too despite its shortcomings. SPH is based on integration of a field function to describe the property of continuum. For any function f (x), the integral is represented as f (x) =
( ) ( ) f x ' W x − x ' , h dx,
(2.1)
Ω
where h is called the smoothing length, W (x − x' ) is called the smoothing function/kernel (which is discussed in the next part). The discrete form of above equation is shown as follows:
54
N. Mubarak and R. Kumar
Fig. 1 Support domain of an SPH particle
f (xa ) =
∑
m b f b /ρb W (rab , h),
(2.2)
b
where a is any central particle and b represents particles in its neighborhood. m and ρ are field variables representing mass and density of particles, respectively (Fig. 1). Kernel Function in SPH. The choice of the Kernel function affects accuracy, stability, and efficiency of an SPH scheme. The most commonly used functions are the Cubic Spline Function and the Wendland Function. In the current study, the Cubic Spline Function as shown below has been used. (3) 2 (3) 3 ⎧ q + 4 q 0≤q≤1 ⎨ 1( − 2 ) 1 W (r, h) = α D − q)3 1≤q≤2 (2 ⎩ 4 0 q≥2
(2.3)
where q = r/h and r = |x − x ' |. Boundary Conditions in SPH. The most common approach toward the treatment of boundary condition in SPH so far is the concept of ghost/virtual particles. In order to determine the velocity of virtual boundary particles, the non-slip boundary condition was proposed by [17]. The particles are created on a regular lattice, and relative velocity between real and boundary particles is given by v AB = v A − v B = β(v A − vwall ),
(2.4)
where β is given by [18]. Artificial Viscosity. In order to allow SPH to model shock waves, or to stabilize a numerical scheme, an artificial viscosity is employed in many SPH implementations. The most widely accepted is the one provided by Monaghan. Referred to as Monaghan-type artificial viscosity, Pij , it dissipates kinetic energy in the form of heat at the shock front and also prevents unphysical penetration of particles approaching
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
55
each other. After the insertion of artificial viscosity, the momentum equation is written as ( αβ ) αβ N ∑ σj σi Dviα ∂ Wi j mj + 2 + ∏i j + F. (2.5) = β 2 Dt ρi ρj ∂ xi j=1 Formulas for different terms in Eq. 2.5 have been given in [5]. Tensile Instability and Artificial Stress. The issue of tensile instability arises when the concept of SPH is applied to solids. To counter this problem, the technique called artificial stress method has been developed. This method is based on the idea that a short-range repulsive force can be introduced between two neighboring particles to prevent them from getting too close under tension. The below expression is the modified form of momentum equation after the artificial stresses have been introduced. ( αβ ) αβ N ( ) ∂W ∑ σj σi Dviα ij αβ αβ n mj + 2 + ∏i j + f i j Ri + R j + F, (2.6) = β 2 Dt ρi ρj ∂ xi j=1 where f ij is defined by the ratio, fi j =
Wi j . W (Δd, h)
(2.7)
In the above equation, R αβ is the artificial stress tensor which can be found in detail in (Man et al. 2012). Time Integration. After getting the rate of change of density and velocity at some time T, these parameters need to be obtained for another time step, say T + ΔT. In order to integrate the SPH equations, many methods have been implemented over time, like the Leap-Frog method, Predictor–Corrector method, the Runge–Kutta method, etc. In our model, we have implemented the Leap-Frog method which is highly efficient and practical. The Leap-Frog method can be found in detail in works of [2].
2.1 Soil Constitutive Model The soil constitutive model used in this study is the elastic–plastic model based on Drucker–Prager criterion. This model was implemented into SPH originally by [2]. The yield criterion in Drucker–Prager model is given by f (I1 , J2 ) =
√
J2 + α∅ I1 − kc ,
(2.8)
56
N. Mubarak and R. Kumar
where α∅ and kc are the Drucker–Prager constants such that α∅ is the function of friction angle and kc is the function of cohesion. I1 is the first invariant of the Cauchy stress tensor given by the summation of σ αα , σ ββ , and σ γ γ , and J2 is the second invariant of the deviatoric stress tensor given by j2 =
1 αβ αβ s s , 2
(2.9)
where s αβ is the deviatoric stress tensor. After many transformations, the constitutive equation for Drucker–Prager, elastic– perfectly plastic soil model to be used in SPH was derived as ( )T σ˙ αβ = ω˙ αβ σ αβ + σ αβ ω˙ αβ + 2G e˙αβ ) ( G + K ε˙ γ γ δ αβ − λ˙ 9K sin ψδ αβ + √ s αβ . J2
(2.10)
In the above equation, σ˙ αβ is the total stress rate tensor; G and K are shear modulus and bulk modulus, respectively; δ αβ is the kronecker delta; ψ is the dilatancy angle; ε˙ γ γ and ω˙ αβ are the total strain rate tensor and the rotational strain rate tensor, respectively.
3 Problem Statement The large deformation problem chosen for this study is that of the famous Daguangbao landslide of China, the largest landslide triggered by the Wenchuan earthquake (Magnitude 7.9) of 2008. This landslide covered an area equal to 7.2 km2 and had a maximum width of 2.2 km. The run-out distance was 4.5 km, and the volume of sliding mass was 7.5 × 108 m3 [11].
3.1 Ground Motion In order to analyze the said slope under the seismic action of the Wenchuan earthquake, the horizontal component of the acceleration time history along the North– South direction was used, peak value of which is 0.803 g. This acceleration was recorded at the Qingping station which is 4.3 km far from the landslide site. This acceleration was applied as an external load to each SPH particle to trigger the failure process in the slope. In the code, a user-defined vector function has been introduced to apply an acceleration of 0.803 g to all the SPH particles at the beginning of simulation. (For whole acceleration time history, refer to Zhang et al. [20]).
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
57
Table 1 Soil properties at the Daguangbao site Property
Density ρ (g/cm3 )
Elastic modulus E (GPa)
Poisson’s ratio υ
Friction angle φ (°)
Cohesion c (MPa)
Value
2.5
1.86
0.2
10.8
1.276
3.2 Soil Data for Daguangbao Site (Taken from Zhang et al. [20]) See Table 1.
3.3 Methodology A code based on SPH formulations and principles, written in C++ language, has been modified in the Visual Studio. The Drucker–Prager constitutive model for soil has been incorporated into the SPH formulations to capture the stress–strain behavior. The topographical data and soil and stratum properties of the Daguangbao site were entered into the code to generate output files which were of the XMF format. The slip surface was pre-defined from the field data, and below that, fixed boundary condition was assumed. For visualization of the deformation process, the output files were opened in the ParaView software. The flowchart below summarizes different stages of SPH simulation: Flowchart showing working of SPH code
58
N. Mubarak and R. Kumar
START Modify the SPH based code in visual Studio Incorporate the Drucker Prager formulation into SPH Determine the input information + introduce coordinates for initial geometry Generate the particle list
Apply horizontal PGA of Wenchuan earthquake to each SPH particle Useracc = vec_t (0.803g, 0.0, 0.0), (in addition to the gravitational load) Computation of forces between particles
Post-processing (generates output files of xmf extension) OneTime-step Update input information at next time step Visualize results in Paraview (visualization software) END
4 Results and Discussions 4.1 Validation To validate the model, the problem chosen was the experiment of granular column collapse, carried out by [2]. The model was arranged into a rectangular column of 200 mm width and 100 mm height. To represent the soil particles, aluminum bars of diameter 1 and 1.5 mm were used. The friction angle was found out through the direct shear test as 19.8°. The bulk ratio was determined as 0.7 MPa, and the Poisson’s ratio was kept constant as 0.3. Figure 2 represents the initial setup of the validation problem. Green particles represent the fixed boundary, while as the blue particles are the free slip granular particles.
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
59
Fig. 2 Demonstration of setup of the validation problem. Green particles represent fixed boundary and blue particles represent the granular column in initial state
Figure 3 shows different stages during the collapse of the granular column. Maximum deformation is obtained within 0.55 s. Failure is initiated at the free tip as can be seen in Fig. 3b. The velocity of particles has been tracked and maximum velocity magnitude has been found out to be 0.38 m/s. Figure 4 shows the comparison of deformed profiles obtained in the experiment by [2] and the one from numerical analysis, and both have been found to be in very good agreement.
Fig. 3 Failure process of the granular column
60
N. Mubarak and R. Kumar
Fig. 4 Comparison of maximum deformation obtained in the experiment with that obtained from SPH simulation
4.2 Propagation of Daguangbao Landslide The simulation for Daguangbao slide was carried out for 70 s. Figure 5 shows the velocity of particles at different time intervals, right from the initiation to the state of maximum deformation. As is evident from Fig. 5b, sliding starts at 10 s. For the first 30 s, increase in velocity is maximum. It was observed that maximum velocity was achieved after 30 s and was equal to 35 m/s. In the similar analysis carried out by (Man et al. 2012), the maximum velocity achieved by SPH particles was 30 m/s. Figure 5f shows the maximum deformation, which was achieved within 60 s. It is clear from the final profile that there is some kind of separation between the particles. The material seems to be showing expansive behavior which is quite unlikely and needs to be investigated. Figure 6 shows the comparison of actual deformed profile to the one obtained through simulation. It clearly shows that good agreement has been achieved in the first 1042 m and after 3000 m along the distance. However, in the middle portion, the simulation results are varying quite a bit. This shows that the SPH model is overestimating the volume and needs to be modified.
5 Summary The focus of this study was to develop a numerical model which could precisely capture the post-failure phase of landslides, where large deformations are involved. For that purpose, the Daguangbao landslide triggered by the Wenchuan earthquake of 2008 has been modeled using SPH while incorporating the Drucker–Prager soil constitutive model. The slip surface was pre-defined from field data, and the slope was analyzed for the peak value of the north–south component of the ground motion. This
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
61
Fig. 5 Failure process of the Daguangbao landslide (showing variation of velocity with time)
Fig. 6 Comparison of pre- and post-failure topographies
acceleration was applied as an external load to each SPH particle. The final deformed profile obtained from numerical modeling was found to resemble the actual deformed profile of the landslide very closely, except for a small stretch where our model overestimated the volume of the sliding mass. Moreover, an anomaly in the form of separation between the particles could be seen in the final stages, which needs to
62
N. Mubarak and R. Kumar
be investigated. Even though some deficiencies were found in the initial model, the main objective has been chased very closely.
References 1. Bui, H.H., Fukagawa, R.: Sako: an improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: case of hydrostatic pore-water pressure. Int. J. Numer. Anal. Meth. Geomech. 37(1), 31–50 (2013). https://doi.org/10.1002/nag.1084 2. Bui, H.H., Fukagawa, R., Sako, K., Ohno, S.: Lagrangian mesh-free particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. Int. J. Numer. Anal. Methods Geomech. 32(12), 1537–1570 (2008) 3. Bui, H.H., Fukagawa, R., Sako, K., Wells, J.C.: Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH). Geotechnique 61(7), 565–574 (2011) 4. Chen, W., Qiu, T.: Simulation of earthquake-induced slope deformation using SPH method. Int. J. Numer. Anal. Methods Geomech. 38(3), 297–330 (2014) 5. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977) 6. Griffiths, D.V., Fenton, G.A.: Probabilistic slope stability analysis by finite elements. J. Geotech. Geoenviron. Eng. 130(5), 507–518 (2004) 7. Griffiths, D.V., Huang, J., Fenton, G.A.: Influence of spatial variability on slope reliability using 2-D random fields. J. Geotech. Geoenviron. Eng. 135(10), 1367–1378 (2009) 8. Griffiths, G.V., Fenton, D.A.: Seepage beneath water retaining structures founded on spatially random soil. Geotechnique 43, 4(577) (1993) 9. Hiraoka, N., Oya, A., Bui, H.H., Rajeev, P., Fukagawa, R.: Seismic slope failure modeling using the mesh-free SPH method. Int. J. Geomate 5(1), 660–665 (2013) 10. Hu, M., Liu, Q., Wu, F., Yu, M., Jiang, S.: GIS enabled SPH-soil modeling for the post-failure flow of landslides under seismic loadings. Int. J. Comput. Methods 15(6), 1850046 (2018) 11. Huang, Y., Zhang, W.J., Xu, Q., Xie, P., Hao, L.: Run-out analysis of flow-like landslides triggered by the Ms 8.0 2008 Wenchuan earthquake using smoothed particle hydrodynamics. Landslides 9(2), 275–283 (2012) 12. Korzani, M.G., Galindo-Torres, S., Scheuermann, A., Williams, D.J.: Smoothed Particle Hydrodynamics for Investigating of Flood Impacts on Failure Behaviour of an Embankment Under Action of an Overburden Load. Postgraduate Engineering Conference (PEC2016), Brisbane, Australia (2016) 13. Lane, P.A., Griffiths, D.V.: Assessment of stability of slopes under drawdown conditions. ASCE 126, 5(443) (2000) 14. Li, L., Wang, Y.: Identification of failure slip surfaces for landslide risk assessment using smoothed particle hydrodynamics. Georisk (2019) 15. Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics: A Mesh-Free Particle Method, 1st edn. World Scientific, Singapore (2003) 16. Liu, X., Wang, Y., Li, D.: Investigation of slope failure mode evolution during large deformation in spatially variable soils by random limit equilibrium and material point method. Comput. Geom. 111, 301–312 (2019) 17. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82, 1013– 1024 (1997). https://doi.org/10.1086/112164 18. Morris, J.P.: Analysis of Smoothed Particle Hydrodynamics with Applications. Monash University Australia (1996)
Preliminary Studies on Developing a Physics-Based Smoothed Particle …
63
19. Qin, Z., Wang, Y., Liu, X., Li, L.: Development of random smoothed particle hydrodynamics method for landslide risk assessment. In: ISGSR: Proceedings of the 7th International Symposium on Geotechnical Safety and Risk (2019) 20. Zhang, Y., Chen, G., Zheng, L., Li, Y.: Numerical analysis of the largest landslide induced by the Wenchuan earthquake, May 12, 2008 using DDA. In: Earthquake Induced Landslides, 617–626, Springer, Berlin (2013)
Optimization of Single-Track PSC I-Girder for Metro Viaduct A. S. Kidwai, I. Rahman, and Md. I. Ansari
Abstract Metro is becoming a popular mode of urban transportation in the rapidly developing modern world (India). There are two major components in a metro viaduct, substructure and superstructure. Various types of girders used in superstructure are U-Girder, Box Girder, I-Girder, etc. I-Girder is the focus of research in this paper. Design engineers involved in metro projects have used either codal provisions or previously laid down thumb rules for the design of I-Girder. Designs as per these standards give satisfactory results but optimizing the design to obtain an economical section needs further investigation. Optimization of I-Girder is a challenging task due to complexity and correlation among the variables. A large number of variables play an important role in the design of I-Girder such as span, depth of I-Girder, cross-section, grade of concrete, number of I-Girders, Pre/Post tensioning, number of strands. This paper focuses on the computation of optimum cost for different spans and span-to-depth ratio for I-Girder under the influence of dynamic loading. FEM software Midas Civil is used for the analysis. Computation of results and graphical presentation are performed using MS Excel. Results presented in this study may provide a cost-effective guideline for the design solution of an I-Girder metro viaduct superstructure. Keywords Cost optimization · Prestressed I-Girder · Dynamic analysis
1 Introduction In India, metro rail system development is at different stages. Some cities have fully operational system, some at construction stage and some in the planning/design phase. Invariably, metro network is either underground or elevated system. Earlier elevated systems used segmented girders for the viaduct superstructures. I-Girders are better option for wide range of span length and crossing over existing structures. Due A. S. Kidwai (B) · I. Rahman · Md. I. Ansari Department of Civil Engineering, Jamia Millia Islamia, New Delhi, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_6
65
66
A. S. Kidwai et al.
to their light to moderate self-weight, good structural efficiency, ease of fabrication, low maintenance, etc., post-tensioned simply supported prestressed concrete (PSC) I-Girder is commonly used for short and medium span (20–50 m) bridges in many countries. In conventional structure design process, the design method proposes a certain solution that is corroborated by mathematical analysis in order to verify that the problem requirements or specifications are satisfied. Before the design can be finalized, the procedure must go through numerous manual iterations, which makes it slow and expensive process. The design process relies primarily on the experience, intuition and creativity of the designer, which results in a high time, cost and efforts. Optimal design is a solution for the traditional design methodology. An optimum design generally implies the most cost-effective structure without compromising the functional goals. Optimization of metro viaduct I-Girder is not attempted extensively due to complexities such as involvement of a large number of variables, discrete values of variables, difficulties in problem formulation and codal restrictions. Due to use of different materials for construction of prestressed concrete structures, relating the design process to cost optimization is challenging. Hassanain [1] has developed an optimal design model for continuous, precast, pretensioned I-Girder highway bridge using high-performance concrete (100 MPa), that is utilized to perform extensive economic studies [1]. A review of research related to cost optimization of prestressed concrete bridge structures is discussed by [2]. Some studies have been done discussing the optimized design of I-Girder superstructure bridge taking into account the overall cost of materials, fabrication and execution [2]. Sirca and Adeli [3] suggested an approach for lowering the overall cost of the pretensioned PSC I-Girder bridge system by taking into account the amount of concrete used, the thickness of the deck slab, the amount of reinforcement, the surface area of the formwork and the number of beams. The patented resilient neural dynamics model is used to solve the problem, which is formulated as a mixed integer-discrete nonlinear programming problem. They used standard AASHTO sections rather than taking into account cross-sectional dimensions as design factors [3]. Reddy [4] developed a procedure by coupling the design program in FORTRAN language with the standard genetic algorithm tool. The design variables considered are width of top flange, depth of top flange, width of bottom flange, depth of bottom flange, thickness of web and overall depth of girder with the objective of minimization of mass of the structure [4]. Rana et al. [5] have presented a cost optimization method of a post-tensioned precast I-Girder bridge system. The objective was to minimize the sum of the costs of materials, fabrication and installation. The design variables considered were girder spacing, several cross-sectional dimensions of the girder, number of prestressing strands per tendon, number of tendons, tendons’ arrangement, thickness of slab and main reinforcement for deck slab and girder. An optimization algorithm termed as Evolutionary Operation (EVOP) is used for solution [5]. Samir [6] developed a software application for cost optimization of beam bridges. The software application was limited to road bridges in concrete that are straight and have a constant width of the bridge deck [6].
Optimization of Single-Track PSC I-Girder for Metro Viaduct
67
Mantur and Bhavikatti [7] have developed a computer program in C-programming language to design the deck slab and PSC I-Girder. Optimization is carried out by using improved move limit method of sequential linear programming [7]. Fernandes and Bhinge [8] carried out optimized design for PSC I-Girder Bridge of span 30 m. Genetic algorithm method is used for the optimization of I-Girder Bridge and design is carried out by limit state method. A computer program is coded using MATLAB CSI-API software for optimization, and analysis result is retrieved form CSiBridge V20 software to carry out optimization process [8]. Qasim et al. [9] critically reviewed previous bridge structure’s optimization research, provided a detailed examination of optimization goals and outlined recent research field limitations. Structure’s optimization four key steps, including modeling, optimization techniques, formulation of optimization concerns and computational tools, are also researched and examined in depth [9]. The optimal solutions available in the existing literature proposed by different researchers are mostly applicable to the highway bridges and are cumbersome to implement in the design steps. Moreover, there is no specific study available for the optimization of metro viaduct. None of the previous studies have imbibed the provisions of Indian Codes in their modeling/optimization. Therefore, present study is framed in order to conduct the optimization of PSC I-Girder bridge commonly used in the metro viaduct. An optimization process is presented in this study through the cost optimization example of a single-track I-Girder superstructure for elevated metro viaduct.
2 Methodology
Repeat for all Cases
The study presents a well-defined process for the optimization of a PSC I-Girder bridge. The process involves the finite element analysis, design and cost optimization sequence. The process of optimization is presented in the flowchart depicted in Fig. 1. The above figure clearly indicates the optimization steps proposed in the study. I-Girder section is first checked under the design criteria such as SLS and ULS for
Select Span/ Depth/ Grade of Concrete for I-Girder
Analysis using FEM software
Fail - Redesign Calculate optimum cost of I-Girder section
Fig. 1 Optimization process for I-Girder
Pass
Design for ULS Section & Shear Capacity
Design for SLS Optimum PreStressing Layout
Fail - Redesign
Pass
68
A. S. Kidwai et al.
different spans, depth and grade of concrete for I-Girder sections. Once the section satisfies the SLS and ULS criteria, all the I-Girder sections are compared based on the cost. The optimum cost is then proposed for different span lengths (20, 30 and 40 m) of the metro viaduct. In order to depict the optimization process, an example of cost optimization process for a typical PSC I-Girder for metro viaduct is presented in the study. The modeling and analyses are carried out using Midas Civil software. A total of 27 different cases for I-Girder are considered based on nine different variables related to span, depth and concrete grade of bridge, i.e., 20, 30, and 40 m spans, 1.5, 2 and 2.5 m depths and M40, M50 and M60 grades of concrete. The process starts with selecting any one combination of span/depth/grade of concrete and is checked for Serviceability Limit State (SLS) and Ultimate Limit State (ULS) combinations. If the section is found safe at each step, then optimization process is continued till the cost optimization. This process should be repeated for all possible cases. The present study presents a total of 27 number of cases.
2.1 Finite Element Analysis and Design of I-Girder I-Girders of spans 20, 30 and 40 m with depth of girder 1.5, 2 and 2.5 m are modeled in Midas Civil as per the typical structural drawings shown in Figs. 2, 3 and 4. After laying out the geometry of I-Girder, material properties are assigned to the respective structural members and support conditions are assigned. The girder bearing support condition (simply supported) for the I-Girder is shown in Fig. 5.
Fig. 2 Elevation view of I-Girder
Fig. 3 Top plan of I-Girder
Optimization of Single-Track PSC I-Girder for Metro Viaduct
69
Fig. 4 End-section and mid-section of I-Girder
Fig. 5 I-Girder bearing support condition
222
224 Y Z
221
223 Fix Free
After supports are assigned, loads are applied. For dead load, self-weight command is added to assign dead loads to the structure. The dead load includes the self-weight of the I-Girder in the initial stage and composite weight (I-Girder and top slab) in the later construction stage. Super-imposed dead load or SIDL is taken as per DMRC Phase IV Specifications [10]. The dynamic load or live load of metro train is taken as per DMRC Phase IV Specifications [10]. The Train Live Load will have the following axle configuration (trailer/motor car) as shown in Fig. 6. All axle loads = 17 tons = 166.8 KN. Maximum number of successive cars: 6. Fig. 6 Metro coach axle configuration
70
A. S. Kidwai et al.
Configuration: a = 2.25 m. b = 2.50 m. c = 12.60 m → (2a + 2b + c = 22.1 m). Impact factor is calculated as per IRS Bridge Rule Clause 2.4.1.1 [11]. Braking/traction load of metro train is taken as per DMRC Phase IV Specifications. Braking load is taken as 18% of the unfactored axle load. Traction load is taken as 20% of the unfactored axle load. Since only one track is considered in our problem, load applied is that of traction as it is larger and more critical of the two cases [10]. Seismic design philosophy as stated in IRS Seismic Code has been considered [12]. The wind load shall be calculated as per § 2.11 of IRS: Bridge Rules and as per § 5.3 of IS: 875 (Part 3) [11, 13]. Differential temperature loads are calculated as per DMRC Phase IV Specifications [10]. It is calculated for the top and bottom parts of I-Girder in case of temperature rise and temperature fall and is applied in Midas Civil with the help of inbuilt standard functions. Prestressing steel will be conforming to IS: 14268 [14], class 2 Low Relaxation-uncoated stress-relieved strands with the following characteristics: Pretensioning (superstructure): Nominal area of strand: As = 140 mm2 . Nominal ultimate stress: f pu = 1860 MPa. Initial jacking has been taken as 75% of ultimate stress. Maximum jacking stress: 0.75 f pu = 1395 MPa. Modulus of elasticity: E p = 195,000 MPa. Yield strength: f y = 1618 MPa. Serviceable Limit State or SLS combinations and Ultimate Limit State or ULS combinations are taken as given in DMRC Phase IV Specifications [10]. SLS combinations are used to check stresses developed in I-Girder, and ULS combinations are used for shear capacity check as per IRS Concrete Bridge Code:1997 [15]. Typical Midas Civil model used for analysis is shown in Fig. 7.
Fig. 7 Midas Civil model for I-Girder (isometric and front views)
Optimization of Single-Track PSC I-Girder for Metro Viaduct
71
3 Result and Discussion Midas Civil is used to perform the analysis and design of I-Girder superstructure of metro viaduct. The results obtained from Midas Civil are checked and verified with the help of basic calculations to ensure that the results are correct. The analysis and design of all the 27 cases, i.e., 3 × 3 × 3 matrix of 20, 30 and 40 m spans, 1.5, 2 and 2.5 m depths and M40, M50 and M60 grades of concrete for I-Girder are carried out and presented in the form of summary in Table 1. Based on the results obtained, various graphs are plotted so as to understand the relation between variables more clearly, and accordingly, conclusions are made. The typical analysis results obtained from Midas Civil for SLS/ULS combinations are shown in Figs. 8 and 9. The governing case for prestressing strands is SLS stresses developed in top and bottom fibers. It is clear from Fig. 8 that the stress margin is of 0.5 MPa so as to optimize the section. ULS shear force governs the shear capacity of the section. From Table 1, it can be observed that for M40 grade of concrete and 1.5 m depth of I-Girder, all of 20, 30 and 40 m spans are unsafe. Hence, for M40 grade of concrete, optimum span-to-depth ratio comes out to be 10. For other higher grades—M40 and above, optimum span-to-depth ratio may be taken as 13.3 for safe design considering both SLS and ULS load combinations.
Fig. 8 SLS stress at bottom fiber of I-Girder
72
A. S. Kidwai et al.
Fig. 9 ULS shear force diagram for I-Girder
3.1 Cost of I-Girder for 20, 30 and 40 m Spans To study the variation of cost, a graph is plotted with cost on the vertical axis and grade of concrete, depth of I-Girder on the horizontal axis. It would not be possible to compare the cost of individual spans of I-Girder. Figure 10 depicts the results obtained after analysis and design of different cases of I-Girder. Figure 10 shows that the I-Girder is found to be unsafe with respect to design parameters whenever its cost is reduced to a value of Rs. 18,00,000 or below.
3.2 Cost of 120 m Elevated Viaduct Variables considered to draw the graph shown in Fig. 11 are grade of concrete, span and depth of I-Girder on the horizontal axis and combined cost of pier, pier cap and I-Girder on the vertical axis. Spans of I-Girder such as (M40, 20, 1.5 m), (M40, 30, 1.5 m), (M40, 40, 1.5 m) failed in shear capacity criteria and are not considered.
4 Conclusion Before tendering of any construction project, preliminary design is carried out and an approximate optimized cost is calculated and proposed. Optimization of I-Girder for metro viaduct is a challenge due to complexity and correlation among the variables.
Optimization of Single-Track PSC I-Girder for Metro Viaduct
73
Table 1 Summary of results for I-Girder Grade of concrete for I-Girder
Span (m)
M40
20
30
40
M50
20
30
40
M60
20
30
40
Depth (m)
PT strands per I-Girder
Shear capacity
1.5
27.00
FAIL
2
23.00
PASS
2.5
21.00
PASS
1.5
51.00
FAIL
2
39.00
PASS
2.5
34.00
PASS
1.5
59.00
FAIL
2
59.00
FAIL
2.5
54.00
PASS
1.5
27.00
PASS
2
23.00
PASS
2.5
21.00
PASS
1.5
51.00
PASS
2
39.00
PASS
2.5
34.00
PASS
1.5
59.00
FAIL
2
59.00
PASS
2.5
54.00
PASS
1.5
27.00
PASS
2
23.00
PASS
2.5
21.00
PASS
1.5
51.00
PASS
2
39.00
PASS
2.5
34.00
PASS
1.5
59.00
FAIL
2
59.00
PASS
2.5
54.00
PASS
Bold, Italics and bold italics refer to the approval of design parameters
A large number of variables play an important role in the design such as span, depth of I-Girder, cross-section, grade of concrete, number of I-Girders, Pre/Post-tensioning, number of strands. In the present study, three variables are considered in the present study, i.e., span, depth of I-Girder and grade of concrete. The study is conducted assuming: two number of I-Girders are laid, I-Girder spans are straight, prestressing properties of each strand is constant, size of flange and thickness of web are constant, temperature conditions remain same throughout, live load conditions remain same, support condition remains same. A 120 m span length is selected for the cumulative
74
A. S. Kidwai et al.
Fig. 10 Cost of I-Girder for 20, 30 and 40 m spans
Fig. 11 Cost of I-Girder for 120 m span
calculation for different spans while optimizing the cost. The optimized cost of all the spans is calculated and compared. From the results, it is observed that the most optimized I-Girder is of 20 m span with 2 m depth and M40 grade of concrete, while the most expensive I-Girder is being 40 m span with 2.5 m depth and M60 grade of concrete. Based on the results presented, for 1.5 m depth of I-Girder and considering M40 grade of concrete, all I-Girder spans from 20 to 40 m are found to be unsafe.
Optimization of Single-Track PSC I-Girder for Metro Viaduct
75
Another important proposal of this research is optimum span-to-depth ratio. The optimum span-to-depth ratio may be taken as 10 for M40 grade of concrete, and this ratio may be increased to 13.3 for M50 and higher grades. For further studies, a greater number of tracks can be incorporated; depth below 1.5 m, spans above 40 m and below 20 m, cost of pier cap, pier and foundation, etc. may be considered for the optimization process.
References 1. Hassanain, M.A.: Optimal Design of Precast I-Girder Bridges Made with High-Performance Concrete, Calgary, (1998) 2. Hassanain, M.A., Loov, R.E.: Cost optimization of concrete bridge infrastructure. Can. J. Civ. Eng. 30, 841–849 (2003). https://doi.org/10.1139/l03-045 3. Sirca, G.F., Adeli, H., ASCE, F.: Cost optimization of prestressed concrete bridges. J. Struct. Eng. 131, 1–9 (2005). https://doi.org/10.1061/ASCE0733-94452005131:3380 4. Reddy, M.S.: Optimum Design of Prestressed Concrete Girders Using Genetic Algorithms— Dissertation (2007) 5. Rana, S., Ahsan, R., Ghani, S.N.: Design of prestressed concrete I-Girder bridge superstructure using optimization algorithm. In: IABSE-JSCE Joint Conference on Advances in Bridge Engineering-II, Dhaka, 2010, pp. 1–13 6. el Mourabit, S.: Optimization of Concrete Beam Bridges Development of Software for Design Automation and Cost Optimization. KTH Royal Institute of Technology (2016) 7. Mantur, P.D., Bhavikatti, S.S.: Optimization of precast post-tensioned concrete I-Girder bridge. Int. Res. J. Eng. Technol. (2017). www.irjet.net 8. Fernandes, R.J., Bhinge, D.: Optimization of I-girder bridge using genetic algorithm method. Int. J. Sci. Res. 7, 1–3 (2018) 9. Zaheer, Q., Yonggang, T., Qamar, F.: Literature review of bridge structure’s optimization and it’s development over time. Int. J. Simul. Multi. Design Optim. 13, 1–18 (2022). https://doi. org/10.1051/smdo/2021039 10. Delhi Metro Rail Corporation Ltd.: Outline Design Specifications for Phase-IV (Revision-1) (2019) 11. Research Designs and Standards Organization Lucknow, Bridge Rules (2014) 12. IRS Seismic Code: Seismic Code for Earthquake Resistant Design of Railway Bridges (2020) 13. IS:875-Part-3: Design Loads (Other Than Earthquake) for Buildings and Structures—Code of Practice (2015) 14. IS 14268: 2017: Uncoated Stress Relieved Low Relaxation Seven-Wire (Ply) Strand for Prestressed Concrete—Specification (2017). www.standardsbis.in 15. Indian Railway Standard: Code of Practice for Plain, Reinforced & Prestressed Concrete for General Bridge Construction (Concrete Bridge Code) (1997)
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation A. M. George and S. Veeraraghavan
Abstract The seismic response of a structure depends on many factors such as earthquake fault properties, local site conditions like local topography, soil stratigraphy, soil saturation, and structure material. For structures like dams that are located near a large water body, to simulate a realistic site response, the effect of pore water on seismic wave propagation must be coupled with the local site conditions. The present study aims to investigate the effect of a fluid-saturated porous medium on seismic wave propagation at a fundamental level. The MASTODON/MOOSE software developed by Idaho National Laboratory is used for numerical analysis. A threefield coupled model (u-p-w) is implemented in a finite element framework to analyze the problem and verified using analytical results. Models of the 1D soil column and 2D idealized dam geometry in saturated and dry conditions subjected to vertically propagating Ricker SV wave are simulated. To isolate the impact of pore water, the estimated response for each case is compared against similar scenarios with the dry condition. The results from this study give an insight into seismic wave propagation in saturated porous medium and will facilitate different structures’ economical and optimal design and liquefaction studies. Keywords Wave propagation · Saturated porous medium · Dynamic response
1 Introduction The dynamic behavior of a saturated and partially saturated porous medium is of high importance for many civil engineering constructions. To ensure structures’ safety in earthquake-prone regions, the design must consider all the site-specific parameters related to the structure. For structures like embankment dams, due to their proximity A. M. George (B) · S. Veeraraghavan Department of Civil Engineering, IISc Bangalore, Bangalore, India e-mail: [email protected] S. Veeraraghavan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_7
77
78
A. M. George and S. Veeraraghavan
to a large water body, it is vital to study the effect of saturation in the soil on its seismic response. Additionally, saturated cohesionless soils subjected to earthquake loads and the subsequent possibility of liquefaction are also widely studied. The transient response of a completely saturated soil medium will be significantly different from a corresponding dry medium, and a fully coupled approach is required to effectively analyze the same. The works from Biot [1, 2] are considered the first study on the transient response of a saturated porous medium. He developed a mathematical formulation for the problem, and later, many researchers extended the study further. Simon et al. [3] published an analytical solution for Biot’s framework for the materials which satisfy dynamic compatibility conditions. de Boer et al. [4] developed 1D analytical solutions based on Laplace transform techniques for formulations based on mixture theories. Apart from these solutions, Gajo et al. [5], Hiremath et al. [6], and Garg et al. [7] also provided analytical solutions for the dynamic response of saturated porous media and studied the wave propagation through the saturated medium. Zienkiewicz et al. [8–10] proposed three mathematical formulations (u-p, u-p-w, and u-w) based on Biot’s theory in a numerical context and compared the different formulations. The u-p-w formulation has solid displacement (u), fluid pressure (p), and relative fluid velocity (w) as unknowns and considers relative acceleration of the fluid. The u-p formulation is a simplified version and neglects the fluid’s relative acceleration, and the u-w formulation assumes the solid–fluid system as compressible. The present study aims to implement a fully coupled three-field formulation (u-pw) in a finite element framework to understand the dynamic behavior of a completely fluid-saturated poroelastic medium. Results obtained from the numerical simulations are then compared with standard analytical solutions for different loading scenarios. The verified model is used to compare the behavior of a dry porous medium with a fully saturated medium.
2 Governing Equations By applying Biot’s theory for elastic waves with various assumptions, governing equations for a completely saturated porous medium subjected to dynamic loads can be developed. The displacement of the solid skeleton is coupled with fluid pressure and relative fluid velocity with the solid. The first equation represents the momentum balance of the overall solid–fluid system. σi j, j − ρ u¨ i − ρ f w˙ i = 0.
(1)
The sign convention used in formulating the equations is such that the tensile stress is taken as positive, where u¨ i is the soil skeleton acceleration and w˙ i is the relative fluid acceleration, and its convective part is neglected. Body forces are also
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation
79
not considered in the equations to single out other significant forces in the system. σ ij is the total Cauchy stress on the system and is related to effective stress (σij ) and fluid pressure (p) by the relationship, σij = σi j + αδi j p,
(2)
where α is the Biot’s constant which is generally assumed to be one for soils, and δ ij is the Kronecker delta. ρ and ρ f are the combined system’s density and fluid’s density, respectively. The densities can be related by the equation, ρ = (1 − n)ρs + nρ f ,
(3)
where n is the porosity and ρ s is the density of the solid. Considering the equilibrium of the pore fluid, the second governing equation can be written as: − P,i − Ri − ρ f w˙ i −
ρ f w˙ i = 0, n
(4)
where R is the frictional drag from viscous coupling and provided by the relation Ri = ki−1 j wj,
(5)
where k ij is the permeability of the medium. Viscous coupling between fluid and solid phases has a crucial role in wave propagation in the saturated medium as the coupling makes the medium dispersive in nature [11]. The final equation derives from the mass conservation equation applied to the fluid phase, which can be expressed as: wi,i + α ε˙ ii +
p˙ = 0, Q
(6)
where Q is the combined compressibility of the solid and fluid phases, and it is given by the relationship: n 1 α−n = + . Q Kf Ks
(7)
K f and K s are the bulk moduli of fluid and solid phases, respectively. Equations 1, 4, and 6 and a constitutive model set up the governing mathematical framework for analyzing a saturated porous medium. The equation of motions for total system (1) and fluid (4) along with flow conservation Eq. (6) takes care the wave propagation mechanism in the saturated soil medium. The unknowns in the problem are solid displacement (ui ), fluid pressure (p), and relative fluid velocity (wi ).
80
A. M. George and S. Veeraraghavan
3 Nerical Modeling The weak form of the system of Eqs. (1, 4, and 6) is developed by multiplying the terms with the corresponding shape functions and integrating them over the domain. N u , N p , and N w are the test functions for the variables solid displacement, fluid pressure, and relative fluid velocity, respectively. The weak form can be written as:
ρ u¨ N u d +
ρ f w.N ˙ u d
σ.dN u d −
+
p.dN u d −
σ n. N u d = 0,
(8)
Boundary term
w
ρ f u.N ¨ d +
w
ρf w.N ˙ w d n
R.N d −
+
w
pn. N w d = 0
p.dN d +
(9)
boundary term
p α∇.(u).N ˙ d
p ∇.(w).N ˙ d +
+
p˙ p .N d = 0. Q
(10)
3.1 Model Description Numerical simulations for the problem are done using the open-source software MASTODON (multi-hazard analysis of stochastic time-domain phenomena) developed by the Idaho national laboratory. The saturated medium is modeled using the “Porous Flow” and “Tensor mechanics” modules available in the software. The existing framework was inadequate for dynamic simulations, so specific terms which were not available in the above-mentioned modules were coded separately to overcome that. A soil column of 10 m length is simulated, and it was discretized using QUAD9 second-order elements. The element size and time step size were selected by the thumb rule in which wavelength is resolved by ten elements [12]. The porous medium is assumed to be linearly elastic, and the properties of the soil used in the
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation Table 1 List of properties [4]
81
Properties
Value
Young’s modulus
2 × 107 Pa
Poisson’s ratio
0.2
Solid density
2000 kg/m3
Bulk modulus of solid
36 × 109 Pa
Porosity
0.33
Coefficient of permeability
0.01 m/s
simulation are given in Table 1. The Newmark–Beta method is used for the time integration with U = 0.7 and β = 0.4. The boundary conditions are set so that for lateral boundaries, displacements in lateral directions are constrained, and displacements in all directions are fixed to zero in the bottom boundary. The pore pressure is set to zero in the top boundary to establish a free flow condition. A schematic of the model is given in Fig. 1. Fig. 1 Representation of the soil column subjected to dynamic loading
82
A. M. George and S. Veeraraghavan
4 Results and Discussion 4.1 Verification The numerical model developed for the saturated porous medium is verified with already established analytical solutions. The comparison is made for both sinusoidal loading and step loading cases. Sinusoidal loading Simon and Zienkiewicz [3] presented analytical solutions for a set of properties (Table 2) which obey Biot’s dynamic compatibility condition, where there is zero relative motion between solid and fluid phases. A load in a sinusoidal pattern of frequency 10 Hz and unit amplitude is applied to the model in the top boundary, as shown in Fig. 1. The response is compared with the analytical solution and matched well. The comparison of results is given in Fig. 2. Time is normalized in such a way that τ = ρkt and displacement is normalized by u∼ = u(0, t) σV0ck , where k is the permeability, V c is the wave propagation velocity, and σ 0 is the amplitude of the stress applied. De Boer et al. [4] provided analytical solutions for transient response of saturated porous medium for a general case of material parameters. The list of properties used for the verification is given in Table 1. A sinusoidal load of the form – 3000 * sin(75t) Table 2 Set of properties which satisfy dynamic compatibility condition expressed in non-dimensional form [3]
Properties
Value (dimensionless)
Young’s modulus
3000
Poisson’s ratio
0.2
Bulk density (ρ)
0.3060
Coefficient of permeability (k)
0.004883
Fluid density
0.2977
Porosity
0.33
Normalized displacement(ṵ)
20 0
0
50
100
150
-20
200
250
simulation analytical
-40 -60
Normalized Time(τ)
Fig. 2 Comparison of analytical and numerical solutions for the surface response of the soil column subjected to sinusoidal excitation
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation
83
Displacement(mm)
0.15 0.1 0.05 0 -0.05
simulation analytical
0
0.05
0.1
0.15
-0.1
0.2
0.25
0.3
Time(sec)
Fig. 3 Comparison of analytical and numerical solutions for the surface response of the soil column subjected to sinusoidal excitation for a general case of material properties
Displacement(mm)
0.35 0.3 0.25 0.2 0.15
Simulation
0.1
Analytical
0.05 0
0
0.05
0.1
0.15
0.2
0.25
Time(sec)
Fig. 4 Comparison of analytical and numerical solutions for the surface response of the soil column subjected to a step loading
is applied at the top boundary, and displacement at the top surface is compared with the analytical solution and is in good agreement, as shown in Fig. 3. Step Loading The numerical model developed is also verified with an analytical solution for a step loading scenario where a load of 3000 N/m2 is given to the top boundary. The model is simulated for properties listed in Table 1. The comparison between analytical and simulated results is shown in Fig. 4. This indicates that the implemented u-p-w model can model response to a wide frequency range loading as a step load contains different frequencies.
4.2 Dry and Wet Models’ Comparison in a 1D Soil Column The transient behavior of a completely saturated poroelastic media is compared with a corresponding completely dry medium to analyze the effect of saturation on its dynamic response. The dry soil column was modeled with zero damping. A Ricker
84
A. M. George and S. Veeraraghavan
wavelet of energetic frequency 10 Hz is applied at the bottom boundary of a 10 m soil column in the lateral direction as acceleration time history. The properties used are given in Table 1. The Ricker wavelet pulse given as input is shown in Fig. 5. The response spectra at the top of the soil column are plotted and compared with the dry model. The amplitude of response of the saturated model was small compared to that of a dry model. This is due to the extra attenuation happening due to the presence of the water. The natural frequency of the saturated system has shifted to the left compared to that of a dry model, as shown in Fig. 6. From the time history of response at the top surface given in Fig. 7, it is evident that the Ricker pulse traveling through the saturated porous soil column is expanding. At the same time, the Ricker pulse has traveled without any change for the dry model. This is because different frequencies travel at different velocities and are attenuated 1.5
Amplitude
1 0.5 0 -0.5
0
-1
0.1
0.2
0.3
Time (sec)
Fig. 5 Ricker wavelet applied as input to the model
Acceleration in x-direction(m/s2)
30 25 20 Wet
15
Input ricker wavelet Dry
10 5 0 0.1
1
10 Frequency (Hz)
100
1000
Fig. 6 Comparison of response spectra of the soil column at the top boundary for the dry and wet porous mediums for the Ricker pulse excitation
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation
85
Acceleration in x-direction(m/s2)
2.5 2 1.5 Wet Dry
1 0.5 0 -0.5 0
0.5
1
1.5
2
2.5
-1 -1.5 -2 -2.5
Time(sec)
Fig. 7 Acceleration time history at the top surface of both dry and wet porous mediums subjected to a Ricker wavelet
at different rates. This shows that the wave propagation through a saturated porous medium is dispersive in nature.
4.3 2D Idealized Embankment Geometry The verified u-p-w model for saturated porous media is implemented in a 2D idealized embankment geometry. The properties of the porous medium used for simulations are given in Table 1. An illustration of the idealized geometry is shown in Fig. 8. A vertically propagating Ricker SV wavelet is applied on the bottom boundary, and the structure’s response is measured at two different points (A and B). The bottom boundary is modeled as a non-reflecting boundary such that the reflected wave impinging on the surface is completely absorbed, and the lateral boundaries are set as periodic boundaries. The acceleration time history of both the points for dry and wet models is presented in Figs. 9 and 10, respectively, and response spectra for both cases are given in Figs. 11 and 12. The amplification seen in the dry model is not visible in a wet model, which may be due to the attenuation from the presence of water. Similarly, there is a significant shift in natural frequency for the saturated model to the left compared to the dry model. Fig. 8 Illustration of the idealized embankment geometry
86
A. M. George and S. Veeraraghavan
10
Acceleration in x-direction(m/s2)
8 6
B (free-field)
4
A (Top)
2 0 -2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
-4 -6 -8 -10 -12
Time(sec)
Fig. 9 Acceleration time history of free-field and top points for fully saturated 2D embankment model 400
Acceleration in x-direction(m/s2)
300 B (Free-field)
200
A(Top)
100 0 0
0.2
0.4
0.6
0.8
1
1.2
-100 -200 -300 -400
Time(sec)
Fig. 10 Acceleration time history of free-field and top points for dry 2D embankment model
5 Conclusions • The three-field coupled formulation (u-p-w) implemented in a finite element framework can efficiently model the dynamic behavior of a saturated porous
Fig. 11 Response spectra of free-field and top points for fully saturated 2D embankment model
Acceleration in x-direction(m/s2)
Effect of Saturated Porous Soil Medium on Seismic Wave Propagation
87
35 30 25 20
B(Free-field)
15
A(Top)
10 5 0 0.1
1
10
100
1000
Frequenzy(Hz)
Fig. 12 Response spectra of free-field and top points for dry 2D embankment model
• • • •
medium. It works for a wide range of frequencies, and relative acceleration is also taken into consideration. The seismic wave propagation in a fully saturated porous medium is dispersive in nature. There is considerable attenuation of waves as it travels through the saturated medium. This is due to the additional coupling offered by the water in the medium. A natural frequency shift was also evident in the completely wet scenario when compared to the dry model. Seismic design involving a saturated porous medium must take this shift into consideration. The dynamic behavior of partially saturated soil is beyond the scope of this paper. The effect of degree of saturation on wave propagation and its mathematical formulations can be found in Zienkiewicz et al. [9, 13].
88
A. M. George and S. Veeraraghavan
References 1. Biot, M.A.: Theory of propagation of elastic waves in a fluid saturated porous solid. I. Lowfrequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956) 2. Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range. J. Acoust. Soc. Am. 28(2), 179–191 (1956) 3. Simon, B.R., Zienkiewicz, O.C., Paul, D.K.: An analytical solution for the transient response of saturated porous elastic solids. Int. J. Numer. Anal. Meth. Geomech. 8(4), 381–398 (1984) 4. De Boer, R., Ehlers, W., Liu, Z.: One-dimensional transient wave propagation in fluid-saturated incompressible porous media. Arch. Appl. Mech. 63(1), 59–72 (1993) 5. Gajo, A., Mongiovi, L.: An analytical solution for the transient response of saturated linear elastic porous media. Int. J. Numer. Anal. Meth. Geomech. 19(6), 399–413 (1995) 6. Hiremath, M.S., Sandhu, R.S., Morland, L.W., Wolfe, W.E.: Analysis of one-dimensional wave propagation in a fluid-saturated finite soil column. Int. J. Numer. Anal. Meth. Geomech. 12(2), 121–139 (1988) 7. Garg, S.K., Nayfeh, A.H., Good, A.J.: Compressional waves in fluid-saturated elastic porous media. J. Appl. Phys. 45(5), 1968–1974 (1974) 8. Zienkiewicz, O.C., Shiomi, T.: Dynamic behaviour of saturated porous media; the generalized Biot formulation and its numerical solution. Int. J. Numer. Anal. Meth. Geomech. 8(1), 71–96 (1984) 9. Zienkiewicz, O.C., Chan, A.H.C., Pastor, M., Paul, D.K., Shiomi, T.: Static and dynamic behaviour of soils: a rational approach to quantitative solutions. I. Fully saturated problems. Proc. R. Soc. Lond. A Math. Phys. Sci. 429(1877), 285–309 (1990) 10. Zienkiewicz, O.C., Chang, C.T., Bettess, P.: Drained, undrained, consolidating and dynamic behaviour assumptions in soils. Geotechnique 30(4), 385–395 (1980) 11. Gajo, A.: Influence of viscous coupling in propagation of elastic waves in saturated soil. J. Geotechn. Eng. 121(9), 636–644 (1995) 12. Tasiopoulou, P., Taiebat, M., Tafazzoli, N., Jeremic, B.: Solution verification procedures for modeling and simulation of fully coupled porous media: static and dynamic behavior. Coupled Syst. Mechan. 4(1), 67–98 (2015) 13. Zienkiewicz, O.C., Xie, Y.M., Schrefler, B.A., Ledesma, A., Biˆcaniˆc, N.: Static and dynamic behaviour of soils: a rational approach to quantitative solutions. II. Semi-saturated problems. Proc. R. Soc. Lond. A Math. Phys. Sci. 429(1877), 311–321 (1990)
Formulation of Response Reduction Factor for Wall-Type Bridge Piers Debaraj Bailung Sonowal and Jayanta Pathak
Abstract The response reduction factor also known as R factor is one of the most significant parameters in the force-based analysis to reduce the maximum considered seismic force by a level that is reliable with the implied ductile capacity of the structure under consideration. Currently, there is a notable difference in the values of response reduction factor for wall-type bridge piers as mentioned in the Indian standard codes as compared with the internationally referred code such as AASHTO, EN1998. The primary goal of this investigation is to formulate the response reduction factor for typical reinforced concrete (RC) wall-type bridge piers located in a highly seismic zone in India by pushover analysis and to show how much conventional or non-conventional value is followed in the Indian standard codes and to formulate the most probable value of R factor for wall-type bridge piers, that are needed to be considered in the design. The nonlinear behavior, sequence, and mechanism of plastic hinge formation are carried out in the structural analysis program SAP2000. Keywords Pushover analysis · Response reduction factor · Wall-type pier · SAP 2000
1 Introduction According to many codes and standards, including AASHTO [1], EN1998 [2], IRC [3], IS 1893 [4], and RDSO [5], the design level earthquake force in response spectrum method is used to determine the seismic design philosophy for bridges, which considers nonlinear response in some components. These designs, which are frequently based on the application of elastic force-based analysis taking into account the corresponding static lateral force approach, are still the most preferred way among D. B. Sonowal (B) Tezpur University, Tezpur, Assam 784028, India e-mail: [email protected] J. Pathak Assam Engineering College, Jalukbari, Assam 781013, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_8
89
90
D. B. Sonowal and J. Pathak
Table 1 Response reduction factor for wall-type pier Name
AASTHO
EN1998
IRC 6
IS 1893
RDSO
Wall-type pier
Critical Ductile Ductile Ductile Ductile 1.5 3.5λ* 3 3 3 Essential Nonductile Nonductile 2.5 Nonductile 2.5 Nonductile 2.5 1.5 1.5 Others 2.0 √ λ = 1, for α ≥ 3, λ = (α/3), for 3 ≥ α ≥ 1, where α = L/h is the shear–span ratio
structural engineers due to their straightforward idea and little processing requirements. When using this method, the design base shear (V d ) is calculated (Eq. 1) by dividing the elastic base shear demand (V e ), which is obtained by performing an elastic analysis and taking into account the elastic pseudo-acceleration response spectrum (for a 5% damping), by a factor R, also known as the response reduction factor: Vd = Ve /R
(1)
The R factor is applied at the system level in building design, but it is done at the component level in bridge design. This is the fundamental difference between how the R factor is implemented for seismic design of buildings and bridges. In a building’s seismic design, components chosen to exhibit inelastic behavior during the design base earthquake have the same R-value. However, the R factor is used at the component level for bridge seismic design, meaning that various R values are required for various components of the same structure. To maintain the entire structure within the elastic range, correct R values are necessary for bridge seismic design. The prescribed R factor value, which is given in Table 1, varies significantly between the various codes for reinforced concrete (RC) wall-type bridge piers. A catastrophic situation may result from the under or overestimation of the R factor, which can cause brittle or extremely flexible breakdown modes during seismic occurrences. This study’s major goal is to acquire R for RC wall-type piers that are planned and detailed in conformity with Indian standards of practice. Due to the lack of a clear foundation for assigning a specific value of R to these RC wall piers in the literature, the R factor for RC wall-type piers is calculated in the current study by considering several acceptable performance limit states through nonlinear static (pushover) analysis.
2 Components of Response Reduction Factor Strength, ductility, and redundancy are three key structural system factors that affect the response reduction factor [6]. Recent research as mentioned in ATC [7], is in
Formulation of Response Reduction Factor for Wall-Type Bridge Piers
91
favor of a revised formulation of R, which is written as the product of the following three variables as mentioned in Eq. 2: R = R S Rμ R R Rξ
(2)
where Rs is the strength factor, Rμ is the ductility factor, RR is the redundancy factor, and Rξ is the damping factor. The fourth element Rξ (viscous damping factor), which is incorporated in the revised formulation, applies to buildings with additional energy dissipation devices and principally accounts for the influence of externally applied viscous damping. This damping factor was left out of the new formulation and, thus, was not considered in this investigation because response reduction factors are used with force-based design processes.
2.1 Over-Strength Factor (RS ) The over-strength factor (Rs ) may be defined as the ratio of maximum or ultimate base shear (V u ) to the design base shear (V d ) and is calculated as per equation number 3 as Rs = Vu /Vd
(3)
Due to greater designed capacity than the nominal design actions, higher material strengths than specified nominal strengths, and the provision of a little bit more reinforcing than is necessary, a structure’s maximum lateral strength (V u ) will typically surpass its design lateral strength (V d ). A pushover analysis of the structural system and the creation of a representative force–displacement relation for the structure, such as the base shear against deck displacement relation for a bridge as mentioned in FEMA [8], can be used to determine the over-strength factor. A collection of 25 reinforced concrete (RC) circular bridge piers were the subject of a study by Ghee et al. [9] that considered the effects of axial load, transverse reinforcement, and flexural ductility on over-strength. The over-strength factor was discovered to be between 1.0 and 2.3. In their study of seven bridges in a seismically active region of Europe, Kappos et al. [10] discovered over-strength factors between 1.3 and 3.4 in the longitudinal direction and between 1.2 and 5.8 in the transverse direction of bridge, respectively. In this present study, the over-strength factor is calculated using pushover analyses as the ultimate shear force to yield shear force ratio.
92
D. B. Sonowal and J. Pathak
2.2 Ductility Reduction Factor (Rµ ) The difference between the maximum pier top displacement and the yield displacement is known as the ductility reduction factor (Rμ ). There has been a lot of investigation on the connection between displacement ductility and the ductility-dependent R factor. The ductility factor has been defined in several research, including those by Newmark and Hall [11], Krawinkler and Nassar [12], and Miranda and Bertero [13]. These studies used single degree of freedom (SDOF) systems that were subjected to various kinds of ground motion. In this study, the ductility factor is considered using Newmark and Hall’s [11] approach. The relationship for Rμ as a function of μ, for short, moderate, and long period structures, is shown below in equation number 4–6: Short period T < 0.03 s Rμ = 1
(4)
Intermediate period 0.12 < T < 0.5 s Rμ =
√ (2μ − 1)
(5)
The long period T > 1 s Rμ = μ
(6)
2.3 Redundancy Factor (RR ) According to NCHRP Report 458 [14], redundancy of a bridge substructure is the ability of the substructure system to continue carrying loads if one or more of its components fail. On the redundancy factor of bridge substructure, a brief investigation is conducted. NCHRP Report 458 states that the wall-type bridge pier falls into the non-redundant substructure category and suggests using a system factor of 0.8 as a redundancy factor.
3 Methodology Pushover analysis, a nonlinear static analysis technique, is used to determine the response reduction factors for bridge piers. Pushover curves are generated for the pier in both the longitudinal and transverse directions. In this present study, piers are considered to connect to the deck through bearings, which is common in bridges in India. According to Priestly et al. [15], the lumped mass concept is represented by a
Formulation of Response Reduction Factor for Wall-Type Bridge Piers
93
single pier with contributing mass from the two nearby half spans of the superstructure. The development of plastic hinges at their bases results in the inelastic behavior. The lumped plasticity model in SAP2000 [16] is used to describe these plastic hinges. Foundation compliance was modeled using fixed conditions at the bottom of the bridge pier. The plastic moment capacity of the bridge piers is calculated by moment– curvature (M − ϕ) analysis based on material properties as per CALTRANS [17]. For modeling concrete in the cross-section of bridge piers, Mander’s [18] confinement model has been used. The section has been modeled in the ‘Section Designer’ tool of SAP200 nonlinear software. For longitudinal steel, an elasto-plastic model has been used. The sections and material properties are used to develop the moment– curvature curves for the pier section, which are further used to develop the momentrotation curves. For estimating the moment-rotation curves from the moment–curvature curves, plastic hinge length (L p ), suggested by Priestley et. al., and recommended by CALTRANS has been used ans is mentioned in equation number 7: L p = 0.08L + 0.022 f y dbl
(7)
where L is the length of pier measured from the point of a maximum moment to point of contra-flexure, f y is the yield stress, and d bl is the diameter of the longitudinal reinforcement in the pier section.
4 Numerical Study In this study, a 2-lane superstructure having dead load of 8905 kN and 7242 kN on the intermediate pier is considered for a 35 m and 30 m span, respectively, as per standard plans of MORTH [19]. Cantilever wall-type piers of four different heights (3, 5, 10, and 15 m) with dimensions 4.9 m × 1.3 m are considered for the study. A typical configuration of the bridge pier is shown in Fig. 1. The design and reinforcement detailing of the piers for seismic load are carried as per IRC: 6:2017 and IRC: 112:2011 [20], respectively, for seismic zone V, with an importance factor of 1.2, and a response reduction factor of 3 on rocky or hard soil sites. The piers have 82 numbers of 25 mm dia. longitudinal reinforcement and two different cases of spacing of transverse reinforcement in the form of rectangular ties of 12 mm diameter, one at 140 mm centers and another 250 mm centers, respectively, considered for the study. In all numerical models, the concrete cover of 50 mm, concrete grade of 30 MPa, and reinforcement grade of Fe415 are used.
5 Result and Discussions This section includes the findings of over-strength factor, ductility reduction factor, and response reduction factor estimation which are presented and summarized in
94
D. B. Sonowal and J. Pathak
Fig. 1 Typical cross-section of the bridge pier with reinforcement detailing
Table 2. The bridge considered in this study is only supported T beam girder bridge seated in roller and rocker bearing. For all the piers, a moment–curvature analysis is carried out using section designer in SAP 2000. The pushover analysis is carried out by incrementally increasing the lateral load at the top of the pier to determine the sequence of plastic hinge and collapse mechanism formations. Figures 2 and 3 show the force–displacement relations that were found from the pushover analysis. Table 2 Over-strength factor, ductility factor, and response reduction factor Pier height in m
Span in m
Spacing of stirrups in mm
The time period in s
Rs
μ
Rμ
RR
R (Rs Rμ RR )
15
30
140
1.3
1.2
6.7
3.5
0.8
3.4
10
0.67
1.2
7.8
3.8
0.8
3.6
5
0.3
1.2
9.6
4.2
0.8
4.0
3
0.11
1.0
2.2
1.8
0.8
1.4
1.3
1.2
6.5
3.4
0.8
3.3
10
0.67
1.2
7.1
3.6
0.8
3.5
5
0.3
1.2
8.3
3.9
0.8
3.7
3
0.11
1.0
3.9
2.6
0.8
2.0
1.3
1.2
5.6
3.2
0.8
3.1
10
0.67
1.2
6.2
3.3
0.8
3.2
5
0.3
1.2
7.6
3.7
0.8
3.6
3
0.11
1.0
2.2
1.8
0.8
1.4
15
15
35
30
250
1.3
1.2
5.4
3.1
0.8
2.9
10
0.67
1.2
5.3
3.1
0.8
2.9
5
0.3
1.2
6.0
3.3
0.8
3.2
3
0.11
1.0
3.9
2.6
0.8
2.0
15
35
140
250
Formulation of Response Reduction Factor for Wall-Type Bridge Piers
95
Fig. 2 Pushover curve of wall-type pier for span 30 m with stirrups @140 mm centers
Fig. 3 Pushover curve of wall-type pier for span 35 m with stirrups @140 mm centers
From the study, it has been seen that the over-strength factor value falls in the range of 1–1.2, the ductility factor in the range of 1.8–3.7, and the response reduction factor in the range of 1.4–4.0, respectively. With increasing the pier height (aspect ratio equal to or more than 3.5), the flexural behavior of the member dominates whereas the shear behavior dominates with decreasing pier height (aspect ratio equal to or less than 2.3). Under the flexural condition, the ductility factor and the response reduction factor also increase with decreasing in the spacing of transverse reinforcement. Comparisons are made between the estimated response reduction factor for the piers under study and the values recommended by various international and Indian codes. The IRC 6:2017, IS 1893 part 3:2014 and RDSO prescribed the same value of
96
D. B. Sonowal and J. Pathak
R equal to 3 for piers with ductile detailing in the longitudinal direction irrespective of the flexural or shear behavior of the member. The value prescribed by the Euro code is depending upon the L/h ratio, which implies that the R factor is 3.5 for flexuraldominated pier only. AASTHO specifies the R-value as 1.5, 1.5, and 2 depending upon the operational categories critical, essential, and other, respectively. In this study, the estimated R factor which varies from 1.4 to 6.7 in the longitudinal direction for ductile detailing indicated that the Indian code’s prescribed value holds good for the bridge piers having an aspect ratio equal to and more than 3.5 only.
6 Conclusions A preliminary study has been conducted to check the validity of the response reduction factor (R) value recommended in BIS and IRC for rectangular wall-type cantilever piers. The study of evaluation of the R factor for wall-type bridge piers that design and ductile detailing as per IRC reveals that the R values varied depending upon the predominant mode of failure of the piers. It was found that in all cases the prescribed R values of Indian codes cannot be used. Shear failure predominated in situations where the pier aspect ratio (equal to or less than 2.3) was relatively low, and in these situations, the transverse reinforcement spacing was not a crucial consideration. The value of R for that case is much lower (1.4) than the prescribed value and there may be a probability of underestimation of the seismic force. In that case, the R-value prescribed by AASTHO and EN1998 was found more suitable for the estimation of design base seismic force. The transverse reinforcement spacing is only a crucial factor when the failure was caused by the flexural. In that case, the estimated value is higher than the prescribed by the Indian codes. However, from the study, it has been seen that the current provision for the R factor in the Indian code is sufficient for flexural-dominated piers, and therefore, a need for further study is required for the suitable value of R for shear-dominated piers. The conclusions of the present study are limited by the facts that only a twodimensional configuration (without three-dimensional analysis) in one single seismic zone has been considered. In addition, the structural behavior is not validated by any nonlinear time-history analysis. Therefore, future studies will incorporate the effect of three-dimensional modeling with nonlinear time-history analysis of bridges and soil structure interaction on the evaluation of response reduction of wall-type bridge piers.
Formulation of Response Reduction Factor for Wall-Type Bridge Piers
97
References 1. American Association of State Highway and Transportation Officials (AASHTO): AASHTO LRFD Bridge Design Specifications. 5th Edn., Washington, DC (2010) 2. European Committee for Standardization (CEN): Design of Structures for Earthquake Resistance–Part 2: Bridges. Eurocode 8, EN 1998-2, Brussels (2005) 3. IRC 6: Standard Specifications and Code of Practice for Road Bridges Section: II, Loads and Stresses. Indian Roads Congress, New Delhi (2017) 4. Bureau of Indian Standards (BIS): Criteria for Earthquake-Resistant Design of Structures, Bridges and Retaining Walls. New Delhi, India (1893) 5. RDSO: Seismic Code for Earthquake Resistant Design of Railway Bridges. Indian Railways, Lucknow (2020) 6. Whittaker, A., Hart, G., Rojahn, C.: Seismic response modification factors. J. Struct. Eng. 125(4), 438–444 (1999) 7. Applied Technology Council (ATC): Structural Response Modification Factors. Applied Technology Council, California (1995) 8. Federal Emergency Management Agency (FEMA): Quantification of Building Seismic Performance Factors. Washington, D.C. (2009) 9. Ghee, A.B., Priestley, M.N., Paulay, T.: Seismic shear strength of circular reinforced concrete columns. Struct. J. 86(1), 45–59 (1989) 10. Kappos, A.J., Paraskeva, T.S., Moschonas, I.F.: Response modification factors for concrete bridges in Europe. J. Bridg. Eng. 18(12), 1328–1335 (2013) 11. Newmark, N.M., Hall, W.J.: Earthquake Spectra and Design. Earthquake Engineering Research Institute, Oakland, California (1982) 12. Krawinkler. H.E., Nassar, A.A.: Seismic design is based on ductility and cumulative damage demands and capacities. In: Nonlinear Seismic Analysis and Design of Reinforced Concrete Buildings, 31–48, CRC Press (1992) 13. Miranda, E., Bertero, V.V.: Evaluation of strength reduction factors for earthquake-resistant design. Earthq. Spectra 10(2), 357–379 (1994) 14. NCHRP (458:2001): Redundancy in Highway Bridge Substructures. National Cooperative Highway Research Program, Washington, D.C. (2001) 15. Priestley, M.N., Seible, F., Calvi, G.M.: Seismic Design and Retrofit of Bridges. John Willey & Sons (1996) 16. Computer & Structures, Inc. (CSI): CSI Analysis Reference Manual for SAP2000. Berkeley (2017) 17. Caltrans Seismic Design Criteria (SDC 1.6): California Department of Transportation, Sacramento (2010) 18. Mander, J.B., Priestley, M.N., Park, R.: Theoretical stress-strain model for confined concrete. J. Struct. Eng. 114(8), 1804–1826 (1988) 19. Ministry of Road Transport and Highways (MoRTH): Specifications for Road and Bridge Works. New Delhi, India (2013) 20. Indian Road Congress (IRC): Guidelines for Seismic Design of Road Bridges. New Delhi, India (2018)
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet Pile Driving B. Vinoth
and Ambarish Ghosh
Abstract The rapid growth of infrastructure development in metropolitan cities is increasing in tandem with human evolution. The vibration associated with various construction activities is one of the primary issues that have evolved during infrastructure development in metropolitan cities. The construction-induced vibrations mainly occur due to pile driving, blasting, dynamic compaction, and the operation of heavy machinery on site. The dynamic behavior of the soil medium primarily depends on the magnitude of the shear strain developed in the soil media while the pile penetrates. The development of the magnitude of shear strain due to construction-induced vibration is essential to understand the soil’s stiffness characteristics during pile driving. The magnitude of shear strain induced in the soil medium depends on the vibration amplitude with frequency-dependent wave velocity. A field study has been carried out to determine the ground motion parameters during impact sheet pile driving. The ground motion parameter has been obtained in terms of peak particle velocity (mm/s) with varying radial distances of 5–20 m from the alignment of the sheet pile driving. The 750 kg drop hammer has been used to drive the Z section sheet pile up to a depth of 12 m from ground level. The present research work mainly focuses on estimating the shear strain magnitude induced along or very near the ground surface. The current approach relies on the wave propagation method to estimate the shear strain amplitude during Z section sheet pile driving. The values of maximum shear strain induced near the soil surface are 4.1%, 3.65%, 3.18%, and 1.54% at radial distances of 5 m, 10 m, 15 m, and 20 m, respectively, during the driving of the Z section sheet pile. Keywords Shear strain magnitude · Impact hammer · Z section sheet pile driving · Construction-induced vibration · Peak particle velocity B. Vinoth (B) · A. Ghosh Department of Civil Engineering, Indian Institute of Engineering Science and Technology, Shibpur 711103, India e-mail: [email protected] A. Ghosh e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_9
99
100
B. Vinoth and A. Ghosh
1 Introduction Ground vibrations caused by construction activities, particularly pile and sheet pile driving, have one of the most significant sources of ground vibrations in urban areas [1, 2]. The source of vibration is mainly caused by drop hammer or vibratory hammer in pile driving techniques [3, 4]. The sheet pile driving is a complex process in which numerous factors can affect the ground motion amplitude and dynamic behavior of the soil medium. In many dynamic problems, the response of soil medium to external loading is not only dependent on the stiffness of the soil medium but also depends on the energy source, strain rate, damping characteristics and boundary condition, etc. [5]. The dynamic behavior of the soil medium is strongly dependent on the magnitude of shear strain induced in soil medium. To reduce the possibility of building damage due to construction activities, the design engineer must need to specify the allowable levels of ground vibrations, which is often done early in the project. Unnecessarily, conservative estimates will increase costs, limit the options/choice for construction methods, and cause the project to be delayed. On the other hand, if the vibration level is underestimated, it may cause structural damage, occupant disturbance, and the suspension of construction work. To evaluate ground vibrations in the surroundings, it is necessary to understand the various parameters which can be used to define vibration in the ground. Also, the permissible level of ground vibrations needs to be specified by the design engineer at the early stage of a project to reduce the risk of building damage. Some standards have specified permissible level of peak particle velocity associated with frequency range for different types of structures at their different location. However, the peak particle velocity has been widely used to evaluate structural damage due to various construction activities as recommended in different codes [6, 7]. The effects on soil medium due to pile driving is major concern to geotechnical engineers because the repeated dynamic load causes differential settlement, shear strength reduction, liquefaction, ground distortion, and resonance of the soil medium, and these effects are particularly dependent on the serviceability condition of the structure [8]. In present study, the shear strain (%) has been computed from field data, due to Z section sheet pile driving along or near the soil surface at different radial distances from the source (5–20 m). The variation of shear strain (%) for different depth of pile driving (0–12 m) has also been studied.
2 Displacement Gradient Along the Ground Surface The developed shear strain in soil media due to construction-induced vibration is essential to understand the soil’s stiffness characteristics during pile driving. The magnitude of shear strain induced in the soil medium depends on the particle velocity with frequency-dependent wave velocity [9–11]. Consider an elemental volume of soil as shown in Fig. 1. Owing to application of dynamic stress, the point A undergoes the deformation and it is denoted as a u, v, and w in x, y, and z direction, respectively
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
101
Fig. 1 Concept of strain
[12]. Similarly, the adjacent point B undergoes displacement in a soil medium can dy, and w + ∂w dz in the x, y, and z direction, be expressed as u + ∂∂ux dx, v + ∂v ∂y ∂z respectively. Hence, the normal strain in x, y, and z direction can be written as εx =
∂v ∂w ∂u , εy = , and εz = ∂x ∂y ∂z
(1)
Similarly, the corresponding shear strain (%) induced in a soil medium in x, y, and z direction is expressed as [12] γx y =
( ) ( ) ( ) ∂v ∂w ∂w 1 ∂u 1 ∂u 1 ∂v + , γx z = + , and γ yz = + 2 ∂y ∂x 2 ∂z ∂x 2 ∂z ∂y
(2)
The wave propagation in soil medium during pile driving has been predominantly dominated through surface waves (especially Rayleigh wave) because it carries most of the generated energy compared to body waves and travels far from vibration source [13]. The pile driving simulation in soil medium is modeled as surface wave propagation in elastic half-space [14]. The displacement developed in soil medium due to propagation of Rayleigh wave in the vertical (u z ) and horizontal displacement (u y ) [15] can be expressed as (
) 2qk 2 −sz −qz ei (ωt−ky) e − qe uz = w = uo 2 s + k2 ( ) 2iqsk −sz −qz ei(ωt−ky) u y = v = uo 2 e − ike s + k2
(3) (4)
Similarly, the corresponding shear strain (γ yz ) in y−z direction can be represented as
102
B. Vinoth and A. Ghosh
γ yz
( ) ) [( 2qk 2 −sz 1 −qz i (ωt−ky) e −ku o 2 = e − qe 2 s + k2 ) )] ( ( 2qs 2 k −sz −qz i(ωt−ky) e + uo 2 e + qke s + k2
(5)
The particle velocity (u˙ z and u˙ y ) can be determined by differentiating Eqs. 3 and 4 with respect to time (t); (
) 2qk 2 −sz −qz ei (ωt−ky) e − qe u˙ z = w˙ = i ωu o 2 s + k2 ( ) 2iqsk −sz −qz ei(ωt−ky) e − ike u˙ y = v˙ = i ωu o 2 s + k2 ( The displacement gradient ∂w = ∂y
[(
∂w ∂y
(7)
) along the surface can be determined as
( ) )] 2qk 2 −sz k −qz i(ωt−ky) e . i ωu o 2 e − qe ω s + k2
Substituting Eqs. 6 into 8 and into
(6)
k ω
(8)
= VR then the above equation can be simplified ∂w = ∂y
(
u˙ z VR
) (9)
where u˙ z is the peak particle velocity (mm/s) in vertical direction and VR is the Rayleigh wave velocity (m/s).
3 Field Study—Preconstruction Survey The vibration monitoring has been carried out in Kolkata, India, during impact Z section sheet pile driving. The preconstruction study is an initial stage of assessing the impact of vibration from construction sources, to ensure the safety and serviceability of adjacent and remote buildings. The preconstruction survey involves site location, geotechnical investigation, an inspection of surrounding buildings, and their existing condition, finally, to the study the piling details and source of vibration.
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
103
Fig. 2 Sheet pile driving location
3.1 Site Location and Neighboring Structures The site has been located in Ganguli Sarani (Lee Road), Ward No. 70, Bhowanipore, Kolkata, West Bengal, 700,020, India, and its GPS coordinates are 22° 32, 26.4,, N 88° 20, 60.0,, E. The details of the site location are shown in Fig. 2. From the sheet pile center line, the neighboring structures have been located at a distance of 7.5–8.0 m, and it’s observed as old residential and the office buildings (Figs. 4 and 7).
3.2 Geological Profile The subsoil exploration was conducted up to a depth 37.5 m below the E.G.L. Standard penetration tests (SPT) were carried out in soil strata inside boreholes to determine in situ consistency and strength characteristics of the subsoil, in accordance with IS: 2131. Soil samples, both undisturbed and disturbed, were collected from a borehole to carry out a standard laboratory test to determine the soil classification, in accordance with IS:2720. The geological profile for the proposed test site is shown in Fig. 3.
104
B. Vinoth and A. Ghosh
Fig. 3 Soil profile and its classification as per IS 2720
Fig. 4 Vibration source—drop hammer and Z section sheet pile
3.3 Piling Details and Source of Vibration In all over the construction site, the drop hammering techniques begin used to drive the sheet pile. The total mass of the hammer is 750 kg, and the height of fall is 2 m. The Z section sheet pile has been driven up to a depth of 12 m from the ground level. Figure 4 illustrates the vibration source and sheet pile section used in the test site.
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
105
3.4 Vibration Monitoring Instrument Data Acquisition System: The 16 channel OROS vibration spectrum analyzer has been used to measure the ground motion amplitude during sheet pile driving. The spectrum analyzer consists of front-end input and outputs; the OR36 processes parallel analysis with all plug-in analyzers running simultaneously with the front-end inputs. In the present study, the ground motion parameters have been monitoring in both frequency domain (Fig. 6) and time domain (Fig. 8). Seismic geophones: As per IS 14884, the ground vibrations were measured by using HGS 4.5 Hz (natural frequency) seismic geophones. The seismic geophones have been deployed on the ground surface at different radial distances, and it is a uniaxial geophone which can only measure vertical component of the ground motion. The general specification of the seismic geophones is depicted in Table 1. Figure 5 shows the field instrumentation test setup. Table 1 General specification of the seismic geophones
Parameters
Values
Model
HG-6XT UB (HGS)
Natural frequency
4.5 (Hz)
Typical spurious frequency
> 140 Hz
Resistance
375 (ohm)
Damping
0.56
Distortion
0.3%
Sensitivity range
28.8 (V/(m/s))
Fig. 5 Field instrumentation test setup
106
B. Vinoth and A. Ghosh
Fig. 6 PPV (mm/s) in frequency domain
Fig. 7 Vibration monitoring at test site during Z section sheet pile driving
4 Measurement of Ground Motion Data During Z Section Sheet Pile Driving The peak particle velocity (PPV, mm/s) has been mainly used to assess the damage and serviceability condition of the superstructure due to man-made induced vibrations. The total 9 sheet pile driving vibration measurement was obtained from the field study. During sheet pile driving, the PPV has been monitored at different radial distances from 3 to 20 m (i.e., (3, 6, 9, 12 m), (4, 8, 12, and 16 m), and (5, 10, 15, and 20 m)) and the corresponding receiver spacing (Δx) is 3, 4, and 5 m. In the present study, the radial distance (RD) and the receiver spacing (Δx) have been chosen from the following criteria [16]:
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
107
Fig. 8 a, b Measured particle velocity (mm/s) in time domain, c phase angle from the cross-power spectrum (wrapped phase), and d coherence value (faded region in time history)
(0.3D P )min ≤ RD ≤ (2D P )max
(10)
(0.25D P )min ≤ Δx ≤ (0.5D P )max
(11)
In test site, during different depth of sheet pile driving (0 to 2, 2–3, 3–4, 4–6, 6–8, 8–10, and 10–12 m), the particle velocity was measured on the ground surface at varying radial distances. The acquired signal at a 5 m receiver spacing has been presented in Fig. 8a–d. Figure 8a illustrates the acquired particle velocity (mm/s) with respect to time (s), and Fig. 8b shows an observed ground motion due to single blow at varying distance. Similarly, Fig. 8c illustrates the amplitude and phase for the corresponding ground motion signal in frequency domain, and it represents the wrapped phase angle obtained from the cross-power spectrum between the input 1 and inputs 2, 3, and 4, and Fig. 8d illustrates the corresponding coherence value for the obtained spectrum. The shaded region in Fig. 8a has been transformed into frequency domain by using Fast Fourier Transform (FFT), as shown in Fig. 6.
108
B. Vinoth and A. Ghosh
5 Dispersion Analysis During impact sheet pile driving, the generated Rayleigh wave at ground surface contains wide range of frequencies, and it depends on frequency and mechanical properties of the soil. The dispersion of the surface wave mainly occurs due to inhomogeneity in the soil medium (i.e., soil layering). The dispersion analysis is used to determine the Rayleigh wave velocity (m/s) as a function of frequency (Hz) which will be helpful to evaluate the theoretical dispersion curve [17–20]. The experimental dispersion curve is also known as apparent velocity or phase velocity curve. The dispersion analysis has been performed based on SASW test analysis [16, 21].
5.1 Rayleigh Wave Velocity or Phase Velocity (V R or V ph ) Equation 12 describes the Rayleigh wave velocity as a function of distance between two receivers, as well as the propagation time require to travel between the two receivers. V ph =
ΔX t ph ( f n )
(12)
( ) 5.2 Wave Propagation Time or Time Lag (t ph f n ) The time lag has been obtained from the phase difference between two signals. [ ] 1 Δϕ X Y ( f n ) . t ph ( f n ) = fn 2π
(13)
( ) 5.3 Phase Angle or Phase Difference (Δϕ XY f n ) The cross-correlation techniques have been used to determine the phase difference between various receivers spacing. The principal phase angle of the obtained signal ◦ ◦ varies between −180 and + 180 (wrapped or folded phase, Fig. 8c). Unwrapping the phase angle is an important process in determining the wave velocity because it consists the information of travel time between the two receivers. At each frequency, the folded phase to unfolded phase can be determined from the following Eq. 14:
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
109
Fig. 9 a Unwrapped phase angle and b power spectral density curve (PSD)
Δ∅(x y) ( f n )Unwrapped Phase = Δ∅(x y) ( f n )Wrapped Phase ± 2π N
(14)
where N is number of cycles and the obtained test results for the receiver spacing 5 m are shown in Fig. 9a.
5.4 Determination of Rayleigh Wave Velocity or Phase Velocity (m/s) The Rayleigh wave velocity can be calculated using Eq. 12, and Fig. 10a–d illustrates the test findings. Using the simple linear power model, the relationship between Rayleigh wave velocity (m/s) and frequency (Hz) has been investigated. From Fig. 10d, the Rayleigh wave velocity or apparent wave velocity (m/s) is expressed as a function of frequency (Hz) (i.e., VR = 468.72( f )−0.157 ). The frequency mentioned in above expression is the predominant propagation frequency in the soil medium due to sheet pile driving. The predominant frequency can be estimated from the power spectral density curve (PSD curve), as shown in Fig. 9b. Due to sheet pile driving, the predominant propagation frequency lies in the range of 8–46 Hz (for the different radial distances) and the corresponding wave velocity lies in the range of 255–340 m/s.
6 Results and Discussion In this section based on the analysis of the field data, the following test results have been discussed in the following section; (1) The variation of peak particle velocity with radial distance and pile driving depth, and (2) Shear strain (%) variation has also been highlighted in this section.
110
B. Vinoth and A. Ghosh
Fig. 10 a–c Dispersion curve for varying radial distances (5–20 m) with 5 m receiver spacing and d combined dispersion curve for the receiver spacing of 5 m
6.1 Peak Particle Velocity (mm/s) Versus Radial Distance (m) The acquired ground motion data during sheet pile driving at different radial distance 5, 10, 15, and 20 m have been analyzed, and it has been found that the peak particle velocity decreases with increasing the radial distance from the vibration source [22]. As per IS 14884, the obtained PPV values lie within the permissible limit (i.e., 10.42 mm/s < 50 mm/s). The obtained test results are illustrated in Fig. 11a.
6.2 Peak Particle Velocity (mm/s) Versus Pile Driving Depth (m) The peak particle velocity (mm/s) has been measured at different radial distances on ground surface during the depth of pile driving between 0 and 2, 2–3, 3–4, 4–6,
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
111
Fig. 11 a PPV (mm/s) versus radial distances (m) and b PPV (mm/s) versus pile driving depth (m)
6–8, 8–10, and 10–12 m. The observed test result from the field study is illustrated in Fig. 11b, and it has been found that the particle velocity increases with increasing pile driving depth. For the depth of pile driving between 4 and 8 m the maximum particle velocity acquired at the ground surface for this site-specific soil profile.
6.3 Estimation of Shear Strain Magnitude (%) In this present study, the wave propagation-based approach has been used to estimate the shear strain magnitude (%). In wave propagation approach, the shear strain induced in soil medium depends on peak particle velocity (mm/s) and wave velocity (m/s). During sheet pile driving, the different types of waves generate and propagate in the soil medium (surface and body wave); for the greater distance, the surface wave velocity dominates near ground surface than the body wave velocity [23]. But in the soil medium, the shear wave velocity (Vs ) is slightly greater than the Rayleigh wave velocity (VR ) (i.e., Vs > VR ), and it depends on soil stiffness characteristics. Generally, the primary wave carries a very low vibration amplitude, which has dissipated faster than shear and Rayleigh wave [24]. So, at greater distance, the plane wave propagation in the soil medium nearly becomes one dimensional wave propagation, and it’s described in literature [10, 11]. So, Eq. 2 can be rewritten as (
γ yz =
1 ∂w ∂v + 2 ∂y ∂z
)
( / ) ∂v ∂t ≈ VR (or) VS
(15)
Shear strain (%) due to Rayleigh wave can be determined as Peak pearticle velocity γ = VR
( mm ) s
.
(16)
112
B. Vinoth and A. Ghosh
Fig. 12 Shear strain (%) along with the radial distance (m) was calculated near the ground surface a V R = 255 m/s, and b V R = 340 m/s
Fig. 13 Shear strain (%) for the respective depth of sheet pile driving (although the particle velocity was determined on the ground surface) a V R = 255 m/s, and b V R = 340 m/s
The shear strain magnitude (%) has been determined due to Rayleigh wave ) ( velocity VR , ms , and the computed values of shear strain (%) are illustrated in Figs. 12a, b and 13a, b.
7 Summary and Conclusion This paper presents the determination of shear strain (%) magnitude due to driving of Z section sheet pile on near the ground surface (not in the body of the soil medium) The shear strain (%) has been computed based on the wave propagation method.
Estimation of Shear Strain Magnitude Due to Impact Z Section Sheet …
113
Based on the analysis of the field observation, the following conclusion may be drawn: 1. In the present study, the maximum PPV value was found about 10.42 mm/s at a radial distance of 5 m during the driving of Z section sheet pile by using drop hammering mechanism, and these values lie within permissible limit [7]. As per IS 14884 (2000), the permissible limit of PPV is 0.2–50 mm/s due to pile driving ground borne vibration induced by transient motion. 2. At a distance of up to 0.4 D p (D p is the depth of pile driving) from the sheet pile driving location attained a maximum shear strain magnitude, which lies in the range of 4.1–3.1 (%) which has a potential to cause permanent deformation. Similar to this, the shear strain (%) lies in the range of 3.65–2.74 (%), 3.18–2.38 (%), and 1.54–1.15 (%) are found at a distance of 0.4Dp –0.8Dp , 0.8Dp –1.25Dp , and 1.25Dp –1.5Dp from the sheet pile driving location (Fig. 13). 3. In the present study, it has been found that the shear strain (%) depending on both soil type and the depth of pile driving. As a result of sheet pile driving in loose fill material (stratum I), the shear strain (%) induced on the ground surface lies in the range of 1.44–1.92 (%). Similar to that, the stratum II a brownish-gray silty sand (SM/SP), the maximum shear strain (%) reaches 3.1–3.5 (%). Moreover, it was found that 3.65–4.1 (%) shear strain was calculated during sheet pile driving in stratum III (medium to stiff silty clay/clayey silt—CH) (Fig. 12). 4. The shear strain magnitude (%) decreases with increasing the radial distance from the vibration source because the strain energy carried by the waves will attenuate geometrically [22]. Likewise, the shear strain (%) on the ground surface increases with the pile driving depth and maximum it occurs at a depth of 4– 11.5 m in stratum III (CH). The permanent ground deformation and soil shearing due to sheet pile driving causes an increase in shear strain amplitude, which leads to soil settlement within one pile length (i.e., 12 m), which happens quite near to the pile driving location [2]. Acknowledgements This work is a part of Government funded project entitled as “Construction induced vibration and its development of mitigation strategy.” We thank the Department of science and Technology and Biotechnology, Government of West Bengal, for providing the necessary funding to carry out this research work.
References 1. Athanasopoulos, G.A., Pelekis, P.C.: Ground vibrations from sheetpile driving in urban environment: measurements, analysis and effects on buildings and occupants. Soil Dyn. Earthq. Eng. 19, 371–387 (2000) 2. Grizi, A., Athanasopoulos-Zekkos, A., Woods, R.D.: Ground vibration measurements near impact pile driving. J. Geotechn. Geoenviron. Eng. 142, 04016035 (2016) 3. Deckner, F., Viking, K., Hintze, S.: Aspects of ground vibrations due to pile and sheet pile driving. Electron. J. Geotechn. Eng. 20, 11161–11176 (2015)
114
B. Vinoth and A. Ghosh
4. Massarsch, K.R., Fellenius, B.H., Bodare, A.: Fundamentals of the vibratory driving of piles and sheet piles. Geotechnik 40, 126–141 (2017) 5. Woods, R.D.: Measurement of dynamic soil properties. In: From Volume I of Earthquake Engineering and Soil Dynamics—Proceedings of the ASCE Geotechnical Engineering Division Specialty Conference, June 19–21, 1978, Pasadena, California. Geotechnical Engineering Division of ASCE (1978) 6. Svinkin, M.R.: Predicting soil and structure vibrations from impact machines. J. Geotechn. Geoenviron. Eng. 128, 602–612 (2002) 7. IS 14884: Mechanical Vibration and Shock—Vibration of Buildings—Guidelines for the Measurement of Vibrations and Evaluation of Their Effects on Buildings (2000) 8. Wiss, J.F.: Damage Effects of Pile Driving Vibration. Highway Research Record (1967) 9. Trifunac, M.D., Todorovska, M.I., Ivanovi´c, S.S.: Peak velocities and peak surface strains during Northridge, California, earthquake of 17 January 1994. Soil Dyn. Earthq. Eng. 15, 301–310 (1996). https://doi.org/10.1016/0267-7261(96)00004-8 10. Vucetic, M.: Cyclic threshold shear strains in soils. J. Geotechn. Eng. 120, 2208–2228 (1994) 11. Brandenberg, S.J., Coe, J., Nigbor, R.L., Tanksley, K.: Different approaches for estimating ground strains from pile driving vibrations at a buried archeological site. J. Geotechn. Geoenviron. Eng. 135, 1101–1112 (2009) 12. Timoshenko, S., Goodier, J.N.: Theory of Elasticity. McGraw-Hill (1951) 13. Richart, F.E., Hall, J.R., Woods, R.D.: Vibrations of Soils and Foundations (1970) 14. Kramer, S.L.: Geotechnical Earthquake Engineering. Pearson Education India (1996) 15. Stein, S., Wysession, M.: An Introduction to Seismology, Earthquakes, and Earth Structure. John Wiley & Sons (2009) 16. Chen, L., Zhu, J., Yan, X., Song, C.: On arrangement of source and receivers in SASW testing. Soil Dyn. Earthq. Eng. 24, 389–396 (2004). https://doi.org/10.1016/J.SOILDYN.2003.12.004 17. Foti, S.: Multistation Methods for Geotechnical Characterization Using Surface Waves (2000) 18. Vinoth, B., Ghosh, A.: Evaluation of wave propagation parameters and attenuation characteristics of homogeneous cohesionless soil media. In: Soil Dynamics, pp. 337–351. Springer (2021) 19. Foti, S., Lai, C.G., Rix, G.J., Strobbia, C.: Surface Wave Methods for Near-Surface Site Characterization. CRC Press (2014) 20. Gabriels, P., Snieder, R., Nolet, G.: In situ measurements of shear-wave velocity in sediments with higher-mode Rayleigh waves. Geophys Prospect. 35, 187–196 (1987) 21. Gucunski, N., Woods, R.D.: Numerical simulation of the SASW test. Soil Dyn. Earthq. Eng. 11, 213–227 (1992). https://doi.org/10.1016/0267-7261(92)90036-D 22. Vinoth, B.: Determination of geometric attenuation parameters of surface amplitude in soil medium due to installation of impact pile casing. In: Dey, A.K., Mandal, J.J., Manna, B. (eds.) Proceedings of the 7th Indian Young Geotechnical Engineers Conference, pp. 327–338. Springer, Singapore (2022) 23. Hwang, J.-H., Liang, N., Chen, C.-H.: Ground response during pile driving. J. Geotechn. Geoenviron. Eng. 127, 939–949 (2001) 24. Trifunac, M.D., Lee, V.W.: Peak surface strains during strong earthquake motion. Soil Dyn. Earthq. Eng. 15, 311–319 (1996). https://doi.org/10.1016/0267-7261(96)00005-X
Simulation of Interaction Properties in Confined Masonry Walls at Wall-to-Tie-Column Interface Vaibhav Singhal , Amit K. Singh, and K. K. Fayaz Ahmed
Abstract The confined masonry (CM) structure consists of load bearing walls strengthened with nominally reinforced concrete tie-elements at the perimeter and other key locations. The confined masonry system has evolved based on its satisfactory performance in past earthquakes and can be considered as one of the most suitable alternatives to seismically vulnerable unreinforced masonry systems due to its similar construction practice and economic feasibility. Thus, various numerical studies using finite element (FE) analysis have been performed on CM walls for a better understanding of their response under in-plane and out-of-plane loads. For reliable FE analysis, it is important to simulate the interaction behavior at the wallto-tie-column interface in CM walls. The current method of defining the wall-to-tiecolumn interaction for FE analysis is to consider both masonry wall and tie-column as monolith. However, this simplified assumption results in stiffer response of the CM wall. Thus, in the present study, the wall-to-tie-column interaction properties were evaluated using experimental and analytical investigation. Initially, tension and shear bond tests were conducted on sub-assemblages consisting of masonry and concrete. The tensile and shear bond properties obtained from the experiments were used to calibrate the cohesive and friction interaction properties for FE analysis. Using the iterative procedure for fine-tuning the interaction properties, a reasonable match was achieved between the experimental and numerical simulations. Finally, the interaction properties such as bond stiffness, damage initiation, and evaluation criteria were proposed for simulating the wall-to-tie-column interaction in CM walls. Keywords Confined masonry · Interaction properties · In-plane load response · Cohesive and friction properties · Numerical modeling
V. Singhal (B) · A. K. Singh · K. K. Fayaz Ahmed Indian Institute of Technology Patna, Patna, Bihar 801103, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_10
115
116
V. Singhal et al.
1 Introduction In India, most of the buildings are constructed using traditional techniques without considering the criteria of earthquake resistance to save the construction cost. Confined masonry (CM) systems are gaining popularity over unreinforced masonry (URM) and reinforced concrete (RC) buildings due to its superior performance and lower cost of construction. Nowadays, this construction technique has gained popularity in many earthquake-prone nations like Mexico, Italy, and China [1, 2]. Postearthquake reports have revealed that only 16% of the CM buildings in Chile earthquake were damaged partially or fully as compared to 57% of all URM buildings [3]. The behavior of confined and unconfined masonry walls subjected to in-plane loads was previously studied by Medeiros et al. [4] using both numerical and experimental results. The interaction between the masonry and concrete was taken as monolithic, and the analysis was simulated by using a macro-modeling approach. The study showed that the force–displacement curve was accurately calibrated for unconfined masonry walls in comparison to the CM walls, which emphasizes the importance of defining interaction properties at the interface. To precisely model the in-plane behavior of CM walls, the interaction properties should be specified as a combination of adhesive and frictional force.
2 Interaction Models The interaction at the brick–concrete interface is required to define in two tangential and one normal direction as shown in Fig. 1. To achieve the separation in both tangential directions, it is required to overcome the adhesive as well as the frictional force, as specified by the traction–separation law and the Mohr–Coulomb criterion shown in Fig. 2a, b, respectively. However, adhesion is the only force, susceptible to the contact opening rule during the separation in the normal direction as shown in Fig. 2c.
3 Determination of Interaction Properties The interaction properties at the interface of brick masonry and the tie-elements are defined based on the tension bond test and triplet shear test on brick-concrete sub-assemblages. A Z-shaped specimen as suggested by Khalaf [5] was prepared for the tension bond test using the locally available burnt clay bricks. To define the interactions, the average tension bond strength along the brick’s flat face and side face was used. A triplet shear test with and without pre-compression was carried out to ascertain the value of the coefficient of friction and shear strength. Six samples
Simulation of Interaction Properties in Confined Masonry Walls …
y
117
y
y x
x
x
z
z
z
Normal interaction surface with cohesive properties
Tagential interaction surface with friction and cohesive properties
(a)
(b)
Fig. 1 Interface definition: a tangential direction and b normal direction
Fig. 2 a Traction–separation law, b Coulomb friction model and c contact opening model
for each test were prepared with a specific concrete mixture, and the samples that showed bond failure were selected to evaluate the associated strengths.
3.1 Tension Bond Test (Normal Direction) To perform the tension bond test, Z-shaped specimens were made by casting the brick and concrete together in a staggered manner. In one case, the brick was laid along its flat face, whereas, in the second case, the brick was laid on its side face. The bond length was kept as half the length of the brick. An extensometer was connected to the test specimen as shown in Fig. 3 to measure the relative separation between the brick and concrete. The test was performed under displacement control rate of 0.5 mm/min. The tension bond test is an indirect method in which the specimen is flexed to measure the bond strength, ƒb . To make the analysis simpler, it is further assumed that the variation of bond stress at the contact is linear. Considering the equilibrium of forces, the ƒb can be calculated as given in Eq. 1.
118
V. Singhal et al. L
L
L/2
F (Force applied) 1
2 t
1
2 w
Brick
L/2
F (Force applied)
Concrete
Brick
Concrete
Extensometer
Extensometer
(1): steel plate or ply (3 mm), and (2): capping material
(a)
(1): steel plate or ply (3 mm), and (2): capping material
(b)
(c)
Fig. 3 Test setup a flat face cast specimen, b side face cast specimen and c brick specifications
Wc fb x 2 w = 3(L b − s)
Lc 2
− s + P(L c − x + s) + Wb L c + (L b + L c − x − 2s)
Lb 2
−x −s
−
Wb L b 2(L b − s) (1)
3.2 Triplet Shear Test (Tangential Direction) The test specimen was prepared by sandwiching the brick between the concrete as shown in Fig. 4. A specifically made setup is used to evenly apply the pressure through the steel plates and nut–bolt assemblies. A hydraulic jack is attached to the assembly to apply the pre-compression pressure. The value of pre-compression was measured with the help of a load cell attached to the setup (Fig. 4). Further, a Mohr–Coulomb’s envelope was plotted for the specimen to determine the coefficient of friction. Based on the force at failure and the area in contact, the shear strength at the brick–concrete interface was estimated for the specimen at different pre-compression levels.
3.3 Experimental Results During the tension bond test, three specimens with flat face and five specimens with side face showed bond failure (see Fig. 5a, b). The variation of stress with the bond separation for both tension bond test is shown in Fig. 5a, b. The values of tension bond strengths with coefficient of variation are given in Table 1. To obtain the value of coefficient of friction, the triplet shear test was performed at different pre-compressions such as 0, 0.24, 0.41, 0.63, and 0.82 MPa. The failure
Simulation of Interaction Properties in Confined Masonry Walls …
119
F (Force applied) Concrete Steel plate/Ply (3mm) Brick Nut and Bolt arrangement
Jack
Load Cell
Steel Section Capping material
Support
Fig. 4 Triplet shear test setup with pre-compression
stress at these pre-compressions are plotted against the applied pre-compressions, and the value of coefficient of friction was found to be 1.12. Similarly, the triplet test was also performed without pre-compression to determine the value of shear strength at the interface. The specimens with shear bond failure are shown in Fig. 5c. The average values of bond strength, adhesive stiffness, and plastic displacement are tabulated in Table 1.
4 Finite Element Modeling and Analysis The parameters such as cohesive/adhesive stiffness and plastic displacement cannot be directly determined through experimental data as the tension bond test that was performed is an indirect method. Therefore, the value of these parameters were obtained by calibrating the finite element analysis results with the experimental result. The FE model was simulated by performing the mesh sensitivity analysis, and a mesh size of 25 mm was adopted for the tension bond test and triplet shear test, as shown in Fig. 6. To simulate a numerical model of confined masonry wall, the interaction between wall and tie elements was defined using the calibrated properties. The contact between the wall at the base was assumed to be rough by specifying the coefficient of friction (μ) as 0.8.
4.1 Material Model Masonry The stress–strain curves proposed by Kaushik et al. [6] and Tripathy and Singhal [7] were used to define the compressive and tensile behavior of the masonry, respectively as shown in Fig. 7a. The ascending part of each curves shows the elastic
120
V. Singhal et al. 0.5
Stress (MPa)
0.4 0.3 0.2
S1 S2 S3
0.1 0.0 0
0.05
0.1
0.15
0.2
0.25
Separation (mm)
(a) 0.5
Stress (MPa)
0.4 0.3 0.2 0.1
S1
S2
S4
S5
S3
0 0
0.05
0.1
0.15
0.2
Separation (mm)
(b) 1.4
Traction (MPa)
1.2 1.0 0.8 0.6 0.4
S1 S3 S5
0.2
S2 S4 S6
0.0 0.0
0.2
0.4
0.6
0.8
1.0
Separation (mm)
(c) Fig. 5 Failure pattern and stress versus separation curve: a tension bond test (flat face), b tension bond test (side face) and c triplet shear test Table 1 Experimentally obtained properties Test type
Brick orientation
Cohesive/adhesive stiffness (MPa/mm)
Plastic displacement (mm)
Bond strength in normal direction (σ nn , σ ss /σ tt ) (MPa)
Tension bond test
Flat face
–
–
0.36 (14%)
Side face
–
–
0.41 (16%)
Triplet shear test
–
1.63
0.69
1.11 (15%)
Simulation of Interaction Properties in Confined Masonry Walls …
121
Fig. 6 Finite element modeling of sub-assemblages
behavior, whereas the descending part represents the post-yield behavior. The ultimate compressive strain for the masonry was considered as two times the strain corresponding to the peak stress (see Fig. 7a). Similarly, for tensile behavior, the ultimate strain was taken as 10 times the strain corresponding peak tensile stress as shown in Fig. 7b. Concrete For concrete, the compressive behavior was defined by using Kent and Park [8] model (Fig. 8a) while tensile behavior was defined using stress–strain relationship as proposed by Gopalaratnam and Shah [9] which is based on the tension softening law as shown in Fig. 8b. The compressive strain (εcc ) and tensile strain (εct ) corresponding to the peak stress were defined as 0.002 and 0.00015, respectively. The value of the dilatancy angle was adopted as 30°, and other properties such as flow potential eccentricity, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress, the ratio of second stress invariant, and viscosity parameter were taken as 0.1, 1.16, 0.667 and 1 × 10−5 , respectively.
Fig. 7 Material model for masonry: a compressive stress–strain curve and b tensile stress–strain curve
122
V. Singhal et al.
⎡ 1 ⎛ ε c − ε c′ ⎞ ⎤ c ⎟⎥ f cc = f cc′ ⎢1 − ⎜ c ⎢⎣ 2 ⎝⎜ ε cc50 − ε cc′ ⎠⎟ ⎦⎥
0.5 f cc′
At ⎡ ⎛ ⎤ εt ⎞ f ct = f ct′ ⎢1 − ⎜ 1 − c ⎟ ⎥ t ⎢ ⎜ ε c ′ ⎠⎟ ⎥ ⎣ ⎝ ⎦
f ct′
where At = Stress ( fc t )
Stress ( f cc )
f cc′
⎡ c ⎛ c ⎞2 ⎤ ε 2ε f cc = f cc′ ⎢ c − ⎜ c ⎟ ⎥ ⎢ ε c′ ⎜ ε c′ ⎟ ⎥ c c ⎠ ⎦ ⎝ ⎣
Ec ε cp f ct′
(
f ct = f ct′ exp − kc wcλc
)
Ec 0.2 f cc′
ε cc′
Strain (ε cc )
ε cc50
ε cc20
(a)
ε ct′
Strain (ε c ) t
(b)
Fig. 8 Material model for concrete: a compressive stress–strain curve and b tensile stress–strain curve
5 Calibration of Interaction Properties 5.1 Tension Bond Properties To calibrate the values of normal cohesive stiffness (K nn ) and other unknown properties, a series of FE models were simulated to match the average experimental curve. As per the iterative analysis, when other parameters were kept constant, the change in the curve was insignificant beyond the K nn value of 50 MPa/mm. Further, the FE analysis showed that a similar match between the analytical and the experimental response was obtained when the values of exponential parameter (e) and the plastic displacement were taken as 4.0 and 0.69, respectively, to define the damage evolution. As a result, these values were further considered for the FE analysis of confined masonry walls. The comparison between the analytical and experimental results is shown in Fig. 9a, b for both side face and flat face specimens, respectively, and final calibrated values are given in Table 2.
5.2 Triplet Shear Test For calibrating the tangential (shear) bond properties, the experimentally obtained stiffness and strength properties from triplet shear test were defined. Further, the same value of exponential decay e and plastic displacement as used for normal interaction were defined for damage evolution. Based on series of iterations, a slightly higher value of cohesive stiffness compared to experimental value was obtained, however, it showed a reasonable match with the test results. This calibrated cohesive stiffness
Simulation of Interaction Properties in Confined Masonry Walls … 0.4
0.5 0.4
Experimental average curve FE Model
0.3
Stress (MPa)
Stress (MPa)
123
0.3 Experimental average curve FE Model
0.2
0.2
0.1
0.1
0
0 0
0.03
0.06
0.09
0.12
0
0.15
0.1
0.2
0.3
Separation (mm)
Separation (mm)
(a)
(b)
0.4
Fig. 9 Comparison of traction–separation response obtained from FE analysis and experiment. a Side face interaction and b flat face interaction
Table 2 Calibrated interaction properties for normal and shear behavior Strength (MPa)
Cohesive stiffness (MPa/mm)
Normal direction, σ n
Tangential direction, σ s or σ t
Normal direction, K nn
Tangential direction, K ss or K tt
0.38
1.10
50
2
Total/plastic displacement (mm)
Exponential parameter (e)
0.6–0.7
4
in tangential directions (K ss or K tt ) was found to be 2 MPa/mm. Figure 10 shows the comparison of traction response obtained from the experiment and the FE model. 1.2 Experimental average curve
1
Traction (MPa)
Fig. 10 Comparison of traction–separation response obtained from FE analysis and experiment
FE model
0.8 0.6 0.4 0.2 0 0
0.3
0.6
0.9
Displacement (mm)
1.2
1.5
124
V. Singhal et al.
6 Validation of Interaction Properties The proposed interaction properties (Table 2) were validated by simulating the inplane behavior of the confined masonry (CM) wall tested by Gavilan et al. [10]. The details of the specimen considered for the FE analysis are shown in Fig. 11. The wall used in the study was having the length and height of 1.65 m and 2.5 m, respectively. The eight-noded three-dimensional solid continuum elements with reduced integration (C3D8R) from the explicit element library were used for the concrete frame and masonry. The reinforcement bars were modeled using two-noded three-dimensional truss elements (T3D2). A proper bonding between reinforcement and concrete was ensured by applying embedded body constraints. The nonlinear behavior of concrete and masonry were simulated using the concrete damage plasticity (CDP) model and the previously discussed material models were used to define the stress–strain values. For the embedded steel bars, the elasticperfectly plastic model was used to simulate the uniaxial response. The material properties reported in the study were used for masonry, concrete, and steel. The compressive stress of masonry and concrete was reported as 5.17 MPa and 20.4 MPa, respectively. The elastic modulus of these materials was given as 4371 MPa and 25,249 MPa, respectively. For steel, the yield stress was reported as 412 MPa. The efficacy of the proposed interaction properties in simulating the in-plane response was also examined by comparing the response obtained from the FE model consisting of two commonly adopted interaction definitions. These commonly used wall-to-tie-column interaction considered for the comparison were tie-constraints and friction. The comparison of load-deformation responses obtained from FE analyses with experimental results is shown in Fig. 12, and the key parameters such as peak force, initial stiffness, and displacement at peak load are compared in Table 3. Table 3 illustrates that the model with tie-constraint have shown higher in-plane stiffness as compared to other cases. Further, in the case of model with friction interaction property, the in-plane stiffness was found to be lower. It may be due to ignoring the adhesion between the interfaces which leads to the local failures. As a result, the peak force and accompanying displacement in this case was high. Fig. 11 a CM wall tested by Gavilan et al. [10] and b FE model of CM wall
Simulation of Interaction Properties in Confined Masonry Walls …
125
90 75
Force (kN)
60 45 Experimental [2] Proposed Interaction Tie interaction Friction Interaction
30 15 0 0
5
(a)
10 15 20 Displacement (mm)
25
30
(b)
Fig. 12 a Cracking pattern obtained from the FE analysis and b force versus displacement curve with various interaction properties
Table 3 In-plane response of confined masonry wall with various interactions (values in parenthesis shows the percentage error) Model types
Stiffness (K) (MPa) Peak force (kN) Displacement at peak force (mm)
Experimental [2]
28.1
75.2
7.54
Monolithic (tie-constraint) 44.8 (59)
74.3 (01)
5.98 (20)
Friction interaction
21.9 (22)
82.1 (09)
8.27 (09)
Proposed interaction
34.5 (22)
77.8 (03)
6.96 (08)
Table 3 also shows that the model with the proposed interaction properties more closely resembled the experimental results. Moreover, the crack pattern in the wall for pushover load was demonstrated using PEMAG in Fig. 12, which is the distribution of plastic strain magnitude. The obtained cracking from the FE model with the proposed interaction properties matches well with the experimental response.
7 Conclusions A series of experiments were performed to evaluate the tension and shear bond properties at the wall-to-tie-column interface of confined masonry. The obtained traction– separation relationships were used to calibrate the finite element model. The calibrated interaction properties such as strength, cohesive stiffness, and damage evolution parameters were recommended to define the normal and tangential interaction at the wall-to-tie-column interface. It was observed that the presumption considering monolithic or friction contact between the masonry and tie elements results in stiffer or flexible response, respectively, causing incorrect depiction of the distribution of stress in confined masonry
126
V. Singhal et al.
walls. The FE model with the recommended interaction properties closely predicted the peak force and corresponding displacement within an error of 10%. From analytical investigation, it can be concluded that defining wall-to-tie-column interaction as combination of cohesion and friction provides better analytical results compared to other methods.
References 1. Brzev, S., Astroza, M., Moroni, O.: Performance of Confined Masonry Buildings in the February 27, 2010 Chile Earthquake. Earthquake Engineering Research Institute (EERI), California (2010) 2. Meli, R., Brzev, S., Astroza, M., Boen, T., Crisafulli, F., Dai, J., Farsi, M., Hart, T., Mebarki, A., Moghadam, A.: Seismic Design Guide for Low-Rise Confined Masonry Buildings. Earthquake Engineering Research Institute (EERI), CA, USA (2011) 3. Matthews, T., Riahi, Z., Centeno, J., Charlet, A., Garcia, H., Hoffman, C., Safaie, S., Elwood, K.J..: Evaluation of Confined Masonry Guidelines for Earthquake-Resistant Housing, Confined Masonry Network. Earthquake Engineering Research Institute. http://www.confinedmasonry. org/ (2008) 4. Medeiros, P., Vasconcelos, G., Lourenço, P.B., Gouveia, J.: Numerical modeling of nonconfined and confined masonry walls. Constr. Build. Mater. 41, 968–976 (2013) 5. Khalaf, F.M.: New test for determination of masonry tensile strength. J. Mater. Civ. Eng. 17(6), 725–732 (2005) 6. Kaushik, H.B., Rai, D.C., Jain, S.K.: Stress-strain characteristics of clay brick masonry under uniaxial compression. J. Mater. Civ. Eng. 19(9), 728–739 (2007) 7. Tripathy, D., Singhal, V.: Estimation of in-plane shear capacity of confined masonry walls with and without openings using strut-and-tie analysis. Eng. Struct. 188, 290–304 (2019) 8. Kent, D.C., Park, R.: Flexural members with confined concrete. J. Struct. Div. 97(7), 1969–1990 (1971) 9. Gopalaratnam, V.S., Shah, S.P.: Softening response of plain concrete in direct tension. ACI J. 82(3), 310–323 (1985) 10. Gavilán Pérez, J.J., Flores, L.E., Alcocer, S.M.: An experimental study of confined masonry walls with varying aspect ratios. Earthq. Spectra 31(2), 945–968 (2015)
Seismic Design of Periphery RC Beams in Buildings with Large Plan Aspect Ratio P. Bansode
and R. Goswami
Abstract Seismic behavior of buildings with large plan aspect ratio is affected by the in-plane flexibility of the floor diaphragms. Generally, reinforced concrete (RC) monolithic slab–beam system with plan aspect ratio less than or equal to 3 is considered to provide rigid diaphragm action. This helps in distribution of lateral load to the individual lateral load resisting systems in proportion to their stiffness. According to Indian Standard, a diaphragm is considered to be flexible if it deforms such that the maximum in-plane displacement is more than 1.2 times the average displacement of its ends. This study presents quantitatively additional reinforcement requirement in the periphery beams of buildings, arising due to in-plane flexibility of floor diaphragms with large plan aspect ratios. For the purpose, buildings with various plan aspect ratios are studied including the influence of different configuration of RC structural walls and URM brick infill. It is observed that 5% to about 240% more longitudinal reinforcement is required in the periphery beams to resist the additional tensile forces induced in them due to in-plane flexibility of the floor diaphragms. Keywords In-plane bending · Diaphragm · Axial tension · P–M interaction · Shear design
1 Introduction Floor/roof diaphragms are important structural elements in buildings that help in carrying and distributing both vertical and lateral loads [1]. For distributing lateral earthquake induced effects to various lateral load resisting frames/systems in a building, the in-plane stiffness of these diaphragms play important role. Rigid diaphragms help to distribute the induced seismic forces to different lateral load resisting elements in proportion to their stiffness; this action is commonly known as rigid diaphragm action. IS 1893 (Part 1) 2016 considers a floor diaphragm to be P. Bansode (B) · R. Goswami Department of Civil Engineering, I.I.T. Madras, Chennai, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_11
127
128
P. Bansode and R. Goswami
rigid, if it deforms such that the maximum lateral displacement measured from the chord of the deformed shape at any point of the diaphragm is less than 1.2 times the average displacement of the entire diaphragm (see Fig. 1). This also helps to reduce the computational efforts required for analysis. In general, floors/roofs in buildings with plan aspect ratio greater than 3 may not provide rigid diaphragm action [2, 3]. Thus, in buildings with large plan aspect ratios resulting in flexible diaphragms, the in-plane bending deformation of the diaphragm causes (i) the lateral earthquake induced forces to not get distributed to the different lateral load resisting frames in proportion to their lateral stiffness and (ii) additional axial tensile and compressive forces to get generated in the exterior or periphery beams (see Fig. 2). This study aims to quantify the effect of plan aspect ratio of floor diaphragms and stiffness distribution along the length of building on the later. Physical tests of 1/3rd scale model of monolithic slab–beam floor systems demonstrated that as the thickness of slab increases, the in-plane diaphragm stiffness increases and thereby decreases the in-plane diaphragm deformability [1]. Most Fig. 1 Definition of flexible diaphragm (Source IS 1893(1) 2016)
Fig. 2 In-plane deformation of diaphragm
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
129
studies on performance and effect of floor diaphragm flexibility focus on the overall deformation and load transfer mechanism to the lateral load resisting system in timber, reinforced concrete, and steel and composite structures [3–6]. Also, it is understood that diaphragm forces first transfer into the beams through friction and through shear studs in composite, prefabricated or precast constructions, and then from the beams into the lateral load resisting systems; although in monolithic reinforced concrete constructions, this transfer is natural [7]. Hence, in this study, emphasis is placed on highlighting the significance of the periphery beams as an important component of the diaphragm system working as a load path for smooth transfer of the earthquake induced inertia forces from the diaphragm to the foundations through columns or walls. When transfer of loads occurs to the periphery beams through flexible diaphragms, additional axial forces are induced in these periphery beams. In general, both bending moment and shear force capacities of reinforced concrete beams decrease with increase in axial tension [8]. Further, two distinct diaphragm deformation modes, namely (1) in-plane bending due to lateral loads in the transverse direction and (2) twisting due to lateral loads about its longitudinal direction, have caused axial and shear failures of periphery beams in the past [9, 10]. In addition, diaphragm flexibility may induce excessive lateral drift demand and failure of gravity load carrying system [11]. The in-plane stiffness and strength of diaphragm systems depend on the plan aspect ratio and thickness of the diaphragm. Yet, the adverse effects of diaphragms with large plan aspect ratio are generally not realized in regular bare frame building models [4]. The presence of lateral load resisting systems with difference in stiffness along the length of the diaphragm causes flexible diaphragms to undergo in-plane bending deformation. This is generally the case in real buildings with URM infill walls or RC shear walls; here, the effects of (i) stiffness of walls and (ii) flexibility of diaphragm should not be ignored. This study presents quantitatively the additional reinforcement required in the periphery beams of buildings arising due to in-plane flexibility of floor diaphragms with large plan aspect ratios, considering the stiffness of moment frames with walls. Also, the implication of increase in longitudinal reinforcement in the periphery beams is discussed in the context of seismic design of those frames.
2 Numerical Study Three-dimensional five-story regular space frame building models are considered with plan aspect ratio of 4, 6, 8, and 10. For the purpose, three bays each of 4 m length are considered along the Y-direction in each building model, while increasing number of bays (12, 18, 24, and 30) of 4 m each are considered in the X-direction. Diaphragm thickness of 110 mm is considered. In each building, initially, only 230mm-thick periphery/exterior unreinforced masonry (URM) infill walls are considered, followed by addition of interior partition URM infill walls. Further considering the recommendation of IS 1893 (1) 2016, 250-mm-thick reinforced concrete (RC)
130
P. Bansode and R. Goswami
Member Sizes Beams : 300 × 400 mm Columns : 400 × 400 mm Infill strut area : 222,180 mm2 Material Properties Grade of Concrete : M30 Grade of Steel : Fe415 Brick Masonry Prism Strength; f''m = 7.5 N/mm2 Modulus of Elasticity of Masonry; Em = 4,162.5 N/mm2 Loading Dead Load of infills on beams : 10 kN/m Floor Finish : 1.5 kN/m2 Live Load on floor : 3 kN/m2 Equivalent Static Load : X and Y direction Seismic Zone : V Importance Factor : 1.5 Response Reduction Factor : 5 (SMRF)
Fig. 3 Plan and elevation of RC frame building models
structural walls are used to replace some or all of the URM infill walls. Thus, in total, 72 building models are analyzed and designed using a structural analysis program [12]. The basic inputs are listed in Fig. 3. Analysis and design are carried out using equivalent static procedure following provisions of IS 1893(1), IS 456, and IS 13920 [13–15]. Beams and columns are modeled as 3D frame elements while shell elements are used to model floor diaphragms and structural walls. Infill walls are modeled as equivalent diagonal strut with properties as given in Fig. 3 [16]. The ends of diagonal strut are considered as pin-jointed to RC frames.
3 Results and Discussion 3.1 Lateral In-Plane Deformation of Diaphragm The in-plane deformation profile of the floor diaphragms along the length of the buildings with plan aspect ratio (AR) 4, 6, 8, and 10 are summarized in Fig. 4. The results presented belong to the roof diaphragms, where the deformations are maximum, which in turn demands maximum additional longitudinal reinforcement in the periphery beams. All the building models without any (URM infill or RC) walls
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
131
Fig. 4 In-plane floor deformation of buildings with different plan aspect ratio and only end walls
undergo lateral deformation of about 35 mm under the design lateral force, exhibiting more or less rigid diaphragm action. But the presence of walls along the periphery of the buildings causes non-uniform distribution of stiffness along the length of the building, which in turn triggers the in-plane bending action in the floor diaphragms; the in-plane bending deformation increases with (i) increase in the diaphragm plan aspect ratio and (ii) increase in stiffness of the end walls, i.e., when RC walls with higher lateral stiffness walls are used in place of URM infill walls (see Fig. 4). Use of walls only at the ends of the buildings introduce non-uniform distribution of stiffness of lateral load resisting system per unit area along the length of the buildings, which leads to non-uniform in-plane bending deformation of the diaphragms along the length of the buildings. Non-uniform lateral deformation of the floor diaphragms owing to flexibility of the diaphragm with large plan aspect ratio can be reduced by uniformly distributing the stiffness of the lateral load resisting system along the length of the buildings (see Figs. 5, 6 and 7). Thus, well-distributed URM infill walls or RC structural walls help improve the diaphragm action; depending upon the functionality of building and internal circulation required, distribution of stiffness of the lateral load resisting systems can be configured to minimize the in-plane deformation of the floor/roof diaphragms. But, it is evident that in general, diaphragms do not act as rigid in buildings with plan aspect equal to or greater than 4.
3.2 Axial Tensile Force Non-uniform lateral deformation of diaphragms seen in Figs. 5, 6, and 7 results in development of axial force in the periphery beams along the length of the buildings. Buildings with RC structural walls only at the ends without intermediate walls result in the largest axial force induced. Also, the axial force induced in the periphery beams increases with increase in the plan aspect ratio of the building. The axial force developed in the periphery beams along the building lengths is listed in Table 1.
132
P. Bansode and R. Goswami
Fig. 5 Lateral deformation of diaphragms with different configurations of URM infill walls in buildings with plan aspect ratio of a 4, b 6, c 8, and d 10
Fig. 6 Lateral deformation of diaphragms with different configurations of RC structural walls in buildings with plan aspect ratio of a 4, b 6, c 8, and d 10
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
133
Fig. 7 Lateral deformation of diaphragms with different configurations of RC wall at ends and uniformly spaced intermediate infill walls in buildings with plan aspect ratio of a 4, b 6, c 8, and d 10
Also, as the aspect ratio increases from 4 to 6, the axial tensile force induced in periphery beams increases, while in buildings with aspect ratio 8 and 10, a slight decrease in axial force is observed (see Fig. 8). In buildings with uniformly distributed RC or URM infill walls, the axial force increases with increase in aspect ratio. This additional axial force would not be observed if the diaphragms are considered as ‘rigid’ during analysis. Consequently, the periphery beams would be designed only for bending moment and shear force. The P–M interaction of a typical beam section (of 300 mm × 400 mm with 0.67% top and bottom reinforcements in buildings with 5 walls) designed considering ‘rigid’ diaphragm condition is shown in Fig. 9a. Also shown are the design axial force and bending moment combination values obtained by considering the flexibility of the diaphragms. It is seen that most design P–M combination values fall outside the design P–M failure envelope. This indicates under-designing of these periphery beams; the P–M interaction envelope of the redesigned beam cross-section requiring additional longitudinal reinforcement is also shown in Fig. 9b.
134
P. Bansode and R. Goswami
Table 1 Axial tension in periphery beam of buildings with different aspect ratio and walls Description
Axial tensile force (kN)
Buildings (L/B > 3) with different wall configurations
AR4
AR6
AR8
AR10
4
5
7
8
W0
Bare moment frame W2 2 URM infill walls at ends
340
290
372
315
2 RC walls at ends
670
760
680
558
3 URM infill walls
162
160
194
209
W3
3 RC walls
205
338
479
536
2 RC walls at ends + 1 intermediate infill wall
520
698
621
440
4 URM infill walls
120
135
158
159
W4
4 RC walls
124
178
259
358
2 RC walls at ends + 2 intermediate infill walls
509
601
522
422
5 URM infill walls
68
–
126
–
W5
5 RC walls
75
–
169
–
2 RC walls at ends + 3 intermediate infill walls
447
–
455
–
–
–
–
–
–
–
W6 6 URM infill walls
109
6 RC walls
–
–
–
169
2 RC walls at ends + 4 intermediate infill walls
–
–
–
337
W7 7 URM infill walls
–
77
91
94
7 RC walls
–
56
89
125 (continued)
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
135
Table 1 (continued) Description
Axial tensile force (kN)
Buildings (L/B > 3) with different wall configurations
AR4
AR6
AR8
AR10
–
480
395
306
2 RC walls at ends + 5 intermediate infill walls W9 9 URM infill walls
–
–
69
–
9 RC walls
–
–
52
–
2 RC walls at ends + 7 intermediate infill walls
–
–
247
–
W11 11 URM infill walls
–
–
–
59
11 RC walls
–
–
–
54
2 RC walls at ends + 9 intermediate infill walls
–
–
–
239
3.3 Increase in Area of Longitudinal Reinforcement in Periphery Beams Modern structural analysis and design programs are robust enough to consider appropriate stiffness and strength of structural elements. It is the responsibility of the engineer to use them appropriately. In buildings with large plan aspect ratio resulting in flexible diaphragms, the design of periphery beams will result in additional reinforcement (see Table 2); the engineer should not discard such result by opting to use ‘rigid’ diaphragm option as that would result in lesser reinforcement and hence economic design. In general, buildings with RC structural walls at ends require higher amount of reinforcement to counteract the effect of in-plane bending deformation of diaphragm, than the buildings with URM infill walls. For buildings with different aspect ratios, 5–240% of additional reinforcement is required when the building is configured with only RC structural walls, whereas 5–75% additional reinforcement is required when the building is configured with only URM infill walls. And in buildings with RC structural walls at end and intermediate URM infill walls, 50–200% of additional reinforcement is required; the amount of increase depends on the number and stiffness of the walls acting as the lateral load resisting system in buildings.
136
P. Bansode and R. Goswami
Fig. 8 Axial tensile force induced in periphery beams
3.4 Increase in Transverse Reinforcement in Periphery Beams The increase in longitudinal reinforcement in the periphery beams increases the requirement of transverse reinforcement too. This is because the periphery frames are usually designed as the lateral load resisting special moment frames requiring ductile design and detailing following capacity-based design as per IS 13920 [14]. Thus, the issue of diaphragm flexibility and distribution of stiffness of the lateral load resisting system, especially those with walls, has critical implication on the design and detailing of the periphery beams in buildings with large plan aspect ratio.
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
137
Fig. 9 Design P–M interaction diagram
4 Conclusion This study demonstrates the effect of plan aspect ratio of diaphragms on design of RC periphery beams in RC buildings. The salient conclusions drawn are as follows: (a) Buildings with plan aspect ratio of 4 and above are required to be analyzed considering the effect of flexible floor diaphragm and stiffness of lateral load resisting systems, especially those of RC or URM infill walls. (b) The increase in in-plane deformation of floor diaphragms due to increase in plan aspect ratio causes increase in axial tensile/compressive force in the periphery beams. (c) The increase in reinforcement requirement in the periphery beams increases from 5 to 240% with increase in plan aspect ratio from 4 to 10 in buildings with only RC structural walls. (d) The magnitude of axial force induced in periphery beams in buildings with large plan aspect ratio decreases with increase in the number of uniformly spaced intermediate walls. (e) The increase in reinforcement requirement in the periphery beams is 50–200% in buildings with RC structural walls at ends and intermediate URM infill walls. (f) The increase in reinforcement requirement in the periphery beams is 5–75% in buildings with only URM infill walls. Hence, it is recommended that rigid diaphragm option available in many commercially available structural analysis and design programs should not be used especially in buildings with large plan aspect ratio and non-uniform distribution of stiffness of
138
P. Bansode and R. Goswami
Table 2 % steel increase in periphery beams of buildings with different aspect ratio and walls Description
% increase in steel
Long buildings (L/B > 3) with different wall configurations
AR4
AR6
AR8
AR10
0
0
0
0
W1
URM infill wall W2
2 URM infill walls at ends
33
75
76
71
2 RC walls at ends
215
240
208
169
W3
3 URM infill walls
14
25
29
35
3 RC walls
41
90
139
157
2 RC walls at ends + 1 intermediate infill wall
151
197
145
121
4 URM infill walls
12
20
15
19
W4
4 RC walls
22
31
59
95
2 RC walls at ends + 2 intermediate infill walls
144
174
133
116
W5
5 URM infill walls
11
–
14
–
5 RC walls
13
–
29
–
2 RC walls at ends + 3 intermediate infill walls
125
–
123
–
6 URM infill walls
–
–
–
12
W6
6 RC walls
–
–
–
29
2 RC walls at ends + 4 intermediate infill walls
–
–
–
87
W7
7 URM infill walls
–
15
12
11
7 RC walls
–
6
13
23
2 RC walls at ends + 5 intermediate infill walls
–
132
102
76 (continued)
Seismic Design of Periphery RC Beams in Buildings with Large Plan …
139
Table 2 (continued) Description
% increase in steel
Long buildings (L/B > 3) with different wall configurations
AR4
AR6
AR8
AR10
W9
9 URM infill walls
–
–
11
–
9 RC walls
–
–
6
–
2 RC walls at ends + 7 intermediate infill walls
–
–
74
–
W11
11 URM infill walls
–
–
–
8
11 RC walls
–
–
–
10
2 RC walls at ends + 9 intermediate infill walls
–
–
–
50
lateral load resisting system per unit plan area of buildings; considering diaphragms as rigid in such cases is likely to result in under-designing of the periphery beams along the length of the building.
References 1. Zhang, Z., He, R., Mao, G., Shu, X.: Experimental and numerical study on the in-plane behaviour of a new long-span assembly composite floor system under lateral load. J. Asian Architect. Build. Eng. (2021). https://doi.org/10.1080/13467581.2021.1909595 2. Rezaeian, H., Clifton, G.C., Lim, J.: Inertial forces from floor diaphragms in braced multi-story buildings. In: Proceedings on New Zealand Society for Earthquake Engineering, Wellington 6140, New Zealand (2017) 3. Ruggieri, S., Porco, F., Uva, G.: A numerical procedure for modeling the floor deformability in seismic analysis of existing RC buildings. J. Build. Eng. 19, 273–284 (2018). https://doi.org/ 10.1016/j.jobe.2018.05.019 4. Hassan Saffarini, B.S., Qudaimat, M.M.: In-plane floor deformations in RC structures. J. Struct. Eng. (ASCE) 118(11), 3089–3102 (1992). https://doi.org/10.1061/(asce)0733-9445(1992)118: 11(3089) 5. Basu, D., Jain, S.K.: Seismic analysis of asymmetric buildings with flexible floor diaphragms. J. Struct. Eng. (ASCE) 130(8), 1169–1176 (2004). https://doi.org/10.1061/(ASCE)0733-944 5(2004)130:8(1169) 6. Piazza, M., Baldessari, C., Tomasi, R.: The role of in-plane floor stiffness in the seismic behaviour of traditional buildings. In: Proceedings on 14th World Conference on Earthquake Engineering, Beijing, China (2008) 7. Gardiner, D.R., Bull, D.K., Carr, A.J.: Internal forces of concrete floor diaphragms in multistorey buildings. In: Proceedings of New Zealand Society for Earthquake Engineering, Wellington 6140, New Zealand (2008) 8. Pham, D.T., Foure, B., Pinoteau, N., Abouri, S., Mege, R.: Influence of axial tension on the shear strength of RC beams without stirrups. J. Struct. Concrete 22(2), 1037–1053 (2021). https://doi.org/10.1002/suco.202000077
140
P. Bansode and R. Goswami
9. Fleischman, R.B., Sause, R., Pessiki, R., Rhodes, A.: Seismic behaviour of precast parking structure diaphragms. PCI J. 43(1), 38–53 (1998). https://doi.org/10.15554/pcij.01011998. 38.53 10. Gould, N.C., Kallros, M.K., Dowty, S.M.: Concrete parking structures and the Northridge earthquake. Struct. Mag., 48–54 (2019) 11. Fleischman, R.B., Farrow, K.T.: Dynamic behavior of perimeter lateral-system structures with flexible diaphragms. Earthquake Eng. Struct. Dynam. 30, 745–763 (2001). https://doi.org/10. 1002/eqe.36 12. CSI, Analysis Reference Manual, ETABs 2016, Version 20.0.0, Computers and Structures Inc., Berkeley, U.S.A. 13. IS 1893 (Part 1) (2016): Indian Standard Criteria for Earthquake Resistant Design of Structures—Part 1: General Provisions and Buildings. Bureau of Indian Standards, New Delhi, India. 14. IS 456 (2000): Indian Standard Plain and Reinforced Concrete. Bureau of Indian Standards, New Delhi, India. 15. IS 13920 (2016): Indian Standard Ductile Design and Detailing of Reinforced Concrete Structures Subjected to Seismic Forces—Code of Practice. Bureau of Indian Standards, New Delhi, India. 16. Kaushik, H.B., Rai, D.C., Jain, S.K.: Uniaxial compressive stress–strain model for clay brick masonry. Curr. Sci. 92(4), 497–501 (2007). http://www.jstor.org/stable/24097563
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund Fault Phibe Khalkho
and I. D. Gupta
Abstract The seismic hazard is most commonly described in terms of various parameters defining the intensity ground shaking. Other parameters like liquefaction potential, landslides, ground subsidence, tsunami, etc., have been also used. However, permanent ground displacement due to surface rupture along a fault is also an important parameter to be used for characterization of seismic hazard, and it occurs only on the fault unlike other hazards. This can cause tremendous damages especially to lifeline structures such as highway bridges, tunnels, and buried pipelines (oil and gas pipelines), if they lie across a fault. This study emphasizes the need of estimation of ground displacement using the probabilistic seismic hazard analysis (PSHA) method. Various examples resulting in the damages due to permanent ground displacement followed by the earthquakes displaying vertical displacements has been presented. Necessary modifications in the commonly used probabilistic seismic hazard analysis (PSHA) approach have been described for its application to permanent ground displacement which in turn can be helpful to mitigate the risk on buried lifeline system. Keywords Probabilistic · Ground displacement hazard · Lifelines
1 Introduction Earthquake hazard refers to a threatening earthquake or probability of occurrence of potentially damaging earthquake within a given time period and area, which may cause significant loss of life and property. The important parameters characterizing seismic hazard include Fourier and response spectrum amplitudes [13, 1, 23] (Lee and Trifunac 1985) strong motion duration [15], peak strains [21], surface faulting P. Khalkho (B) Research Scholar Department of Civil Engineering, IIT Roorkee, Roorkee, India e-mail: [email protected] I. D. Gupta Independent Scholar, Pune, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_12
141
142
P. Khalkho and I. D. Gupta
[22], soil liquefaction [19], and landslides [3]. Apart from other hazards which are also quite damaging, the consequences of fault movements and fault displacements may be very severe. In high seismicity regions, faults are often found to exist beneath long structures, such as bridges, tunnels, pipelines, dams, and buried structures. Some typical examples of damage to structures include gas main damage and water main damage along the Sylmar segment of San Fernando fault zone in 1971 San Fernando earthquake [14], failure of Shih-Kang dam in 1999 Chi-Chi earthquake [11], buckling of the roadway surfacing on the Trans European motorway in 1999 Kocaeli earthquake (Erdik 1999) passing of fault rupture under the Arifiye Overpass with a right-lateral offset of 1.5 m [23]. It is life-threatening tectonic expression if surface slip is along an identified fault zone under a dam, and such situations can mould the safety of a dam. So, to ensure safety against such possible fault displacements, there is a dire need for evaluation of the likelihood of displacement along the fault during the lifetime of these structures. According to Wieland et al. (2008), earthquakes are multiple hazard events, which have the features of ground shaking causing vibrations in dams, appurtenant structures and equipment, and their foundations; fault movements in the dam foundation causing structural distortions; fault displacement in the reservoir bottom causing water waves in the reservoir or loss of freeboard; and mass movements into the reservoir causing impulse waves in the reservoir. Some cautious estimates of the maximum possible fault movements are essential for design and safety checks because of cumulative nature of fault and exposure of dams to foundation movements. Permanent ground displacement is the amount of irreversible deformation that ground undergoes from its original position during an earthquake. There are two types of permanent ground displacement—primary and secondary. Primary permanent ground displacement occurs only on the fault, whereas secondary permanent ground displacement occurs away from the fault, mainly due to response of ground to vibration away from the fault. Unlike other parameters, the primary permanent displacement can occur only along the line of intersection of fault plane and the ground surface, the probabilistic seismic hazard analysis (PSHA) method for estimation of other hazard parameters is not directly applicable to the permanent displacement.
1.1 Objective of the Study The objective of this study is to modify and apply the conventional probabilistic seismic hazard methodology to estimate permanent ground displacement along a fault. It comprises the following components: • Modifying the probabilistic seismic hazard analysis (PSHA) methodology for permanent ground displacement. • Carrying out probabilistic hazard analysis for estimation of permanent displacement along selected real fault.
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
143
• Summary and conclusion of the study.
2 Methodology Cornell [2] developed the PSHA formulation originally in terms of the peak ground acceleration (PGA) without considering the random distribution of ground motion amplitudes around the least squares median attenuation relationship. A formulation was developed by taking the probabilistic nature of ground motion attenuation into account and also extended the PSHA to the spectral amplitudes at different natural periods of vibration (Anderson and Trifunac 1978).
2.1 General PSHA Formulation The PSHA in a generalized form is summarized in the following: Let z be a specified value of a random variable Z describing a strong motion parameter of interest. ) To consider random nature of the ground motion attenuation, ( let q Z > z|M j , Ri be the probability that a value z is being exceeded ( from)an R from a site of interest. If λ earthquake of magnitude M j at distance n M j , Ri is ( ) i the annual occurrence rate of the M j , Ri type of the earthquakes, the corresponding occurrence rate of the events Z > z due to all earthquakes around the site can be written as ν(Z > z) =
J I Σ Σ
( ) q(Z > z|M j , Ri ) × λn M j , Ri ,
(1)
i=1 j=1
where J and I are the total number of magnitude and distance ranges. The average return period for the events Z > z can be determined in terms of the probability F(Z > z|Y ) as T (Z > z) =
1 . ν(Z > z)
(2)
( ) Assuming the occurrence of M j , Ri type of earthquakes is following a Poisson distribution, the events Z > z at the site of interest can also be described by a Poisson distribution with occurrence rate equal to ν(Z > z). The probability that the ground displacement level z may be exceeded due to some earthquakes is thus given by F(Z > z|Y ) = 1 − exp{−Y.ν(Z > z)}.
(3)
For practical implementation of above mathematical formulation, the PSHA is described as a procedure of four steps:
144
P. Khalkho and I. D. Gupta
The first step is identification and characterization of the earthquake sources. Characterization of probability distribution of potential rupture locations within the source zone is done. Division of each source into a large number of small size elements and the distribution of required seismicity among all the elements is done. The geometric centre of each of the elements is assumed to be the probable location of the earthquake. The probability distribution function of source-to-site distance is defined as shown in Fig. 1. The frequency magnitude relationship due to Gutenberg–Richter [7] for each source zone is defined to estimate the total number of earthquakes Nn (Mmin ) with magnitude above Mmin . A magnitude distribution function F(M) for each source zone is specified for each source zone to distribute magnitude among different magnitude intervals between M min and M max (Fig. 1). With the help of predictive relationships, the ground motion produced at the site by earthquakes of any possible size occurring at any possible point in each source zone must be determined. This is used to calculate the probability q(Z > z|M, R) as shown in (Fig. 1).
Fig. 1 a Identification and characterization of earthquake sources; b Linear Gutenberg-Richter recurrence law; c Suitable attenuation relationships providing a probabilistic description of amplitudes of hazard parameter [5]
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
145
Finally, the magnitude and distances in all the source zones are integrated to estimate the hazard curve.
2.2 PSHA Formulation for Permanent Ground Displacement To extend the seismic hazard methodology for permanent ground displacement due to surface rupture along a fault, it is essential to define the probability of exceeding a specified value of permanent displacement due to a given earthquake magnitude on a fault plane. It is also necessary to estimate the probability that the rupture reaches the ground surface and also reaches to the site of interest. With the knowledge of these two probabilities, formulation developed previously can be applied easily for probabilistic estimation of permanent ground displacement.
2.2.1
Mathematical Formulation
Permanent displacement can occur due to earthquakes on a fault plane. Therefore, locations of all the earthquakes on the fault plane are to be considered. Further for peak ground displacement, the fault rupture should approach ground surface and the selected site. Thus, only those earthquakes are to be considered which can rupture the ground surface as well as rupture reaches the site of interest [20]. Equation (1) is modified for permanent ground displacement to estimate ν(D > d), occurrence rate of exceeding a specified value d, of random permanent ground displacement D as follows: ν(D > d) =
Jn Σ
) ( ) ( q(D > d|M j ) × λ M j , Ri × Prupture M j .
(4)
j=1
In this relationship, ν(D > d) is the occurrence rate for exceeding permanent that value d is exceeded due ground displacement d, q(D > d|M j )( is the probability ) to magnitude M j on the fault plane, λ M j , Ri is the occurrence rate of earthquakes of magnitude ( M) j at i th location on the fault plane at a distance Ri from the site, and Prupture M j is the probability that the rupture due to magnitude M j reaches the earth’s surface and also reaches the selected site on the fault trace on the surface. Estimation of various quantities involved in the summation on the right-hand side of Eq. (1) is described in the following subsections.
2.2.2
Estimation of q( D > d|M j , Ri )
The q(D > d|M j ) can be estimated by using a lognormal distribution with mean value of log d as μ and standard deviation as σ .
146
P. Khalkho and I. D. Gupta
{
P D > d|M j
}
(
) [ 2 −1 log x − μ)/σ ] ∫ exp =√ dx 2 2π σ −∞ log d
1
(5)
The values of μ and σ can be obtained in a very simple and straight forward manner using the following empirical scaling relations due to Wells and Coppersmith [26]: μ = 0.82M − 5.46; σ = 0.42.
(6)
An alternative method for defining μ and σ is the scaling relationship for the dynamic displacement due to Lee et al. [12], which predicts peak ground displacement as a function of earthquake magnitude, distance from the source and various combinations of geologic site and local site conditions. The permanent ground displacement is defined as twice the peak displacement at zero value of the epicentral distance [20]. Thus, mean value of permanent displacement and its standard deviation is given by [ 2dmax = μ H/ V = M − 2.2470 log10
] Δ + 0.6489M + 0.0518 ∗ 2 − 0.3407ν LR
− 2.9850 − 0.1369M 2 − 0.0306 + log10 2 − 0.0090;
σ = 0.3975 (7)
where M is the earthquake magnitude,Δ represents the representative source-tostation distance,L R is the rupture length, and ν represents the direction of motion (ν = 0 for horizontal and 1 for vertical component). The distance Δ depends on both the physical distance and the size of the rupture [6]. /( Δ=S
ln
) R 2 + H R2 + S 2 , R 2 + H R2 + S02
(8)
where H R —focal depth, S-source dimension, and S0 = source coherence radius. R is taken as zero and H R = 0.5WR sin δ with WR as rupture width and δ is the dip angle. The source dimension, S, is given by S = {0.0729(5.5 − M)100.5M , M < 4.5 {−25.34 + 8.51M, 4.5 ≤ M ≤ 7.25.
(9)
( ) The source coherence radius S0 is given by S0 = 21 min S f , S , where S f, is defined as ⎧ M < 3.5 ⎨ L R (M), (M) S f = L R2.2 (10) + WR6(M) , 3.5 < M ≤ 7 . ⎩ L R (Mmax ) WR (Mmax ) + , M > M = 7 max 2.2 6
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
147
The rupture length L R and rupture width WR are log10 L R (M) = 0.5M − 2
(11)
log10 WR (M) = {L R , M ≤ 4.25 {0.25M − 1, M > 4.25 The relationship of Eq. (7) gives horizontal and vertical components of permanent displacement separately, whereas the relationship of Wells and Coppersmith [26] gives the average resultant displacement to match the seismic moment of the earthquake. Therefore, to be consistent with the displacement value of Wells and Coppersmith [26], we define the resultant mean displacement by the root-mean-square (rms) of the horizontal and vertical components of the permanent displacement as / μ=
(μ2H + μ2V ) ; σ = 0.3975. 2
(12)
The actual direction of the displacement may be taken as the direction of the fault rupture. The probabilities P(D > d|M j ) as computed from Eq. (5) using μ and σ values from the relation of Wells and Coppersmith [26] and that from the relationship of Eq. (12), Lee et al. [12], Todorvska et al. [20] are compared in Fig. 2 for several values of the magnitude. It is seen that the results from both the methods are quite consistent and is in reasonably good agreement. But, the relationship of Todorvska et al. [20] based on 1
0.8
0.6
P(D>d)
Fig. 2 Probability of exceedance for permanent ground displacement at different magnitudes (M = 5 > 6 > 7 > 8) and compares the models of Wells and Coppersmith [26] and Lee et al. [12]. The dashed line corresponds to the law given by Wells and Coppersmith [26], and the solid lines correspond to the model of Lee et al. [12]
M=5.0 M=5.0 M=6.0 M=6.0 M=7.0 M=7.0 M=8.0 M=8.0
0.4
0.2
0 0.0001
0.001
0.01
0.1
PGD(m)
1
10
100
148
P. Khalkho and I. D. Gupta
the work of Lee et al. [12] leads to slightly higher probabilities for the same value of permanent displacement.
2.2.3
( ) Estimation of λ M j , Ri
) ( The occurrence rate, i.e.λ M j , Ri in Eq. (4) is defined by first estimating the total number n(M j ) of earthquakes on the fault plane per year and then distributing this number over the entire fault plane. This requires to define the Gutenberg-Richter’s [7] relation for the fault plane. log N (M) = a − bM,
(13)
where N (M) is the annual occurrence rate of earthquakes of magnitude greater than or equal to M, and a and b are constants is evaluated from the past earthquake data and/or the average rate of fault dislocation. In terms of the earthquakes occurrence rate above a threshold magnitude, N (Mmin ), Eq. (13) can be expressed as N (M) = N (Mmin ) exp(−β(M − Mmin ); β = b ln 10.
(14)
However, in Eq. (14), it does not have any upper bound or maximum magnitude Mmax . With an upper bound magnitude Mmax , the occurrence rate at large magnitudes can be defined as exponential and characteristic models. The relationship for exponential decaying recurrence model is expressed [2] as N (M) = N (Mmin )
e(−β(M−Mmin )) − e(−β(Mmax −Mmin )) . 1 − e(−β(Mmax −Mmin ))
(15)
Certain faults are seen to produce frequent earthquakes closer to Mmax than that described by the exponential model. In the characteristic recurrence model, the total number of earthquakes in the magnitude range Mc to Mmin is expressed as ⎧ ⎨ N (Mmin ) exp(−β(M − Mmin )) − exp(−β(Mc − Mmin )) 1 − exp(−β(Mc − Mmin )) N (M) = ⎩ +n(M ˙ c )ΔMc ; Mmin ≤ M < Mc {n(M ˙ c )(Mmax − M) ; Mc ≤ M < Mmax ,
(16)
whereas Mc = Mmax − ΔMc and M ' = Mc − ΔM ' ; the intervals ΔMc and ΔM ' are ˙ c ) is the probability density for the commonly taken as 0.5 and 1.0, respectively. n(M occurrence rate of characteristic earthquakes and is defined as ( ( )) β exp −β M ' − Mmin . n(M ˙ c ) = N (Mmin ) 1 − exp(−β(Mc − Mmin ))
(17)
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
149
To use the rate of deformation on a fault to define the recurrence relations of Eq. (15) and (16), we develop a theoretical relationship for the moment release rate M˙ ◦ . For this purpose, seismic moment in dyne/cm released during an earthquake can empirically be related to the magnitude through an expression of the form [8] is expressed as log M◦ (M) = c + d M; c = 16.0 and d = 1.5.
(18)
The seismic moment release rate due to all the earthquakes up to magnitude Mmax can be obtained as. Mmax
M˙ ◦ = ∫ M◦ (M)n(M)dM.
(19)
−∞
By defining n(M) = exponential model [5]
−d N (M) d(M)
from Eq. (15) gives the moment release rate for
M˙ ◦ = N (Mmin )e(−β(Mmax −Mmin )) M◦ (Mmax )
b . d −b
(20)
Similarly, the moment release rate for characteristics earthquakes is defined as M˙ ◦ = N (Mmin )e(−β(Mc −Mmin )) M˙ ◦ (Mmax ) ) (( ( )) b b ' ' 10−dΔMc + 10bΔM 1 − 10−bΔM . d −b d
(21)
Also, the moment release rate in terms of slip rate u, ˙ fault rupture area A, and shear modulus of rock μ is defined as Brune (1968) ˙ M˙ ◦ = μAu,
(22)
where μ is the shear modulus of rock mass at the fault in dyne/cm2 , A is rupture area of the total fault, and u˙ is the geologically estimated long-term slip. Equating the M˙ ◦ from Eq. (22) with those from Eqs. (20) and (21) gives the N (Mmin ) for the exponential and characteristic recurrence models for a given value of parameter b. As the past data on an individual fault may not be adequate to estimate the value of b using maximum likelihood method [24], it may be taken as regional value. ( ) From the recurrence relations defined (as above, the occurrence ) rate n M j of earthquakes in a small magnitude interval M j − δ M j , M j + δ M j can be obtained as ( ) ( ) ( ) n Mj = N Mj − δMj − N Mj + δMj .
(23)
150
P. Khalkho and I. D. Gupta
Fig. 3 Fault plane with centres of rectangular elements as the location of the earthquakes
) ( Finally, to get the occurrence rate λ M j , Ri , the entire fault plane is divided into large number of small sizes of rectangular elements with ) centre of each element ( the as the possible location of earthquakes. The number n M j is then divided equally among all the elements with Ri as the distance of the ith element from the selected site.
2.2.4
( ) Estimation of Prup M j
( ) To define the Prup M j , probability that the rupture breaks the ground surface and extends horizontally to the site, we assume the fault plane of given length L and width W to be divided into a large number of small elements with their geometric centres as the probable location of the future earthquakes as shown in Fig. 3. By taking each possible earthquake location sequentially for a given magnitude M j with rupture length l and width w, it is examined that whether the rupture surface reaches the ground as well as selected site or not. The number of such counts divided by the total no. of epicentral locations for magnitude M j is taken as desired ( possible ) probability Prup M j as ( ) No. of epicentral locations for M j causing rupture to the site . (24) Prup M j = Total no. of possible epicentral locations for M j It may be noted that this probability is independent of the choice of the unilateral or bilateral propagation of the rupture, provided it is taken to be identical for all possible earthquake locations on the fault plane. This is explained and illustrated in the following paragraph. Let us first assume a unilateral rupture to right and the down-dip of the fault plane. As illustrated in Fig. 4a, the first possible earthquake location can be taken the top left corner element with the rupture area of length l and width w shown by the shaded portion. The earthquake locations can be then considered sequentially to the left side and down-dip of the fault plane. Along the fault length, the last possible earthquake location will be the elements at distance (L − l) from the other end of the fault. For this location, the rupture will reach the end of the fault, and thus, no further location is possible. Similarly, along the fault width, the last possible location will
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
151
Fig. 4 a Unilateral and b bilateral rupture propagation of the fault plane
be the elements at distance (W − w) along the dip. Thus, total number of possible locations of earthquakes on the fault plane will be the grid points within an area of (L − l) × (W − w) of the fault plane from the top left corner. Next, let us consider a symmetrical bilateral rupture with length and width of l/2 and w/2 rupturing on both sides of the possible locations of earthquakes. As illustrated in Fig. 4b, in this case, all possible earthquake locations will also lie within an area of size (L − l) × (W − w), but it will span from l/2 to (L − l/2) along the length and w/2 to (W − w/2) along the width. From Fig. 4b, it can be seen that the rupture scenarios in this case also will be identical to( those ) in case of unilateral rupture propagation in Fig. 4a. As the probability Prup M j in Eq. (24) depends on the final rupture scenarios rather than on the process in which the rupture takes place, it is independent of uni or bilateral nature of the rupture Thus, ( propagation. ) for simplicity and ease of understanding, the probability Prup M j can be calculated assuming unilateral rupture to the left side. The rupture length l and rupture width w for a given value of the magnitude are estimated using the empirical relations due to Wells and Coppersmith [26] for different fault types as follows: ⎧ ⎨ 0.74M − 3.55; σ = 0.91 log l = 0.63M − 2.86; σ = 0.88 ⎩ 0.50M − 2.01; σ = 0.81 ⎧ ⎨ 0.27M − 0.76; σ = 0.84 log w = 0.41M − 1.61; σ = 0.88 ⎩ 0.35M − 1.14; σ = 0.86
for Strike Slip for Reverse fault for Normal fault
(25)
for Strike Slip for Reverse fault for Normal fault
(26)
It is seen that the mean estimates of log l and log w are associated with very large standard deviations, leading to considerable epistemic uncertainties ( ) in the values of l and w. To take this uncertainty into account, probability Prup M j has been estimated for the mean, mean plus one standard deviation (σ ), and mean minus one standard deviation (σ ) values of l and w. Final probability is defined as the weighted average
152
P. Khalkho and I. D. Gupta
of these three cases with a weight of 0.6 for the mean and 0.2 for mean plus standard deviation and mean minus standard deviation values of l and w.
3 Case Study of Real Fault—Allah Bund Fault The modified PSHA methodology for permanent ground displacement is now implemented for the real fault, i.e. Allah Bund fault. The permanent ground displacement is calculated at different sites along the length of the faults for exponential and characteristic model. The results are compared with the actual upliftment measured during that earthquake.
3.1 Allah Bund Fault The Kachchh region in Gujarat is highly seismic intracontinental regions of the world, which has witnessed many destructive earthquakes in the past. Historically, some of the major earthquakes have occurred which are 1668 Indus delta (MM X), 1819 Kachchh (Mw 7.8) and 1845 Lakhpat (MM VIII). The Great Kutch Earthquake which occurred on 6 June 1819 (Mw = 7.8) in the western Great Rann of Kachchh is known to be biggest earthquake in the Gujarat region. It produced the prominent “Allah Bund” meaning the “Dam of God”. The earthquake uplifted the 80 km long and 16 km wide region of Rann at the elevation of 3–6 m [16], 90 km long, 6.3 km wide and 4.3 km high ridge [16]. Bilham (1998) suggested a shallow (from 10 km to near the surface) reverse-slip rupture on a fault plane of 90 km length dipping at an angle of 50°–70° N. 50 km length of the fault is ruptured approximately in 1819 event, dipping at 45° to the north with vertical dislocation of 3–8 m slip. It has been observed that the crustal shortening ~ 12 mm/yr [9] in the Kachchh region which involves the cumulative slip of four faults like KHF, Island belt Fault, Allah Bund fault, and KMF. Figure 5 shows the epicentres of earthquakes M ≥ 2.0 is shown during the period of 1668–2008.
3.2 Results and Discussions The analyses are done for estimation of permanent ground displacement for different sites along the length of the fault for both characteristic and exponential model. The comparison has been made between Lee et al. [12] and Wells and Coppersmith [26] model, represented by solid lines and dashed lines, respectively. The length of the fault and width of the fault are 85 km and 40 km, respectively (Chopra et al. 2012), dipping at an angle of 60° N with a strike of 285°. The parameter a = 4.60 of the Guternberg–Richter’s relation for Kachchh region is defined by using
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
153
Fig. 5 Epicentres of earthquakes M ≥ 2.0 occurred in the Kachchh region during the period 1668–March 2008 [16]; India Meteorological Department; Geological Survey of India, NEIC, USGS; ISC; Gujarat Engineering Research Institute, Gujarat, India; National Geophysical Research Institute, India; Institute of Seismological Research (ISR), India)
moment-rate relationships, given b = 1.05 ± 0.12 [17], shear modulus of rock for Kachchh, μ = 3.63 ×1011 dyne/cm2 and slip rate = 3 mm/yr [9]. The particular value of permanent ground displacement at distance along the fault is shown with Mmax = 8.5 and Mmin = 5.0. Figure 6 shows the results for permanent ground displacement at different sites along the distance of the fault for exponential and characteristic models. The results in Fig. 6 for estimation of permanent ground displacement along the real faults at various sites shows the following: • The permanent ground displacement values for Lee et al. [12] model is higher compared to the Wells and Coppersmith [26] along the length of the fault.
Fig. 6 Permanent ground displacement along the fault at various sites for a exponential model and b characteristic model for different return periods
154
P. Khalkho and I. D. Gupta
• The characteristic model produces more displacement than exponential model as it is defined to have higher occurrence rates of large magnitude earthquakes. • With increase in the return period, the values of permanent ground displacement also increase. As for 500 yrs. of return period for Lee et al. [12] model, the permanent ground displacement is 7.24 m which is ~ 50 for 2500 yrs. of return period in Kachchh region for characteristic model. • At the centre of the fault, the permanent ground displacement is at peak and gradually decreases when moves towards the end of the fault.
4 Summary and Conclusions Some of the past great earthquakes have demonstrated the upliftment of the ground up to the surface causing severe damages especially to the long structures such as aqueducts, gas and water lines, bridges, highways, and dams and tunnels which are in the vicinity of the fault or lie across the fault. The probabilistic seismic hazard analysis (PSHA) is modified and described in detail for permanent ground displacement. The whole study is done to estimate the permanent ground displacement for the Allah Bund fault which has exposed some vertical displacement during the events for both characteristic and exponential models. It is concluded that at the centre of the fault the permanent ground displacement is at peak and gradually decreases when moves towards the end of the fault. So, the lifeline structures or tunnels or dams are at higher risks if the fault is either beneath or lie across or are in close proximity of these structures. The plots for permanent ground displacement along the fault at different return periods is extremely profitable for design and retrofitting purpose of long structures during the future earthquakes.
References 1. Anderson, J.G., Trifunac, M.D.: On uniform risk functionals which describe strong earthquake ground motion: definition, numerical estimation, and an application to the Fourier amplitude spectrum of acceleration. Report CE 77-02, Univ. South Calif. Los Angeles, U.S.A (1977) 2. Cornell, C.A.: Engineering seismic risk analysis, Bulletin of the seismological society of america, 58(5), 1583–1606 (1968) 3. Del Gaudio, V. and Wasowski, J.: Time probabilistic evaluation of seismically induced landslide hazard in irpinia (Southern Italy), Soil Dynam. Earthq. Eng. 24(12), 915–928 (2004) 4. ERDIK, MUSTAFA.: REPORT ON 1999 KOCAELIAND DüZCE (TURKEY) EARTHQUAKES. In structural control for civil and infrastructure engineering: Proceedings of the 3rd international workshop on structural control: Paris, France 6-8 July 2000, p. 149. World Scientific, (2001) 5. Gupta, I.D.: Probabilistic seismic hazard analysis method for mapping of spectral amplitudes and other design specific quantities to estimate the earthquake effects on man-made structures. ISET J. Earthq. Technol., Paper No. 480 44(1), 127–167 (2007)
Probabilistic Mapping of Ground Displacement Hazard for Allah Bund …
155
6. Gusev A.A.: Descriptive statistical model of earthquake source radiation and its application to an estimation of short-period strong motion. Geophys. J. Royal Astr. Soc. 74(3):787–808 (1983) 7. Gutenberg & Richter.: Frequency of earthquakes in California. Bulletin of the seismological society of america, 34, 185–188 (1944) 8. Hanks, T.C. and H. Kanamori.: A moment magnitude scale, Jour. Geophys. Res. 84, 2348–2350 (1979) 9. Jade, S., Mukul, M., Parvez, I.A., Ananda, M.B., Kumar, P.D., Gaur, V.K.: Estimates of coseismic displacement and post deformation using Global Positioning System geodesy for the Bhuj earthquake of 26 January 2001. Curr. Sci. 82, 748–752 (2002) 10. Lee, Y. H., M. L. Hsieh, S. T. Lu, T. S. Shih, and W. Y. Wu.: Slip vectors of the surface rupture of the 1999 Chi-Chi earthquake, Western taiwan, J. Struct. Geol. 25, 1917–1931 (2003) 11. Lee, George C. and Chin-Hsiung L.: Preliminary report from MCEER-NCREE workshop on the 921 taiwan earthquake, MCEER-NCREE response (1999) 12. Lee, V.W., Trifunac, M.D., Todorovska, M.I., Novikova, E.I.: Empirical equations describing attenuation of the peaks of strong ground motion, in terms of magnitude, distance, path effects and site conditions. Report No. 95-02, Department of Civil Engineering, University of Southern California, Los Angeles, California (1995) 13. McGuire, R.K.: Seismic design spectra and mapping procedures using hazard analysis based directly on oscillator response. Earthq. Eng. Struct. Dyn. 5(3), 211–234 (1977) 14. O’ Rourke, T.D. and C.H.Trautmann.: Buried pipelines response to permanent earthquake ground movements, ASME Paper 80/C2 PVP-78 (1980) 15. Papazachos, B.C., Papaioannou, Ch.A., Margaris, V.N. and Theodulidis, N.P.: Seismic hazard assessment in greece based on strong motion duration, Proceedings of the tenth world conference on earthquake engineeing, Madrid, Spain, 2, 425–430 (1992) 16. Rajendran C.P., Rajendran K.: Characteristics of deformation and past seismicity associated with the 1819 kutch earthquake, north western India. Bull. Seismol. Soc. Am. 91, 407–426 (2001) 17. Singh, A.P., Mishra O.P., Kumar D., Kumar S. and Yadav R.B.S.: Spatial variation of the after shock activity across the kachchh rift basin and its seismotectonic implications” , J. Earth Syst. Sci. 121(2), 439–451, Indian Academy of Sciences (2012) 18. Stepp, J.C., Wong, I., Whitney, J., Quittmeyer, R., Abrahamson, N., Toro, G., Youngs, R., Coppersmith, K., Savy, J., Sullivan, T.: Probabilistic seismic hazard analyses for ground motions and fault displacement at Yucca Mountain, Nevada. Earthq. Spectra 17(1), 113–151 (2001) 19. Thakkar M. G., Ngangom M., Thakker P. S. and Juyal N.: Terrain response to the 1819 allah bund earthquake in western great rann of kachchh, Gujarat, India, Curr. Sci. 103(2), (2012) 20. Todorovska, M.I., Trifunac, M.D., Lee, V.W.: Shaking hazard compatible methodology for probabilistic assessment of permanent ground displacement across earthquake faults. Soil Dyn. Earthq. Eng. 27, 586–597 (2007) 21. Todorovska, M.I. and Trifunac, M.D.: Hazard mapping of normalized peak strain in soils during earthquakes: Microzonation of a metropolitan area, Soil Dyn. Earthq. Eng. 15(5), 321–329 (1996) 22. Trifunac, M.D.: 23rd ISET Annual lecture: 70-th Anniversary of biot spectrum, ISET J. Earthq. Technol. 40:(1),19–50 (2003) 23. Ulusay, R., Aydan, Ö., and Hamada, M.: The Behaviour of structures built on active fault zones: Examples from the recent earthquakes of turkey, Seismic fault induced failures, 1–26 (2001) 24. Weichert, D.H.: Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes, Bull. Seism. Soc. Am. 70(4), 1337–1346 (1980) 25. Weiland M., Bozovic A.,. and Brenner R.P.: Effects of potential movements along faults and discontinuities in Dam foundations on Dam design, International water power and dam construction. (2008) 26. Wells, D.L., Coppersmith, K.J.: New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seism. Soc. Am. 84(4), 974–1002 (1994)
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based Method Prakash Singh Badal
and Ravi Sinha
Abstract Critical buildings such as hospitals, communication facilities, and emergency operations centers play vital roles during the response to extreme seismic events. Recent research shows that the inability to ensure continued functionality of such buildings in the aftermath of an earthquake severely impacts the post-disaster response and recovery. Importance factors have been used in the prescriptive forcebased design standards to increase the seismic design forces and thereby provide higher safety for such buildings. These importance factors are based on judgment, and the associated enhancement of the performance of buildings is not quantified. The present paper describes a generalized risk-targeted importance factor formulation meeting pre-specified seismic risk target levels that is suitable for use with prescriptive force-based design standards. The framework extends the performance-based seismic design methodology to calibrate the risk-targeted importance factors. The framework also accounts for the uncertainty in seismic demand, structural capacity, and inter-building variation within a specific typology. Sensitivity studies for parameter selection are also presented. The methodology is applied to special RC moment frame archetype buildings located in two metropolises in high and very high seismic regions of India (Delhi in Zone-IV and Guwahati in Zone-V). The paper shows that regular RC moment frame building typology conforming to Indian Standards has an additional risk margin of 25–30% for important buildings (importance factor 1.2) and 65–85% for critical buildings (importance factor of 1.5). The study underlines the need to consider both the seismic hazard and the structural response for the design of critical buildings requiring enhanced performance. Keywords Important buildings · Risk-targeted seismic design · Performance-based seismic design · Disaster risk reduction · Force-based design · Importance factor
P. S. Badal University of California, Davis 95616, USA R. Sinha (B) Indian Institute of Technology Bombay, Mumbai 400076, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_13
157
158
P. S. Badal and R. Sinha
1 Introduction Most national seismic design standards follow a semi-probabilistic approach in the form of partial material safety and load factors and adopt a prescriptive design approach [1–4]. Although the reliability-based approach promise improvement in designs, it has only seen minimal adoption due to the difficulty with the estimates of the failure probability [5]. Ellingwood [6] has highlighted the limitations of semiprobabilistic and reliability-based standards. The present paper is focused on a third approach, which is entirely based on the risk-informed design and overcomes the limitations of both other approaches. The buildings that are associated with severe consequences of damage or where the functionality is required to continue following a seismic event require higher seismic resistance. Most design standards prescribe a deterministic magnification factor to estimate seismic design forces for different risk categories of buildings [11]. Table 1 shows the values and bases of importance factors from some national standards. The safety levels achieved by using the prescribed importance factors in these standards are often implicit and remain unquantified. Although adoption of performance-based seismic design (PBSD) instead of prescriptive design overcomes this lacuna in terms of the predictable seismic performance of buildings [12], implementing an explicit PBSD is a challenging task due to the significant additional knowledge and skill required by the structural designers. As a result, despite its superiority, the adoption of the PBSD approach in design standards is rare, and a vast majority of buildings worldwide continue to be designed using prescriptive force-based standards [13]. Luco et al. [14] were the first to assimilate probabilistic building response in design standards by introducing the concept of risk-targeted seismic design (RTSD) [15]. They pegged the collapse capacity of code-compliant buildings to design force without considering the uncertainty within and across the building typology. The prevalent risk-based design procedures continue to peg importance factors to the conditional probability of collapse for a single event. The present paper proposes an innovative framework to determine risk-targeted importance factors that meet the intent of the PBSD approach while being suitable for Table 1 Typical importance factors in different national design standards Country
Basis
Canada [7]
Judgment
India [8]
Judgment
Risk category and importance factors Normal
High importance
Post-disaster
1.00
1.30
1.50
Common
High occupancy
Important
1.00
1.20
1.50
Important
Vital
Europe [9]
Hazard
Ordinary 1.00
1.20
1.40
USA [10]
Risk
Low risk
High risk
Essential facilities
1.00
1.25
1.50
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
159
use with prescriptive standards. The framework decouples probabilistic assessments required in the PBSD approach to expert groups, such as the standards committee in a country. The probabilistic assessments are carried out for building typologies and not for each building being designed. The structural designers then use these results with the conventional prescriptive design approach. While rooted in performance-based methodology, the framework retains the simplicity of the widely-adopted prescriptive approach for the design. The framework allows specialized groups to assess the risk-targeted seismic design parameters for building typologies and makes these parameters amenable to inclusion in the design standards. Carrying out force-based design of a building by structural designers using these parameters would require only incremental additional knowledge and skill compared to conventional RTSD procedure. Thus, the framework provides a strategy for adopting the PBSD approach in the prescriptive design of buildings and paves the way for the gradual adoption of the PBSD approach in the design standards.
2 PEER Framework The Pacific Earthquake Engineering Research (PEER) framework for PBSD acts as a foundation building block for the risk-informed decoupled design approach. The PEER framework [16] estimates the exceedance probability of decision variables such as dollar loss, downtime, injuries, and casualties by combining all possible seismic events and corresponding building behavior using the total probability theorem [17, 18]. The seismic risk of exceeding a given damage state ds is given by (∞ λds,IM = HIM ∗Fds,IM =
HIM (a)
d Fds,IM (a)da, da
(1)
0
where the hazard function HIM (a) is the probability that intensity measure IM exceeds a; the fragility function Fds,IM (a) is the probability of exceeding the damage state ds conditional on IM = a. Selecting an appropriate intensity measure (IM) is crucial for seismic risk assessment. The present study uses an optimal period of vibration for damage state dsk determined by minimizing the dispersion in its fragility in the period range of interest: ( ) To,dsk = arg min βdsk ,Sa (T j ) , T j ∈[0,Tco ]
(2)
where βdsk ,Sa (T j ) is as defined earlier and Tco is the cut-off period beyond which hazard curves may not be reliable. The geometric mean of individual optimal periods, Togm , is adopted as the common period of vibration for the fragility of building [19]. )1/n ( n Togm = Πi=1 To,dsk .
(3)
160
P. S. Badal and R. Sinha
3 Proposed Framework for Risk-Targeted Importance Factors In this paper, a novel framework for the development of generalized importance factors which can be used in the force-based design has been proposed. These importance factors are risk-based in that they strive to meet a pre-defined risk level. Next, we provide the basis of the formulation followed by a stepwise procedure to implement the proposed framework.
3.1 Formulation of Risk-Targeted Importance Factor Based on previous research [20], a linear relationship has been adopted between the logarithmic of risk, log λds and the importance factor. A given building’s design for two importance factors, I1 and I2 , is considered. The seismic risk associated with a damage state ds for these buildings is denoted by λds,I1 and λds,I2 , respectively. The log-linearity assumption allows to express an importance factor IR for the target risk of λ∗ as ) ( ( ) I2 − I1 log λ∗ − log λds,I1 . (4) IR = I1 + log λds,I2 − log λds,I1 Substituting for I1 = 1 and I2 = 1 + β, where β is a calibration parameter, we have ) ( ( ) β log λ∗ /λds,I1 . (5) IR = 1 + log(λds,I2 /λds,I1 ) It is worth noting that the design with I1 = 1 corresponds to the code-specified ordinary building. To indicate the same, we now denote λds,I1 by λds,code . Similarly, we denote λds,I2 by λds,1+β to emphasize the value of I2 . Let the ratio of λds,code to λds,1+β be denoted by α, i.e., α(β) =
λds,code λds,I1 = . λds,I2 λds,1+β
(6)
Substituting α in (5), we have ( ) ( ) IR = 1 + β logα λds,code /λ∗ ⇒ IR = 1 + c log10 λds,code /λ∗ ,
(7)
where c = β/ log10 α. It is observed from (7) that a lower target risk leads to an increase in the target risk ratio, λds,code /λ∗ . A positive value of the coefficient c indicates an increase in IR . . Thus, targeting a lower risk (say, for a hospital) will result in a higher importance factor.
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
161
3.2 Framework for Determination of Generalized Risk-Targeted Importance Factor Based on the above formulation, a stepwise procedure for the framework is provided below: Step 1. Develop an ensemble of index archetype buildings for the typology of interest. Let De be the design configuration of these buildings, where e ∈ {1, 2, . . . , Nbl } and Nbl is the number of buildings in the ensemble. Perform eigenvalue analysis to determine building modal properties. Step 2. Develop hazard-consistent suites of ground motion records suitable for the regional seismicity for each index building based on the PSHA of the region of interest. Step{ 3. Determine a set of }fragility functions Fdsk corresponding to damage states dsk ∈ DS1 ,(DS2 ,). . . , DS Nds . Based on analysis results, choose a suitable IM, for instance, Sa Togm as expressed in (3). Step 4. For each De , estimate the associated risk λdsk ,code,e for each damage state dsk . Estimate a single risk value λdsk ,code as a statistical measure of all buildingspecific risk, λdsk ,code,e . Step 5. Estimate the risk associated with De but with a higher importance factor I2 from the results of the nonlinear structural analyses using the suite of ground motions obtained in Step 3. Let this seismic risk be λdsk ,I2 . Step 6. Estimate parameter αk for different damage states given by (6), i.e., as the ratio of λdsk ,code to λdsk ,I2 . Next, calculate the parameter ck = β/ log10 αk for each damage state dsk , where β = I2 − I1 = I2 − 1. Step 7. Express risk-targeted importance factor IR as a function of the targeted risk ratio, given by (7). Further details of Step 3 and Step 4 have been discussed elsewhere [19]. The above procedure is generally applicable to any lateral load-resisting system or set of damage states and can be used with any seismic design standard. In the next section, the framework is illustrated for two RC special moment frame buildings designed per Indian standards [8, 21]. The adopted analysis is only for illustration. A set of drift-based damage states is chosen [22, 23] for the study.
4 Example Assessment of Risk-Targeted Importance Factor Two four-story RC frame buildings in Zone-IV and Zone-V are considered to illustrate the proposed framework. Figure 1 shows the common plan, elevation, and section details for both buildings. Example buildings are located in a high seismic region (Zone-IV) and a very high seismic region (Zone-V) in India [8]. The average peak ground acceleration for Zone-IV and V is 0.24g and 0.36g, respectively. The general design details of the buildings are given in Badal and Sinha [19]. Some structural properties of interest are given in Table 1. The ground floor columns of the buildings have a height of 4.5 m compared to a typical story height of 3.9 m
162
P. S. Badal and R. Sinha
Fig. 1 a Common building plan. b Elevation and cross-section with required longitudinal reinforcement for building in (b) seismic Zone-IV and c seismic Zone-V. The beam size is 350 × 750 mm for building in Zone-IV and 400 × 750 mm in Zone-V
to incorporate the influence of the foundation depth. These buildings are selected from a larger ensemble of RC special moment frame archetypical buildings [19]. The buildings have been detailed for capacity-based shear design [8, 21]. Design base shear coefficient, Cs,D , for the two buildings are 4.0% and 5.9%.
4.1 Analytical Models A nonlinear analytical model with concentrated plasticity has been developed in OpenSees [24] for seismic risk assessment. The backbone curve and hysteresis rules for RC members have been defined using Ibarra-Medina-Krawinkler (IMK) model
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
163
Fig. 2 Nonlinear analytical model for RC special moment frames
Table 2 Design details of the buildings used for illustration Zone
Stories
T a (s)
Cs,D (%)
T 1 (s)
Ω0
IV
4
0.61
4.0
1.72
3.5
V
4
0.61
5.9
1.55
2.9
[25]. Figure 2 shows the schematic sub-assemblage of the model. Due to a capacitybased shear design, a dominant flexural failure preceding the shear failure is considered. The finite size of the beam-column joint has been modeled using the compression strut mechanism [26]. The numerical model has been validated in an earlier research both on the member- and building-level [19]. Expected values of materials properties and loads are used for the assessment. Concrete grade of M40 (charac' teristic strength of 150 mm cubes after 28 days; ≈ 1.25 × f c ) and steel of Fe500D have been used as materials for construction. Rayleigh damping of 5% is employed in the first and third modes. Table 2 lists the design base shear (Cs,D ), approximate period Ta , and the over-strength factor Ω0 , the ratio of maximum pushover base shear capacity to the design shear force. The value of 2.9 and 3.5 is typical of the modern lateral load-resisting frames [10].
4.2 Ground Motion Selection Figure 3a shows the PSHA-based seismic hazard curve, while Fig. 3b compares the design response spectra with PSHA-based response spectra for two locations of interest, Delhi for Zone-IV and Guwahati for Zone-V [8]. Coordinates of Delhi are
164
P. S. Badal and R. Sinha
(a)
(b)
(c)
(d)
Fig. 3 a PSHA-based hazard curve for peak ground acceleration, ag [32]. Dashed horizontal lines mark DBE (Tr = 475 y) and MCE (Tr = 2475 y). Standard-based [8] design hazard for Delhi and Guwahati are denoted by solid and hollow markers, respectively. Different slopes, k, in log–log space are also marked. b Comparison of PSHA-based and standard-based uniform hazard spectrum for 475 y return period. Seismic hazard curves for c Delhi and d Guwahati for spectral accelerations at different periods
considered as (28.62° N, 77.22° E) and that of Guwahati as (26.17° N, 91.77° E). The geotechnical conditions are considered as a reference rock site (shear wave velocity in upper 30 m, Vs30 = 760 m/s).
4.3 Fragility Assessment Incremental dynamic analysis (IDA) [27] is used to assess the fragility functions of example buildings (Step 3 of the proposed framework). An ensemble of ground motion records for each building has been selected to match the site’s conditional spectrum [28, 29]. Buildings’ first analytical period has been taken as the conditioning period. Further, 22 × 2 records have been selected from the PEER strongmotion database [30] to be concordant with PSHA-based local hazard characteristics. Figure 4 shows the selected ground motion suites for both buildings. A close
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
165
(b)
(a)
Fig. 4 Response spectra of ground motion suites, conditional mean spectrum, and 2.5–97.5 percentile spectral ordinates for the building in a Zone-IV and in b Zone-V
(a)
(b)
Fig. 5 Fragility functions of the building in a Zone-IV and b Zone-V
representation of the conditional spectra by selected ground motions indicate their suitability. Further, details of ground motion have been provided in Badal and Sinha [31]. Figure 5 shows the resulting fragility functions for the two buildings.
5 Results 5.1 Generalized Risk-Targeted Importance Factor for Example Buildings Following the procedure outlines in Sect. 3.2, the generalized risk-targeted importance factor for example RC special moment frames is expressed as
166
P. S. Badal and R. Sinha
Fig. 6 Seismic risk of example buildings corresponding to immediate occupancy (IO), life safety (LS), collapse prevention (CP), and collapse performance when designed with different importance factors
IR
⎧ ⎪ ⎪ 2.1, ⎨ ( ) 2.2, ∗ = 1 + c log10 λds,code /λ , where c = ⎪ 2.5, ⎪ ⎩ 2.7,
for ds = Collapse for ds = CP . for ds = LS for ds = IO
(8)
The coefficients in (8) have been obtained using β = 2. Figure 6 shows the plot of the proposed IR , as in (8), with the target risk ratio for all four damage states for the ensemble of example buildings. It can be seen that the difference in values of IR for different damage states increases with the increase in the targeted risk ratio. As expected, it is observed that IR is the highest for IO and the smallest for collapse. For example, an IR of 2.26 is required for the fourfold reduction in Collapse risk, whereas for an equal risk reduction ratio in IO, the required IR value is 2.63, which is approximately 15% higher. This indicates that for critical buildings, performance levels of interest (e.g., operationality) need to be explicitly considered instead of benchmarking their design with a generic damage measure used for ordinary buildings (i.e., collapse risk).
5.2 Risk Margin Important and Critical Buildings as Per IS 1893–2016 Using the generalized expression in the previous section, the additional risk margins for important (I = 1.2) and critical buildings (I = 1.5) are assessed. It is found (that Ie = 1.2 results )in an average reduction of collapse risk by approximately 30% λcoll,code /λe = 1.30( , whereas Ie = 1.5)results in an average reduction of collapse risk by around 85% λcoll,code /λe = 1.85 . Similarly, Ie = 1.2 and Ie = 1.5 translate to a risk reduction for IO damage state by 25% and 65%, respectively.
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
167
6 Summary and Conclusions The performance-based seismic design has witnessed immense developments since its inception in the late 1990s and second-generation advancements in the 2000s. However, due to its complexity and required skillset for implementation, force-based seismic design procedures remain prevalent in the national design standards. The importance factors in the national standards are used for higher safety of critical buildings, but do not explicitly quantify associated additional safety margins. The present paper presents a framework for the risk-targeted design of critical buildings. The framework is rooted in rigorous performance-based methodology while ending with simple design factors suitable for use with prescriptive design standards. The framework decouples probabilistic assessments required in the PBSD approach to expert groups while allowing the structural designers to continue with the conventional design approach. The framework retains the simplicity of the widely adopted prescriptive approach for the design while exploiting the advantages of PBSD. The framework is demonstrated for a 4-story RC special moment frame building. The main characteristics of the proposed framework and major conclusions are summarized below: 1. A novel framework is proposed for the risk-targeted seismic design of buildings for use with prescriptive standards. The proposed framework duly considers the probabilistic nature of seismic demand, uncertainty in building response, and inter-building variation in seismic capacity. The proposed framework covers a wide range of risk targets corresponding to different damage states. 2. The framework provides a strategy to transition toward the principles of PBSD in the force-based design standards without requiring extensive enhancement of knowledge and skills of the design engineers that are otherwise required for implementing complete PBSD procedure. 3. Generalized risk-targeted expressions are developed for RC special moment frame buildings complying with Indian standards. The results also show that performance levels of interest (for instance, operationality) need to be explicitly considered for critical buildings. 4. The risk margins for RC moment frame building typology conforming to Indian standards were quantified in the study. The additional risk margins were found to be in the range of 25–30% for important buildings (importance factor of 1.2) and 65–85% for critical buildings (importance factor of 1.5). It was also found that the code-specified importance factor for a critical building is inadequate for meeting enhanced performance objectives.
168
P. S. Badal and R. Sinha
References 1. European Committee for Standardization (CEN). EN 1990:2002 Eurocode 0—Basis of Structural Design (2002) 2. ASCE (American Society of Civil Engineers): AF&PA/ASCE 16-95 Standard for Load and Resistance Factor Design (LRFD) for Engineered Wood Construction (1996) 3. AASHTO (American Association of State Highway and Transportation Officials): LRFD Bridge Design Specifications (2015). 4. Fédération Internationale du Béton (fib): Fib Model Code for Concrete Structures 2010 (2013) 5. Reid, S.G.: Uncertain reliability of structural design standards. Struct. Saf. 88, 102043 (2021) 6. Ellingwood, B.R.: Acceptable risk bases for design of structures. Prog. Struct. Mat. Eng. 3(2), 170–179 (2001) 7. NBCC: National Building Code of Canada, 2020 by Canadian Commission on Building and Fire Codes. National Research Council Canada (2022). https://doi.org/10.4224/w324-hv93 8. IS 1893. (Part 1) Criteria for Earthquake Resistant Design of Structures. Bureau of Indian Standards, New Delhi (2016) 9. EC 8. Eurocode: Design of Structures for Earthquake Resistance. Part 1: General Rules, Seismic Actions and Rules for Buildings. The European Standard (2004). 10. ASCE 7. Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-16). American Society of Civil Engineers, Reston, VA (2016) 11. Ditlevsen, O., Madsen, H. Structural Reliability Methods (Internet Edition 2.3.7). Wiley, Chichester (2007). 12. Meacham, B.J.: Accommodating innovation in building regulation: lessons and challenges. Build. Res. Inf. 38(6), 686–698 (2010) 13. Žižmond, J., Dolšek, M.: Formulation of risk-targeted seismic action for the force-based seismic design of structures. Earthquake Eng. Struct. Dynam. 48(12), 1406–1428 (2019) 14. Luco, N., et al.: Risk-targeted versus current seismic design maps for the conterminous United States. In: 76th Annual Convention Structural Engineers Association of California (2007) 15. ASCE 7. Minimum Design Loads for Buildings and Other Structures (ASCE/SEI 7-10). American Society of Civil Engineers, Reston, VA (2010) 16. Cornell, C.A., Krawinkler, H.: Progress and challenges in seismic performance assessment. PEER Center News 3(2), 1–2 (2000) 17. Cornell, C.A., Jalayer, F., Hamburger, R.O., Foutch, D.A.: Probabilistic basis for 2000 SAC federal emergency management agency steel moment frame guidelines. J. Struct. Eng. 128(4), 526–533 (2002) 18. Jalayer, F., Cornell, C.A.: A technical framework for probability-based demand and capacity factor (DCFD) seismic formats. RMS (2003) 19. Badal, P.S., Sinha, R.: A framework to incorporate probabilistic performance in force-based seismic design of RC buildings as per Indian standards. J. Earthquake Eng. 26(3), 1253–1280 (2022) 20. Pozos-Estrada, A., Liu, T.J., Gomez, R., Hong, H.P.: Seismic design and importance factor: Benefit/cost for overall service time versus per unit service time. Struct. Saf. 58, 40–51 (2016) 21. IS 13920. Ductile Design and Detailing of Reinforced Concrete Structures Subjected to Seismic Forces-Code of Practice. Bureau of Indian Standards, New Delhi (2016). 22. FEMA 356. Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, Washington, DC (2000). 23. ASCE 41. Seismic Rehabilitation of Existing Buildings (ASCE/SEI 41-06). American Society of Civil Engineers, Reston, VA (2006) 24. McKenna, F., Fenves, G., Scott, M., et al.: Open System for Earthquake Engineering Simulation. University of California, Berkeley, CA (2000) 25. Ibarra, L.F., Medina, R.A., Krawinkler, H.: Hysteretic models that incorporate strength and stiffness deterioration. Earthquake Eng. Struct. Dynam. 34(12), 1489–1512 (2005) 26. Lowes, L.N., Altoontash, A.: Modeling reinforced-concrete beam-column joints subjected to cyclic loading. J. Struct. Eng. 129(12), 1686–1697 (2003)
Risk-Targeted Seismic Design of Critical Buildings Using Force-Based …
169
27. Vamvatsikos, D., Cornell, C.A.: Incremental dynamic analysis. Earthquake Eng. Struct. Dynam. 31(3), 491–514 (2002) 28. Baker, J.W.: Conditional mean spectrum: tool for ground-motion selection. J. Struct. Eng. 137(3), 322–331 (2011) 29. Jayaram, N., Lin, T., Baker, J.W.: A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance. Earthq. Spectra 27(3), 797–815 (2011) 30. Chiou, B., Darragh, R., Gregor, N., Silva, W.: NGA project strong-motion database. Earthq. Spectra 24(1), 23–44 (2008) 31. Badal, P.S., Sinha, R.: Supplementary Information with ‘Risk-Targeted Importance Factors for Seismic Design of Critical Buildings’ (2021). www.civil.iitb.ac.in/~rsinha/TechRep_RiskTar getedImpFac_Supp 32. Raghukanth, S.: Development of probabilistic seismic hazard map of India (Personal Communication, Jan 11, 2020) (2020)
Study of Liquefaction Potential at Jaigarh Port Using Standard Penetration Test Data and Consequences: A Case Study Supratim Chanda, M. Kumar, Neeraj Kumar, and R. P. Shukla
Abstract Indian ports are rapidly expanding their infrastructures all along the coastlines. Many of the important ports are located in seismically active zones. The paper presents the study of liquefaction potential and analysis is carried out for Jaigarh Port at Ratnagiri, Maharashtra. The focus is mainly on determination of liquefiable layers in the region of multi-layered soil stratigraphy. The SPT data shows that the ground is composed of loose sand with silt underlain by basalt rock (−15 m from Natural Ground Level or NGL). The water table at shallow depth and loose sand in the reclaimed fills make the area susceptible to liquefaction hazards. The IS 1893 Part 1: 2016 is used to figure out the ground safety factor (FOS) against liquefaction for the Port. The soil tests and subsequent quantitative analysis suggest potential liquefaction of loose upper layers. Keywords Liquefaction · SPT · Reclaimed fill
1 Introduction The study of potential liquefaction is indeed not a new concept and dates back to the early twenties of the past century by Hazen [1]. In India the same was neglected and was assessed by some dedicated contractors with the help of established foreign codes and journals. Though in recent days the study of liquefaction has received traction as bureau of Indian standard (BIS) has issued revised code of practice for Earthquake Resistant Design of Structures, IS 1893 Part 1: 2016 [2] which contains S. Chanda · N. Kumar (B) Central University of Haryana, Mahendergarh, Haryana 123031, India e-mail: [email protected] M. Kumar Grafix Engineering Consultants Pvt. Ltd, New Delhi, Delhi 110016, India R. P. Shukla National Institute of Technology Srinagar, Srinagar, Jammu & Kashmir 190006, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_14
171
172
S. Chanda et al.
some cutting-edge techniques regarding valuation of ground liquefaction based on past works [3–6]. There are broadly three major ways to collect site parameters needed namely Standard Penetration method (SPT), Cone Penetration method (CPT) and advanced geo-physical study. In India due to easy availability and economy, SPT technique is widely accepted. CPT is not suitable in Indian subcontinent where rocks are encountered under subgrade. One more advantage of standard penetration test over the others is that it can collects nearly undisturbed sample with suitable precautions and supervision. In this paper we will focus ourselves in Port area with high seismic hazard of Zone IV. It is a real challenge as well as almost novel in a country like India where the subject like liquefaction near marine area is almost unexplored. Marine area has its own challenges like high water table and loose sediment deposits. We have chosen the site Jaigarh due to its high seismicity and economical backdrop as well. The most challenging part apart from the above is reclaimed fill with fine dredge geomaterial. We will examine layer wise the “factor of safety” (FOS) against liquefaction. At least twelve boreholes are made to collect soil data in different locations of the area. Standard penetration is performed until hard rock is encountered. Though first fifteen metres are observed very carefully due to multiple reasons and will be unfolded gradually herein. Apart from noting SPT values, there will be extensive laboratory studies like GSA, consistency limit of Atterberg, determination or finding specific gravity, etc. of collected soil samples. Based on these analyses and required superstructure to be built, we will discuss some consequences of string ground motion and some suggestive observation to mitigate the challenge.
2 Study of Subsoil Geotechnical examination was carried out as Standard Penetration Test (SPT) with guidelines given in IS 2131, “Method for Standard Penetration Test of Soil” [7]. Besides, the handbooks like SP 36 Part I and II, “Compendium of Indian Standards on Soil Engineering” [8, 9] were used extensively for laboratory-based analysis of collected geomaterials. The site is located at Ratnagiri, JSW Jaigarh Port. The boring/drilling operation has been carried out by deploying rotary drilling rig. The sampling work comprises of collecting disturbed (DS) as well as undisturbed (UDS) samples as obtained from SPT split spoon sampler wherever possible. The test is conducted by releasing a mallet of mass 63.5 kg on to a drive head from an altitude of 760 mm. The number of blows (N) are recorded in three stages for each 150 mm penetration of the sampler for a particular layer. The first stage blow counts are rejected and remaining two are added to find the field (N) value. Following Table 1 is a quick summary of above investigation. Water level has been monitored in the boreholes for at least 24 hours after completing the process of drilling the bore hole. Though seasonal variation of water table can be expected. Whereas Fig. 1 will show the exact plot plan of the above-mentioned boreholes. Figure 2 is a landscape view of the site where reclamation is partially complete and future work will start soon.
Study of Liquefaction Potential at Jaigarh Port Using Standard …
173
Table 1 Field locations of boreholes at site S. No.
BH No.
Zone
Co-ordinates Easting
Northing
Water level
R.L
Termination depth
(m)
(m)
(m)
1
BH-1
43Q
309,045.98
1,913,920
3.3
6.18
31.0
2
BH-2
43Q
308,985.90
1,913,818
5.5
5.93
31.0
3
BH-3
43Q
309,126.91
1,913,918
3.2
6.50
29.5
4
BH-4
43Q
309,073.66
1,913,833
2.8
5.90
28.5
5
BH-5
43Q
309,018.68
1,913,747
3.9
6.40
31.0
6
BH-6
43Q
309,159.89
1,913,848
3.5
6.49
30.0
7
BH-7
43Q
309,096.52
1,913,748
3.2
5.97
29.5
8
BH-8
43Q
309,242.06
1,913,846
4.5
5.75
27.5
9
BH-9
43Q
309,188.35
1,913,761
6.5
6.35
27.5
10
BH-10
43Q
309,133.36
1,913,675
3.5
6.65
28.0
11
BH-11
43Q
307,278.87
1,913,772
3.9
6.17
26.5
12
BH-12
43Q
309,215.59
1,913,672
3.5
6.30
26.0
Fig. 1 Plot plan of site at Ratnagiri, JSW Jaigarh Port
3 Stratigraphy of the Region The formation level of reclaimed ground is varying from +5.5 M CD to +6.5 M CD. Based on geotechnical Investigation Report, the existing soil up to 10 M depth consists of very loose to medium dense silt or no cohesive geomaterial. Afterwards, stiff silty clay supported on weathered Basalt rock base was found. The top level of rock varies from −14 M CD to −23.5 M CD (approx.) which is the competent
174
S. Chanda et al.
Fig. 2 Landscape view of the reclaimed area at Jaigarh Port, Maharashtra
founding strata for pile foundations at site. The principal rock formations of the area are the Deccan lava flows, which are extensively covered by laterite. Deccan Trap flows are exposed on the eastern parts while the laterite occurs on a low coastal plateau. This plateau is cut by rivers & streams in all of which the basalts are exposed with an intervening horizons of lithomarge clays. The Deccan basalts occur in a series of thick horizontal flows, separable from one another by beds of yellowish-brown clays and red boles. Individual flows vary in thickness from 30 to 60 m and are composed of greyish black, medium grain basalts. Precisely the followings are the main formations in order from natural ground level. Stratum I: Overburden Soil Stratum II: Completely to highly weathered rock Stratum III: Highly to moderately weathered rock Stratum IV: Moderately weathered rock Stratum V: Mildly weathered rock Stratum VI: Slightly weathered to Fresh rock.
4 Recorded Past Earthquake The earthquake zonation map of India published by the Bureau of Indian Standards (BIS) includes the districts of Raigad, Ratnagiri and Satara in Zone four [2], where the maximum expected intensity is VIII corresponding to Modified Mercalli Scale or 6.5 magnitude (M w ) on Richter Scale. This region has experienced number of tectonic
Study of Liquefaction Potential at Jaigarh Port Using Standard … Table 2 Past history of major seismic events near Ratnagiri [10]
S. No.
Seismic magnitude
Date
175 Epicentre
i
6.6
December 10, 1967
P¯atan
ii
6.2
September 29, 1993
Ausa
iii
5.5
September 02, 1980
M¯akhjan
iv
5.3
September 20, 1980
M¯akhjan
v
5.2
December 08, 1993
P¯atan
vi
5.1
December 08, 1993
L¯anja
vii
5.0
February 01, 1994
M¯akhjan
viii
5.0
March 12, 2000
M¯akhjan
ix
5.0
September 16, 2008
P¯atan
disturbances in the past. Some of the major earthquakes happened near Ratnagiri, Maharashtra are listed herein Table 2.
5 Semi-Empirical Correlations with SPT (N) In determination of Factor of Safety (FOS) against potential liquefaction based on SPT (N) values, basic approach is due to Youd and Idriss [4]. The same is adopted in latest Indian code of practice IS 1893 Part 1: 2016 with minor modifications. Following are equations proposed in this code of practice to estimate FOS. FOS =
CRR CSR
(1)
where “CRR” stands for cyclic resistance ratio of ground and “CSR” stands for cyclic stress ratio (Ref. Eq. (2)) as originally proposed in Seed and Idriss [3]. If “FOS” less than unity, soil liquefies. FOS between 1.0 and 1.2 may exhibit small ground deformations. σvo amax rd CSR = 0.65 (2) g σvo Here “amax ” is peak ground acceleration (PGA), “g” is constant of gravitational is effective overburden pressure and acceleration, σ vo is total overburden pressure, σvo ” “r d is stress reduction factor due to deformability of soil mass. For stress reduction factor we will use following Eq. (3) of Youd and Idriss [4]. rd =
1.0 − 0.4113z 0.5 + 0.04052z + 0.001753z 1.5 1.0 − 0.4177z 0.5 + 0.05729z − 0.006205z 1.5 + 0.00121z 2
(3)
176
S. Chanda et al.
“z” is depth of the layer under consideration from top of natural ground level. The next important thing is to formulate “CRR”. Here also we will adopt from IS 1893 Part 1: 2016 as follows in Eq. (4). CRR = CRR7.5 (MSF)K σ K α
(4)
where CRR7.5 as formulated in Eq. (5) and proposed by Youd, Idriss [4] is standard cyclic resistance ratio for 7.5 magnitude tremor obtained using SPT(N). “MSF” is magnitude scaling factor to scale the ratio up to required demand level given in Eq. (6) and found in the same above-mentioned reference. “K σ ” is overburden correction related to looseness and “K α ” is kept unity due to level ground assumed are as per IS 1893 Part 1: 2016. CRR7.5 =
50 1 1 (N1 )60CS + + 2 − 34 − (N1 )60CS 135 200 10(N1 )60CS + 45 102.24 Mw2.56 ( f −1) σvo Kσ = Pa MSF =
(5)
(6)
(7)
“Pa ” is the atmospheric pressure. “f ” is a function of density index of soil (Dr ) and values are as follows. For Dr = 40–60% f = 0.8–0.7, for Dr = 60–80% f = 0.7– 0.6. Also (N 1 )60CS is corrected SPT(N) values of the strata after fine correction. The procedures to achieve this from uncorrected field “N” values are given in the above discussed code (Annex F) and will not be repeated here.
6 Calculations, Results and Findings From Bore log data and Grain size analysis, it is reported that top 10–15 m are hazardous for potential liquefaction. As the land is reclaimed with hydraulic fill dredge geomaterial, the particles which percolated through water will be comparatively dense. Hence top 5–8 m needs much attention. Also, if top layer contains bolder with little fines (Non-Plastic), the same will have a narrow chance to be liquefied. For sufficient amount of plastic fines (say less than 0.005 mm size) the intergranular bond will not be loose and prompted good behaviour against liquefaction. In this qualitative inference apart from determining FOS, the following criteria may be helpful.
Study of Liquefaction Potential at Jaigarh Port Using Standard …
177
6.1 Chinese Criteria [11] • % Finer than 0.005 mm less than 15% (Clay Content) • Liquid limit less than 35 • Water content greater than 0.9 × Liquid Limit. Soils having all the above characteristics are susceptible for severe loss of strength during shaking. Also subsoil with corrected “N” value greater than 30 will not liquefy [4]. Besides that, Tsuchida [12] had shown that if median grain size “D50 ” of natural strata less than 0.02 mm or larger than 2.0 mm do not liquefy. Based on these qualitative–quantitative theories we have studied the borehole SPT data and followings are some sample analyses in tabular form. Table 3 is presented here for comparative understanding of the depth wise corrected SPT “N” values of each borehole as mentioned in Table 1. Sample calculations as in Tables 4 and 5 reveal that very low SPT “N” value corresponds to less relative density and hence prone to liquefaction. Clay content more than 15 per cent saves a stratum from potential loss of strength during strong ground motion. Boulders with huge void ratio will not liquefy is clearly seen from top layers of BH03. Also layers below 15 m are dense and reported less hazardous. Some graphical layer wise (vertical axis represents depth below ground level in metre) presentation (Fig. 3) of factor of safeties (FOS) against liquefaction of boreholes are shown. Comparison between Table 3 and Fig. 3 clearly infers that higher penetration values correspond to greater factor of safety of ground.
7 Conclusion It is evident from our analysis that loose clean sands with non-plastic silt in reclaimed land are most hazardous to be liquefied. Besides these the expected ground acceleration and average height of water table play prominent role. Also, we can see that Boulder with sufficient drainage path does not liquefy. Dense sand with moderate to high relative density responds well in strong shaking. It was also observed here that strata below 15 m are less hazardous towards liquefaction and also rocks are excellent subgrade to withstand periodic loadings.
27.6
29.5
28.9
−27.0
−30.0
28.4
−25.5
−28.5
18.3
21.0
−22.5
18.7
−21.0
−24.0
17.1
17.5
−18.0
14.8
−16.5
−19.5
15.7
16.2
−13.5
−15.0
14.1
−12.0
15.0
14.2
14.6
13.5
−7.5
−9.0
5.7
−10.5
12.7
14.5
−4.5
−6.0
9.3
…
45.0
46.2
47.5
63.7
41.9
31.9
42.2
20.0
15.8
13.2
13.6
15.4
13.3
13.6
13.2
12.7
16.1
20.4
−1.5
BH-02
N Corr
BH-01
N Corr
−3.0
Depth from NGL (M)
48.6
49.7
51.0
67.8
69.6
19.0
17.8
17.4
16.1
15.6
16.0
16.5
16.0
14.4
14.5
13.2
12.4
10.9
17.5
20.5
N Corr
BH-03
…
27.2
27.8
28.6
16.1
20.8
14.8
19.3
18.1
15.0
15.4
14.8
15.3
15.9
15.5
11.6
10.3
8.9
3.3
6.6
N Corr
BH-04
Table 3 Tabulation of depth wise corrected SPT “N” values BH-05
49.2
50.4
51.8
27.7
19.0
17.0
18.2
20.4
19.2
18.8
20.3
16.0
14.2
15.0
18.2
24.9
20.9
9.7
7.0
8.5
N Corr
BH-06
…
49.9
51.2
52.6
54.1
55.8
19.5
18.3
16.2
15.7
16.1
16.6
17.1
15.6
12.7
13.2
12.0
9.5
8.5
19.6
N Corr
BH-07
49.1
50.4
51.7
53.1
26.4
20.7
20.6
15.2
14.7
13.1
13.4
12.6
12.9
13.3
12.7
10.8
10.4
10.2
9.0
9.3
N Corr
BH-08
…
50.6
52.0
53.4
44.6
36.8
19.3
20.7
18.6
17.3
17.8
19.5
18.1
20.0
17.9
16.6
15.3
28.7
21.0
28.5
N Corr
BH-09
…
51.2
52.6
54.1
61.1
56.1
30.0
33.4
30.4
25.7
23.6
21.4
22.4
21.1
20.0
18.7
12.2
7.0
4.5
3.0
N Corr
BH-10
…
50.2
51.6
53.0
58.8
77.6
42.5
37.5
39.5
40.1
31.2
26.6
22.5
19.1
15.9
16.7
15.2
14.0
7.2
6.7
N Corr
BH-11
…
50.5
51.8
53.3
59.4
61.3
63.3
18.7
17.5
14.3
14.6
15.1
13.4
16.2
15.2
14.8
13.2
5.9
6.1
17.3
N Corr
BH-12
(continued)
94.1
50.0
51.3
52.7
58.4
60.2
62.1
64.2
66.5
39.1
13.4
14.7
15.2
15.4
13.1
10.4
10.8
12.6
10.4
25.7
N Corr
178 S. Chanda et al.
28.2
27.7
27.1
−34.5
…
…
… …
…
…
N Corr
N Corr
N Corr
−31.5
BH-03
BH-02
BH-01
−33.0
Depth from NGL (M)
Table 3 (continued)
…
…
…
N Corr
BH-04
…
46.9
48.0
N Corr
BH-05
…
…
…
N Corr
BH-06
…
…
48.0
N Corr
BH-07
…
…
…
N Corr
BH-08
…
…
…
N Corr
BH-09
…
…
…
N Corr
BH-10
…
…
…
N Corr
BH-11
…
…
…
N Corr
BH-12
Study of Liquefaction Potential at Jaigarh Port Using Standard … 179
16
16
59.0
49.0
49.0
49.0
49.0
49.0
43.0
43.0
43.0
3.00
4.50
6.00
7.50
9.00
10.50
12.00
13.50
15.00
16
16
16
16
16
16
16
14
59.0
1.50
Water Table = 0.430 m from EGL, Mw = 6.5, amax /g = 0.24
γ sat (KN/m3 )
Depth from E.G.L. (M)
Description (BH02)
% of fine Contents (75 micron passing)
7
7
8
6
7
5
5
5
5
3
Field SPT ‘N’ Value
Table 4 Tabulation of calculation, ref bore hole: BH02
13.21
13.64
15.44
13.35
14.95
12.74
13.58
13.19
12.71
9.34
Corrected (N1) 60cs
39.5
39.5
42.5
39.5
41.0
38.0
39.5
39.5
38.0
31.7
Dr (%)
–
–
–
–
–
–
–
–
–
–
D50
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
% finer than 0.005 mm
39
39
39
36
36
36
36
36
0
0
Liquid limit (LL)
0.305
0.324
0.340
0.353
0.361
0.365
0.364
0.358
0.342
0.315
CSR
0.208
0.219
0.252
0.225
0.258
0.229
0.254
0.260
0.267
0.227
CRR
0.68
0.68
0.74
0.64
0.71
0.63
0.70
0.73
0.78
0.72
FOS
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Liquefiable
Remark
180 S. Chanda et al.
59.0
64.0
64.0
12.00
13.50
15.00
18
63.0
59.0
9.00
10.50
16
63.0
7.50
16
18
18
18
18
16
82.0
82.0
4.50
18
18
γ sat (KN/m3 )
6.00
2.0
2.0
1.50
Water Table = 3.300 m from EGL, Mw = 6.5, amax /g = 0.24
% of fine Contents (75 micron passing)
3.00
Depth from E.G.L. (M)
Description (BH03)
12
12
11
9
9
7
6
5
17
17
Field SPT ’N’ Value
Table 5 Tabulation of calculation, ref bore hole: BH03
16.00
16.46
15.98
14.44
14.46
13.20
12.43
10.91
17.49
20.48
Corrected (N1) 60cs
44.0
44.0
42.5
41.0
41.0
39.5
38.0
35.0
45.5
50.0
Dr (%)
0.01
0.01
0.06
0.06
0.07
0.07
0.05
0.05
21.00
21.00
D50
48
48
13
13
8
8
20
20
0
0
% finer than 0.005 mm
46
46
0
0
0
0
44
44
–
–
Liquid Limit (LL)
0.209
0.218
0.224
0.225
0.222
0.209
0.190
0.163
0.153
0.155
CSR
0.223
0.234
0.232
0.216
0.221
0.212
0.206
0.188
0.309
0.443
CRR
1.07
1.07
1.04
0.96
0.99
1.02
1.08
1.15
2.02
2.87
FOS
Non-liquefiable
Non-liquefiable
Non-liquefiable
Liquefiable
Liquefiable
Non-liquefiable
Non-liquefiable
Non-liquefiable
Non-liquefiable
Non-liquefiable
Remark
Study of Liquefaction Potential at Jaigarh Port Using Standard … 181
182
S. Chanda et al.
Fig. 3 Layer wise factor of safeties of different boreholes
References 1. Hazen, A.: Hydraulic fill dams. Trans. Am. Soc. Civ. Eng. 83, 1717–1745 (1920) 2. Indian Standard IS-1893:2002 (Part 1), Criteria for earthquake resistant design of structures— Part 1: General provision and buildings. Bureau of Indian Standards, New Delhi (2016) 3. Seed, H., Idriss, I.: Simplified procedure for evaluating soil liquefaction potential. J. Soil Mech. Found. Div., ASCE. 97(SM9), 1249–1273 (1971) 4. Youd, T.L., Idriss, I.M.: Liquefaction resistance of soils: summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. J. Geotech. Geoenv. Eng. 127(4), 297–313 (2001) 5. Dixit, J., Dewaikar, D.M., Jangid, R.S.: Assessment of liquefaction potential index for Mumbai city. Nat. Hazards Earth Syst. Sci. 12, 2759–2768 (2012) 6. Duman, E.S., Ikizler, S.B. and Angin, Z.E.K.A.I.: Evaluation of soil liquefaction potential index based on SPT data in the Erzincan, Eastern Turkey. Arab. J. Geosci. 8(7), 5269–5283 (2015)
Study of Liquefaction Potential at Jaigarh Port Using Standard …
183
7. Indian Standard IS-2131:1997, Method for Standard Penetration Test for Soils. Bureau of Indian Standards, New Delhi (1997) 8. Indian Standard IS-SP 36:1987 (Part I), Compendium of Indian Standards on Soil Engineering, Part 1 Laboratory Testing of Soils for Civil Engineering Purposes. Bureau of Indian Standards, New Delhi (1987) 9. Indian Standard IS-SP 36:1988 (Part II), Compendium of Indian Standards on Soil Engineering, Part 2 Field Testing of Soils for Civil Engineering Purposes. Bureau of Indian Standards, New Delhi (1988) 10. Chandra, U.: Earthquakes of Peninsular India—a seismotectonic study. Bull. Seism. Soc. America. 67(5), 1387–1413 (1977) 11. DMG Special Publication: Guidelines for Analysing and Mitigating Liquefaction in California. University of Southern California, 117 (1999) 12. Tsuchida, H.: Estimation of liquefaction potential of sandy soils. In: Proceedings of the 3rd Joint Meeting of the US–Japan Panel on Wind and Seismic Effects, Tokyo, Japan (1971)
Seismic Assessment of Tunnels in Near Fault Ground Motion Bhavesh Banjare
and Swetha Veeraraghavan
Abstract Underground tunnels are an essential part of transportation and utility networks, and their vulnerability to earthquakes has significant socio-economic impacts. Tunnels have suffered substantial damage in past earthquakes, including the 2008 Wenchuan (China) earthquake, the 1995 Kobe (Japan) earthquake, the 2004 Niigata (Japan) earthquake, and the 1999 Chi-Chi (Taiwan) earthquake. Past studies on the 2D plane strain analysis of tunnel cross-sections subjected to vertically propagating seismic waves provide essential insights on the racking and ovaling of the tunnel cross-section during an earthquake. However, during the recent 2008 Wenchuan (China) earthquake, tunnels located near earthquake faults suffered damage not just to the cross-section but also in the longitudinal direction, which previous 2D studies cannot explain. The primary reason for the failure of the 2D studies in these near-fault scenarios is because the wave field near the fault is much more complex than a simple vertically propagating seismic wave. Therefore, a 2D plane strain approximation of the problem considering only the tunnel cross-section subjected to a uniform vertically propagating seismic loading in the out-of-plane direction is no longer valid in this case. The present study aims at understanding the coupled longitudinal and transverse response of underground tunnels subjected to obliquely incident (with respect to tunnel axis) seismic waves. The wave fields are generated through earthquake fault rupture simulations using earthquake faults with different dip angles. The numerical simulation of the soil-tunnel system is conducted using the open-source finite element software called MASTODON, developed by Idaho National Laboratory. Four different earthquake fault rupture scenarios for 2D and 3D are considered for this study. Analysis results reveal that the seismic responses of the tunnels increase with the increase in dip angle up to a fault dip of 45°. Additionally, the results showed that the 3D model needs to be considered for more general earthquake scenarios to capture both in-plane and out-of-plane responses (bending and cross-sectional changes) of the tunnel structure during the seismic loading. B. Banjare (B) · S. Veeraraghavan Department of Civil Engineering, IISc Bangalore, Bangalore, India e-mail: [email protected] S. Veeraraghavan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_15
185
186
B. Banjare and S. Veeraraghavan
Keywords Underground Tunnels · Seismic analysis · Soil-structure interaction · Seismic wave propagation · Longitudinal seismic response
1 Introduction Underground Tunnels constitute a significant part of civil infrastructure and serve as public transportation facilities, irrigation utilities, and storage infrastructure [1]. In seismically active areas, these underground tunnels are under earthquake-induced risks. Recent earthquake events, such as the Wenchuan earthquake in China (2008), the Kobe earthquake in Japan (1995), and the Chi-Chi earthquake in Taiwan (1999), have shown that tunnels are susceptible to irrecoverable damage due to seismic loading. The observed damage provides sufficient evidence to suggest that the safety of underground tunnels in seismically active areas is an important issue but not well understood yet, or at least not well considered during design. Designing a tunnel to withstand earthquake loading is distinct from other surfacestructures. Underground structures have inherent features that make their seismic response different from other surface structures; it’s mainly due to: (a) their complete enclosure in the soil/rock, (b) length of the structure, and (c) the inertia of the surrounding soil/rock is large relative to the inertia of the underground tunnel. Thus, the seismic response of an underground tunnel is dominated by the surrounding ground response and not by the inertial properties of the tunnel itself [2]. The seismic safety of structures is often examined under the assumption of vertically seismic wave propagation; this assumption is valid for locations that are far from earthquake faults. The near-fault (< 25 km) wave fields are significantly more complex due to: (i) The presence of body waves (P and Shear waves) of different incidence angles; (ii) The presence of surface waves (Rayleigh waves) [3]. The observed tunnel deformation modes due to seismic waves are presented in Fig. 1 and Table 1. A 2D plane strain analysis assuming vertically propagating seismic waves can only predict the first type of deformation, a 3D simulation with a more complex seismic wave field is required to capture the other forms of deformation. In this analysis, an unlined circular tunnel is embedded in a linear elastic soil domain. To understand the response of tunnels under different types of ground motion, the 2D/3D transverse and longitudinal response of the tunnel is examined under different fault dip angles generating inclined planar P and SV-waves. Surface waves can alter the response of the underground structure [5]. Hence, it is important to examine the response of tunnels due to surface waves. To include the effect of surface waves, four earthquake fault dip angles (both less than and greater than the critical incidence angle (i c )) are considered in the simulation, and their effect on the tunnel is studied. For SV-waves incidence angle greater than the critical incidence angle (i c ), surface waves are generated (Rayleigh wave) on interaction with the free surface [6]. The finite element MASTODON application [3], developed at Idaho National Laboratory, is used in the analysis. MASTODON is
Seismic Assessment of Tunnels in Near Fault Ground Motion
187
Fig. 1 Deformation types of tunnels due to seismic waves [4]
Table 1 Tunnel deformations due to seismic loading Types of tunnel deformations
Component of the seismic wave causing this deformation
1. Ovaling of the tunnel cross-section (Fig. 1e, f) A shear wave propagating normal to the tunnel axis 2. Longitudinal Bending (Fig. 1c, d)
Seismic wave-producing particle motion normal to the longitudinal axis
3. Axial compression and extension (Fig. 1a, b)
Seismic waves that produce particle motion parallel to the axis of the tunnel
an open-source software extension of the Multiphysics Object-oriented Simulation Environment (MOOSE) application [7].
2 Numerical Simulation 2.1 Two-Dimension Model Description A 1000-m × 500-m 2D homogeneous linear elastic soil domain with a tunnel diameter of 15 m is considered for this study, as shown in Fig. 2a. The soil-tunnel interaction analysis is performed in the linear–elastic domain. This constitutive model, although quite simplistic, help us understand the general trend in the response of the tunnel as shown by [8–10]. The shear modulus of the soil is 1.996 GPa, Poisson’s ratio is 0.3, and the density is 1800 kg/m3 . The resulting shear and P-wave velocities are 1053 m/s and 1969.1 m/s, respectively. To accurately model the propagation of waves with a maximum frequency of 10 Hz, the soil domain is meshed using threenoded triangle elements. The mesh size was less than 7.5 m, and the simulation time
188
B. Banjare and S. Veeraraghavan
Fig. 2 a 2D 1000-m × 500-m soil model with four earthquake faults with a different dip angle. b Slip-displacement time history at each point on the earthquake fault
step was set to 0.005 s. This element size and time step criteria satisfy the guidelines outlined in [11]. In this case, the model size was chosen such that it is large enough for the generation of an inclined plane wave from a series of point sources, and boundary effects do not significantly affect the response of the tunnel. Four earthquake fault configurations with dip angles of 22.5°, 34.5°, 45°, and 55° are considered in this study. These earthquake faults are simulated using a set of 501-point sources spread evenly along each fault shown in Fig. 3a–d. Each point source is a double couple, and the energy released by this double couple depends on the fault configuration (i.e., the dip of the fault, slip-displacement time history, and rake angle), area of fault rupture, average slip-displacement time history, and the shear modulus of the soil around the fault [12]. The finite fault considered in Fig. 2a can only simulate an approximation of a plane wave traveling parallel to the center part of the fault. To simulate the plane shear wave that travels normal to the fault line, all the point sources are given the same slip-displacement time history and slip direction, and all the point sources are activated at the same time instant. Modeling the earthquake fault rupture using these point sources ensures that the same amount of energy is released in all four cases, as only the dip angle parameter changes from one case to another. As we can observe from Fig. 3, the approximate plane waves generated from the earthquake fault rupture travel in both directions upward and downward w.r.t. fault. The waves which are traveling in the downward direction and the scattered waves generated by the tunnel need to be absorbed by the left, right, and bottom boundaries of the soil-structure domain. Lysmer dampers [13] are prescribed at these boundaries to absorb these downward traveling waves. Lysmer dampers can only absorb waves that are perpendicular to the boundaries. Newmark-beta [14] integration parameters, γ , and β, are set to 0.5 and 0.25 to avoid numerical damping, and since the integration using those parameters is unconditionally stable. Rayleigh damping [15] as 0.5% (based on the shear wave velocity of the soil) is used throughout the soil-structure domain to dampen any residual waves that are not completely absorbed by the Lysmer dampers.
Seismic Assessment of Tunnels in Near Fault Ground Motion
(a)
(b)
(c)
(d)
189
Fig. 3 Snapshots of the earthquake simulations with a 22.5° dip, b 34.5o dip, c 45° dip, and d 55° dip showing the acceleration magnitude for each simulation. The wavefront with the highest acceleration magnitude (red color) is the SV wavefront. The (white color) line indicates the earthquake fault
The SV-waves that travel in the upward direction interact with the free surface, and the incidence angle of the SV-waves determines whether surface waves are generated or not. The reflected angle of the P-wave (see Table 2) is obtained using Snell’s law as sin(i ) sin(r ) = Vs VP
(1)
where i and r are the incidence angle of the SV-wave and reflected angle of the P-wave, respectively; V S and V P are the S and P-wave speeds, respectively. The incidence angle for which the reflected angle becomes 90o is called the critical incidence angle (i c ). The incident angle 32° is the critical incidence angle for soil, having Poisson’s ratio of 0.3.
2.2 Three-Dimensional Model Description A 500-m × 500-m × 1000-m 3D homogeneous linear elastic soil domain with a tunnel diameter of 15 m is considered for this study, as shown in Fig. 4. The same material properties and Rayleigh damping parameters as in 2D are considered for
190
B. Banjare and S. Veeraraghavan
Table 2 Different waves in the domain based on incidence angle (i) Earthquake fault The incidence The reflected The reflected rupture angle of SV-wave angle of SV-wave angle of P-wave inclination angle (i) (r) (r) r= sin−1
VP Vs
Surface-wave generated or not (critical incidence angle (i c ) = 32°) sin(i )
22.5°
22.5°
22.5°
45.69°
No, i < 32°
34.5°
34.5°
34.5°
No reflected P-wave, as Surface waves are generated
Yes, i > 32° (Rayleigh will be generated)
45°
45°
45°
45° is a special scenario. All the energy is reflected back as an SV-wave. No surface waves are generated
55°
55°
55°
No reflected P-wave, as Surface waves are generated
Yes, i > 32° (Rayleigh will be generated)
the 3D analysis as well. The soil domain is meshed using four-noded tetrahedron and eight-noded brick elements. The element size and time step criteria satisfy the guidelines outlined in [11]. In addition to left, right, and bottom boundaries, the front and back boundaries also contain Lysmer dampers. Four earthquake fault configurations with dip angles of 22.5°, 34.5°, 45°, and 55° are considered in this study. These earthquake faults are simulated using an area fault of width 300-m × length of Fault (L)-m; where L is 783.93-m, 529.65-m, 424.26-m, and 366.232-m for dip angles of 22.5°, 34.5°, 45°, and 55o , respectively, as shown in Figs. 5a–b and 6a–d. The fault is maintained to the same extent in the YZ plane as
Fig. 4 3D 500-m × 500-m × 1000-m soil model with four earthquake faults, each with a different dip angle
Seismic Assessment of Tunnels in Near Fault Ground Motion
191
in the XY plane for 2D simulations so that the effect of the same earthquake hitting the tunnel in different orientations can be analyzed. The fault is discretized using 16,032-point sources spread evenly on the fault surface, as shown in Fig. 7. We are increasing the area used in each point source
Fig. 5 Snapshots of the cross-sectional view of 3D earthquake simulations with a 22.5° dip, b 45° dip showing the acceleration magnitude for each simulation. The wavefront with the highest acceleration magnitude (red color) is the SV wavefront
(a)
(b)
(c)
(d)
Fig. 6 Snapshots of the longitudinal view of 3D earthquake simulations with a 22.5° dip, b 34.5° dip, c 45° dip, and d 55° dip showing the acceleration magnitude for each simulation. The wavefront with the highest acceleration magnitude (red color) is the SV wavefront. The (white color) line indicates the earthquake fault
192
B. Banjare and S. Veeraraghavan
Fig. 7 Snapshots of the 3D point sources distributed over the planar fault
using an appropriate scale factor so that the energy released per unit area matches between the corresponding 2D and 3D simulations.
3 Results and Discussion The 2D response of the tunnel is examined under the four different fault rupture scenarios (22.5°, 34.5°, 45°, and 55°). To understand the response of the structure, spectral acceleration in the X and Y direction at different locations (0°, 90°, 180°, and 270°) is examined. Spectral acceleration in the X and Y at 0° (see Fig. 8a, b) and 270° (see Fig. 8c, d) is presented. In Fig. 8, the 2D response spectra for the 45° fault dip scenario produces maximum horizontal and vertical spectral acceleration as compared to the 22.5°, 34.5°, and 55° fault dip; it is likely due to all the energy reflected back as SV-wave from the free surface, but in other cases, some part of the energy is converted to P or Rayleigh waves. The peak response comes around 8.31 Hz and 9.06 Hz in the X and Y directions, respectively. It is observed from Fig. 8a–d that the horizontal (X) and vertical (Y) response of the structure increase with the dip angle up to 45°, after which the response decreases for the dip angle of 55°. The 3D response of the structure is analyzed under four different fault rupture scenarios. To understand the effect of transverse and longitudinal responses of structure, spectral accelerations in the X, Y, and Z directions at the different points along the longitudinal direction of the tunnel (0°, 90°, and 270°) at 200-m, 400-m, 500-m, 600-m, and 800-m are presented in Figs. 9a–d, 10a–f, and 11a–b.
Seismic Assessment of Tunnels in Near Fault Ground Motion
(a)
(c)
193 0o
(b)
(d)
270o
Fig. 8 Spectral acceleration (Sa) as a function of frequency in the horizontal and vertical direction for four different earthquake fault dip scenarios: a horizontal (X) Sa at (0°), b vertical (Y) Sa at (0°), c horizontal (X) Sa at (270°), and d vertical (Y) Sa at (270°)
In Fig. 9, the response spectra in the horizontal direction vary along the longitudinal direction. It is also observed that the maximum response was at 400-m (redcurve) for 45° fault dip as compared to the other fault dip scenarios. This is likely because the main SV wavefront interacts with the tunnel at this location. It is also noticed from Fig. 9a–d that the horizontal (X) response of the structure increases with the dip angle up to 45°, after which the response decreases for the dip angle of 55°. From Y (Figs. 10a, c, e, 11a and Z (Figs. 10b, d, f, 11b) spectral acceleration plots, it is noticed that response of the structure is not the same along the length of the tunnel, its response is varying with the space and time for different earthquake fault dip scenarios. The maximum response was observed for the dip angle of 45° as compared to other scenarios. The finite element size and time step (t) used for the study can accurately capture the numerical wave propagation up to 10 Hz; the response spectra are truncated to 20 Hz for this study. The actual earthquake frequency content lies in the range of 0.01 to 10 Hz. Finer mesh size and smaller time step (t) are required to capture higher frequency effects on the soil-structure domain. Also, there are significant
194
B. Banjare and S. Veeraraghavan
90o (a)
(b)
(c)
(d)
90o
Fig. 9 a X Spectral acceleration for Fault dip 22.5° (at 90D), b X Spectral acceleration for Fault dip 34.5° (at 90D), c X Spectral acceleration for Fault dip 45° (at 90D), and d X Spectral acceleration for Fault dip 55° (at 90D)
differences in the responses at locations around the circumference of the tunnel, indicating deformation of the tunnel cross-section along with axial deformation in the 3D scenario. From the preliminary results presented in this section, it is found that both inplane and out-of-plane responses (bending and cross-sectional changes) of the tunnel structure during the seismic loading were significant in causing deformation of the structure, and the out-of-plane responses cannot be captured by a 2D plane strain simulation.
4 Conclusion The 2D/3D response of underground tunnels to inclined earthquake waves is examined in this study using MASTODON finite element application. Four earthquake
Seismic Assessment of Tunnels in Near Fault Ground Motion
(b)
(a)
195
0o
270o
(c)
(d)
(e)
(f)
Fig. 10 a Y Spectral acceleration (Sa) for Fault dip 22.5° (at 270D), b Z Spectral acceleration (Sa) for Fault dip 22.5° (at 0D), c Y Sa for Fault dip 34.5° (at 270D), d Z Sa for Fault dip 34.5° (at 0D), e Y Sa for Fault dip 45° (at 270D), and f Z Sa for Fault dip 45° (at 0D)
fault rupture scenarios with different fault dip angles are considered for this study. A plane shear wave is generated and propagated, and if the inclination angle (i c ) is greater than 32°, then surface waves are generated (Rayleigh waves) on interaction with the free surface. The underground tunnel response increases with an increase in dip angle up to a dip of 45°; then, it decreases for 55° dip angle. The results from preliminary analyses shows that the overall response (transverse and longitudinal direction) of the structure varies along the axis of the tunnel. The
196
B. Banjare and S. Veeraraghavan
(a)
(b)
Fig. 11 a Y Spectral acceleration (Sa) for Fault dip 55° (at 270D), and b Z Spectral acceleration (Sa) for Fault dip 55° (at 0D)
2D plane strain simulation cannot capture the longitudinal deformations. Hence, 3D simulation is needed to capture the underground tunnel response subjected to near-field earthquake fault rupture. It is important to emphasize that the analysis conducted in this study considers that the soil-structure system responds linearly. In real situations, the soil near the tunnel will deform nonlinearly due to the high strains induced by soil-structure interaction. Also, for lined tunnels, the tunnel lining and the soil lining interface condition (slip or no-slip condition) may alter the overall response of the structure. These effects also need to be incorporated into the soil-structure system to get the actual response of the structure, which could be used for the safe design of the tunnel in earthquake-prone areas. Acknowledgements The authors gratefully acknowledge Science and Engineering Research Board for funding this project (SRG/2020/001540).
References 1. Yu, H., Yuan, Y., Qiao, Z., Gu, Y., Yang, Z., Li, X.: Seismic analysis of a long tunnel based on multi-scale method. Eng. Struct. 49, 572–587 (2013) 2. Okamoto, T., Yagita, M.: The experimental investigation on the flow past a circular cylinder of finite length placed normal to the plane surface in a uniform stream. Bull. JSME 16(95), 805–814 (1973) 3. Veeraraghavan, S., Bolisetti, C., Slaughter, A., Coleman, J., Dhulipala, S., Hoffman, W., Kim, K., Kurt, E., Spears, R., Munday, L.: MASTODON: an open-source software for seismic analysis and risk assessment of critical infrastructure. Nucl. Technol. 207(7), 1073–1095 (2021) 4. Owen, G.N., Scholl, R.E.: Earthquake engineering of large underground structures (1981)
Seismic Assessment of Tunnels in Near Fault Ground Motion
197
5. Wang, G., Yuan, M., Miao, Y., Wu, J., Wang, Y.: Experimental study on seismic response of underground tunnel-soil-surface structure interaction system. Tunn. Undergr. Space Technol. 76, 145–159 (2018) 6. Achenbach, J.: Wave Propagation in Elastic Solids. Elsevier (2012) 7. Gaston, D., Newman, C., Hansen, G., Lebrun-Grandie, D.: MOOSE: a parallel computational framework for coupled systems of nonlinear equations. Nucl. Eng. Des. 239(10), 1768–1778 (2009) 8. Tao, M., Zhao, H.T., Li, Z.W., Zhu, J.B.: Analytical and numerical study of a circular cavity subjected to plane and cylindrical P-wave scattering. Tunn. Undergr. Space Technol. 95, 103143 (2020) 9. Alagha, A.S., Chapman, D.N.: Numerical modelling of tunnel face stability in homogeneous and layered soft ground. Tunn. Undergr. Space Technol. 94, 103096 (2019) 10. Zhang, X., Jiang, Y., Wang, G., Cai, Y., Iura, T.: Three-dimensional seismic performance of mountain tunnel with imperfect interface considering P wave. Tunn. Undergr. Space Technol. 108, 103720 (2021) 11. Ihlenburg, F., Babuška, I.: Finite element solution of the Helmholtz equation with high wave number Part I: the h-version of the FEM. Comput. Math. Appl. 30(9), 9–37 (1995) 12. Aki, K., Richards, P.G.: Quantitative seismology (2002) 13. Lysmer, J., Kuhlemeyer, R.L.: Finite dynamic model for infinite media. J .Eng. Mech. Div. 95(4), 859–877 (1969) 14. Newmark, N.M.: A method of computation for structural dynamics. J .Eng. Mech. Div. 85(3), 67–94 (1959) 15. Coleman, J., Slaughter, A., Veeraraghavan, S., Bolisetti, C., Numanoglu, O.A., Spears, R., Hoffman, W., Hurt, E.: MASTODON theory manual (No. INL/EXT-17–41930). Idaho National Lab. (INL), Idaho Falls, ID (United States) (2017)
Effect of Reinforced Soil Interaction with Other Components on Static and Dynamic Performance of MSE Wall Sajan Malviya and Prishati Raychowdhury
Abstract Mechanically stabilized earth (MSE) walls are reputed for demonstrating improved static and seismic performance over conventional retaining walls. The stabilization of the earth is generally done by placing reinforcing elements such as metal strips, geosynthetic layers or micro-piles in different layers of the backfill soil. There is no scarcity of literature on numerical analysis of MSE walls for both static and dynamic loading. However, the present state of the research lacks a comprehensive analysis of the combined effect of the various contributing factors on the performance of the wall. The reinforced fill interacts with other components, namely the wall, retained fill, reinforcement and foundation. Under operational conditions all these interactions occur simultaneously and therefore also have a combined effect. For dynamic analysis additional factors have to be accounted for such as seismic wave passage effect on the wall and backfill, acceleration and displacement amplification through the backfill. The present study aims to develop a finite element model that can effectively analyze the effect of these factors on the wall performance under static and dynamic loading. The performance of the wall is assessed by the lateral displacement and strain levels in the reinforcement layers at the end of construction and during a seismic event. Keywords Finite-element analysis · Mechanically stabilized earth (MSE) walls · Seismic motions · Geogrid reinforcement · Soil-geogrid interface
1 Introduction Mechanically stabilized earth (MSE) walls or reinforced earth (RE) walls, basically comprises of three main components: backfill, reinforcement and facing. The stabilization of the earth is generally done by placing reinforcing elements such as S. Malviya (B) · P. Raychowdhury Indian Institute of Technology Kanpur, Kanpur, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_16
199
200
S. Malviya and P. Raychowdhury
metal strips or geosynthetic layers in the backfill soil. They are known to perform satisfactorily under static and seismic loads [13, 25]. The pioneering work in seismic analysis of full-scale MSE wall was conducted by Richardson and Lee [22], Richardson [21] and Richardson et al. [23]. They performed seismic full-scale model test on the 6 m-high walls. The reinforcement used in the model was steel strip and a discrete concrete block was considered for facing. Another approach adopted was shake table studies, conducted by various researchers [19, 26]. Shake table studies conducted by Fairless [9] indicated that seismic shaking accompanied by permanent displacement in MSE walls results in a significant increase in reinforcement stresses. Prototype studies were conducted to enhance the understanding of seismic MSE wall design acquired from model studies [20]. Besides these laboratory and field studies, numerical and analytical studies have been undertaken to provide further insights into the behavior of MSE wall when subjected to seismic loads. Significant contributions have been made in this field of study over a period of time by several authors [1, 2, 5, 6, 14, 15, 27, 29, 31]. However, since there are various factors at play simultaneously such as non-linear behavior of fill and/or foundation soil, interaction between various components, effect of seismic wave passage on the wall and backfill, acceleration amplification through the backfill, the task of accurately assessing deformation characteristics and stress distribution within the system under seismic loading is a complicated one. The present study aims to address these factors.
2 Model Development A 2-D finite element code is written in MATLAB R2019b using discrete approach to analyze the seismic performance of geosynthetic reinforced MSE walls with fullpanel. The wall geometry and components of MSE wall can be seen in Fig. 1 the details of the components, material models, construction sequence, loading and boundary conditions are discussed in subsequent sections.
2.1 Backfill: Reinforced and Retained 4 noded isoparametric quad elements [6, 16] for modeling the soil. The mesh distribution is finer and uniform in the reinforced zone and coarser in retained zone and foundation soil. An elasto-plastic material model is adopted here [12]. The behavior in the elastic region is considered non-linear and, is represented by a hyperbolic stress–strain relationship [7]. The elastic tangent modulus (E t ) is evaluated using:
Effect of Reinforced Soil Interaction with Other Components on Static …
201
Fig. 1 Schematic of Finite element mesh: Geometry, model components and boundary conditions
E t = K e pA
σ3 pA
n 1−
Rf (1 − sin φ) σ1 − σ3 2c cos φ + 2σ3 sin φ
2 (1)
where Rf is the failure ratio; ϕ is the angle of internal friction for soil; σ1 and σ3 are major and minor principal stress, respectively; c is the soil cohesion; K e is soil elastic modulus number; n is soil elastic modulus exponent; and pA is atmospheric pressure. The failure criterion considered is the one used for a Mohr–Coulomb material. The plastic potential function used is suggested by Zienkiewicz et al. [30] using dilation angle ψ. For simulating behavior under cyclic loading, an unloading and reloading modulus, E ur is adopted. E ur = kur pA
σ3 pA
n (2)
Jaky’s equation is employed for computing confining pressure. σ3 = σ1 (1 − sin ϕ)
(3)
The Poisson’s ratio is considered as 0.3 [14]. The above-mentioned constitutive model was used for both backfill and foundation soil. For simplicity parameter values were kept identical for backfill and foundation.
2.2 Wall Facing Three noded isoparametric curved Mindlin beam element have been used for modeling the wall facing [8]. This element effectively becomes a shell element for a
202
S. Malviya and P. Raychowdhury
plane strain analysis. Full height panel of 6 m height is considered for facing in this analysis. The material model for the facing wall is chosen to be linear elastic.
2.3 Reinforcements Geogrid reinforcement is considered for this analysis. The reinforcement layers in MSE walls were often modeled using linear, elastic–plastic [2, 15, 29, 31] cable elements with negligible compressive strength and an equivalent cross-sectional area. Another approach chosen by authors is to employ a linear elastic model with no failure limits [5, 32]. Membrane elements capable of transmitting only the forces tangential to surfaces are employed in this study. The material model considered is linear elastic. Reinforcement strains are computed as axial strains in the element of a given reinforcement. The length of reinforcement considered here is 4.25 m Table 1.
2.4 Interfaces The interface modeling is probably one of the most important aspects of a discrete FE model. The zero-thickness elements using a simple linear elastic perfectly plastic constitutive model have been employed for soil-wall and soil-reinforcement interactions with fair degree of success [4, 10]. The interface stress is characterized by the normal and shear stresses, σ and τ . The governing constitutive law which relates these stresses to the corresponding elemental ‘strains’, ε and γ is given by: τ γ = [D] σ ε
(4)
It is noteworthy that the term interface element ‘strain’ here refers to the relative displacement between the top and bottom of the interface element. The constitutive matrix, [D] is represented as,
k 0 [D] = s 0 kn
(5)
Different authors have proposed different formulations and values for normal and shear stiffness. Studies based on FLAC [11, 14], use a recommended value, relating stiffness to bulk modulus (B), shear modulus (G) and the smallest width of the adjacent zone in the normal direction:
Effect of Reinforced Soil Interaction with Other Components on Static …
B + 43 G Apparent stiffness = max zmin
203
(6)
This formulation is adopted in the study to ensure that the normal and shear stiffness at an interface is representative of normal stress and elastic properties of soil at that location. The shear and normal interfaces are of the order of 105 kN/m3 and 106 kN/m3 , respectively. These values are within the range that is found in the literature. In this study all interfaces are assumed to be purely frictional. The interfaces are modeled as Mohr–Coulomb material characterized by δ (interface friction angle) and a yield criterion. The values of interface friction angles soil-geogrid, δsg and soil-facing, δsf are taken as tan−1 23 tan ϕ .
2.5 Reinforcement–Wall Connections The first node in a reinforcement layer (adjacent to the facing) is assumed to be rigidly connected to a node in facing panel at the same elevation through a spring element with a relatively high stiffness value. The reaction force in any of this spring element corresponds to the connection load for the given wall-reinforcement connection. The connection strength is assumed to be 50 kN/m (Table 1). Table 1 Material properties considered for the study
Soil properties Angle of internal friction, ϕ
35o
Cohesion, c
0 kPa
Dilation, ψ
5o
Unit weight, γ
18 kN/m3
Poisson’s ratio, νs
0.3
Ke
1100
n
0.5
Rf
0.9
Facing properties Young’s modulus of elasticity, E w
24,000 MPa
Poisson’s ratio, νw
0.15
Wall thickness
165
Reinforcement properties Stiffness, J
1000 kN/m
Tensile strength, Ty
200 kN/m
Equivalent Area, Aeq
0.002 m2
204
S. Malviya and P. Raychowdhury
Table 2 First five natural frequencies for the MSE wall
Mode
Frequency (Hz)
I
2.234
II
2.709
III
3.213
IV
4.115
V
4.411
3 Dynamic Analysis 3.1 Modal Analysis The modal analysis was done for consistent mass matrix and global stiffness matrix. The natural frequencies were observed to be dependent on the boundary conditions. The results for the standard case (Fig. 1) are tabulated (Table 2).
3.2 Input Motion The current study limits itself to an exercise in the verification of applicability of the developed model for a seismic input. For the same, recorded ground motion for Uttarkashi earthquake (Mw-7.0, October 20 1999), has been selected as input data for the seismic simulation. The input motion has been scaled for zone IV. For a real field application like seismic design of an MSE wall, the selection of a suitable input ground motion is a complex task. The choice will invariably be governed by site specific characteristics. A large number of seismic recorded motions need to be analyzed before applying in order to accomplish a realistic assessment of the wall performance [28]. The acceleration time history and Fourier transform are given in Fig. 2. This input motion is introduced in the analysis as a time dependent inertia force, F. This is computed as a product of lumped mass at node and input acceleration (function of time). The dynamics can be expressed in the form of an equation (Eq. 7): ˙ + [K ]{u} = [F] ¨ + [C]{u} [M]{u}
(7)
[M] is the global mass matrix (consistent mass matrix is considered here) and [K ] is the global stiffness matrix. A Newmark non-linear time step integration algorithm is developed and used for the dynamic analysis where stiffness matrix and damping matrix need to be updated with load increment.
Effect of Reinforced Soil Interaction with Other Components on Static …
205
Fig. 2 Scaled input motion. a Time history for input acceleration, b Fourier analysis
3.3 Damping Rayleigh damping of 5% is considered for the present study. The damping matrix [C] is computed as Eq. 8 [18]. [C] = α[M] + β[K ]
(8)
Here, α and β represent the proportional damping parameters for mass and stiffness, respectively. The damping parameters are evaluated based on Spears and Jenson [24]. Lysmer and Kuhlemeyer’s [17] proposed an approach to accommodate for the numerical difficulties resulting from the effect of reflected waves. In application, this is akin to placing a viscous dash-pot at the boundary node (Fig. 1). The viscous damping matrix [C]ve for a given boundary element is computed as: [C]ve =
[N ]T [C]∗ [N ]ds
(9)
where [N] is the shape function for element under consideration
aρV p 0 [C] = 0 aρVs ∗
(10)
V p and Vs , the compression and shear velocities, respectively, are back calculated from elastic properties of the soil (confining pressure dependent) for the given element. The constants, a and b are generally taken as unity [3]. The mass density is represented by ρ. The global viscous damping matrix is formed by assembling all the elemental viscous damping matrix. This matrix is then added to the one given in Eq. (8) prior to solving for equilibrium.
206
S. Malviya and P. Raychowdhury
Fig. 3 a Displacement of wall facing during the shaking period. b Deformation profile of the wall post shaking period
4 Results The results are presented considering the ‘end of construction’ stage displacement as datum. The elemental stresses are retained from the gravity analysis. Selected results are presented in graphical form.
4.1 Lateral Deformation Wall deformation for three different heights above the base of wall facing are given in Fig. 3. The wall deformation is accumulative over the time period of vibration. The peak observed in deformation, on expected lines is synchronous with acceleration time history. The residual deformation is lower than the peak value. It is also observed that the point of peak deformation, the response flattens considerably. Maximum deformation is observed at the top of the wall (Fig. 3a). A deformation profile is shown in Fig. 3b. It can be observed that maximum deformation in soil occurs in a region in proximity with the top of the facing. The deformation gradually decreases to zero, in moving toward horizontal boundary.
4.2 Acceleration Amplification The acceleration response in the soil (measured as nodal acceleration) is seen to exhibit an amplification as we move upwards from base of the foundation (Fig. 4). The amplification has been computed as the root mean square acceleration over the period at a given depth to the same value at the foundation base [5].
Effect of Reinforced Soil Interaction with Other Components on Static …
207
Fig. 4 Acceleration amplification versus elevation
The value of amplification is 1.68 at the base of wall and 3.72 at the top surface. Amplification has been computed as the root mean square acceleration over the period at a given depth to the same value at the foundation base [5]. The value of amplification is 1.68 at the base of wall and 3.72 at the top surface.
4.3 Reinforcement Strains Selected strain profiles (reinforcement layer I, III, V, VII) have been shown in Fig. 5. The maximum strain observed is in the lowermost reinforcement layer (1.6%) and it keeps decreasing with increase in height of the reinforcement layer. Furthermore, the point of location of maximum strain moves away from the wall (Fig. 5).
5 Conclusions and Future Scope A FE model is developed for seismic analysis of MSE wall using discrete approach. The material model and values of model parameters for various components have been carefully chosen based on the available literature for numerical modeling for MSE wall. The current study retains the elemental stresses in soil elements developed during gravity analysis performed prior to the dynamic analysis. The Eigen value analysis was carried out to get an insight into the natural frequencies of the MSE wall system. Subsequently, a recorded ground motion (Uttarkashi earthquake) was used as input to assess the performance of the model. A conservative value for damping ratio (5%) has been chosen for the analysis. The model performs satisfactorily well in computing lateral displacement and reinforcement strains when the seismic load is
208
S. Malviya and P. Raychowdhury
Fig. 5 Reinforcement strains
applied. The interface interaction is considered by carefully choosing material model parameters and more importantly the stiffness parameters. The developed model is robust and can be employed to investigate its sensitivity to the wall geometry, material model parameters and interface parameters for static and dynamic loads. The model is capable of factoring in compaction induced stresses but this has not been attempted in the current analysis. Several ground motions can be applied as input to more accurately predict the performance of the given wall in a seismic event. Further a time dependent and/or strain dependent constitutive model for reinforcement will improve the performance of this FE model.
References 1. Bachus, R.C., Fragaszy, R.J., Jaber, M., Olen, K.L., Yuan, Z., Jewell, R.: Dynamic response of reinforced soil system. Civil Engineering Labaratory, Tnydall Air Force Base, Florida (1993) 2. Bathurst, R.J., Hatami, K.: Seismic response analysis of a reinforced soil retaining wall. Geosynth. Int. 5(1–2), 127–166 (1998) 3. Bao, H., Hatzor, Y.H., Huang, X.: A new viscous boundary condition in the two-dimensional discontinuous deformation analysis method for wave propagation problems. Rock Mech. Rock Eng. 45, 919–928 (2012). https://doi.org/10.1007/s00603-012-0245-y 4. Beer, G.: An isoparametric joint/interface element for finite element analysis. Int. J. Numer. Methods eng. 21, 585–600 (1985) 5. Bhattacharjee, A., Krishna, A.M.: Strain behavior of backfill soil in rigid faced reinforced soil walls subjected to seismic excitation. Int. J. Geosynth. Ground Eng. 1, 14 (2015). https://doi. org/10.1007/s40891-015-0016-4 6. Cai, Z., Bathurst, R.J.: Seismic response analysis of geosynthetic reinforced soil segmental retaining walls by infinite element method. Comput. Geotech. 17, 523–546 (1995) 7. Duncan, J.M., Byrne, P.M., Wong, K.S., Mabry, P.: Strength, stress-strain and bulk modulus parameters for finite element analyses of stresses and movements in soil masses. Ep. No.
Effect of Reinforced Soil Interaction with Other Components on Static …
8. 9. 10. 11.
12.
13.
14. 15. 16. 17. 18. 19.
20. 21. 22. 23. 24. 25.
26.
27.
209
UCB/GT/80-01, Department of Civil Engineering, University of California, Berkeley, CA (1980) Day, R.A., Potts, D.M.: Curved Mindlin beam and axi-symmetric shell elements—a new approach. Int. J. Num. Meth. Eng. 30, 1263–1274 (1990) Fairless, G.J.: Seismic performance of reinforced earth walls. Research Report, Department of Civil Engineering, University of Canterbury, New Zealand (1989) Gens, A., Carol, I., Alonso, E.E.: An interface element formulation for the analysis of soilreinforcement interaction. Comput. Geotech. 7(1, 2), 133–151 (1989) Hatami, K., Bathurst, R.J.: Development and verification of a numerical model for the analysis of geosynthetic reinforced soil segmental walls under working stress conditions. Can. Geotech. J. 424, 1066–1085 (2005) Huang, B., Bathurst, R.J., Hatami, K: Numerical study of reinforced soil segmental walls using three different constitutive soil models. J. Geotech. Geoenviron. Eng., 1486–1498 (2009). https://doi.org/10.1061/(ASCE)GT.1943-5606.0000092 Koseki, J., Bathrust, R.J., Guler, E., Kuwano, J., Maugeri, M.: Seismic stability of reinforced soil walls. Keynote Lecture. In: Proceedings of 8th International Conference on Geosynthetics, Yokohama, vol. 1, pp. 51–77 (2006) Krishna, A.M., Latha, G.M.: Modeling the dynamic response of wrap-faced reinforced soil retaining walls. Int. J. Geomech. ASCE 12(4), 439–450 (2012) Lindquist, D.D.: Seismic modeling of a 135-foot-tall MSE wall. Geotechnical Earthquake Engineering and Soil Dynamics IV GSP 181, 2008 ASCE, 1–10 (2008) Ling, H.I., Cardany, C.P., Sun, L.-X., Hashimoto, H.: Finite element study of a geosyntheticreinforced soil retaining wall with concrete-block facing. Geosynth. Int. 7(3), 163–188 (2000) Lysmer, J., Kuhlemeyer, R.L.: Finite dynamic model for infinite media. J. Eng. Mech. 95, 859–877 (1969) Rayleigh, J.W.S., Lindsay, R.B.: The Theory of Sound, 2 (1). Dover Publications, New York (1945) Rea, D., Wolfe, W.E.: Earthquake induced permanent displacements in model reinforced earth walls. Proceedings 7th World Conference Earthquake Engineering, Turkey, vo. 7, pp. 273–280 (1980) Reid, R.A.: Conventional weapons effects on reinforced soil walls. Ph.D. Thesis, Georgia Institute of Technology, Georgia (1995) Richardson, G.N.: The seismic design of reinforced earth walls. Nat. Science Found., School of Engrg. and Appl. Sci., Univ. of California, Los Angeles, CA (1976) Richardson, G.N., Lee, K.L.: Seismic design of reinforced earth walls. J. Geotech. Engrg. Div. 101(2), 167–188 (1975) Richardson, G.N., Feger, D., Fong, A., Lee, K.L.: Seismic testing of reinforced earth walls. J. Geotech. En. Div. 103(1), 1–17 (1977) Spears, R.E., Jensen, S.R.: Approach for selection of Rayleigh damping parameters used for time history analysis. J. Pressure Vessel Technol. 134 / 061801-1 (2012) Suzuki, M., Shimura, N., Fukumura, T., Yoneda, O., Tasaka, Y.: Seismic performance of reinforced soil wall with untreated and cement treated soils as backfill using a 1-g shaking table. Soils Found. 55(3), 626–636 (2015) Sommers, S.A., Wolfe, W.E.: Earthquake induced responses of model retaining walls. In: Proceedings 8th World Conference Earthquake Engineering, San Francisco, vol. 3, pp. 517–524 (1984) Walthall, R.M., Wang, J., Kiousis, P., Khan, A.: Finite-element analyses of mechanically stabilized earth walls subjected to midlevel seismic loads. J. Performance Constr. Facilities 27(2) (2013). ISSN 0887-3828/2013/2-171–180
210
S. Malviya and P. Raychowdhury
28. Woodward, P.K., Griffiths, D.V.: Comparison of the pseudo-static and dynamic behaviour of gravity retaining walls. Geotech. Geol. Eng. 14, 269–290 (1996) 29. Yazdandoust, M.: Investigation on the seismic performance of steel-strip reinforced-soil retaining walls using shaking table test. Soil Dyn. Earthq. Eng. 97, 216–232 (2017) 30. Zienkiewicz, O.C., Humpheson, C., Lewis, R.W.: Associated and non associated viscoplasticity and plasticity in soil mechanics. Géotechnique 25(4), 671–689 (1975) 31. Belal A. M., George, K.P.: Finite element analysis of reinforced soil retaining walls subjected to seismic loading. 12th World Conference on Earthquake Engineering (2000) 32. Bhattacharjee, A., Krishna, A.M: Development of numerical model of wrap-faced walls subjected to seismic excitation. Geosynthetics International, 19(5), 354–369 (2012)
Numerical Solution for 1-D Consolidation of Partially Saturated Soil Under Cyclic Loading D. K. Singh, S. Mehndiratta, and R. J. Vishwakarma
Abstract The distribution of consolidating load in a partially saturated soil is directly related to the dispersion of pore-water and pore-air pressures within the soil matrix. This paper presents a numerical solution to 1-D consolidation equation proposed by Fredlund and Hasan for two layered partially saturated soil subjected to various cyclic loadings. It is assumed that during consolidation process rate of volume change and coefficient of permeability remain constant. Particularly, an implicit finite-difference method is used to find numerical solution. A computer program is developed and based on the developed formulation the response of pore-air, porefluid and soil-mass along with degree of consolidation for pore-air and pore-water is presented. Validation for analytical method is also presented for constant loading using numerical techniques. Keywords Partially saturated soil · Finite-difference method · 1-D consolidation · Numerical solution · Cyclic loading
1 Introduction Numerous analytical solutions have been put forth by researchers based on Terzaghi’s classic 1-D consolidation theory [1] and the solutions presented are noted to be analyzed for various boundary, drainage and loading conditions. However, all these solutions played well only for saturated soils and therefore a need was felt to transform or extend these classic solutions into the realm of partially saturated soils [2–5]. D. K. Singh (B) · S. Mehndiratta · R. J. Vishwakarma Department of Civil Engineering, MNIT Jaipur, Jaipur, India e-mail: [email protected] S. Mehndiratta e-mail: [email protected] R. J. Vishwakarma e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_17
211
212
D. K. Singh et al.
Ample research is present wherein scholars formulated and presented completely coupled models for air and flow of water in permeable and deformable media for partially saturated soils [6–9]. Research also shows that for swelling clays difference appears between uncoupled and coupled solutions [10]. Generally, completely coupled solutions have seemingly greater accuracy than the results for uncoupled solutions however; uncoupled methodology is satisfactorily accurate regarding most field engineering problems [5]. Within these uncoupled models, Fredlund and Hasan’s theory for1-D consolidation [4] is widely known and used for problems of consolidation in partially saturated soils. Fully coupled numerical solutions for consolidation problem was presented by implementing a finite element code by Mehndiratta and Sawant [11]. Numerical method, i.e., the finite-difference method is widely used to solve consolidation problems for both saturated and partially saturated states for various boundary, initial and loading conditions. Other numerical procedures like the discrete element method and finite element method have also been widely used by researchers [5, 12–16]. Nonetheless, analytical solutions such as Eigen function, Laplace transform, Fourier transform and others can be set as a benchmark to validate the precision of the numerical and semi-analytical solutions and so as to present the problems correctly. An analytical solution presented by Qin et al. [17] using Eigen function and Cayley-Hamilton mathematical methods for Fredlund and Hasan’s 1-D partially saturated soil consolidation model having a freely draining boundary at the upper surface and an impermeable boundary at the lower extremity. Similar exact solutions have also been published by Shan et al. for a lone partially saturated soil layer [18]. This paper introduces a new numerical solution to Fredlund and Hasan’s [4] 1D consolidation model for partially saturated soils. Finite-difference technique is employed to solve the water and air movement equations for 1-D consolidation. The water and air movement partial differential equations have been solved as a couple using an implicit central difference technique to find the numerical solution. It should be noted here that the rate of volume change during the consolidation process and the coefficient of permeability remain constant. A computer code is written and on the basis on the developed code the rate of consolidation for air and water phase (response of pore-air, pore-fluid and soil-mass) is evaluated for different cyclic loadings and validation of the analytical solution with the numerical techniques used in the present study is also given. Validation shows good agreement between analytical and numerical methods marking the reliability of the numerical technique used in the present study.
2 Methodology 2.1 Governing Equation for Water Phase Based on Darcy’s Law [4, 5]
Numerical Solution for 1-D Consolidation of Partially Saturated Soil …
∂u w ∂u a ∂ 2uw ∂q = −cw + cvw 2 + cσw ∂t ∂t ∂z ∂t
213
(1)
where 1−m w /m w
mw
2 1k cvw = γwKmw w , cw = m w /m and cσw = m w1 . w 2 2 2 1k u a = pore-air pressure u w = pore-water pressure m w2 and m a2 = coefficients of water and air volume change with respect to a change in matric suction (ua − uw ) m w1k and m a1k = coefficients of water and air volume change with respect to a change in net normal stress (σ − ua ).
2.2 Governing Equation for Air Phase Based on Conservation of Mass [4, 5] ∂u a ∂u w ∂ 2ua ∂q = −ca + cva 2 + cσa ∂t ∂t ∂z ∂t
(2)
where ca = cva =
m a2 m a1k −m a2 −
u atm n 0 (1−Sr 0 ) (u a0 )2 K a RTabs
u n (1−S ) gu a M m a1k −m a2 − atm 00 2 r 0 (u a )
ma
1 cσa = m a −m a −n 0 (1−S r 0 )/u a 1 2 u a = (u a + u atm ) absolute pore-air pressure and u atm = atmospheric pressure u a0 = average initial pore-air pressure n 0 = initial porosity R = Universal gas constant (8.314 J/mol/K) Tabs = absolute temperature (temp. (in °C) + 273) K g = acceleration due to gravity (9.8 m/s2 ) Sr 0 = initial degree of saturation q, qu and qt = loading, the ultimate value of loading q and time-dependent loading, respectively K a /K w = ratio of permeability of air to the permeability of water within the soil matrix γw = Unit weight of water H = thickness of the soil layer.
214
D. K. Singh et al.
3 Problem Statement A partially saturated soil layer having thickness H is exposed to a time-dependent loading qt as depicted in Fig. 1, while the top soil surface is permeable to both water and air the bottom surface is impermeable to both air and water. The various loadings used to study the 1-D consolidation problem are given in the Fig. 2.
Fig. 1 Schematic representation of problem statement
Fig. 2 Various loadings considered in the present study: a Constant loading. b Triangular loading. c Trapezoidal loading. d Haversine cyclic loading
Numerical Solution for 1-D Consolidation of Partially Saturated Soil …
215
Fig. 3 Validation of results from numerical method (present study) with analytical methods given by Qin et al. [17]: a Variation of pore-water pressure with time. b Variation of pore-air pressure with time
4 Validation For validation of the numerical techniques used in the present study the analytical solutions presented by Qin et al. [17] have been charted along with the solutions arrived at using the implicit finite-difference scheme in the present study. It can be perceived from Fig. 3 that the results from the present study are in good agreement with the results given by Qin et al. [17].
5 Parametric Study The soil layer is assumed to be infinitely long in the horizontal direction with a bottom impermeable boundary and a freely draining boundary at the top. The properties of the material adopted in this study are given as: n 0 = 0.50 Sr 0 = 80% H = 10 m K a /K w = 0.1, 1, 10 m w1k = −0.5 × 10−4 kPa−1 m w2 = −2.0 × 10−4 kPa−1 m a1k = −2.0 × 10−4 kPa−1 m a2 = 1.0 × 10−4 kPa−1 γw = 10 kN/m3 q = 100 kPa
216
D. K. Singh et al. 0
0 Ka=0.1Kw
α =0.2, β = 1.0, T0 = 106
α =0.2, β = 1.0, T0 = 106
10
Ka=Kw
5
Ka=0.1Kw Ka=Kw Ka=10Kw
Ka=10Kw
20
10
U a (%)
U a (%)
30 15 20
40 50 60
25
70
30
80 35 0.00E+00
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
0.00E+00
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
Time (Sec)
Time (Sec)
(a)
(b)
Fig. 4 Consolidation rates in partially saturated soil due to changes in K a /K w for haversine loading: a Average degree of consolidation of pore-water with time. b Average degree of consolidation of pore-air with time
u a0 = 20 kPa R = 8.314 J/(mol K) Tabs = (Temp. (in ◦ C) + 273) K
5.1 Effect of Ka /Kw Figures 4, 5 and 6 illustrate the consolidation rates in partially saturated soils for different K a /K w ratios. The parameters for loading cycles considered are α = 0.2, β = 1.0 and T0 = 106 s. It is evident from these figures that degree of consolidation is also cyclic in nature just like the applied loads. It can also be seen that the rate of consolidation increases with increase in K a /K w ratios while it still fluctuates with increasing amplitudes.
5.2 Effect of Loading The process of dissipation of pore pressures as seen in Fig. 7 is not completed even after a long time rather it goes on oscillating with a definite amplitude. This can be attributed to the fact that during a repetitive load there is a cycle of loading and unloading wherein the pore-water is first squeezed out during the loading stage and during the unloading stage it is pulled back into the pores. For trapezoidal loading both pore-air and pore-water pressures dissipate faster as compared to haversine and triangular loadings. As a result of which degree of consolidation is achieved faster for trapezoidal loading, i.e., after 10 cycles pore-water
Numerical Solution for 1-D Consolidation of Partially Saturated Soil … 0
217
0
α =0.2, β = 1.0, T0 = 106
Ka=0.1Kw
5
α =0.2, β = 1.0, T0 = 106
10
Ka=10Kw
Ka=10Kw
20
10
Ka=0.1Kw Ka=Kw
Ka=Kw
U a (%)
U a (%)
30 15 20
40 50
25
60
30 35 0.00E+00
70
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
80 0.00E+00
3.00E+07
5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
Time (Sec)
Time (Sec)
(a)
(b)
Fig. 5 Consolidation rates in partially saturated soil due to changes in K a /K w for triangular loading: a Average degree of consolidation of pore-water with time. b Average degree of consolidation of pore-air with time 0
0
α =0.2, β = 1.0, T0 = 106
5 10
Ka=0.1Kw
30
Ka=Kw Ka=10Kw
20 25
Ka=Kw Ka=10Kw
40
U a (%)
U w (%)
20
Ka=0.1Kw
15
50 60
30
70
35
80
40 45 0.00E+00
α =0.2, β = 1.0, T0 = 106
10
90 5.00E+06
1.00E+07
1.50E+07
2.00E+07
2.50E+07
3.00E+07
100 0.00E+00
5.00E+06
Time (Sec)
1.00E+07
2.00E+07
1.50E+07
2.50E+07
3.00E+07
Time (Sec)
(a)
(b)
Fig. 6 Consolidation rates in partially saturated soil due to changes in K a /K w for trapezoidal loading: a Average degree of consolidation of pore-water with time. b Average degree of consolidation of pore-air with time 25
50 Haversine
Pore Water Pressure (kPa)
30
20 15
Trapezoidal
20 10 0 -10 -20 1E+03
Haversine Triangular
Triangular
Pore Air Pressure (kPa)
40
Trapezoidal
10 5 0 -5 -10 -15
1E+04
1E+05
1E+06
1E+07
-20 1E+03
1E+04
1E+05
1E+06
Time (Sec)
Time (Sec)
(a)
(b)
1E+07
1E+08
Fig. 7 Dissipation of pore-water and pore-air pressures in partially saturated soil for K a = K w with cyclic loadings under consideration: a Pore-water with time. b Pore-air with time
218
D. K. Singh et al. Time (Sec)
0E+00 0
2E+06
4E+06
Time (Sec) 6E+06
8E+06
0E+00 0
Haversine 5
Trapezoidal
6E+06
8E+06 Haversine Triangular
20
Trapezoidal 30
15
U a (%)
U w (%)
4E+06
10
Triangular
10
2E+06
20
40 50 60
25
70 30
80
35
90
(a)
(b)
Fig. 8 Consolidation rates in partially saturated soil for K a = K w with cyclic loadings under consideration: a Average degree of consolidation of pore-water with time. b Average degree of consolidation of pore-air with time
and pore-air pressures become constant. For K a = K w however, pore-air pressure dissipates faster than pore-water pressure at the same instant. Similarly, at the same instant degree of consolidation for air phase is 80% complete whereas degree of consolidation for water phase is 30% complete as seen in Fig. 8.
6 Conclusion In this study, numerical solutions using implicit finite-difference scheme are derived for 1-D consolidation of partially saturated soils under various cyclic loadings such as triangular, haversine and trapezoidal functions. The effects of variation of K a /K w ratio on 1-D consolidation of partially saturated soils under various cyclic loadings are inspected. Following conclusions are drawn: • The validation of the analytical solution with the numerical solutions derived in this study are in good agreement and can be deemed reliable for further studies. • Rate of consolidation increases with increase in K a /K w ratios while it still fluctuates with increasing amplitudes. • During a repetitive load there is a cycle of loading and unloading of the cyclic load wherein the pore-water is first squeezed out during the loading stage and during the unloading stage it is pulled back into the pores. • For trapezoidal loading both pore-air and pore-water pressures dissipate faster as compared to haversine and triangular loadings.
Numerical Solution for 1-D Consolidation of Partially Saturated Soil …
219
References 1. Terzaghi, K.: Theoretical Soil Mechanics. Wiley, New York (1943) 2. Blight, G.E.: Strength and consolidation characteristics of compacted soils. Ph.D. thesis, University of London, London, England (1961) 3. Barden, L.: Consolidation of compacted and unsaturated clays. Géotechnique 15, 267–286 (1965) 4. Fredlund, D.G., Hasan, J.U.: One-dimensional consolidation of layered systems. Can. Geotech. J. 17, 521–531 (1979) 5. Fredlund, D.G., Rahardjo, H.: Soil Mechanics for Unsaturated Soils. Wiley, New York (1993) 6. Schrefler, B.A., Zhan, X.: A fully coupled model for water flow and airflow indeformable porous media. Water Resour. Res. 29, 155–167 (1993) 7. Bolzon, G., Schrefler, B.A., Zienkiewicz, O.C.: Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique 46, 279–289 (1996) 8. Santagiuliana, R., Schrefler, B.A.: Enhancing the Bolzon–Schrefler–Zienkiewicz constitutive model for partially saturated soil. Transp. Porous Media 65, 1–30 (2006) 9. Conte, E.: Consolidation analysis for unsaturated soils. Can. Geotech. J. 41, 599–612 (2004) 10. Vu, H.Q.: Uncoupled and coupled solutions of volume change problems in expansive soil. Ph.D thesis, University of Saskatchewan, Saskatoon, SK (2003) 11. Mehndiratta, S., Sawant, V.A.: Numerical modelling of mechanical behaviour of partially saturated soils using coupled FEA. Int. J. Geotech. Eng. 11(5), 452–466 (2017) 12. Zhou, W.H., Zhao, L.S.: One-dimensional consolidation of unsaturated soil subjected to timedependent loading under various initial and boundary conditions. Int. J. Geomech. (2013); In press. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000314 13. Chen, R.P., Zhou, W.H., Wang, H.Z., Chen, Y.M.: One-dimensional nonlinear consolidation of multi-layered soil by differential quadrature method. Comput. Geotech. 32(5), 358–369 (2005) 14. Chen, R.P., Zhou, W.H., Wang, H.Z., Chen, Y.M.: Study on one-dimensional nonlinear consolidation of multi-layered soil using differential quadrature method. Chin. J. Comput. Mech. 22(3), 310–315 (2005). (In Chinese) 15. Wang, H.Z., Chen, R.P., Zhou, W.H., Chen, Y.M.: Computation of 1-D nonlinear consolidation in double-layer foundation by using differential quadrature method. J. Hydraul. Eng. 4, 8–14 (2004). (In Chinese) 16. Zhou, W.H., Tu, S.: Unsaturated consolidation in a sand drain foundation by differential quadrature method. Procedia Earth Planet. Sci. 5, 52–57 (2012) 17. Qin, A.F., Chen, G., Tan, Y., Sun, D.A.: Analytical solution to one-dimensional consolidation in unsaturated soils. Appl. Math. Mech. (English Edn.) 29, 1329–1340 (2008) 18. Shan, Z., Ling, D., Ding, H.: Exact solutions for one-dimensional consolidation of single-layer unsaturated soil. Int. J. Numer. Anal. Meth. Geomech. 36(6), 708–722 (2012)
13 August 2021 Chenab River Coalescent Disaster: A Geo-informatics-Based Investigation D. K. Dwivedi, A. K. Saraf, and J. D. Das
Abstract A huge landslide blocked the flow of the Chenab River near Nalda village in Himachal Pradesh’s Lahaul-Spiti district on the morning of 13 August 2021, which led to the flooding of several villages (Nalda, Jasrath, Tarang, etc.) in Udaipur subdivision. The slope on the left bank of the Chenab River failed which brought huge soil and debris blocking the Chenab River, near Leh Baring village which lies upstream of Nalda Village Bridge and opposite to Junde village creating a huge water reservoir that later started overflowing, posing a major threat to downstream villages. This caused damage to houses located downstream which were submerged, animals were also washed away, and a large part of agricultural land was also inundated. This event was observed and studied using high-resolution satellite images from Google Earth. The spatio-temporal images from Google Earth were used to observe the scars developed from several landslides in the past along the river, which evidently show the early signatures of slope failure. To analyse the stability of the hill slope, factor of safety of the hill was evaluated using SLOPE/W GeoStudio software. Considering the vulnerability of the Chenab valley, where several hydroelectric power projects are planned on Chenab River and its tributaries, it is important to consider the effect of highly fragile terrain conditions while planning any such project. The paper also emphasizes monitoring of such vulnerable areas based on high-resolution time series satellite images which are available on regular basis to avoid the loss of human lives in future. Keywords Spatio-temporal images · Factor of safety · GeoStudio
D. K. Dwivedi (B) Centre of Excellence in Disaster Mitigation and Management, IIT Roorkee, Roorkee, India e-mail: [email protected] A. K. Saraf Department of Earth Sciences, IIT Roorkee, Roorkee, India J. D. Das Department of Earthquake Engineering, IIT Roorkee, Roorkee, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_18
221
222
D. K. Dwivedi et al.
1 Introduction Landslide is a complex natural phenomenon in which downward movement of mass takes place under the influence of gravity. Landslides were first classified by Varnes [10] based on the type of movement and type of material. The names for the types of materials are rock, debris, earth and the types of movement are falls, topples, slides, spreads, and flows. However, further modifications were made by Cruden and Varnes [1], Hutchinson [5], Hungr et al. [3, 4]. In new classification schemes, the types of materials are rock, earth, soil, mud, debris, and distinct types of movement are described as fall, topple, slide (rotational and translational), spread, and flow. So, the classification is made after combining the two terms like rock fall, rock topple, debris slide, debris flow, earth slide, earth spread, etc. A landslide movement was observed on 13 August 2021 near Nalda village in Udaipur subdivision of the district Lahaul-Spiti where a hill slope failed, bringing down huge soil and debris which later blocked the Chenab River, creating a large water reservoir. The flow of Chenab was blocked near Leh Baring village just upstream of Nalda Village Bridge and opposite to Junde village, leading to formation of a huge lake which later started overflowing, posing a major threat to villages (Nalda, Jasrath, Tarang, etc.). This caused damage to houses in the downstream villages, which were submerged, animals were washed away, and a large part of agricultural land was also inundated.
2 Study Area Lahaul-Spiti is a district of Himachal Pradesh, which is in the north-eastern part. The entire hilly district comprises of two major valleys; Lahaul and Spiti, where Lahaul valley lies in the north-western part of the district, while the Spiti valley is in the south-eastern part. Udaipur is a subdivision in the Lahaul-Spiti district where the Chenab River flows and exists gently to the sloping alluvial river terrace. The Chenab River is known as the Chandra-Bhaga in its upper course through the Lahaul Valley. It is formed by the rivers Chandra and Bhaga, which meet at Tandi; thus, the combined river constitutes the Chandra-Bhaga or the Chenab River (Fig. 1). As the river flows through Lahaul, a large amount of debris consisting of huge boulders and finer clastic is brought down by Miyar Nala and deposited in the valley called Pattan valley. The exact location of damming is on the left bank of Chenab River near Leh Baring site, which is just upstream of Nalda Village Bridge and opposite to the village named Junde, shown inside red circle (Fig. 2).
13 August 2021 Chenab River Coalescent Disaster: …
223
Fig. 1 River map of Lahaul-Spiti district where Chandra and Bhaga Rivers are shown meeting at Tandi village, thus constitutes Chandrabhaga or Chenab River
Fig. 2 Photograph taken by a villager at the time of the event. Source https://images.news18.com/ ibnkhabar/uploads/2021/08/7-3.jpg
224
D. K. Dwivedi et al.
3 Data and Methodology 3.1 Datasets and Tools The satellite datasets from Google Earth were used in the present study. Google Earth images are collected by various satellites orbiting the planet. The images are sourced from various satellite companies and are combined into a mosaic of images taken over a period of time. The collected imagery is then displayed as one blended image and has high spatial resolution. SLOPE/W is one of the products of GeoStudio software, which is used as a primary slope stability software for soil and rock slopes. SLOPE/W can efficiently analyse almost any slope stability problem for various slip surface shapes, porewater pressure conditions, soil properties, and loading conditions. In our present study, SLOPE/W software is used to calculate the factor of safety of slope using general limit equilibrium formulation.
3.2 Methodology The approach in the methodology has been presented in two different stages (Fig. 3). In first stage, multi-temporal and high-resolution satellite images are used to study the landslide event. The second stage uses soil properties obtained from field data [9] to do the probabilistic analysis of slope using the general limit equilibrium method, also known as the Morgenstern-Price method. In this, the slope profile obtained from Google Earth is taken as one of the inputs in slope analysis. Spatio-temporal Data The high-resolution Google Earth images were used to determine the spatio-temporal evolution of the landslide (Table 1). The images (pre- and post-event) were used to
Fig. 3 Flowchart depicts the adopted methodology
13 August 2021 Chenab River Coalescent Disaster: … Table 1 List of satellite data used in the study
S. No.
225
Date
Source
1
04 May 2008
Google Earth
2
29 June 2013
Google Earth
3
05 May 2014
Google Earth
4
30 September 2016
Google Earth
16 August 2021
Google Earth
Pre-event
Post-event 5
ascertain the cause of the event and to observe the changes caused by the event. Since the study area lies in the highly rugged terrain of the Himalaya and hence, all the satellite images suffered from the false topographic perception phenomenon (FTPP). Due to FTPP, all the satellite images were rotated in a way to keep the North direction downwards to avoid FTPP for accurate interpretation of the highly rugged terrain and have a better understanding of the event [8]. Probabilistic Analysis of Slope There are basically two approaches to analyse the stability of a slope, named as the deterministic approach and probabilistic approach [2]. In deterministic analysis, all the input parameters which cause the slope failure are supposed to be known. The probabilistic analysis is different from the deterministic method mainly because it considers the variability of the parameters. In the probabilistic analysis, some input parameters are not known with precision therefore, taken as statistical distributions, which helps to consider the uncertainties associated with the input parameters [7]. The probabilistic analysis was performed in this study, using the limit equilibrium method (LEM), which is the most widely used analytical method and works on the principle of static equilibrium to study slope stability. The slope is analysed using equivalent Mohr–Coulomb (MC) criteria for determining the shear strength along the failed surface, considering slope material to be homogenous. In this study, the general limit equilibrium (GLE) formulation has been used, which is based on two equations to calculate factor of safety, followed from the work of Spencer [11]. To know the slope of the hill (study area), slope profile was drawn in the Google Earth (Fig. 4) and the value of elevation along with distance was taken. Now, in defining analysis properties, the data (elevation and distance) obtained from Google Earth was used in the definition view to define points and draw the geometry of the slope. After drawing the slope, the material property was defined, here in our case the material is phyllite [9], and its properties like unit weight, cohesion, and angle of friction [6] are shown (Table 2). The final step was to draw the entry and exit slip surface, which defines the trial slip surface. The whole processing was done in the solve manager window, and thus factor of safety was calculated for different trial slip surfaces using GLE/ Morgenstern-Price method.
226
D. K. Dwivedi et al.
Fig. 4 Elevation profile of the study area drawn in Google Earth
Table 2 Slope material properties
Rock type
Phyllite
Unit weight
20 kN/m2
Cohesion
150 kPa
Angle of friction
33°
4 Results and Discussions Based on the time series satellite images of different years, it is observed that there was distinct evidence of toe cutting of the hill, which promoted slope failure (Fig. 5a). It might be possible that the process of toe cutting started developing before 2008, however, due to the lack of availability of cloud-free satellite images of the location, the scar got noticed only in the image of the year 2008. Further, it continued to develop in the consequent years 2013, 2014, and 2016 (Fig. 5b–d), and eventually, the slope failed on 13 August 2021, which is evidently visible on the image of 16 August 2021 (Fig. 5e). As it can be evidently seen from the Google Earth images that the hill slope failed on 13 August 2021 so, the factor of safety of the hill slope was calculated using GLE/Morgenstern-Price method in GeoStudio software. The factor of safety was found to be 1.56, and the slope failure type was found to be toe failure as shown in (Fig. 6a). The FOS value 1.56 states that the slope is critically stable and susceptible to stress-controlled failure. The variation in the colour of the slip surface indicates the factor of safety along the slip surface (Fig. 6b). Slip surface refers to an assumed surface along which slipping or rupture might occur. Several slip surfaces must be considered to find the slip surface that produces a minimum factor of safety, which
13 August 2021 Chenab River Coalescent Disaster: …
227
Fig. 5 Google Earth images (a–e) of the years 2008, 2013, 2014, 2016, and 2021 where the image of year 2008 clearly showing the evidence (marked by red colour arrow) of toe cutting of the hill (a); also these scars continue to develop in subsequent years 2013 (b); 2014 (c); 2016 (d); and then, the slope eventually failed in the year 2021 (e); where slope failure is marked with red colour and the lake developed after damming is marked with the blue colour arrow
is known as the critical slip surface (Fig. 6a). All the valid trial slip surfaces are grouped into bands having same factor of safety, this shows the zone of potential slip surfaces within a factor of safety range known as safety map (Fig. 6c). The GLE/Morgenstern and Price method is based on two factor of safety equations and allows for a range of interslice shear normal force assumptions (Fig. 7). First equation gives the factor of safety with respect to moment equilibrium, while the second equation gives the factor of safety with respect to horizontal force equilibrium (Fig. 8).
5 Conclusions The present study emphasizes on the importance of high-resolution time series satellite images to evaluate the damage and to assess various parameters causing the slope
228
D. K. Dwivedi et al.
Fig. 6 Factor of safety with critical slip surface (a); trial slip surfaces and corresponding factor of safety (b); and safety map showing potential slip surfaces (c)
Fig. 7 Free body diagram and force polygon of slice having critical slip surface
failures with the help of the SLOPE/W product of GeoStudio software. GeoStudio is an essential software to analyse slope stability and acts as a combined tool to study the effect of several soil parameters on the stability of slopes. Moreover, this event has brought our attention towards monitoring of such vulnerable areas of Himalaya on regular basis so, that we can minimize the loss of human lives in near future. And this can be done using high-resolution satellite images on a systematic basis which are now easily available on various platforms. Further, various tools can be developed to detect even small changes in the vulnerable areas to provide forecasts of similar events using change detection algorithms. Also, seeing the vulnerability of the Chenab valley, where a series of hydropower projects are proposed on Chenab and key tributaries like Miyar, Chandra, and Bhaga Rivers; therefore, proper planning is required keeping in view the fragile terrain conditions.
13 August 2021 Chenab River Coalescent Disaster: …
229
Fig. 8 Graph showing the factor of safety of critical slip surface with respect to moment and force equilibrium where lambda is the ratio of specified function to the applied function
References 1. Cruden, D.M., & Varnes, D.J.: Chapter 3 Landslide Types and Processes. Landslides: Investigation and Mitigation, Transportation Research Board Special Report 247, Washington D.C., Bell 1992, 36–75 (1996) 2. Duncan, J.M., Wright, S.G., Brandon, T.L.: Soil Strength and Slope Stability. Wiley (2014) 3. Hungr, O., Evans, S.G., Bovis, M.J., Hutchinson, J.N.: A review of the classification of landslides of the flow type. Environ. Eng. Geosci. 7(3), 221–238 (2001). https://doi.org/10.2113/ gseegeosci.7.3.221 4. Hungr, O., Leroueil, S., Picarelli, L.: The Varnes classification of landslide types, an update. Landslides 11(2), 167–194 (2014). https://doi.org/10.1007/s10346-013-0436-y 5. Hutchinson, J.N.: GR_30_1_13_ Hutchinson.pdf (1994) 6. Lopes, M., da C.: Comportamento Geotécnico E Mecanismos Mina Córrego Do Sítio (2006) 7. Mondal, S.K., Bharti, R.: Glacial burst triggered by triangular wedge collapse: a study from Trisul Mountain near Ronti glacier valley. Geomat. Nat. Haz. Risk 13(1), 830–853 (2022). https://doi.org/10.1080/19475705.2022.2042402 8. Saraf, A.K., Sinha, S.T., Ghosh, P., Choudhury, S.: A new technique to remove false topographic perception phenomenon and its impacts in image interpretation. Int. J. Remote Sens. 28(5), 811–821 (2007). https://doi.org/10.1080/01431160701269796 9. Srtkantia, S.V, Bhargava, O.N.: The Tandi group of Lahaul—its geology and relationship with the Central Himalayan gneiss. J. Geol. Soc. India 20 (1979) 10. Varnes, D.: Slope movement types and processes. Special Report 176, 11–33 (1978) 11. Spencer, E.: A method of analysis of the stability of embankments assuming parallel inter-slice forces. Geotechnique 17(1), 11–26 (1967)
Numerical Simulation of Special Moment Resisting Frame with Reduced Beam Section Under Cyclic Load A. H. Rangoonwala, S. Paul, and S. K. Deb
Abstract In this paper, seismic performance of steel special moment resisting frame (SMRF) with reduced beam section (RBS) was evaluated. In this study, radius-cut RBS was considered for facilitating the formation of plastic hinge in the desired location in the beam because of its excellent performance during past experiments. Two 5 storied sample steel SMRFs, with and without RBS, were designed as per IS 800. NPB and WPB sections from IS 12778 were used for the beam and column of the connection respectively. Beam and column of the frame were connected through welded connection. Each of the beam-column subassemblies was modeled using finite element software ABAQUS (Version 6.14-1). Moment-rotation curves were then extracted after applying quasi-static cyclic load at beam tip as per AISC. These moment-rotation curves for each connection were then used to define plastic hinge properties in software SAP2000 (Version 22.0.0). First mode pushover analyzes were then carried out for both conventional frame and frame with RBS. The yielding at the location of RBS was observed earlier than the yielding of beam at corresponding location in the conventional frame. Some reduction in strength was also observed in SMRF with RBS. Formation of plastic hinges observed to spread in all the stories in SMRF with RBS, whereas in conventional SMRF, plastic hinge was concentrated in lower stories. Thus, SMRF with RBS satisfied strong column weak beam criterion and thereby ensured higher ductility and energy dissipation. Keywords SMRF · RBS · Beam-column connections · Finite element analysis · Pushover analysis
A. H. Rangoonwala · S. Paul (B) · S. K. Deb Department of Civil Engineering, IIT Guwahati, Guwahati, India e-mail: [email protected] S. K. Deb e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_19
231
232
A. H. Rangoonwala et al.
1 Introduction Strong column weak beam (SCWB) design philosophy is used to design structures located in seismically active regions. The primary objective of this design philosophy is to keep column elastic, while beams are allowed to form the plastic hinges. This will ensure beam-sway mechanism and it prevents the devastative story mechanism type of failure. Beam sway type of mechanism ensures ductility and better energy dissipation capacity of the moment resisting frames (MRFs), which is prerequisite in earthquake-prone regions. This perception of ductile behavior of MRF was significantly challenged by Northridge (1994) and Kobe (1995) earthquakes [1]. The effects of these earthquakes, particularly on steel MRFs were brittle beam-column connection failure. These events raised a question to subsequent design and detailing practices among the engineers and researchers. This led to extensive research to find better design and detailing methods to ensure ductility and energy dissipation capacity, and one of the methods was provision of reduced beam section (RBS). Provision of RBS is one type of weakening strategy in which a small portion of beam flange is trimmed in appropriate proportions, some distance away from the column face. This cut in the beam flange forces the plastic hinge formation within the reduced section away from more vulnerable beam-column connection. The working principle of RBS is similar as that of the fuse in electrical circuit. Various types of RBS were experimentally and numerically investigated, but the behavior of radius cut type of RBS was found excellent (plastic rotations were well above 0.03–0.04 rad). Due to these advantages, radius cut type of RBS was used in the present study. Geometry of a typical radius cut RBS is presented in Fig. 1. Parameters a, b, c, and R in Fig. 1 represent the distance of cut from the face of the column, length of cut, depth of cut, and radius of cut respectively.
2 Building Archetype and Design For evaluation of seismic performance of steel SMRFs with RBS, a typical 5 story bare steel MRF was selected and designed using SAP2000 (Version 22.0.0) [2] software with and without provision of RBS. The plan and elevation of this sample building are shown in Figs. 2 and 3. The sample building has six bays and three bays in longitudinal and lateral directions respectively with center-to-center spacing of 5 m. Floor-to-floor height was considered as 3.5 m. The location of the sample building was assumed as Guwahati city, and the soil type was considered as soft. The design loads (i.e., dead, live, earthquake, and wind loads) were considered from the Indian Standard, and design was carried out following IS 800 [3]. Strength and serviceability criteria were satisfied for the design of the sample steel SMRF. For beam and column sections, narrow parallel flange beam (NPB) and wide parallel flange beam (WPB) sections were used respectively. The design results are tabulated in Table 1.
Numerical Simulation of Special Moment Resisting Frame …
Reduced Beam Section
Protected Zone Fig. 1 Typical radius cut RBS geometry
3 bays @ 5 m c/c = 15 m
X
X’
Fig. 2 Plan of the sample steel SMRF
6 bays @ 5 m c/c = 30 m
233
234
A. H. Rangoonwala et al.
3 bays @ 5 m c/c = 15 m
G+4 @ 3.5 m c/c = 17.5 m
Fig. 3 Elevation of the sample steel SMRF
Table 1 Steel SMRF design results
Member
Story/type
Section
Column
External
WPB 38
Internal
WPB 46
Roof
NPB 34
3–4
NPB 48
1–2
NPB 52
Beam
Note These sections were considered from IS 12778 [4]
3 Numerical Modeling 3.1 Simulation for Validation of the Modeling Approach A specimen, designated as EEP, of steel beam-column connection studied by Elflah et al. [4], is modeled using ABAQUS finite element software as shown in Fig. 4. The specimens are analyzed under the increasing monotonic load, and the numerical results are compared with experimental ones. The moment-rotation response obtained from both numerical and experimental studies was plotted. Numerically simulated and experimental moment-rotation curves for the connection were found to be in good agreement as shown in Fig. 5. It may be observed that both simulated and experimental failure modes of the connections were found to be in reasonably good agreement. Validation of this numerical
Numerical Simulation of Special Moment Resisting Frame …
235
Fig. 4 Failure modes between tests and FE simulation adopted for present study: a Experimental failure modes of EEP, b numerical failure modes of EEP, c numerical failure modes of EEP (present study)
model established that interaction properties, mesh size, mesh types, and boundary conditions of the simulated specimen are good enough to replicate the results obtained by experimental work. Hence, a similar modeling method can be adapted for computation of response of the sample model RBS-CFT connections with bidirectional bolts using ABAQUS finite element program.
3.2 Finite Element Modeling of Present Beam-Column Connection Each beam-column connection of sample steel SMRF was modeled in the finite element software ABAQUS (Version 6.14-1) to obtain the moment-rotation (M −θ )
236
A. H. Rangoonwala et al. 90 80
Moment M (kN -m)
70 60 50 40 30 Experimental
20
Elflah et al. (2019)
10 0
Present study 0
20
40
60
80
100
120
140
Rotation θ (mrad)
Fig. 5 Validation of numerically simulated M–θ curve
relationship of each connection. C3D8R type of elements were used in the modelling of each part of beam-column assembly. These parts were then assembled in the assembly module. For material modeling, E250B grade of steel was used. The values of yield strength, ultimate strength, elongation percentage, modulus of elasticity, and Poisson’s ratio of the steel material were 250 MPa, 410 MPa, 23%, 200,000 MPa, and 0.3 respectively. The material properties were kept same for all the parts of the beam-column assembly. Top and bottom end of the column were assigned pinned boundary condition, since in frames subjected to lateral loads, the point of inflection occurs approximately at the mid height of the column. Axial load obtained by gravity analysis of the sample frame was applied at the top end of the column. The longitudinal movement of the top end of the column was allowed to accommodate the axial movement due to the effect of axial load applied on the column. Quasi-static cyclic loading, following AISC [5] loading protocol guidelines as shown in Fig. 6, at the free end of the beam was applied. The details of the boundary conditions for an external beam-column connection are depicted in Fig. 7. For validation of the present simulation, numerical model of similar type of beam-column assembly considered in the experimental investigation by Kulkarni and Vesmawala [6] was developed using ABAQUS (Version 6.14-1). The results obtained after carrying out simulation were then compared with the experimental results of referred literature for validation of the numerical model. During past research on RBS, it was found that the presence of slab stabilizes the beam against lateral-torsional buckling. So, to simulate the slab presence, the beam edges were restrained in the out-of-the plane movement. The type of beamcolumn connection was of fillet welding. The weld was not modelled explicitly
237
0.04
100
0.02
50
0.00
0
−0.02
−50
−0.04
−100 0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Number of Cycles Fig. 6 Loading protocol adopted in the present study
Fig. 7 Finite element model of beam-column assembly in ABAQUS (Version 6.14-1)
Displacement (mm)
Interstory Drift Ratio (θ)
Numerical Simulation of Special Moment Resisting Frame …
238
A. H. Rangoonwala et al.
Fig. 8 Meshing details of beam-column assembly in ABAQUS (Version 6.14-1)
in the modeling; rather ‘Tie’ constraint was used to simulate the welding effect. ‘Tie’ constraint was applied between beam-column flange face and continuity plate (stiffener)-internal column surface. Parts with finer and coarse mesh size were selected as ‘Slave’ and ‘Master’ surface respectively. For meshing of the beam-column assembly, finer mesh size was adopted near connection due to high stress gradients. The finer and coarse mesh size were kept as 15 mm and 30 mm respectively. This mesh size was obtained after carrying out mesh sensitivity analysis. For that, simulations were carried out with different mesh size and optimum size was then obtained considering accuracy of results and computational time requirement. Meshing of the beam-column assembly is depicted in Fig. 8. Figure 9 shows Von Mises stress contours developed in beam-column assembly after conducting finite element analysis using ABAQUS (Version 6.14-1). It is evident from the figure that a distinct plastic hinge is formed within the reduced flange area of the beam. ‘Gray colored’ portion shows the yielded portion of the beam (stress reaching or exceeding the yield value of material which is 250 MPa). Stresses in the panel zone and column are far below yield value of the material. Figure 10 depicts moment-rotation characteristic of an external beam-column connection of the sample steel SMRF with RBS. Reaction force and displacement responses were measured at the beam tip. Moment and rotation values were derived by multiplying and dividing the force and displacement values by length of the beam respectively. This length was measured from center of RBS to beam tip. Some dropin strength in the hysteretic behavior at higher cyclic amplitude of 0.04 radians was also observed. The reason could be material degradation or local instability of the beam flange.
Numerical Simulation of Special Moment Resisting Frame …
239
Fig. 9 Von Mises stress contours of beam-column assembly in ABAQUS (Version 6.14-1) 600
Moment (kNm)
400
200
0
−200
−400
−600 −0.12
Hysteresis Curve Backbone Curve
−0.08
−0.04
0.00
0.04
0.08
0.12
Rotation (θ)
Fig. 10 Moment-rotation hysteresis characteristic for an external beam-column connection of the sample steel SMRF
4 Nonlinear Static Analysis Pushover analysis is a step-by-step analysis procedure, for which the lateral loads of constant relative magnitude are applied to a given structure and progressively
240
A. H. Rangoonwala et al.
increased until a target displacement is reached, while gravity loads are kept constant. Pushover analysis is a static method that uses a simplified nonlinear procedure to estimate and predict the seismic deformations of the structure. In the present study, to investigate the seismic performance of the steel SMRFs with and without RBS, first mode pushover analysis was carried out using SAP2000 (Version 22.0.0) software.
4.1 Modeling of Nonlinear Plastic Hinges To model nonlinear hinges of RBS using SAP2000 (Version 22.0.0), extracted moment-rotation curves of each beam-column connection were idealized in a quadrilinear plot. To idealize the plots, area under both backbone curve and idealized curve was equated (equal work done). For modelling of nonlinear hinges of column and conventional beam sections, guidelines of FEMA 356 [7] were used in the study. For beam sections, M3 type of hinges were used, and the axial force in the beam was considered as zero. For column section, P-M2-M3 type of hinges were used in the study.
4.2 Pushover Analysis of Sample Steel SMRF with and Without RBS First mode pushover analysis using SAP2000 (Version 22.0.0) was carried out for steel SMRFs with and without RBS. The target roof displacement was considered as 6.86% (1.2 m) roof drift. This value was selected such that the SMRF loses its strength by 85%, for calculation of ductility. Geometric and material nonlinearity were considered in the study. The gravity load combination considered during pushover analysis is expressed below: Gravity Load Combination: DL + 0.5LLLL>3 kN/m2 + 0.25LLLL≤3 kN/m2
(1)
The pushover curve for both the steel SMRF, i.e., with and without RBS is shown in Fig. 11. The building performance levels, i.e., immediate occupancy (IO), life safety (LS), and collapse prevention (CP) were also mentioned in the plot. These performance level limits were referred from FEMA 356 [7]. It can be observed that the initial stiffness remains almost same for both the steel SMRFs. The yielding in the members initiated earlier in case of frame with RBS as compared to that of the frame with conventional frame. The peak base shear value was dropped by almost 4%. The reduction in the base shear value after attaining its peak value was more gradual in case of frame with RBS. The calculation of ductility for both the steel SMRF was also carried out. To obtain the yield displacement value of both the steel SMRF, initial stiffness line was extended
Numerical Simulation of Special Moment Resisting Frame …
241
1600 1400
Base Shear (kN)
1200 1000 800 600
Without RBS With RBS IO LS CP
400 200 0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Displacement (m) Fig. 11 Pushover curve for steel SMRFs with and without RBS
up to the horizontal line passing through the peak base shear. The displacement value at the point of intersection was considered as the yield displacement of the steel SMRF. The ultimate displacement was taken as the value where peak base shear drops by 85%. The ductility values for steel SMRF with and without RBS were obtained as 4.09 and 5.28. Hence, increase of 29% in the ductility was observed. The hinge formation in both types of frames is depicted in Fig. 12. It can be observed that the plastic hinge formation is limited to the lower stories, while in case of frame with RBS, the hinge formation distributed over the entire height of the frame. This indicated improved energy dissipation capacity of frame with RBS. Story mechanism was also formed in case of frame with conventional beam sections. Formation of story mechanism was observed in SMRF with conventional beam section with column achieving CP damage state. While such type of behavior was not observed in the SMRF with RBS.
5 Summary and Conclusions In this paper, seismic performance of steel SMRF with and without RBS was evaluated, and results were then analyzed. Following major conclusions can be drawn from the presented numerical study. 1. Provision of RBS facilitates the formation of plastic hinge in the desired location, and the stresses in the column and panel zones were reduced.
242
A. H. Rangoonwala et al.
E
D
C
CP
LS
IO
B
(a)
(b)
Fig. 12 Hinge formation in steel SMRFs a without RBS, b with RBS
2. Fulfillment of the AISC requirement for SMRF can be achieved by providing the RBS connection. 3. Provision of RBS increases the ductility of the steel SMRFs and it enhances the energy dissipation capacity. 4. The formation of plastic hinges is limited to lower stories for conventional frame, while the plastic hinges formation in the frame with RBS distributed to the entire height of the steel SMRF.
References 1. Brunaeu, R.S.M., Uang, C.: Ductile Design of Steel Structures, 2nd edn. The McGraw-Hill Companies, Inc. (2011) 2. CSI (2022). SAP2000 Integrated Building Design Software, Version 22.0.0, Computers and Structures, Inc., Berkeley 3. IS 800 (2007): Indian Standard—General Construction in Steel, code of practice. Bureau of Indian Standards, New Delhi (2007) 4. Elflah, M., Theofanous, M., Dirar, S.: Behaviour of stainless-steel beam-to-column joints-part 2: numerical modelling and parametric study. J. Constr. Steel Res. 152, 194–212 (2019). https:// doi.org/10.1016/j.jcsr.2018.04.017 5. IS 12778 (2004): Hot Rolled Parallel Flange Steel Sections for Beams, Columns and Bearing Piles—Dimensions and Section Properties. Bureau of Indian Standards, New Delhi (2004). 6. Swati, A.K., Gaurang, V.: Study of steel moment connection with and without reduced beam section. Case Stud. Struct. Eng. (2014). https://doi.org/10.1016/j.csse.2014.04.001 7. FEMA 356 (2000): Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Washington (2000)
Seismic Stability Analysis of Partially Saturated Slope Reinforced with Pervious Anti-slide Piles Subjected to Repeated Shaking Using Shaking Table Tests R. Ram Kumar , S. K. Jeeva , P. Madhiyarasu , and S. Ganesh Kumar Abstract Occurrence of sudden cloudbursts found common in slopes of Uttarakhand region, especially during monsoon seasons. This led to a sudden increment in water content within the slope, causing a variation in slope saturation. In case, when these partially saturated slopes are subjected to dynamic events, the consequences are highly unexpected and can cause serious threat to the adjacent infrastructures located nearby. To improve the stability of slope, various slope improvement measures such as providing drainage, use of slope reinforcement, and installation of anti-slide piles are adopted in the field. However, very limited studies were available on the combined effect of drainage and slope reinforcement techniques. Also, detailed studies regarding the influence of these combined effects in partially saturated slope under dynamic loading are not available. Considering this, an attempt has been made to evaluate the influence of pervious anti-slide pile for slope reinforcement and drainage is proposed in this study. For understanding dynamic improvement characteristics, repeated shaking tests were performed to evaluate the efficiency of this control measure during multiple shaking events. The selection of repeated loading events simulates the occurrences of repeated shaking events as reported in several case studies in past. For experimental testing, debris soil collected from the Uttarakhand region was used. A 1:1 slope having dimensions of 600 mm × 600 mm slope with 200 mm bed depth and 750 mm width was prepared with 45% saturation and 16 kN/m3 density equivalents to in-situ field density as observed in similar site in Narendra Nagar, Uttarakhand. The slope was subjected to repeated incremental shaking of loading intensity 0.1g, 0.2g, and 0.3g with 5 Hz frequency. To simulate slope-structure interaction, a scaled down G + 3 storey building structure was installed at 200 mm distance from the crest portion of the slope. Parameters such as pore pressure response, acceleration response, slope, and structure displacement under repeated shaking loading have been evaluated. For assessing the slope and structural response, 2-Digital Image Correlation technique was used. Based on the R. Ram Kumar (B) · S. K. Jeeva · P. Madhiyarasu · S. Ganesh Kumar Geotechnical Division, CSIR—CBRI, Roorke, India e-mail: [email protected] S. Ganesh Kumar e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_20
243
244
R. Ram Kumar et al.
obtained test results, the seismic stability of the reinforced slope was assessed and presented. Keywords Slope stability · Partially saturated slope · Pervious anti-slide piles · 2D DIC
1 Introduction In slopes, the movement of soil mass (also referred to as landslide) can cause infrastructure damage, casualties, and can affect economic development. In general, the landslides are caused by the (i) natural phenomena viz. rainfall, earthquakes, and (ii) anthropogenic activities [1]. The seismic atlas elucidates that the seismic hazard is moderate in peninsular shield (except Kutch region of Gujarat), whereas it was high in the north and northeast India and Andaman-Nicobar region [2]. Yin et al. [3] investigated the landslides occurred in South China due to 2008 Wenchuan earthquake. It was observed that, the earthquake initiated numerous landslides, debris flow, and rock fall hazards. In most of the cases, influence of slope saturation due to rainfall events initiated landslide hazard under earthquake occurrence. Recently, vulnerability assessment studies showed increment in geo-hazards possibilities such as landslides, failure of potential unstable slopes and rockfall raised about 123%, 157%, and 617% respectively when considering possibility of earthquake incidence. A case study on Wenchuan earthquake showed that both river overflow and overtopping during rainy season causing major damages in dam which can also contribute in initiating landslides [4]. Occurrence sudden cloudbursts in and around the southern rim of the Indian Himalayas is often causing flash floods and landslides [5]. With the increment in rainfall intensity, there is a larger probability of landslide occurrence [6, 7]. Generally, occurrence of rainfall initiated slope saturation which reduces the stability of the slope [8]. Liu et al. [9] performed tests on a clayey slope and concluded that when saturation was not considered, slope was found stable, and when saturation (i.e. about 80%) was considered, the slope was found unstable. Also, occurrence of shallow saturation zone found immediate for slope having slope angle range between 30° and 40° [10]. The above studies elucidate the influence of slope saturation on slope instability without considering earthquake incidence and when earthquake occurred in these partially saturated slopes, the effects are highly critical. In order to improve slope stability, various slope stabilization measures were suggested and among all the measures use of anti-slide pile is a popular and commonly used technique for slope improvement. Tsai et al. [11] investigated the performance of piles made of solid concrete, hollow concrete, timber and steel pipe in slope reinforcement and found that anti-slide piles improve the stability of slopes against landslides. Though literatures pertaining to the use of anti-slide pile in slope improvement was available, studies on the development of pervious type anti-slide pile for improving drainage and reinforcement characteristics in partially saturated slope under repeated dynamic events were not available. Considering the above, use of pervious anti-slide
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
245
pile is developed in this study for improving slope drainage and reinforcement characteristics in partially saturated ground, and its performance under repeated shaking events was studied experimentally. To compare the performance of anti-slide pilesstructure interaction in slopes similar to field conditions, a scaled down structure also installed on partially saturated slope, and its anti-slide pile-slope-structure interaction under repeated events was studied. Parameters influencing the behavior of reinforced slope were evaluated, and results were discussed.
2 Material Used 2.1 Debris Soil Debris soil collected from the landslide site in lesser Himalayan region in Uttarakhand was used for experimental testing. Table 1 presents the index properties of the collected debris soil.
2.2 Model Development Methodology To study the performance of actual structures, developing a prototype model is an effective solution. However, it has its own constraints such as economy, time, and number of models for testing. Under such situation, use of similitude laws will be highly beneficial in developing scaled down model for representing prototype structures. In this study, a scaled down factor of 1:20 was chosen for surface structure model following dynamic laws. The developed scaled down surface structure consist of G + 3 with piled raft as a foundation in this study. All the columns and floors were connected by bolt-screw connection. The properties of aluminum material were given in Table 2. Similarly, the anti-slide piles were scaled down using Buckingham Table 1 Properties of collected debris soil
S. No.
Properties
Values
1
Specific gravity
2.7
2
Grain size analysis
Grave—24.9% Sand—66.4% Silt—4.7% Clay—4.0%
3
Cohesion
9 kPa
4
Angle of internal friction
33°
5
Permeability
6.3 × 10–4 cm/s
6
IS classification
GW
246
R. Ram Kumar et al.
Table 2 Properties of aluminum [12] Properties
Density (g/cc)
E (GPa)
G (GPa)
Bulk modulus (GPa)
Values
2.7
70.3
26.1
75.5
Fig. 1 Pervious steel anti-slide pile
‘π’ theorem to simulate prototype pile in real conditions. The piles were fabricated using steel material having 20 mm diameter and 400 mm length. To improve drainage characteristics, 2 mm holes at 10 mm spacing were made longitudinally across the fabricated pile model. The holes were selected considering the grain size distribution characteristics of the collected debris soil to facilitate drainage within the slope. Further, the selected material was chosen to simulate reinforcement characteristics in real field conditions. Photograph showing the developed pile model is shown in Fig. 1.
3 Experimental Program 3.1 Slope Preparation and Instrumentation Scheme For experimental studies, a Perspex tank having dimensions 1.75 m × 0.75 m × 1 m was selected for slope preparation. Studies by researchers in Wadia Institute of Himalayan Geology found that 51% of the Uttarakhand, falls under high and very high landslide susceptible zones. For this study, a typical slope observed in Narendra Nagar, Uttarakhand, was selected for the experimental investigations. The slope angle as observed in the site ranging between 40° and 60° facing more landslides during monsoon seasons. Considering the above, slope having 45° was chosen replicating typical slope angle available in Uttarakhand region. The slope was prepared with an in-situ density of 16 kN/m3 equivalent to field conditions. In this study, a slope having dimensions 1.65 × 0.8 × 0.75 m was selected. A schematic diagram showing
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
247
Fig. 2 a Schematic view of prepared slope. b Locations of piles on the slope
the details of slope is given in Fig. 2. The sample preparation involves initial estimation on the quantity of sample for slope preparation. This was calculated based on the selected in-situ density, and accordingly, the quantity of soil required for slope preparation was estimated. The volumetric water content under different suction pressure was calculated initially for estimating SWCC characteristics. To simulate partial saturation, slope with 45% saturation replicating the typical slope wetting after rainfall conditions was chosen. The quantity of water required for simulating partially saturated conditions was estimated using the formula S × e = w × G. Then the total quantity of soil and water has been divided in to five layers, and slope was prepared layer by layer for achieving uniformity in sample preparation. Samples were also collected during sample preparation for confirming density and water content in slope preparation. The scaled down structure was installed once the required depth of embedment (250 mm) for the foundation was reached during slope preparation. The slope was then reinforced with scaled down pervious anti-slide piles. In total, five pervious anti-slide piles were selected for the study. Four piles were installed vertically and one pile horizontally within the slope for facilitating reinforcement and drainage respectively. All the piles were installed at 125 mm c/c for improving the stability of the slope (Fig. 2). For monitoring acceleration response, pore pressure generation, and displacement; contact-type instruments such as acceleration transducers, pore pressure transducers and non-contact-type instrumentation, i.e., 2D-digital image correlation system were used in this study. In 2D digital image correlation system, a set of cameras were positioned parallel to the slope and recorded continuously during shaking. The comparison between un-deformed images (which was taken before test) with the recorded images during test estimated displacement and strains in the test model. The detailed instrumentation scheme selected in the study is shown in Fig. 3.
248
R. Ram Kumar et al.
Fig. 3 Experiment modal of slope
3.2 Testing Conditions Recently, occurrences of repeated shaking events were frequently observed due to the development of foreshock and aftershock effects associated during earthquake incidence. Further, these repeated shaking events also induced structural failures as evidenced from the case studies. Hence, in this study, an attempt has been made to evaluate the influence of repeated shaking events on partially saturated reinforced slope to validate and compare the efficiency of slope reinforcement. Accordingly, input motions having amplitude of 0.1g, 0.2g, 0.3g with 5 Hz frequency representing medium to high earthquake events were selected and applied to the reinforced slope. Further, the sinusoidal shaking selection represents the critical input motion to evaluate the influence of anti-slide pile treatment in slopes. The details of the selected input motions are given in Table 3. During testing, the subsequent acceleration loading was applied to the reinforced slope only after dissipation of generated pore water pressures from previous loading, which was monitored through pore pressure transducers installed inside the slope. The same procedure was repeated till 0.3g acceleration loading condition. The obtained acceleration response, pore pressure response, soil, and structural displacement were monitored continuously, and results were compared for estimating the behavior of reinforced slope under repeated shaking conditions. Table 3 Properties of input seismic motion Acceleration
Frequency (Hz)
Type of wave
0.1g
5
Sine
Amplitude (mm)
Phase angle (°)
0.99
0.2g
1.98
0.3g
2.97
0
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
249
4 Results and Discussion 4.1 Displacement of Slope Using 2-Digital image correlation system, horizontal displacement of the slope was monitored during repeated shaking conditions, and based on the obtained images, the test results were compared. To compare the slope behavior, four points were selected beneath the slope portion, i.e., D1, D2, D3, and D4 at 200 mm intervals respectively such that D1 is on the crest and D4 is at 600 mm depth. Similarly, four points were selected across the slope portion, i.e., S1, S2, S3 and S4 to estimate the slope displacement for better comparison. The details of the selected points are shown in Fig. 3. Figures 4 and 5, presents the obtained horizontal displacements at the selected locations during 0.1g and 0.2g repeated shaking events respectively. Since, slope failure was observed during 0.3g shaking conditions, images were not available for this loading conditions, and results obtained during 0.1g and 0.2g shaking only shown here. It can be seen from Fig. 4a and b at 0.1g acceleration loading, the locations beneath the slope portion, i.e., behind pile installation portions (D1, D2, D3, and D4) showed increment in horizontal displacement compared to slope portion, i.e., S1, S2, S3, and S4. This may be due to partial saturation conditions, i.e., 45% saturation which displaces the soil grains during longer shaking duration and compacted the ground. In slope portion, the installed pervious anti-slide piles induce minimum generation of pore water pressures due to better drainage characteristics which improve the slope stability and minimizes horizontal displacement during shaking. Further, the obtained soil displacement with depth was not uniform in both the selected regions due to uneven compaction experienced by the partially saturated slope during 0.1g shaking. This was found evident from the generated pore water pressures and acceleration response which is given in the following sections. In subsequent 0.2g repeated shaking event, similar observations were made along the selected points of the slope. About 1.2 to 2 times increment in horizontal displacement was observed at both the selected locations during repeated shaking conditions. However, in both the cases slope portion showed comparatively lesser displacement than points D1 to D4. This was mainly due to the installed pervious anti-slide piles which improves reinforcement mechanism across the slope and also provides better drainage in partially saturated slope which postpones generation of pore water pressures and improves the stability of the slope even during repeated shaking events.
4.2 Acceleration Response of Slope The acceleration response plays a major role in influencing the seismic response of slopes. Hence, using 2D-DIC system, the acceleration response during repeated shaking events was estimated. Since, maximum displacement was observed during
250
R. Ram Kumar et al.
Fig. 4 Horizontal displacement along depth at 0.1g (a) and 0.2g (b)
Fig. 5 Horizontal displacement along slope at 0.1g (a) and 0.2g (b)
0.3g shaking conditions, 2D DIC images were not available for this loading conditions, and results obtained during 0.1g and 0.2g shaking only shown here. For comparison, two portions with four selection points at 200 mm distance as shown in Fig. 2, namely, Across the Slope (A-S) and Across the depth (A-D) were selected. Using the estimated velocity–time domain from the 2D-DIC software, the acceleration responses were obtained using differentiation method using data analysis software. Typical obtained acceleration time plot for the selected point across slope portion during 0.1g and 0.2g shaking condition are shown in Fig. 6. Similarly, the obtained values at different locations for the selected portions are given Table 4. The estimated acceleration values between the two portions at different depth showed increment in acceleration response from bottom to top during shaking events. This found common for both the selected locations. However, the obtained acceleration response at A-S found high compared to A-D. This may be due to the lack of confinement across the slope portion which increased the acceleration response across slope region. About 1.36–1.17 times increment in acceleration values were observed at A-S compared to A-D at 0.1g shaking condition. The increment in acceleration may be due to the influence of partially saturated condition which induces generation of pore water pressures. With the increment in pore pressure response,
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
251
Fig. 6 Horizontal Acceleration at S3 along in 0.1g (a) and 0.2g (b)
Table 4 Peak acceleration response of the slope at various depth Depth (mm)
0.1g @ A-S (g)
0.2g @ A-S (g)
0.1g @ A-D (g)
0.2g@A-D (g)
0 (top)
0.192
0.263
0.1403
0.276
200
0.153
0.242
0.137
0.291
400
0.138
0.239
0.127
0.271
600 (bottom)
0.136
0.221
0.116
0.223
the acceleration response increases near the slope portion. This was similar with [13] However, in the subsequent 0.2g acceleration loading, A-D showed higher response than A-S due to (i) uneven densification in the selected region during repeated shaking and (ii) generation of pore water pressures due to non-uniform densification. About 1–1.2 times increment in acceleration response was observed at A-D compared to A-S. In spite of repeated loading events which induces increment in acceleration response, the installed pervious anti-slide piles at the slope reinforces the slope portion and dissipates the generated water pressure as observed during continuous shaking events. It was also evidenced from slope displacement and acceleration response, anti-slide piles showed better performance during higher shaking events. The behavior of pervious anti-slide pile in slop reinforcement is further examined estimating the amplification co-efficient for every 200 mm depth. Figure 7 presents the depth versus amplification co-efficient for the locations A-S and A-D at 0.1g and 0.2g shaking respectively. At 0.1g shaking, estimated values found high for A-S than A-D which is mainly due to lack of confinement and initial ground densification induced by the applied acceleration loading. However, at higher acceleration loading, i.e., 0.2g, the values found reversed due to generation of pore water in the densified soil portion (A-D) and due to un-drained conditions, the values found higher compared to A-S. The installed pervious anti-slide piles minimize and dissipate generated pore water pressures faster which improve the stability of the slope during higher intensity shaking conditions.
252
R. Ram Kumar et al.
Fig. 7 Amplification ratio along A-D and A-S w.r.t 0.1g (a) and 0.2g (b)
4.3 Porewater Pressure (PWP) Response Generation of pore water pressures plays a major role in destabilizing the slopes during rainfall and dynamic events. Considering this anti-slide pile is developed as a pervious member to facilitate drainage and reinforcement in partially saturated slope in this study. The generated pore water pressures during repeated shaking events, i.e., 0.1g and 0.2g along portion A-S and A-D are shown in Fig. 8. In both the locations, pore pressure transducers were installed to monitor generation of pore water pressure during testing. Generation of pore water pressures was not significant up to 0.2g shaking. This was mainly due to the provision of drains in the slope. Comparatively, A-S section shows lesser generation of pore water pressure where the pervious anti-slide piles were installed. At high-intensity shaking conditions, the continuous densification and increment in overburden stress encouraged generation of pore water pressures. Comparatively, section A-D showed increment in pore pressure generation due to increment in soil density with un-drained repeated shaking conditions. About 50% reduction in pore pressure generation was observed along the slope portions due to installation of pervious piles. The observations highlighted that anti-slide pile as drainage member improves drainage characteristics, minimizes generation of pore water pressures, and helps in improving the stability of slopes even repeated shaking events.
4.4 Structural Response During Repeated Shaking Events In addition to slope stability studies, studies relating to structure-slope-pervious antislide piles interaction also attempted in this study. For this objective, a scaled down 5 storey structure was installed at 250 mm depth and at 250 mm distance from the crest portion of the slope. Using 2-D DIC system, the displacement and acceleration response of the structure were estimated. The obtained peak displacement at each
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
253
Fig. 8 Peak PWP at A-D (a) and A-S (b) w.r.t input acceleration
Table 5 Peak displacement (mm) of structure at various storey
Input acceleration
3rd storey
4th storey
0.1g
0.701
0.742
0.2g
1.915
2.122
0.3g
50.04
60.78
5th storey 0.767 2.589 70.24
storey during repeated shaking event is given in Table 5. A typical displacement results obtained from 2D DIC system is also shown in Fig. 9 for 0.1g, 0.2g, and 0.3g respectively. The displacement found significant from 3rd level to 5th level during repeated shaking events. It can be seen from Table 5 about 2.7–28.6 times increment in displacement was observed during incremental acceleration loading, i.e., 0.1g– 0.3g. This was mainly due to the occurrence of continuous densification in slope at repeated shaking condition. The occurrence of densification was mainly due to the influence of longer shaking duration which induces soil compaction and resulting in increment in displacement. At higher intensity loading, the slope found unstable causing collapse of the structure. During testing, it was observed that the installed anti-slide piles reinforced the slope and postponed structural displacement up to 0.2 acceleration loading. The performance of this reinforcement can be improved further by modifying spacing and area of treatment which can sustain during repeated shaking events.
5 Conclusion Using shaking table tests, response of partially saturated slope reinforced with pervious anti-slide piles was studied. The efficiency of the selected treatment was further validated by comparing slope-structure-pervious anti-slide pile interaction
254
R. Ram Kumar et al.
Fig. 9 Displacement of the structure at 0.1g (a), 0.2g (b), and 0.3g (c) respectively
during repeated shaking events. Based on observations, following conclusions were made: • Installation of pervious anti-slide piles reinforced the slope efficiently and minimized the horizontal displacement. The slope portion showed minimum displacement compared to soil portion at crest level A-D during repeated shaking events. • The embedment depth for piled raft foundation in model structure together with pervious anti-slide pile postponed structural displacement up to 0.2g shaking condition. This validates the contribution made by the pervious anti-slide in pileslope-structure interaction during repeated shaking events. • Pervious anti-slide piles perform better with drainage and reinforcement characteristics in this study. Under repeated shaking events, the installed piles effectively mitigate generation of pore water pressure across the slope region and also reinforces the slope effectively. The test results elucidate that selecting proper spacing with adequate area replacement ratio can further improve the stability of slope and structure even during repeated shaking events. Acknowledgements The authors are thankful to Director, CSIR-Central Building Research Institute, Roorkee for giving permission to publish this research work.
Seismic Stability Analysis of Partially Saturated Slope Reinforced …
255
References 1. Sumantra, S.B., Raghunath, P.: Causes of landslides in Darjeeling Himalayas during June–July, 2015. J. Geogr. Nat. Dis. 6(173), 2167–2587 (2016) 2. Kolathayar, S., Sitharam, T.G., Vipin, K.S.: Deterministic seismic hazard macrozonation of India. J. Earth Syst. Sci., 1351–1364 (2012) 3. Yin, Y., Wang, F., Sun, P.: Landslide hazards triggered by the 2008 Wenchuan earthquake, Sichuan, China. Landslides 6, 139–152 (2009) 4. Zhou, J.W., Cui, P., Fang, H.: Dynamic process analysis for the formation of Yangjiagou landslide-dammed lake triggered by the Wenchuan earthquake, China. Landslides 10, 331–342 (2013) 5. Dimri, A.P., Chevuturi, A., Niyogi, D., Thayyen, R.J., Ray, K., Tripathi, S.N., Pandey, A.K., Mohanty, U.C.: Cloudbursts in Indian Himalayas: a review. Earth-Sci. Rev., 1–23 (2017) 6. Parthasarathy, K.S., Deka, P.C., Saravanan, S., Abijith, D., Jennifer, J.J.: Assessing the impact of 2018 tropical rainfall and the consecutive flood-related damages for the state of Kerala, India. In: Indrajit, P., Rajib, S. (eds.) Disaster Resilience and Sustainability, pp. 379–395. Elsevier (2021) 7. He, F., Tan, S., Liu, H.: Mechanism of rainfall induced landslides in Yunnan Province using multi-scale spatiotemporal analysis and remote sensing interpretation. Microprocess. Microsyst., 90 (2022) 8. Kim, J., Jeong, S., Regueiro, R.A.: Instability of partially saturated soil slopes due to alteration of rainfall pattern. Eng. Geol., 28–36 (2012) 9. Qiu, X., Li, J., Jiang, H., Ou, J., Ma, J.: Evolution of the transient saturated zone and stability analysis of slopes under rainfall conditions. KSCE J. Civil Eng., 18–31 (2022) 10. Liu, Z., Wang, X., Yin, Y., Li, J., Shao, G.: Stability analysis of an unsaturated clay slope based on the coupled effect of temperature and saturation. Q. J. Eng. Geol. Hydrogeol. 55(2) (2022) 11. He, J., Wang, S., Liu, H., Nguyen, V., Han, W.: The critical curve for shallow saturated zone in soil slope under rainfall and its prediction for landslide characteristics. Bull. Eng. Geol. Env. 80(3), 1927–1945 (2021) 12. Tsai, P.H., Feng, Z.Y., Jen, T.L.: Three-dimensional analysis of the screening effectiveness of hollow pile barriers for foundation-induced vertical vibration. Comput. Geotech. 35(3), 489–499 (2008) 13. Royal Society of Chemistry, https://www.rsc.org/periodic-table/element/13/aluminium. Last accessed 24 July 2022
Investigations on Rubber-Sand Mixture Reinforced with Geogrid as a Low-Cost Geotechnical Seismic Base Isolation Technique T. Suyal and R. M. Varghese
Abstract Nowadays, several structural base isolation techniques, such as dampers or elastomeric bearings, are commonly used to isolate structures from earthquake vibrations. However, the installation and maintenance costs of these energy-absorbing materials are quite expensive. Thus, studies are conducted on decoupling the structure from the base using a geotechnical seismic isolation (GSI) system, which can safeguard the structure from earthquake-induced vibrations. GSI system consists of soil mixed with high damping materials like shredded tires provides an efficient and economical option. However, the compressive nature of the rubber-sand mixture (RSM) layer restricts its wide usage. The excessive strains in the RSM layer can be controlled by introducing geogrid. This paper presents the use of RSM-reinforced with geogrid to provide a seismic isolation layer below the building foundation. Numerical analysis was done for a residential building using the finite element software PLAXIS 3D. Various parametric studies were conducted to find the minimum thickness of the RSM layer, the location of geogrid, and the number of geogrid layers to control the transmission of seismic vibrations. The effectiveness of the GSI was determined by comparing the parameter like peak spectral acceleration (PSA) and settlement of the system for various earthquake input motion with and without a rubber-sand mixture layer. The results showed that the introduction of an RSM layer of thickness 0.05–0.15 times the width of the foundation can reduce the PSA up to 30–55%, and the addition of geogrid as a reinforcing material can reduce the seismic-induced vertical settlement up to 68% which will ultimately lead to the broad applicability of RSM layer as a low-cost seismic base isolator. Keywords Geotechnical seismic isolation · Rubber sand mixture · Geogrid · Peak spectral acceleration · PLAXIS 3D
T. Suyal (B) · R. M. Varghese Department of Civil Engineering, NIT Calicut, Calicut, Kerala, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_21
257
258
T. Suyal and R. M. Varghese
1 Introduction An earthquake is a natural disaster that occurs when energy stored in the earth’s crust is released in the form of seismic waves. These seismic waves when reaching the earth’s surface causes vibrations and ground shaking. The structure’s built-on earthquake-prone area has a risk of cracks, settlement, or even collapse due to these vibrations. More than half of our country is susceptible to damaging earthquakes. The entire Himalayan belt is susceptible to damaging earthquakes of magnitude greater than 8. In the past few decades, India has experienced several major earthquakes which have resulted in the death of thousands of people and all of these deaths were due to the collapse of structures [1]. Due to this, the earthquake-resistant design of the structures is important, especially in the field of civil engineering. The traditional method focuses on strengthening the structural parts to withstand seismic forces in order to prevent the structure from collapsing, but their operation after the earthquake cannot be assured. An alternate method of geotechnical seismic isolation (GSI) can also be used to safeguard the structure from earthquakes induced vibrations. GSI is a method of decoupling the structure from the base by providing an energy-absorbing system. Using a GSI system, the amount of energy that is transferred to the structure can be reduced significantly. Earlier isolation devices and dampers were used as an isolation layer [2], but these isolation devices are very costly and are not economical to be used in residential buildings. Recent studies on alternate systems consisting of materials of high damping properties like rubber provide an economical option. The addition of shredded rubber particles in sand changes the structure and interparticle forces resulting in an improvement in the dynamic performance of the host sand. Due to the high damping, low stiffness, and low shear modulus of rubber compared to natural soil, it can be used as a seismic isolation layer below the building foundation [3]. A series of resonant column tests done by [4] finds that the addition of shredded rubber particles in the sand can improve the dynamic performance of host soil by reducing the shear stiffness and improving the dynamic shear modulus. Previous studies found that the introduction of a rubber sand mixture (RSM) layer of thickness of 2–3 m below the foundation is likely to achieve adequate levels of acceleration reductions [5, 6]. The introduction of rubber-sand mixture as an isolation layer reduces the seismic response. However, the compressive nature of the pure RSM layer restricts its wide usage. The excessive strains in the RSM layer can be controlled by reinforcing the soil with geosynthetic materials. Numerical analysis and laboratory tests on various geosynthetic materials concluded that geogrids through their apertures can achieve an efficient anchoring effect and it serves as a superior form of reinforcement in soil [7, 8]. 2D analysis done by [9] on a two-storey building showed that reinforcing the soil with geogrid increases the bearing capacity up to two to three times, and settlement was reduced up to 30–45%. As the studies on combined response of rubber sand mixture are very less and limited to 2D analysis only. In the present study, 3D analysis has been done to explore the possibility of using a rubber sand mixture reinforced with geogrid as
Investigations on Rubber-Sand Mixture Reinforced with Geogrid …
259
a geotechnical seismic base isolation technique. Numerical modeling was done for a low-rise building resting over a geogrid reinforced RSM layer using the FEM software PLAXIS 3D to understand the dynamic response of the building by varying various parameters like the thickness of the rubber sand layer, number of layers of geogrid, and earthquake input motion.
2 Building Details The present study aimed to explore the possibility of using a rubber sand mixture layer reinforced with geogrid as a geotechnical seismic base isolation technique for a low-rise residential building (G + 2 Storey) located in the Indo-Gangetic Plain, which was classified as A4 according to the National Building code of India [10]. Figure 1 shows the schematic diagram of the building. The height of each storey was 3.5 m, and the length and width of each bay were 4 m. The size of the column and beams was 400 mm × 350 mm. The imposed loads on the building were taken according to IS Code [11]. The structure was supported by a 14 m × 14 m raft foundation having thickness of 0.3 m made of M40 grade concrete, designed according to load-bearing and settlement criteria. Building design and analysis software ETABS were used to evaluate the stability of the building frame. The building was analyzed for different load combinations. From these various loads, a maximum load of 1226 kN and a surface load of 22.5 kN/m2 were taken as critical loads for further analysis. FEM software PLAXIS 3D was used to study the seismic response.
Fig. 1 Details of the building structure
260
T. Suyal and R. M. Varghese
3 Numerical Modeling The seismic analysis of the geotechnical seismic isolation system was done in finite element software PLAXIS 3D. The soil profile of a site in Kanpur city, located in the Indo Gangetic Plain which lies in seismic zone III [12] was taken for the study. The soil layer with dimensions 150 m × 150 m × 27 m was created, and the properties were taken from ground response analysis of soil along Indo-Gangetic Plains done by [13]. The soil was divided into 18 layers of 1.5 m thickness having layers of silty sand and clayey soil, water table was also considered at a depth of 5.5 m. The Poisson’s ratio µ was calculated from the relation between standard penetration resistance (SPT) value and Poisson’s ratio as given by [14] and shear modulus of the soil was calculated from the formula below. μ = 0.2 + 0.005N Gmax = ρ.V2s where Gmax = Maximum Shear Modulus (MPa), ρ = Density of soil (kN/m3 ), V s = Shear Velocity (m/s), μ = Poisson’s ratio, and N = SPT resistance Figure 2 shows the model developed in PLAXIS 3D. The raft footing was modelled as a plate element, rubber-sand mixture below the footing was modeled as a volume, and properties of rubber-sand mixture layer having a rubber content of 30% taken from a study done by [4] were taken. For reinforcing the rubber sand, geogrid was used. The properties of geogrid were taken from the study conducted by [15]. The material properties of different elements used in the study are shown in Table 1. The maximum column loads calculated from ETABS were applied at the column location as a point load; along with this, a surface load was also applied. A mediumquality mesh was generated. After creating the geometry, interfaces were introduced below the footing. Free-field boundary condition was used along lateral boundaries, and the compliant base was taken at the bottom. A prescribed surface displacement was introduced at the bottom of the model, i.e., at depth of 27 m, and seismic excitation of the various earthquakes was given in the form of acceleration time history. Fig. 2 FEM model developed in PLAXIS 3D
Investigations on Rubber-Sand Mixture Reinforced with Geogrid … Table 1 Material Properties used in the present study
261
Sr. no.
Property
Value
References
1
Rubber sand mixture • Shear modulus (G) • Unit weight (U) • Cohesion (C) • Angle of internal friction (F) • Poisson’s ratio (μ)
11.3 MPa 15.5 kN/m3 8 kN/m2 12.03 degree 0.4
[4]
2
Raft footing • Thickness (d) • Unit Weight (U) • Modulus of elasticity (E) • Poisson’s ratio (μ)
0.3 m 24 kN/m3 3.1 × 104 MPa 0.2
[16]
3
Geogrid • Poisson’s ratio (μ) • Density (U) • Tensile stiffness
0.3 450 kg/m3 1000 kN/m
[15]
The record of four significant earthquakes namely the Nepal earthquake 2015, Bhuj earthquake 2001, Chamoli Earthquake 1999, and Uttarkashi Earthquake 1991 were used for the dynamic analysis of structure. Strong-motion data were collected from COSMOS and USGS virtual data center. The dynamic input motion was taken for 60 s. The seismic response of the raft footing in terms of peak spectral acceleration (PSA) was checked to understand the efficiency of the geotechnical seismic isolation system. The PSA value was checked at the center of the raft footing. The efficiency of the seismic isolation system was checked with a factor as described below: SIE (Seismic isolation Efficiency) =
PSAs − PSARSM × 100 PSARSM
where PSAs = Peak Spectral Acceleration of soil (g) PSARSM = Peak Spectral Acceleration of Rubber Sand Mixture (g). Initially, numerical analysis was done to find the response of the structure without rubber sand mixture, and then with rubber-sand mixture, and finally for rubber sand mixture reinforced with geogrids. Further, the parametric study was done by varying various parameters like the thickness of the rubber-sand mixture, the number of geogrids, and earthquake input motion.
262
T. Suyal and R. M. Varghese
Fig. 3 Comparison of response spectra for footing resting on a natural soil, b the RSM layer
3.1 Validation of Model The model was validated by comparing the results of the current numerical model with the results of shaking table studies done by [17] on model footing isolated with the RSM layer. The geometry of the model was the same as the experimental model. The model was provided a sinusoidal input motion of frequency of 3.5 Hz and an amplitude of 0.4 g, and the dynamic response of the footing was investigated. Figure 3 shows the Peak spectral acceleration (PSA) values for the footing resting on natural soil and the RSM layer. The results of the numerical model and shake table test were within range of 10%. Hence, the same numerical modeling technique was extended to investigate the response of a GSI system.
4 Results and Discussions The seismic response of raft footing with and without the RSM layer was checked in terms of PSA and seismically induced settlement. The reduction of PSA was expressed in terms of seismic isolation efficiency as defined earlier. To reduce the seismically induced settlement geogrids were used, and the percentage reduction in settlements was compared. The efficiency of the GSI system was also checked corresponding to different earthquake motions.
4.1 Seismic Response Reduction by RSM The magnitude of reduction of acceleration response spectrum is directly related to the thickness of the RSM layer. To find the optimum thickness of the RSM layer
Investigations on Rubber-Sand Mixture Reinforced with Geogrid …
263
Fig. 4 Variation of PSA with respect to the thickness of the RSM layer for the 2001 Bhuj earthquake
the thickness was varied as 0.05, 0.1, and 0.15 times the width of the foundation. The maximum thickness was restricted to 0.15 times the width of the foundation considering cost efficiency and practicality for field applications. A clear understanding of the characteristics of the acceleration response spectra (5% damping) at the center of footing resting on natural soil and rubber-sand mixture layer subjected to the Bhuj earthquake as dynamic input motion can be obtained from Fig. 4. Without the RSM layer, the PSA value was 0.6758 g which was reduced to 0.46 g when 0.05 B RSM (i.e., 0.05 × 14 m = 0.7 m) was placed below the foundation. A percentage reduction of 31.93% was observed on PSA values by including a 0.05 B thick RSM layer. This sharp decrease in PSA value shows the high damping nature of the rubber sand mixture. For more efficiency, the thickness of RSM was increased to 0.1 B (i.e., 1.4 m); for this depth, PSA reduces to 0.3542 g which in turn reduces the PSA to 47.58%. Further, the depth was increased to 0.15 B (i.e., 2.1 m) and PSA was reduced to 0.3087 g, a 54.3% reduction was achieved. It is evident that there is a reduction in PSA value by using a rubber sand mixture layer, and the reduction in the PSA value was prominent with the RSM layer of thickness 0.1 B. Further increase in thickness of the RSM layer has negligible influence on the reduction of PSA values. The reduction of spectral acceleration was pronounced in up to 1.2 s. Further, the reduction in spectral acceleration was less evident or negligible. It was also observed that the use of rubber sand mixture shifts the predominant period from 0.36 s to a higher value of 0.66 s. From this, it can be concluded that there is the lengthening of the period with the introduction of the RSM layer. From Fig. 5, it is evident that with the increase in D/B ratio (Thickness of RSM/Width of Foundation) seismic isolation efficiency (SIE) increased, and the PSA value decreased. The increase in SIE was significant up to the D/B ratio of 0.1 increasing the D/B ratio beyond 0.1 has a very less change in SIE and PSA value
264
T. Suyal and R. M. Varghese
Fig. 5 Percentage reduction and PSA corresponding to different D/B ratios (thickness of RSM/width of foundation)
which confirms that for the present condition, the optimum thickness of the RSM layer was 0.1 B.
4.2 Seismically Induced Settlement Due to RSM The use of the RSM layer reduced the PSA value to a considerable limit, but at the same time, it increased the settlement of the foundation which can lead to the failure of the foundation. Figure 6 shows the seismically induced settlement of footing due to the Bhuj earthquake. From this figure, it is evident that the settlement is increasing by increasing the thickness of the rubber-sand mixture layer. There was a settlement of 19.98 mm without using RSM which was increased to 39.97 mm after using 0.05 B thick RSM. Further on increasing the thickness of RSM to 0.1 B settlement increases to 66.17 mm and for 0.15 B it increased to 99.25 mm. This settlement is more than the permissible settlement for a raft foundation [18] and may cause the failure of footing. Hence, the thickness of RSM should not be increased beyond a specific limit, to avoid this drastic increase in settlement. In the present study, to get an economical and efficient GSI system, the thickness of RSM was fixed to 0.1 B, but for this depth of RSM, the settlement was 2.5 times that of soil which can cause the failure of the foundation. To reduce this settlement various geosynthetic materials can be used which increases the strength of the soil. Previous studies done by authors [19, 20] showed that geogrids can be used to increase the bearing capacity of sand and decrease settlement.
Investigations on Rubber-Sand Mixture Reinforced with Geogrid …
265
Fig. 6 Variation of seismically induced settlement of the footing with respect to different thicknesses of RSM layer subjected to the 2001 Bhuj earthquake input motion
For the present study to reduce the seismically induced settlement, three cases were analyzed with one, two, and three layers of geogrids at different spacing. The length of the geogrid was 1.3 times the width of the raft foundation [16]. For the first case, one layer of geogrid was placed in the middle of the RSM layer. For the second case, two layers of geogrid were placed at a spacing of 0.05 B (where B = width of foundation) and a cover of 0.025 B from top and bottom. For the third case, three layers of geogrid were placed at an equal spacing of 0.025 B. Figure 7 shows the variation of seismically induced settlement of the footing for different layers of reinforcement subjected to the 2001 Bhuj earthquake. For one layer of geogrid reinforcement, the seismically induced settlement was reduced to 41.43 mm, i.e., a percentage reduction of 37% was achieved as compared to the unreinforced RSM. With two layers of geogrid settlement was reduced by 56% (i.e., 28.99 mm). Further on increasing the number of geogrid layers to three, the settlement was reduced to 63% (i.e., 24 mm). From the above results, the settlement value obtained for two or three layers of geogrid reinforcement was almost similar. Hence, for further analysis, a GSI system of 0.1 B thickness of rubber sand mixture and double-layer geogrid reinforcement was taken.
4.3 Effect of Earthquake Input Motion The effect of earthquake input motion on the GSI system was studied by considering four different earthquakes having different predominant frequencies. The earthquakes were considered as low-frequency earthquakes for (f < 1 Hz), medium frequency (1 Hz < f < 2 Hz), high frequency (>2 Hz) [21]. Accordingly, the Nepal earthquake was considered low frequency, and Bhuj, Chamoli, and Uttarkashi were considered high-frequency earthquakes.
266
T. Suyal and R. M. Varghese
Fig. 7 Variation of Seismically induced settlement of the footing for different layers of reinforcement subjected to the 2001 Bhuj earthquake
Table 2 shows the effect of earthquake input motion values on peak spectral acceleration values for the footing resting on natural soil and geogrid-reinforced RSM layer. For the Nepal earthquake, i.e., a low-frequency earthquake result shows that with the introduction of the GSI system, there is a sharp decrease in PSA and seismic isolation efficiency (SIE) of 50.45% was achieved. For high-intensity earthquakes, i.e., Bhuj, Chamoli, Uttarkashi SIE of 45–52% was achieved. For all cases, the introduction of the GSI system reduced the peak spectral acceleration. It is also observed that the introduction of the GSI system shifts the predominant period by 0.06–0.21 s for different cases. Hence, the period was also lengthened by the introduction of the RSM layer. Table 3 shows the settlement reduction in the 0.1 B thick RSM layer using double geogrid reinforcement for different earthquake input motions. With the use of geogrid, there is a percentage reduction of 52–68% in settlement values. Table 2 Effect of Earthquake input motion on peak spectral acceleration Earthquake
Peak spectral acceleration on the footing resting on (g) Natural soil
RSM + Geogrid
Predominant period for footing SIS (seismic resting on (s) isolation Natural soil RSM + geogrid efficiency) %
Nepal
1.697
0.841
0.23
0.32
50.44
Bhuj
0.6758
0.3542
0.36
0.57
47.58
Chamoli
1.125
0.546
0.31
0.37
51.46
Uttarkashi
1.77
0.986
0.14
0.34
44.26
Investigations on Rubber-Sand Mixture Reinforced with Geogrid …
267
Table 3 Settlement reduction in 0.1 B RSM using geogrid Earthquake
Settlement of the footing (mm) Without geogrid
Nepal
54.63
52
Bhuj
66.17
28.99
56.18
Chamoli
99.1
31.2
68
148.6
50.95
65
Uttarkashi
113.8
Percentage Settlement reduction (%)
With geogrid
5 Conclusions The following conclusions have been drawn based on the numerical study. • The results from the numerical analysis for the Bhuj earthquake show that by using the RSM layer 30–55% reduction in acceleration response spectrum could be achieved, but this reduction was significant only up to a certain depth of 0.1 times the width of the foundation. The use of rubber-sand mixture shifts the predominant period from 0.36 s to a higher value of 0.66 s. The reduction of spectral acceleration was pronounced up to 1.2 s. Further, the reduction in spectral acceleration was less evident or negligible. Hence, for achieving an economic and efficient GSI system the thickness of the RSM layer should be restricted to 0.1 B. • With the use of rubber-sand mixture, there was an increase in the settlement which can lead to the failure of the foundation. To avoid this, settlement the RSM layer was reinforced with different layers of geogrid, and the double layer of geogrid reinforcement was found to be the most suitable and economical for the GSI system. For 0.1 B (B = Width of foundation) thickness of RSM, a reduction of 56% was achieved for the double geogrid reinforced case as compared to the unreinforced case. • The GSI system was checked for different low- and high-frequency earthquake input motions and a seismic isolation efficiency of 45–52% was achieved, the use of geogrid reduced the settlement up to 52–68% for different cases. As a result of the numerical analysis, it was found that a geotechnical seismic base isolation system consisting of a rubber sand mixture layer having a rubber content of 30% and thickness 0.1 times the width of foundation, reinforced with double layers of geogrid is an efficient and a low-cost seismic base isolation method.
References 1. Jain, S.K.: Indian earthquakes: an overview. Indian Concrete J. 72(11), 555–561 (1998) 2. Mohan, M., Shekhar, S., Shukla, S.P., Zafar, S.: Seismic isolation devices. [Online]. Available: http://www.krishisanskriti.org/Publication.html 3. Tsang, H.H.: Seismic isolation by rubber-soil mixtures for developing countries. Earthq. Eng. Struct. Dynam. 37(2), 283–303 (2008). https://doi.org/10.1002/eqe.756
268
T. Suyal and R. M. Varghese
4. Wu, Q., Jia Ma, W., Liu, Q., Zhao, K., Chen, G.: Dynamic shear modulus and damping ratio of rubber-sand mixtures with a wide range of rubber content. Mater. Today Commun. 27, 15–18 (2021). https://doi.org/10.1016/j.mtcomm.2021.102341 5. Brunet, S., de la Llera, J.C., Kausel, E.: Non-linear modeling of seismic isolation systems made of recycled tire-rubber. Soil Dyn. Earthq. Eng. 85, 134–145 (2016). https://doi.org/10.1016/j. soildyn.2016.03.019 6. Yildiz, Ö.: Geotechnical seismic isolation method using rubber-soil mixtures. NATURENGS MTU J. Eng. Nat. Sci. Malatya Turgut Ozal Univ. (2021). https://doi.org/10.46572/naturengs. 872231 7. Ari, A., Misir, G.: Three-dimensional numerical analysis of geocell reinforced shell foundations. Geotext. Geomembr. 49(4), 963–975 (2021). https://doi.org/10.1016/j.geotexmem.2021. 01.006 8. Guido, V.A., Chang, D.K., Sweeney, M.A.: Comparison of geogrid and geotextile reinforced earth slabs. [Online]. Available: www.nrcresearchpress.com 9. Dhanya, J.S., Boominathan, A., Banerjee, S.: Performance of geo-base isolation system with geogrid reinforcement. Int. J. Geomech. 19(7), 04019073 (2019). https://doi.org/10.1061/(asc e)gm.1943-5622.0001469 10. BIS, “National Building Code of India, 2016 Volume 1,” National Building Code of India, vol. 80, p. 1 v. (various pagings) (2016) 11. B. of Indian Standards, “IS 875-2 (1987): Code of Practice for Design Loads (Other Than Earthquake) For Buildings and Structures, Part 2: Imposed Loads.” 12. B. of Indian Standards, “IS 1893-1 (2002): Criteria for Earthquake Resistant Design of Structures, Part 1: General Provisions and Buildings.” 13. Jishnu, R.B., Naik, S.P., Patra, N.R., Malik, J.N.: Ground response analysis of Kanpur soil along indo-gangetic plains. Soil Dyn. Earthq. Eng. 51, 47–57 (2013). https://doi.org/10.1016/ j.soildyn.2013.04.001 14. Kumar, R., Bhargava, K., Choudhury, D.: Estimation of engineering properties of soils from field SPT using random number generation. INAE Lett. 1(3–4), 77–84 (2016). https://doi.org/ 10.1007/s41403-016-0012-6 15. Dhanya, J.S., Boominathan, A., Banerjee, S.: Response of low-rise building with geotechnical seismic isolation system. Soil Dynam. Earthq. Eng. 136, 106187 (2020). https://doi.org/10. 1016/j.soildyn.2020.106187 16. Xu, R., Fatahi, B.: Influence of geotextile arrangement on seismic performance of mid-rise buildings subjected to MCE shaking. Geotext. Geomembr. 46(4), 511–528 (2018). https://doi. org/10.1016/j.geotexmem.2018.04.004 17. Bandyopadhyay, S., Sengupta, A., Reddy, G.R.: Performance of sand and shredded rubber tire mixture as a natural base isolator for earthquake protection. Earthq. Eng. Eng. Vib. 14(4), 683–693 (2015). https://doi.org/10.1007/s11803-015-0053-y 18. B. of Indian Standards, “IS 1904 (1986): Code of practice for design and construction of foundations in soils: general requirements.” 19. Patra, C.R., Das, B.M., Atalar, C.: Bearing capacity of embedded strip foundation on geogridreinforced sand. Geotext. Geomembr. 23(5), 454–462 (2005). https://doi.org/10.1016/j.geotex mem.2005.02.001 20. Lavasan, A.A., Ghazavi, M., Schanz, T.: Analysis of interfering circular footings on reinforced soil by physical and numerical approaches considering strain-dependent stiffness. Int. J. Geomech. 17(11), 04017096 (2017). https://doi.org/10.1061/(asce)gm.1943-5622.0000992 21. Adimoolam, B., Banerjee, S.: Response of soil-tyre mixture subjected to cyclic loading (2017)
Performance Evaluation of Partially Saturated Slope Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments S. K. Jeeva , M. D. Godson , and S. Ganesh Kumar
Abstract The rainfall in the state of Uttarakhand has a dynamic version. The erratic cloudbursts with unpredictability in rainfall intensity usually cause sudden variation in slope saturation especially during monsoon seasons. This led to frequent rainfall-induced slope failures in past years. Additionally, the region is also categorized under seismic zone IV and V as per the Indian seismic zonation map. When unforeseeable seismic events may associate with these partially saturated slopes, the sudden slope failures can endanger human lives and can affect major infrastructures in these regions. The observed repeated shaking events such as the Japan earthquake (Tohoku) (2011), Nepal earthquake (2015), etc., highlighted the possibility of multiple shaking events and its influence on the infrastructures. Considering the above, this study aims to evaluate the behaviour of the partially saturated slope subjected to repeated dynamic loading conditions. Using 1-g shaking table experiments, the dynamic response of slope was evaluated. For experimental studies, debris material collected from the lower Himalayan region in Uttarakhand was used for model slope preparation for simulating field behaviour. For experimental testing, slope having 45º slope angle with 60% density was prepared using 10% water content for achieving 40% partial saturated conditions. The model slope was then subjected to repeated incremental dynamic loading conditions of 0.1 g, 0.2 g, 0.3 g, and 0.4 g acceleration intensity respectively. To compare the influence of repeated shaking on the slope and its interaction with the adjacent structures, a scaled-down model structure was installed at a 250 mm distance from the crest portion of the slope. The influence of acceleration response, pore pressure generation, soil settlement, and structure displacement were evaluated and compared. In addition to above instrumentation scheme, a 2-D digital image correlation system was additionally used for slope and structural displacement. An attempt also made to model the experiments using FLAC 3D software for estimating the failure conditions. Based on the obtained test results, parameters influencing the stability of partially saturated slope subjected S. K. Jeeva (B) · M. D. Godson · S. G. Kumar Geotechnical Division, CSIR-CBRI, Roorkee, India e-mail: [email protected] S. G. Kumar e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_22
269
270
S. K. Jeeva et al.
to repeated acceleration loading events have been evaluated, and its influence on the adjacent structure is presented. Keywords Partially saturated slope · 2-D digital image correlation · Slope failure · Repeated dynamic events · FLAC3D
1 Introduction Uttarakhand is located on the northern portion of the mighty Himalayas, which is full of natural resources, thick forest cover, rivers, glaciers, and snow-clad mountain peaks exerting a profound influence on monsoon and rainfall patterns. That expounds one of the reasons for heavy rainfall in these regions [1], which can also result in the occurrence of continuous natural disasters in this region, i.e., landslides. Landslides were the movement of rock masses, debris, or earth down a slope [2]. They can be triggered by various external stimuli such as earthquakes, intense rainfall, ground water level fluctuation, artificial disturbance, or rapid stream erosion [3, 4]. However, earthquake-triggered landslides have been studied in seismic regions considering its significance as a geological disaster [5–7]. It has caused colossal losses of properties and lives in the past [8–10]. However, successive earthquake motions are further too complex in nature, and their influence on slopes cannot be predicted accurately. The recent repeated ground-shaking events associated during earthquakes as observed in New Zealand 2010–2011; Tohoku (Japan), 2011; Nepal, 2015; Kumamoto, 2016; Indonesia, 2018 and Canada, 2019, etc., evidenced that there is a possibility for multiple seismic events that can occur at a particular location within a short period [11]. According to the seismic zonation map by the Bureau of Indian Standards, Uttarakhand falls in zone IV and zone V, i.e., more volatile to earthquake susceptibility with intensity 0.2 g and greater than 0.4 g PGA [12]. As of now, limited/no studies were available due to earthquake-induced landslides after heavy rainfall events [13, 14]. Considering the above, an attempt has been made in this research to study the dynamic behaviour of partially saturated slope through 1-g shaking table experiments with repeated incremental acceleration loading conditions, i.e., 0.1, 0.2, 0.3, and 0.4 g. For assessing structure response, the slope contains a scaled down G + 3 building model at the crest since majority of the studies showed that the slope-reflected waves are the main cause of surface motion amplification in the vicinity of the crest [15, 16]. The investigations were performed with sinusoidal input motions having 200 cycles with 40 s duration. In order to measure the displacement and failure pattern of the slope, a non-contact based measuring technique called digital image correlation (DIC) was used; in addition to that contact type instruments such as pore pressure transducers and accelerometers, LVDT,. Numerical analysis was performed to validate and to predict the displacement contour to determine the critical location in the prepared ground. For this objective, Fast Lagrangian Analysis of Continua in 3D (FLAC3D) software by Itasca was used. Based on the obtained
Performance Evaluation of Partially Saturated Slope Subjected …
271
Fig. 1 a 3-D diagram of the model slope b transducer location
experimental and numerical observations, the parameters influencing the behaviour or partially saturated conditions were analysed and compared.
2 Experimental Set-Up 2.1 Shake Table The experimental tests were carried out on a uni-axial shaking table having dimensions of 2 m × 2 m connected with a servo-hydraulic actuator which facilitates a horizontal movement of the table and is controlled by a digital data acquisition system. The slope was prepared inside a specially fabricated rigid Perspex rectangular glass tank of dimensions 1.75 m × 0.75 m × 1 m, as shown in Fig. 1a. To minimize the boundary effects, a thick polyurethane foam of 50 mm was placed on both sides, i.e., perpendicular to shaking directions inside the tank, as shown in Fig. 1a [17].
2.2 Sample Preparation The debris soil sample used for slope preparation was taken from the actual landslide site in the lower Himalayan region. The basic soil properties are listed in Table. 1. The grain size distribution curve showed that the soil was well-graded. The debris soil was mixed with 10% water content to achieve 40% saturation simulating partially saturated conditions. The slope was prepared with 16 kN/m3 density equivalent to field in-situ density. DCPT tests were performed to confirm the density distribution with depth. Using large-scale direct shear test, the shear strength parameters at the
272 Table 1 Soil properties
S. K. Jeeva et al. Properties
Value
Specific gravity
2.7
Soil type
SM
Permeability
6.3 × 10–4 cm/s
Cohesion
9 kPa
Angle of internal friction
33°
Fig. 2 a Completed slope prepared at 45° b slope with structure in the vicinity of crust
prepared density was estimated. For experimental testing, slope having 45° angle was prepared with 800 mm height with cross sections 1650 mm × 750 mm. The sample depth was divided into four layers to achieve maximum uniformity, and the quantity of soil sample for each layer required for slope preparation was estimated prior. The distribution of required saturation within the slope was verified using the water content values obtained from the collected soil samples during sample preparation. The prepared slope is shown in shown in Fig. 2a. This study also considered to analyse the response of surface structure situated at the crest of the slope. Hence, a scaled-down G + 3 surface structure with raft foundation was placed at 100 mm from the crest of the prepared slope as shown in Fig. 2b. For performing dynamic soil-structure interaction (SSI) using 1-g shaking table the scaling of the model is necessary to minimize the 1 g test limitations. Therefore, similarity relations between the model structure and the prototype design were developed using Buckingham-π theorem. Considering the limitations of tank dimensions, the geometric similarity ratio was adjusted to 1/20. Since the study is considered for repeated incremental shaking series with longer duration, aluminium material was taken for the structural model to examine the dynamic response of the structure adjacent to the slope. The similarity ratio for elastic modulus was found to be 1/0.425, and for the acceleration similarity ratio was taken as 1 for this study. Based on three fundamental scale factors, i.e., geometry, material, and dynamic conditions, the other similarity ratios were determined.
Performance Evaluation of Partially Saturated Slope Subjected …
273
For monitoring the slope response during shaking events, strain-based accelerometers and pore pressure transducers were installed inside the slope. The transducers were connected to a dynamic data logger system. To study the generation of pore pressure from the toe to the crust, sensors are placed at an equal interval of 200 mm from the bottom. In order to study the peak amplification inside the slope during repeated shaking events, accelerometers were placed at the face of the slope at 400 and 600 mm depth. The instrumentation arrangement is shown in Fig. 1b.
2.3 2D-DIC Setup In the case of engineering applications, measurement of displacement and deformation on materials subjected to external loadings plays an essential role for its performance enhancement. Digital Image Correlation (DIC) is a precise, non-contact, and non-interferometric optical method for measuring the displacement and deformation of a material subjected to external loading. This method belongs to the group of optical, non-interferometric techniques which determine deformation by comparing the changes in the image of the surface of a tested object before and after deformation [18]. The idea of the DIC method is based on the principles of continuum mechanics (rigid body mechanics) [19]. DIC was based on sequential image capturing; a CMOS (Complementary Metal Oxide Semiconductor) sensor-based high-speed camera was used for dynamic purposes. In this study, two cameras of 130 fps (frames per second) and 30 fps were used for capturing images during dynamic testing. The sample preparation for image capturing involves coating a thin layer of aerosol white paint over the selected surface structure, and after drying the surface got speckled with black dots for image processing, as shown in Fig. 3b. In the case of soil, high-density polystyrene beans were placed in between layers during slope preparation at the front layer of the Perspex sheet, as shown in Fig. 3a. These beans will displace along with the soil and help to detect the soil displacement during dynamic conditions. The camera’s optical source and exposure condition are critical for image capturing; hence, a 200W LED flood light was used to get a better image of the soil. The full DIC experimental setup is shown below in Fig. 3c. In implementing the 2D DIC processing, the calculation area (i.e., area of interest, AOI) in the reference image should be specified or defined first, further divided into evenly spaced virtual grids. The position of the deformed subset is determined. The differences in the positions of the reference subset centre and the target subset centre yield the in-plane displacement vector at point P. Based on these testing conditions, the displacement and strains developed within the slope were estimated.
274
S. K. Jeeva et al.
Fig. 3 a Slope with beans for image detection b speckled model structure c complete digital image correlation setup
3 Testing Condition In this study, a series of repeated shaking loading were given to the prepared slope to estimate the slope-structure interaction in partially saturated condition. To achieve this, repeated incremental acceleration loading of 0.1, 0.2, 0.3, and 0.4 g at 5 Hz frequency replicating low to severe earthquake intensity was selected with 200 cycle simulating longer shaking duration [11], as shown in Fig. 4. During testing, the subsequent incremental acceleration load was given to the ground bed only after complete dissipation of pore pressure generated during the previous loading which was monitored by the pore pressure transducers installed at a different depth within the slope.
4 Numerical Modelling In addition to experimental testing, studies on numerical modelling to validate the obtained test results also attempted in this study. To achieve this, objective FLAC 3D software was used. The model slope was created by generating two bricks, a base and a slope, as shown in Fig. 5. Then, the interface was given between the faces to make a uniform slope. The Mohr–coulomb constitutive model was selected and given for the model, and a plate load was given at the top to simulate structural load. Further, fluid properties, fixity conditions, and soil properties were defined. In FLAC3D, the dynamic input can be given in terms of acceleration, velocity, and stress ratio. Hence, acceleration input in a sinusoidal wave pattern (0.1 g), as shown in Fig. 4, was given to the model. The DIC results have been validated with FLAC3D and discussed in the following section.
Performance Evaluation of Partially Saturated Slope Subjected …
275
Fig. 4 Time history of the input motion a 0.1 g; b 0.2 g; c 0.3 g; d 0.4 g [11]
Fig. 5 Slope model
5 Results and Discussion In this study, settlement and acceleration response of the slope, structural response (lateral displacement), and development of pore water pressure under repeated shaking events were monitored and compared. The observations on these parameters are discussed below.
276
S. K. Jeeva et al.
Fig. 6 a Soil settlement contour from DIC b peak soil settlement versus input ground motion
5.1 Slope Settlement Using 2D-DIC The slope settlement was estimated using the 2D-digital image correlation technique based on the obtained images taken during shaking. Due to the longer shaking duration, the slope started to displace in both horizontal and vertical directions. The horizontal displacement of the soil mass on the slope resulted in a reduction in soil shear strength, causing displacement in the lateral direction and settlement in the longitudinal direction. Figure 6a below shows a typical vertical settlement contour for the slope at 0.2 g ground motion condition. This image was extracted during the analysis of DIC by VIC-2d software. The contour verified the disturbances induced during shaking event. Due to this, soil confinement reduces at shallow depth causing increased soil displacement and settlement. Further, the displaced soil increased the overburden stress at deeper depths. Figure 6b shows the peak settlement of soil mass after 0.1, 0.2, and 0.3 g input motion at six different portions on the slope. The initial densification observed during 0.1 g shaking influenced the rate of settlement in the subsequent loading, i.e., 0.2 g as evident from Fig. 6b which showed comparatively lesser displacement and settlement. However, during 0.3 g input motion, the soil loses its maximum shear strength due to repeated incremental longer shaking events together with the continuous generation of pore water pressures from bottom to top and resulting in increment in lateral displacement on top soil and adjacent structure. After 0.4 g, the soil mass ultimately losses its shear strength, leading to the failure of the slope and structure. About 47% to 75% increment in slope displacement was observed during repeated shaking.
5.2 Acceleration Response on the Slope The acceleration response of the soil was taken from the accelerometer transducer placed at the face of the slope. The positioning of the transducers was shown in Fig. 1b. Four accelerometers AT1, AT2, AT3, and AT4 were used for monitoring
Performance Evaluation of Partially Saturated Slope Subjected …
277
Fig. 7 Peak acceleration response versus input ground acceleration
acceleration response at 400 mm and 600 mm depth from the bottom respectively. Figure 7 presents the peak acceleration response of the slope when subjected to repeated input motion of 0.1, 0.2, 0.3, and 0.4 g. Out of the installed four transducers, accelerometers AT1 and AT3 got malfunctioned during testing. Based on the response obtained from the other two accelerometers, the plot has been prepared and presented. It can be seen that the dynamic response was not uniform along the slope. As discussed in the previous section, the longer shaking event induces displacement of soil at shallow depths causing uneven densification during initial loading. Due to this, the response found increases from bottom to top. Similar results have been found in [18, 19], where the author’s concluded that slope-reflected waves induce amplification near the crest. This is found evident during repeated shaking events, where AT4 (shallow depth) experiences more acceleration response (i.e., about 16– 76% higher) compared to AT2 (deeper depth). This evidenced that the induced densification at the bottom portion of the slope results in reduction in acceleration response at the deeper depth.
5.3 Structure Response During Repeated Shaking Events In this study, an attempt has been made to evaluate the slope-surface structure interaction during repeated shaking events. Figure 8a shows the structural displacement obtained during repeated shaking. As shown in Fig. 2, a G + 3 structure is placed in the crest position for understanding its behaviour during repeated shaking events. The induced incremental acceleration response on the slope during repeated shaking events affects the stability of the structure, as observed in Fig. 8a. With the increment in acceleration intensity, the structure displacement also increases.
278
S. K. Jeeva et al.
Fig. 8 a Peak storey displacement of the ground, first, second, third floor and roof versus input ground acceleration b storey displacement of the ground, first, second, third floor and roof versus number of images with the contour of structure along the lateral direction
As discussed, slope reflected waves cause displacement in the installed model structure causing continuous displacements during repeated loading, which is found evident from the obtained acceleration response. For estimating the acceleration response of the structure at different height, the obtained velocity–time domain results in DIC were differentiated using data analysis software. It can be seen that the acceleration amplification increases with the height of the structure causing continuous structural displacement. Figure 8b shows a typical obtained peak acceleration value. As discussed, the induced displacement in soil at shallow depth amplifies the acceleration response which increases the acceleration response of the structure. Comparatively, about 33–64% increment in acceleration was observed during repeated loading from bottom to top. The obtained structural acceleration response highlighted that, when the partially saturated slope is subjected to repeated shaking events occurrence of soil displacement and non-uniform densification at shallow depth disturbs the confinement characteristics of the slope. When the slope was subjected undrained repeated loading, the stability of slopes and structure affected causing slope failures at higher acceleration loading.
5.4 Pore Pressure Response During repeated shaking events, pore water pressure generation was measured using the strain-based transducer placed at 200 and 400 mm depth as shown in Fig. 9a. The obtained peak pore water pressure developed during repeated shaking at different depths is shown in Fig. 9b. It can be seen that the generation of pore water pressures was not significant in this experimental study. During the 0.1 g shaking condition, both PT1 and PT2 showed comparatively higher pore water pressures than PT3 and PT4 installed at shallow depths due to occurrence of soil densification during longer shaking duration. However, during 0.2–0.4 g repeated shaking events, PT3
Performance Evaluation of Partially Saturated Slope Subjected …
279
Fig. 9 a Transducer location b peak pore pressure of transducer versus input ground acceleration
(shallow depth) and PT4 (adjacent to slope) showed a higher generation of pore water pressure due to the displacement of soil particles at shallow depth together with uneven densification after shaking, which results in increment in pore pressure generation than PT1 and PT2. Similarly, the induced horizontal displacements at shallow depth develop tension crack, which facilitates the dissipation of generated pore water pressures in the subsequent shaking events. With repeated shaking, the crack widened due to water infiltration and generation of pore water pressures from bottom to top, which affects the stability of the slope. The observed displacement during repeated shaking validates the instability in slope conditions, and failure was observed at 0.4 g shaking conditions. The development of pore water pressures during the study clearly elucidates the requirement of drainage member in slope stabilization especially during repeated shaking events. The continuous increment (or widening) in the drainage path (i.e., cracks in this study) developed by the generated pore water pressures during repeated shaking reduces the stability of the slope and causes failure at higher acceleration shaking events. A typical crack pattern developed during the study and induced structural failure is shown in Fig. 10a and b, respectively.
Fig. 10 a Failure at 0.4 g acceleration load b crack at the surface of the crest
280
S. K. Jeeva et al.
Fig. 11 a Vertical displacement from DIC b vertical displacement from FLAC3D c vertical settlement comparison between DIC and FLAC3D
5.5 Numerical Modelling An attempt has been made in this study to compare the displacement profiles of the slope obtained in FLAC3D and with the digital image correlation results for verifying the performance of the non-contact based instrumentation system and vice versa. The model slope developed was subjected to 0.1 g acceleration loading to compare the numerical results. Only vertical displacement is considered for comparison. For this, five points A, B, C, D, and E as shown in Fig. 11c, were selected from DIC (Fig. 11a) and similar in FLAC3D (Fig. 11b) model was used for comparing vertical displacement, and the results are shown in Fig. 11c. It can be seen that the prediction between both DIC and FLAC3D fairly matches well, suggesting that the developed numerical model can predict the experimental test results. Also, the use of 2D DIC was found effective in non-contact-based instrumentation measurements.
6 Conclusion In this study, a partially saturated slope was subjected to repeated seismic load with a G + 3 building in the vicinity of the crest to estimate the behaviour of slopestructure interaction through experimental investigations. Based on the observations, the following conclusions were given below. • Occurrence of repeated shaking affects the soil confinement at shallow depth and induces horizontal displacement continuously. Due to this, uneven densification was observed at the end of shaking which increases the increment in overburden stress at deeper depths and affects the stability of soil at shallow depth
Performance Evaluation of Partially Saturated Slope Subjected …
281
• The acceleration amplification increases from bottom to top due to the disturbances induced at shallow depth. Further, the rate of acceleration amplification from bottom to top also increases during repeated incremental acceleration loading. About 16–76% increment in acceleration amplification was observed during 0.1–0.4 g shaking which affects both the slope and the structural stability. • The uneven densification together with acceleration amplification develops tension cracks at shallow depth due repeated shaking. Due to this, an inappropriate drainage path was developed during repeated loading which facilitates the removal of sand fines as a result of generated pore water pressures. This resulting in continuous crack widening and soil displacement. • In partially saturated slope, the instability was mainly caused by disturbances in soil mainly due to uneven settlement which reduces the strength of the soil. This reduction increases with increment in shaking. The study highlighted that, in spite of observed densification during initial shaking condition, i.e., 0.1 g, the subsequent incremental repeated shaking induces horizontal displacements which minimized soil confinement and due to acceleration amplification slope instability was observed. Due to this structural failure was observed at higher shaking event. Considering the above, the research work highlights the need for proper slope reinforcement measures together with drainage for slope stability improvement especially during repeated shaking events. Acknowledgements The authors would like to thank the Director, CSIR-Central Building Research Institute, Roorkee, for giving the opportunity and support to publish this research.
References 1. Nandargi, S., Gaur, A., Mulye, S.S.: Hydrological analysis of extreme rainfall events and severe rainstorms over Uttarakhand, India. Hydrol. Sci. J. 61(12), 2145–2163 (2016) 2. Cruden, D.M.: A simple definition of a landslide. Bull. Int. Assoc. Eng. Geology-Bulletin de l’Association Internationale de Géologie de l’Ingénieur 43(1), 27–9 (1991) 3. Keefer, D.K.: Statistical analysis of an earthquake-induced landslide distribution—the 1989 Loma Prieta, California event. Eng. Geol. 58(3–4), 231–249 (2000) 4. Arvin, M.R., Askari, F., Farzaneh, O.: Seismic behavior of slopes by lower bound dynamic shakedown theory. Comput. Geotech. 39, 107–115 (2012) 5. Sepúlveda, S.A., Murphy, W., Jibson, R.W., Petley, D.N.: Seismically induced rock slope failures resulting from topographic amplification of strong ground motions: the case of Pacoima Canyon, California. Eng. Geol. 80(3–4), 336–348 (2005) 6. Jibson, R.W., Harp, E.L.: Ground motions at the outermost limits of seismically triggered landslides. Bull. Seismol. Soc. Am. 106(2), 708–719 (2016) 7. Marc, O., Meunier, P., Hovius, N.: Prediction of the area affected by earthquake-induced landsliding based on seismological parameters. Nat. Hazard. 17(7), 1159–1175 (2017) 8. Rodrıguez, C.E., Bommer, J.J., Chandler, R.J.: Earthquake-induced landslides: 1980–1997. Soil Dyn. Earthq. Eng. 18(5), 325–346 (1999) 9. Bommer, J.J., Rodr´ıguez, C.E.: Earthquake-induced landslides in Central America. Eng. Geol. 63(3–4), 189–220 (2002)
282
S. K. Jeeva et al.
10. Uzuoka, R., Sento, N., Kazama, M., Unno, T.: Landslides during the earthquakes on May 26 and July 26, 2003 in Miyagi, Japan. Soils Found. 45(4), 149–163 (2005) 11. Padmanabhan, G., Shanmugam, G.K.: Reliquefaction assessment studies on saturated sand deposits under repeated acceleration loading using 1-g shaking table experiments. J. Earthq. Eng. 26(6), 2888–2910 (2022) 12. Verma, M., Singh, R.J., Bansal, B.K.: Soft sediments and damage pattern: a few case studies from large Indian earthquakes vis-a-vis seismic risk evaluation. Nat. Hazards 74(3), 1829–1851 (2014) 13. Lin, C.W., Liu, S.H., Lee, S.Y., Liu, C.C.: Impacts of the Chi-Chi earthquake on subsequent rainfall-induced landslides in central Taiwan. Eng. Geol. 86(2–3), 87–101 (2006) 14. Tang, C., Zhu, J., Li, W.L., Liang, J.T.: Rainfall-triggered debris flows following the Wenchuan earthquake. Bull. Eng. Geol. Env. 68(2), 187–194 (2009) 15. Shabani, M.J., Shamsi, M., Ghanbari, A.: Slope topography effect on the seismic response of mid-rise buildings considering topography-soil-structure interaction. Earthq. Struct. 20(2), 187–200 (2021) 16. Zhao, C., Valliappan, S.: Seismic wave scattering effects under different canyon topographic and geological conditions. Soil Dyn. Earthq. Eng. 12(3), 129–143 (1993) 17. Bhattacharya, S., Lombardi, D., Dihoru, L., Dietz, M.S., Crewe, A.J., Taylor, C.A.: Model container design for soil-structure interaction studies. In: Role of Seismic Testing Facilities in Performance-Based Earthquake Engineering. Springer, Dordrecht, pp. 135–158 (2012) 18. Pan, B., Qian, K., Xie, H., Asundi, A.: Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Measure. Sci. Technol. 20(6), 062001 (2009) 19. Chu, T.C., Ranson, W.F., Sutton, M.A.: Applications of digital-image-correlation techniques to experimental mechanics. Exp. Mech. 25(3), 232–244 (1985)
Numerical Study on One-Dimensional Aperiodic Foundations for Seismic Isolation of Structures Sanjay R. Kumawat, Sumiran Pujari, Manish Kumar, and Arghadeep Laskar
Abstract The concept of frequency band gaps in the wave propagation physics of crystalline solids has suggested the possibility of attenuating and filtering seismic waves with the provision of a periodic foundation. One-dimensional periodic foundations are basically an ordered arrangement of material layers of constant thickness repeated in a particular sequence. The periodicity of these foundations prevents the destructive seismic waves from reaching the superstructure. Despite numerous benefits of these foundations over conventional earthquake-resistant design techniques, past research has highlighted the limitation with the starting frequency and range of frequency band gaps over which these can be effective for seismic applications. The periodic foundation intended for seismic application needs to have a low starting frequency and wide frequency bandgap (typically between 0 and −20 Hz). However, it has been observed that the reduction in the starting frequency is accompanied by a reduction in the bandgap as well. This paper proposes the idea of using an aperiodic, instead of the periodic, arrangement of material layers in such foundations that can result in wider attenuation frequency ranges including a better lower starting frequency closest to earthquake ground motion. The aperiodicity refers to the irregularity induced due to the varying thicknesses of alternate rigid and softer layers arranged in the foundation. The idea is to take advantage of Anderson’s theory of localization in disordered systems. A detailed comparative study has been carried out on periodic and aperiodic foundations, and the possibility of reliable outcomes for the application in seismic isolation has been discussed. S. R. Kumawat (B) · M. Kumar · A. Laskar Department of Civil Engineering, IIT Bombay, Bombay, India e-mail: [email protected] M. Kumar e-mail: [email protected] A. Laskar e-mail: [email protected] S. Pujari Department of Physics, IIT Bombay, Bombay, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_23
283
284
S. R. Kumawat et al.
Keywords Aperiodic foundations · Anderson’s theory · Phononic crystals
1 Introduction The meta-material-based isolation systems, also commonly known as “periodic foundations” have been a topic of research for many years due to their wave filtering capability without significant physical deformation of the systems in which they are implemented. Unlike conventional isolation systems such as the elastomeric rubber bearing, friction pendulum bearing, and sliding bearings, the periodic foundation does not produce large deformations or residual displacements at the substructure and superstructure interface. The periodic foundations are classified into one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) periodic structures based on their directions of periodicity. The theory of periodicity in a system can be understood by vaguely discretizing a continuous system into a chain of spring-mass systems. This discretization of a continuous system produces periodic velocity-dependent frequency-wavenumber relation. The replacement of the single mass discretization of continuous systems with two mass discrete periodic systems creates two branch frequency-wavenumber relations showing frequency stop bands and pass bands [1]. The working mechanism of the stop bands is well explained by the Bragg scattering mechanism and local resonance mechanism for 1D periodic foundations and 2D, 3D periodic foundations, respectively [2]. The propagation of the waves is hindered in the stop band region of frequencies thereby exponentially reducing the response, while the wave can still freely propagate through the pass band without any alteration. The periodic foundations are effective only when the wave filtering stop bands of such foundations fall into the predominant frequency content of earthquake ground motions [3, 4]. Many researchers have carried out parametric studies to show the effect of geometric and material properties on the starting frequency and stop band of the periodic foundations [5, 6]. Due to the limitation in the availability of materials, to achieve the desired frequency range the dimensions of the foundations increase tremendously. Thus, this paper presents an attempt to reduce the starting frequency of the stop band and suppress the response in the passbands by adopting the concept of electron diffusion in disordered solids. Anderson [7] showed that the metallic conduction in disordered solids can be limited by localizing the electron eigenstates. This concept of localization due to irregularities in solids was extended to the field of structural dynamics. The propagation of the wave in a disordered elastic structural system is confined to a small region near the source. This confinement of the vibration near the source is termed as mode localization which prevents the wave propagation at a long range within the solids. The mode localization works similar to that of damping but is not associated with any energy dissipation in the system. Hodge [8] has illustrated the confinement phenomenon qualitatively as well as quantitatively by using the mechanical models namely coupled pendula and vibrating strings, respectively.
Numerical Study on One-Dimensional Aperiodic Foundations …
285
An experimental demonstration of the mode localization in disordered solids was carried out by Hodge et al. [8] by using a stretched string with masses attached to it. The experimental results showed a good correlation with the theoretical study. Pierre et al. [9] developed a perturbation method for obtaining the localized mode of vibration for a disordered system from the individual modes of vibrations. Xie et al. [10] numerically studied the mode localization in a randomly disordered large periodic planar truss and found the localization phenomenon to be significant as no structure can be made perfectly periodic. Thus, it is well known that the mode localization phenomenon due to the presence of irregularities in the periodic pattern of the structural system acts like a barrier to the injected wave energy and confines it to a small region of the system. Now this concept of disorder in the solids has been applied to the one-dimensional periodic foundation in the present study to make it aperiodic and to investigate its effect on the starting frequency and stop band width. An aperiodic foundation with alternate steel and rubber layers of varying thicknesses has been adopted in the present study. The thickness of the layers has been selected in a uniformly random manner. The transfer matrix method has been used to find the steady-state response of the aperiodic foundation. The detailed design approach of an aperiodic foundation is discussed in Sects. 2 and 3.
2 Proposed Aperiodic Foundation The present study proposes an aperiodic foundation that replicates disordered solids with some degree of randomness in the regular periodic arrangements. The goal here is to take advantage of the mode localization phenomenon which limits the propagation of vibration over a small region near the source thereby reducing the overall response exponentially. The literature shows that the chances of mode localization are higher with a stronger variation of disorder in the solids [8, 9]. Thus, instead of introducing mild impurity in 1D periodic foundation with few random thickness layers, the foundation would be analysed for completely randomized layer thicknesses i.e. all the alternate rigid and softer layers of the foundation will have completely random thicknesses. Schematic diagrams of the periodic and the adopted aperiodic foundation are shown in Fig. 1. The properties of steel and rubber materials for alternate rigid and softer layers to be arranged in a 1D foundation considered in the present study are shown in Table 1. Steel is used for rigid layers instead of concrete due to its better attenuation properties. The thicknesses of the layers in the aperiodic foundation are selected uniformly randomly from a set of different cases as discussed in Sect. 3. The comparative output/input response of the aperiodic foundation was evaluated using the transfer matrix method. The transfer matrix method has been commonly used for the calculation of starting frequency and stop bands in 1D periodic foundations. The wave transfer from one layer to another layer in a unit cell has been evaluated using the transfer matrices. Thereafter, Bloch-Floquet’s theorem (infinite boundary conditions) has been used to get the stop bands in an ideal infinitely extended 1D periodic foundation. The
286
S. R. Kumawat et al.
u t, ζ t
u t, ζ t
hn
Steel
h4
h2 h1
Rubber
h3 h2 h1
h2 h1
u b, ζ b
Incident wave
u
(a)
b,
ζ
b
Incident wave
(b)
Fig. 1 a Periodic arrangement of layers b aperiodic arrangement of layers
Table 1 Material properties
Material
E (MPa)
Density (kg/m3 )
Poisson’s ratio
Steel
2 × 105
7850
0.3
Rubber
0.1586
1277
0.463
infinite boundary conditions cannot be used for the aperiodic problem due to the randomization of the layer thicknesses. Thus, the transfer matrices connecting the top and bottom fields of the foundations [Eq. (1)] have been arranged to get the ratio of the out-to-input response [Eq. (2)] for identifying the attenuation zones. The detailed formulation of the transfer matrix can be referred to in Zhao et al. [3].
ut τt
T11 T12 = T21 T22
ub τb
(1)
where ut and ub are the top and the bottom displacement fields, τ t and τ b are the top and the bottom stresses, T ij are elements of the transfer matrix. At the top surface, τ t = 0 t u = T11 − T12 T21 ub T22
(2)
Equation (2) gives the comparative output/input response of the 1D foundation which can be used for plotting the frequency response curve (FRF). The stop bands and pass bands can be predicted from FRF.
Numerical Study on One-Dimensional Aperiodic Foundations …
287
3 Aperiodic Arrangements and Attenuation Results The aperiodicity in the 1D foundation is introduced by adopting five different combinations of thicknesses selected randomly from an assumed set of values both for steel and rubber. Each combination of thicknesses selected randomly from a set has been repeated for ten different trials and the corresponding FRFs have been plotted. The results of the ten trials are then used to plot find the deviation at each frequency point. An error graph has been plotted for each case which shows the deviation of FRFs in the form of a band. Finally, the weighted average of the FRFs has been compared with the FRF of an equivalent average heightened periodic foundation. The set of thicknesses selected has been uniformly spaced between a particular range and has been presented in the form m:s:n i.e. the thickness ranges between m and n equally spaced by a constant value s. For the first case, an aperiodic foundation of 50 layers with steel and rubber having thickness varying between 50:50:500 in millimeter has been adopted. The FRF for this case has shown that the aperiodic arrangement gives wider frequency stop bands compared to that of the periodic arrangement. This can be ascribed to the mode localization effects in the response as a result of the irregularity in the layer arrangement. The starting frequency has also lowered for the aperiodic case. The aperiodic arrangement of the first case has shown a low starting frequency of 1.6 Hz with a wide stop band of 65 Hz (refer to Fig. 2 Case 1). However, the average height of the foundation for this case is 14.9 m which is impractical. Also, the thickness of the rubber used in this case is not feasible from the stability point of view. Thus, for further cases, the rubber height has been limited to 15 mm, to keep a higher shape factor for better stability. In the second trial, the steel and rubber thicknesses have been varied from 10:10:100 mm and 1:1:15 mm, respectively with a total of fifty layers. A starting frequency of 32 Hz has been obtained for the aperiodic arrangement compared to a starting frequency of 40 Hz in the periodic case with an average foundation height of 1.56 m which is acceptable at construction sites (refer to Fig. 2 Case 2). It has been realized that higher thickness of the rubber layers would be required to further lower the starting frequency. Hence, the rubber layer thicknesses have been varied from 10:1:15 (still limiting the overall height of rubber layers to 15 mm) for the same variation in steel thickness and same total 50 number of layers. Starting frequencies of 27 Hz and 32 Hz have been obtained for the aperiodic and periodic arrangement, respectively for 1.68 m height of foundation (refer to Fig. 2 Case 3). In the fourth and fifth trials, the thickness of the steel layers has been varied (since the height of the rubber is limited due to the bulging issues). The steel thickness has been varied with a range of 20:20:200 mm, while still keeping the rubber thickness variation to 10:1:15 mm. Since the thicknesses of steel are higher for this case, the number of layers has been limited to 30 (to restrict the total height of the foundation). Starting frequencies of 18 Hz and 23 Hz have been obtained for the fourth trial for the aperiodic and periodic cases, respectively with an average height of 1.72 m (refer to Fig. 2 Case 4). Finally, the same variation of the fourth trial has been repeated in the fifth trial with a fixed base steel layer of 500 mm. Starting frequencies of 13 Hz and 20 Hz
288
S. R. Kumawat et al.
Case 1: n = 50, Steel-50:50:500 & Rubber-50:50:500, havg = 14950 mm 0
0
Normalized Amplitude
10
-10 -20
-20
10
-30 -40
10
-40 -50
-60
10
0
20
40
60
80
-60
100
0
20
40
60
Frequency (Hz)
Frequency (Hz)
(a)
(b)
80
100
0
Normalized Amplitude
10
-20
10
-40
10
Aperiodic Periodic -60
10
0
20
40
60
80
100
Frequency (Hz) (c)
Fig. 2 a FRFs for ten trials of material thicknesses selected uniformly randomly from chosen set b error plot showing band of FRF c average FRF plot of ten trials for periodic and aperiodic arrangements
have been obtained for the fifth trial for the aperiodic and periodic arrangements, respectively with an average foundation height of 2.25 m (refer to Fig. 2 Case 5). The aperiodic arrangement configurations and the results are summarized in Table 2. It is clear from all five cases that the stop bandwidth reduces with the reduction in the starting frequency. The bandgaps are calculated considering the frequency results only up to 100 Hz, as higher frequencies are unlikely to induce any damage a civil structure. The starting frequency has been also lowered for the aperiodic cases. Also, the error plots of all five cases show that the method adopted for randomization of the layer won’t change the starting frequency much for any randomly selected set and will remain within the thin error band as indicated in Fig. 2c.
Numerical Study on One-Dimensional Aperiodic Foundations …
289
Case 2: n = 50, Steel-10:10:100 & Rubber-1:1:15, havg = 1560 mm 10
Normalized Amplitude
10
0 -5
0
10
-10 -10
10
-15 -20
-20
10
-25 -30
-30
10
0
20
40
60
80
100
0
20
Frequency (Hz)
40
60
80
100
Frequency (Hz)
(a)
(b) 0
Normalized Amplitude
10
-20
10
Aperiodic Periodic -40
10
0
20
40
60
80
100
Frequency (Hz) (c)
Fig. 2 (continued)
4 Summary and Conclusion The purpose of this study was to enhance attenuation characteristics of meta-materialbased periodic foundation. The problem with periodic foundation was the dimensions of the foundation increased to unrealistic values (not feasible for construction) and the width of the stop band also reduced in the attempt to lower the starting frequency. The only way to limit the size of the foundation with a lower starting frequency and a wider stop band is to use a rigid layer of high-density material and a softer layer of low-shear modulus material which again is not possible from a material availability perspective. The concept of mode localization in disordered solids was extended from the metallic conduction phenomenon in solid-state physics and other contexts such as optical and acoustic wave propagation in metamaterials to the propagation of mechanical vibrations in structural dynamics at civil engineering scale in the present study. The mode localization phenomenon was introduced in the periodic
290
S. R. Kumawat et al.
Case 3: n = 50, Steel-10:10:100 & Rubber-10:1:15, havg = 1680 mm 10 0
Normalized Amplitude
10
0
-10 -20
10
-20
-30 -40
-40
10
0
20
40
60
80
0
100
20
40
60
Frequency (Hz)
Frequency (Hz)
(a)
(b)
80
100
0
Normalized Amplitude
10
-20
10
Aperiodic Periodic -40
10
0
20
40
60
80
100
Frequency (Hz) (c)
Fig. 2 (continued)
foundation by making it aperiodic. The aperiodic foundation no longer consists of repetitive rigid and softer layers of constant thickness but has alternate layers of any random thicknesses. A strong variation in the disorder was chosen to achieve higher chances of mode localization which prevents the wave propagation to a farther distance from the source. The material layer thicknesses within the aperiodic foundations were selected uniformly randomly from an equally spaced set of thicknesses. Based upon the attenuation results, the set of material thicknesses was selected taking care of the overall height of the foundation and instability issues. However, in the future, more advanced ways of selecting the material layer thicknesses can be used. The FRFs were plotted for ten trials of randomly selected thicknesses, and an error graph of the FRF was plotted, showing the deviation of FRF values. Thereafter, the weighted average of the ten FRF plots was compared with the equivalent periodic arrangement
Numerical Study on One-Dimensional Aperiodic Foundations …
291
Case 4: n = 30, Steel-20:20:200 & Rubber-10:1:15, havg = 1720 mm 0
0
Normalized Amplitude
10
-5 -10
-10
10
-15 -20
-20
10
-25 -30
-30
10
0
20
40
60
80
100
0
20
40
60
Frequency (Hz)
Frequency (Hz)
(a)
(b)
80
100
0
Normalized Amplitude
10
-10
10
-20
10
Aperiodic Periodic -30
10
0
20
40
60
80
100
Frequency (Hz) (c)
Fig. 2 (continued)
of the averaged aperiodic case. The exercise was repeated for five different sets of material thicknesses. Major conclusions observed in the study are: 1. Wider frequency stop bands and lower starting frequency confirms the mode localization phenomenon in aperiodic foundations. 2. The aperiodic foundations intend to show a lower starting frequency compared to the equivalent periodic foundation of similar content of material and geometric properties. 3. Zero stop band frequency can be achieved using an aperiodic arrangement with higher material thicknesses. Thus, the aperiodic foundations are beneficial compared to the periodic foundations in the view of achieving lower starting frequency and wider stop bands.
292
S. R. Kumawat et al.
Case 5: n = 30, Steel-20:20:200 & Rubber-10:1:15 with fixed base steel layer of 500 mm, havg = 2250 mm
Normalized Amplitude
10
0
0
-5 10
-10
-10
-15 10
-20
-20 -25
10
-30
0
20
40
60
80
-30
100
0
20
40
60
Frequency (Hz)
Frequency (Hz)
(a)
(b)
Normalized Amplitude
10
10
100
10
10
10
80
0
-10
-20
Aperiodic Periodic
10
-30
0
20
40
60
80
100
Frequency (Hz) (c)
Fig. 2 (continued) Table 2 Analysis results Case No. of Steel no. layers thickness set (mm)
Rubber thickness set (mm)
Average Starting frequency Stop band width height of (Hz) (Hz) the Periodic Aperiodic Periodic Aperiodic foundation (mm)
1
50
50:50:500
50:50:500 14950
2.6
1.6
97.4
98.4
2
50
10:10:100
1:1:15
1560
40
32
60
68
3
50
10:10:100
10:1:15
1680
32
27
68
73
4
30
20:20:200
10:1:15
1720
23
18
77
82
5
30
20:20:200, 10:1:15 500fixed
2250
20
13
80
87
Numerical Study on One-Dimensional Aperiodic Foundations …
293
5 Future Scope The current study is just an indication of various advantages of aperiodic arrangements of layers over periodic arrangement in meta-material-based isolation systems. However, some future study would be required to make the foundations useful for practical applications. Some of the work that can be carried out are as follows: 1. The selection of randomized material thicknesses should be optimized for lower starting frequency and wider stop bands. 2. Numerical models of finite-sized aperiodic foundations have to be simulated to observe the effect of plan size. 3. Time history analysis using real-time ground motion on an aperiodic foundation has to be carried out.
References 1. Romeo, F., Ruzzene M., eds.: Wave Propagation in Linear and Nonlinear Periodic Media: Analysis and Applications, Vol. 540. Springer Science & Business Media (2013) 2. Kaina, N., Fink, M., Lerosey, G.: Composite media mixing Bragg and local resonances for highly attenuating and broad bandgaps. Sci. Rep. 3, 3240 (2013) 3. Zhao, C., Zeng, C., Witarto, W., wen Huang, H., Dai, J., Mo, Y.L.: Isolation performance of a small modular reactor using 1D periodic foundation. Eng. Struct. 244, 112825 (2021) 4. Xiang, H.J., Shi, Z.F., Wang, S.J., Mo, Y.L.: Periodic materials-based vibration attenuation in layered foundations: experimental validation. Smart Mater. Struct. 21(11), 112003 (2012) 5. Jain, S., Shaik, A.V., Laskar, A., Alam, A.: Application of innovative one-dimensional periodic isolation systems for seismic response reduction of bridges. Adv. Struct. Eng. 23(7), 1397–1412 (2020) 6. Witarto, W., Wang, S.J., Nie, X., Mo, Y.L., Shi, Z., Tang, Y., Kassawara, R.P.: Analysis and design of one dimensional periodic foundations for seismic base isolation of structures. Int. J. Eng. Res. Appl. 6(1), 5–15 (2016) 7. Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109(5), 1492 (1958) 8. Hodges, C.H.: Confinement of vibration by structural irregularity. J. Sound Vib. 82(3), 411–424 (1982) 9. Pierre, C., Dowell, E.H.: Localization of vibrations by structural irregularity. J. Sound Vibrat. 114(3), 549–564 (1987) 10. Xie, W.-C.: Vibration mode localization in disordered large planar lattice trusses. Chaos, Solitons Fractals 8(3), 433–454 (1997) 11. Hodges, C.H., Woodhouse, J.: Vibration isolation from irregularity in a nearly periodic structure: theory and measurements. J. Acoust. Soc. Am. 74(3), 894–905 (1983)
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: An Analytical Approach for Natural Frequency Estimation Somya Ranjan Patro , Arnab Banerjee , and G. V. Ramana
Abstract With the increasing demand for renewable harvested energy, the size of the turbine blade keeps on increasing which makes the turbine tower much taller and slender. Owing to the advantage of stable wind velocity and space availability, the offshore wind turbines have become prevalent. Wind turbine tower undergoes various dynamic loading in regular operation such as rotor excitation (1P), vibration due to passing of blade (3P), in addition to wind, storm, wave (in case of offshore) and earthquake. Thus, estimation of natural frequency of a wind turbine is of utmost importance to avoid any frequency matching with the regular excitation, 1P and 3P. In this paper, a transfer matrix-based analytical methodology has been proposed to estimate the natural time period of an offshore wind turbine with a mono-pile foundation. Fluid–structure interaction has been incorporated within the study by using hydrodynamic mass throughout the length of transition piece and monopile, and soil-structure interaction has been considered by providing linear elastic p–y springs throughout the length of monopile. A complete parametric study has been considered which shows the dependency of natural frequency on the various geometric and material properties of both tower and monopile, and the material properties of soil. The natural frequency was found to be significantly affected by soil properties, which shows the importance of soil-structure interaction in the design of offshore structures. Keywords Wind turbine · Natural frequency · Transfer matrix
S. R. Patro (B) · A. Banerjee · G. V. Ramana Indian Institute of Technology, Delhi, New Delhi 110016, India e-mail: [email protected] A. Banerjee e-mail: [email protected] G. V. Ramana e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_24
295
296
S. R. Patro et al.
1 Introduction For accepting more stringent emission reduction target towards the decarbonation and fossil reduction, all countries are investing on the projects in line with renewable, clean and green energy. Wind energy harvesting is one of the valuable alternatives in the sector of renewable energy; therefore, the research on offshore and onshore wind turbine proliferates in recent years. Horizontal Axis Wind Turbines (HAWT) are being increasingly preferred over Vertical Axis Wind Turbine (VAWT) owing to its high altitude and perseverance of stable wind flow [1]. In late eighties, the capacity of wind turbine was about 65 kW, and as of today with the advancement of technology, 5 MW wind-turbine are being successfully installed in which the height and the mass of the rotor nacelle assembly (RNA) have been increased from 21.9 m and 4.3 ton [2, 3] to 90 m and 350 ton [4], respectively. Basically, the tower height has been increased to accommodate longer blades which can provide larger swept area. Generated power is proportional to the swept area and the cube of the velocity of wind [5]; thus, increasing the height of wind turbine is of utmost importance. The strong winds, storms or earthquakes are not every day loading, but a wind turbine goes through several cyclic loading on a regular basis due to operating wind speed, 1P (rotor frequency) and 3P (blade passing frequency) [6, 7]. Three bladed wind turbines are found to be the most economical choice for wind energy harvesting. Due to the imbalance in the rotor mass and aerodynamic excitation caused by differences in the pitch of individual blades, a wind turbine is subjected to rotor excitation [8]. In addition to that, wave loading [9] also effects on an offshore wind turbine. Typical range of wave and rotor excitation lies approximately between 0.1 and 0.2 Hz [5] or 0.63–1.27 rad/s range, and the 3P frequency range is almost three times the rotor frequency [4, 10]. That means, frequency range for 3P excitation lies between 0.3 and 0.6 Hz or 1.88–3.77 rad/s. For simulating wave and wind loading, JONSWAP and Kaimal spectrum are widely used [11]. In addition to these, torque and the speed of the blade may also vary due to the electrical faults in the wind turbines [12, 13]. Generally, natural frequencies of wind turbines are close to the different forcing frequencies of dynamic loads imposed on them [10]. The objective of the design of the tower structure is to keep the natural frequency of the complete wind-turbine tower outside the band of 1P and 3P excitation to avoid any resonance [5, 7, 14, 15]. The stiffness of soil and foundation play an important role in estimating the natural frequency of the wind turbine tower. Due to the flexibility of the foundation, time period of the structure increases. Also, the natural frequencies are strongly dependent on the shear strain level in the soil next to the pile. Accumulation and repeated shear strains may also reduce the stiffness of soil as highlighted by [16]. Yu et al. [17] demonstrated that the natural frequency of the wind turbine structure increases with the cyclic load cycles, but the rate of increase is reduced with accumulated soil strain. Pile-soil structure interaction is typically modelled as either series of horizontal p-y springs [18]–[20] or Kelvin element along the depth of the pile or by horizontal, vertical and rotational spring at the bottom end [6, 7]. For wind turbines installed in sandy seabed, dynamic forces may cause stiffness degradation or induce
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: …
297
liquefaction of the foundation soil. A wind turbine is typically subjected to 32,000 to 172,000 cycles of loading in its lifespan of 25–30 years [10]. Thus, very little is known about long-term soil foundation structure interaction. The dynamic response of wind turbine foundation is dependent on loading type, pile installation method, soil properties, pile embedment length and pile/soil relative stiffness ratio [21, 22]. In case of offshore wind turbine, fluid interaction should also be taken into account. Surrounding fluid contributes additional hydrodynamic mass to the structure which also decreases its natural frequency. However, this effect has not been thoroughly analysed in the existing state of the art of offshore wind turbines. Thus, the main aim of this paper is to develop a complete analytical algorithm to estimate the natural frequency of an offshore wind turbine considering the effects of fluid-soil structure interaction. The proposed algorithm is validated with numerical simulations, and a parametric study is also conducted showing the mesh dependencies of the fluid and soil elements with the natural frequency of the entire system.
2 Mathematical Model of Offshore Wind Turbine 2.1 Development of Governing Equations An offshore wind turbine can typically be divided into four different parts, i.e., tower and mono pile (i) above the water level, (ii) submerged in the water and (iii) embedded within the soil, as illustrated in Fig. 1. Each part of the offshore wind-turbine has different governing equations as the underlying physics varies with the location. For instance, the tower and the part of the monopile above the water surface can be modelled as a Timoshenko or Euler–Bernoulli beam. Fluid–structure and soilstructure-interaction is essential in modelling the part of the mono-pile between the water surface and ground level and beneath the ground level. Adding the rigid hydro-dynamic masses at the surface of the monopile in the submerged region, fluid– structure interaction can be performed. Lateral springs of varying coefficients along the depth are attached with the underground part of the mono-pile. Thus, the physics of the underground part can be conceptualized as a vibration of a beam on the elastic foundation; however, the Euler–Bernoulli or Timoshenko beam theory with addition of the mass is sufficient to model the submerged fluid-soil interaction. For brevity, Euler–Bernoulli beam theory has been adopted in this paper. Present study is mainly focused in estimating the undamped natural frequency since it will consider a more critical case scenario and will further helps us in avoiding the resonant frequency. Tower and mono-pile above water surface the governing equation of motion can be written as: E i Ii
∂ 2 wi ∂ 4 wi + ρi Ai 2 = 0 4 ∂t ∂z i
(1)
298
S. R. Patro et al.
Fig. 1 Offshore wind turbine used: a schematic model, b mathematical model
where E i ; I i ; ρ i ; Ai represents young’s modulus, second moment of area, density and cross-sectional area of the ith beam. wi denotes the transverse deflection and zi is the axis. As, Eq. 1 is applicable for the tower and the part of monopile above water level, respectively t and p are used as suffix instead of i in subsequent discussions. The submerged part of the monopile the governing equation of motion can be written as: E p Ip (z f )
) ∂ 2 wf ∂ 4 wf ( + ρ A + m(z =0 ) p p f ∂t 2 ∂z f4
(2)
where m(zf ) is the added hydro-dynamic mass for consideration of the fluid-soilstructure interaction at the submerged part of the mono-pile and zf denotes the height above the base of the fluid. The amount of m(zf ) can be expressed as [23]: ⎡
⎤ ( ) ∞ j−1 ∑ λr K 16H (−1) 1 p f ( ) ( ) cos(λz f )⎦ m(z f ) = ρw πrp2 ⎣ 2 π rp j=1 (2 j − 1)2 K 0 λrp + K 2 λrp
(3)
in which Hf is the water depth, z f is the distance above the base of the tower, ρw is water density, λ = (2 j−1)π , K n is the modified Bessel function of order n of the 2h second kind, In is the modified Bessel function of order n of the first kind and rp is the outside radius of the monopile respectively. The embedded part of monopile inside soil this part of the monopile is surrounded by the soil or rock. Considering the effect of the soil-structure interaction, the governing equation of motion can be written as:
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: …
E p Ip
∂ 4 ws ∂ 2 ws + E + ρ A =0 (z )w s s s p p ∂z s4 ∂t 2
299
(4)
where E s (zs ) is the secant modulus of soil with variation of the depth. The variation of E s can be computed from the p-y curve of a pile foundation. The slope of the p-y curve represents the elastic modulus of the soil E s at a depth of zs . ( E s (z s ) = E b
zs Hs
)n c (5)
where value of E b can be taken as 0.5–2.0 MPa for soft, 5–10 MPa for medium and 20–60 MPa for stiff soil [24]. Different values of nc , such as 0, 0.5 and 1 can be chosen to obtain the constant, parabolic and linear variation of the young’s modulus throughout the depth, respectively.
2.2 Solutions for Governing Differential Equations Implementing the concept of variable separation, transverse deflection of the beam can be expressed as the multiplication of the space and time domain as: wi (z i , t) = φi (z i )e−i ωt
(6)
where ϕ (zi ) can be assumed as: φi (z i ) = B1i cos(λi z i ) + B2i sin(λi z i ) + B3i cosh(λi z i ) + B4i sinh(λi z i )
(7)
By substituting Eq. (6) in Eqs. (1), (2) and (4), different relationships between ω and different λ. ω2 = λi4 ) ( m(z f ) 4 4 λ λf = 1 + ρp Ap p E s (z s ) λ4s = λ4p − E p Ip
(8)
2.3 Formulation of Transfer Matrix State vector formulation Four state vectors, namely transverse displacement (w), rotation (θ ), bending moment (M) and shear force (V ) are associated at a single end
300
S. R. Patro et al.
of a typical beam element; which can be written in terms of the unknown coefficients Θi as: ⎧ ⎫ wi ⎪ ⎪ ⎪ ⎪ ⎪ ⎨θ ⎪ ⎬ i = ⎪ Mi ⎪ ⎪ ⎪ ⎪ ⎩ ⎪ ⎭ Vi ⎡
ψi
⎤ cos(λi z i ) sin(λi z i ) cosh(λi z i ) sinh(λi z i ) ⎢ −λi sin(λi z i ) λi cos(λi z i ) λi sinh(λi z i ) λi cosh(λi z i ) ⎥ ⎢ ⎥ ⎣ −E i Ii λ2 cos(λi z i ) −E i Ii λ2 cos(λi z i ) E i Ii λ2 cosh(λi z i ) E i Ii λ2 sinh(λi z i ) ⎦ i i i i E i Ii λi3 sin(λi z i ) −E i Ii λi3 cos(λi z i ) E i Ii λi3 sinh(λi z i ) E i Ii λi3 cosh(λi z i ) ⎧ ⎫ A1i ⎪ ⎪ ⎪ ⎪ ⎨ ⎬ A2i e−i ωt ⎪ A3i ⎪ ⎪ ⎪ ⎩ ⎭ A4i
Fi
(9)
Θi
The state vectors ψ of both the side of the beam can be expressed by substituting the ordinate of zi into the expression of the functional matrix F. For the starting and end node of a beam element, the state vector can be expressed in terms of coefficient vector of that beam Θi as: ψi (0) = K (λi )Θi ψi (h i ) = H (λi , h i )Θi = H (λi , h i )K −1 (λi )ψi (0)
(10)
Formulation of continuity equation the state vectors of each part must maintain the continuity with the successive parts to maintain the integrity of the system. The continuity equations for the system are very straight forward as in junction between two successive elements displacement, rotation, bending moment and shear force are same. Therefore, the continuity equations can be written in matrix form as: ⎫ ⎧ ⎫ ⎧ wi (0) ⎪ wi−1 (h i−1 ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎨ ⎬ ⎨ θi (0) θi−1 (h i−1 ) = ⇒ ψi (0) = H (λi−1 , h i−1 )K −1 (λi−1 ) ψi−1 (0) ⎪ ⎪ ⎪ Mi (0) ⎪ Mi−1 (h i−1 ) ⎪ ⎪ ⎪ ⎪ ⎭ ⎩ ⎭ ⎩ T (λi−1 ,h i−1 ) Vi (0) Vi−1 (h i−1 ) (11) Complete Transfer Matrix The state vectors of the two extreme ends, i.e. tip of the tower (ψ t (0)) and bottom of the embedded pile (ψ p (hs )) of the wind-turbine
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: …
301
tower-pile system, could be related using the transfer matrix combining from each part. Let’s assume the tower, mono-pile over water, mono-pile submerged and monopile embedded parts are discretized in nt , np , nf , ns . Thus, transfer matrix from top of the tower to the bottom of the pile is: j ( ) ∏ ) ( ψj h j = T λ ji h ji ψ j (0) = Ts T f T p Tt ψt (0) i=1 T
n
(12)
Tj
where j can be replaced as s, f , p and t for monopile embedded in soil, transition piece in fluid, transition piece above fluid and tower.
2.4 Boundary Conditions In order to complete the definition of the system, imposition of boundary condition is quintessential. A typical offshore wind-turbine tower carries a heavy RNA mass at the tip of the tower. That mass provided a shear force at the end of the tower during vibration owing to wind, earthquake, wave, general operation of the wind turbine and other multi-hazard scenario. Therefore, the boundary condition for tip mass can be expressed as: E t It
∂ 3 wt (0) ∂ 2 wt (0) + Mr = 0 ⇒ Vt (0) = ω2 Mr wt (0) 3 ∂t 2 ∂z t
(13)
and Mt (0) = 0
(14)
Similarly, the boundary condition for flexible base could be formulated as: Vs (h s ) = Ms (h s ) = 0
(15)
Substituting the boundary conditions of Eqs. (13), (14) and (15) in transfer matrix equation Eq. (12), we obtain ⎧ ⎫ ⎫ ⎧ ws (h s ) ⎪ wt (0) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ]( ( ) [ ) ⎨ ⎬ ⎬ ⎨ wt (0) T 11 T32 0 θs (h s ) θt (0) ⇒ = =T ⎪ ⎪ T 21 T42 0 θt (0) ⎪ 0 ⎪ ⎪ ⎪ ⎪ 0 ⎪ ⎩ ⎭ ⎭ ⎩ 0 Vt (0) T trans
(16)
302
S. R. Patro et al.
(a)
(b) OpenSEES Proposed
Fig. 2 a Variation of excitation frequency (ω) with logarithmic of |T trans | for 5 MW wind turbine; b variation of RNA mass with the natural frequency considering both analytical and numerical methods
( where, T =
T31 T41
)
( + ω 2 Mr
) T34 . T44
3 Results and Discussions 3.1 Eigen Value Extraction The eigenvalues of the wind-turbine system considering fluid-soil-structure interaction could be derived from the determinant of T trans matrix given in Eq. (18). T trans can be expressed as the function of either ω or λp . Within a certain domain-independent parameter ω using bi-section method, we can compute the natural frequency of the system by observing the peaks as shown in Fig. 2a. The geometric and material properties of a 5 MW wind turbine are listed in table.
3.2 Validation Study For validation of above proposed mathematical model, a finite element software Open System for Earthquake Engineering Simulation (OpenSEES) [25] has been used. In this software, a numerical model based on finite element method is developed and eigen value analysis is done to estimate the natural frequency of the wind turbine system for different values of RNA mass as shown in Fig. 2b. From Fig. 2b, it can be observed that the proposed analytical expression gives reasonable predictions with numerical techniques which provides essential confidence in the proposed analytical model.
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: …
303
3.3 Mesh Convergence In the present study, FSI and SSI are modeled as discrete elements and decision of no. of elements plays a crucial role in estimation of natural frequency of the entire system. thus, variation of first natural frequency (ω) with no. of spring elements (ns ) for SSI and with no. of hydrodynamic mass elements (nf ) for FSI has been shown in Fig. 3. From Fig. 3, it is observed that after a particular no. of elements i.e. 100, the natural frequency becomes constant for both the cases (Table 1). (a)
(b)
Fig. 3 a Variation of first natural frequency (ω) with no. of soil elements (ns ); b variation of first natural frequency (ω) with no. of hydrodynamic mass elements (nf )
Table 1 Geometric and material properties of wind turbine system as listed in [5] Property
Symbols
Units
Values
Height of tower
Ht
m
90
Height of transition piece above water
Hp
m
15
Height of transition piece below water
Hf
m
15
Height of monopile
Hs
m
54
Profile of soil stiffness along the depth
nc
–
0.5
Average outer diameter of tower
dt
m
5.6
Diameter of pile
dp
m
6.5
Thickness of tower
T
m
0.04
Density of tower
ρt
kg/m3
7870
Density of monopile
ρp
kg/m3
2500 1000
Density of water
ρw
kg/m3
Young’s modulus of tower
Et
GPa
200
Young’s modulus of monopile
Ep
GPa
25
Secant modulus of soil
Es
MPa
60
Mass of rotor nacelle assembly (RNA)
Mr
tonne
350
304
S. R. Patro et al.
4 Conclusions A classical mechanics-based methodology towards the estimation of natural frequency of an offshore wind turbine system using transfer matrix method has been communicated in this paper. The tower and the monopile have been modelled as a hollow cylinder beam using the Euler–Bernoulli beam theory. The RNA and the blades are combinedly considered as a tip mass at the top of the tower. The FSI has been modelled as multiple no. of hydrodynamic mass, and the SSI has been modelled as multiple no. of linear elastic springs throughout the length of monopile. The tower, the transition piece inside fluid and the monopile embedded in soil is connected by continuity equations and a relationship between the state vectors of tower top and bottom of the monopile is established using the transfer matrix method. By imposing the boundary conditions in the transfer matrix and obtaining its determinant, the natural frequency of the entire system is evaluated. A validation study has been conducted with the numerical simulations (OpenSEES) for the free vibration analysis using the geometric and material parameters of a prototype 5 MW wind turbine. Finally, a mesh convergence study has been conducted deciding the no. of spring and hydrodynamic mass elements for the proposed methodology. Thus, the novelty lies in proposing an analytical methodology to estimate the natural frequency of the offshore wind turbine system considering the effects of FSSI. Due to severe change in climatic condition in recent years, the demand of stable, clean and green energy production becomes the primary mission of several countries. Towards this mission, the developed methodology contributed for easy simulation of entire structure and provides a generalized method for better design which can be used in design firms and practicing engineers for next generation wind turbine design. Further, this analytical could be extended in the future study considering the effects of eccentric mass due to the blades as well as for inhomogeneous soil stratum.
References 1. Wang, X., Zeng, X., Li, J., Yang, X., Wang, H.: A review on recent advancements of substructures for offshore wind turbines. Energy Convers. Manag. 158, 103–119 (2018). https://doi. org/10.1016/j.enconman.2017.12.061 2. Bazeos, N., Hatzigeorgiou, G.D., Hondros, I.D., Karamaneas, H., Karabalis, D.L., Beskos, D.E.: Static, seismic and stability analyses of a prototype wind turbine steel tower. Eng. Struct. 24(8), 1015–1025 (2002). https://doi.org/10.1016/S0141-0296(02)00021-4 3. Prowell, I., et al.: Experimental and Numerical Seismic Response of a 65 kW Wind Turbine. J. Earthq. Eng. 13(8), 1172–1190 (2009). https://doi.org/10.1080/13632460902898324 4. Jonkman, J., Butterfield, S., Musial, W., Scott, G.: Definition of a 5-MW Reference Wind Turbine for Offshore System Development, Colorado (2009) 5. Bhattacharya, S.: Design of Foundations for Offshore Wind Turbines. Wiley (2019) 6. Arany, L., Bhattacharya, S., Macdonald, J., Hogan, S.J.: Simplified critical mudline bending moment spectra of offshore wind turbine support structures. Wind Energy 18(12), 2171–2197 (2015)
Fluid-Soil-Structure Interaction of Offshore Wind Turbine: …
305
7. Arany, L., Bhattacharya, S., Adhikari, S., Hogan, S.J., Macdonald, J.H.G.: An analytical model to predict the natural frequency of offshore wind turbines on three-spring flexible foundations using two different beam models. Soil Dyn. Earthq. Eng. 74, 40–45 (2015). https://doi.org/10. 1016/j.soildyn.2015.03.007 8. Ramlau, R., Niebsch, J.: Imbalance estimation without test masses for wind turbines. J. Sol. Energy Eng. 131(1), (2009) 9. Hasselmann, K. et al.: Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Ergaenzungsh. zur Dtsch. Hydrogr. Zeitschrift, R. A. (1973) 10. Lombardi, D., Bhattacharya, S., Muir, D.: Dynamic soil—structure interaction of monopile supported wind turbines in cohesive soil. Soil Dyn. Earthq. Eng. 49, 165–180 (2013). https:// doi.org/10.1016/j.soildyn.2013.01.015 11. Patro, S.R., Banerjee, A., Adhikari, S., Ramana, G.V.: Kaimal spectrum based H2 optimization of tuned mass dampers for wind turbines. J. Vib. Contr. (2022). https://doi.org/10.1177/107754 63221092838 12. Wei, M., Chen, Z.: “Intelligent control on wind farm”, in. IEEE PES Innov. Smart Grid Technol. Conf. Euro. (ISGT Europe) 2010, 1–6 (2010) 13. Staino, A., Basu, B.: Dynamics and control of vibrations in wind turbines with variable rotor speed. Eng. Struct. 56, 58–67 (2013) 14. Adhikari, S., Bhattacharya, S.: Vibrations of wind-turbines considering soil-structure interaction. Wind Struct. 14(2), 85–112 (2011) 15. Adhikari, S., Bhattacharya, S.: Dynamic analysis of wind turbine towers on flexible foundations. Shock Vib. 19(1), 37–56 (2011). https://doi.org/10.3233/SAV-2012-0615 16. Achmus, M., Kuo, Y., Abdel-rahman, K.: Computers and geotechnics behavior of monopile foundations under cyclic lateral load. Comput. Geotech. 36(5), 725–735 (2009). https://doi. org/10.1016/j.compgeo.2008.12.003 17. Yu, L., Wang, L., Guo, Z., Bhattacharya, S., Nikitas, G., Li, L.: Long-term dynamic behavior of monopile supported offshore wind turbines in sand. Theor. Appl. Mech. Lett. 5(2), 80–84 (2015). https://doi.org/10.1016/j.taml.2015.02.003 18. Bisoi, S., Haldar, S.: Dynamic analysis of offshore wind turbine in clay considering soil— monopole—tower interaction. Soil Dyn. Earthq. Eng. 63, 19–35 (2014). https://doi.org/10. 1016/j.soildyn.2014.03.006 19. Bisoi, S., Haldar, S.: Design of monopile supported offshore wind turbine in clay considering dynamic soil—structure-interaction. Soil Dyn. Earthq. Eng. 73, 103–117 (2015). https://doi. org/10.1016/j.soildyn.2015.02.017 20. Patro, S.R., Sasmal, S.K., Suneel Kumar, G., Sarkar, P., Behera, R.N.: Seismic analysis of vertical geometric irregular building considering soil–structure interaction BT. In: Proceedings of the Indian Geotechnical Conference 2019, pp. 545–556 (2021) 21. Lin, S.-S., Liao, J.-C.: Permanent strains of piles in sand due to cyclic lateral loads. J. Geotech. Geoenviron. Eng. 125(9), 798–802 (1999) 22. Gavin, K., Igoe, D., Doherty, P.: Piles for offshore wind turbines: a state-of-the-art review. Proc. Inst. Civ. Eng. Eng. 164(4), 245–256 (2011) 23. Goyal, A., Chopra, A.K.: Simplified evaluation of added hydrodynamic mass for intake towers. J. Eng. Mech. 115(7), 1393–1412 (1989) 24. Matlock, H.: Correlation for Design of Laterally Loaded Piles in Soft Clay (1970) 25. Mazzoni, S., McKenna, F., Scott, M.H., Fenves, G.L.: OpenSees command language manual. Pacific Earthq. Eng. Res. Cent. 264(1), 137–158 (2006)
Seismic Performance Assessment of Reinforced Concrete Moment Resisting Frame Designed by Force-Based Design Method and the Performance-Based Plastic Design Method R. Vyas
and A. I. Shirkol
Abstract Performance-based plastic design (PBPD) method is an advance method of seismic analysis since it includes preselected target drift and inelastic behaviour of structure during a seismic event. In this study, a 4, 8 and 12 storied RC-MRF have been analysed and designed by force-based design (FBD) which is also known as codal method of design and by performance-based plastic design (PBPD) method. A comparison is prepared in terms of seismic performance of the study building. The design guidelines and parameters are adopted as per IS code. A nonlinear static pushover analysis is the tool utilized to assess the seismic performance of study frames in terms of base shear displacement curve and drifts for specified limits. The result indicates that the base shear value for all PBPD frames at performance point is almost 2.2 times higher than the analytical solution. Similarly, all PBPD frames are within drift ratio limit of 0.02, while FBD frames surpassed the permissible drift ratio limit of 0.004 from which it can be said that PBPD frames have better seismic performance than FBD frames. Keywords RC-MRF · Force-based design (FBD) · Performance-based plastic design (PBPD) · Performance level · Pushover analysis
1 Introduction In recent years, nonlinear and inelastic failure of structures were observed during a major seismic event. The current seismic codal [1] method is unable to explain the nonlinear and inelastic behaviour of structure. So an advance method called performance-based plastic design (PBPD) is proposed by [2]. PBPD selects the target drift and used R. Vyas (B) · A. I. Shirkol Malaviya National Institute of Technology, Jaipur 302017, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_25
307
308
R. Vyas and A. I. Shirkol
Fig. 1 Energy balance concept for PBPD method [3]
energy balance concept is used to analyse the structure up to nonlinearity and inelasticity as shown in Fig. 1 from which condition of complete collapse may avoided. To justify the efficacy of PBPD method, 4, 8 and 12 storey RC-MRF frames are selected in this study which are analysed and design by both FBD and PBPD method. Nonlinear static pushover analysis is the tool utilized to calculate seismic performance of study frames in terms of base shear displacement curves and drift ratios. Terminology used Ah
Design horizontal earthquake acceleration
wn
Lumped weight of top floor
Sa
Spectral acceleration coefficient
Z
Earthquake zone factor
Sd
Design spectral displacement
βi
Shear distribution factor PBPD
T
Fundamental natural period
γ
Energy modification factor
G
Gravitational acceleration
VB
Design base shear
H
Height
W
Lumped weight of structure
hn
Top floor height
wi
Lumped weight at ith level
I
Importance factor
μ
Ductility factor
Qi
Lateral load at ith level
θ max
Selected target drift
V
Shear at interior column
θp
In-elastic drift
V'
Shear at exterior column
θy
Selected yield drift
Vo
Base shear at performance point
M
Mass of system
C.vi
Lateral load distribution factor PBPD
Fi
Lateral load distribution FBD
Seismic Performance Assessment of Reinforced Concrete Moment …
309
Table 1 Frame description S. no. Parameters 1
Height of building (m)
4 Storey
8 Storey
12 Storey
12.8
25.6
38.4
2
Storey height (m)
3.2
3.2
3.2
3
Number of bays
4
4
4
4
Bay width (m)
4
4
4
(kN/m2 )
5
Live load
3.0
3.0
3.0
6
Floor finish load (kN/m2 )
1
1
1
7
Earthquake zone
Zone-V
Zone-V
Zone-V
8
Importance factor
1
1
1
9
Response reduction factor (R)
5
5
5
10
Spectral acceleration (sa /g)
2.5
1.59
1.18
0.85
1.16
11
Fundamental natural period (T ) 0.51 s
12
Type of soil
Type II, medium Type II, medium Type II, medium
13
Size of beam
300 × 400 mm
300 × 450 mm
300 × 500 mm
14
Size of column
450 × 450 mm
600 × 600 mm
600 × 600 mm
15
Slab thickness
120 mm
120 mm
120 mm
16
Lumped weight (W ) (kN)
11,442.65
21,638
36,216
17
Concrete grade
M25
M25
M25
18
Steel grade
HYSD (Fe415)
HYSD (Fe415)
HYSD (Fe415)
2 Description of the Study Frame Study frame consists of 4, 8 and 12 storey RC-MRF frame with storey height of 3.2 m each. The frame situated in earthquake zone-V for which spectral acceleration (S a ) and fundamental natural period (T ) is calculated. Complete details of study frames are shown in Table 1. Figures 2 and 3 show the plan and elevation of the study frame.
3 Earthquake Forces 3.1 Earthquake Forces and Its Distribution in FBD Frames To calculate base shear and its distribution, response spectrum analysis is performed with complete quadratic combination method described in [1]. The equations used to calculate design seismic horizontal coefficient (Ah ) are as follows: ( z )⎛ sa ) Ah =
2
g
(R) , I
(1)
310
R. Vyas and A. I. Shirkol
Fig. 2 Plan of study frame
Fig. 3 Elevation of a 4 storey, b 8 storey and c 12 storey study frame
VB = Ah .W,
(2)
Wi h 2 Qi = i 2 , Wi h i
(3)
Fi = Q i .VB .
(4)
The response acceleration coefficient (S a /g) for medium type of soil is described in Table 1 from which spectral acceleration coefficient is identified for FBD frame. For
Seismic Performance Assessment of Reinforced Concrete Moment …
311
earthquake zone 5, the vertical seismic effect is considered as two third of horizontal seismic effect. It is observed that base shear and its distribution in FBD method is based on assumption and engineering judgement given in [1] which is the main reason for inelastic deformations in structures during strong ground motion. The lateral load and its distribution of study frames are shown in Table 2.
3.2 Earthquake Forces and Its Distribution in PBPD Frames To calculate base shear and its distribution by PBPD method, target drift (θ max ) of value 0.02 is considered as per [7] where it was stated that “A 2% maximum storey drift ratio for ground motion hazard with 10% probability of exceedance in 50 years (10/50 or 2/3MCE)” and yield drift (θ y ) of value 0.004 has been considered as per Indian seismic code [1] recommendation from which total plastic drift (θ p ) to be 0.016 is found. After that principal of virtual work is applied for elasto-plastic SDOF system suggested by [4]. In PBPD method, columns are considered as non-yielding members for which one hinge is provided at the base of column and 2 hinges are provided at the both ends of beams. Lateral load and its distribution is calculated as per Eqs. 5–8 as suggested by [5] ⎛ VB = ⎝
−Ah +
/
A2h + 4γ Sa2 2
γ =
⎞ ⎠W,
(4)
2μ − 1 , Rμ2
(5)
⎛ n )⎛ )0.75T −0.2 ⎛ )
θp 8π 2 wn h n n , Ah = (βi − βi+1 )h i T 2g i=1 wi h i i=1 ⎛ n βi = [
wi h i wn h n
)0.75T −0.2
i=1
⎛
(6)
wn h n Q i = (βi − βi+1 ) n i=1 wi h i
,
(7)
)0.75T −0.2 ] VB .
(8)
The spectral acceleration coefficient (S a ) for the PBPD frame has been calculated by dividing the response acceleration coefficient (S a /g) for medium type of soil described for FBD method to the ductility reduction factor (Rµ ) as described in [6]. Value of Rµ is same as ductility ratio (μ) for 8 and 12 storey frame, but it is less for 4 storey frame as fundamental natural time period (T ) is less than 0.55 s. In elasto-plastic system, energy is considered as input unit but due to nonlinearity this energy needs to be modified. So an energy modification factor (γ ) is introduced as
Total
3.2
1
9617.5
2647
2647
2647
9.6
6.4
3
2
12.8
4
274,677.76
363.45
243,947.52
654,151.68
27,105.28
108,421.12
322.79
865.58
35.86
143.46 21,638
2832
2832
2832
2832
2832
2832
19.2
16
6
5
2832
22.4
7
1814
28.8
5,248,778.24
28,999.68
115,998.72
260,997.12
463,994.88
724,992
1,043,988.48
1,420,984.32
1,188,823.04
W j hj 2
8 Storey frame W j (kN)
25.6
1676.5
F i (kN)
9
32
10
W j hj 2
4 Storey frame
W j (kN)
8
38.4
35.2
12
11
hi (m)
Floor level
Table 2 Lateral load distribution for FBD frames
1241.13
6.86
27.43
61.72
109.72
171.43
246.86
336.00
281.11
Fi (kN) 1984
36,216
3112
3112
3112
3112
3112
3112
3112
3112
3112
3112
3112
19,050,168.3
31,866.88
127,467.52
286,801.92
509,870.08
796,672
1,147,207.68
1,561,477.12
2,039,480.32
2,581,217.28
3,186,688
3,855,892.48
2,925,527.04
W j hj 2
12 Storey frame W j (kN)
1532.61
2.56
10.25
23.07
41.01
64.09
92.29
125.62
164.08
207.66
256.37
310.21
235.36
F i (kN)
312 R. Vyas and A. I. Shirkol
Seismic Performance Assessment of Reinforced Concrete Moment …
313
per [7]. The variation in energy modification factor with respect to time is shown in Fig. 4. The parameters used to analyse the study frames and lateral load distribution by PBPD method are described in Tables 3 and 4. Figures 5 and 6 show the lateral load distribution pattern for both FBD and PBPD frames. It is observed from the calculations of Tables 2 and 4 that the base shear of 4, 8 and 12 storey PBPD frame is 2.02, 1.85 and 1.55 times, respectively, lesser than FBD
Fig. 4 Energy modification factor ‘γ ’ versus time period T as per [8]
Table 3 Design parameters of study frame by PBPD method
Parameters
4 Storey frame
8 Storey frame
12 Storey frame
W (kN)
9617.5
21,638
36,216
T (s)
0.5075
0.854
1.156937
θy
0.004
0.004
0.004
θ max
0.02
0.02
0.02
θp
0.016
0.016
0.016
μ (θ max /θ y )
5
5
5
Rµ
4.6912
5
5
S a /g
0.5329
0.319
0.235104
[
0.409
0.36
0.36
Ah
4.6987
3.301
2.710007
V B/W
0.0246
0.011
0.007323
V B (kN)
236.49
238.8
265.2034
V B (p-delta)
192.35
432.8
724.32
Total V B (kN)
428.8
671.6
989.52
314
R. Vyas and A. I. Shirkol
Table 4 Lateral load distribution for PBPD frames Floor hi (m) 4 storey frame level β i − C ' vi Qi (kN) β i+1
8 storey frame β i − C ' vi β i+1
12 storey frame Qi (kN)
βi − β i+1
C ' vi
Qi (kN)
12
38.4
1
0.192 190.11
11
35.2
0.914
0.176 173.74
10
32
0.703
0.135 133.58
9
28.8
0.576
0.111 109.52
8
25.6
0.481
0.092
1
0.236 158.37
91.453
7
22.4
0.95
0.223 150.1
0.402
0.077
76.484
6
19.2
0.71
0.168 112.63
0.333
0.064
63.376
5
16
0.55
0.13
0.271
0.052
51.475
4
12.8
1
3
9.6
0.956 0.337 144.49
0.352 151.1
2
6.4
0.594 0.209
1
3.2
0.288 0.102
Total
171.43
0.42
0.1
87.403 91.453 0.041
40.392
0.31
0.072
66.848 0.157
0.03
29.869
89.702 0.2
0.047
48.672 0.104
0.02
19.721
43.54
0.023
31.838 0.052
0.01
428.84
0.1
671.61
9.8052 989.52
frames. It is due to high ductility demand in PBPD frames as described in Table 3. The lateral load and base shear distribution for both frames are shown in Figs. 5 and 6, respectively. The P-delta effect is also considered in PBPD frames at initial stage of calculations by multiplying respective drift limits to the lumped weight which is quite helpful to compensate the reduction of base shear due to higher μ value [9].
4 Design of Sections Sections are designed for the considered study frame by both FBD and PBPD methods. Lateral forces are applied on all the joints of all the bays along with gravity loads in vertical direction. In FBD frames, beam and column moments are calculated by using ETABS software, whereas in PBPD method beam and column moments are calculated analytically by applying principle of virtual work for defined yield mechanism and plastic theory as per [10]. It is observed from Figs. 7, 8 and 9 that the column moments are higher than beam moments, hence strong column weak beam theory is justified. Later sections are designed as per [11, 12] guidelines. Design details of sections are shown in Tables 5, 6, and 7 respectively. Figures 8 and 9 show the external and internal column moments for the study frames. By observing Fig. 8a, b and c, it can be said that the maximum external column moments for FBD model are 240.98 kN for 8 storey frame and 218.56 kN for 12 storey frame which is found less than 8 storey frame. Similarly by observing Fig. 9a, b and c for inner column sections, the maximum 8 storey moment is 356.98
0
1
2
3
0
50
150
200
250
300
350
(a)
Lateral Load Distribution (kN)
100
FBD PBPD 400
Storey Number 0
1
2
3
4
5
6
7
8
0
50
150
200
250
300
(b)
Lateral Load Distribution (kN)
100
350
FBD PBPD
Fig. 5 Lateral load distribution curve for a 4 storey, b 8 storey and c 12 storey study frames
Storey Number
4
0
2
4
6
8
10
12
0
50
150
200
250
300
(c)
Lateral Load Distribution (kN)
100
350
FBD PBPD
Seismic Performance Assessment of Reinforced Concrete Moment … 315
Storey Number
1 100
2
3
200
400
500
600
700
800
(a)
Base Shear Distribution (kN)
300
900
FBD PBPD
Storey Number 1
2
3
4
5
6
7
8
0
200
600
800
1000
(b)
1200
FBD PBPD
Base Shear Distribution (kN)
400
Fig. 6 Base shear distribution curve for a 4 storey, b 8 storey and c 12 storey study frames
Storey Number
4
1400
1
2
3
4
5
6
7
8
9
10
11
12
0
200
600
800
1000
1200
(c)
Base Shear Distribution (kN)
400
1400
FBD PBPD
1600
316 R. Vyas and A. I. Shirkol
Storey Number
1
2
3
40
60
100
120
140
(a)
Beam Moments (kN-m)
80
160
FBD PBPD
Storey Number 1
2
3
4
5
6
7
8
0
50
150
200
250
(b)
Beam Moments (kN-m)
100
300
FBD PBPD
Fig. 7 Beam moment comparison curve for a 4 storey, b 8 storey and c 12 storey study frame
Storey Number
4
1
2
3
4
5
6
7
8
9
10
11
12
0
50
100
200
250
300
350
(c)
Beam Moment (kN-m)
150
400
450
FBD PBPD
500
Seismic Performance Assessment of Reinforced Concrete Moment … 317
Storey Number
1
2
3
20
160
180
200
220
0
50
100
150
200
250
300
350
400
450
500
1 0
100
200
300
400
500
600
(c)
140
(b )
120
700
FBD PBPD
(a)
100
2
3
4
5
6
7
8
9
10
11
12
External Column Moment (kN-m)
80
FBD PBPD
External Column Moment (kN-m)
60
1
2
3
4
5
6
7
8
Storey Number
External Column Moment (kN-m)
40
FBD PBPD
Storey Number
Fig. 8 External column moment comparison curve a 4 storey, b 8 storey and c 12 storey study frames
Storey Number
4
318 R. Vyas and A. I. Shirkol
1
2
3
0
100
150
200
250
(a)
Internal Column moment (kN-m)
50
300
FBD PBPD
1
2
3
4
5
6
7
8
0
50
150
200
250
300
350
400
(b)
External Column Moment (kN-m)
100
450
FBD PBPD
500
Storey Number
Storey Number
Fig. 9 Internal column moment comparison curve for a 4 storey, b 8 storey and c 12 storey study frames
Storey Number
4
1
2
3
4
5
6
7
8
9
10
11
12
0
200
300
400
500
600
(c)
External Column Moment (kN-m)
100
FBD PBPD
700
Seismic Performance Assessment of Reinforced Concrete Moment … 319
Interior column section
Exterior column section
PBPD frame Beam sections
Interior column section
Exterior column section
0.4
0.4
0.5
0.6
300 × 400 1.7
300 × 400 1.7
300 × 400 1.8
300 × 400 1.8
4
3
2
1
450 × 450 1.4
450 × 450 1.2
450 × 450 1.1
450 × 450 1.0
450 × 450 1.2
450 × 450 1.1
450 × 450 1
450 × 450 0.8
300 × 450 2.4
300 × 450 2.4
300 × 450 2.0
300 × 450 2.0
1.07
1.07
0.81
0.8
500 × 500 2.1
500 × 500 2.1
500 × 500 1.5
500 × 500 1.5
500 × 500 2.1
500 × 500 2.1
500 × 500 1.5
500 × 500 1.5
Size (mm) Bottom Top pt . % Size (mm) pt . % Size (mm) pt. % Size (mm) Bottom Top pt . % Size (mm) pt. % Size (mm) pt. % pt . % pt . %
Beam sections
Floor FBD frame
Table 5 Design of sections of 4 storey frame
320 R. Vyas and A. I. Shirkol
0.79
0.93
1.06
1.16
1.21
1.56
2.01
300 × 450
300 × 450
300 × 450
300 × 500
300 × 500
300 × 500
300 × 500
6
5
4
3
2
1
1.06
1.06
0.96
0.92
0.83
0.78
0.78
600 × 600
600 × 600
600 × 600
600 × 600
550 × 550
550 × 550
550 × 550
550 × 550
1.7
1.7
1.5
1.5
1.5
1.3
1.3
1.3
600 × 600
600 × 600
600 × 600
600 × 600
550 × 550
550 × 550
550 × 550
550 × 550
2.3
2.1
2.1
2.1
1.8
1.6
1.6
1.6
350 × 550
350 × 550
350 × 550
350 × 550
300 × 500
300 × 500
300 × 500
300 × 500
1.78
1.78
1.78
1.55
1.81
2.3
2.01
2.01
Bottom pt %
7
0.78
Size (mm)
0.79
pt %
300 × 450
Size (mm)
8
pt %
Size (mm)
Bottom pt %
Size (mm)
Top pt %
PBPD fram Beam sections
Exterior column section
Interior column section
Beam sections
Floor
FBD frame
Table 6 Design of sections of 8 storey frame
0.95
0.95
0.95
0.83
0.83
0.83
0.83
0.73
Top pt %
700 × 700
700 × 700
700 × 700
700 × 700
600 × 600
600 × 600
600 × 600
600 × 600
Size (mm)
1.6
1.6
1.6
1.6
1.4
1.4
1.4
1.4
pt %
700 × 700
700 × 700
700 × 700
700 × 700
600 × 600
600 × 600
600 × 600
600 × 600
1.6
1.6
1.6
1.6
1.4
1.4
1.4
1.4
pt %
Exterior column section Size (mm)
Interior column section
Seismic Performance Assessment of Reinforced Concrete Moment … 321
1.72
1.72
1.72
1.86
1.86
1.86
2.01
2.01
300 × 450
300 × 450
300 × 450
300 × 450
300 × 500
300 × 500
300 × 500
300 × 500
10
9
8
7
6
5
4
0.91
0.91
0.91
0.91
0.78
0.78
0.78
0.64
600 × 600
600 × 600
600 × 600
550 × 550
550 × 550
550 × 550
550 × 550
550 × 550
550 × 550
1.6
1.6
1.4
1.4
1.4
1.0
1.0
0.8
0.8
600 × 600
600 × 600
600 × 600
550 × 550
550 × 550
550 × 550
550 × 550
550 × 550
550 × 550
1.2
1.1
1.1
1.0
1.0
1.0
0.8
0.8
0.8
400 × 600
400 × 600
400 × 600
400 × 500
400 × 500
300 × 500
300 × 500
300 × 500
300 × 500
1.41
1.41
1.41
1.55
1.55
2.07
2.07
2.07
2.07
Bottom pt %
11
0.64
Size (mm)
1.72
pt %
300 × 450
Size (mm)
12
pt %
Size (mm)
Botttom pt %
Size (mm)
Top pt . %
PBPD frame Beam sections
Beam sections
Exterior column section
Interior column section
FBD frame
Floor
Table 7 Design of sections of 12 storey frames
0.58
0.58
0.58
0.54
0.54
0.85
0.85
0.85
0.85
Top pt %
850 × 850
850 × 850
850 × 850
750 × 750
750 × 750
750 × 750
750 × 750
750 × 750
750 × 750
Size (mm)
1.4
1.4
1.4
1.8
1.8
1.8
1.8
1.8
1.8
pt %
Interior column section
850 × 850
850 × 850
850 × 850
750 × 750
750 × 750
750 × 750
750 × 750
750 × 750
750 × 750
Size (mm)
(continued)
1.4
1.4
1.4
1.8
1.8
1.8
1.8
1.8
1.8
pt %
Exterior column section
322 R. Vyas and A. I. Shirkol
2.12
2.12
300 × 500
300 × 500
1
1.16
1.16 600 × 600
600 × 600
600 × 600
2
1.16
1.9
1.8
1.8
600 × 600
600 × 600
600 × 600
1.2
1.2
1.2
400 × 600
400 × 600
400 × 600
1.41
1.41
1.41
Bottom pt %
2.01
Size (mm)
300 × 500
pt %
3
Size (mm)
Size (mm)
Botttom pt %
Size (mm)
pt %
Beam sections
Top pt . %
PBPD frame
Beam sections
Exterior column section
Interior column section
FBD frame
Floor
Table 7 (continued)
0.58
0.58
0.58
Top pt %
850 × 850
850 × 850
850 × 850
Size (mm)
1.4
1.4
1.4
pt %
Interior column section
850 × 850
850 × 850
850 × 850
Size (mm)
1.4
1.4
1.4
pt %
Exterior column section
Seismic Performance Assessment of Reinforced Concrete Moment … 323
324
R. Vyas and A. I. Shirkol
and 346.18 kN for 12 storey frame which is also lesser than 8 storey moment. So it can be said that FBD model underestimates the moments as the number of storey increases and presenting reduction of the section. But to maintain the uniformity, all sections kept same for FBD frames. In the case of PBPD model, column moments for 8 and 12 storey frames are 393.03, 580.62 and 538.26 kN, 779.36 kN for external and internal columns, respectively. Hence, it can be said that as the storey number increases the moment increases and sections are provided at different storey level accordingly.
5 Seismic Performance Evaluation Nonlinear static pushover analysis is the tool utilized to identify the seismic performance of the study frame. Since there are no guidelines provided by standard seismic code, so the procedure suggested by [13–15] are followed for seismic analysis. Hinges are provided at 0.1 times of total length from one end and 0.9 times of total length at other end for beam and column sections. Lateral load is applied at all the joints of all bays along vertical gravity load at suitable location with higher mode effects as per [15]. The performance point is identified by plotting base shear displacement curve with respect to three seismic performance levels named as immediate occupancy (IO), life safety (LS) and collapse prevention (CP), respectively [16]. ETABS software [17] is used to perform pushover analysis. From Fig. 10a–c, it is found that both FBD and PBPD frames have well defined displacement and base shear points for immediate occupancy but on increasing the storey number PBPD frames have has higher base shear and lower displacement for immediate occupancy point. Similarly, for all PBPD frames, the base shear obtained after performing pushover analysis is 1058.89, 1420.71 and 1863.39 kN for 4, 8 and 12 storey study frame which is 2.47, 2.22 and 1.87 times, respectively, higher than analytical solution as shown in Table 4 which means that PBPD frames have higher stiffness and strength from expectations. It is also observed that the performance point of all FBD frame lies between life safety (LS) and collapse prevention (CP) range. Similarly, for all PBPD frames, performance point lies between immediate occupancy (IO) and life safety range. Figures 11 and 12 represent the hinge pattern formation for all FBD and PBPD frames, respectively, at ultimate point of pushover analysis from which it is observed that number of plastic hinges formed beyond collapse prevention are much higher in FBD frames as compared to PBPD frames. It is also observed that the higher number of plastic hinges is formed for both column and beam sections in FBD frames and at lower storeys most of them are beyond collapse prevention (CP) range, whereas for PBPD frames, plastic hinges for column sections are formed only at base of the column and within collapse prevention (CP) range which clearly indicates that PBPD frames efficiently justified the weak beam-strong column concept as compared to FBD frame. After performing pushover analysis, inter-storey drift ratio is also calculated for study frames as shown in Fig. 13. It is found that maximum drift ratio values for 4, 8
Seismic Performance Assessment of Reinforced Concrete Moment … 2000
2000 PP IO LS CP
1800
PP IO LS CP
1800 1600
Base Shear (kN)
1600
Base Shear (kN)
325
1400 1200 1000 800
1400 1200 1000 800 600
600 400
400
FBD PBPD
200
FBD PBPD
200
0
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Displacement (m)
Displacement (m)
(a)
(b)
2000
Base Shear (kN)
1800
PP IO LS CP
1600 1400 1200 1000 800 600 400
FBD PBPD
200 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
Displacement (m)
(c) Fig. 10 Pushover curve for a 4 storey, b 8 storey and c 12 storey study frames
Fig. 11 Hinge pattern for a 4 storey, b 8 storey and c 12 storey FBD frames
0.8
0.9
1.0
326
R. Vyas and A. I. Shirkol
Fig. 12 Hinge pattern for a 4 storey, b 8 storey and c 12 storey PBPD frames
and 12 storey FBD frame are 0.011, 0.0073 and 0.0084, respectively, which is over the permissible limit of 0.004. Similarly, maximum drift ratios for 4, 8 and 12 storey PBPD frame are 0.014, 0.018 and 0.019, respectively, which is under the target drift value of 0.02. So we can say that PBPD frames have better performance than FBD frames in terms of drift ratios.
6 Conclusion 4, 8 and 12 storey RC-MRF are analysed and deigned by FBD method and PBPD method. Codal guidelines are followed for FBD frames whereas analytical method is used for PBPD method. Initially, base shear values of PBPD frames are found quite lesser than FBD frames due to high ductility demand in PBPD. As discussed earlier, all the PBPD frames are designed for higher bending moments than beam moments from which we can say that PBPD justifies weak beam-strong column concept. It is also observed that moment distribution curves for all PBPD frames are uniformly distributed whereas FBD frames underestimate the moment distribution with respect to the storey number. Later nonlinear static pushover analysis is performed to evaluate seismic performance in terms of base shear displacement curve, it is found that for lower storeys both FBD and PBPD frames have well defined immediate occupancy point for displacement and base shear values but on increasing the storey number PBPD has lower displacement and high base shear values as compared to FBD frames. It is also found that all PBPD frames have almost 2.2 times higher base shears values in pushover analysis as compare to analytical method which concludes
0 0.000
1
2
3
0.003
0.006
0.012
(a)
Drift Ratio
0.009
0.015
0.018
FBD PBPD
Storey Number 0 0.000
2
4
6
8
0.005
(b)
Drift Ratio
0.010
0.015
Fig. 13 Drift ratio comparison curve for a 4 storey, b 8 storey and c 12 storey study frames
Storey Number
4
0.020
FBD PBPD
0 0.000
1
2
3
4
5
6
7
8
9
10
11
12
0.005
0.010
0.015
(c)
Drift Ratio
0.020
0.025
0.030
FBD PBPD
Seismic Performance Assessment of Reinforced Concrete Moment … 327
Storey Number
328
R. Vyas and A. I. Shirkol
that it has higher stiffness or reserve strength from expectations. The hinge pattern formation for both FBD and PBPD frames indicates that the frames designed with PBPD method are more efficient to justify weak beam-strong column concept as compared to FBD method. Similarly, drift ratios for both method are identified and it is found that FBD frames surpassed the permissible drift ratio of 0.004, whereas all PBPD frames are under permissible limit of drift ratio value of 0.02. On the basis of observations, it is concluded that PBPD frames have better seismic performance than FBD frames.
References 1. IS 1893: Criteria for Earthquake Resistant Design of Structures, Part-1 General Provisions and Buildings, Sixth Revision. Bureau of Indian Standard, New Delhi (2016) 2. ASCE/SEI 41-17: Seismic evaluation and retrofit of existing buildings. Am. Soc. Civ. Eng. (2017) 3. Chao, S.H., Goel, S.C.: Performance-Based Design of EBF Using Target Drift and Yield Mechanism, Research Report UMCEE 05–05. University of Michigan, Ann Arbor, USA (2005) 4. Goel, S.C., Liao, W.C., Bayat, M.R., Chao, S.H.: Performance-based plastic design (PBPD) method for earthquake-resistant structures: an overview. Struct. Des. Tall. Spec. Build. 19, 115–137 (2010) 5. Chao, S.H., Goel, S.C., Lee, S.S.: A seismic design lateral force distribution based on inelastic state of structures. Earthq. Spectra 23, 547–569 (2007) 6. Qammer, S.S., Dalal, S.P., Dalal, P.D.: Seismic performance evaluation of rc frames designed by PBPD method attuned with Indian code of practice. In: 16th Symposium Earthquake Engineering, Roorkee: Indian Society of Earthquake Technology, Paper no 12 (2018) 7. Liao, W.C., Goel, S.C.: Performance based plastic design and energy based evaluation of seismic resistant RC moment frame. J. Mar. Sci. Technol. 20(3), 304–310 (2012) 8. Dalal, S.P.: Performance Based Plastic design of Moment Resisting frame using the Proposed Inelastic Design Spectra, Doctoral dissertation, Ph.D. Thesis (2015) 9. Dalal, S. P., Dalal, P.: Strength, deformation and fragility assessment of reinforced concrete moment resisting frame designed by force based design and the performance based plastic design method for seismic loads. J. Struct. 29, 1154–1164 (2021) 10. Goel, S.C., Chao, S.-H.: Performance based plastic design: Earthquake Resistant Steel Structure. ICC publication, USA (2008) 11. IS 456: Plain and Reinforced Code of Practice (Fourth Revision). Bureau of Indian standard, New Delhi (2000) 12. IS 13920: Ductile Detailing of Reinforced Concrete Structures Subjected to Seismic Forces. Bureau of Indian standard, New Delhi (1993) 13. ATC 19: Structural response modifictaion factors. Appl. Technol. Counc., 1–69 (1995) 14. FEMA 356: Prestandard and commentary for the seismic rehabilitation of buildings. Fed. Emerg. Manag. Agen. (2000) 15. Chopra, A.K., Goel, R.K.: A modal pushover analysis procedure for estimating seismic demands for buildings. Earthq. Eng. Struct. Dyn. 31, 561–582 (2002) 16. Biradar, B.B., Shirkol, A.I., Bush, R.: Comparative study and performance evaluation of steel moment resisting frames design with: Force-based design and performance-based plastic design. In: Structures, vol. 43, pp. 696–709. Elsevier (2022) 17. ETABS Version 19: Structural and Earthquake Engineering Software, Computers and Structures, America (2019)
Influence of Existing Tunnel—Surface Structure Interaction Under Repeated Dynamic Loading Conditions M. D. Godson , S. Ganesh Kumar , and J. Visuvasam
Abstract According to past studies, subsurface spaces induce variation in ground response during an earthquake incidence and directly impact the surface structures’ seismic behaviour. Though, these subsurface structures (tunnels) are less susceptible to deformation than superstructures; its interaction with the surface structures during dynamic loading needs to be assessed carefully. Especially when these tunnels are located in partially saturated sand deposits, the interaction between soil-tunnelstructure is more complicated. The generation of pore water pressures, acceleration response during dynamic conditions may induce soil deformation and create deformations in the tunnel and superstructure system. Recently, repeated shaking events (i.e. continuous foreshock/aftershock associated events during earthquake incidence) posing a serious threat to the safety of significant infrastructures (Christ church earthquake 2011, Japan earthquake 2011, etc.) Hence, it is crucial to consider the response of surface structures with an existing tunnel under multi-seismic events where the studies were very limited. Considering the above, this study aims to understand the dynamic interaction behaviour between the surface structures with a shallow tunnel under repeated dynamic loading conditions. The experimental studies were conducted on a 1-g uni-axial shaking table with ground having 25% saturation replicating partially saturated conditions. A scaled-down structural member fixed on a pile foundation was used for simulating surface structure. Similarly, a scaled-down square tunnel of dimension 280 × 280 × 750 mm embedded at 420 mm depth was used for simulating shallow tunnel system. The tunnel-structure embedded ground was then subjected to repeated incremental sinusoidal acceleration loading of 0.1, 0.2, 0.3, 0.4 and 0.5 g with 5 Hz frequency. The effects of acceleration response, structural displacement, soil displacement, and pore water pressure were compared M. D. Godson (B) · J. Visuvasam School of Civil Engineering, VIT Vellore, Vellore, India e-mail: [email protected] J. Visuvasam e-mail: [email protected] S. Ganesh Kumar Geotechnical Division, CSIR-CBRI Roorkee, Roorkee, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_26
329
330
M. D. Godson et al.
and analysed. The tunnel and structural displacement during testing were monitored and estimated using 2D digital image correlation. The parameters influencing tunnel-soil-surface structure interaction under repeated seismic loading conditions were analysed and presented. The results show that, the irrespective of improved soil reinforcement induced by the pile foundation, occurrence of repeated shaking with longer duration affects the performance of the surface structure, and its interaction with the tunnel embedded ground. Keywords Tunnel-soil-surface structure interaction · Partially saturated sand · 2D digital image correlation · 1-g shaking table · Repeated seismic events
1 Introduction When urban transportation becomes exceptionally challenging due to reduction in space availability, the engineers started utilizing underground areas to its maximum potential for developing underground infrastructures. One among the significant underground space technology was tunnel system which has a tremendous influence in country’s economy and growth. In recent years, tunnel constructions with longer lengths have accelerated significantly which requires serious attention when constructed beneath superstructures in seismic prone areas. Generally, due to the depth of location which offers better confinement characteristics made to considered underground structures are notably safer than surface structures even when exposed to seismic activities [1]. However, occurrence of dynamic events in the past caused more severe damage to tunnels at shallow depths than tunnels at deeper depths [1, 2]. The earthquakes, such as the Hanshin earthquake (1995), Chi-Chi earthquake (1999), and Wenchuan earthquake (2008), significantly damaged many underground structures and manifested that the seismic response of underground structures cannot be disregarded. During earthquakes, the structural integrity of the soil got disturbed due to the existence of underground structures which contributed in developing the multiple reflections and refractions of seismic waves, thus affecting the dynamic response characteristics of soil in the site and also have an impact on above surface structures. Similarly, the inertial effect of the near or above surface structure during a seismic excitation induces disturbances in soil stress, which influences the fluctuation in field stress in close soil ground and affecting the seismic response of underground structure [3]. This reveals that, the existence of underground structures cannot be ignored when considering the influence of surface structures. During earthquake incidence, the presence of an adjacent pile foundation amplifies the acceleration response in the near field conditions and weakens the acceleration in the far field conditions whereas the presence of tunnel magnifies the acceleration response in the far field and slightly diminishes the dynamic reaction in the near field conditions [4]. Further, the influence of the nearby building on tunnel’s seismic performance also changes when the distance between both the structures either increases or decreases. For
Influence of Existing Tunnel—Surface Structure Interaction Under …
331
instance, several underground projects and adjacent above-ground structures were destroyed after the Wenchuan earthquake. Thus, the published literatures emphasized the significance of surface structures—soil—underground structures and highlight the importance of its interactions during dynamic events [5]. Recently, occurrence of repeated shaking events (i.e. continuous foreshock/aftershock associate events during earthquake incidence) continuously posing a serious threat to safety of significant infrastructures (Christ church earthquake 2011, Tohoku earthquake 2011, Nepal Earthquake (2015), Kumamoto 2016, Indonesia 2018, Canada 2019, etc.). For example, in 2015 Nepal earthquake, the occurrence of repeated shaking events [i.e. on 25 April 2015 had a main-shock event of magnitude (ML) 7.8 at 06:11:26 UTC, and followed by several aftershocks, including a magnitude (ML) 7.3 earthquake at 07:05:19 UTC and then a magnitude (ML) 6.3 earthquake at 07:36:53 UTC, both on 12 May 2015 (USGS, 2015)] created major destruction to the infrastructures and posed constraints in country’s economic development [6]. During dynamic events, the fluctuation in groundwater table conditions is crucial and contributes in affecting the soil stresses. This found more influential in case of silty ground conditions. When tunnels are located under these conditions, the tunnel and superstructure system deform continuously due to generation of pore pressures as a result of soil saturation by the groundwater levels during dynamic loading. Hence, it is crucial to look into the response of surface structures with an existing tunnel during a multi-seismic event in partially saturated ground. Further, no or few studies are available to assess the tunnel-soil-surface structure’s performance in partially saturated ground conditions particularly under repeated shaking events. This study aims to understand the dynamic behaviour of surface structure interaction with a shallow tunnel under repeated dynamic loading conditions (i.e. test conditions simulating foreshocks/aftershock occurrences during earthquake events) in a partially saturated ground. For the experimental evaluation, 1-g uni-axial shaking table was used to analyse the interaction between soil-tunnel-surface structures during dynamic events. The model ground was prepared with 60% relative density having 25% saturation. A scaled-down underground tunnel and surface structures models used in this study assessing the interaction studies. The scaled-down structural member, i.e. column member, was fixed on an elevated piled foundation (EPF) as shown in Figs. 1 and 2. Similarly, a scaled-down square tunnel having dimensions 280 × 280 × 750 mm was installed at 420 mm depth was used for simulating shallow tunnels. The tunnel-structure embedded ground was then subjected to repeated incremental sinusoidal acceleration loading of 0.1, 0.2, 0.3, 0.4 and 0.5 g with 5 Hz frequency. The effects of acceleration response, amplification factor, structure displacement, soil displacement, and pore water pressure ratio were compared and analysed. The displacement of the tunnel and structure model was assessed using 2D digital image correlation (2D-DIC). The parameters influencing tunnelsoil-surface structure interaction under repeated dynamic loading conditions were analysed and presented.
332
M. D. Godson et al.
Fig. 1 Typical example of structure to resist high flood [9]
Fig. 2 Schematic 3-D view of the experimental setup
2 Experimental Programme 2.1 Uni-Axial Shaking Table Setup The shaking table tests were conducted on uni-axial shaking table in the soil dynamics lab at CSIR-CBRI. The uni-axial shaking table consists of a 2 m × 2 m platform which capable of carrying a maximum payload of 3 tonnes. The table works with an operating frequency range of 0.01–50 Hz with a maximum peak velocity of 2 m/s and an acceleration range from 0.001 to 1 g. The entire operation of the shaking table was performed through a digitally controlled data acquisition system. A rigid Perspex rectangular tank having dimensions 1.75 m × 0.75 m × 1.0 m was used for performing laboratory scaled model tests. Since the experimental studies involve use of 2D-DIC technique for measuring displacement and strains, rigid
Influence of Existing Tunnel—Surface Structure Interaction Under …
333
container was used in this study. To minimize the boundary effects, a 50 mm thick polyethylene foam was attached to the side walls perpendicular to the excitation direction [7]. The bottom of the rigid test tank was made rough by sandblasting before the experiment to ensure the transfer of input motion and shear stress from the base to the prepared soil bed layer.
2.2 Development of Scaled-Down Model Structures When performing dynamic soil-structure interaction (SSI) studies using the shaking table equipment, getting absolute consistency in similitude ratios of all physical quantities in the SSI system is exceptionally challenging due to prototype and testing environment limitations. To minimize these limitations, Buckingham-π theorem (i.e. similarity relations between the model structure and the prototype design) was established [8]. Considering the test equipment’s fundamental characteristics and the model box dimensions, the geometric similarity ratio was set to 1/20 for the tunnel model. The gypsum material was chosen for the model structure due to its compatibility characteristics in elastic modulus relation in simulating prototype model. The similarity ratio in terms of elastic modulus was found to be 1/12.65. The similarity ratio in respect of the acceleration was selected as 1. Based on three fundamental scale factors, i.e. geometry, material, and dynamic conditions, the similarity ratios were obtained and listed in Table 1. For testing, a scaled-down model of a square tunnel with 230 mm at the inner cross-section and having a tunnel lining thickness of 25 mm was fabricated using a gypsum slurry of 1:0.7 to meet the similarity relations as listed in Table 1. Further, the longitudinal length of the tunnel model was taken the same as the width of the tank, i.e. 750 mm. Both the sides of the tunnel were attached to the plexiglass with a geomembrane to restrict the entry of soil and water. For the above structural model, a scaled-down column member resting on pile foundation was considered in the study. The geometric and acceleration similarity ratios were considered the same as that of the tunnel model. At the same time, high Table 1 Similarity ratios of the tunnel model Type
Parameters
Relationship
Similarity ratio
Geometry
Length l
λl
1/20
Displacement D
λD = λl
1/20
Elastic modulus E
λE
1/12.65
Density ρ
λρ = λE / λa λl
1/0.63
Stress σ
λσ = λE
1/12.65
Material
Dynamic
Strain ε
λε = λσ / λE
1
Frequency f
λf = λa 0.5 λl −0.5
4.47
Acceleration a
λa
1
334
M. D. Godson et al.
stiffness material was proposed for the above structure along with piled foundation as the test series includes series of repeated incremental shaking events. The similarity ratio for elastic modulus was found to be 1/0.24, and the remaining parameters could be calculated using the relationship listed in Table 1. For simulating super structure, a square column of 25 mm size which attached to pile foundation was used to study the horizontal displacement in the surface structure with an existing tunnel model during repeated shaking events. The pile foundation was elevated to 150 mm above existing ground level to replicate high flooded areas, as shown in Fig. 1. The ground was then subjected to series of repeated shaking events to assess the surface structure-soil-underground structure interaction.
2.3 Experimental Preparation For experimental testing, soil collected from the Solani River bed, Roorkee was used. The soil characterization results showed that soil falls under the category of poorly graded fine silty sand having uniformity coefficient (C u ) and coefficient of curvature (C c ) of 2.65 and 1.15, respectively. The other properties are listed in Table 2. In laboratory testing sample, preparation methods are crucial in mimicking the initial stress conditions especially when studying dynamic response of soil-tunnelsurface structure interactions in partially saturated ground conditions. This study attempted to prepare a 25% saturation (partially saturation) of the ground with 60% density using the sand pluviation technique. Using weight volume relationship, the required quantity of sand and water was estimated for the selected density. Then, the ground bed was divided equally into layers of 50 mm thickness to maintain more uniformity, and the estimated quantity of sand followed by water was filled in the container. In order to provide a uniform soil bed, the sand was poured down at a calculated height through a conical hopper arrangement with an inverted solid cone attached at the end at a 60° angle. By performing numerous relative density Table 2 Properties of the soil model Sl. no.
Parameters
Value
1
Soil type (SP)
Poorly graded sand
2
Specific gravity
2.66
Unit No unit
3
Minimum density (γ min )
1.4023
g/cc
4
Maximum density (γ max )
1.6599
g/cc
5
Density (γ )
1.549
g/cc
6
Void ratio (e)
0.7201
No unit
7
Cohesion (c)
0
kPa
8
Angle of internal friction (ϕ)
34
9
Young’s modulus
12000
kPa
Influence of Existing Tunnel—Surface Structure Interaction Under …
335
tests under IS 2720—Part XIV, the height at which the sand was to be poured into achieving the desired density was previously calculated. After completion of each layer, the soil samples were collected for measuring in-situ water content was taken to verify the uniformity in developing partial saturation in each prepared layer. Also, the container was left undisturbed for at least an hour after every layer preparation to attain maximum uniformity. The ground was prepared to a height of 900 mm in which the tunnel model and surface structural model were placed at 200 mm and 750 mm, respectively, from the bottom of the container. The schematic 3-D view of the complete experimental setup is shown in Fig. 2. Detailed instrumentation is an integral part of data collection during the experimental testing. This study adopted non-contact type measurement technique, i.e. digital image correlation (DIC) system. Over the past few years, the DIC technique has undergone substantial research and development and minimized computation complexity, achieved high accuracy deformation measurement, and continuously expanding the application space. Hence, 2D-DIC (correlated solutions, USA) has been used to monitor the structural deformations and responses. The viewing surface of both the structures has been smoothened and speckled (black dots on white background) before the experimental preparation. The structures (tunnel and surface structure element), along with the speckled surface, have been placed inside the soil, and two cameras were used to capture both the structures individually. During the testing, cameras were placed precisely horizontal to the plain/area of interest (AOI) along with required lighting (series of LEDs), as shown in Fig. 3. Apart from DIC contact type strain-based four pore water pressure transducers, two accelerometers and two linear variable differential transformers (LVDT) at various locations were used for monitoring the response of the partially saturated ground model during dynamic testing. The schematic view of installed transducers and 2D-DIC set up are given in Fig. 4. The experimental testing conditions were planned to replicate repeated shaking conditions which generally observed during earthquake incidence, i.e. generation Fig. 3 DIC setup along with prepared sample Structural element
Tunnel Model
336
M. D. Godson et al.
Fig. 4 Schematic view of instrumentation used
of foreshock and aftershock events. After considering the PGA of several earthquakes, sinusoidal incremental input motion of 0.1, 0.2, 0.3, 0.4 and 0.5 g with 5 Hz frequency have been adopted simulating low to very high shaking conditions and applied to the uni-axial shaking table. The testing series from 0.1 to 0.5 g were given sequentially during the study. Each shaking event was carried out for 200 cycles since the testing condition neglects the time similarity ratio to understand the interaction behaviour over a longer shaking duration. After each loading, the subsequent incremental loading was applied after the dissipation of generated excess pore water pressures observed during the previous loading.
3 Results and Discussion 3.1 Acceleration Response of Interaction System In this segment, the acceleration response of the soil-tunnel-surface structure and its interaction during incremental repeated input motion is presented. For the soil response, two accelerometers were used at different depths, i.e. at 420 and 700 mm (from the top surface). In addition, both underground and surface structures were monitored using DIC through VIC-snap software, and VIC-2D software was used to analyse the captured images. The structural acceleration responses were calculated by differentiating the velocity–time domain data obtained from the software using a data analysis software. A typical graph is illustrating the response of transducers in acceleration time domain at 700 and 420 mm depth obtained during 0.1 g input motion is shown in Fig. 5 and observed that the acceleration response of the soil increases from bottom to top. In tunnel and surface structure interaction, the response at three
Influence of Existing Tunnel—Surface Structure Interaction Under …
337
points (at the top (T), middle (M), and bottom (B)) were calculated, and the peak has been demonstrated in Fig. 6. The obtained results showed the interaction between soil, tunnel, and the surface structure during repeated shaking events, i.e. 0.1–0.5 g. It was observed that, the acceleration response of soil at 420 mm (depth equals to the depth of tunnel top) increases more than 50% compared to the deeper depth, i.e. 700 mm, respectively, (depth equals to the depth of tunnel bottom) during the first input motion. This increment found increases during repeated acceleration loading conditions. This can be mainly due to the inertial effect of the tunnel embedment, which creates soil deposition due to longer shaking duration. Further, the confinement provided by the soil around the tunnel increases and affects the overall response of underground structure inside the soil. With incremental repeated shaking events, the load taken by the soil is found comparatively higher than that of the tunnel due to occurrence of soil densification. Thus, the presence of an underground structure inside the partially saturated ground moderately reduces the system’s overall stiffness (system stiffness weakening effect) which affects the above-ground structure’s seismic response comparatively during repeated shaking events as can be seen from Fig. 6. Up to 0.3 g incremental loading, the structural responses increase or found uniform indicating the influence of partial saturation on soil compaction characteristics during repeated loading events with longer shaking duration. At 0.4 g, the acceleration response in both the structures found reduced by around 30% this was mainly due to soil dilation which was evident from the developed cracks as shown in Fig. 7 at the surface above the tunnel observed after 0.4 g shaking. After then, the acceleration responses of both structures showed more than 60% increment due to higher incremental loading with longer shaking duration. Thus, with the incremental repeated shaking, the interaction behaviour between the different systems also varies affecting the structural stability. The influence of soil compaction in partially saturated ground under repeated shaking can be further compared from the obtained soil displacement and pore pressure response, which are explained in the following section.
Fig. 5 Acceleration response of soil (0.1 g)
338
Fig. 6 Peak acceleration response of the interaction system Fig. 7 Crack development
M. D. Godson et al.
Influence of Existing Tunnel—Surface Structure Interaction Under …
339
3.2 Effect of Settlement Response of Interaction System The observed settlement in soil and structure highlights the dynamic amplification and attenuation characteristics and explains the interaction between the systems during repeated loading conditions. To measure the soil displacement, two LVDTs were placed at P1 (above the tunnel location) and P2 (400 mm adjacent to the tunnel location), as shown in Fig. 4. The soil settlement and structural settlement (through DIC) observed during the repeated loading have been compared in Figs. 8 and 9. Figure 8 presents a typical time settlement plot obtained during 0.1 g input motion. Figure 9 presents the peak obtained settlement for each input motion. It can be seen that the displacement of soil at P1 and P2 location during 0.1 g input motion was approximately 1 mm and 1.35 mm, respectively. Up to 0.3 g input motion, more than 35% increment increase was observed indicating the occurrence of soil compaction and at 0.4 g, to the settlement was reduced about 25% suggesting that soil attained its complete compaction. Similarly, the incremental percentage in the underground and surface structure settlement was found gradual, and a slight variation was observed at 0.4 g input motion confirming the soil compaction. The obtained test results also showed that the settlement of the underground structure is about 50% lesser than the surface structure due to soil confinement around the underground structure and validated soil densification. Since the surface structure was placed adjacent to the tunnel location (similar to P2), the settlement of the surface structure was about 30% more than that of the soil which induces deformation in structure. It can be concluded that repeated shaking events induce particle rearrangement which enhances soil compaction in the partially consolidated ground. However, the repeated shaking also affects the confining characteristics of surrounding soil which reduces the stability of underground system and impart structural instability to the surface structure.
3.3 Structural Deformations During Repeated Input Motion To understand the horizontal displacement of the underground and surface structure, 2D-DIC has been used. After each input motion, the captured images were analysed. A typical obtained horizontal displacement contours for both the structures during analysis is shown in Fig. 10. The obtained peak horizontal displacement for the underground and surface structures is shown in Figs. 11 and 12. The horizontal displacement of the tunnel showed a gradual percentage decrement of 45% during 0.1–0.2 g and about 23% during 0.4–0.5 g due to soil confinement characteristics due to experienced soil densification during repeated input motion. However, at 0.5 g, the top portion of the tunnel showed 6% increment in tunnel deformation than bottom portion due to disturbances in the deposited soil induced by the higher shaking event. In case of surface structure, structure 15 and 28% increment in displacement during 0.2 and 0.3 g. Similar to reduction in tunnel deformation, the increment percentage in deformation reduced about 4% compared to previous results during 0.4 g. At
340
M. D. Godson et al.
Fig. 8 Settlement in time domain (0.1 g)
Fig. 9 Maximum settlement obtained
higher repeated input motion of 0.5 g, the top portion of the surface structure shows approximately 15% increment to the bottom portion and failure of elevated pile foundation was observed at higher shaking. The combined deformation effects of
Influence of Existing Tunnel—Surface Structure Interaction Under …
341
Fig. 10 Horizontal displacement contours in VIC-2D software
Fig. 11 Peak horizontal displacement of underground structure
underground structure together with soil displacement induce structural failure at higher shaking condition.
3.4 Influence of Pore Water Pressures The generation of pore water pressures and its impact on structure-soil-underground structure response in partially saturated ground during repeated shaking events is discussed in this section. For measuring PWP, four pore pressure transducers were kept at 700, 560, 420 and 100 mm along the depth of the soil bed from bottom, respectively. Figure 13 presents a typical pore water pressure response with time
342
M. D. Godson et al.
Fig. 12 Peak horizontal displacement of surface
during 0.1 g shaking condition. Figure 14 showed peak pore water pressure generated during repeated shaking event for comparing its influence at different depth. The obtained values highlighted that, the soil experience slightly suction potential during initial 5–10 s throughout the depth due to partially saturated conditions. As discussed in previous sections, the repeated shaking with longer shaking duration induces soil densification which can be verified from the pore pressure generation at 0.1 g and peak pore pressure values for 0.1–0.5 g shaking conditions. No considerable pore pressure generation was observed which evidenced occurrence of soil compaction which contributed in improving confining characteristics around the tunnel system. However, when the partially saturated ground subjected to repeated shaking events, soil dilation induces instability in the deposited ground and caused deformation in soil-structure system. Hence, proper understanding on soil behaviour is highly required in partially saturated ground during repeated shaking events to ensure the safety of infrastructures.
4 Conclusion This paper aims to understand the dynamic behaviour of surface structure interaction with shallow tunnel under repeated dynamic loading conditions in partially saturated ground. The interaction between tunnel-soil-surface structures was studied based on the obtained acceleration response, settlement, horizontal displacement of both the
Influence of Existing Tunnel—Surface Structure Interaction Under …
343
Fig. 13 PWP development in 0.1 g
Fig. 14 Peak PWP developed
structures, and pore water pressure response under incremental repeated dynamic loading conditions. The following conclusions were drawn based on these results. 1. Irrespective of the expected positive performance from the piled foundation in terms of soil reinforcement and improvement in confinement characteristics within the ground, the performance reduces under repeated shaking conditions in the partially saturated ground due to increment in acceleration loading and longer
344
M. D. Godson et al.
shaking duration. This was evidenced from the observed super and sub-structure displacements during the study. 2. Occurrence of soil densification was observed in the case of partially saturated ground which improves the confining characteristics of surrounding soil around the tunnel system at low to medium repeated shaking conditions. However, at higher acceleration loading conditions, dilation was observed which affects the interaction between surface structure-soil-underground structure dynamic behaviour. 3. Even though application of repeated shaking contributed in improving soil densification; the densification was not uniform with depth due to the embedded underground structure. This resulted in uneven load distribution between the tunnel and the soil which affect the stability of surface structure during repeated shaking events. Hence, proper care is required in designing surface structure when there is an existing tunnel system in close proximity. Acknowledgements The authors would like to thank the Director, CSIR-Central Building Research Institute, Roorkee, for giving the opportunity and support to publish this research work.
References 1. Hashash, Y.M., Hook, J.J., Schmidt, B., John, I., Yao, C.: Seismic design and analysis of underground structures. Tunn. Undergr. Space Technol. 16(4), 247–293 (2001) 2. Li, Y., Tian, Y., Zong, J.: Shaking Table Test on Seismic Response of Tunnel-Soil Surface Structure System considering Soil-Structure Interaction. Shock and Vibration (2022) 3. Navarro, C.: Effect of adjoining structures on seismic response of tunnels. Int. J. Numer. Anal. Meth. Geomech. 16(11), 797–814 (1992) 4. Lu, S., Zhao, D., Yin, H., Liu, S., Xu, H., Zhang, Y.: Shaking Table Test and Numerical Simulation Study on a Tunnel-Soil-Bridge Pile Structure Interaction System (2022) 5. Lou, M., Wang, H., Chen, X., Zhai, Y.: Structure–soil–structure interaction: literature review. Soil Dyn. Earthq. Eng. 31(12), 1724–1731 (2011) 6. Padmanabhan, G., Shanmugam, G.K.: Reliquefaction assessment studies on saturated sand deposits under repeated acceleration loading using 1-g shaking table experiments. J. Earthq. Eng. 26(6), 2888–2910 (2022) 7. Lombardi, D., Bhattacharya, S., Scarpa, F., Bianchi, M.: Dynamic response of a geotechnical rigid model container with absorbing boundaries. Soil Dyn. Earthq. Eng. 69, 46–56 (2015) 8. Lu, S., Xu, H., Wang, L., Liu, S., Zhao, D., Nie, W.: Effect of flexibility ratio on seismic response of rectangular tunnels in sand: experimental and numerical investigation. Soil Dyn. Earthq. Eng. 157, 107256 (2022) 9. https://timesofindia.indiatimes.com/city/kochi/stilt-houses-can-defyfloodwaters/articlesh-ow/ 70666254.cms
Similitude Characteristics Between Small-Scale Model and Full-Scale Piles Under Dynamic Excitations Shiva Shankar Choudhary, Sanjit Biswas, and Bappaditya Manna
Abstract In this study, it is intended to use a flexural rigidity-based scaling law proposed by Wood (Geotechnical Modeling, CRC Press, pp. 1–488, 2004) to predict the dynamic frequency–amplitude responses of the full-scale piles from small-scale model pile responses. To obtain this objective, axial harmonic tests on hollow steel single and 2 × 2-pile group having a diameter of 0.114 m and pile length of 3 m are performed in the field for different magnitudes of dynamic forces (0.868 and 1.944 Nm). The frequency versus amplitude responses obtained from the test show a single peak at resonance within the range of the dynamic test (0–50 Hz) for both types of pile foundation. The responses also exhibit nonlinear characteristics by virtue of reducing the resonant frequency with the increase of dynamic forces. The single pile responses also indicate lower resonant frequency and higher amplitude values as compared to the pile group responses. Using these experimental responses, the responses of the full-scale piles are calculated by assuming the scaling factors of 6, 8, and 10 to consider the full-scale pile lengths of 18 m, 24 m, and 30 m, respectively, without changing the aspect ratio of the piles. It is found from the full-scale pile responses that the resonant frequency values are decreased about 4–6 times, and the resonant amplitudes are increased about 15–32 times as compared to the small-scale piles. However, the basic characteristics of soil-pile responses of the small-scale model and full-scale piles are observed to be similar for both the single pile and 2 × 2-pile group. Keywords Model pile · Axial harmonic tests · Full-scale pile · Dynamic responses · Scaling law S. S. Choudhary (B) Department of Civil Engineering, NIT Patna, Patna 800005, India e-mail: [email protected] S. Biswas Department of Civil Engineering, NIT Warangal, Warangal 506004, India e-mail: [email protected] B. Manna Department of Civil Engineering, IIT Delhi, New Delhi 110016, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_27
345
346
S. S. Choudhary et al.
1 Introduction In model testing of pile, behaviour of prototype pile is approximated using scaling laws [1] so that it can qualitatively resemble prototype behaviour. One of the most significant barriers to applying physical modelling to an existing prototype is due to the experimental constraints imposed by the size of the model. To overcome these limitations, the experimental facility for 1-g model testing [2] has grown in size, allowing real-scale models to be tested. However, the development of a larger research facility for geotechnical structures is still a challenge due to limitation in testing instrument capacity and budget. Under the aforementioned constraints, demand for large prototype testing is increasing. To address these objectives and constraints, the generalized scaling law [3], was developed which combines the scaling law for centrifuge testing and 1-g dynamic model testing. Other researchers [4, 5] used the ‘modelling-of-models’ solution proposed by Schofield [6] to conduct a centrifuge model experiments to evaluate the utility of the generalized scaling law for the dynamic behaviour of sand layers. The application of the generalized scaling law [7] is also investigated for the pile foundations in different conditions of soil layers with a rigid container and for the fully dynamic domain of a foundation with structure system with generated strain levels of 10% in order of magnitude [8]. The findings showed that the generalized scaling law may be applied to a fully dynamic combined system subjected to cumulative shear strain due to cyclic sand movement during dynamic loadings. The selected aspects of a geotechnical centrifuge experiment were conducted [9] to investigate the effects of saturated soil condition with single pile foundation system under both lateral force and bending moment. The data reveals that soil partial saturation has a significant impact on pile response. The displacement of the head of the pile under operating loads is significantly smaller than that recorded under saturated conditions. In the present study, the similitude characteristics between small-scale model and full-scale piles, with particular emphasis on the scaling law for axial harmonic loading, are investigated through the dynamic response of model pile foundations. Under machine-based soil-pile loading systems, two soil-pile setups (single pile and 2 × 2-pile groups) are used to study the generalized scaling law based on the Wood [3] method.
1.1 Brief Review of the Scaling Law Physical centrifuge modelling is a valid methodology for investigating soil–structure interaction problems experimentally. Following scaling laws, the small-scale model is linked to the full-scale prototype, as initially investigated by Schofield [6]. When the model’s scale is ‘1/n’, it must be subjected to a centrifuge g-level of ‘n’, where ‘n’ is the scaling factor. Studies have traditionally been carried out on fully wet or entirely dry soil models. Nowadays, centrifuge modelling has been used to investigate unsaturated soil behaviour [10–12]. Different authors have experimented with
Similitude Characteristics Between Small-Scale Model and Full-Scale …
347
Table 1 Scale factors summarized by Wood [3] Quantity
General
1 g (Laboratory)
ng (Centrifuge)
Length
nl
1/n
1/n
Mass density
nρ
1
1
Acceleration
ng
1
n
Stiffness
nG
1/nα
1
2 /n
1/n2−α
1/ n
Displacement
nρ ng nl
Time (dynamic)
nl (nρ /nG )1/2
1/n1−α/2
1/ n
Frequency
(nG /nρ )1/2 /nl
n1−α/2
n
1/n1−α/2
1
Shear wave velocity
(nG /nρ
)1/2
G
scaling laws for unsaturated soils at various g-levels and for different soils. Table 1, provided by Wood [3], summarizes the scaling factors. The ratios of model and prototype values, which are symbolically listed under the term ‘general’, illustrate the basic linkage between the numerous modelling selections that might be made. The specific factors indicated under the headings ‘1 g (laboratory)’ and ‘ng (centrifuge)’. These are the result of typical modelling consideration parts. However, the other consideration could be made based on the output and suitability of models. The table shows aspirational guidance. When all of the governing laws of similitude are in place, a real model emerges. However, it will often be necessary to make do with an adequate model that maintains first-order similarity for geotechnical modelling [13] by arguing that some of the constraints imposed by dimensional analysis are of second-order importance based on a proper consideration of the likely mechanisms of response. There are a variety of scaling variables to choose from, and there may be some debate regarding which set is the most fundamental. Some of the added components will be viewed as independent variables, while it will be demonstrated that the soil may often regulate the apparent (and possibly beneficial) independence. It is found from the various literatures that the scaling law of wood is one of the popular choices to scale up the model pile responses for nonlinear conditions. Hence, in the present study, wood scaling law is adopted.
2 Soil Properties and Small-Scale Model Preparation A dynamic excitation test is carried out in the field to understand the nonlinear variation of frequency and amplitude for single and pile group in the axial direction. To determine the soil properties in the testing location, different geotechnical tests are performed in the field as well as in the laboratory. From the tests, two soil layers are found [0–2.5 m and 3.5–6.5 m] which are mostly clayey silt type of soil. The dynamic field tests are conducted on small-scale hollow steel tube piles (external diameter =
348
S. S. Choudhary et al.
Fig. 1 Mechanical oscillator with rotating masses
11.4 cm, thickness = 0.3 cm) driven into the soil for 300 cm. A pile spacing of 3d is maintained during the pile installation into the ground. The dynamic axial forces are generated on the soil-pile loading systems with the help of a rotating mechanical oscillator. As per requirement, the axial magnitude of the excitation increases or decreases with the help of an outer valve of eccentricity (θ ), which is part of two counters rotating-mass inside the oscillator. The working principle of a mechanical oscillator is shown in Fig. 1. The dynamic responses of pile foundation in terms of frequency and amplitude are obtained for two different eccentric moments or excitation forces [W.e = 0.868 Nm (θ = 40°) and 1.944 Nm (θ = 100°)] under a static load (W s ) of 14 kN. Oscillator is placed horizontally on a pile cap loading system to generate excitation forces in an axial direction. For the single and group piles, a square steel pile cap (0.9 m × 0.9 m × 0.037 m) is affixed to the top. A mechanical oscillator and steel plates are added to the pile cap’s top after it has been installed to produce the desired static load. Static load is used to bring the pile’s resonance frequency into the exciter’s frequency range. Steel plates, an oscillator, and a pile cap are all closely attached to one another using rods and nuts to create the pile cap loading system. For the single and group piles, a square steel pile cap (0.9 m × 0.9 m × 0.037 m) is placed on the top of the piles and connected rigidly with the piles. After that, a mechanical oscillator and steel plates are kept on top of the pile cap and tightened together. An accelerometer is connected to the top and centre of the soil-pile loading set-up to measure the axial amplitude. To measure the frequency during testing, one end of the frequency measuring sensor is connected to the DC motor, and to record the data, the other end is connected to the data logger. The dynamic excitation field test set-up is shown in Fig. 2.
2.1 Test Results From the test results (Fig. 3), it is found that the basic properties and variation of frequency with amplitude are found almost same for both single and pile group. However, for pile group, the values resonant frequency are found higher and the resonant amplitudes are found lower with respect to single pile. This phenomenon may indicate the increase of soil-pile stiffness for pile groups as the number of piles increases. The dynamic field response curves reveal nonlinear behaviour by displaying a decrease in resonant frequencies and a disproportional increase in resonant amplitudes with increasing eccentric moments. For example, due to an increase
Similitude Characteristics Between Small-Scale Model and Full-Scale …
349
Fig. 2 Complete soil-pile loading system under dynamic excitation test
in eccentric moment from 0.868 to 1.944 Nm (= 2.2 times), the resonant frequency of a single pile is reduced from 28 to 22 Hz, and the resonant amplitude is enhanced by nearly 2.4 times (from 0.142 to 0.340 mm). From Fig. 3, it is also found that the amplitudes increase with frequency, and after the resonance frequency, the amplitudes decrease.
350
S. S. Choudhary et al.
Fig. 3 Dynamic field response of single pile and 2 × 2-pile group under excitation test
3 Scaling to Prototype In the current investigation, dynamic field tests are performed on small-scale model piles. The dimensions and properties of the model piles are converted and dimensions and properties of the prototype piles based on the similitude law proposed by Wood [3] which are summarized in Table 2. The values of full-scale prototype soil-pile system are determined for the model by using a scaling factor (n) of 6, 8, and 10. The ‘α’ value quantifies the effect of the stress level on the stiffness of soil-pile system, and as per the proposed law, it is taken as 0.5 for clayey soil. To determine the diameter of the prototype pile, flexural rigidity similitude formulation (E m I m /E p I p = 1/n4+A , where E m , I m and E p I p are the Young’s modulus and moment of inertia of the model and prototype pile, respectively) is used. The experimental resonant frequency and amplitude values of the model single pile and 2 × 2-pile groups are also converted to resonant frequency and amplitude values of prototype piles which are presented in Table 3. It is found from the full-scale pile soil-pile responses that the resonant frequency values are decreased about 4–6 times, and the resonant amplitudes are increased about 15–32 times as compared to the small-scale piles under a scaling factor of 6–10. It can also be observed from the tabular results that the prototype single pile and 2 × 2-pile groups show similar types of nonlinear patterns as obtained from the model pile tests with the consideration of suitable scaling factor ‘n’ using scaling law. Three sets of parameters are investigated to understand the influence of scaling factors from small-scale models to full-scale prototype soil-pile systems. For example, after introducing the scaling law, the length and outer diameter of model piles (l = 3.0 m and d = 0.114 m) become 18 m, 24 m, and 30 m in length and
Similitude Characteristics Between Small-Scale Model and Full-Scale …
351
Table 2 Scaled value of dynamic properties Quantity Shear wave velocity (m/s)
Up to 1.0 m
Scaling law (prototype/model)
Model values
nA/2
Prototype values n=6
n=8
n = 10
83
130
140
148
Up to 2.0 m
109
171
183
194
Up to 3.0 m
127
199
214
226
Up to 4.0 m
137
214
230
244
Up to 5.0 m
146
229
246
260
Up to 6.0 m
126
197
212
224
Pile length (m)
n
3.0
18
24
30
Pile diameter (m)
n
0.114
0.684
0.912
1.14
Pile thickness (mm)
E p I p /E m I m = n4+A 3.0
47.0
73.7
104.8
Stiffness of pile (GPa)
1
200
200
200
200
Eccentric moment (Nm)
n5−α
0.868
2755
10,056
27,449
1.944
6171
22,522
61,475
Static weight (kN)
n3
14
3024
7168
14,000
Frequency (Hz)
1/n1−A/2
50
13.04
10.51
8.89
Amplitude (mm)
n2−α
0.10
1.47
2.26
3.16
Table 3 Scaled values of resonant frequency and amplitude of single pile and 2 × 2-pile group Model prototype W.e (Nm)
f n (Hz)
An (mm)
f n (Hz) n=6
An (mm) n=8
n= 10
n=6
n=8
n = 10
4.49
Single pile 0.868
28
0.142
7.3
5.9
5.0
2.09
3.21
1.944
22
0.340
5.7
4.6
3.9
4.99
7.69
10.8
2 × 2-pile group 0.868
39
0.049
10.2
8.2
6.9
0.72
1.11
1.55
1.944
37
0.126
9.7
7.8
6.6
1.85
2.85
3.98
f n = resonant frequency and An = resonant amplitude
0.684 m, 0.912 m, and 1.14 m in diameter for full-scale, assuming the scaling factors of 6, 8, and 10, respectively. It is found from the increment of length and diameter that the ratio of l/d is the same for all scaling factors, i.e. 26.3. With the increase of a single scaling factor (n = 1), the resonant frequency of the model pile decreases by approximately 40% and the resonant amplitude increases by approximately 182%. In case of eccentric moments, the values are found to be very high for the prototype model. Due to higher excitation forces, the soil-pile stiffness decreases and, with that
352
S. S. Choudhary et al.
respect, the values of resonant frequencies decrease and amplitudes increase, which indicates the correct pattern of dynamic responses. The average resonant frequency values of the 2 × 2-pile group are found to be approximately 53% higher when compared to the single pile, and the values of resonant amplitude are found to be approximately 64% lower for both the model pile and the full-scale soil-pile system. The reliability of the presented results may be verified by experimental tests based on the dimensions of prototype soil-pile systems under same soil conditions. However, to limit the cost, time and effort, the scaling law is widely considered and applied in many geotechnical solutions. A similar solution based on scaling law is considered and investigated by many researchers [3, 14, 15] to predict the response of full-scale piles.
4 Conclusions To study the scaling law in dynamic excitation tests to a nonlinear regime of soil-pile systems subjected to machine-based pile foundation, single and group pile field tests are performed. From the test results, it is found that the scaling law also follows the pattern of nonlinearity as measured in field tests, which indicate a decrease in resonant frequencies and a disproportional increase in resonant amplitudes with an increase in excitation forces. For both the model pile and the full-scale soil-pile systems, the average resonant frequency values of the 2 × 2-pile group are found to be roughly 53% higher than the single pile, and the values of resonant amplitude are found to be approximately 64% lower. It is also observed that the resonant frequency of the model pile decreases by approximately 40% and the resonant amplitude increases by approximately 182% with the increase of every single scaling factor.
References 1. Garnier, J., Gaudin, C., Springman, S.M., Culligan, P.J., Goodings, D., Konig, D., Kutter, B.L., Phillips, R., Randolph, M.F., Thorel, L.: Catalogue of scaling laws and similitude questions in geotechnical centrifuge modelling. Int. J. Phys. Modell. Geotech. 7(3), 1–23 (2007) 2. Tokimatsu, K., Suzuki, H., Tabata, K., Sato, M.: Three-dimensional shaking table tests on soilpile-structure models using E-defense facility. In: 4th International Conference on Earthquake Engineering, pp. 1–11, Greece (2007) 3. Wood, D.M.: Geotechnical Modeling. CRC Press, pp. 1–488 (2004) 4. Tobita, T., Iai, S., von der Tann, L., Yaoi, Y.: Application of the generalised scaling law to saturated ground. Int. J. Phys. Modell. Geotech. 11(4), 138–155 (2011) 5. Tobita, T., Escoffier, S., Chazelas, J. L., Iai, S.: Generalized scaling law for settlements of dry sand deposit. In: 15th World Conference on Earthquake Engineering, Lisbon, Portugal, No. 4104 (2012) 6. Schofield, A.N.: Cambridge geotechnical centrifuge operations. Géotechnique 30(3), 227–268 (1980)
Similitude Characteristics Between Small-Scale Model and Full-Scale …
353
7. Tobita, T., Iai, S.: New modelling of models for dynamic behavior of a pile foundation. In: The 15th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, Fukuoka, Japan, No. JPN-026 (2015) 8. Ueda, K., Sawada, K., Wada, T., Tobita, T., Iai, S.: Applicability of the generalized scaling law to a pile-inclined ground system subject to liquefaction-induced lateral spreading. Soils Found. 59(5), 1260–1279 (2019) 9. Lalicata, L.M., Rotisciani, G.M., Desideri, A., Casini, F., Thore, L.: Physical modelling of piles under lateral loading in unsaturated soils. In: 4th European Conference on Unsaturated Soils (E-UNSAT 2020), vol. 195, pp. 1–6, Portugal (2020) 10. Casini, F., Muñoz, J., Lorenco, S., Thorel, L., Vaunat, J., Delage, P., Gallipoli, G.: In Between theory and practice in unsaturated soil mechanics. In: Tarantino, A., Mancuso, C. (eds.) Rotterdam (2009) 11. Thorel, L., Ferber, V., Caicedo, B., Khokhar, I.M.: Physical modelling of wetting-induced collapse in embankment base. Géotechnique 61(5), 409–420 (2011) 12. Soranzo, E., Tamagnini, R., Wu, W.: Face stability of shallow tunnels in partially saturated soil: centrifuge testing and numerical analysis. Géotechnique 65(6), 454–467 (2015) 13. Harris, H.G., Sabnis, G.: Structural Modeling and Experimental Techniques, 2nd edn. CRC Press, Boca Raton (1999) 14. Goit, C.S., Saitoh, M., Mylonaki, G.: Principle of superposition for assessing horizontal dynamic response of pile groups encompassing soil nonlinearity. Soil Dyn. Earthq. Eng. 82, 73–83 (2016) 15. Subramanian, R.M., Boominathan, A.: Dynamic experimental studies on lateral behaviour of batter piles in soft clay. Int. J. Geotech. Eng. 10(4), 317–327 (2016)
Numerical Simulations and Validation of a Rocking Foundation Model for Seismic Loading S. Soundararajan, S. Gajan, and P. Raychowdhury
Abstract The objective of this study is to develop a numerical model for rocking shallow foundations supporting shear wall and bridge-pier structures and to validate the numerical model using centrifuge experimental results. OpenSees finite element framework was used to build the numerical model, where a contact interface model (CIM) was used to model the rocking behavior of soil-foundation system, and the structural components were modeled using elastic beam-column elements. The numerical model was first developed using soil properties obtained from theoretical and empirical relationships and validated using the cyclic moment-rotation results of foundations obtained from centrifuge experiments. The numerical model was then used to calculate seismic energy dissipation in soil during rocking, peak rotation of foundation during shaking, and tipping-over stability ratio of rocking systems for the same base accelerations of earthquake motions used in centrifuge experiments. Numerical model predictions for seismic energy dissipation of rocking foundations as a function of arias intensity of the earthquake motion and peak rotation of rocking foundation as a function of peak ground acceleration of the earthquake motion compare reasonably well with the corresponding experimental results (with mean absolute percentage errors of 0.5–0.6). For 24 out of 26 centrifuge experiments considered, the tipping-over stability ratio obtained from both the numerical simulations and experimental results vary between 0.85 and 1.0, demonstrating (i) the excellent stability of rocking systems against tipping-over failure and (ii) the numerical model’s ability to capture the tipping-over stability of rocking systems. Keywords Rocking foundation · Contact interface model · Seismic energy dissipation · Peak rotation · Tipping-over stability
S. Soundararajan (B) · P. Raychowdhury Indian Institute of Technology Kanpur, Kalyanpur, Kanpur, Uttar Pradesh 208016, India e-mail: [email protected] S. Gajan SUNY Polytechnic Institute, Utica, NY 13502, USA © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_28
355
356
S. Soundararajan et al.
1 Introduction The rocking behavior of shallow foundations is an emerging performance-based design methodology in which plastic shearing of soil and formation of a plastic hinge occur in the soil beneath the footing during seismic loading [1, 2]. The concerns related to rocking foundations include permanent settlement of foundation, peak and permanent rotation of foundation, and tipping-over stability of structure, as excessive deformations are possible due to yielding and plastic shearing of soil. Previous experimental studies [3–7] have demonstrated the potential advantages of rocking behavior of conventional footings and possible ways to control the foundation deformations within tolerable limits when subjected to dynamic loading. Commonly used numerical modeling techniques to capture the non-linear soil-foundation-structure interaction in rocking foundations include (i) bean on nonlinear Winkler foundation (BNWF) modeling [8, 9] and (ii) macro-element modeling [10, 11]. Recent studies on rocking foundations also include regression analysis [12], meta-analysis of experimental data [13], and application of machine learning algorithms to develop predictive models [14]. The current Indian practice for seismic design of shallow foundations is given in detail in Nandyala and Jakka 2022 [17]. To this end, the major objective of this study is to develop a numerical model for rocking shallow foundations supporting shear wall and bridge-pier structures and to validate the numerical model using centrifuge experimental results. The model is developed using a macro-element contact interface model (CIM) available in OpenSees finite element platform. The experimental results and data utilized in this study are available in a database in Digital Environment for Enabling DataDriven Science (DEEDS) website (https://datacenterhub.org/deedsdv/publications/ view/529). The concept and implementation of CIM is shown in Fig. 1. In CIM, the soil-footing interface and soil in the zone of influence is considered as a macroelement and modeled by tracking the geometry of the soil surface below footing, the opening and closing of gaps, footing-soil contact area, and the kinematics of footing-soil system. The coupling between vertical (V), shear (H), and moment (M) is incorporated in CIM through interaction diagrams in normalized V-H-M space [10].
2 Performance Parameters of Rocking Foundations The performance parameters of the rocking system primarily considered are the moment capacity, seismic energy dissipation, maximum and permanent rotation at the soil-footing interface, and the tip-over stability ratio. The theoretical ultimate moment capacity (M ult ) can be expressed as [3] Mult =
[ ] Ac Pst .L 1− . 2 A
(1)
Numerical Simulations and Validation of a Rocking Foundation Model …
357
Fig. 1 Concept of contact interface model used in OpenSees numerical model (see Gajan and Kutter 2009 [10] for more details)
The rocking coefficient (C r ) of a soil-footing system is defined as the ratio of ultimate moment capacity (M ult ) of the foundation to the applied static weight on the foundation normalized by the effective height of the structure (height from the base center point of the footing to the center of gravity of the structure, h). C r is expressed as [16] Cr =
] [ L Ac , . 1− 2.h A
(2)
where Pst is the static weight on the foundation, Ac /A is the inverse of critical contact area ratio. Critical contact area ratio is the ratio of total base area of the footing (A) to the minimum footing contact area with the soil required to support the applied vertical loads on the foundation (Ac ) (which can be calculated from conventional bearing capacity equation and the associated shape and depth factors [3]). The area of the hysteresis loops of cyclic moment-rotation gives the seismic energy dissipation (E) of the soil-footing interface of the rocking system θ E=
M.dθ.
(3)
0
The energy dissipation is normalized using Pst and the dimension of the footing along the direction of shaking (L) as E nor =
E . Pst .L
(4)
Permanent rotation is the residual tilt of the foundation at the end of base shaking. Maximum rotation (θ peak ) is the peak rotation of the soil-foundation system during shaking. The maximum rotation is a function of aspect ratio of structure-foundation
358
S. Soundararajan et al.
system (h/L) and peak ground acceleration (amax ). The tip-over stability ratio is expressed as [13] TSR = 1 −
θpeak . θcrit
(5)
Critical rotation of the structure (θ crit ) can be defined as the magnitude of rotation that would possibly cause tipping-over failure of the structure-foundation system during earthquake. The θ crit can be expressed as [13] θcrit = tan−1 (Cr ).
(6)
If θ peak is zero during the shake, TSR is equal to one, indicating a perfect stability against tipping-over failure (e.g., fixed-based system), and if θ peak is equal to θ crit , TSR is equal to zero, indicating that the structure is on the verge of tipping-over failure.
3 Development and Validation of Numerical Model The shear wall model test series T1-SSG03, T2-SSG04 consists of 11 events, and the bridge-pier model test series T3-LJD01, T4-LJD03 consists of 15 events with wide range of soil properties, foundation properties, and structural properties. The following Table 1 gives a summary of all the events and references used in this study. The capacity parameters such as the dimension of the footings (L, B, and D), vertical factor of safety (FSv ), critical contact area ratio (A/Ac ), aspect ratio (h/L), rocking coefficient (C r ) and demand parameter such as peak ground acceleration and arias intensity (I a ) and soil parameters such as density of soil (γ ), peak friction angle (φ), relative density (Dr ) of the events considered are given in Tables 2 and 3, respectively. The major user-defined CIM parameters include (i) dimension of the footing along the direction of loading (in this study, it is the length of the footing for all the events), (ii) factor of safety with respect to vertical load (FSv ), (iii) ultimate vertical load of foundation (V ult ), (iv) initial vertical stiffness (k v ), (v) rebounding ratio (Rv ), and (vi) footing internal node spacing (ΔL). The sample calculation of CIM parameters, Table 1 Summary of the test series and references used in this analysis Test series
Event no
Test type
References
Soil-structure type
T1
1–6
Centrifuge
[3]
Dry Nevada sand—rigid shear wall
T2
7–11
Centrifuge
[3]
Dry Nevada sand—rigid shear wall
T3
12–17
Centrifuge
[15]
Dry Nevada sand—bridge pier
T4
18–26
Centrifuge
[4]
Dry Nevada sand—bridge pier
Numerical Simulations and Validation of a Rocking Foundation Model …
359
Table 2 Capacity parameters of the events considered Test series
L (m)
B (m)
D (m)
A/Ac
FSv
Cr
h/L
T1
2.8
0.65
0.7
7.1–10
7.2–11.5
0.235–0.236
1.78–1.89
T2
2.8
0.65
0
2.2–3.2
2.6–4
0.147–0.176
1.78–1.89
T3
6.7
4.28
2.24
14
16.1
0.25
1.624
T4
7.35
4.7
2.24
10
11
0.353
1.267
Table 3 Demand parameters and soil parameters of the events considered Test series
PGA (g)
φ (deg)
I a (m/s)
γ (kN/m3 )
Dr (%)
Pst (kN)
T1
0.12–0.90
0.159–8.043
42
16.2
80
361–569
T2
0.12–0.90
0.190–3.048
42
16.2
80
361–569
T3
0.62–0.95
0.773–7.4
36
16.24
73
6002
T4
0.22–0.88
0.039–2.518
32.7
15.02
38
6186
mesh generation, and validation OpenSees code for shear wall and bridge-pier model can be referred in [16]. The experimental setup of test series T1 and T3 is shown in Fig. 2, and the acceleration-time history of sample event from the test series T1, T2, T3, and T4 is shown in Fig. 3. Some of the calculated input parameters of CIM are given in Table 4, where G is shear modulus of soil. The values of Rv and ΔL are taken as 0.1 and 0.01, respectively, [10] for all the events. The validation plots are shown in Figs. 4 and 5 for the SSG and LJD series, respectively. The validation plots are expressed as moment-rotation hysteresis loop for SSG and LJD series. The moment-rotation plot is compared with theoretical moment capacity value to visualize how far the energy dissipation is achieved numerically and experimentally. From Fig. 4a, it can be seen that the maximum normalized moment value obtained from numerical analysis is approximately 0.85, whereas the maximum normalized moment is close to 5.68 T3 – LJD01
PGA = 0.12 – 0.9g FSv = 7.2 – 11.5 A/Ac = 7.1 – 10 Cr = 0.235 – 0.236 Tapered Sine wave
Rigid Shear Wall
T1 – SSG03
10.15
0.7
2.80 Dry Nevada Sand Dr = 73%
4.0
PGA = 0.62-0.95g FSv = 16.1 8.88 A/Ac = 14 Cr = 0.25 Step wave 2.24 excitation
3.11 1.87
12.12
6.70 11.20
Dry Nevada Sand Dr = 73%
Fig. 2 Experimental setup of test series T1 and T3 (all dimensions are in prototype meters)
360
S. Soundararajan et al.
Fig. 3 Acceleration-time histories of sample events used in centrifuge experiments
0.7 which is obtained experimentally for PGA of 0.487 g and FSv of 7.2. And from Fig. 4b, the maximum normalized moment obtained from numerical and experimental analysis are approximately 0.75 and 0.6, respectively, for the PGA of 0.727 g and FSv of 4. Hence, from the validation plots of shear wall model shown in Fig. 4, it can be observed that numerical model captured the moment-rotation close to the experimental results. In case of LJD series, the prototype bridges considered in the experimental modeling are the Sanguinetti off-ramp located at I-105 for LJD01 and CA-108 overcrossing the Sanguinetti Rd for LJD03. From Fig. 5a, it can be observed that the maximum normalized moment for numerical and experimental analysis are approximately 0.8 for the PGA of 0.62 g and FSv of 16.1. And from Fig. 5b, the maximum normalized moment values obtained numerically and experimentally are 0.9 and 1.2, respectively, for the PGA of 0.393 g and FSv of 11. Therefore, from Fig. 5, the validation plots show that the CIM for bridge pier effectively captures the moment-rotation plot with experimental results. It should be noted that the moment-rotation hysteretic response of rocking foundations in numerical simulations do not match exactly with the experimental results. The differences could partially be attributed to the assumptions and simplifications of the numerical model used. However, the major purpose of this study is to capture some of the essential, summary features of rocking foundations using a simple numerical Table 4 CIM parameters of the events considered
Test series
G (MN/m2 )
K v (MN/m)
V ult (MN)
T1
92.51
856
2.59–6.45
T2
92.51
545
0.92–2.29
T3
183.38
5474
95.43
T4
113.61
3636
67.79
Numerical Simulations and Validation of a Rocking Foundation Model …
(a)
361
(b)
Fig. 4 a Validation of SSG03 normalized moment-rotation plot with experimental results; FSv = 7.2, Pst = 569 kN, PGA = 0.487 g, C r = 0.236; A/Ac = 7.1; b validation of SSG04 normalized moment-rotation plot with experimental results: FSv = 4.0, Pst = 361 kN, PGA = 0.727 g, C r = 0.176; A/Ac = 3.2
(a)
(b)
Fig. 5 a Validation of LJD01 normalized moment-rotation plot with experimental results: FSv = 16.1, Pst = 6002 kN, PGA = 0.62 g, C r = 0.25; A/Ac = 14; b validation of normalized momentrotation plot with experimental results; FSv = 11, Pst = 6186 kN, PGA = 0.393 g, C r = 0.353, A/Ac = 9.5
362
S. Soundararajan et al.
model that has only six user-defined input parameters for dynamic soil-foundation interaction model (CIM).
4 Comparisons of Numerical Model Predictions for Performance Parameters with Experimental Results The validated numerical models of shear wall and bridge pier are used to obtain the performance parameters such as seismic energy dissipation, peak rotation, and tipping-over stability ratio of rocking foundations for the other experiments in test series T1, T2, T3, and T4. The computed performance parameters using the numerical model are compared with the experimental results to further validate the accuracy of the numerical model as there are wide range of soil, foundation, structural, and ground motion properties considered in the study. The variation of normalized energy dissipation with arias intensity of earthquake ground motion (I a ) and rocking coefficient (C r ) is plotted for both experimental results and numerical model predictions in Fig. 6. As can be seen from Fig. 6, numerical model predictions for normalized energy dissipation increase as I a increases, and for a given I a , the normalized energy dissipation increases as C r decreases. Both of these observations are consistent with the experimental results. Overall the numerical model simulations for energy dissipation compare reasonably well with the experimental results, except when I a = 0.1–0.2 m/s. Considering all 26 experiments, the mean absolute percentage error (MAPE) in numerical model predictions of normalized energy dissipation (compared to experimental results) is 0.5. Fig. 6 Comparison of normalized energy dissipation with arias intensity and rocking coefficient for numerical model predictions and experimental results
Numerical Simulations and Validation of a Rocking Foundation Model …
363
The variation of the maximum (peak) rotation of rocking foundations with maximum base acceleration and rocking coefficient obtained from numerical simulations and experimental results is shown in Fig. 7. For most cases, numerical model predictions are slightly higher than the experimental results for peak rotation, especially for rocking foundations with higher C r values (C r = 0.25 to 0.35). The overall mean absolute percentage error in numerical model predictions of peak rotation compared to experimental results is 0.6. The variation of the tipping-over stability ratio (TSR) with maximum base acceleration for both numerical model predictions and experimental results is shown in Fig. 8. As can be seen from Fig. 8, the numerical model predictions of TSR compare well with the experimental results (both vary between 0.85 and 1.0), expect for two events where the maximum base shaking acceleration is close to 1.0 g. The overall mean absolute percentage error in numerical model predictions of TSR compared to experimental results is 0.02. Fig. 7 Comparison of maximum rotation of rocking foundation with maximum base acceleration and rocking coefficient for numerical model predictions and results
Fig. 8 Comparison of tipping-over stability ratio with maximum base acceleration and rocking coefficient for numerical model predictions and experimental results
364
S. Soundararajan et al.
Fig. 9 Comparison of moment capacity with critical contact area ratio and maximum acceleration for numerical and experimental results for 26 events
The normalized maximum moment (Mmax) of rocking foundations during shaking in numerical simulations is plotted with A/Ac of rocking foundations along with the corresponding experimental results in Fig. 9. Also shown in Fig. 9 is the theoretical normalized ultimate moment capacity of rocking foundations as a function of A/Ac (Eq. 1). Both experimental results and numerical model predictions show that the rocking foundations did not reach the theoretical ultimate moment capacity during relatively smaller shaking events (amax < 0.2 g). In general, the numerical model predictions for maximum moment are slightly higher than the experimental results. Considering all 26 experiments, the mean absolute percentage error in numerical model predictions of normalized maximum moment is 0.22.
5 Summary and Conclusions To simulate the rocking behavior of shallow foundations and to quantify the consequences of rocking in terms of performance parameters, a numerical model is developed using OpenSees finite element framework. A contact interface model (CIM), available in OpenSees is used to model the soil-foundation system, and elastic beamcolumn elements are used to model shear wall and bridge-pier structural elements. The numerical model is first validated using cyclic moment-rotation response of rocking foundations and comparisons with centrifuge experimental results. Further numerical simulations are carried out to compare selected performance parameters of rocking foundations with those obtained during experiments. The numerical model captures the cyclic moment-rotation behavior and seismic energy dissipation characteristics of rocking shallow foundations reasonably well. Numerical model predictions for seismic energy dissipation of rocking foundations as a function of arias intensity of the earthquake motion and peak rotation of rocking foundation as a function of peak ground acceleration of the earthquake motion compare reasonably well with the corresponding experimental results (with mean absolute percentage errors of 0.5–0.6). For 24 out of 26 experiments considered, the
Numerical Simulations and Validation of a Rocking Foundation Model …
365
tipping-over stability ratio obtained from both the numerical simulations and experimental results vary between 0.85 and 1.0, demonstrating (i) the excellent stability of rocking systems against tipping-over failure and (ii) the numerical model’s ability to capture the tipping-over stability of rocking systems.
References 1. Gajan, S., Kutter, B.L., Phalen, J.D., Hutchinson, T.C., Martin, G.R.: Centrifuge modeling of load-deformation behavior of rocking shallow foundations. Soil Dyn. Earthq. Eng. 25, 773–783 (2005) 2. Storie, L., Pender, M., Clifton, G., and Wotherspoon, L.: Soil foundation-structure interaction for buildings on shallow foundations in the Christchurch earthquake. In: Proceedings of 10th NCEE, Anchorage, Alaska (2014) 3. Gajan, S., Kutter, B.L.: Capacity, settlement, and energy dissipation of shallow footings subjected to rocking. J. Geotech. Geoenviron. Eng. ASCE 134(8), 1129–1141 (2008) 4. Deng, L., Kutter, B.L.: Characterization of rocking shallow foundation using centrifuge model tests. Earthq. Eng. Struct. Dyn. 41(5), 1043–1060 (2012) 5. Tsatsis, A., Anastasopoulos, I.: Performance of rocking systems on shallow improved sand: shaking table testing. Front. Built Environ. 1(9), 1–19 (2015) 6. Antonellis, G., Gavras, A.G., Panagiotou, M., Kutter, B.L., Guerrini, G., Sander, A.C., Fox, P.J.: Shake table test of large-scale bridge columns supported on rocking shallow foundations. J. Geotech. Geoenviron. Eng. ASCE 141(5), 04015009 (2015) 7. Turner, M., Ghayoomi, M., Ueda, K., Uzuoka, R.: Performance of rocking foundations on unsaturated soil layers with variable groundwater levels. Géotechnique (2021) 8. Raychowdhury, P., Hutchinson, T.C.: Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results. Earthq. Eng. Struct. Dyn. 38, 679–698 (2009) 9. Pelekis, I., McKenna, F., Madabhushi, G.S.P., DeJong, M.J.: Finite element modeling of buildings with structural and foundation rocking on dry sand. Earthq. Eng. Struct. Dyn. 50, 3093–3115 (2021) 10. Gajan, S., Kutter, B.: A contact interface model for shallow foundation subjected to combined cyclic loading. J. Geotech. Geoenviron. Eng. 135, 407–419 (2009) 11. Cavalieri, F., Correia, A.A., Crowley, H., Pinho, R.: Dynamic soil-structure interaction models for fragility characterisation of buildings with shallow foundations. Soil Dyn. Earthq. Eng. 132, 106004 (2020) 12. Zhang, J., Xie, Y., Wu, G.: Seismic responses of bridges with rocking column-foundation: a dimensionless regression analysis. Earthq. Eng. Struct. Dyn. 48, 152–170 (2019) 13. Gajan, S., Soundararajan, S., Yang, M., Akchurin, D.: Effects of rocking coefficient and critical contact area ratio on the performance of rocking foundations from centrifuge and shake table experimental results. Soil Dyn. Earthq. Eng. 141 (2021) 14. Gajan, S.: Application of machine learning algorithms to performance prediction of rocking shallow foundations during earthquake loading. Soil Dyn. Earthq. Eng. 151 (2021) 15. Deng, L., Kutter, B.L., Kunnath, S.K.: Centrifuge modeling of bridge systems designed for rocking foundations. J. Geotech. Geoenviron. Eng. 138(3), 335–344 (2012) 16. Soundararajan, S.: Seismic Energy Dissipation, Self-centering, and Settlement of Rocking Foundations: Analysis of Experimental Data with Comparisons to Numerical Modeling. MS thesis, North Dakota State University, Department of Civil and Environmental Engineering, USA (2019) 17. Nandyala, R.K., Jakka, R.S.: Seismic Design of Shallow Foundations: Principles, Design Methodologies and Current Indian Practices. Theory and Practice in Earthquake Engineering and Technology, pp. 99–131 (2022)
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated Ground Subjected to Repeated Shaking Events Using 1-g Shaking Table Experiments K. S. Amith , S. Ganesh Kumar , and M. D. Godson Abstract Underground structures are increasingly used worldwide mainly for transportation and utility services and have become a major component in infrastructure development. Although underground structures are considered safer than above ground structures due to its confinement characteristics, past earthquake events such as Kobe earthquake (1995), Wenchuan earthquake (2008), etc., revealed that tunnels are equally vulnerable under dynamic events. Based on Tohuku, Japan Earthquake (2011), Nepal Earthquake (2015) repeated shaking events (i.e., foreshocks and aftershock occurrences during earthquake) also contributed equally in inducing failures in infra-structures. In India, major portion of tunnel projects were carried out in Northern parts, i.e., Indo-Gangetic plains which contains significant portion of silty sand deposits. In case of dynamic events, the changes in soil saturation in these deposits due to variation in ground water table conditions may results in pore pressure generation and can affect the structural stability of the tunnel system. Considering the above aspects, the present study aims to assess the dynamic behavior of shallow tunnels embedded in partially saturated silty sand bed under repeated shaking events. For this purpose, 1-g shaking table experimental study was conducted on scaled down square tunnel embedded in partially saturated sand bed having 60% relative density with 25% saturation. Incremental repeated shaking events of 0.1 and 0.2 g were applied sequentially, and tunnel-soil interaction behavior was evaluated in terms of acceleration response, developed pore water pressure, pore water pressure ratio, dynamic earth pressure, and displacement of soil, respectively. The displacement of tunnel and strain developed during dynamic events were evaluated using 2D digital image correlation technique. Based on the obtained test results, the factors influencing the dynamic behavior of tunnels in partially saturated ground under repeated incremental shaking events were evaluated and presented.
K. S. Amith (B) · S. G. Kumar Academy of Scientific and Innovative Research (AcSIR), Ghaziabad 201002, India e-mail: [email protected] K. S. Amith · S. G. Kumar · M. D. Godson Geotechnical Engineering Division, CSIR-CBRI, Roorkee 247667, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_29
367
368
K. S. Amith et al.
Keywords Tunnel-soil interaction · Soil saturation · Repeated shaking events · 2-digital image correlation technique · Liquefaction
1 Introduction In recent decades, urbanization posed huge requirement in transportation infrastructure facilities. Due to limited land space availability, underground structures were continuously chosen to improve transportation requirement. The underground structures are relatively safer and more efficient compared to above ground structures in terms of seismic performance. However, recent damages to several tunnels due to earthquakes such as Kobe Earthquake (1995), Chi Chi Earthquake (1999), and Wenchuan Earthquake (2008) evidenced excessive deformation in tunnel systems, which suggest the need for vulnerability assessment of tunnels particularly situated at shallow depth. Additionally, studies on soil tunnel interaction under dynamic conditions are most essential to improve the stability and to mitigate economic loss during earthquakes. In India, majority portion of on-going/completed tunnel construction lies in Northern India where the sub-surface profile contains significant portion of silty sand deposits. Usually in silty sand deposits, effect of water table plays a significant role in altering soil saturation and pore water pressure generation during dynamic events. To study tunnel-soil response in saturated ground, series of 1-g shaking table experimental studies were conducted in the laboratory by few researchers to understand the seismic behavior of tunnels. Wang et al. [5] conducted 1-g shaking table tests to estimate the dynamic performance of box shaped immersed tunnel model considering the influence of water table with, El Centro, San Fernando, Taft and artificial wave as input motions. It was observed that strain on the tunnel increases with increase in water table depth. Similarly, Ding et al. [1] conducted shaking table tests on rectangular tunnel model with varying water table conditions in coral sand under 0.2 g sinusoidal wave excitations. They concluded that existence of tunnel induced generation of pore water pressure and contributed in development of strains and deformation in tunnel model. Although, above studies focused on seismic behavior of tunnel considering the influence of water table depth, limited/no studies were available in understanding tunnel-soil interaction in partially saturated sand especially under repeated dynamic conditions. Considering the above, a series of 1-g shaking table tests were conducted in this study to understand tunnel-soil interaction behavior in a partially saturated ground under repeated dynamic loading conditions. For simulating repeated incremental shaking events, input motions having amplitude 0.1 and 0.2 g were chosen. For testing, tunnel of 280 mm × 280 mm × 730 mm was used and installed in ground having 25% saturation with 60% density. The tunnel-soil interaction behavior in partially saturated ground was studied in terms of acceleration response, pore water pressure development, pore water pressure ratio, dynamic earth pressure, and displacement of soil, respectively. Also, the displacement and strains developed by the tunnel was evaluated using 2D-DIC technique.
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated …
369
Finally, the factors influencing the tunnel-soil behavior in partially saturated ground under dynamic conditions are discussed.
2 Methodology 2.1 Uni-Axial Shaking Table Experimental investigations were conducted on a uni-axial shaking table of dimension 2 m × 2 m with maximum load carrying capacity and actuator displacement of 3 T and ± 160 mm, respectively. The operating frequency range and acceleration range for the shake table were 0.01 to 50 Hz and 0.001g to 1g, respectively. For experimental testing, a perspex tank was fabricated and mounted over the shaking table for conducting the experiments. The dimensions of the test tank were 1.7 m × 0.75 m × 1 m. To minimize the boundary effects, PU foam of 50 mm thickness was used and installed on both sides of the tank perpendicular to shaking directions.
2.2 Soil Selected for the Experimental Study The soil selected for the experimental study was locally available Solani River sand which was characterized as poorly graded sand as per IS 2720 Part III and IV, [2,3] respectively. The minimum and maximum density of sand were found to be 14.5 KN/m3 and 16.7 KN/m3 , respectively. The other details are given in Table 1.
2.3 Sample Preparation for Experimental Testing For experimental testing, a partially saturated sand bed having 900 mm depth was prepared with 60% density. For partially saturated conditions, the soil bed was prepared corresponding to 25% saturation using sand pluviation technique. Prior Table 1 Properties of soil used in the experimental study Soil characteristics
Value
Specific gravity
2.67
Uniformity coefficient (C u )
2.6
Coefficient of curvature (C C )
1.14
Void ratio corresponding to 60% relative density
0.75
Soil type
Poorly graded
370
K. S. Amith et al.
to sample preparation, relative density test was performed on Solani sand as per IS 2720 Part XVI [4] to determine maximum void ratio emax and minimum void ratio emin . The natural void ratio corresponding to 60% relative density was estimated using the equation, e = emax − Dr (emax − emin ). Based on the estimated void ratio, the unit weight of soil corresponding to the desired relative density was calculated. The quantity of sand required for ground preparation was then estimated and prepared in equal layers. Similarly, the quantity of water to be filled for each layer was calculated corresponding to 25% saturation using the equation, S × e = w × G. Initially, calculated amount of water was poured for the first 200 mm layer and sand was rained using hopper arrangement from a calculated height 190 mm for achieving 60% relative density. The sample preparation was continued up to a total height of 900 mm. Figure 1a, b shows the sample preparation set-up adopted in the current experimental study.
Fig. 1 Sample preparation and experimental set up for tunnel-soil interaction using shaking table test
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated … Table 2 Scaling laws adopted in the experimental study [6]
371
Variable
Scale factor
For λ = 10
Length
Ʌ
10
Density
1
1
Force
λ3
1000
Stress
Ʌ
10
Strain
1
1
Elastic modulus
Ʌ
10
Acceleration
1 √ λ √ 1/ λ
1
Time Frequency
3.16 1.77
2.4 Scaling Laws Scaling laws are essential to develop the relationship between scale down model and prototype structure. In the current experimental program, dimensional analysis method was used for deriving the scaling factor for different variables. The scale factor for density of soil is considered as 1. Similarly, acceleration and strain are considered as 1 to simulate equivalent conditions in the field as per dynamic similitude laws. The scaling factors for different variables are summarized and presented in Table 2. A scaled down tunnel model, i.e., 1:10 to prototype conditions with dimensions 280 mm × 280 mm × 730 mm and thickness of 30 mm, was prepared using gypsum water mix. For casting tunnel model, gypsum was mixed with water at 1:0.7 for the targeted cube compressive strength of 3 N/mm2 . The scaled down tunnel model was placed at a depth of 200 mm inside the prepared partially saturated ground. To minimize water ingress into the tunnel model, a silicon sealant was used around the tunnel model. The primary objective of the study is to evaluate the tunnel-soil interaction behavior in partially saturated ground bed under repeated shaking events. For this purpose, sinusoidal input motion of 0.1 and 0.2 g having 5 Hz frequency were selected as input motions in this study. After 0.1 g loading, subsequent 0.2 g input motion was applied after dissipation of excess pore water pressures generated during previous loading. The selected input motion replicates low to medium intensity shaking in prototype conditions.
2.5 Instrumentation A dense instrumentation array of accelerometers, pore pressure transducers, displacement sensors, and dynamic earth pressure cells were used for measuring acceleration response of soil, pore water pressure and pore pressure ratio, settlement of soil, and
372
K. S. Amith et al.
Fig. 2 Sensor arrangement for experimental test program
dynamic earth pressure developed so as to investigate the tunnel-soil interaction due to repeated shaking events. The complete instrumentation scheme is shown in Fig. 2. The soil tunnel interaction behavior due to repeated shaking events was evaluated in terms of acceleration response, pore water pressure measurement, pore water pressure ratio, dynamic earth pressure, displacement of soil along with displacement and strain developed on the tunnel, respectively.
2.6 2D Digital Image Correlation Technique To monitor displacements and surface strains developed on the tunnel model during testing, a non-contact 2D strain measuring technique 2D digital image correlation (DIC) technique was used. The 2D-DIC set up includes a camera, a set of LED lights, and VIC 2D software. It is a subset-based strain measuring technique in which the surface (area of interest, AOI) to which deformation and strains need to be obtained is sprayed with white paint followed by application of black dot speckles to the AOI. Application of speckles are most essential to track the points on the tunnel specimen which are unique from one another. These unique points are tracked by tracking the neighborhood pixels which are called as subsets. After speckles are applied to the AOI, following procedure was followed in VIC 2D software in conjunction with camera for obtaining displacement of tunnel and strains. (i) Initially, a reference image is captured before the start of the test and subsequent series of images are captured till the end of the test which are called as deformed images. (ii) The obtained reference image and deformed images are calibrated and correlated using VIC 2D software to obtain the deformation and strains developed on the tunnel during repeated shaking events.
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated …
373
3 Results and Discussions 3.1 Acceleration Response of Soil In this section, the acceleration response of soil at different depths observed during repeated shaking events of 0.1 and 0.2 g input motion is presented. For this purpose, 4 accelerometers were used, i.e., at 100 mm depth from top (A1), 420 mm depth from top (A2), 560 mm depth from top (A3), and 700 mm depth from top (A4), respectively. Due to malfunctioning of A1 and A3 during the tests, acceleration responses from A2 and A4 were only presented in this section. Figures 3 and 4 illustrate the acceleration response of transducers in time and frequency domain at 420 mm (A2) and 700 mm (A4) depth obtained during repeated shaking events of 0.1 and 0.2 g input motion, respectively. It can be observed that the acceleration response found increases from bottom to top and about 50% increase in acceleration response was observed during 0.1 g input motion. The increment in acceleration response at shallow depth (A2) compared to deeper depth (A4) was mainly due to the tunnel embedment together with disturbances experienced by the ground due to longer shaking duration. However, the applied longer shaking duration induced soil grains rearrangement and associated densification which results in reduction in acceleration response at shallow depth during 0.2 g input motion. Thus, the prepared ground having 6% water content experienced soil densification at the end of 0.1 g acceleration loading and resulting soil compaction posed reduction in acceleration response during 0.2 g acceleration shaking at shallow depth. At deeper depth, the void created by the tunnel embedment showed comparatively higher acceleration response than shallow depth. The influence of soil compaction can be further evidenced from the obtained soil pressure response, pore pressure response, and obtained soil displacements which are explained in the following section as follows.
3.2 Development of Pore Water Pressures in the Soil For measuring generated pore water pressures at different depths, pore pressure transducers were placed at 100 mm (PP 1), 420 mm (PP 2), 560 mm (PP 3), and 700 mm (PP 4) depths, respectively. Figure 5 presents the generated pore water pressure at different depths of soil during repeated loading tests. It can be observed that, generation of pore water pressures was not significant during 0.1 and 0.2 g loading conditions. This was mainly due to the partially saturated condition and associated longer duration shaking which encouraged soil densification. The continuous rearrangement of soil grains during repeated longer shaking improved soil compaction which minimizes generation of pore water pressures during repeated loading conditions. This was clearly evident from the generated pore water pressures and pore pressure ratio as shown in Fig. 5.
374
K. S. Amith et al.
Fig. 3 Acceleration response due to 0.1 g input motion
The pore water pressure ratio (r u ) was calculated using the formula ru = Uexcess σ' ' where U excess is the developed excess pore water pressure and σ is the effective overburden stress. As mentioned earlier, the continuous shaking increased overburden stress inside the prepared ground which showed reduction in pore pressure ratio during repeated loading events. About 30–59% reduction in generated pore water pressures was observed in pore pressure values during repeated loading events throughout the depth which verified the occurrence of soil densification. The variation in pore water pressure ratio with respect to depth decreased initially from 100 to 420 mm, and then, sudden increment in pore water pressure ratio was observed at 560 mm depth and again decreases at 700 mm depth during 0.1 g input motion. Similar behavior was observed in the case of 0.2 g shaking duration. The initial densification at shallow depth resulted in decrease in pore water pressure ratio at shallow depth (as seen in acceleration response) followed by an increment in pore water pressure ratio at deeper depths which is mainly due to tunnel-soil interaction where the void created by the tunnel induced variation in pore pressure generation.
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated …
375
Fig. 4 Acceleration response of soil due to 0.2 g input motion
3.3 Dynamic Earth Pressure The dynamic earth pressures developed during repeated shaking events were assessed by placing dynamic earth pressure cell at tunnel top (P1), at 560 mm depth inside the soil, (P2), and at tunnel bottom (P3) 700 mm. Accordingly, Fig. 6 shows the developed dynamic earth pressure at corresponding location, respectively. It can be observed that the dynamic earth pressure at tunnel top increases with the increase in input motion and the increment was uniform during both 0.1 and 0.2 g input motion. About 65% increment in dynamic soil pressures at tunnel top was observed suggesting that the soil tend to undergo increment in in-situ stresses due to continuous shaking events. However, the developed dynamic earth pressure at tunnel top observed to be less compared to the dynamic earth pressure installed at 560 mm depth adjacent to the tunnel. About 5–15 times variation in load sharing was observed between soil and tunnel, respectively, during repeated shaking conditions. In case of continuous shaking events, the surrounding soil experiences higher dynamic stresses as a result of soil densification mechanism which confines the tunnel system and minimum stresses transmitted to the tunnel top. The continuous shaking resulted in densification which
376
K. S. Amith et al.
Fig. 5 Development of pore water pressure and calculated pore water pressure ratio due to 0.1 and 0.2 g input motion
improves the load sharing mechanism which was found evident from Fig. 6. Thus, the influence of partial saturation in soil densification improvement is evident from the figure and due to this; surrounding soil provides effective confinement which minimizes tunnel deformation during repeated loading events. However, the repeated loading events increase the load transfer between soil and tunnel which also found evident from the figures.
Fig. 6 Dynamic earth pressure at 560 mm depth inside the soil, tunnel top
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated …
377
Fig. 7 Displacement of soil at left side surface and mid surface of the prepared soil bed
3.4 Effect of Displacement of Soil To measure the soil displacement during repeated loading, two displacement transducers were placed at the top of the ground at two different locations D1 (adjacent to tunnel location) and D2 (above tunnel location) as shown in Fig. 2. The obtained soil displacement during 0.1 and 0.2 g repeated shaking events is shown in Fig. 7, respectively. It can be observed that the displacement of soil at D1 was about 1.2 mm during 0.1 g input motion, and the displacement of soil at same location was 0.6 mm during subsequent 0.2 g input motion. Similarly, the displacement obtained at D2 during repeated shaking events of 0.1 and 0.2 g input motion found to be about 1.1 mm and 0.7 mm, respectively. The obtained displacements suggested that, comparatively uniform settlement was observed on ground during repeated loading and validated accumulation of soil densification. The obtained reduction in settlement during subsequent loading, i.e., 42% verified the occurrence of soil densification. It can be concluded that, the particle rearrangement in partially consolidated ground improves soil compaction and this found reduces during repeated shaking which contributed variation in confining characteristics of soil surrounding tunnel as seen Sect. 3.3.
3.5 Displacement and Strains Developed on the Tunnel The displacement and strains obtained during repeated shaking events was monitored using 2-DIC technique. Figure 8 shows the obtained displacement vs time of model tunnel during 0.1 and 0.2 g repeated loading conditions, respectively. It can be observed that with increase in acceleration loading, displacement of tunnel increased. In-spite of longer shaking duration, no failure was observed during repeated loading
378
K. S. Amith et al.
Fig. 8 Displacement and strains developed during repeated shaking events
conditions. The displacement of tunnel was about 2.4 mm during 0.1 g input motion, whereas the displacement of tunnel was found to be 4.4 mm during subsequent input motion. Around 45% increment in displacement of tunnel during subsequent repeated shaking event of 0.2 g input motion was observed. The increment is mainly due to the influence of longer shaking duration, i.e., 40 s. However, the improvement in soil densification due to continuous shaking improved confinement characteristics and improves the stability of tunnel model. The performance of tunnel model was further verified by evaluating the strain measurement in different portions of the model. For measuring the strains, three positions were selected at top of the tunnel which are designated as R0, R1, R2; three positions were selected at bottom of the tunnel which are designated as R3, R4, R5 and two points on left and right-side wall of the tunnel, R6, R7 were selected. The corresponding selected locations can be seen from Fig. 1d. The obtained results from DIC calculations on tunnel model under repeated loading events showed that right corner of the tunnel (R2) found to develop maximum compressive strain when compared to all other locations during 0.1 g input motion. It can also be observed that the mid wall of the tunnel (R6), (R7) found to develop maximum tension strain which can be attributed to longer shaking duration which influence in tunnel displacement during shaking. This can be verified from the strain response obtained in the subsequent loading, where all the portions showed tension pattern in strain accumulation suggesting tunnel displacement. In-spite of increment in tunnel displacement, the occurrence of soil compaction improves the stability of model tunnel during repeated shaking events (Fig. 9).
Experimental Studies on Tunnel-Soil Interaction in Partially Saturated …
379
Fig. 9 Obtained strain response during repeated loading at different portions in tunnel
4 Conclusions This paper presents the behavior of tunnel in partially saturated sand under repeated shaking conditions to understand the tunnel-soil interaction under repeated loading conditions. The tunnel-soil interaction was studied in terms of acceleration response, developed pore water pressure, pore water pressure ratio, displacement of soil, dynamic earth pressure, displacement of tunnel and developed strain, respectively. Based on the study, following conclusions were drawn. (1) The occurrence of repeated shaking induces soil densification in partially saturated ground which minimizes generation of pore water pressures and improves the soil confinement characteristics around the tunnel model. (2) The occurrence of soil densification together with tunnel embedment influences acceleration response during repeated loading events. This was evident from the non-uniform acceleration response during repeated loading events. (3) Influence of increment in soil densification influences the load sharing mechanism between the soil and the tunnel model in partially saturated ground. About 5–15 times variation in load sharing was observed between soil and tunnel, respectively, during repeated loading event. The above conclusions clearly elucidate the need for understanding the dynamic behavior of tunnel systems in partially saturated ground which is highly essential for improving the structural stability especially during repeated loading events. Acknowledgements The authors would like to thank the Director, CSIR-Central Building Research Institute, Roorkee, for giving permission to publish this research work.
380
K. S. Amith et al.
References 1. Ding, X., Zhang, Y., Wu, Q., Chen, Z., Wang, C.: Shaking table tests on the seismic responses of underground structures in coral sand. Tunn. Undergr. Space Technol. 109, 103775 (2021) 2. IS 2720-Part 3: Methods of Test for Soils—Determination of Specific Gravity, Bureau of Indian Standards, New Delhi (1983) 3. IS 2720-Part 4: Methods of Test for Soils—Grain size Distribution, Bureau of Indian Standards, New Delhi (1983) 4. IS 2720-Part 16: Methods of Test for Soils, Determination of Density index (Relative Density) of Cohesionless Soils, Bureau of Indian Standards, New Delhi (2006) 5. Wang, Z.Z., Jiang, L., Gao, Y.: Shaking table test of seismic response of immersed tunnels under effect of water. Soil Dyn. Earthq. Eng. 116, 436–445 (2019) 6. Wood, D.M., Crewe, A., Taylor, C.: Shaking table testing of geotechnical models. Int. J. Phys. Modell. Geotech. 2(1), 01–13 (2002)
Assessment of Liquefaction Potential of Allahabad, India: A Future Smart City Keshav Kumar Sharma, Kumar Pallav, Manjari Singh, Ashhad Imam, and Alvin Harrison
Abstract In the present work, seismic hazard assessment is performed for Allahabad city in terms of liquefaction potential index (LPI) for a hypothetical earthquake along the Allahabad fault of magnitude Mw 6.7 for different surface peak ground acceleration (PGA) levels (0.06, 0.1, 0.15 and 0.2 g). Factor of safety against liquefaction (FS) has been estimated using modified semi-empirical process from Idriss and Boulanger (Soil Dyn Earthq Eng 26, 115–130, 2006 ( Mogami, T., Kubo, K.: The behaviour of soil during vibration. In: 3rd International Conference on Soil Mechanics and Foundation Engineering, pp. 152–155 (1953))) for all depths of 116 boreholes across Allahabad. Estimated FS values are used for computing LPI (deterministic) valuwheres. Liquefaction potential hazard contour maps are shown in terms of spatial distribution of FS and LPI indices. It is observed that a large part of Allahabad is safe against FS for lower PGA values (0.06 and 0.1 g) but has a potential to liquefy under high intensity shaking of 0.15 g and 0.2 g PGA at depth 15 m or more. In terms of LPI, most places have “low” to “very low” liquefaction severity (i.e. LPI < 5) for (0.06 and 0.1) g. It gets modified to “high” (i.e. LPI b/w 5–15) for (0.15 and 0.2) g at Naini, Jhalwa, Sangam area, near railway station and Jhunsi region. Keywords Liquefaction · Cyclic stress ratio · Peak ground acceleration · Lateral spreading · LPI
K. K. Sharma · A. Imam · A. Harrison Department of Civil Engineering, NIT Jamshedpur, Jamshedpur, India e-mail: [email protected] K. Pallav Cape Peninsula University of Technology, Cape Town, South Africa M. Singh (B) Structural Engineering Department, VJTI Mumbai, Mumbai, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_30
381
382
K. K. Sharma et al.
1 Introduction Earthquakes accompanying liquefaction have been detected for several ages. Detailed records dating back hundreds of years have described failures during earthquakes that are now thought to be related to liquefaction. Even though the impacts of liquefaction have long been known but it more thoroughly grabbed the attention of engineers and researchers after the 1964 Alaska (USA) and Niigata (Japan) earthquake. Initial studies described the strength loss in loose sands leading to flow failures in the form of liquefaction [1]. It can be defined as a development in which saturated/partially saturated soils, in response to stress, lose their strength and stiffness [2]. The effective stress of soil reduces to zero, resulting in a complete loss of shear strength and it start behaving viscous liquid rather than a solid [3]. Liquefaction potential relies upon the susceptibility of a soil deposit to liquefy and the level of shaking to exceed the threshold value required for liquefaction to occur. In India, liquefaction analysis was performed on various regions such as Ahmedabad [4], Kolkata [5], Bangalore [6], Imphal [7], Roorkee [8], Mumbai [9], NCR Region [10], Agartala [11], Kanpur [12]. Naik et al. [13] presented liquefaction potential studies for Allahabad using FS and laboratory investigations, but they did not performed site specific analysis to determine liquefaction severity. Vijay et al. [14] used ANN technique and compared results with Idriss and Boulanger method [15], Vijay et al. [16] and Yaseen and Bind [17] used neuro-fuzzy techniques for the same, but they too do not talk about probability of liquefaction failures at specific locations. Moreover, liquefaction hazard maps have also not been yet prepared for the region. Estimation of liquefaction potential with depth at a specific site will be important in earthquake hazard planning and mitigation. Comprehensive research on liquefaction damage due to scenario earthquakes for Allahabad has not been done in accordance with the best of found knowledge. Within the confines of this study, Idriss and Boulanger’s [18] semi-empirical method which is based on standard penetration test data is used to compute liquefaction potential of Allahabad city in terms of FS and LPI for a hypothetical earthquake of magnitude Mw 6.7 and for different surface PGA levels (0.06, 0.1, 0.15 and 0.2 g). Liquefaction potential hazard contour maps are also prepared to show geographic variability of liquefaction severity in Allahabad.
2 About Allahabad City and Its Development Allahabad city (25° 28' N, 81° 54' E) is situated in Indian state of Uttar Pradesh at an elevations of 98 m above sea level and lies at the confluence of two rivers, Ganga and Yamuna [19]. It is among the biggest cities of north central India with metropolis area of 70.5 km2 . Allahabad is the most-populous district in the state of Uttar Pradesh with estimated population of about 6 million [20].
Assessment of Liquefaction Potential of Allahabad, India: A Future …
383
Past earthquake histories indicate that, the area is low to moderate seismic. The region has been assigned Zone II in the seismic zoning map of India [21]. However, destruction caused by these earthquakes are not readily available. Such incidents happened at a time when Allahabad was confined in scope to its population and infrastructure. With population growth in recent times, several important infrastructural projects viz., multi-storey buildings, bridges, rail and road links, etc., have been taken up in the area. Allahabad city is also selected for smart city project, Government of India with the collaboration of USA [22]. New infrastructure projects such as roads, railway, bridges and utility lines will be taken up in the city under the smart city plan, and thus the vulnerability to the damages of earthquake has also been increased. Hence, assessment of liquefaction severity has become more important in order to mitigate damages.
3 Geology and Seismotectonic Setup Allahabad lies in between the Faizabad and Munger-Saharsa ridge, which signifies the prolongation of Bundelkhand and Satpura massif. As per Dasgupta et al. [23], the study area may be characterized into Ganga, Yamuna alluvial plain and Vindhyan Plateau. The area lies in the E–W tectonic basin, which has many concealed faults and ridges at the basement of Gangetic basin [24, 25]. The various faults around the study area with their features are gathered from various publications [23, 26] as shown in Fig. 1. Such subsurface faults have an oblique and transverse orientation around the tectonic pattern of the Himalayas [27, 28]. Past seismic data have shown that many of these faults are neotectonically active, with the possibility of large earthquakes in the near future [29]. Out of the various faults, Allahabad fault (Bhairwan Fault) is the one nearest to the study area and most critical from analysis point of view. Lucknow–Faizabad fault lies near Allahabad continuing towards the Himalayas in Nepal, and this fault has been sedentary for more than 350 years and under heavily stressed and would be originate great earthquake in future [30].
4 Standard Penetration Test Data Extensive borehole data with detailed soil investigations and standard penetration tests (SPT) values has been obtained from various public/private organizations and engineering firms (MNNIT Allahabad, Allahabad Engineering Consultants (Allahabad), Ashok and Associates (Allahabad) and Universal Test House (Lucknow)) involved in soil investigation projects across Allahabad. These tests were performed following Indian Standard code of practice [32]. Data from 116 boreholes across 35
384
K. K. Sharma et al.
Fig. 1 Location of various surface and subsurface faults around Allahabad city [31]
sites in Allahabad is used in the study. These locations are scattered all over Allahabad (Fig. 2). At 1.5 m depths intervals, the N values were measured. SPT has been measured to a depth of more than 20 m for several significant building sites.
5 Determination of Peak Ground Acceleration for Allahabad Ground motion is a significant parameter for estimating the FS against liquefaction. The size of the largest earthquakes that might be produced by a particular fault or earthquake source can be estimated from fault rupture parameters. On the basis of a worldwide data base of source parameters compiled from 421 historical earthquakes, Wells and Coppersmith [33] suggested relations among earthquake magnitude and the fault parameters. For “ALL” type of “subsurface” faults, the relation is Mw = 4.38 + 1.49 log(RLD),
(1)
where Mw = moment magnitude, RLD = sub surface rupture length (km). Present study estimates the maximum possible earthquake based on nearest seismic source, i.e. Allahabad fault. The maximum earthquake magnitude which can occur due to Allahabad fault is 6.27, obtained from Eq. 1 and rupture parameters of Allahabad fault.
Assessment of Liquefaction Potential of Allahabad, India: A Future …
385
Fig. 2 Allahabad city with Borehole locations
As the region lacks recorded strong motion data, it is very hard to recommend a PGA value. So, an attenuation relationship recommended by Abrahamson et al. [34] can be used. They recommended a relation (Eq. 2) based on 585 records from 76 worldwide earthquakes: ) ( log(a) = − 0.62 + 0.177 × M − 0.982 × log r + e(0.284M) + 0.132 × F − 0.0008 × Er,
(2)
where a r (Km ) M F and Er
PGA distance to closest approach of zone of energy release arthquake magnitude dummy variables.
Note: (F = 1 → reverse/reverse oblique fault, F = 0 → otherwise) and (Er = 1 → interplate, Er = 0 → intraplate events). Allahabad fault is most prominent and closest source for the study region. Thus, the design PGA value attained from Eq. 2, for a hypothetical earthquake of 6.27 Mw along Allahabad fault, is 0.057 g. Naik et al. [13] also estimated PGA ranging between 0.063 and 0.15 g for Allahabad city. Thus, it is found suitable to use PGA
386
K. K. Sharma et al.
value of 0.06 g as the starting point to estimate LPI and LSI, which is further increased intermittently up to 0.2 g, where most of the sites are found to be liquefiable.
6 Methodology In the present study, FS for each soil strata at all sites have been estimated from soil property and ground motion as inputs, as per Idriss and Boulanger’s method [15]. Then, FS values are used to compute liquefaction potential of sites as LPI. The mentioned methods are based on SPT-N values and cyclic stress-based approach and briefly described in subsequent sections.
7 Semi-Empirical Approach The semi-empirical approach is an updated technique of Seed and Idriss [35] and proposed by Idriss and Boulanger [15]. It is used for computing liquefaction potential. It, a methodology which evolved over years. In this approach, liquefaction potential of soil is defined in the terms of FS, which is a ratio of cyclic resistance ratio (CRR) to cyclic stress ratio (CSR), expressed in Eq. 3. At places where seismic loading exceeds the soil resistance, i.e. FS < 1.0, liquefaction is expected to be triggered. CRR , (CSR) Mw=7.5,σ =1.0 ( ( rd 1 σv amax , cyclic stress ratio : (CSR) Mw=7.5,σ =1.0 = 0.65 σv' MSF K σ FS =
(3) (4)
where (CSR) Mw=7.5,σ =1.0 corresponds to the equivalent uniform shear stress due to earthquake having a moment magnitude of Mw = 7.5 and σ (overburden pressure) = 1 atmosphere. In Eq. 5, amax refers to maximum horizontal acceleration at the ground level σv , σv' is total and effective vertical stress at depth z, respectively. Factor (0.65) is used to modify peak cyclic shear stress ratio to a cyclic stress ratio that is representative of most significant cycles over the full duration of loading. The stress reduction factor (rd ) accounts for the flexibility of the soil column, and it measures the attenuation of peak shear stress with depth due to non-elastic behaviour of soil [15]. It is calculated as per Idriss [36] and Golesorkhi [37] ) ( z + 5.133 ln(rd ) = − 1.012 − 1.126 sin [ (11.73 )] z + 0.106 + 0.118 sin + 5.142 Mw . 11.28
(5)
Assessment of Liquefaction Potential of Allahabad, India: A Future …
387
If Mw larger or smaller than 7.5 is scaled by magnitude scaling factor (MSF) (Eq. 6) to modify CSR value to equivalent uniform shear stress caused by an equivalent earthquake of Mw of 7.5. (
−Mw MSF = 6.9 exp 4
( − 0.058 ≤ 1.8
(6)
The efficient use of SPT blow counts as indicators for liquefaction characteristics requires the separation of the effects of soil density and effective confining stress on penetration resistance [18]. As the resistance to liquefaction rises with rising confining pressure, overburden pressure correction (K σ ) is implemented in such a manner that CSR values correspond to equivalent overburden pressure (1 atm) as shown in Eq. 7. ( K σ = 1 − Cσ × ln
σv' pa
( ≤ 1.0,
(7)
where the Cσ can be calculated as Cσ =
1 ≤ 0.3, √ 18.9 − 2.55 (N1 )60
(8)
where pa denotes atmospheric pressure (100 kPa) (N1 )60 = (C N × N60 ) < 37,
(9)
where N60 = SPT-N value after correction to an equivalent 60% hammer efficiency. C N denotes correction factor for overburden pressure [18] is ( CN =
pa σv'
(0.784−0.0768√(N1 )60
≤ 1.7.
(10)
As shown in Eq. 10, due to their independence on each other, C N and (N1 )60 are computed by iterative process. CRR based on SPT-N values for a cohesionless soil with any fine content (FC) can be calculated as [15] [
(N1 )60cs + C R R = exp 14.1
(
(N1 )60cs 126
(2
( −
(N1 )60cs 23.6
(3
( +
(N1 )60cs 25.4
]
(4
− 2.8 , (11)
(N1 )60cs = clean sand corrected SPT - N value [ ( (2 ] 15.7 9.7 − = (N1 )60 + exp 1.63 + . FC + 0.1 FC + 0.1
(12)
388
K. K. Sharma et al.
By combining these two factors (CSR, CRR), FS can be calculated by Eq. 3 for all depths of boreholes. If FS < 1, the soil is considered as liquefiable else non-liquefiable [15].
8 Liquefaction Potential Index LPI was formerly developed in Japan by Iwasaki et al. [31, 38, 39] to evaluate the liquefaction potential of soils to cause foundation damage at a site. The vulnerability of region to liquefaction may be stated as a cumulative impact of layerwise liquefaction potential across overall depth of soil under consideration. LPI is defined as thickness of the liquefied layer, its proximity to ground level and FS values of each layer of soil. LPI can be defined as shown in Eq. 13 [39] 20 LPI =
F(z) × w(z)dz,
(13)
0
F(z) = 1 − FS(z); FS < 1,
(14)
F(z) = 0; FS ≥ 1,
(15)
w(z) = 10 − 0.5z; z ≤ 20 m,
(16)
w(z) = 0; z > 20 m,
(17)
where
where z denotes depth from ground level (m). Liquefaction susceptibility is classified into 4 classes given by Iwasaki et al. [39] depending on the value of LPI. LPI values can range from zero at a site with no potential for liquefaction to a maximum value of 100 at a site which has zero FS over whole 20 m depth range. The simplified procedure only estimates performance of a particular soil element, whereas LPI calculates the overall liquefaction resistance of entire soil column up to 20 m depth. Iwasaki et al. [39] proposed that severe liquefaction is very likely at sites with LPI greater than 15 and it is unlikely at sites with LPI less than 5. Toprak and Holzer [40] correlated observations of liquefaction occurrences with LPI for Loma Prieta (1989) earthquake and concluded that both sand boils and lateral spreading primarily occur at the locations where LPI ranges between 5 and 12.
Assessment of Liquefaction Potential of Allahabad, India: A Future …
389
9 Results and Discussions SPT-N values and variation in FS against liquefaction with increase in PGA at one sample site (George Town) are shown in Fig. 3. Furthermore, FS variation for 1.5 m, 4.5 m depth (shallow foundation level) and 15 m depth (deep foundation level) is plotted for all PGA values of 0.06, 0.1, 0.15 and 0.2 g, at Allahabad city. Figure 4a–d shows FS for 1.5, 4.5 and 15 m depth for all the events. Following observations can be made from the plots. For 1.5 m depth, areas near George Town, Tagore Town, Colonel Gang, Allahabad University, Jhalwa, Kareli and Manauri are critical to liquefaction failures at 0.2 g PGA, as evident from Fig. 4d. At the depth of 4.5 m and PGA 0.15 g, areas near rivers like Sangam area, Arail ghat, Gaughat and Mahewa east are susceptible to liquefaction (Fig. 5c). Being close to river, this area has coarse sand to non-plastic silty sand with low compressibility clay in its soil profile, thus making it critical to liquefaction failures at the time of seismic shaking. As evident from Fig. 5d, areas near Jhalwa, Kareli, Allahabad high court, Sangam area, Chowk, Rambagh and Cheonki railway station are susceptible to liquefaction at 0.2 g PGA.
Fig. 3 Soil profile with SPT-N value along with FOS against liquefaction at different PGA levels (at George Town)
390
K. K. Sharma et al.
Fig. 4 Simulated FS against liquefaction at depth 1.5 m for PGA a 0.06 g, b 0.1 g, c 0.15 g and d 0.2 g
At 15 m depth, the situations are however observed to be more critical. Places such as Naini, Jhalwa, Kareli, Sangam area, Manauri, Chowk and area near Allahabad airport show liquefaction possibility at 0.15 g PGA, as evident from Fig. 6c. Figure 6d shows that most of the area of Allahabad including commercially important area of civil lines is also critical at 0.2 g PGA. Whereas other part of this region has low compressibility clay with gravels and sands at shallow depth and medium compressibility clay with gravel, sand, silt and kankar in lower layers, which make it quite safe against liquefaction at lower PGA values. Table 1 displays the FS-based liquefaction hazard for important areas in Allahabad. It should also be noted that that FS does not state the extent of the liquefaction of a site, but it can be used as input parameter to assess liquefaction severity rely on 2 indices viz., LPI and LSI. Figure 7a–d shows the variation of LPI in Allahabad for different events. As evident from Fig. 7a, b, for PGA (0.06 and 0.1)g, LPI is less than 5 and therefore based on the LPI classification [39], liquefaction susceptibility of Allahabad city is “low” to “very low”. It gets modified to “high” (i.e. LPI b/w 5
Assessment of Liquefaction Potential of Allahabad, India: A Future …
391
Fig. 5 Simulated FS against liquefaction at depth 4.5 m for PGA a 0.06 g, b 0.1 g, c 0.15 g and d 0.2 g
to 15) for PGA 0.15 and 0.2 g at Naini, Jhalwa, Kareli, Sangam area, near Railway station, Jhunsi, etc. (Fig. 7c, d and Table 2).
10 Conclusions The geological structure of Allahabad city, proximity to active faults and seismically active regions of Himalayas make it susceptible to liquefaction. It has been established as per IBC [51] that mostly sites in Allahabad city belongs to E and D Type category, hence evaluation of their potential to liquefy under seismic loadings needs to be done. Liquefaction potential hazard studies have been done for a hypothetical earthquake along the Allahabad fault of magnitude Mw 6.7 and for different surface PGA levels (0.06, 0.1, 0.15 and 0.2 g), with the help of liquefaction potential index (LPI) [61], using factor of safety against liquefaction (FS) as input [10], for Allahabad city. The findings of liquefaction hazard for Allahabad city are provided in the form of a contour map. It has been observed based on FS studies that most of the areas in Allahabad city are liquefiable (FS < 1.0) for 0.2 g PGA. As per LPI studies,
392
K. K. Sharma et al.
Fig. 6 FS against liquefaction at depth 15 m for PGA a 0.06 g, b 0.1 g, c 0.15 g and d 0.2 g Table 1 Liquefiable places in Allahabad city based on FS Depth (m) PGA 0.06 g 0.1 g
0.15 g
0.2 g
1.5
None
None None
George Town, Tagore Town, Colonel Gang, Allahabad University, Jhalwa, Kareli and Manauri
4.5
None
None Sangam area, Arail ghat, Gaughat and Mahewa east
Jhalwa, Kareli, Allahabad high court, Sangam area, Chowk, Rambagh and Cheonki railway station
15
None
None Naini, Jhalwa, Kareli, Sangam Area near Allahabad high court, area, Manauri, Chowk and area Civil lines, Georgetown, Sulem near Allahabad airport Sarai, Sangam area, Chowk, Jhalwa, Kareli, Rambagh, Naini, Manauri, Allahabad university, etc.
Assessment of Liquefaction Potential of Allahabad, India: A Future …
393
Fig. 7 LPI map for PGA a 0.06 g, b 0.1 g, c 0.15 g and d 0.02 g
liquefaction susceptibility of Allahabad city is “low” to “very low” at PGA 0.06 and 0.1 g. It get modified to “high” for PGA 0.15 and 0.2 g at Naini, Jhalwa, Kareli, Sangam area, near Railway station, Jhunsi, etc. This work offers an understanding of variation of liquefaction risk in the region. Contour maps may play a major role in the selection of a site and assist administration in planning and reducing potential risks from earthquakes.
394
K. K. Sharma et al.
Table 2 Results of LPI analysis for Allahabad Places
PGA 0.06 g
0.1 g
0.15 g
0.2 g
Civil lines
Very low
Low
Low
Low
George town
Low
Low
Low
Low
Near railway station
Very low
Low
Low
High
Kareli
Low
Low
Low
High
Sangam area
Low
Low
Low
High
Naini
Low
Low
High
High
Jhalwa
Low
Low
High
High
Jhunsi
Low
Low
High
High
Manauri
Low
Low
Low
Low
Near Allahabad university
Very low
Low
Low
Low
Mahewa (East)
Low
Low
High
High
Near MNNIT
Very low
Low
Low
Low
References 1. Mogami, T., Kubo, K.: The behaviour of soil during vibration. In: 3rd International Conference on Soil Mechanics and Foundation Engineering, pp. 152–155 (1953) 2. Kamao, S., Takezawa, M., Yamada, K., Jinno, S., Shinoda, T., Fukazawa, E.: A study of earthquake-caused liquefaction: the case of Urayasu City. In: Earthquake–Soil Interaction, pp. 149–161. WIT Press (2014). https://doi.org/10.2495/978-1-84564-978-4/012 3. Greene, M., Power, M., Youd, T.: Liquefaction—What it is and What to Do About It (1994) 4. Pancholi, V., Dwivedi, V., Bhatt, N.Y., Choudhury, P., Chopra, S.: Geotechnical investigation for estimation of liquefaction hazard for the Capital City of Gujarat State, Western India. Geotech. Geol. Eng. (2020). https://doi.org/10.1007/s10706-020-01454-8 5. Nath, S.K., Srivastava, N., Ghatak, C., Adhikari, M. Das, Ghosh, A., Sinha Ray, S.P.: Earthquake induced liquefaction hazard, probability and risk assessment in the city of Kolkata, India: its historical perspective and deterministic scenario. J. Seismol. 22, 35–68 (2018). https://doi.org/ 10.1007/s10950-017-9691-z 6. Anbazhagan, P., Sitharam, T.G.: Seismic microzonation of Bangalore. India. J. Earth Syst. Sci. 117, 833–852 (2008). https://doi.org/10.1007/s12040-008-0071-5 7. Pallav, K., Raghukanth, S.T.G., Singh, K.D.: Liquefaction Hazard Scenario of Imphal City for 1869 Cachar and a hypothetical earthquake. Int. J. Geotech. Earthq. Eng. 3, 34–56 (2012). https://doi.org/10.4018/jgee.2012010103 8. Muley, P., Maheshwari, B.K., Paul, D.K.: Liquefaction potential of Roorkee Region using field and laboratory tests. Int. J. Geosynth. Gr. Eng. 1, 37 (2015). https://doi.org/10.1007/s40891015-0038-y 9. Mhaske, S.Y., Choudhury, D.: GIS-based soil liquefaction susceptibility map of Mumbai city for earthquake events. J. Appl. Geophys. 70, 216–225 (2010). https://doi.org/10.1016/j.jap pgeo.2010.01.001 10. Mukherjee, S., Jain, V., Gupta, A., Pandey, D.A.: Determination of liquefaction potential of NCR Region. In: Advances in Sustainable Construction Materials and Geotechnical Engineering, pp. 171–181. Springer, Singapore (2020). https://doi.org/10.1007/978-981-13-74807_15
Assessment of Liquefaction Potential of Allahabad, India: A Future …
395
11. Das, S., Ghosh, S., Kayal, J.R.: Liquefaction potential of Agartala City in Northeast India using a GIS platform. Bull. Eng. Geol. Environ. 78, 2919–2931 (2019). https://doi.org/10.1007/s10 064-018-1287-5 12. Naik, S.P., Patra, N.R.: Generation of liquefaction potential map for Kanpur City and Allahabad City of Northern India: an attempt for liquefaction hazard assessment. Geotech. Geol. Eng. 36, 293–305 (2018). https://doi.org/10.1007/s10706-017-0327-4 13. Naik, S.P., Patra, N.R., Malik, J.N.: Assessment of Liquefaction Potential of Alluvial Soil of Indo-Gangetic Interfluves, Northern India. In: GeoCongress 2012, pp. 1859–1868. American Society of Civil Engineers, Reston, VA (2012). https://doi.org/10.1061/9780784412121.191 14. Kumar, V., Venkatesh, K., Kumar, Y.: Liquefaction potential evaluation of Alluvial Soil by neuro-fuzzy technique. Int. J. Emerg. Technol. Adv. Eng. 2, 174–184 (2012) 15. Idriss, I., Boulanger, R.: Semi-empirical procedures for evaluating liquefaction potential during earthquakes. Soil Dyn. Earthq. Eng. 26, 115–130 (2006) 16. Kumar, V., Venkatesh, K., Kumar, Y.: Liquefaction potential evaluations of soils using ANN technique. In: Indian Society of Earthquake Technology Department of Earthquake Engineering. IIT Roorkee, Roorkee (2012). 17. Yaseen, L., Bind, Y.: Neuro-fuzzy technique for the estimation of liquefaction potential of soil. Int. J. Sci. Res. Technol. Res. 3, 0617–0623 (2014) 18. Idriss, I., Boulanger, R.: Semi-empirical procedures for evaluating liquefaction potential during earthquakes. In: Proceeding of 11th International Conference on Soil Dynamics and Earthquake Engineering and 3rd International Conference on Earthquake Geotechnical Engineering, pp. 32–56. , Berkeley, Calif (2004) 19. Singh, M., Duggal, S.K., Pallav, K., Sharma, K.K.: Correlation of shear wave velocity with standard penetration resistance value for Allahabad City. In: Prashant, A., Sachan, A.D.C. (eds.) Advances in Computer Methods and Geomechanics, Lecture Notes in Civil Engineering. Springer, Singapore, pp. 467–481 (2020). https://doi.org/10.1007/978-981-15-0890-5_39. 20. Census: Allahabad District: census 2011 data (2011) 21. IS 1893: Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1— General Provisions and Buildings. Bureau of Indian Standards, New Delhi (2016) 22. MyGov: Smart City Allahabad 23. Dasgupta, S., Narula, P., Acharyya, S., Banerjee, J.: Seismotectonic Atlas of India and Its Environs. Geological Survey of India, Kolkata (2000) 24. Gansser, A.: The Ophiolitic Melange, a world-wide problem on Tethyan examples. Eclogae Geol. Helv. 67, 479–507 (1974) 25. Valdiya, K.S.: Himalayan transverse faults and folds and their parallelism with subsurface structures of North Indian plains. Tectonophysics 32, 353–386 (1976). https://doi.org/10.1016/ 0040-1951(76)90069-X 26. Kayal, J.: Microearthquake Seismology and Seismotectonics of South Asia. Springer Netherlands, Dordrecht (2008). https://doi.org/10.1007/978-1-4020-8180-4 27. Agarwal, R.: Structure and tectonic of Indo-Gangetic plains. Geophysical case histories of India. MB Ramchandra Rao Vol. Assoc. Expl. Geophys. India, 27–46 (1977) 28. Dasgupta, S., Mukhopadhyay, M., Nandy, D.: Active transverse features in the central portion of the Himalaya. Tectonophysics 136, 255–264 (1987) 29. Bilham, R.: Location and magnitude of the 1833 Nepal earthquake and its relation to the rupture zones of contiguous great Himalayan earthquakes. Curr. Sci. 69, 101–128 (1995) 30. Singh, M., Duggal, S.K., Singh, V.P.: A study to establish regression correlation between shear wave velocity and “N”-value for Varanasi City, India. Proc. Natl. Acad. Sci. India Sect. A Phys. Sci. 91, 405–417 (2021). https://doi.org/10.1007/s40010-020-00686-w 31. Iwasaki, T., Tokida, K., Tatsuoka, F.: Soil liquefaction potential evaluation with use of the simplified procedure. In: International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, pp. 209–214 (1981) 32. IS 2131: Method for standard penetration test of soils. Bureau of Indian Standards (BIS), New Delhi (1981).
396
K. K. Sharma et al.
33. Wells, D., Coppersmith, K.: New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement. Bull. Seismol. Soc. Am. 84, 974–1002 (1994) 34. Abrahamson, N.A., Litehiser, J.J.: Attenuation of vertical peak acceleration. Bull. Seismol. Soc. Am. 79, 549–580 (1989) 35. Seed, H.B., Idriss, I.M.: Simplified procedure for evaluating soil liquefaction potential. J. Soil Mech. Found. Div. 97, 1249–1273 (1971) 36. Idriss, I.: An update to the Seed-Idriss simplified procedure for evaluating liquefaction potential. In: Proceeding of TRB Workshop on New Approaches to Liquefaction. Publication No. FHWARD-99-165, Federal Highway Administration (1999) 37. Golesorkhi, R.: Factors Influencing the Computational Determination of Earthquake-Induced Shear Stresses in Sandy Soils (1989) 38. Iwasaki, T., Tatsuoka, K., Tokida, K., Yasuda, S.: A practical method for assessing soil liquefaction potential based on case studies at various sites in Japan. In: II International conference on microzonation, San Francisco, pp. 885–896 (1978) 39. Iwasaki, T., Tokida, K., Tatsuoka, F., Watanabe, S., Yasuda, S., Sato, H.: Microzonation for soil liquefaction potential using simplified method. In: Proceedings of the 13th international conference on Microzonation, Seattle, USA, pp. 1319–1330 (1982) 40. Toprak, S., Holzer, T.L.: Liquefaction potential index: field assessment. J. Geotech. Geoenvironmental Eng. 129, 315–322 (2003). https://doi.org/10.1061/(ASCE)1090-0241(2003)129: 4(315)
Seismic Evaluation of Assam-Type Building Using ABAQUS® P. Boruah and A. K. Dutta
Abstract Assam-type housing is a building typology that was promoted by the British PWD after the 1897 Assam Earthquake, in which a light-weight construction was made possible by suitable use of locally accessible resources such as timber, bamboo, ikra (a reed which is locally accessible) for the superstructure, while modern masonry confined with RCC posts were used till sill level. This low-cost, green and sustainable housing typology is slowly replaced by costly, environmentally degrading, unsustainable RCC frame structures. In this study, an attempt is made to promote this green, cost-effective and safe housing typology by showing its efficacy analytically against seismic excitation using appropriate finite element modelling. Modelling is done using state-of-the-art Finite Element Analysis software ABAQUS® , which could capture the intricate joinery details of different materials such as timber, bamboo and ikra, interfacing with modern minimal elements such as masonry and concrete/RCC. Dynamic characteristics are evaluated using modal analysis so as to test the efficacy of the model. Seismic evaluation is performed using response spectrum method of IS 1893(Part 1): 2016. It has been observed that the model is safe against the seismic excitation for this region. Keywords Assam type building · Finite element modelling · ABAQUS® · Modal analysis · Response spectrum analysis
1 Introduction Assam-type houses/buildings are most common to the North-eastern of India and owes its nomenclature to building typology coined by the Britishers. This type of distinctive housing style is developed by the local people using indigenous knowledge P. Boruah (B) Department of Civil Engineering, Jorhat Engineering College, Jorhat, India e-mail: [email protected] A. K. Dutta Department of Civil Engineering, Jorhat Institute of Science and Technology, Jorhat, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_31
397
398
P. Boruah and A. K. Dutta
Fig. 1 Typical Assam-type house front view
in order to counteract high seismicity of the region as well as high precipitation. The building technique and the materials used (locally available) is suitable to the local conditions. This kind of architecture is easy to construct (trained local labours can easily construct with local techniques), maintain and cost-effective. The materials used (bamboo, reed, wood, etc.) are locally available and light weight. The ability of Assam-type houses to withstand seismic events has been proven in past earthquakes. Figure 1 shows a typical Assam-type house front view.
1.1 Region: Assam Assam is located in the north-eastern part of Assam sharing state borders with the other 5 states of the north-east–Arunachal Pradesh, Nagaland, Manipur, Mizoram, Tripura and Meghalaya and international borders with Bangladesh and Bhutan. It occupies a total area of 78,523 km2 and is comprised of the fertile Brahmaputra and Barak valleys and the hills of Karbi-Anglong and Dima Hasao. It falls under seismic zone V and with an average annual rainfall of approximately 2818 mm.
Seismic Evaluation of Assam-Type Building Using ABAQUS®
399
1.2 History Assam-type houses/buildings are a kind of design evolved by the British after the massive earthquakes of the nineteenth century. Initially, the British implemented their typical thick masonry wall type building architecture in Assam, as they did in the other parts of the country. However, they soon realized their blunder as these houses failed miserably during the 1897 earthquake. At that time the typical local houses were made of thatch roof and bamboo meshed walls plastered with mud-cowdung mix. These houses performed exceptionally during the major earthquakes. This made the Britishers realize the importance of local knowledge in house construction. They adopted a modified version of local houses. They used the locally available materials like wood, bamboo, reed, etc. to construct a type of house that supplements the masonry structure constructed upto sill level. The roofs of such houses followed the local style and are usually covered by thatch or galvanized sheets over wooden truss. They named these type of houses as the Assam-type house and they performed very well during the earthquake of 1950. Subsequently all the important Government buildings like courts, hospitals, administrative buildings, etc. were build in the Assam-type style. Though due to population pressure, RCC structures have replaced these traditional buildings. However, they still have a great significance in rural areas.
1.3 Climate of the Region Assam experiences a tropical monsoon rain forest kind of climate. It experiences high humidity and intense rainfall mostly throughout the year. Assam has mainly three distinct seasons–summer, winter and monsoon. High rainfall in the area makes Assam-type of houses and ideal building design.
1.4 Disasters Geographically Assam is highly disaster prone. The Brahmaputra and Barak valley region of the state is highly flood prone. Every year lakhs of people in the state are affected by flood. The hilly areas of the state are also landslide prone and poses threat to both lives and properties of the people. Assam lies in seismic zone V and has a long history of massive earthquakes. Two of the major earthquakes recorded in India’s recent history, i.e. 1897 Great Assam Earthquake (M 8.7) and the 1950 Assam Earthquake (M 8.4).
400
P. Boruah and A. K. Dutta
2 Methodology In order to achieve the objectives, a methodology has been structured. The next step is to do a detailed modelling of the structure in the ABAQUS® software. Once the modelling is done we will find out the mode shapes and run the response spectrum analysis. In Fig. 2 a detailed methodology has been structured.
Fig. 2 Shows the detailed methodology of the modelling of Assam-type building in ABAQUS®
Seismic Evaluation of Assam-Type Building Using ABAQUS®
401
3 Description of the Structure 3.1 Overview Assam-type houses are most common in high rainfall humid climate as in North-east India. Though with the increase in population pressure concrete structures are the most preferred style of housing in urban areas and slowly taking over Assam-type houses, yet they hold a great significance in rural areas. Even in Urban spaces, there are many important buildings which are Assam-type and are functioning wonderfully.
3.2 Assam-Type House Assam-type houses usually have simple geometry and are usually single storied. However, double storied and sometimes triple storied houses are also not uncommon. The materials used are generally the locally available materials like bamboo, timber, reeds “Ikora”, etc [1]. Concrete is also nowadays commonly used. The frame of the structure is usually made of timber and is of regular shape. The simple framework makes the structure cheap and easy to construct but effective in high seismic conditions. As the frame is devoid of any diagonal members, Assam-type houses are very suitable for high seismic zone areas. Use of low weight materials with high flexibility, simple frame, less number of members are some of the factors that makes Assam-type house very flexible in resisting lateral loads [2]. Typically in an Assam-type building, the intermediate vertical timber components are ended at sill level. This brings in a discontinuity and hinders the rise of moisture in the structure and thereby ensuring longevity of the materials. This aspect is very important for high rainfall areas like Assam. The presence of less number of members also facilitates easy introduction of openings like doors and windows. Thus the construction cost and maintenance cost of such structures is quite less. Figure 3 shows a schematic diagram of a typical Assam-type house with its various components. The foundation of the Assam-type houses are usually of reinforced concrete. Concrete pedestals are built monolithically over the foundation. Wooden posts, usually made out of timber locally known as sal (Shorea roubusta) are clamped to the concrete pedestals through bolted L-clamps. To complete the frame, a timber beams are attached to the top of the timber columns [3]. Assam-type houses are usually characterized by masonry walls upto sill level. Above the sill height the frames are usually separated into square panels using timbers frame elements (both horizontal and vertical) known as studs. These panels are than filled up with locally available materials like bamboo, ikra, etc. The horizontal timber members of the frame are joined to the main columns. Figure 4 shows ikra panel showing ikra and bamboo mesh [4].
402
P. Boruah and A. K. Dutta
Fig. 3 Schematic diagram and details of various components of a typical frame Assam-type houses
Fig. 4 Ikra panel showing ikra and bamboo mesh
The stability of the bamboo/ikra mesh is ascertained by inserting the mesh elements into the frame members by making holes into the members. The mesh is than covered with mud/mud-cowdung mixture or cement plaster in the form of plaster usually filled in two layers. Ceilings are made of wooden planks/bamboo mats/bamboo poles/plywood, etc. which acts as an insulating layer. The false ceiling is also used by the people as storage cabins for storing light objects. The roof truss of the house is usually made of timber covered by corrugated galvanized iron sheets or thatch. The sloped roofs of these kind of houses makes it favourable in high rainfall areas.
Seismic Evaluation of Assam-Type Building Using ABAQUS®
403
4 Seismic Analysis of Assam-Type Building 4.1 Finite Element Software ABAQUS® Powerful engineering simulation software called ABAQUS® is based on the finite element approach. The following are some of ABAQUS® ’s features: 1. ABAQUS® has a large library of elements that makes it possible to simulate any type of structure or geometry and performs both static and dynamic analysis. 2. Using ABAQUS® , it is possible to use different kinds of materials in the model. Some of the materials like polymer, reinforced concrete, crushable and flexible foams and geotechnical materials (such as soil, rock, etc.), can be simulated to understand their behaviour. 3. ABAQUS® can also be used to simulate various linear and non-linear applications..
4.2 Finite Element Modelling The non-linear behaviour of the construction materials of the traditional houses makes it difficult for numerical modelling. Moreover, there is a gap in complete experimental characterization of the mechanical properties of these materials that are usually used in traditional houses. These factors make it very difficult to analyse static and dynamic behaviour of these houses through modelling. An attempt has been made in the report to model using Finite Element Modelling [5].
4.3 Plan of the House to Be Modelled in ABAQUS® On this basis a three-dimensional Finite Element model of Assam-type house is developed, and the various procedures concerned with modelling is addressed as follows. Figure 5 shows AutoCAD plan of the Assam-type house to be modelled in the software.
4.4 Structural Modelling in ABAQUS® The 10 modules Part, Property, Assembly, Step, Interaction, Load, Mesh, Job, Visualization and Sketch make up each analytical model in ABAQUS® . For structural modelling in ABAQUS®, a proper understanding of these modules is crucial [6]. Part module. The geometry of each component of the model is specified in the part module. The fundamental units of an ABAQUS® CAE model are parts. Each body in
404
P. Boruah and A. K. Dutta
Fig. 5 AutoCAD plan of the Assam-type house
the finite element model ultimately has a portion assigned to it. Each component can be divided into “regions,” each of which needs to be connected to certain material and cross-sectional characteristics (Table 1). Property Module. Material and section properties are defined in the property module. A section is created by the property module and assigned to a part. This aids in defining a part’s attributes. Every element’s material attributes must be specified during modelling [7, 8]. However, the ikra’s mechanical characteristics are not Table 1 Modelling data in part module
Sl. No.
Element
Dimension (mm) (m2 )
6000 mm × 9000 mm
1
Plan area
2
RCC post
300 mm × 300 mm × 1000 mm
3
Timber post
200 mm × 200 mm × 2500 mm
4
Timber beam
200 mm × 200 mm × 2800 mm
5
Footing
600 mm × 600 mm × 400 mm
6
Brick
190 mm × 90 mm × 90 mm
7
Reinforcement
4500 mm
8
Door
400 mm × 100 mm × 2300 mm
9
Window
400 mm × 100 mm × 1100 mm
10
Bamboo
20 mm × 50 mm × 800 mm
11
Ikra
10 mm × 20 mm × 1100 mm 10 mm × 20 mm × 800 mm
Seismic Evaluation of Assam-Type Building Using ABAQUS®
405
Table 2 Basic material parameters for concrete and reinforcement Material
Modulus of elasticity (MPa)
Poisson’s Ratio
Density (Kg/m3 )
Tensile Compressive strength strength standard standard value value (MPa) (MPa)
Concrete
20,000
0.2
2400
2.25
26
Reinforcement
210,000
0.2
7850
400
400
Table 3 Basic material parameters for timber and brick
Material Modulus of Poisson’s Ratio Density (Kg/m3 ) elasticity (MPa) Timber
100,000
0.35
665
Brick
14,000
0.165
1600
Bamboo 14,900
0.278
1160
Ikra
0.278
1160
0.3
7850
14,900
GI sheet 200,000
yet known. Therefore, we are utilizing the characteristics of bamboo as the ikra. Since they both have comparable material characteristics (Tables 2 and 3). Assembly module. Even though a model can only accommodate one assembly, it can have numerous parts. The assembly module positions the instances of the parts to one another in a global coordinate system. Then, part instances are placed in the preferred location by applying position constraints in a sequential manner that align desired faces, edges, or vertices, or through basic translations and rotations (Fig. 6). Step module. It is used to generate analysis steps, define output requirements, specify adaptive meshes and specify analysis controls. The step portion provides an excellent approach for capturing changes in model load and boundary conditions, removal or addition of components and other changes that may occur during the analysis. Interaction module. To make the parts to act compositely and concurrently, the interaction function is applied after the model is assembled. To prevent distortion during loading and motion, the reinforcement cage is used as the “embedded region” and the concrete beam as the “host region”. The mortar between the bricks is create by setting the friction coefficient to 0.15 in the contact interaction property in the software. This interaction was simulate using the “Tie” function in ABAQUS® (Figs. 7 and 8). Boundary Conditions. Boundary conditions are applied to regions with well-known displacements and rotations in structural analysis. Regions such as these may either be constrained to stay fixed (zero displacement/rotation) throughout the simulation or may be specified (Fig. 9).
406
P. Boruah and A. K. Dutta
Isometric view
Front Elevation
Side Elevation
Front view in the wireframe
Fig. 6 Model of Assam-type house in assembly module
Fig. 7 Surface interaction applied on the brick surfaces
Seismic Evaluation of Assam-Type Building Using ABAQUS®
407
Fig. 8 Surface interaction created on the model
Fig. 9 Fixed base of the model
Mesh module. In every finite element analysis procedure, this step is vital as it enables all applied loads on a structure to be dispersed evenly across the entire model. The ABAQUS® software then calculates the solutions for each individual element. Figure 10 illustrates the meshing of the model with a global cuboid size of 1000 mm × 1000 mm × 1000 mm [9].
408
P. Boruah and A. K. Dutta
Fig. 10 Meshed finite element model
Job module. The Jobs module is used to analyse the model for all necessary tasks related to model definition. The jobs module allows you to generate jobs, make them available for analysis and monitor their progress. Result of the Modal Analysis See Fig. 11 and Table 4.
4.5 Response Spectrum Analysis Response spectrum evaluates the maximum structural response due to the seismic action. This analysis provides deep insight into dynamic behaviour by measuring pseudospectral acceleration, velocity, displacement as a function of structural period for specific time courses and damping levels. In this study response spectrum analysis is done considering [10] IS 1893(Part 1): 2016 for the Assam-type house [11]. Total deformation and axial stress on the whole structure are checked. Figure 12 shows the total deformation and Fig. 13 shows the axial stress on the models. This is a standard static finite element analysis. From the results below, we see that the stress is concentrated around the post of the structure. Also, from the roof, the Von Mises stress is distributed through the post to the ground, which makes sense that the loads are carried by the structure post. Result of the Response Spectrum Analysis See Figs. 12 and 13.
Seismic Evaluation of Assam-Type Building Using ABAQUS®
409
1st mode
2nd mode
3rd mode
4th mode
5th mode
6th mode
Fig. 11 Mode shapes obtained for the model of Assam-type house Table 4 Modal frequency of the models
Mode No
Frequency of Assam-type house frame (Hz)
Mode 1
2.4216
Mode 2
2.4589
Mode 3
2.4780
Mode 4
2.4935
Mode 5
2.5115
Mode 6
2.5562
410
P. Boruah and A. K. Dutta
Fig.12 Total displacement of the Assam-type building in response spectrum analysis
Fig.13 Image shows the Von Mises stress distribution of the Assam-type house in response spectrum analysis
5 Conclusions The study approaches the assessment of static and dynamic behaviour of a traditional Assam-type house through a finite element methodology. In modelling, it is necessary to give material properties to every element. But as the mechanical properties of ikra are not yet known, we have used bamboo’s properties as the ikra since both exhibit similar material properties. Based on the dynamic analysis, the first six mode shapes of the Assam-type house have been present. The static analysis shows that the Assam-type house with fixed base consideration is safe for seismic activity as less displacement and
Seismic Evaluation of Assam-Type Building Using ABAQUS®
411
stress are observed in the response spectrum analysis. It concludes that the finite element software ABAQUS® is competent for modelling the vernacular architecture of Assam.
References 1. Kakkad, M.D., Sanghvi, C.S.: Comparative study of bamboo (Ikra) housing system with modern construction practices. In: National Conference on Recent Trends in Engineering & Technology , pp. 1–3 (2011) 2. Chand, B., Kaushik, H.B., Das, S.: Lateral load behavior of traditional Assam-type wooden house. J. Struct. Eng. 145(8), 04019072 (2019) 3. Chand, B., Kaushik, H.B., Das, S.: Experimental study on traditional Assam-type wooden house for seismic assessment. In 16th World Conference on Earthquake, 16WCEE, Santiago Chile (2017) 4. Sharma, B., Gatoo, A., Bock, M., Ramage, M.: Construction and Building Materials, Vol. 81. Published by Elsevier Ltd. (2015) 5. Boakye, E.O., Osei, J.B., Adom-Asamoah, M.: Finite element modelling of bamboo reinforced concrete beams. J. Constr. Build. Mater. Eng. 4 (2) (2018) 6. ABAQUS User’s Manual: Version 6.6-1. ABAQUS, Inc., Providence, RI (2006) 7. IS 883: 1994, Design of Structural Timber in Building – Code of Practice, Fourth Revision, BIS, New Delhi, India 8. IS: 15912-2012: Structural Design Using Bamboo-Code of Practice. Bureau of Indian standards, New Delhi, India 9. Burman, S., Kumar, P., Singh, K.D.: Finite element modelling of ‘Rang Ghar’monument, Assam. Int. J. Innov. Res. Sci. Eng. Technol. (2013) 10. IS 1893(Part 1):2016, Criteria for Earthquake Resistant Design of Structures, Sixth Revision, Bureau of Indian standards, New Delhi, India 11. Choudhury, C.P., Pathak, J.: Analytical study of seismic response of traditional Assam-type housing in North- East India. In: 15th Symposium on Earthquake Engineering Indian Institute of Technology, Roorkee (2014)
Suitability of Foam Concrete and Confined Masonry for Retaining Walls Application in Seismically Active Regions: A Review Abhishek Kamisetty, Abhishek Kumar, and Indu Siva Ranjani Gandhi
Abstract The self-weight of retaining wall and the supported backfill play a vital role in its stability, particularly in weak soil conditions. Further, the seismic activity and moisture content in this soil condition aggravates the instability of retaining wall leading to its failure. Hence, the self-weight and seismic resistance of retaining walls is of utmost importance along with pore water pressure dissipation. It is to be noted that any structure’s seismic behaviour is primarily influenced by its mass, strength, and stiffness, as well as by all other factors that may have an impact on those characteristics. This paper presents a detailed review on the seismic performance and energy absorption characteristics of foam concrete, which contribute to the stability of retaining walls through optimisation in self-weight along with pore water pressure dissipation. Later, the limitations of using foam concrete in various types of retaining walls is discussed. Though masonry retaining walls is a potential solution, reinforced concrete confining elements along with foam concrete interlocking blocks could be more effective in enhancing their ductility, integrity, stability, and strength against inplane and out-of-plane seismic excitation. Further, few researchers have shown that confinement of wall with reinforced concrete tie-columns improve lateral resistance and deformation capacity of an unreinforced masonry wall by more than 1.5 times and five times, respectively. This is in addition to a six to seven times enhancement in the energy dissipation capacity. This way, the stability of retaining walls could be enhanced by the use of foam concrete, interlocking blocks, and confined masonry technologies. It should be highlighted here that though the combination of these technologies has a lot of potential in the aforementioned application, very limited research exists in the literature on use of foam concrete and confined masonry for retaining wall applications. In this light, the present work also presents an in-depth A. Kamisetty (B) · A. Kumar · I. S. R. Gandhi Department of Civil Engineering, IIT Guwahati, Guwahati, India e-mail: [email protected] A. Kumar e-mail: [email protected] I. S. R. Gandhi e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_32
413
414
A. Kamisetty et al.
review on dynamic properties of foam concrete, enumerating the seismic resistance mechanism. Keywords Foam concrete · Confined masonry · Interlocking blocks · Retaining wall
1 Introduction The development of any hilly terrain mainly depends upon the infrastructure such as buildings, road ways, and railways and the stability of slope on which these are developed. The north-east Indian region is a hilly terrain with an unique condition of very severe seismic intensity zone (seismic zone V), shallow ground water table at 0 to 20 m bgl, which rises-up to 0 to 10 m bgl during monsoon seasons and incessant rainfalls [1–3]. This critical condition can be attributed as the factor leading to the classification of this region as moderately high hazard to very high hazard zones of landslides [4, 5]. Further, several incidents in this region were reported by geological survey of India stating that aforementioned factors were responsible for instability of retaining walls and slope, causing damage to various infrastructure and disruption to the services provided (GSI) [6]. Particularly, in the case of Tawang, Arunachal Pradesh incident (2016), incessant concentrated pre-monsoon rainfall for 10 days and it’s close proximity to the main central thrust resulted in more than 31 landslides in this area [7]. In this line, there are also many incidents reported on failure of retaining wall in places with higher ground water table due to buildup of pore water pressure behind retaining wall (GSI). Even in static condition, occurrence of excessive rains leads to addition of more water to the backfill material which subsequently increases its unit weight and compromise the factor of safety. Further, seismic excitations also results in development of excess pore pressure, which could not get easily dissipated even in case of sandy soil as the duration of loading is minimal and this eventually leads to failure. The commonly adopted technique to address the above issue in retaining wall is provision of weep-holes which allow free flow of water from the backfill, and thus prevents the generation of any hydrostatic head behind the retaining structure. Though weep-holes are commonly provided, their effectiveness in terms of dissipation of hydrostatic head changes depending upon effective design and construction. In this context, Kamisetty et al. [8], have proposed the use of foam concrete (FC), a type of cellular lightweight concrete to facilitate reliable drainage path for pore water pressure dissipation owing to its high permeation nature. Seismic event being one of the key factors triggering landslides and hence, the seismic behaviour of retaining wall, is also of utmost importance along with the pore water pressure dissipation. In this regard, there is a need for simple aseismic construction technology that can be executed by unskilled manpower along with enhanced affordability. Generally, any structure’s seismic behaviour is primarily influenced by its mass, strength, and stiffness, as well as by all other factors that may have an impact on those characteristics [9]. The main principle for seismic
Suitability of Foam Concrete and Confined Masonry for Retaining Walls …
415
resistant design is to avoid unnecessary mass, and hence the use of lightweight FC can reduce the structure’s self-weight and subsequently reduce the intensity of seismic forces [10–12]. In this line, few researchers have verified the energy dissipation and seismic isolation properties of FC for various applications such as pavement subbase, tunnel lining, and underground reactors [13–15]. Despite the huge potential of use of FC in seismic resistant structures, to date, there are not many studies reported in India addressing the seismic behaviour of FC. Further, technical and engineering unfamiliarity about the material in Indian context can be attributed to its limited usage for structural applications [16]. There are also evidences reported in literature about the challenges in attaining stable FC mix for cast in situ applications particularly for greater casting heights. [17, 18]. Further, if FC is used in cantilever retaining walls, the protection of reinforcement from risk of corrosion is also questionable [19, 20]. To address the aforementioned issues, it is preferable to use FC in masonry retaining wall for slope stabilisation and seismic resistance. In the same line, many studies have proved that confined masonry (CM) buildings showed enhanced seismic performance than infilled reinforced concrete frames and unreinforced masonry wall [21]. Adding to above, Chourasia et al. [22], proved that seismic performance of CM buildings can be further enhanced through use of lightweight FC. The above literature evidences prompt for review on the advantages of CM concept for the enhancement in seismic performance of masonry retaining walls. Further, the advantage of superior integration between adjacent masonry blocks to resist lateral loads is also discussed. Furthermore, it also emphasises FC’s unique attributes, such as seismic isolation and energy absorption. Additionally, it should be mentioned that there aren’t many studies reported in the literature on potential use of combination of CM, interlocking blocks (IB) and FC for the seismic resistant structures. Particularly, there is no study reported in literature addressing the use of CM type of construction for retaining wall applications.
2 Potential of the Use of Confined Masonry in Retaining Walls CM construction which is an effortless and tolerant construction methodology has demonstrated effective performance against damaging seismic excitations in the past and is practiced in Latin America and Mediterranean Europe and has been incorporated in national building codes [23]. In some Asian countries, such as china and Indonesia, it is considered to be a standard construction methodology. It was practiced in China since 1966 [24] in Argentina since 1920 [25] and in Chile since 1930 [26]. Studies have reported that very less damage has occurred to CM buildings during seismic excitation [26, 27]. Further, it has been proposed that unconfined and unreinforced masonry shall not be adopted for the buildings in high seismicity zones [27].
416
A. Kamisetty et al.
Two essential characteristics, namely confinement and bond between masonry walls and the confining elements made of reinforced concrete that surround these walls, are necessary in modern CM construction for their efficient performance during seismic excitations [28]. Since the Assam earthquake in 1897, these two characteristics have been recognised by Indian architects and engineers. The idea of lateral confinement is used in “Assam type housing” that has developed in the earthquakeaffected region, while the 1931 Baluchistan earthquake illustrated the significance of bond for improved seismic performance of masonry structures. The strength, stability, ductility, and integrity of masonry walls against both in-plane and out-ofplane seismic excitation are reported to be improved by reinforced concrete confining elements [28]. Further, the distinctive building sequence used in this method yields enhanced integration between the masonry and neighbouring reinforced concrete sections. As per [21], confining a wall with tie-columns made an unreinforced masonry wall more than 1.5 times more lateral resistant, nearly five times more deformation capacity, and six to seven times more capable of dissipating energy. In addition to the benefits mentioned above, it needs less attention during design and construction and yet holds up well during seismic excitations. Hence, to enhance the seismic resistance of masonry retaining wall, it is more rational to adopt CM construction technique.
3 Potential of Interlocking Blocks for Use in Seismic Resistant Retaining Walls Appropriately designed masonry type of construction is considered to be a costeffective and low-energy alternative. Further many studies have proved that the manual error, construction cost, time and resource consumption can be reduced through the incorporation of interlocking concept in masonry [29, 30]. IB, also known as mortarless bricks, is a construction technique that pioneers the concept of dry stacking bricks. Several researchers have developed various forms of IB classified based on their geometry (hollow, solid, curved, and provisions for reinforcement), function (load bearing, partition or cladding walls), and method of construction [31]. The basic idea behind interlocking concept is to restrict the relative movement between the adjacent blocks and enhance mechanical interactions to achieve the required stability [32]. For instance, Wang et al. [33] has developed a block with imperfection in all 3 directions to establish the interlocking effect and has studied the stability of an Igloo. These imperfections may take the shape of interlocking characteristics including projections and recesses, tongues and grooves, and nibs and cuts. However, the absence of mortar in the IB is expected to result in reduced lateral load resistance. Hence, to address this, Thamboo et al. [30] and Ali et al. [31], recommended provision of horizontal interlocking features along with the vertical interlocking features which could enhance lateral resistance against horizontal as well as vertical bending. Furthermore, the lateral resistance and stability of structure
Suitability of Foam Concrete and Confined Masonry for Retaining Walls …
417
against static and dynamic forces can be enhanced with additional measures such as reinforcement, posttensioning, internal grouting, and surface rendering [30, 31, 34]. Also, the geometry of the blocks need to be carefully designed with a tolerance of ±0.25 mm accuracy, as the IB units demand high levels of dimensional accuracy that adhere to the “standard” unit dimension [30]. In this line, it is to be noted that imperfections in surface geometry and contact surface could cause negative impact on mechanical properties leading to failure [35]. Further, to address the doubts related to water permeation behaviour of IB masonry, studies conducted by Anand et al. [36] and Forghani et al. [37] have shown that the performance is comparable with that of conventional masonry. Also, the use of mortar paste along with the IB is reported to enhance the compressive strength of the system by 30% while maintaining the inherent characteristics of masonry construction [38]. Adding to above, the other benefits of IB are higher production rate (2.5–5 times higher than conventional brick), labour saving (60–80%), elimination of shrinkage cracks, self-alignment, robustness, etc. [30, 35, 39]. Hence, it is evident that the aforementioned benefits of IB along with that of CM wall technique, can facilitate construction of retaining walls even in remotely placed locations. However, it is to be noted that, the type of IB selected for the construction of retaining wall plays a major role in transferring the lateral loads from backfill to the adjacent blocks and further to the confining elements and the base of retaining wall.
4 Potential of Use of Foam Concrete in Seismic Resistant Confined Masonry Retaining Wall Literature review highlights that studies reported on use of FC in seismic resistant applications is very scarce. For instance, Qin et al. [40] has carried out comparative analysis of seismic performance of FC composite wallboard using renewable nanomaterials and concrete hollow block-filled walls. Their research outcome indicated that FC composite wallboard exhibited relatively more energy dissipation capacity, deformation capacity, bearing capacity, and subsequently better seismic resistance than the concrete hollow block-filled wall. In the same line Johnson et al. (2020) proved that U-shaped walls composed of fibre-reinforced FC might perform better than plain FC in structural and seismic applications. Another study by Xu et al. (2018) on the seismic performance of cold-formed steel shear walls filled with lightweight and high-strength FC, proved that use of FC resulted in relatively more ductile failure. In this line few researchers have also reported the use of FC as seismic isolation material in lining of tunnel [41] and underground reactor containments [14]. Based on the experimental outcomes it has been proved that poissons ratio and shear modulus of FC were lower than the conventional concrete and FC exhibited good energy absorption characteristics. Further numerical analysis carried out by Zhao et al. [41] demonstrated that even when the FC layer is just 0.1 m thick, it may greatly reduce the stress and plastic zone of the tunnel’s final lining when subjected to seismic waves
418
A. Kamisetty et al.
and hence can act as good seismic isolation material. Further, the study proved that unlike the test curves for brittle materials like rock, dynamic tests on FC have not revealed any evident failure sites [41, 42]. This could be explained by the fact that the failure of FC is ductile and that the majority of the energy does not accrue but instead dissipates during the test by deforming the sample. The above evidences of applications of FC proves the potential of its use in seismic resistant structures. Hence the proposal of CM retaining wall model with lightweight interlocking FC blocks can be an innovative promising aseismic solution. Also, to the best of author’s knowledge, there is no study reported in this regard in Indian context which highlights the major research gap. As a next step, the design parameters which supports the use of FC in CM model need to be analysed. Equations 1 and 2 are basic equations which governs the compressive strength of wall in CM [43]. Pcomp = ks ∗ f m
(1)
where Pcomp : ultimate compressive strength of wall due to gravity load k s : stress reduction factor based on slenderness ratio and eccentricity F m : compressive strength of masonry. Pcomp ≥ 2.6σ dl
(2)
where σ dl: stress generated due to vertical loading (dead + live) on the wall panel. Here, we can observe from Eq. 2 that, use of lightweight material in the construction of CM wall reduces the dead load of the structure, ultimately resulting in lower Pcomp required. Further, reduction in requirement of Pcomp enables the use of FC blocks with lower compressive strength. Also, it is to be noted that the wall density is directly proportional to ns and inversely proportional to Pcomp as per Eq. 3 [43]. Wd ≥ f g ∗ w ∗ n s / Pcomp
(3)
where W d : Wall density, calculated by dividing the total cross-sectional area of all walls (Aw ) by the plan area (AP ) f g = Safety factor for gravity load w = Weight of unit area of floor system (also includes self-weight of walls) ns = Number of stories in the building. Further, it is to be noted that the most crucial factor in the design of masonry structures is the compressive strength of the wall, which is mostly determined by the mechanical properties of the block units [44]. Here in Eq. 3, it is to be noted that, for a given wall density, higher Pcomp of lightweight concrete blocks enables us to design CM structures with a greater elevation (equivalent to ns ).
Suitability of Foam Concrete and Confined Masonry for Retaining Walls …
419
In the same line, Chourasia et al. [22], have studied the seismic performance of full-scale CM buildings using FC blocks of 800 kg/m3 density. The use of FC panels instead of burnt clay bricks has shown 14% reduction in maximum lateral load for 90% increase in the base shear coefficient, exhibiting superior seismic performance. Further, grooves of IB were found to be effective in preventing crack propagation at the vertical block-block interface, thus demonstrating integral behaviour of the CM building with FC blocks. Adding to above, the provision of reinforcement and concrete through the holes of IB in the form of core columns is reported to further enhance the lateral strength [22, 30, 31, 34]. The above discussion on various literature evidences highlights the fact that use of FC IB in CM retaining wall (see Fig. 1) can be a potential aseismic solution which could enhance the stabilisation of slopes. Hence more research is necessitated in this context to validate the abovementioned fact.
Fig. 1 A schematic representation of the proposed CM retaining wall with interlocking FC blocks
420
A. Kamisetty et al.
5 Summary The factors contributing to the stabilisation of slopes has emphasised the refinement in pore water pressure dissipation capacity and seismic resistance of retaining walls. Though applicability of FC in retaining wall applications has limitations, and it’s ability to dissipate pore water pressure compels us to recognise masonry type of retaining walls as a potential alternative. Further, the adoption of CM concept enhances the strength, stability, ductility, and integrity of masonry retaining walls. Implementation of interlocking concept to FC blocks intensifies the stress transfer capacity of masonry units through superior integration and homogeneity between the blocks. The lightweight, seismic isolation and energy dissipation properties of FC has highlighted its ability for use in seismic resistant structures. The proposed retaining wall with FC IB and CM technique is an efficacious construction methodology, imparting speed and efficiency. Though these concepts have a lot of potential for usage in the aforementioned applications, it is clear from the literature review that there hasn’t been much research on using CM, FC, and IB for slope stabilisation, thus further study is required in this area.
References 1. IS 1893-1: 2021.: Criteria for Earthquake Resistant Design of Structures. Bureau of Indian standards (2021) 2. GWYB, Ground Water Year Book—India 2012–2013. Ministry of Water Resources, Government of India (2013) 3. NHAI.: Rehabilitation and Up Gradation of Existing 2 Lane to 2 Lane with Paved Shoulder from Jowai (km 69.2) to Meghalaya/Assam Border (km 173.20) Section of NH-44 in the State of Meghalaya under NHDP Phase-III Programme (Package No. NN/DL2/4), Draft Environment impact assessment report, National highways authority of India (2012) 4. NDMA.: Landslide Zoning Map. National Disaster Management Authority, Government of India, https://ndma.gov.in/en/landslides-zone-map.html 5. Kaur, K., Gupta, S., Prakash. S.: Comparative evaluation of various approaches for landslides hazard zoning: a critical review in Indian perspectives. Spat. Inf. Res. 25, 389–398 (2017) 6. GSI.: Geological Survey of India, Government of India, https://www.gsi.gov.in/webcenter/ portal/OCBIS/pageQuickLinks/pageLandslideIncidents?_adf.ctrl-state=zkmfscik5_5 (2009– 2022) 7. Rocky, W.S., Rongmei, G., Keshari, S.C.: Report on the Preliminary Post Disaster Landslide Studies in and Around Tawang town, Tawang district, Arunachal Pradesh. Geological survey of India (2017) 8. Kamisetty, A., Ranjani, I.S., Kumar, A.: Exploring the suitability of using foam concrete as pore pressure dissipation measure for slope stability: a state of art review. In: Materials today Proceedings of International Conference on advances in Construction Materials and Structures (ICCMS 2021), 15–17 Dec 2021, (2022) 9. Kılıc, C.D., Atis, E., Yasar, F., Ozcan.: High-strength lightweight concrete made with scoria aggregate containing mineral admixtures. Cem. Concr. Res. 33(10), 1595–1599 (2003) 10. Bertero, V.V., Popov, E.P., Forzani, B.: Seismic behaviour of lightweight concrete beam column sub assemblages. ACI J. 77-7 (1980) 11. Bhattacharyya, S.K., Agarwal, A.K.: National Labs: Research Highlights 2014. CSIR–Central Building Research Institute, Roorkee 247667, India (2014)
Suitability of Foam Concrete and Confined Masonry for Retaining Walls …
421
12. Talukdar, P., Bora, R., Dey, A.: Finite element based identification of the triggering mechanism of a failed hill slope. In: IACMAG, China (2017) 13. Zhao, W.S, Chen, W.Z., Tan, X.J., Huang, S.: Study on foamed concrete used as seismic isolation material for tunnels in rock. In: Materials Research Innovations, Taylor & Francis group, ISSN: 1432-8917 (2013) 14. Mohrenholtz, O., Reddy, D.V., Bobby, W.: Limit analysis of internally pressurised cut-andcover type underground reactor containments. ACI J. 79–24 (1982) 15. Kadela, M., Koz, M., Kukie, A.: Application of foamed concrete in road pavement—weak soil system. Procedia Eng. Elsevier 193, 439–446 (2017) 16. Amarnath, Y., Ramachandrudu, C.: Production and properties of foam concrete. In: Cemcon 2013 (2013) 17. Zhao, W., Huang, J., Su, Q., Liu, T.: Models for strength prediction of high-porosity cast-insitu foamed concrete. In: Advances in Building Technologies and Construction Materials 2018, Hindawi, Volume 2018 |Article ID 3897348 (2018) 18. Raj, A., Sathyan, D., Mini, K.M.: Physical and functional characteristics of foam concrete: a review. Constr. Build. Mater. 221, 787–799 (2019) 19. Kearsley, E.P., Booyens, P.J.: Reinforced foamed concrete, can it be durable. Concrete/Beton 91, 5–9 (1998) 20. Kearsley, E.P., Wainwright, P.J.: Porosity and permeability of foamed concrete. Cem. Concr. Res. 31(5), 805–812 (2001) 21. Borah, B., Singhal, V., Kaushik, H.B.: Sustainable Housing Using Confined Masonry Buildings. Springer Nature Switzerland AG 2019 (2019) 22. Chourasia, A., Singhal, S., Parashar, J.: Seismic performance evaluation of full scale confined masonry buildings using lightweight cellular panels. J. Build. Eng. 32, 101473 (2020) 23. Schacher, T., Hart, T.: Construction guide for low rise confined masonry buildings. In: World Housing Encyclopedia, EERI, IAEE, Swiss Re, SDC (2015) 24. Gaochuang, C., Su, Q., Tsavdaridis, K.D., Degee, H.: Simplified density indexes of walls and tie columns for confined masonry buildings in seismic zones. J. Earthquake Eng. 24(3), 447–469 (2020) 25. Michelini, R.J., Maldonado, N.G.: Design and construction in seismic-resistant masonry standards in force in the province of Mendoza, Argentina. In: Brick and Block Masonry (1991) 26. Moroni, M. O., Astroza, M., Acevedo, C.: Performance and seismic vulnerability of masonry housing types used in Chile. J. Perf. Const. Facil. 18(August), 173–179 (2004) 27. Zhao, B., Taucer, F., Rossetto, T.: Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China. Eng. Struct. Elsevier Ltd 31(8), 1707–1723 (2009) 28. Jain, S.K., Basu, D., Ghosh, I., Rai, D.C., Brzev, S., Bhargava, L.K.: Application of confined masonry in a major project in India. In: Tenth U.S. National Conference on Earthquake Engineering (2014) 29. Anand, K.B., Ramamurthy K.: Techniques for accelerating masonry construction. Int. J. Housing Appl. 23(4):233–41 (1999) 30. Thamboo, J.A., Zahra, T., Dhanasekar, R.: Development of design methodology for mortarless masonry system: case study—a resettlement housing colony. J. Build. Eng. 27, 100973 (2020) 31. Ali, M., Gultom, R.J., Chouw, N.: Capacity of innovative interlocking blocks under monotonic loading. Constr. Build. Mater. 37, 812–821 (2012) 32. Lecci, F., Mazzoli, C., Bartolomei, C., Gulli, R.: Design of flat vaults with topological interlocking solids. Nexus Netw. J. 23, 607–627 (2021) 33. Wang, Z., Song, P., Isvoranu, F., Pauly, M.: Design and structural optimization of topological interlocking assemblies. ACM Trans. Graph. 38(6, Article 193) (2019) 34. Ramamurthy, K., Nambiar, E.K.K.: Accelerated masonry construction review and future prospects. Progr. Struct Eng. Mater. 6(1), 1–9 (2004) 35. Shi, T., Zhang, X., Hao, H., Chen, C.: Experimental and numerical investigation on the compressive properties of interlocking blocks. Eng. Struct. 228, 111561 (2021)
422
A. Kamisetty et al.
36. Anand, K.B., Vasudevan, V., Ramamurthy, K.: Water permeability assessment of alternative masonry systems. Build. Environ. 38, 947–957 (2003) 37. Forghani, R., Totoev, Y., Kanjanabootra, S., Davison, A.: Experimental investigation of water penetration through semi-interlocking Masonry walls. J. Archit. Eng. 23(1) (2016) 38. Ahmad, S.: To study the behavior of interlocking of masonry units/blocks. IOSR J. Eng. 4(3), 39–47 (2014) 39. Whelan, L.: Hollow concrete masonry unit shape modification to improve productivity of placement: results of the preliminary research effort. In: Proceedings of the 3rd North American Masonry Conference, Arlington, Texas, pp. 9.1–9.8 (1985) 40. Qin, L., Qian, K., Ding, J., Zhao, Y.: Experimental study on seismic performance of new foam concrete composite wall panel based on nanomaterials. Nanotechnol. Environ. Eng. 7, 201–207 (2022) 41. Zhao, W.S., Chen, W.Z., Tan, X.J., Huang, S.: Study on foamed concrete used as seismic isolation material for tunnels in rock. In: Materials Research Innovations, Taylor & Francis group, ISSN: 1432-8917 (2013) 42. Li, H.B., Zhao, J., Li, T.J.: Triaxial compression tests of a granite at different strain rates and confining pressures. Int. J. Rock Mech. Min. Sci. 36(8), 1057–1063 (1999) 43. Chourasia, A.: Design Guidelines for Confined Masonry, by CSIR, Roorkee, (2017) 44. Thanoon, W.A., Jaafar, M.S., Kadir, M.R.A., Ali, A.A.A., Trikha, D.N., Najm, A.M.S.: Development of an innovative interlocking load bearing hollow block system in Malaysia. Constr. Build. Mater. 18(6), 445–454 (2004)
Role of Hydrodynamic Forces on the Seismic Response of a Dam Dhananjay Vyas , Jithin P. Zachariah , Alla Kranthi Kumar, and Ravi S. Jakka
Abstract The static and seismic response of dams is always a serious concern in the design and construction phases of these massive manmade structures. The gravitational stability of these structures is continually challenged by various forces acting on the dam structure, including the upstream water. But the role of hydrodynamic forces on the seismic response of dams is not been much studied in the past. Moreover, the hydrodynamic forces vary with the depth and shape of a dam, leading to an underestimation of its effect on the seismic response of a dam. This paper studies the seismic response of a concrete gravity dam using finite element analysis, considering the hydrodynamic effects. The hydrodynamic impact on the dam structure is simulated using two methods, the inertial mass concept and water as a structure. Three natural seismic motions, Koyna, Kobe, and Chi-Chi, are used to study the influence of seismic motions on the hydrodynamic effects on the dam. The study shows that the hydrodynamic forces contribute to stresses on the dam structure in seismic activity, and the hydrodynamic forces acting on the dam are proportional to the shaking intensity. Moreover, the study also reveals the underestimation of hydrodynamic forces in the inertial mass approach with the help of modeling water as a continuum. Keywords Concrete dams · Seismic response · Hydrodynamic forces · Inertial mass concept · Finite element modeling
1 Introduction Dams are massive manmade structures used for various purposes, from simply retaining water to using that water for hydropower generation to developing tourism around the reservoir. So, the failure of these megalithic structures causes catastrophic effects on downstream life and community. Failure of a dam can be because of several D. Vyas · J. P. Zachariah · A. K. Kumar · R. S. Jakka (B) Indian Institute of Technology Roorkee, Roorkee 247667, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_33
423
424
D. Vyas et al.
reasons, loss of stability, transverse, and longitudinal cracking, overtopping due to inadequate capacity, etc. From the engineering point of view, dams are in a class of their own relative to other vital structures. Yet, several dams have failed and suffered significant displacement during earthquakes in the past that caused severe effects on the region [1–3]. This shows the necessity of a comprehensive seismic analysis of the dam structure. The seismic response studies of the dam structures are mainly carried out with the help of finite element tools. However, model tests are also being conducted. Finite element linear elastic models help in effectively modeling the dam structure in the safety evaluation methodology of concrete gravity dams along with the determination of the demand capacity ratio (DCR) of the structure, which is the ratio of induced to the allowable tensile stress of the material [4, 5]. Discrete Crack Approach (DCA), Smeared Crack Approach (SCA), Co-axial Rotation Crack Model (CRCM), and Continuum Damage Mechanics (CDM) are a few of the philosophies used in the evaluation of concrete structures in FEM [1, 6–9]. The presence of the upstream water body also plays a significant role in the seismic response of the dam structure. The horizontal and vertical ground motions and deformations at the upstream face of a dam will induce hydrodynamic forces in the reservoir, leading to structural deformations and instability of the structure. To break this severe closed cycle of cause and effect, the formulation of the problem must recognize the dynamic interaction of the dam-water system. The effect of hydrodynamic forces on the dam structure in the seismic analysis is often represented with the help of inertial masses or added mass at the dam’s upstream face [10]. Many researchers have used this concept to analyze the influence of hydrodynamic forces on the dam [11, 12]. However, this estimation only takes the partial value of the hydrodynamic force by assuming that hydrodynamic force varies with the depth and shape of the dam body only and neglecting the temporal variation throughout the time period of an earthquake and thus undermines its effect on the seismic response of the dams. The fluid–structure interaction in the dams is also defined using the incompressibility of the fluid and null shear strength of the material [13], whereas the crack patterns on the concrete dam structure are modeled with the help of particle-based computations. This helps to identify the regions susceptible to cracks i4n a dam structure [14]. Indian standards also use pseudo-static analysis by assuming that hydrodynamic forces vary in parabolic form with the depth and shape of a dam, and maximum value occurs at the base of the dam for the whole time period of the earthquake, thus ignoring its temporal variation [15]. The pseudo-static analysis considers the worst possible scenario and leads to an over-safe design [16]. It is observed that most of the previous studies evaluating the seismic safety of concrete dams attempt to use the inertial mass approach to model the fluid– structure interactions. Nevertheless, the efficiency of this approach is questionable. This paper attempts to estimate the hydrodynamic effect on the concrete dam structure by adopting two different methods. Moreover, the seismic response of the dam under various natural earthquake motions is also studied.
Role of Hydrodynamic Forces on the Seismic Response of a Dam
425
2 Methodology The two-dimensional static and dynamic analysis of the dam structure is carried out with the help of the FEM tool Abaqus CAE. The loading conditions were selected following IS 6512 [17]. The following sections carry out a detailed discussion on the various load conditions. The dynamic analysis is performed for different load combinations by time history analysis. The concrete dam body is supported on the rock foundation. 1.5 times dam height foundation width is considered on either side of the dam structure and as the depth of the foundation rock. A detailed FEM sketch of the dam and foundation is shown in Fig. 1. Moreover, infinite boundaries have been provided at both sides of the foundation during the seismic analysis to account for the reflection of the incoming seismic waves.
2.1 Modeling of the Dam The Koyna Gravity dam is constructed on the Koyna River in the west of the Indian Peninsula. The dam structure has a height of 103 m with a width of crest = 14.8 m and covers a length of 807.2 m and 70 m width in upstream to the downstream direction at its base. The freeboard of 11.3 m is given on the upstream side. The model consists of 2 parts–the dam body and the bedrock. Hydrodynamic forces are modeled using two methods, added mass method and water as a part. FEM modeling is done in Abaqus/CAE, 2016 (Table 1).
Fig. 1 Mesh diagram of the dam structure (seismic condition)
426 Table 1 Material properties used in the analysis of the Koyna Dam [18]
D. Vyas et al. Properties
Value
Mass density of dam
2630 kg/m3
Mass density of foundation bedrock
2600 kg/m3
Elastic modulus of dam
3 × 104 MPa
Elastic modulus of foundation bedrock
3 × 104 MPa
Poisson ratio
0.2
Damping ratio
5%
2.2 Load Conditions The finite element analysis of the dam is performed by considering all the available load conditions acting on the dam structure under static as well as dynamic conditions as given in IS:6512 [17]. Load Condition A. Under this load case, the dam is analyzed for the geostatic stresses during empty reservoir conditions. This stage represents the conditions just after the construction of the dam. Displacement/rotation is restricted in a vertical direction on the sides of the bedrock, and the base of the bedrock is fixed. Load Condition B. Full reservoir level of the dam is considered in this condition. Hydrostatic pressure is applied in triangular variation with 0 value at the reservoir water level that is at 91.7 m from the base of the dam and a maximum value of 89,977 N/m2 at the base in the positive x-axis direction. The surcharge of 89977N/m2 is also applied on the upstream side of the bedrock surface. Load Condition D. This load condition helps to simulate the response of an empty dam during seismic conditions. The model is a linear elastic model in plane stress conditions with the assumption that the dam and bedrock are perfectly rigid and the upstream face of the dam is vertical. Also, the damping ratio of 0.05 is chosen for both materials. To prevent the reflection of compressive seismic waves, either side of the bedrock has a layer of infinite elements, or the movement of the bedrock is restricted in the vertical direction. Load Condition E-1. Because of the presence of water with a freeboard of 11.3 m, the hydrostatic forces and surcharge is considered in this case. The hydrostatic forces (Hydrostatic pressure, P = γ h, where γ is the weight density of water and h is the depth in m from the reservoir level) are calculated, having a triangular variation with depth having zero value at the top and maximum value at the base of the dam. Load Condition E-2. The Inertial Mass approach is used to provide the effects due to hydrodynamic forces caused by reservoir water during seismic conditions. The inertial masses are calculated using Westergaard’s equation of inertial masses at each node on the upstream face of the dam. The inertial masses are the partial representation of water during seismic motion and follow parabolic variation with depth for the whole time period of earthquake motion [10] and are calculated by the
Role of Hydrodynamic Forces on the Seismic Response of a Dam
427
equation given: Mi =
(B1 + B2 ) √ 7 (ρw ) × (hYi ) × 8 2
(1)
where M i is the inertial mass at ith node point, ρ w is the mass density of water as 1000 kg/m3 , h is the depth of reservoir level equal to 91.7 m, Y i is the depth of ith point from reservoir level, and B1 and B2 are the distance between ith and (i − 1)th node points and ith and (i + 1)th node points. The values of inertial masses will change with a change in mesh size that is B1 and B2 . Load Condition E-3. In this state, unlike State 3, in which all forces due reservoir is applied separately, the water reservoir itself is modeled so that the reservoir water behavior during dynamic condition also cater to the temporal variation and the variation due to depth. This approach is developed so that the effect of the hydrodynamic forces can be applied entirely instead of partially compared to the inertial mass concept. The water in the reservoir is modeled as a quasi-elastic medium with a minimal value of young’s modulus and a very large Poisson’s ratio value (=0.495). Using a very small young’s modulus ensures that the value of the shear modulus remains very small and high volumetric module. The assumption is that the bulk modulus for water at 20 °C and atmospheric pressure is taken as K = 2.2 GPa. Thus, by taking ν = 0.495, Young’s modulus is kept to a minimal of E = 132 Pa. These properties are provided to the shell instance sketched using appropriate dimensions. This ensures that the whole water can be moved as a part, and low shear modulus provides the required fluidity to the reservoir.
2.3 Frequency Analysis Frequency analysis or free vibration analysis is performed to determine the mode shapes and natural frequency of the dam body. These parameters play an important role in the seismic response of the dam structure. The natural frequencies of the structure at different modes are tabulated in Table 2, and the first five modal shapes are shown in Fig. 2. Table 2 The first five frequencies of the 2D model of the dam
Mode
Frequency (cycles/s)
1st
2.5004
2nd
4.8912
3rd
4.9650
4th
5.6739
5th
5.9321
428
D. Vyas et al.
Fig. 2 The first five modal shape of the 2D model of the dam
2.4 Time History Analysis The seismic analysis or the time history analysis is the most rigorous method of estimating dynamic structural response under loading, which may vary according to the specific time function. It will give the response of a structure over time during and after the application. The seismic response of the dam structure in the present study is carried out using four loading conditions. The Koyna earthquake of 1967 is used as the basic motion for the analysis. Two other natural bedrock motions, Kobe (0.074 g, 1995) and Chi-Chi (0.12 g, 1999) are also used to study the influence of hydrodynamic effects on the dam structure. These time histories are converted into
Role of Hydrodynamic Forces on the Seismic Response of a Dam
429
Fig. 3 Matched response spectrum of considered natural time histories
spectrum compatible motions using SeismoMatch [19]. The response spectrums of these spectrum compatible motions are shown in Fig. 3. The spectrum compatible acceleration time histories are extracted after matching the raw acceleration time histories to the standard response spectra. This helps in synchronizing the existing raw time history to that of the desired seismic zone. The spectrum compatible acceleration time histories are shown in Fig. 4.
3 Results and Discussion 3.1 Static Analysis The static analysis of the Koyna Dam is performed for both the empty dam (Load case A) and full reservoir level (Load case B) to determine the geostatic and in-situ stresses. It is observed that the stress contours vary linearly because only the gravity is acting during empty reservoir conditions (Fig. 5a), i.e., just after construction is completed. When the reservoir is full (Load case B), due to hydrostatic force and reservoir surcharge on the upstream side, there is a shift in the stress contours toward the right in Fig. 5b. There is also an increase in the maximum tensile stress in full reservoir level condition as compared to empty dam condition. This shows the increased risk of the structure with the presence of water when it is subjected to seismic forces.
430
D. Vyas et al.
Fig. 4 Input motions used in the analysis a Koyna, b Chi-Chi, c Kobe
3.2 Seismic Analysis The seismic response of the Koyna dam is simulated under the Koyna motion of 1967, under which the dam failed. The analysis is further extended for two more natural input motions weaker than Koyna motion to determine stresses under different load conditions. To determine the failure of the concrete gravity dam under these conditions, the demand capacity ratio (DCR Value) is used. The DCR value is the ratio of induced tensile stress in the dam to the tensile stress of the concrete. The calculated DCR less than 1 represents the dam under linear elastic range with less to no damage under the load condition. The induced tensile stress of the dam is the maximum principal (tensile) stress determined from stress contours shown in Fig. 6 obtained from dynamic analysis. The maximum tensile stress of the dam, tensile stresses at different nodes and DCR values are shown in Table 3. The tensile stresses on various critical points of the dam structure such as heel, toe, and slope changing points are also evaluated. The dynamic analysis shows that the tensile stress values are not changing much when hydrodynamic forces are applied in the LCE-2 condition (using inertial mass) as compared to the LCE-1 condition where hydrodynamic forces are absent. It is observed that this variation is large under the LCE-3 condition when the hydrodynamic forces are applied using the waterbody approach, which considers the temporal
Role of Hydrodynamic Forces on the Seismic Response of a Dam
431
Fig. 5 Maximum tensile stresses under static analysis of the Koyna dam for a Empty reservoir, b Full reservoir level
variation also as well as variation due to the depth of the upstream surface. A similar trend is observed under two more input motions confirming that the inertial mass approach underestimates the effect of hydrodynamic forces. The results revealed that the change in stress value due presence of hydrodynamic forces reduced under the weaker motions. The maximum tensile stress values are less in the case of Kobe and Chi-Chi motions which have PGA lower than the Koyna motion.
432
D. Vyas et al.
Fig. 6 Maximum (tensile) principal stress in dam body, and the zones (shown by gray color) exceeding DCR = 1 at load conditions a Load condition D, b Load conditions E-1, c Load conditions E-2, d Load conditions E-3, (1) Koyna motion (2) Chi-Chi motion (3) Kobe motion
4 Summary and Conclusions Static and seismic analysis of Koyna concrete dam structure is carried out with the help of the finite element tool Abaqus CAE. The analysis considers the dam structure under various loading conditions as recommended by the Indian Standards. Apart from the conventional method of incorporating hydrodynamic effects using inertial masses, a new method of hydrodynamic forces, i.e., modeling water as a body structure, is also applied. The load conditions were subjected to three different seismic motions: Koyna, Kobe, and Chi-Chi. Following significant conclusions are drawn from the study. • The maximum principle tensile stress induced in the dam structure increases when the hydrodynamic forces are considered. This demonstrates the need to consider
10.993
LCE-3
31.880
0.466
0.459
2.059
31.670
0.496
0.480
2.083
33.700
3.966
0.526
3.218
Maximum tensile stress
8.760
0.303
0.321
0.107
5.053
0.293
0.286
0.245
9.383
0.126
0.205
0.138
Toe
16.340
0.303
0.321
1.038
16.500
0.334
0.314
1.020
17.200
3.966
0.225
1.059
Downstream mid-point
1.483
0.304
−0.569 31.880
0.107 0.321
−0.824 −0.539
1.273
0.314 0.293
−0.548 −0.576 27.900
0.245
−0.641
1.261 5.447
−0.798 33.370
0.138 0.225
−0.782 −0.665
Upstream slope change
Downstream slope change
−6.349 −14.117
−2.770
−7.410 −1.569
−0.539
−8.273
−14.073
−6.390 −0.566
−7.528
−7.443
−7.722 −2.314
−0.548
−0.445
−8.316 −14.230
−3.402
−7.799
−8.147
Heel
−2.424
−1.558
−1.300
Above heel
Note (1) LCD = Empty reservoir level under dynamic condition; (2) LCE-1 = Full reservoir level under dynamic condition (hydrodynamic force absent); (3) LCE-2 = Full reservoir level under dynamic condition (hydrodynamic force modeled using inertial mass concept); (4) LCE-2 = Full reservoir level under dynamic condition (hydrodynamic force modeled using waterbody concept)
0.161
LCE-2
0.710
0.165
LCE-1
Kobe
10.921
LCE-3
LCD
0.166
0.171
LCE-1
0.718
LCD
LCE-2
1.368
11.621
LCE-2
LCE-3
Chi-Chi
1.110
Koyna
0.181
DCR value
Motion
LCE-1
LCD
Load condition
Table 3 DCR values and maximum principal (tensile) stresses (in MPa) at different node points and under different loading conditions and input motions from dynamic analysis of the Koyna dam
Role of Hydrodynamic Forces on the Seismic Response of a Dam 433
434
D. Vyas et al.
the effects of hydrodynamic forces on the seismic response studies of concrete dams. • The effect due to hydrodynamic forces on the seismic response of the dam varies with the intensity of shaking; thus, if a site is expecting stronger earthquake motion, the underestimation of these effects can cause catastrophic scenarios. • The stresses induced on the dam structure are more when the influence of hydrodynamic forces is considered with the help of a waterbody. This shows the underestimation of the inertial mass concept in studying the seismic response of dam structures. The seismic strength of a dam structure is the most critical parameter in the design of a dam structure in an active seismic region. Various methodologies are considered in past studies. However, a proper estimation of hydrodynamic response on the dam structure is yet unexplored. The paper point toward a new method of analysis which considers the hydrodynamic effects on the dam structure. The study mainly focused on the strength parameter with the help of DCR. The study demonstrates the need for consideration of hydrodynamic forces in the seismic analysis of dams and other retaining structures. Further, it is recommended to consider the effect of hydrodynamic forces with the help of the water body than using inertial mass concepts. Nevertheless, additional studies assessing the overturning moments and stability of the structure and soil structure interactions are yet to be considered in future studies.
References 1. Ayari, M.L., Saouma, V.E.: A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks. Eng. Fract. Mech. 35(1–3), 587–598 (1990) 2. Hall, J.F.: The dynamic and earthquake behaviour of concrete dams: review of experimental behaviour and observational evidence. Soil Dyn. Earthq. Eng. 7(2), 58–121 (1988) 3. Li, Q.S., Li, Z.N., Li, G.Q., Meng, J.F., Tang, J.: Experimental and numerical seismic investigations of the Three Gorges dam. Eng. Struct. 27(4), 501–513 (2005) 4. Chopra, A.K.: Earthquake response analysis of concrete dams. In: Jansen, R.B. (Ed.) Advanced Dam Engineering for Design, Construction, and Rehabilitation. Van Nostrand Reinhold, New York (1988) 5. Lee, G., Fenves, G.L.: A plastic-damage concrete model for earthquake analysis of dams. Earthq. Eng. Struct. Dyn. 27(9), 937–956 (1998) 6. Bazant, Z.P.: Comment on anisotropic models for concrete and geo-materials. Eng. Mech. ASCE 109(3), 849–865 (1983) 7. Bhattacharjee, S.S., Léger, P.: Application of NLFM models to predict cracking in concrete gravity dams. J. Struct. Eng. ASCE 120(4), 1255–1271 (1994) 8. Mazars, J., Pijaudier-Cabot, G.: Continuum damage theory application to concrete. J. Eng. Mech. ASCE 115(2), 345–365 (1989) 9. Skrikerud, P.E., Bachmann, H.: Discrete crack modelling for dynamically loaded, unreinforced concrete structures. Earthq. Eng. Struct. Dyn. 14(2), 297–315 (1986) 10. Westergaard, H.M.: Water pressures on dams during earthquakes. Trans. Am. Soc. Civ. Eng. 98(2), 418–433 (1933) 11. Calayir, Y., Karaton, M.: A continuum damage concrete model for earthquake analysis of concrete gravity dam–reservoir systems. Soil Dyn. Earthq. Eng. 25(11), 857–869 (2005)
Role of Hydrodynamic Forces on the Seismic Response of a Dam
435
12. Chopra, A.K., Gupta, S.: Hydrodynamic and foundation interaction effects in earthquake response of a concrete gravity dam. J. Struct. Div. 107(8), 1399–1412 (1981) 13. Sadeghi, M.H., Moradloo, J.: Seismic analysis of damaged concrete gravity dams subjected to mainshock-aftershock sequences. Eur. J. Environ. Civ. Eng. 26(6), 2417–2438 (2022) 14. Lahiri, S.K., Shaw, A., Ramachandra, L.S., Maity, D.: Fracture in concrete gravity dams under dynamic loading conditions. Eng. Anal. Boundary Elem. 143(3), 591–605 (2022) 15. IS: 1893: Part 1: Criteria for Earthquake Resistant Design of Structures: General Provisions and Buildings. Bureau of Indian Standards, New Delhi (2016) 16. Dey, A., Sawant, M.B.: Seismic response of a concrete gravity dam considering hydrodynamic effects. In: 5th Asia-Pacific Congress on Computational Mechanics (APCOM) and 4th International Symposium on Computational Mechanics (ISCM), pp. 1–4. Singapore (2013) 17. IS: 6512: Criteria for Design of Solid Gravity Dams. Bureau of Indian Standards, New Delhi (1984) 18. Sun, D., Ren, Q.: Seismic damage analysis of concrete gravity dam based on wavelet transform. Shock. Vib. 2016, 1–8 (2016) 19. NCSDP Guidelines: Guidelines for Preparation and Submission Site Specific Study Report of River Valley Project. National Committee on Seismic Design Parameters, New Delhi (2014)
2020 Tuipuiral Earthquake Review R. Ramhmachhuani, C. Lallawmawma, H. Laldintluanga, M. L. Sharma, K. Seshagiri Rao, A. K. Jain, and Laldinpuia
Abstract Tuipuiral is located in the eastern end of Mizoram in Champhai District sharing its international border with Myanmar. The region is frequented by many microearthquakes along with some of the noticeable disastrous earthquakes in the past in this area. An earthquake of magnitude Mw 5.6 was reported on the 22 June 2020 at 10:46:25 IST at 23.8867 latitude and 93.1256 longitude at a depth of about 12 km followed by another earthquake of Mw 5.6 on 22 June 2020 at 04:10:52 IST at similar focal depth. This resulted in sporadic damages around Champhai District, Mizoram. The tremors were felt strongly in the capital city Aizawl. The earthquake was followed by a number of aftershock as well. The present paper is a report on the damage observed around the area. It was observed that, though the earthquake may be placed under minor-moderate earthquake, yet the damage observed was much greater than expected. The paper highlights macroseismic effects of the earthquake through field observations, assessing the damage pattern of buildings and wrong construction practices occurring in the area along with its remedial measures. The relatively more damage observed is attributed to the vulnerable construction practices and poor quality workmanship. Maps Disclaimer: The presentation of material and details in maps used in this chapter does not imply the expression of any opinion whatsoever on the part of the Publishers or Author concerning the legal status of any country, area or territory or of its authorities, or concerning the delimitation of its borders. The depiction and use of boundaries, geographic names and related data shown on maps and included in lists, tables, documents, and databases in this chapter are not warranted to be error free nor do they necessarily imply official endorsement or acceptance by the Publisher or Author. R. Ramhmachhuani · H. Laldintluanga · Laldinpuia Department of Civil Engineering, Mizoram University, Aizawl, India C. Lallawmawma (B) · M. L. Sharma Department of Earthquake Engineering, IIT Roorkee, Roorkee, India e-mail: [email protected] K. S. Rao · A. K. Jain Department of Civil Engineering, IIT Delhi, New Delhi, India Laldinpuia Center for Disaster Management, Mizoram University, Aizawl, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_34
437
438
R. Ramhmachhuani et al.
Keywords Tuipuiral · Earthquakes · Construction practices
1 Introduction On 21–24 June 2020, a series of earthquakes occurred in the eastern part of Mizoram, Champhai district, with the largest magnitude from these small to moderate earthquakes was reported as Mw 5.6(USGS) 22 June 2020 at a depth of about 12.62 km from the ground surface. The epicentre was located near Vanzau village, Champhai district, where huge panic in the surrounding areas was reported with people experiencing emotional distress and having difficulty in sleeping. The tremors were widely felt strongly across this region. Damages to property were mainly concentrated within the epicentre areas, more than 100 buildings were partially damaged including small size landslides and open ground cracks. Fortunately, this earthquake did not cause any huge property losses or human lives. 23 affected villages were visited to observe the general effects on the built environment and assess the damage pattern of buildings. Visited sites and the details of these earthquake activities taken place on this area are shown in Fig. 1. The damage survey has been carried out with the objective to assign intensity to the places and provide isoseismal map for the earthquake.
2 Seismotectonic of the Mizoram Region The north-eastern India is one of the most seismically active regions in the world and have experienced large and devastating earthquakes in the past as shown in Fig. 2. As per the seismic zoning map of India given in the earthquake-resistant design code of India [BIS 1893(Part I) 2016] [1], the region has been placed in seismic zone V. Many seismic hazard studies have reported higher seismic hazard in this region [2–5]. The seismic activity of this region is attributed to the collision tectonics between the Indian plate and the Eurasian plate in the north and subduction tectonics along the Indo-Burma region in the east [6]. This collision has resulted in the formation of the Himalaya thrust front in the north, Arakan-Yoma, Naga Hills, and Tripura folded belt in the east, and also the uplift of the Shillong plateau [7]. Mizoram, a part of Surma valley which is related to the eastward subduction of the Indian plate along the Arakan-Yoma suture during Eocene time and the subsequent development of the Indo-Burman Orogenic belt [8]. The Indo-Burman organic belt is an arcuate sedimentary belt with north–south trending fold and thrusts and may be further divided into the outer and inner wedge and core [9]. The recent earthquake activities occurred within Outer Indo-Burmese Wedge (OIBW). From past seismicity compared to the Inner Indo-Burmese Wedge (IIBW) and Core part of the subduction zone, the OIBW between Kaladan fault and Churachanpur Mau fault is seismically
2020 Tuipuiral Earthquake Review
Fig. 1 Location of places visited during a damage survey
439
440
R. Ramhmachhuani et al.
less active. Another prominent tectonic feature trending NW–SE right-lateral strikeslip fault is Mat Fault. Mat fault is located on the central part of the outer wedge of the IBW and is seismically less active and no large magnitude earthquake has been observed in this region. Geologically, this region is a part of Surma Basin, and there are many NE–SW and NW–SE lineaments/faults in this basin [10].
Fig. 2 Seismotectonic map of Mizoram region
2020 Tuipuiral Earthquake Review
441
3 Common Construction Practices Though every building are distinct and most of the dwellings are low-rise and nonengineered construction, three main types of building which are widely used for construction in this region are: (a) Traditional Assam-type building construction. These are generally one or two dwelling units and usually do not have common walls with adjacent buildings, wood-based materials is the primary construction material. (b) Semi-pucca structures which are lightweight wall buildings with reinforced concrete beams and columns, and (c) reinforced concrete moment resisting frame buildings with unreinforced brick infill walls which often referred to as RCC (Table 1).
3.1 Traditional Timber Building Construction Assam-type building construction is mostly one or two storey structures. About 1 m above the plinth level, a brick or stone masonry walls are usually laid out. The roof is usually made up of galvanized iron (GI) sheets that are supported by wood/bamboo trusses that link the parallel walls laterally. During the earthquake, no serious damage to these types of structures was reported. As shown in Fig. 3, traditional lightweight timber construction shows good performance.
3.2 Semi-Pucca Building Construction The majority of these structures are constructed by masons without appropriate engineering design considerations, and they are lightweight wall structures with reinforced concrete beams and columns that are typically lighter than reinforced concrete buildings due to the absence of concrete floor slabs and brick walls. During this survey, observed damages in this type of buildings are generally in the form of inclined shear cracks and vertical cracks. Cracks are generally observed at corners, Table 1 Reported earthquakes between 21 and 24 June 2020 Sl. No.
Location Latitude
Longitude
Depth
Mag
Matype
Date
Hr
Min
Sec
1
23.867
93.1256
40.42
5.1
mww
21
10
46
25
Magnitude
Time
2
23.1449
93.2856
12.62
5.6
mww
21
22
40
52
3
23.9312
93.0128
10
3.6
mb
23
13
47
32
4
23.1852
93.2444
10
4.5
mb
24
2
32
35
5
23.1303
93.193
10
4.8
mb
24
19
44
44
442
R. Ramhmachhuani et al.
Fig. 3 Traditional lightweight timber construction has shown good performance
also at location of openings at the windows and doors. Many cracks have been located at the extension of wall on the cantilever beam.
3.3 Reinforced Concrete Construction Building age, height, configuration, level of seismic design, and construction quality of reinforced concrete structures in this region vary significantly. Majority are nonengineered construction with poor quality workmanship, reinforced concrete lintels are widely absent above the doors and windows. Soft storey building, poor reinforcement detailing which makes them vulnerable under earthquake effects and badly mixed cement concrete are the detectable features which cause damages to the structures.
4 Field Observations and Observed Damages The largest tremor (Mw 5.6) occurred on 22 June 2020, Champhai district and several neighbouring districts in eastern Mizoram comprising more than 30 villages strongly felt this tremor. Soon after this, 23 villages nearby the epicentre area, field investigation and damage survey were carried out, damages and its effects on the built environment were observed. Based on field observation, interaction with local people, and information from news agencies, these earthquakes had severely affected most of the villages in the Khawbung RD block, namely Vaphai, Khawbung, Samthang, Leithum, Khuangleng, Vanzau, Farkawn, Zawlsei, Chawngtui, and Dungtlang. Major damages were also observed in Zokhawthar village.
2020 Tuipuiral Earthquake Review
443
4.1 Serchhip District Information was collected starting from Tuichang Lui, located approximately 38 km (aerial distance) from the epicentre and 4 villages of the Serchhip district such as Khawlailung, Chekkawn, North Mualcheng, and East Lungdar. Information obtained through interaction with local people and field observation, most of the people felt this quake very strongly. No significant damages to buildings except at few places where minor cracks in brick walls were observed. As observed, most of the minor damages in this region is due to poor construction and weak support of pillar columns. An intensity of VI has been assigned at these places.
4.2 Ruantlang Rural Development Block Five villages, Dilkawn, Kelkang, Mualkawi, and Melbuk, were visited for field investigation from this Rural Development block. The shaking was strongly felt by most of the people, and they got terrified and ran out of their homes. Many of the buildings, market complexes, churches, and government office premises reported minor damages in walls and cracks at the re-entrant corners. Presbyterian church in Melbuk experienced minor cracks at the column and at the window corner (Fig. 4). Affected villages in these places falls under intensity VI. Most of the damaged buildings were caused due to poor construction materials, poor quality workmanship, absence of proper engineer building plan and design.
Fig. 4 Minor crack at column and window corner in Melbuk Church
444
R. Ramhmachhuani et al.
Fig. 5 a Wide shear and vertical cracks at the infilled brick wall, b failure of corner beam-column joint, shear cracks at concrete walls and column
4.3 Khawbung RD Block More than 10 villages were visited within this block including the epicentre areas Vanzau, Vaphai, and East Chawngtui villages. Strong tremors were widely felt across this area, as per report more than 30 buildings were damaged. From field observation, the damages pattern in most of the villages was similar which includes cracks on walls and windows panels, cracks between walls and beam/columns especially in the cantilever part of the buildings, cracks on floors made from cement poured directly on the earthen floors. In Vaphai village, one building which is constructed on steep slope in which foundations of buildings rest at different levels shows wide shear and vertical cracks at the unreinforced brick infilled wall (Fig. 5a). Nearby this building, one building shows failure of corner beam-column joint and shear cracks at concrete walls and column (Fig. 5b). Infill brick walls of one building in Vaphai village which was under construction got completely collapse (Fig. 6). In Khawbung village, the Salvation Army Centenary building was one of the worst affected buildings which experienced diagonal crack at concrete wall and wide vertical crack at the brick wall in which the the horizontal and diagonal cracks started from the beam column joint and extended through the walls (Fig. 7). One open ground building supported by open beam-column frame suffered damage at the column with wide crack on the ground near the column also damage to window infill walls near the window sill is also observed (Fig. 8). Similar damage pattern, minor horizontal crack at wall-beam joint (Fig. 9) in many buildings were observed in Khuangthing village. An intensity of VII has been assigned to these places.
4.4 Zokhawthar Zokhawthar a border village between Mizoram with neighbouring Myanmar was the worst affected village. Many buildings in Zokhawthar had minor to major cracks, including police station complex with damages at the walls and columns in which low quality brick and low mortar mix is used which make the infill walls very weak and
2020 Tuipuiral Earthquake Review
445
Fig. 6 Under-construction brick wall collapse
Fig. 7 Diagonal crack at concrete wall and wide vertical crack at brick wall
thus collapsed (Fig. 10). Presbyterian church built of brick walls with the roof made of light GI sheets, thick walls with large openings are provided, collapsed ceilings, major cracks on walls as many large openings are provided in the walls (Fig. 11). An intensity of VII has been assigned to this village.
446
R. Ramhmachhuani et al.
Fig. 8 Wide crack on ground near the column and damage on column
Fig. 9 Horizontal crack at beam-wall joint
5 Other Effects A wide ground cracks having a gap of about 3–12 cm extending more than 110 m long and an incidences of rock fall were observed at one of mizo cultural heritage known as ThasiamaSenoneihna as shown in Fig. 12. Figure 13a shows cracks on the road about 100 m long extending in E-W direction at Vanzau which affects primary school and 5 buildings. In Vaphai villages, poorly constructed masonry retaining wall was damaged as shown in Fig. 13b. Small-sized rock fall as shown in Fig. 14 occurred between Samthang and Duntlang village.
2020 Tuipuiral Earthquake Review
447
Fig. 10 Collapse wall of mess hall of Zokhawthar police station
Fig. 11 Collapse wall and ceiling of Zokhawthar Presbyterian Church
6 Isoseismal Map Based on the study of macroseismic effects of the earthquake through field observations, assessment of damage pattern on buildings, different intensities have been
448
R. Ramhmachhuani et al.
Fig. 12 Wide ground cracks and small rock fall at Thasiamama Se no neihn
Fig. 13 a Road cracks and b Damaged retaining wall at Vaphai village Fig. 14 Small size rock fall between Samthang and Dungtlang village
2020 Tuipuiral Earthquake Review
449
assigned to the visited places using MSK-64 scale. The MSK scale gives detailed information for determining the extent of damage to various buildings. The intensity was assigned at the visited villages keeping in view the type of structure, the grade of damage to each structure (e.g. Grades I–V) and the number of structures that suffered a specific grade of damage (e.g. single, few, many, or most). The intensities thus assigned to visited places are shown in Fig. 15. . Fig. 15 Isoseismal map
450
R. Ramhmachhuani et al.
7 Lesson Learnt and Remedial Measures The philosophy is to design structures that would be able to safely withstand the earthquakes that they are most likely to experience during their service life, without significant damage and without being over-designed to an extent that they become inefficient. This leaves the possibility of unusually large earthquakes that may lead to a significant damage that requires repair or even dismantling of the building after the earthquake. Even in the event of such unusually large earthquakes, the structures are designed so as to prevent collapse and the loss of lives. Un-engineered RCC structures at the earthquake affected zone, on the other hand, often are not based on sound engineering practice and experience. These structures are often built or expanded by owners, without consulting a qualified structural engineer. Many a times, floors are added to existing structures as and when funds become available with the owners. The time mismatch between the floors may be so long. The mismatch in type and quality of construction at various levels increases the seismic vulnerability of these structures. Almost all the building construction in earthquake affected area was built in the sloping terrain that result in existence of basement. This basement portion is often neglected, acting as a soft storey and remain like a skeleton frame structure only. Strengthening of column at open soft storey by providing cross stiffener or X bracing may be adopted to prevent on the damage of column. X bracing is economical and will be the best solution against the seismic when there is fund constraint. The quality of construction materials and method of construction is not up to the mark which leads to the early ageing of the concrete. Quality control before construction, during construction and after construction, is the key for sustainable building.
8 Conclusions Based on the damage survey, isoseismal map has been prepared and intensity VII could be assigned to the area where maximum damage has occurred. The damage caused by the earthquake is relatively severe than expected mainly due to improper type and quality of construction with poor workmanship. Regularity and continuity are the basic rules for seismic safety of the building, which seems to be missing from most of the construction found here. Walls not confined by the columns and beams (hanging wall) have suffered severe damage and not at all recommended in earthquake prone area. The column fails in some building has pose a serious issue may be due to unengineered structure and open ground storey. It should be avoided as it can cause the column failure at the time of earthquake. It is also observed that the Reinforce Concrete framed structure has reduced the scale of intensity of earthquake. Awareness on engineered structure is utmost
2020 Tuipuiral Earthquake Review
451
important. Providing cross stiffener or X bracing at open soft storey which will enhance structural stability is suggested at the low-income rural areas.
References 1. Bureau of Indian Standards (BIS): Indian Standard Criteria for Earthquake Resistant Design of Structure Part 1-Resistant Provisions and Buildings, BIS 2016 IS1893-2016, Bureau of Indian Standards, New Delhi, India (2016) 2. Sharma, M.L., Arora, M.K.: Prediction of seismicity cycles in the Himalayas using artificial neural network. Acta Geophysica Polonica. 53(3), 299–309 (2005) 3. Shanker, D., Sharma, M.L.: Estimation of seismic hazard parameters for the Himalayas and its vicinity from complete data files. Pure Appl. Geophys. 152, 267–279 (1998) 4. Sharma, M.L., Douglas, J., Bungum, H., Kotadia, J.: Ground-motion prediction equations based on data from the Himalayan and Zagros regions. J. Earthq. Eng. 13, 1191–1210 (2009) 5. Nath, S.K., Thingbaijam, K.K.S.: Probabilistic seismic hazard assessment of India. Seismol. Res. Lett. 83(1), 135–149 (2012) 6. Kayal, J.R.: Seismicity of northeast India and surroundings—development over the past seismotectonics of Northeast India: a review. J Geophys. 19, 9–34 (2016) 7. Das, R., Sharma, M.L., Wason, H.R.: Probabilistic seismic hazard assessment for Northeast India Region. Pure Appl. Geophys. 173, 2653–2670 (2016) 8. Nandy, D.R.: Geodynamics of Northeast India and the Adjoining Region, 3rs edn. Abc publication, Kolkata (2001) 9. Maurin, T., Rangin, C.: Structure and kinematics of the Indo-Burmese Wedge: Recent and fast growth of the outer wedge. Tectonics 28(2) (2009). https://doi.org/10.1029/2008TC002276 10. Tiwari, R.P., et al.: No evidence for shallow shear motion on the Mat Fault, a prominent strike slip fault in the Indo-Burmese wedge. J. Earth Syst. Sci. 124(5), 1039–1046 (2015)
Experimental Investigations on the Pervious Concrete Piles in Saturated Ground Under Repeated Shaking Conditions R. V. Yogesh , S. Ganesh Kumar , and G. Santha Kumar
Abstract Soil liquefaction has a significant influence in inducing structural failures during seismic events. Further, the recent repeated seismic events such as Christchurch earthquake (2010–2011) and Tohoku earthquake (2011) raised alarm over the possibility of reliquefaction occurrence in saturated grounds. To alleviate liquefaction effects, various ground improvements methods were being used continuously for improving the seismic resistance of saturated ground. Among those ground improvement techniques, use of stone column and sand compaction piles is the most commonly used ground reinforcement techniques. The improvement in load-carrying capacity and drainage characteristics highly benefits the seismic improvement in saturated ground. However, the performance of these conventional ground treatment systems also depends upon the confinement provided by the surrounding soils and its assessment under repeated shaking events also not available/limited. Considering this, use of the pervious concrete pile (PCP) as an alternative to conventional stone column technique is attempted in this study. Considering the sustainability approach, the pervious concrete pile was prepared with construction and demolition waste. Further, the efficiency of the pervious concrete pile in mitigating the liquefaction and reliquefaction potential is also attempted in this study. For experimental studies, saturated ground having 40% relative density was prepared with and without the pervious concrete pile treatment technique. Both, the unreinforced and the pervious concrete pile reinforced ground was then subjected to repeated incremental acceleration of 0.1 g, 0.2 g, 0.3 g, and 0.4 g with 5 Hz frequency to evaluate the seismic resistance of the prepared ground with and without improvement system. The variation in generation of excess pore water pressures ratio and settlement of untreated
R. V. Yogesh (B) · S. G. Kumar Geotechnical Engineering Division, CSIR-CBRI, Roorkee, Uttarakhand 247667, India e-mail: [email protected] G. S. Kumar CSIR-CBRI Ghaziabad Center, Ghaziabad, India R. V. Yogesh · S. G. Kumar · G. S. Kumar Academy of Scientific and Innovative Research, Ghaziabad, India © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_35
453
454
R. V. Yogesh et al.
and the pervious concrete pile treated ground was compared, and observations on the obtained results were presented. Keywords The pervious concrete pile · Reliquefaction · Excess pore water pressure ratio
1 Introduction Soil liquefaction and reliquefaction are one of the major hazards as a result of earthquake occurrence which exhibits devastating effects on the infrastructure system. Further, the case studies from past few decades have also evidenced the possibility of reliquefaction on same site when subjected to repeated seismic events [1, 2]. The pore water pressures developed during these seismic events play a major role in destabilizing the strength of the soil causing soil liquefaction. Various ground modification methods have been adopted throughout the world to improve the seismic resistance of liquefiable deposits to mitigate the soil liquefaction. Among those ground modification methods, ground reinforcement methods such as stone columns, sand compaction piles, and rammed aggregates piles were the commonly used popular techniques. These ground reinforcement methods improve the performance of soil by improving the bearing capacity and reducing total and differential settlements and acceleration of drainage in case of liquefiable deposits [3]. However, the distortion of granular column due to occurrence of shearing during seismic events reduces load-carrying capacity and drainage characteristics which affect the performance of the improvement technique [4]. An innovative porous pile with higher stiffness with comparable permeability can be an alternative to this conventional granular method which is known as pervious concrete pile (PCP). The merits of this technique include improvement in loadcarrying capacity, excellent drainage characteristics, and improved stress transfer mechanism. Generally, the pervious concrete pile (PCP) is made up of cement, gap graded aggregates, and water with limited/absence of fine aggregate. The absence or very limited portion of fine aggregates results in development of pores within aggregate skeleton which develops high permeability characteristics similar to granular columns with better stiffness and strength [5]. The past numerical studies carried out on PCP have reported that PCP-reinforced ground exhibited lower lateral displacement and quicker pore water pressure dissipation as compared to stone columnreinforced ground [6]. Further, no experimental studies have been carried out to understand the behavior of PCP in liquefiable saturated ground and its performance behavior in dissipation of developed pore water pressure, ground, and foundation settlement under dynamic loading conditions. In the present study, an attempt has been made to develop and study the behavior of PCP in saturated ground against liquefaction and reliquefaction susceptibility under repeated shaking events. To achieve aforementioned objective, 1 g-shaking table studies were carried out on a saturated
Experimental Investigations on the Pervious Concrete Piles in Saturated …
455
ground having relative density of 40% with unreinforced and PCP-reinforced conditions. The obtained pore water pressure ratio, ground, and foundation settlement for the untreated and treated ground were compared and discussed.
2 Materials Characterization 2.1 Soil Characterization The experimental investigations were carried out on locally available Yamuna River sand. Figure 1 shows the grain size distribution of sand used for the experimental investigations. The soil was classified as poorly graded sand. The index properties of the soil are given in the Table 1.
Fig. 1 Particle size distribution curve of Yamuna River sand
456 Table 1 Properties of soil
R. V. Yogesh et al. Material Soil
Property
Value
Specific gravity
2.55
Coefficient of uniformity (C u )
1.93
Coefficient of curvature (C C )
1.10
Maximum void ratio (emax )
0.918
Minimum void ratio (emin )
0.777
Medium to coarse sand (%)
16.8
Fine sand (%)
80.1
Silt (%)
3.1
Relative density %
40
Saturation %
100
2.2 The Pervious Concrete Development and Characterization The PCP in the study was prepared using cement, coarse aggregate, and water. The fine aggregates were eliminated to enhance the permeability of PCP. Ordinary portland cement of 43 grade with specific gravity 3.15 and specific surface area 3960 cm2 /g was used as binder. For sustainability approach, construction and demolition wastes were used as recycled coarse aggregates (RCA) in this study. For pile development, the RCA of gradation band between 22.5 mm and 16.0 mm was used for casting PCP for encouraging development of pores [7]. The aggregates exhibited a relative density (saturated surface dry) of 2.69 and water absorption of 6.19%. The cement to aggregate ratio of 0.25 and water to cement ratio of 0.35 was used in PC mix preparation [8]. The PCP was prepared by initially mixing the recycled concrete aggregate (RCA) (saturated surface dry state) with cement for three minutes followed by addition of water and mixing continued for another five minutes. The fresh PC mix was poured into the PC pile mold in six layers. Each layer was compacted by 25 stokes. Table 2 shows percentage of aggregate constituents and 28th day measured properties of PC. Table 2 Properties of the pervious concrete
Material
Property
The pervious concrete
22.5–20.0 mm
5.72%
20.0–16.0 mm
94.28%
Value
Compressive strength, MPa
8.41
Permeability, cm/sec
0.65
Porosity, %
24.42
Experimental Investigations on the Pervious Concrete Piles in Saturated …
457
3 Experimental Methodology 3.1 Experimental Setup, Sand Bed Preparation For experimental testing, a perspex tank having dimensions 1.7 m × 0.75 m × 1.0 m was used. The tank was divided in to two equal half for preparing untreated and treated ground. Figures 2 and 3 show the layout of test setup, instrumentation scheme, and dimension of the divided experimental tank. The table was mounted on a uniaxial servo-controlled shake table of dimension of 2 m × 2 m which is having a maximum pay load capacity of 35kN. In order to reduce the boundary effects, expanded poly ethylene foam sheet of thickness 50 mm was placed in both ends and at the middle of the model tank perpendicular to the shaking direction as shown in Fig. 2.
Fig. 2 Experimental setup for reinforced and unreinforced ground with instrumentation details 295 mm
395 mm
PCP reinforced ground
Foundation system Untreated ground
Fig. 3 Plan view of experimental setup for reinforced and unreinforced ground
375 mm
Foundation system
275 mm
200 mm
100 mm dia PCP
395 mm
375 mm
200 mm
275 mm
295 mm
458
R. V. Yogesh et al.
The sand bed having 910 mm height was prepared using wet sedimentation method. The required quantity of sand and water for achieving 40% relative density was estimated using phase relationship, i.e., estimating target void ratio for achieving required density, and based on the estimated void ratio, the required quantity of sand was calculated. Then, the required water quantity for achieving complete saturation was calculated [9]. The height at which sand to be poured was calculated prior using relative density tests (IS 2720-part 14). The total estimated sand and water quantity were then divided into nine layers. Initially, water was poured up to the target first layer. Then, sand pouring was carried out at the target height of 15.5 cm for achieving 40% density. The procedure was repeated to a height 910 mm. The sample preparation was done parallel in both the divided portions simultaneously to achieve uniformity in ground preparation. During sample preparation, pore pressure (PP) transducer of capacity 200 kPa was placed at the depth 160, 460, and 810 mm depth from top surface as shown in Fig. 2. Displacement transducers were used for monitoring foundation settlement of treated and untreated ground during repeated shaking events. The ground settlement was measured after each test manually.
3.2 PCP Design and Installation The design and construction of PCP were carried out similar to the stone column and as per IS 15284 (part 1):2003. An area replacement ratio of 5%, considering the scaling ratio of length to diameter (L/d) of 9 as mentioned by McKelvey et al. [10] and spacing of 2D, was chosen in this study, and accordingly, PCP having 100 mm diameter and 910 mm height was casted prior to sample preparation. For treatment, square pattern with 200 mm c/c spacing was chosen. Since, the PCP piles were used for first time in ground improvement; its efficiency under minimum area replacement ratio was evaluated experimentally. Pile installation was carried out after 24 h from sand bed preparation. The pile installation procedure for ground improvement was given below as follows. 1. Positioning: The position of PCP as per plan marked on the saturated sand bed. 2. Casing pipe installation: The PVC pipe of inner diameter 110 mm with both ends opening was used as casing pipe. The casing was selected such that the thickness of casing was minimal. External surface of casing pipe was coated with oil to reduce friction during installation and withdrawal of casing. Horizontal steel angle was used to restrain the PVC encasement to ensure vertical movement of pipe. The pipe was pushed to depth of 910 mm using vibratory drop hammer. 3. Sand excavation and precast PCP installation: Soil auger having 100 mm diameter was used for removing soil inside the casing pipe as shown in Fig. 4a. After soil excavation completed, the precast PCP was installed inside the casing pipe. 4. Casing withdrawal: The casing pipe was then pulled out carefully without causing much disturbance to the surrounding soil. After removal of casing pipe, little disturbances around the PCP resulting in soil subsidence were observed for initial
Experimental Investigations on the Pervious Concrete Piles in Saturated …
459
Fig. 4 a Soil excavation from the pile encasement using soil auger. b Soil subsidence occurrence after pile encasement withdrawal
PCP as shown in Fig. 4b. However, this soil subsidence diminishes with continuous installation of piles due to the induced densification in the saturated ground. This may be due to the applied vibration to the casing pipe during penetration which generates soil disturbances. After PCP installation, the ground was left undisturbed for 24 h for dissipating excess pore water pressures generated during installation. The procedure was repeated for all the PCP installation.
3.3 Testing Conditions The experimental study investigates the influence of repeated shaking events on saturated ground with and without PCP treatment. The selection of repeated shaking events was based on the observed repeated shaking events in the past (i.e., Christchurch earthquake 2010–2011 and Tohoku earthquake 2011) at same location with main shock associated with fore shock or aftershock which induces ground deformations and causing failure of major infrastructures. An attempt has been made in this study to evaluate the behavior of PCP treatment in saturated ground under repeated shaking conditions simulating observed main shocks and after shock event in the past. For this objective, repeated incremental sinusoidal acceleration loading of intensities 0.1 g, 0.2 g, 0.3 g, and 0.4 g with 5 Hz frequency was applied in sequentially to the prepared ground. The selected repeated incremental acceleration represents medium to high intensity shaking simulating main shocks and associated aftershocks events. Further, the sinusoidal shaking selection represents the critical input motion to evaluate the influence of PCP treatment. The loading was applied sequentially to the ground only after dissipation of excess pore water pressures generated during the previous loading. This was ensured from the pore pressure transducers installed at different depths. A scaled down shallow type of foundation model of 160 mm diameter and 20 mm thickness with a scaling factor of 30 [11] was used in this study for monitoring foundation settlement during repeated shaking.
460
R. V. Yogesh et al.
4 Results and Discussion 4.1 Influence of Excess Pore Water Pressure Ratio on Unreinforced and PCP Treated Ground The influence of the pervious concrete pile on saturated ground subjected to repeated shaking events is discussed in this section. A typical pore water pressure ratio at 0.1 g-shaking condition for untreated and treated ground is shown in Fig. 5a and b, respectively. PP1, PP2, and PP3 were installed at 160 mm, 460 mm, and 810 mm, respectively, for both untreated and treated ground. It can be seen that the generated pore water pressure ratio was found to be higher at top depth followed by middle depth and bottom depth. The pore water pressure ratio was found to be in the range of 0.99–0.78 in case of untreated ground. About 23.58–26.92% increment in pore water pressure ratio was observed in untreated ground from bottom to top. The increment was mainly due to the influence of overburden effects with longer shaking duration which induces non-uniform densification in ground. Due to this, quicker generation of pore water pressures was observed in the subsequent loading events which also made soil more susceptible to reliquefaction. After each loading, sufficient time of 24 h was given to both untreated ground and treated ground to dissipate the generated pore water pressures. It is also evident from Fig. 5b that PCP treated ground effectively mitigate generation of pore water pressures resulting in lower pore pressure ratio. No significant pore pressure ratio was observed in the case of treated ground. This was mainly due to the development of internally connected pores within aggregate skeleton of PCP system which dissipate the generated pore water pressure quickly and improve the resistance of saturated ground. Comparatively, PP1 installed at shallow depth showed maximum pore pressures ratio due to the disturbances induced in the surrounding soil at shallow depth during installation which slightly affects the performance. However, the observed pore pressure ratio values showed better performance in arresting generation of pore water pressures, i.e., 90.0–99.1% compared to untreated ground even with longer shaking duration which validate the performance of PCP improvement technique. The performance PCP treatment was further verified by comparing the obtained peak pore pressures ratio generated during repeated shaking events with unreinforced ground. Figure 6 depicts the comparative results of obtained peak pore pressure ratio development in unreinforced and PCP-reinforced ground under repeated incremental acceleration. Both the ground showed different patterns when subjected to repeated shaking events. Comparatively, unreinforced ground showed higher generation of pore water pressures ratio than PCP treated ground. However, there is a variation in generated pore water pressures ratio during repeated shaking events at repeated incremental shaking events. It was observed that there is an alternative decrement and increment in peak pore water pressures ratio during repeated increment loading in the case of untreated ground. This was mainly due to the occurrence of soil densification during repeated shaking events. After 0.1 g shaking, the suspended sand-water mixture settled down inducing soil densification in the saturated ground.
Experimental Investigations on the Pervious Concrete Piles in Saturated …
461
Fig. 5 Time history of excess pore water pressure ratio (r u ) of a unreinforced ground, b PCPreinforced ground at various depths for input acceleration 0.1 g
Due to this initial densification, there is a reduction in pore water pressure ratio in the subsequent acceleration loading of 0.2 g, and the reduction was about 17.17–26.44%. When the ground was subjected to 0.3 g shaking, application of higher incremental shaking disturbs the densified soil, and increment in peak pore water pressure ratio was observed. The same phenomenon observed up to 0.4 g. Thus, the observations verified that, in addition to soil densification, drainage also equally plays a significant role in mitigating generation of pore water pressures during repeated shaking events and improves the performance of saturated ground. Comparatively, the PCP-reinforced ground showed reduction in pore pressure ratio up to 0.3 g shaking conditions. About 39.48% to 99.10% reduction in pore pressure ratio was observed at all depths. As it can be seen from Fig. 6, up to 0.3 g shaking, the generated pore water pressures ratio was found to be more or less uniform at different depths. However, there is a gradual increment in pore water pressures ratio Fig. 6 Influence of repeated incremental acceleration on excess pore water pressure ratio development of untreated and PCP treated ground
462
R. V. Yogesh et al.
Fig. 7 Clogged PCP cross section obtained from middle portion of pile
(about 1.41–18.06 times) which highlights the possibility of intrusion of surrounding finer sand grains inside the pile. At 0.4 g, the generated pore water pressures ratio was higher which validates column clogging effects as seen from Fig. 7. Figure 7 depicts the clogged portion obtained from the middle cross section of PCP at the end of test, i.e., after 0.4 g shaking. Due to the combined confinement and densification characteristics due to repeated shaking, the finer particles entered in interconnected pores of the pervious pile during repeated loading conditions. Further, the horizontal movement of sand grains toward the installed drainage member during dynamic loading reduces the drainage characteristics of the treated system which was found evident from the observed values at 0.4 g shaking conditions. Thus, the test results also validate that the selected area replacement ratio was not adequate to mitigate the generation of pore water pressures at higher acceleration loading conditions during repeated shaking events. .
4.2 Effect of Incremental Acceleration on Ground Displacement and Foundation Settlement When the ground was subjected to dynamic shaking event, the pore water pressure generated from bottom to top resulting in floatation of sand grains in suspended form. After the end of the shaking, the suspended sand grains deposited resulting in uneven densification. The same phenomenon was observed during the experimental study for untreated deposits at 0.1 g loading condition. When the same ground subjected to repeated incremental shaking, the continuous reorientation of sand grains encourages uneven densification throughout the depth. The observed soil displacement for the shaking events is shown in Fig. 8a. Similarly, the obtained foundation settlement also monitored during the study. For estimating soil displacement and foundation settlement, 2 LVDTs were used. The obtained foundation settlement response is shown in Fig. 8b. Figure 8a, b also compares the soil displacement and foundation settlement for untreated and treated ground. It can be seen from Fig. 8a that the
Experimental Investigations on the Pervious Concrete Piles in Saturated …
463
maximum ground settlements increase with increase the increase in input acceleration during repeated shaking events for both unreinforced and reinforced ground. This suggests the possibility of reorientation in sand grains during repeated shaking events. In spite of induced densification due to continuous shaking, the observed soil displacement values for the untreated ground inferred the influence of drainage member in improving the seismic resistance of ground deposits during repeated shaking events. Due to this, the generated pore water pressures affect the seismic resistance of saturated ground and causing instability to ground and foundation. This was found predominant in shallow depth as evident from generated pore water pressures and soil displacement and foundation settlement values. Further, the increment in the ground settlement for unreinforced ground was found to be 2.14 times, 3 times, and 3.46 times at 0.2 g, 0.3 g, and 0.4 g, respectively. Due to this soil displacement, the foundation settlement also increases with the increase in acceleration loading. About 1.5–2.25 times increment in foundation settlement was observed as the acceleration loading increases. The above observations concluded the occurrence of densification in untreated ground and the necessity of drainage member for seismic improvement in untreated ground especially during repeated shaking events. Due to PCP installation, the ground experiences maximum settlement and the combined drainage with the soil densification resulting in minimum soil displacement compared to untreated ground. About 87.15–90.52% reduction in soil displacement was observed up to 0.3 g acceleration loading compared to untreated ground. As mentioned in the previous section, the performance of the PCP system reduced at 0.4 g due to the continuous clogging in drainage path due to intrusion of surrounding sand grains during repeated shaking which reduced the performance. Similarly, foundation settlement of PCP-reinforced ground was found increased about 10.38 times for input acceleration 0.4 g as compared to the settlement occurred during the input acceleration 0.1 g. However, the rate of settlement reduces with increase in the repeated incremental input acceleration up to 0.3 g, and it was about 2.91 times and 1.09 times for input acceleration 0.2 g and 0.3 g as compared to settlement occurred
Fig. 8 Influence of repeated incremental acceleration on a ground settlement, b foundation settlement
464
R. V. Yogesh et al.
during input acceleration 0.1 g and 0.2 g, respectively. At 0.4 g shaking, there is a rapid increase in ground settlement intensity, i.e., about 3.28 times the settlement was observed mainly due to column clogging which affects column characteristics. When comparing soil displacement and foundation settlement, it was observed that the unreinforced ground experienced higher settlement as compared to the PCPreinforced ground. For the same input acceleration, the settlement of unreinforced ground was observed to be 10.55 times, 7.78 times, 9.97 times, and 3.57 times for input acceleration 0.1 g, 0.2 g, 0.3 g, and 0.4 g, respectively, as compared to settlement occurred in the PCP-reinforced ground. The lower settlement of PCP-reinforced ground was due to uniform density throughout the depth of soil which minimized generation of excess pore water pressure development [12]. On contrary, the nonuniformity in the density with depth in unreinforced ground resulted in development of excessive pore water pressure resulting in excessive ground displacement and foundation settlement.
5 Conclusion In this study, a series of shaking table experiments were conducted on saturated sand deposits of relative density 40% with and without PCP reinforcement system. Repeated incremental input acceleration of 0.1 g, 0.2 g, 0.3 g, and 0.4 g of 5 Hz was applied to both the ground to compare the performance of PCP system. The major conclusions from the study are as follows: 1. In untreated saturated ground, application of repeated incremental shaking events induces soil densification. However, in the absence of drainage member; the induced densification was not efficient in minimizing generation of pore water pressures. 2. The pervious concrete pile showed improved performance up to 0.3 g shaking condition in minimizing generation of pore water pressures ratio, soil displacements, and foundation settlements. The improved drainage and modular characteristics reinforce the ground and improve the seismic performance of saturated ground. 3. Due to improved permeability characteristics, the entry of surrounding soil inside the column affects the drainage characteristics during repeated shaking events. The continuous migration due to repeated shaking affected the drainage path and affects the performance of the system. At higher acceleration loading, PCP treated ground showed higher generation of pore water pressures ratio and foundation settlement. Overall, PCP-reinforced ground was found capable of reducing settlement and arresting pore water pressure up to input acceleration of 0.3 g in this study. The performance of the PCP improvement system needs to be conducted with varying replacement ratio to understand the behavior of PCP-reinforced against liquefaction and reliquefaction susceptibility under repeated shaking events.
Experimental Investigations on the Pervious Concrete Piles in Saturated …
465
Acknowledgements The author thanks director CSIR-CBRI for supporting the research and required infrastructure facilities. One of the author Mr. R. V. Yogesh acknowledges the financial support received from council of scientific and industrial research (CSIR), India through CSIR-SRF (Gate) [File no: 31/GATE/24(9)/2019-EMR-I].
References 1. Yasuda, S., Tohno, I.: Sites of reliquefaction caused by the 1983 Nihonkai-Chubu earthquake. Soils Found. 28(2), 61–72 (1988) 2. USGS Homepage: https://www.usgs.gov/news/featured-story/magnitude-78-earthquakenepal-aftershocks. Last accessed 21 Aug 2022 3. Patel, A.: Geotechnical Investigations and Improvement of Ground Conditions, 1st edn. Woodhead Publishing, UK (2019) 4. Krishna, A.M.: Mitigation of liquefaction hazard using granular piles. Int. J. Geotech. Earthq. Eng. (IJGEE) 2(1), 44–66 (2011) 5. Cui, X., Zhang, J., Chen, D., Li, S., Jin, Q., Zheng, Y., Cui, S.: Clogging of pervious concrete pile caused by soil piping: an approximate experimental study. Can. Geotech. J. 55(7), 999–1015 (2018) 6. Rashma, R.S.V., Jayalekshmi, B.R., Shivashankar, R.: Influence of earthquake characteristics on pervious concrete column improved ground. Geotech. Geol. Eng. 40(5), 2615–2630 (2022) 7. Jiang, X., Xiao, L.: Study of the permeability coefficient of pervious concrete with various aggregate grades. In: IOP Conference Series: Materials Science and Engineering, vol. 562, no. 1, p. 012092. IOP Publishing (2019) 8. ACI-522R-10: Report on Pervious Concrete. 9. Padmanabhan, G., Shanmugam, G.K.: Reliquefaction assessment studies on saturated sand deposits under repeated acceleration loading using 1-g shaking table experiments. J. Earthq. Eng. 26(6), 2888–2910 (2022) 10. McKelvey, D., Sivakumar, V., Bell, A., Graham, J.: Modelling vibrated stone columns in soft clay. Proc. Inst. Civ. Eng. Geotech. Eng. 137–149 (2004) 11. Moncarz, P.D.: Theory and Application of Experimental Model Analysis in Earthquake Engineering. Stanford University (1981) 12. Padmanabhan, G., Shanmugam, G.K.: Liquefaction and reliquefaction resistance of saturated sand deposits treated with sand compaction piles. Bull. Earthq. Eng. 19(11), 4235–4259 (2021) 13. Suleiman, M.T., Ni, L., Raich, A.: Development of pervious concrete pile ground-improvement alternative and behavior under vertical loading. J. Geotech. Geoenviron. Eng. 140(7) (2014)
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties of Gravel-Rubber Mixtures Gabriele Chiaro , Ali Tasalloti , Alessandro Palermo , and Laura Banasiak
Abstract The purpose of this study was to investigate the small-strain shear stiffness and strain-dependent dynamic properties (i.e., shear modulus degradation curve) of mixtures of gravel and recycled granulated tire rubber for use in geotechnical applications, including geotechnical seismic isolation foundation systems for buildings. Therefore, bender element and small-strain cyclic triaxial tests were carried out on dried specimens of pure gravel and gravel-rubber mixtures with 10, 25, and 40% rubber content by volume. In this paper, the small-strain shear stiffness (Gmax ) characteristics as well as shear modulus (G) versus shear strain (γ) amplitude curves are presented, and the effects of stress level and rubber content are discussed. Hence, an analytical hyperbolic model for estimating G as a function of the rubber content, stress level, and shear strain amplitude is proposed for gravel-rubber mixtures (GRMs). Keywords Gravel-tire rubber · Bender element · Shear modulus · Damping ratio · Small strain · Cyclic triaxial tests
G. Chiaro (B) · A. Palermo Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand e-mail: [email protected] A. Palermo e-mail: [email protected] A. Tasalloti Beca, Auckland, New Zealand e-mail: [email protected] L. Banasiak Environmental Science and Research Institute, Christchurch, New Zealand e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_36
467
468
G. Chiaro et al.
1 Introduction Gravel-rubber mixtures (GRMs) can be engineered to exhibit exceptional engineering properties [1–5], enabling their use in many geotechnical applications [6], including geotechnical seismic isolation foundation systems for buildings [7–10]. Yet, investigations focusing on the geotechnical characterization of GRMs are still limited and the physical, mechanical, and dynamic properties of GRMs are largely unknown [11]. To provide useful insights on the strength and compressibility response of GRMs required for design purposes, the authors have conducted comprehensive geotechnical investigations on a number of different GRMs with different volumetric rubber content from 0 to 100%—produced by mixing two gravels (mean diameter, D50 = 4 and 6 mm) and three different rubber particle sizes (D50 = 1, 2, 4 mm) [3–6]. It was found that while most GRMs possess suitable engineering properties to be used as structural fills for geotechnical applications (e.g., effective fiction angle at failure ≥ 30°), the volumetric rubber content (VRC) should be limited to 40% to ensure adequate bearing capacity and reduce the long-term settlement associated with the high deformability of low-modulus rubber particles under sustained vertical loads [5, 6]. As well, from an environmental viewpoint, the use of sand-size like (i.e., ≤2 mm) rubber particles in GRMs should be avoided due to potential high level of leached chemicals [12]. The purpose of this study was further characterizing GRMs with specific focus on their small-strain shear stiffness and strain-dependent dynamic properties (i.e., shear modulus degradation relationship). Thus, bender element and cyclic stresscontrolled triaxial tests were carried out on dried specimens of pure gravel and selected GRMs with VRC ≤ 40%. In this paper, the small-strain shear stiffness (Gmax ) characteristics as well as the shear modulus (G) versus shear strain (γ) amplitude curves are presented, and the effects of stress level and rubber content are discussed. An analytical hyperbolic model for estimating G as a function of the rubber content by volume, confining stress level and shear strain amplitude is then proposed for GRMs.
2 Test Materials and Procedure The materials considered in this investigation consist of a washed pea gravel (D50,gravel = 5.8 mm) and recycled granulated tire rubber (D50,rubber = 3.6 mm; free of steel wire and fiber reinforcement). The particle size distributions and photographs of the materials are presented in Fig. 1. The aspect ratio (AR = D50,rubber /D50,gravel ) between the gravel grains and the rubber particles is 0.68. Mixtures prepared at VRC = 10, 25, and 40% were also tested. Note that, in this study, VRC is defined by Eq. (1):
Percentage passing by weight (%)
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties …
469
100
80
Gravel Rubber
60
40
20
0 0.1
1
10
100
Particle size (mm)
Fig. 1 Particle size distribution and photographs of the gravel and rubber tested in this study
VRC =
VR × 100, VR + VG
(1)
where V R and V G are the volume of rubber and gravel in the mixture, respectively. The geotechnical properties of the parent materials (gravel and rubber) and the mixtures are summarized in Table 1. To define the small-strain shear stiffness (Gmax ), a series of bender element tests were conducted in a triaxial apparatus at 20, 40, 60, 80, and 100 kPa confining pressure on specimens of 60 mm in diameter and 130 mm in height. On the other hand, to define the shear modulus (G) versus shear strain amplitude (γ) curves, a series of small-strain cyclic triaxial tests were performed on specimens with diameter of 70 mm and height of 170 mm at 40, 60, and 100 kPa confining pressure. Dry specimens were prepared in 5 layers inside a split mold by tamping method at a degree of compaction of 90–95% (based on the results of standard compaction Proctor tests [6]). Segregation in the specimens was avoided by minimizing any vibration and preventing granular flow. Table 1 Geotechnical properties of the tested materials G100 (MPa)
n
a
γref (%)
Gravel
0
2.71
1754
115.6
0.5
0.57
0.012
VRC10
10
2.51
1621
73.3
0.5
0.62
0.015
VRC25
25
2.33
1487
50.8
0.5
0.67
0.021
VRC40
40
2.09
1315
20.5
0.5
0.75
0.027
Rubber
100
1.15
649
–
–
–
Material
a
VRC (%)
Gs (–)
ρ dry a (kg/m3 )
Proctor standard compaction tests (E = 600
– kJ/m3 )
470
G. Chiaro et al.
In the bender element tests, the confining pressure was applied internally to the specimen by means of a negative vacuum pressure. Shear waves with various frequencies were finally passed through the specimens and the received signals were recorded by oscilloscope for further analysis. In the cyclic triaxial tests, the confining pressure was applied externally to the specimen by increasing the cell pressure up to the desired value. The specimens were then subjected to stress-controlled cycles of shear loading at 0.05 Hz. The amplitude of deviatoric stress varied at any level of confining pressure to determine the shear modulus (G) at different level of shear strain (γ).
3 Results and Discussion 3.1 Bender Element Tests In Fig. 2, an example of transmitted single sinusoidal wave (frequency f = 2 kHz) at the confining pressure (σc ' ) of 60 kPa along with the received responses for the gravel and GRMs are shown. The travel time of transmitted wave (t) was calculated based on the peak-to-peak amplitudes of the input and received wave signals (indicated by the arrows in Fig. 2) using π-point method [13, 14]. The small-strain shear stiffness (Gmax ) from bender element test was calculated using Eq. (2): G max = ρ.VS2 ,
(2)
where ρ is the bulk density of the material (kg/m3 ), and V S is shear wave velocity (m/s). It is evident from Fig. 2 that by increasing the VRC, the arrival time of the received signal is delayed. This means that the shear wave velocity (V S ) value decreases by increasing the VRC. Since the dry density of GRMs decreases linearly with the VRC [6], the resultant Gmax calculated using Eq. (2) will also decrease. Not only V S decreases by increasing the rubber content, but also the attenuation of received signal increases significantly. This is mainly due to the damping and energy absorption characteristics of the rubber particles. In the pure gravel (i.e., VRC = 0%) and mixtures with low rubber content (i.e., VRC < 30%), the majority of particle-toparticle contacts are within the gravel matrix [15, 16]. Since these particles are relatively rigid compared to the rubber particles, the generated V S can travel much faster as compared to the specimens with higher VRC (≥30%) with less particle-toparticle gravel contact within the material matrix. Figure 3 reports a summary of the bender element tests on gravel and GRMs. In a log–log plot, it can be seen that for all material tested, Gmax increases linearly with increasing confining pressure (σc ' ). That is, as σc ' increases the contacts between particles become stronger and stronger resulting in a faster V S transmission between particles. Moreover, it can be observed that Gmax drastically decreases with increasing
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties …
471
Amplitude of the signal (V)
10 0 -10 0.2 0.0 -0.2 -0.4
Gravel
0.2 0.0 -0.2 -0.4
VRC10
0.2 0.0 -0.2 -0.4
VRC25
0.2 0.0 -0.2 -0.4
VRC40 -0.001
0.000
0.001
0.002
0.003
0.004
0.005
Time, t (s) Fig. 2 Example of bender element test results and effects of rubber content on the wave travel time and amplitude of the output signal
VRC. This is due mainly to the contribution of the lower solid density (i.e., specific gravity, Table 1) of rubber particles as compared to that of hard grained gravel, as well as the low-modulus and high energy adsorption properties of rubber that slow down the transmission of V S throughout the specimen. As shown by the fitting lines reported in Fig. 3, the dependency of Gmax to the confining pressure can be expressed by the power-form relationship shown in Eq. (3): Fig. 3 Small-strain shear stiffness (Gmax ) characteristics of gravel and GRMs determined by bender element tests
472
G. Chiaro et al.
( G max = G ref
'
σc ' σref
)n ,
(3)
where Gref is the small-strain shear stiffness at the reference confining pressure σ' ref , and n a material parameter. In this study, n was found to be a constant value equal to 0.5, and Gref was defined at a confining pressure of 100 kPa (i.e., Gref = G100 ) for convenience. Therefore, Eq. (3) could be rewritten as shown in Eq. (4): ( G max = G 100
'
σc 100
)0.5 (4)
The values of G100 are reported in Table 1 for all the tested material, for completeness.
3.2 Small-Strain Cyclic Triaxial Tests The results of bender element tests only provide the value of the maximum shear modulus (Gmax ) in the range of very-small to small shear strain level of 1 × 10–5 – 1 × 10–6 % (Fig. 4, adopted from [17]). In order to establish meaningful shear modulus degradation curves for gravel and GRMs in a wide range of shear strain amplitudes of relevance for many geotechnical applications (i.e., up to 1%), the results of the small-strain cyclic triaxial tests are presented and discussed henceforward. Figure 5a illustrates the variation of shear modulus (G) with shear strain amplitude (γ) for the gravel under three different σc ' levels of 40, 60 and 100 kPa. The results of bender element tests corresponding to γ = 1 × 10–6 % are also reported to complete Fig. 4 Schematic illustration of the characteristic shear modulus-strain behavior of soil with typical strain ranges for laboratory tests and structures. Adopted from [17]
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties …
473
Fig. 5 Shear modulus versus shear strain amplitude curves for: a gravel under different confining pressure levels of 40, 60, and 100 kPa and b gravel and GRMs under the same confining pressure of 100 kPa
the initial portion of curve (i.e., very small strain). The experimental data values are consistent with those reported in the literature for gravels (e.g., [1, 18–20]). Similarly, Fig. 5b compares the results obtained for the gravel and the mixtures VRC10, VRC25, and VRC40 at σc ' = 100 kPa. G is clearly pressure-dependent and increases with increasing the confining pressure. As expected, G also decreases by increasing shear strain amplitude (i.e., shear modulus degradation). Yet, the reduction in G with respect to shear strain becomes less significant as VRC increases in the mixture, which reflects the more ductile behavior of GRMs respect to the brittle one of the hard-grained gravel. Yet, it can be seen that, irrespective of σc ' and VRC, all the curves follow a similar pattern that can described by the hyperbolic model reported in Eq. (5): G 1 = ( )a , G max 1 + γγref
(5)
where γref is the reference shear strain evaluated at G/Gmax = 0.5, and a is a material fitting coefficient. The values of γref and a are reported in Table 1 for all the materials. The results reported in Fig. 5a for the gravel are replotted in Fig. 6a in terms of normalized shear modulus ratio G/Gmax . Figure 6b reports that for VRC40 for comparison. As shown, irrespective of the σc ' level, the experimental data merged into a single pattern and, thus, for each material a unique fitting curve derived from Eq. (6) appears to be sufficient to describe the G/Gmax relationships.
3.3 Analytical Hyperbolic Model The hyperbolic model of Eq. (5) was further modified in this study to Eq. (6):
474
G. Chiaro et al.
Fig. 6 Normalized shear modulus versus shear strain amplitude curves for: a gravel and b VRC40
G 100
G ( ' )0.5 = σc 100
1+
(
1
)0.0044 VRC+0.5706 γ 0.0004V RC+0.0121
.
(6)
This was achieved by incorporating Eq. (4) into Eq. (5) as well as the two linear functions shown in Fig. 7, which introduce the VRC-dependency of the factors γref (= 0.0004 VRC + 0.0121) and a (= 0.0044 VRC + 0.5706). The G/Gmax curves derived using Eq. 6 for all the materials are reported in Fig. 8a. Moreover, the experimentally measured versus the analytically derived shear modulus values are plotted in Fig. 8b. The agreement is quite satisfactory with the correlation coefficient R2 equal to 0.99.
Fig. 7 Variation of γref and a with the volumetric rubber content
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties …
475
Fig. 8 Hyperbolic model for GRMs: a G/Gmax curves derived using Eq. (6) and b comparison between experimentally measured versus analytically derived shear modulus values
4 Conclusion In this paper, the small-strain shear stiffness (Gmax ) characteristics as well as shear modulus (G) versus shear strain amplitude (γ) curves of a gravel and selected gravelrubber mixtures (GRMs) were evaluated by means of bender element and small-strain cyclic triaxial tests, respectively, under different level of confining pressure from 40 to 100 kPa. The main conclusions from this study are the followings: • Both Gmax and G are affected by the confining pressure (σc ' ) and the volumetric rubber content (VRC). Specifically, both increase with increasing σc ' and decrease with increasing VRC. The increase in VRC in the mixtures decreases the gravelto-gravel contact interface leading to a more rubber-like response of the mixtures [1, 15, 16]. • For any mixture, the normalized G/Gmax versus γ curves were found to be independent from σc ' and, therefore, a set of VRC-specific curves could be defined for the investigated materials. • An analytical hyperbolic model incorporating the effects of σc ' and VRC was proposed to predict the G/Gmax versus γ curves over a wide range of shear strain amplitudes (i.e., 1 × 10–6 to 1%) for gravel and GRMs with VRC ≤ 40%—that are of practical importance in many geotechnical applications [6]. It was demonstrated that estimated values are in good agreement with experimental ones. The outcomes of this study provide a useful tool to calibrate advanced constitutive, analytical, and finite element FE models (e.g., [21, 22]) to evaluate the performance of geotechnical structures made of GRMs, including foundation systems, under cyclic loading conditions. The dynamic test results concerning the damping properties of the investigated GRMs were not reported in this paper due to page limitation and will be presented elsewhere.
476
G. Chiaro et al.
Acknowledgements The authors are grateful for the research fund provided by the Ministry of Business, Innovation and Employment of New Zealand (MBIE Smart Ideas Research Grant No. 56289). Laboratory assistant provided by Mr. Abilash Pokhrel, Dr. Sean Rees, and Mr. Siale Faitotonu is also greatly appreciated.
References 1. Senetakis, K., Anastasiadis, A., Pitilakis, K.: Dynamic properties of dry sand/rubber (SRM) and gravel/rubber (GRM) mixtures in a wide range of shearing strain amplitudes. Soil Dyn. Earth Eng. 33(1), 38–53 (2012) 2. Pasha, S.M.K., Hazarika, K., Yoshimoto, N.: Physical and mechanical properties of gravel-tire chips mixture (GTCM). Geosynthetics Int. 26(1), 92–110 (2019) 3. Chiaro, G., Palermo, A., Granello., G., Tasalloti, A., Banasiak L.J.: Reuse of waste tires to develop eco-rubber seismic-isolation foundation systems: preliminary results. In: Lect Notes Civil Engineering, vol. 144, pp. 159–169 (2021) 4. Tasalloti, A., Chiaro, G., Palermo, A., Banasiak, L.J.: Effect of rubber crumbs volumetric content on the shear strength of gravelly soil in direct shear apparatus. ASCE Geotech. Spec. Publ. 319, 259–266 (2020) 5. Tasalloti, A., Chiaro, G., Banasiak, L., Palermo, A.: Experimental investigation of the mechanical behaviour of gravel-granulated tyre rubber mixtures. Constr. Build. Mater. 273, 121749 (2021) 6. Tasalloti, A., Chiaro, G., Murali, A., Banasiak, L., Palermo, A., Granello, G.: Recycling of end-of-life tires (ELTs) for sustainable geotechnical applications: a New Zealand perspective. Appl. Sci. 11(17), 7824 (2021) 7. Pitilakis, D., Anastasiadis, A., Vratsikidis, A., Kapouniaris, A., Massimino, M.R., Abate, G., Corsico, S.: Large-scale field testing of geotechnical seismic isolation of structures using gravelrubber mixtures. Earthquake Eng. Struct. Dyn. 50(10), 2712–2731 (2021) 8. Tsang, H.H., Tran, D.P., Hung, W.Y., Pitilakis, K., Gad, E.F.: Performance of geotechnical seismic isolation system using rubber-soil mixtures in centrifuge testing. Eng. Struct. Dyn. 50(5), 1271–1289 (2021) 9. Hernandez, E., Palermo, A., Granello., G, Chiaro, G., Banasiak, L.: Eco-rubber seismic isolation foundation systems, a sustainable solution for New Zealand context. Struct. Eng. Int. 30(2), 192–200 (2020) 10. Chiaro, G., Palermo, A., Granello, G., Tasalloti, A., Stratford, C., Banasiak, L.J.: Eco-rubber seismic-isolation foundation systems: a cost-effective way to build resilience. In: Proceedings of 2019 Pacific Conference on Earthquake Engineering, Auckland, New Zealand, p. 8 (2019) 11. Tasalloti, A., Chiaro, G., Murali, A., Banasiak, L.: Physical and mechanical properties of granulated rubber mixed with granular soils—a literature review. Sustainability 13(8), 4309 (2021) 12. Banasiak, L.J., Chiaro, G., Palermo, A., Granello, G.: Environmental implications of the recycling of end-of-life tires in seismic-isolation foundation systems. In: Lect Notes Civil Engineering, vol. 144, pp. 43–52 (2021) 13. Brocanelli, D., Rinaldi, V.: Measurement of low-strain material damping and wave velocity with bender elements in the frequency domain. Can. Geotech. J. 35(6), 1032–1040 (1998) 14. Viana da Fonseca, A., Ferreira, C., Fahey, M.: A Framework interpreting bender element tests, combining time-domain and frequency-domain methods. Geotech. Test J. 32(2), 91–107 (2009) 15. Chiaro, G., Tasalloti, A., Chew, K., Vinod, J.S., Allulakshmi, K.: Macro- and micro-scale engineering response of rigid-soft gravel-rubber inclusions: insights from detailed laboratory and DEM numerical investigations. In: Lecture Notes Civil Engineering, vol. 196, pp. 11–27 (2022)
Small-Strain Shear Stiffness and Strain-Dependent Dynamic Properties …
477
16. Chew, K., Chiaro, G., Vinod, J.S., Tasalloti, A., Allulakshmi, K.: Direct shear behavior of gravelrubber mixtures: discrete element modeling and microscopic investigations. Soils Found, in press (2022) 17. Atkinson, J., Sallfors, G.: Experimental determination of soil properties. In: Proceedings of 10th European Conference on Soil Mechanics and Foundation Engineering, Florence, Italy, vol. 3, pp. 915–956 (1991) 18. Modoni, G., Koseki, J., Anh Dan, L.Q.: Cyclic stress–strain response of compacted gravel. Geotechnique 61(6), 473–485 (2011) 19. Modoni, G., Flora, A., Mancuso, C., Viggiani, C., Tatsuoka, F.: Evaluation of gravel stiffness by pulse wave transmission tests. Geotech. Test J. 23(4), 506–521 (2000) 20. Suwal, P.L., Kuwano, R.: Disk shaped piezo-ceramic transducer for P and S wave measurement in a laboratory soil specimen. Soils Found 53(4), 510–524 21. Tsang, H.H., Pitilakis. K.: Mechanism of geotechnical seismic isolation system: analytical modelling. Soil Dyn. Earthquake Eng. 122, 171–184 (2019) 22. Forcellini, D., Chiaro, G., Palermo, A., Banasiak, L.: Numerical evaluation of the seismic performance of GSI foundation systems for buildings using gravel-rubber mixtures. In: Proceedings of 17th symposium earthquake engineering, Roorkee, India, p. 8
Numerical Evaluation of the Seismic Performance of GSI Foundation Systems for Buildings Using Gravel-Rubber Mixtures Davide Forcellini , Gabriele Chiaro , Alessandro Palermo , and Laura Banasiak
Abstract Geotechnical seismic isolation (GSI) using gravel-rubber mixtures (GRMs), as an energy dissipative horizontal layer, is a promising foundation technology to enhance the seismic resilience of low-rise residential buildings. This paper presents preliminary results of a numerical study carried out to evaluate the seismic performance of a selected GSI-GRM system and compare it to that of a standard nonisolated foundation system placed on a compacted gravel layer (i.e., without rubber). To this scope, a three-dimensional FE model is created in OpenSees and calibrated using experimental data. In the model, a 12 m × 6 m × 50 cm concrete raft foundation is placed on a 60-cm-thick layer of GRM (having volumetric rubber content (VRC) of 40%) or gravel (VRC = 0) resting on a 20-m-thick medium-dense dry sand deposit. No structures were placed on the foundation. The model was subjected to a ramped sinusoidal input base acceleration (ab = 0.1 − 0.5 g) at different frequency levels (f = 1–8 Hz). The accelerations at the base (aGIS,base ) and top (aGIS,top ) of the GRM/gravel layer are compared, and it is found that the effectiveness of GSI-GRM systems significantly increased with increasing ab and f . The best seismic performance is attained at f = 8 Hz, where the acceleration reaching the GSI top (aGIS,top ) is reduced up to 60% as compared to that of the non-isolated gravel foundation. Keywords Geotechnical seismic isolation · Gravel-rubber mixtures · Numerical model · Seismic performance D. Forcellini · G. Chiaro (B) · A. Palermo Department of Civil and Natural Resources Engineering, University of Canterbury, Christchurch, New Zealand e-mail: [email protected] D. Forcellini e-mail: [email protected] A. Palermo e-mail: [email protected] L. Banasiak Environmental Science and Research Institute, Christchurch, New Zealand e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_37
479
480
D. Forcellini et al.
1 Introduction Seismic isolation with energy dissipation can significantly improve the seismic performance of buildings and structures. It can be classified into two categories: (i) structural seismic isolation that consists of a flexible or sliding interface positioned between a structure and its foundation for the purpose of decoupling the motions of the ground from that of the structure [1] and (ii) geotechnical seismic isolation (GSI), in which the flexible or sliding interface is in direct contact with geological sediments and the isolation mechanism primarily involves geotechnical elements [2]. The low cost and suitability of such GSI methods can greatly benefit residential buildings [2– 15] for which, otherwise, the use of expensive structural seismic isolation techniques is not feasible. Over the years, several researchers have investigated the use and effectiveness of different typologies of GSI. For example, the effectiveness of GSI with sand-rubber mixtures for low- to medium-rise buildings was examined by means of numerical [3–6] and experimental studies [7]. Dhanya et al. [8] considered a low-rise building equipped with geogrid reinforcements to improve the high deformability and low bearing capacity of the GSI with sand-rubber layer. Banovi´c et al. [9, 10] examined the efficiency of the stone pebble as sliding GSI technique using small-scale model buildings. More recently, the use of GSI with gravel-rubber mixture layers has been proposed, based on the results of experimental [11, 12] and field investigations [13]. From a sustainable viewpoint, the use of soil-rubber layers in GSI systems appears to be particularly beneficial since it offers the possibility to make use not only of materials that are locally available (i.e., sandy and gravelly soils) but also recycled granulated rubber derived from new and stockpiled waste tyres [2, 7, 14]; among others). In this context, to date, the authors have conducted detailed geostructural-environmental laboratory investigations aimed at developing GSI foundation systems with gravel-granulated tyre rubber mixtures (GSI-GRM) suitable for low-rise residential buildings in New Zealand [12, 14, 16–20]. Following the experimental work, an FE numerical investigation assessing the seismic performance of GSI-GRM systems is currently ongoing. In this paper, the FE GSI-GRM model (version 1) is presented and preliminary results are reported for a 600-mm-thick GSI-GRM system with 40% rubber content by volume (VRC), as well as a standard gravel-only non-isolated foundation, subjected to a ramped sinusoidal input acceleration (ab = 0.1 − 0.5 g) at varying frequency level (f = 1–8 Hz). Thus, the seismic performance of the selected GSI-GRM system is compared that of the standard (i.e., non-isolated) gravel foundation by looking at the reduction of the acceleration reaching the top of the GSI/gravel layer (aGIS,top ) with that measured at the base of the layer (aGIS,base ).
Numerical Evaluation of the Seismic Performance of GSI Foundation …
481
2 Finite Element GSI Model In this study, numerical simulations were performed using the open-access software OpenSees [21] which has the capability to accurately model the response of soil subjected to seismic load [22]. Figure 1 shows the FE GSI-GRM (version1) model that was implemented. The GSI domain (33.0 m × 16.5 m × 21.1 m) was modelled using 20 nodes Bbar brick elements (total number: 7590). The natural soil deposit (20 m below the GSI layer) was selected as a medium-dense cohesionless homogenous material as defined in the pressure-dependent multi yield (PDMY) model [22]. The PDMY model was chosen because can capture nonlinear responses, hysteretic damping and permanent deformations. The uppermost 500 mm of the mesh simulates the presence of a shallow concrete raft foundation that is modelled with a pressure-independent multi yield (PIMY) model [22]. The GSI layer was defined with a thickness of 600 mm, according to the current foundation design practice for low-rise residential buildings in New Zealand. No structure was considered in this preliminary study. The GSI layer was simulated using the PDMY model. The model parameters (summarized in Table 1) were calibrated using a set of experimental data for gravelrubber mixtures (GRMs) reported by Tasalloti et al. [16–19], by ensuring that experimentally obtained backbone stress–strain curves were accurately reproduced by the numerical model. The GSI consists of a GRM with 40% volumetric rubber content (called hereafter VRC40). Yet, with the purpose of establishing a benchmark, the performance of a standard gravel-only foundation system (called here GRAVEL) was also assessed in this study. Table 1 summarizes the parameters used for the materials used in the model. Figure 2 shows the G/Gmax curves reported by Chiaro et al. [23] for GRM and gravel and implemented here in the GSI model.
aGIS(TOP) aGIS(BASE)
Input Base Acceleration
Fig. 1 3D view of the FE numerical model
482 Table 1 Geotechnical properties of the materials used in the FE model
D. Forcellini et al. Material
gravel
GRM
Sand
VRC (%)
0
40
0
Bulk mass density (Mg/m3 )
1.75
1.24
2.0
Nonlinear properties Peak friction (degrees) √ Peak shear strain × 2/3 (%)
54
38
37
1.6
6.5
6.0
Elastic properties (at a reference pressure σ ' c = 100 kPa)
Fig. 2 G/Gmax versus shear strain curves implemented in the model
Pressure-dependent coefficient
0.5
0.5
0.5
Maximum shear modulus (MPa)
116
20
100
Maximum bulk modulus (MPa)
193
34
300
Adopted from Tasalloti et al. (2021)
The boundary conditions were modelled as transmitting boundaries in order to dissipate the radiating waves by allowing the shear deformations along the longitudinal and transverse directions (penalty method with a tolerance of 10−4 ). Additionally, the base of the FE GSI model was fixed in all directions. A series of input accelerations ranging from 0.1 g to 0.5 g were applied at the base of the FE GSI model at varying frequencies (i.e., 1, 2, 4 and 8 Hz), in the form of sinusoidal ramping motions (Fig. 3). This allowed the investigation of the effectiveness of GSI with varying input motion parameters.
3 Simulation Results and Discussion A comparison of typical output accelerations measured at the base and top of the GRAVEL or VRC40 GSI layers is shown in Fig. 4. It is evident that a GSI-GRM foundation system made of VRC40 provides a substantial energy dissipation effect, which becomes more prominent with increasing input acceleration level, as compared to a standard GRAVEL foundation. It is important to point out that, even with just
Numerical Evaluation of the Seismic Performance of GSI Foundation …
483
5 3
5
7
N=1
3
9
7
1
9
N = number of loading cycles
(b)
(a)
Fig. 3 Input motions used in this study: a 1 Hz frequency and b 8 Hz frequency
60 cm thickness, a GSI-GRM system with VRC40 essentially acts as a deformable dissipative filter with its ability to reduce the horizontal acceleration reaching the foundation level. To provide more comprehensive insights, a summary of all simulation results attained in this numerical study is reported in Fig. 5, in terms of relationship between the peak values of the accelerations at the base of the GSI/gravel layer (aGIS,base ) versus the peak of the accelerations at the top of the same layer (aGIS,top ). It can be observed that the efficiency of the indeformable GRAVEL layer (i.e., standard nonisolated foundation system) is essentially insignificant since there is no reduction of accelerations within this layer (i.e., all the data points are located above the 1:1 line or 0% energy dissipation line). On the other hand, for the GSI system with VRC40, the data points are located below the 1:1 line. Specifically, there is a moderate reduction of approx. 20% for 1 Hz and 2 Hz conditions, and a more significant reduction in the horizontal accelerations of approx. 40% and 60% for 4 Hz and 8 Hz, respectively.
5
7
3
f = 8Hz
5
1
7
3
9
f = 8Hz 9
1
N = number of loading cycles
(a)
(b)
Fig. 4 Comparison between output accelerations at the base and the top of the filtering layer at a frequency of 8 Hz: a gravel-only layer and b VRC40 layer
484
D. Forcellini et al. 1.0 Amplification zone
0%
GSI Base
GSI Top
0% -2
% -40
0.4 % -60
0.2
Acceleration @ GSI Top [g]
Acceleration @ GSI Top [g]
0.6
Amplification zone
f = 2 Hz 0.8
Gravel VRC = 40%
0.6
GSI Base
GSI Top
0% -2 % -40
0.4
% -60
0.2
(b)
(a) 0.4
0.6
0.8
0.0 0.0
1.0
Acceleration @ GSI Base [g] 1.0
0.8
0% 0% -2
GSI Base
% -40 0.4
% -60
0.2
0.8
Gravel VRC = 40% GSI Top
0.6
0% -2
GSI Base
% -40 0.4
% -60
0.2
(c) 0.0 0.0
0.2
0.4
0.6
0.8
Acceleration @ GSI Base [g]
1.0
Amplification zone
f = 8 Hz
Acceleration @ GSI Top [g]
Acceleration @ GSI Top [g]
0.6
1.0
Damping zone
GSI Top 0.6
1.0 Damping zone
0.8
Gravel VRC = 40%
0.4
Acceleration @ GSI Base [g]
Amplification zone
f = 4 Hz
0.2
0%
0.2
+2 0%
0.0 0.0
Damping zone
0.8
Gravel VRC = 40%
Damping zone
f = 1 Hz
0%
1.0
(d) 0.0 0.0
0.2
0.4
0.6
0.8
1.0
Acceleration @ GSI Base [g]
Fig. 5 Summary of the numerical results in terms of relationships between output accelerations measured at the base and at the top of the GSI or the gravel layer
Overall, therefore, this study demonstrates that the use of the ERGSI system, instead of a traditional foundation on gravel, appears to significantly reduce the seismic demand that would reach low-rise structure placed on the foundation. As a result, it is anticipated that the structure safety during the earthquake shaking would drastically increase due to less likelihood of damage to the structural elements. Moreover, damage to non-structural elements and structure contents would be greatly reduced as well, with significant additional economic benefits. It is important to note that while this study only focused on the performance of an ideal ERGSI system with a 60-cm-thick GRM40 layer, the thickness of the GRM layer may also significantly affect the performance of ERGSI systems (e.g., [8]) and further numerical investigation are, therefore, required to quantify such effects.
Numerical Evaluation of the Seismic Performance of GSI Foundation …
485
4 Conclusion In this paper, the results of finite element numerical investigation aimed at evaluating the effectiveness of a selected GSI foundation system using gravel rubber were presented. It was demonstrated that compared to a standard a 60-cm-thick GSIGRM system with 40% rubber content by volume is capable of effectively acting as a deformable dissipative filter and drastically reducing the horizontal acceleration reaching the foundation level. Its effectiveness progressively increases, up to approx. 60%, with both increasing input acceleration and frequency level. Acknowledgements The authors are grateful for the research fund provided by the Ministry of Business, Innovation and Employment of New Zealand (MBIE Smart Ideas Research Grant No. 56289) and QuakeCoRE, a New Zealand Tertiary Education Commission-funded Centre. This is QuakeCoRE paper No. 0791.
References 1. Kelly, J.M.: Aseismic base isolation: review and bibliography. Soil Dyn. Earthq. Eng. 5(4), 202–216 (1986) 2. Tsang, H.H.: Seismic isolation by rubber–soil mixtures for developing countries. Earthq. Eng. Struct. Dyn. 37(2), 283–303 (2008) 3. Tsang, H.H., Lo, S.H., Xu, X., Neaz Sheikh, M.: Seismic isolation for low-to-medium-rise buildings using granulated rubber–soil mixtures: numerical study. Earthq. Eng. Struct. Dyn. 41(14), 2009–2024 (2012) 4. Pitilakis, K., Karapetrou, S., Tsagdi, K.: Numerical investigation of the seismic response of RC buildings on soil replaced with rubber–sand mixtures. Soil Dyn. Earthq. Eng. 79A, 237–252 (2015) 5. Brunet, S., de la Llera, J.C., Kausel, E.: Non-linear modeling of seismic isolation systems made of recycled tire-rubber. Soil Dyn. Earthq. Eng. 85, 134–145 (2016) 6. Forcellini, D.: Assessment of geotechnical seismic isolation (GSI) as a mitigation technique for seismic hazard events. Geosciences 10(6), 222 (2020) 7. Tsiavos, A., Alexander, N.A., Diambra, A., Ibraim, E., Vardanega, P.J., Gonzalez-Buelga, A., Sextos, A.: A sand-rubber deformable granular layer as a low-cost seismic isolation strategy in developing countries: experimental investigation. Soil Dyn. Earthq. Eng. 125, 105731 (2019) 8. Dhanya, J.S., Boominathan, A., Banerjee, S.: Response of low-rise building with geotechnical seismic isolation system. Soil Dyn. Earthq. Eng. 136, 106187 (2020) 9. Banovi´c, I., Radni´c, J., Grgi´c, N.: Geotechnical seismic isolation system based on sliding mechanism using stone pebble layer: shake-table experiments. Shock Vib. 2019, 9346232 (2019) 10. Banovi´c, I., Radni´c, J., Grgi´c, N.: Foundation size effect on the efficiency of seismic base isolation using a layer of stone pebbles. Earthquake Struct. 19(2), 103–117 (2020) 11. Tsang, H.H., Tran, D.P., Hung, W.Y., Pitilakis, K., Gad, E.F.: Performance of geotechnical seismic isolation system using rubber-soil mixtures in centrifuge testing. Eng. Struct. Dyn. 50(5), 1271–1289 (2020) 12. Chiaro, G., Palermo, A., Granello, G., Tasalloti, A., Stratford, C., Banasiak, L.J.: Eco-rubber seismic-isolation foundation systems: a cost-effective way to build resilience. In: Proceedings of 2019 Pacific Conference on Earthquake Engineering, Auckland, New Zealand, p. 8 (2019)
486
D. Forcellini et al.
13. Pitilakis, D., Anastasiadis, A., Vratsikidis, A., Kapouniaris, A., Massimino, M.R., Abate, G., Corsico, S.: Large-scale field testing of geotechnical seismic isolation of structures using gravelrubber mixtures. Earthq. Eng. Struct. Dyn. 50(10), 2712–2731 (2021) 14. Hernandez, E., Palermo, A., Granello, G., Chiaro, G., Banasiak, L.: Eco-rubber seismicisolation foundation systems: a sustainable solution for the New Zealand context. Struct. Eng. Int. 30(2), 192–200 (2020) 15. Tsang, H.H.: Geotechnical seismic isolation. In: Miura, T., Ikeda, Y. (eds.) Earthquake Engineering: New Research, pp. 55–87. Nova Science Publishers Inc., New York (2009) 16. Tasalloti, A., Chiaro, G., Palermo, A., Banasiak, L.J.: Effect of rubber crumbs volumetric content on the shear strength of gravelly soil in direct shear apparatus. Geotech. Spec. Publ. 319, 259–266 (2020) 17. Tasalloti, A., Chiaro, G., Murali, A., Banasiak, L., Palermo, A., Granello, G.: Recycling of end-of-life tires (ELTs) for sustainable geotechnical applications: a New Zealand perspective. Appl. Sci. 11(17), 7824 (2021) 18. Tasalloti, A., Chiaro, G., Banasiak, L., Palermo, A.: Experimental investigation of the mechanical behaviour of gravel-granulated tyre rubber mixtures. Constr. Build. Mater. 273, 121749 (2021) 19. Tasalloti, A., Chiaro, G., Murali, A., Banasiak, L.: Physical and mechanical properties of granulated rubber mixed with granular soils—a literature review. Sustainability 13(8), 4309 (2021) 20. Banasiak, L.J., Chiaro, G., Palermo, A., Granello, G.: Environmental implications of the recycling of end-of-life tires in seismic-isolation foundation systems. In: Lecture Notes of Civil Engineering, vol. 144, pp. 43–52 (2021) 21. Mazzoni, S., McKenna, F., Scott, M.H., Fenves, G.L.: Open System for Earthquake Engineering Simulation, User Command-Language Manual. (http://opensees.berkeley.edu/OpenSees/man uals/usermannual). PEER Center, University of California, Berkeley, OpenSees version 2.0 (2022) 22. Yang, Z., Elgamal, A., Parra, E.: A computational model for cyclic mobility and associated shear deformation. J. Geotech. Geoenviron. Eng. 129(12), 1119–1127 (2003) 23. Chiaro, G., Tasalloti, A., Palermo, A., Banasiak, L.: Small-strain shear stiffness and straindependent dynamic properties of gravel-rubber mixtures. In: Proceedings of 17th Symposium Earthquake Engineering, India, forthcoming (2022)
A Critical Review on Soil Reliquefaction Resistance Using Physical Modelling Experiments Gowtham Padmanabhan and B. K. Maheshwari
Abstract Liquefaction and associated ground deformations are one of the major causes of the devastating damage to the foundations and structures during earthquakes. Past research works focussed on understanding the liquefaction mechanism and behaviour subjected to the initial/independent seismic loading events. Henceforth, research related to understanding the reliquefaction mechanism and resistance of sand deposits was limited. The instance of historical earthquakes witnessed occurrence of reliquefaction and soil liquefied more than once when subjected to successive earthquakes (e.g. the main shock associated with foreshocks and aftershocks). The recent historic earthquakes (2010–2011 Canterbury earthquakes series, 2011 Tohoku, 2016 Kumamoto, and 2019 Vancouver amongst many) illustrated the destructive nature of the reliquefaction phenomenon. Multiple liquefaction was spotted during these repeated earthquakes/earthquake swarms, despite the earthquake magnitude being less than the previous shaking. Some of the field observations reported an increase in reliquefaction resistance due to the previous liquefaction occurrences and the beneficial effect of preshaking. In contrary to this, some studies reported a significant reduction in the resistance to reliquefaction. The present study critically reviews the complex nature of reliquefaction characteristics in increasing/decreasing the resistance of sand deposits to future liquefaction events. Physical modelling experiments have been used for simulating the liquefaction and reliquefaction phenomenon and in understanding the factors influencing the reliquefaction resistance. Factors such as method of sample preparation, initial relative density, input motion characteristics (acceleration amplitude, dynamic frequency, and shaking duration), and effect of preshaking on reliquefaction resistance was critically reviewed. It is concluded that all the above-mentioned parameters are critical in influencing the reliquefaction resistance to a certain extent. This study will be useful in understanding the reliquefaction mechanism and factors influencing liquefaction resistance when sand deposits subjected to repeated shaking events. This review will be highly useful in achieving G. Padmanabhan (B) · B. K. Maheshwari Department of Earthquake Engineering, IIT Roorkee, Uttarakhand 247667, India e-mail: [email protected] B. K. Maheshwari e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_38
487
488
G. Padmanabhan and B. K. Maheshwari
the efficient design of ground improvement system to mitigate reliquefaction and associated deformations. Keywords Reliquefaction · Physical modelling experiments · Preshaking · Ground improvement system
1 Introduction Soil liquefaction is one of the interesting, complex, and hazardous phenomenon in geotechnical earthquake engineering. Earthquake induced liquefaction was found to be a potential threat to the structures constructed on sand deposits; in addition, significant economic losses were incurred due to collapse of buildings located on liquefiable soil deposits. 1964 Niigata earthquake [1], 1976 Tangshan earthquake [2], 1995 Kobe earthquake [3], 1999 Chi-Chi earthquake [4], 2001 Bhuj earthquake [5], 2011 Christchurch earthquake [6], and the recent 2018 Indonesian earthquake [7] bear testimony. Significant progress has been achieved in liquefaction and associated damages due to extensive studies carried out by the researchers [8–10]. Major research works were focussed on assessment, susceptibility, and mitigation of liquefaction, whereas limited research works were carried out on reliquefaction and its associated deformations. As a result, liquefaction is well understood with help of physical, numerical, and analytical modelling, whilst understanding the mechanism and mitigation of reliquefaction remains a challenge due to its complex behaviour under seismic shaking. Reliquefaction occurs when a potentially liquefiable sand deposit subjected to successive earthquakes or earthquake swarms in a short interval of time. The recent historic earthquakes such as 2011 Tohoku [11], 2015 Gorkha [12], and 2019 Vancouver [13] have witnessed successive earthquake events comprising main shock associated with foreshocks and aftershocks events. Over the past two decades, damages induced by reliquefaction to the structures, underground tunnels, and foundations were reported frequently around the world. Some detailed research works have been published in this regard [14–16]. The welldocumented case studies provide valuable insights in understanding the reliquefaction phenomenon and its consequences on foundations and structures. A summary of 15 repeated earthquake events in the past decade around the world were listed in Table 1. This include special emphasis on earthquake swarms (combination of main shock associated with foreshock/aftershock events or combination of main shock events). Motivated by the complex reliquefaction behaviour of field deposits [17] presented the influence of preshaking on reliquefaction potential with the help of published literatures. Fukuoka-ken Seiho-oki earthquake, 2005 and Kumamoto earthquake swarm, 2016 are considered, and it is important to note that the two earthquakes possess contrasting earthquake history. The case study concluded that the effect of preshaking influenced by magnitude of foreshocks/aftershocks and liquefaction
A Critical Review on Soil Reliquefaction Resistance Using Physical …
489
history and that’s resulted in the increased reliquefaction resistance in Kumamoto region despite several large earthquake events. The objective of the present study is to review the factors influencing the reliquefaction resistance through physical modelling experiments. In the recent years, physical modelling experiments (geotechnical centrifuge modelling and 1-g shaking table) provide valuable insights in understanding the reliquefaction behaviour and Table 1 List of earthquake swarms S. No. Earthquakes
Date
Location
Magnitude (M w )
References
1
Canterbury
September 4, 2010
New Zealand
6.3 and 7.1
Green et al. [18]
2
Christchurch February 22, 2011
New Zealand
6.2, 5.5, 5.6, 4.5, Orense et al. 4.5 and 4.4 [19]
3
Tohoku
4
Christchurch June 13 (3 events) and 15, 2011
March 11, 2011 Japan
9.0, 7.4, 7.9 and 7.7
Bhattacharya et al. [11]
New Zealand
5.3, 6.0, 4.8 and 4.8
Cubrinovski et al. [20]
5
Christchurch December 23 (4 New Zealand events) and 24, 2011
5.8, 5.4, 6.0. 4.7 and 4.9
Cubrinovski et al. [21]
6
Christchurch January 2 (3 New Zealand events), 6 and 7, 2012
4.8, 5.0, 5.1, 4.5 and 4.8
Cubrinovski et al. [6]
7
Emilia
May 20 and 29, 2012
Italy
5.9 and 5.8
Lombardi and Bhattacharya [22]
8
Brawley
August 26 (7 events) and 27, 2012
United States of 4.6, 5.3, 4.9, 4.3, Hauksson et al. America 5.5, 4.3, 4.6 and [23] 4.9 Dobry et al. [24]
9
Greece
January 26 (2 events) and February 3, 2014
Greece
10
Kumamoto
11
6.0, 5.3 and 5.9
Papathanassiou et al. [25]
April 14, 15 and Japan 16, 2016
6.5, 6.2 and 7.3
Bhattacharya et al. [26]
Iran
December 1 and Iran 2 (2 events), 2017
6.0, 6.0 and 6.0
Ziabari et al. [27]
12
Lombok
July 29, August Indonesia 5, 8,19 and September 28, 2018
6.4, 6.9, 5.9, 6.3 and 6.9
Ferrario [7]
13
Vancouver
October 21, 2018
6.5, 6.6 and 6.8
ECH [13]
Canada
490
G. Padmanabhan and B. K. Maheshwari
resistance of sand deposits subjected to repeated shaking events. Factors such as method of sample preparation, initial relative density, input motion characteristics (acceleration amplitude, dynamic frequency, and shaking duration), and effect of preshaking on reliquefaction resistance were reviewed in detail.
2 Reliquefaction Studies Geotechnical centrifuge modelling and 1-g shaking table are the commonly used physical modelling tools in geotechnical earthquake engineering studies. Over the last decade, significant progress has been made in understanding the reliquefaction behaviour and resistance through physical modelling tools. Table 2 shows the details of the published research works on reliquefaction resistance and mechanism using physical modelling experiments. Parameters such as sample preparation methods, initial relative density, and input motion characteristics (acceleration amplitude, dynamic frequency, and shaking duration) are considered. It can also be seen whether the sand specimen was liquefied or not and the corresponding increase or decrease in the reliquefaction resistance subjected to repeated shaking events.
3 Factors Influencing Reliquefaction Resistance In this section, factors influencing the reliquefaction resistance of saturated sand specimen subjected to repeated shaking events were discussed. Though there are several factors influencing the reliquefaction resistance, major factors such as method of sample preparation, initial relative density, preshaking effect, and input motion characteristics alone are discussed.
3.1 Sample Preparation Sample preparation in physical modelling studies is a critical task, as achieving the desired soil density and replicating the field sample are difficult [44–46]. Method of sample preparation and the obtained soil fabric are crucial in influencing the mechanical behaviour of sand specimen. Several methods such as water sedimentation, air pluviation, hydraulic fill deposition, moist tamping, dry pluviation, and water pluviation have been adopted by the researchers worldwide to prepare the specimen. It is expected that the whilst examining soil liquefaction observed during an earthquake, sample preparation method used in physical modelling experiments should replicate the deposition of the in-situ soil in the field. Amongst all the methods, air pluviation and water sedimentation found to be replicate uniform sand deposition at all relative
A Critical Review on Soil Reliquefaction Resistance Using Physical …
491
Table 2 Physical modelling studies S. Deposition No. method
RD (%)
Input motion details g
Hz s
Reliquefaction Soil References resistance liquefied
1
Water 52, 61 0.3 sedimentation & 74
4
20
Decreases
Yes
Ye et al. [28]
2
Water 19–30 0.15 sedimentation
4
5
Increases
Yes
Ha et al. [29]
3
Hydraulic fill deposition
15–40 0.05, 0.1, 2 0.16 & 0.21
12
Increases
Yes
Ecemis et al. [30]
4
Dry pluviation
38
0.035 (Sine) (25 g)
2
7.5–8 & 2.3–3
Increases
No
El-Sekelly et al. [31]
5
Dry pluviation
38
0.12 & 0.8 (Sine) (25 g)
2
7.5–8 & 2.5–3
Decreases
Yes
El-Sekelly et al. [32]
6
Water pluviation
42
0.2
4
1.5–42 Decreases
Yes
Ye et al. [33]
7
Air pluviation 55 & 80
4
Yes
Teparaksa and Koseki [34]
8
Dry pluviation
80–85 0.3, 0.4 & 0.55
15
No
Darby et al. [35]
9
Dry pluviation
38
0.05, 0.1 & 1 0.25
5 & 15
Yes
Dobry et al. [36]
10
Water pluviation
40
0.31 (1995 Hyogo-Ken Nanbu EQ)
24
Decreases and Yes further increases for smaller input motion
Ye et al. [37]
11
Hydraulic fill deposition
0.24 & 0.61 1
24 & 62
Decreases
Salam et al. [38]
12
Air pluviation 40 & 50
0.1, 0.2, 5 0.3, 0.4, 0.5 & 0.8
4
Decreases
13
Wet pluviation
34.8
0.15
1
4
Decreases
14
Dry pluviation
40–45 0.53–0.66 & 85–90
2
15
15
Water 40 & sedimentation 60
0.1, 0.2, 0.3 5 & 0.4
60
0.2, 0.3, 0.4 5 & 0.7 1
Decreases
Decreases
No
Castiglia et al. [39] Yes
Xie et al. [40]
Yes
Orang et al. [41]
No
Padmanabhan and Shanmugam [42] (continued)
492
G. Padmanabhan and B. K. Maheshwari
Table 2 (continued) S. Deposition No. method 16
RD (%)
Water 25 & sedimentation 50
Input motion details g
Hz s
0.1–0.4
3.5 20, 40 & 60
Reliquefaction Soil References resistance liquefied Decreases
No
Padmanabhan & Maheshwari [43]
densities. In case of non-uniform sand deposition, reliquefaction resistance tends to decrease as the dissipation of excess pore water pressure was delayed. Higher the uniformity of sand specimen; larger the resistance to reliquefaction phenomenon.
3.2 Relative Density Initial sand density is an important factor in influencing the reliquefaction resistance of sand specimen. From the past published literature works, it is clear that the higher the initial sand density; higher the resistance to liquefaction and reliquefaction subjected to independent and repeated shaking events irrespective of input motion characteristics. From Table 2, it is understood that the selected relative densities are majorly in the range of 25–50%. Under the action of repeated shaking events, loose sand deposits are more prone to densification and resulted in higher sand density. The increased sand density is due to the dissipation of generated excess pore water pressure and soil settlement. Padmanabhan and Maheshwari [43] reported an increase in sand density of around 35% when subjected to incremental acceleration loading conditions. The increased sand density has contributed to the increased reliquefaction resistance to a certain extent. However, under the action of high intense shaking events, loose sand deposits completely liquefied and resulted in lesser resistance to further liquefaction events. In case of dense sand specimen, under the action of repeated shaking events, specimen will attain threshold sand density and resulted in relatively larger reliquefaction resistance. The initial sand density has the potential to increase/decrease the resistance to reliquefaction events. Figure 1 shows the time taken to achieve maximum pore pressure ratio for different acceleration amplitudes and relative densities. It can be seen that higher the relative density larger the time taken to attain liquefaction. Initial relative density of sand deposits is crucial in influencing the resistance to liquefaction and subsequent reliquefaction events.
A Critical Review on Soil Reliquefaction Resistance Using Physical …
493
Fig. 1 Time taken to achieve maximum pore water pressure for varying accelerations (0.1 to 0.4 g) for top and bottom piezometers at 40% and 60% relative density (RD) after Padmanabhan and Shanmugam [43]
3.3 Input Motion Characteristics Reliquefaction resistance of sand specimen primarily depends on the input motion characteristics. Parameters such as acceleration amplitude, dynamic frequency, and shaking duration are discussed in the further subsections. Acceleration amplitude Table 2 shows the acceleration amplitude adopted by the various researchers for examining reliquefaction mechanism and resistance. Most of the studies simulated sinusoidal waveform to simulate earthquake motion. Literatures stated that the reliquefaction potential increases with the increase in acceleration amplitude. Researchers also reported that the reliquefaction resistance of silty sand deposits increases with the increasing number of mild and medium intense repeated shaking events. However, when the sand deposit subjected to high intense shaking events, which is sufficient enough to induce liquefaction, the reliquefaction resistance decreases as the beneficial effect of preshaking got diminished. The liquefied sample behaves as a freshly prepared sand deposit as the high intense event reset the clock. The effect of acceleration amplitude on reliquefaction resistance (increases/decreases) can be decided only on the basis of generated excess pore water pressure. Padmanabhan and Maheshwari [47] performed shaking table experiments on all possible combinations of seismic sequences (incremental, uniform, and decremental). The authors concluded that the reliquefaction resistance increases for the partially liquefied specimens, and the resistance decreases when the specimen is completely liquefied. Dynamic frequency Dynamic frequency is also a major factor in influencing the liquefaction and reliquefaction potential of sand deposit. Table 2 shows the dynamic frequency adopted by various researchers for liquefaction studies. Most of the researchers have used
494
G. Padmanabhan and B. K. Maheshwari
frequency in the range of 1–5 Hz in the range of low- to high-frequency earthquakes. From the studies, it can be seen that higher the frequency; lower the resistance to reliquefaction events. Shaking duration From the published literatures, it is clear that the reliquefaction resistance was significantly influenced by the shaking duration of the earthquake motion. Shaking duration adopted in the physical modelling experiments by various researchers was shown in Table 2. With the help of physical modelling experiments, researchers simulated short and long duration earthquakes to induce liquefaction and subsequent reliquefaction events. In general, higher the shaking duration; larger the generation of excess pore water pressure which resulted in complete liquefaction and thus reduces the resistance to reliquefaction when subjected to further shaking events. However, if the shaking duration was greater than 20 s, difference in pore pressure ratio was not significant [47]. It can be concluded that influence of shaking duration was applicable for events with duration less than 20 s.
3.4 Preshaking History Preshaking history is critical in improving the reliquefaction resistance of soil deposits. El-Sekelly et al. [32] reviewed the reliquefaction behaviour through 1989 Loma Prieta earthquake and 2010 El-Mayor Cucapah earthquake and concluded that the effect of seismic preshaking history is the most probable explanation for the increased/decreased reliquefaction resistance of soil deposits. Darby et al. [35] conducted similar centrifuge experiments on reliquefaction phenomenon and found that the cyclic resistance ratio depends on seismic shaking history and relative density of the soil deposits. Dobry et al. [36] investigated the complex interaction between the major and minor earthquake events and role of aftershocks in decreasing/increasing the liquefaction resistance of the sand deposits. The researchers concluded that the reliquefaction resistance is associated with magnitude of shaking events, liquefaction pattern, geologic age, and preshaking effect. From the published literatures, it is evident that the preshaking history plays a major role in influencing the reliquefaction resistance of sand deposits.
4 Reliquefaction Resistance As discussed in the previous sections, reliquefaction resistance of sand deposits was critical and depends on several factors. In case of a new sand deposit (natural/artificially deposited or lab specimen), there exist a large number of unstable soil particles that are more prone to collapse, when subjected to a relatively less intense shaking event. In such cases, relative density of sand particles increased to
A Critical Review on Soil Reliquefaction Resistance Using Physical …
495
a smaller extent. Though the low intense shaking events did not contribute much to increased relative density, it positively resulted in the stronger sand fabric with particle interlocking mechanism. Whereas, under high intense shaking events, the continuous upward generation of excess pore water pressure resulted in liquefaction, which eventually disturbed the loose sand specimen and further decreases the resistance to reliquefaction when subjected to repeated shaking events [48]. As reported by researchers, reliquefaction resistance of sand deposits increased due to the influence of interlocking of sand grains and cementation which strengthen the sand grains that accumulates over the time. Research works also reported that the grain size characteristics influence the reliquefaction resistance of sand deposits.
5 Conclusions From the detailed review on the reliquefaction resistance of sand deposits subjected to repeated shaking events, the following conclusions are derived. 1. The existing research works on reliquefaction were focussed on understanding its mechanism and the factors influencing its complex behaviour. However, there is abundant evidence to justify the imprecise reliquefaction mechanism as some shaking events increase and others decrease the resistance to liquefaction and subsequent reliquefaction. 2. The study concluded that the single index property or grain characteristic is not sufficient to examine the trends of complex reliquefaction behaviour and resistance. It is clear that the reliquefaction phenomenon significantly influenced by the initial relative density, preshaking and applied input motion characteristics. 3. A loose sand deposit which is free from preshaking, where the reliquefaction resistance increases when initially subjected to low intense shaking event and for high intense shaking event, reliquefaction resistance decreases when further subjected to repeated shaking events. 4. In general, liquefaction resistance of sand specimens is primarily depending upon acceleration amplitude. Whereas in case of reliquefaction resistance, it depends on whether the sample is completely liquefied or not. In case of partially liquefied specimens, reliquefaction resistance increases with the increase in acceleration amplitude; whereas it decreases in case of completely liquefied sand specimens.
References 1. Ishihara, K., Koga, Y.: Case studies of liquefaction in the 1964 Niigata earthquake. Soils Found. 21(3), 35–52 (1981) 2. Moss, R.E.S., Kayen, R.E., Tong, L.Y., Liu, S.Y., Cai, G.J., Wu, J.: Retesting of Liquefaction/Nonliquefaction Case Histories from the 1976 Tangshan Earthquake. J. Geotech. Geoenviron. Eng. 137(4), 334 (2011)
496
G. Padmanabhan and B. K. Maheshwari
3. Soga, K.: Soil Liquefaction Effects Observed in the Kobe Earthquake of 1995. Proc. Inst. Civ. Eng. Geotech. Eng. 131(1), 34–51 (1998) 4. Chu, D.B., Stewart, J.P., Lee, S., Tsai, J.S., Lin, P.S., Chu, B.L., Seed, R.B., Hsu, S.C., Yu, M.S., Wang, M.C.: Documentation of soil conditions at liquefaction and non-liquefaction sites from 1999 Chi-Chi (Taiwan) earthquake. Soil Dyn. Earthq. Eng. 24(9–10), 647–657 (2004) 5. Hazarika, H., Boominathan, A.: Liquefaction and ground failures during the 2001 Bhuj earthquake, India. In: Proceedings of International Conference on Performance-Based Design in Earthquake Geotechnical Engineering from case history to practice, Tokyo, Japan (2009) 6. Cubrinovski, M., Bray, J.D., Taylor, M., Giorgini, S., Bradley, B., Wotherspoon, L., Zupan, J.: Soil liquefaction effects in the central business district during the February 2011 Christchurch earthquake. Seismol. Res. Lett. 82(6), 893–904 (2011) 7. Ferrario, M.F.: Landslides triggered by multiple earthquakes: insights from the 2018 Lombok (Indonesia) events. Nat. Hazards 98(2), 575–592 (2019) 8. Seed, H.B., Idriss, I.M.: Simplified procedure for evaluating soil liquefaction potential. J. Soil Mech. Found. Div. 97(9), 1249–1273 (1971) 9. Seed, H.B., Martin, P.P., Lysmer, J.: Pore-water pressure changes during soil liquefaction. J. Geotech. Geoenviron. Eng. 102(Proc. Paper# 12074) (1976) 10. Huang, Y., Yu, M.: Review of soil liquefaction characteristics during major earthquakes of the twenty-first century. Nat. Hazards 65(3), 2375–2384 (2013) 11. Bhattacharya, S., Hyodo, M., Goda, K., Tazoh, T., Taylor, C.A.: Liquefaction of soil in the Tokyo Bay area from the 2011 Tohoku (Japan) earthquake. Soil Dyn. Earthq. Eng. 31(11), 1618–1628 (2011) 12. Gautam, D., de Magistris, F.S., Fabbrocino, G.: Soil liquefaction in Kathmandu valley due to 25 April 2015 Gorkha, Nepal earthquake. Soil Dyn. Earthq. Eng. 97, 37–47 (2017) 13. Earthquakes Canada Homepage: https://earthquakescanada.nrcan.gc.ca/recent/2019/indexen.php. Last accessed 31 June 2022 14. Yasuda, S., Tohno, I.: Sites of reliquefaction caused by the 1983 Nihonkai-Chubu earthquake. Soils Found. 28(2), 61–72 (1988) 15. Wang, R., Fu, P., Zhang, J.M., Dafalias, Y.F.: Fabric characteristics and processes influencing the liquefaction and re-liquefaction of sand. Soil Dyn. Earthq. Eng. 125, 105720 (2019) 16. Padmanabhan, G., Shanmugam, G.K.: Liquefaction and reliquefaction resistance of saturated sand deposits treated with sand compaction piles. Bull. Earthq. Eng. 19(11), 4235–4259 (2021) 17. Padmanabhan, G., Maheshwari, B.K.: Case studies on preshaking and reliquefaction potential for different earthquakes in Japan. In: Local Site Effects and Ground Failures, pp. 137–144. Springer, Singapore (2021) 18. Green, R.A., Cubrinovski, M., Cox, B., Wood, C., Wotherspoon, L., Bradley, B., Maurer, B.: Select liquefaction case histories from the 2010–2011 Canterbury earthquake sequence. Earthq. Spectra 30(1), 131–153 (2014) 19. Orense, R.P., Kiyota, T., Yamada, S., Cubrinovski, M., Hosono, Y., Okamura, M., Yasuda, S.: Comparison of liquefaction features observed during the 2010 and 2011 Canterbury earthquakes. Seismol. Res. Lett. 82(6), 905–918 (2011) 20. Cubrinovski, M., Hughes, M., O’Rourke, T.D.: Impacts of liquefaction on the potable water system of Christchurch in the 2010–2011 Canterbury (NZ) earthquakes. J. Water Supply Res. Technol. AQUA 63(2), 95–105 (2014) 21. Cubrinovski, M., Robinson, K., Taylor, M., Hughes, M., Orense, R.: Lateral spreading and its impacts in urban areas in the 2010–2011 Christchurch earthquakes. NZ J. Geol. Geophys. 55(3), 255–269 (2012) 22. Lombardi, D., Bhattacharya, S.: Liquefaction of soil in the Emilia-Romagna region after the 2012 Northern Italy earthquake sequence. Nat. Hazards 73(3), 1749–1770 (2014) 23. Hauksson, E., Stock, J., Bilham, R., Boese, M., Chen, X., Fielding, E.J., Galetzka, J., Hudnut, K.W., Hutton, K., Jones, L.M., Kanamori, H.: Report on the August 2012 Brawley earthquake swarm in Imperial Valley, southern California. Seismol. Res. Lett. 84(2), 177–189 (2013) 24. Dobry, R., Abdoun, T., Stokoe, K.H., II., Moss, R.E.S., Hatton, M., El Ganainy, H.: Liquefaction potential of recent fills versus natural sands located in high-seismicity regions using shear-wave velocity. J. Geotech. Geoenviron. Eng. 141(3), 04014112–04014121 (2015)
A Critical Review on Soil Reliquefaction Resistance Using Physical …
497
25. Papathanassiou, G., Ganas, A., Valkaniotis, S.: Recurrent liquefaction-induced failures triggered by 2014 Cephalonia, Greece earthquakes: spatial distribution and quantitative analysis of liquefaction potential. Eng. Geol. 200, 18–30 (2016) 26. Bhattacharya, S., Hyodo, M., Nikitas, G., Ismael, B., Suzuki, H., Lombardi, D., Egami, S., Watanabe, G., Goda, K.: Geotechnical and infrastructural damage due to the 2016 Kumamoto earthquake sequence. Soil Dyn. Earthq. Eng. 104, 390–394 (2018) 27. Ziabari, S.H., Ghafoori, M., Moghaddas, N.H., Lashkaripour, G.R.: Liquefaction potential evaluation and risk assessment of existing structures: A case study in Astaneh-ye Ashrafiyeh City, Iran. J. Biosci 11, 52–62 (2017) 28. Ye, B., Ye, G., Zhang, F., Yashima, A.: Experiment and numerical simulation of repeated liquefaction-consolidation of sand. Soils Found. 47(3), 547–558 (2007) 29. Ha, I.S., Olson, S.M., Seo, M.W., Kim, M.M.: Evaluation of reliquefaction resistance using shaking table tests. Soil Dyn. Earthq. Eng. 31(4), 682–691 (2011) 30. Ecemis, N., Demirci, H.E., Karaman, M.: Influence of consolidation properties on the cyclic re-liquefaction potential of sands. Bull. Earthq. Eng. 13(6), 1655–1673 (2015) 31. El-Sekelly, W., Dobry, R., Abdoun, T., Steidl, J.H.: Centrifuge modeling of the effect of preshaking on the liquefaction resistance of silty sand deposits. J. Geotech. Geoenviron. Eng. 142(6), 04016012 (2016) 32. El-Sekelly, W., Abdoun, T., Dobry, R.: Liquefaction resistance of a silty sand deposit subjected to preshaking followed by extensive liquefaction. J. Geotech. Geoenviron.Eng. 142(4), 04015101 (2016) 33. Ye, B., Hu, H., Bao, X., Lu, P.: Reliquefaction behavior of sand and its mesoscopic mechanism. Soil Dyn. Earthq. Eng. 114, 12–21 (2018) 34. Teparaksa, J., Koseki, J.: Effect of past history on liquefaction resistance of level ground in shaking table test. Géotech. Lett. 8(4), 256–261 (2018) 35. Darby, K.M., Boulanger, R.W., DeJong, J.T., Bronner, J.D.: Progressive changes in liquefaction and cone penetration resistance across multiple shaking events in centrifuge tests. J. Geotech. Geoenviron. Eng. 145(3), 04018112–04018112 (2019) 36. Dobry, R., El-Sekelly, W., Abdoun, T.: Calibration of non-linear effective stress code for seismic analysis of excess pore pressures and liquefaction in the free field. Soil Dyn. Earthq. Eng. 107, 374–389 (2018) 37. Ye, B., Xie, X., Zhao, T., Song, S., Ma, Z., Feng, X., Zou, J., Wang, H.: Centrifuge tests of macroscopic and mesoscopic investigation into effects of seismic histories on sand liquefaction resistance. J. Earthq. Eng., pp. 1–23 (2020) 38. Salam, S., Xiao, M., Evans, J.C.: Strain history and short-period aging effects on the strength and cyclic response of fine-grained coal refuse. J. Geotech. Geoenviron. Eng. 146(10), 04020113 (2020) 39. Castiglia, M., de Magistris, F.S., Onori, F., Koseki, J.: Response of buried pipelines to repeated shaking in liquefiable soils through model tests. Soil Dyn. Earthq. Eng. 143, 106629 (2021) 40. Xie, X., Ye, B., Zhao, T., Feng, X., Zhang, F.: Changes in sand mesostructure under repeated seismic liquefaction events during centrifuge tests. Soil Dyn. Earthq. Eng. 150, 106940 (2021) 41. Jahed Orang, M., Motamed, R., Prabhakaran, A., Elgamal, A.: Large-scale shake table tests on a shallow foundation in liquefiable soils. J. Geotech. Geoenviron. Eng. 147(1), 04020152 (2021) 42. Padmanabhan, G., Shanmugam, G.K.: Reliquefaction assessment studies on saturated sand deposits under repeated acceleration loading using 1-g shaking table experiments. J. Earthquake Eng. 26(6), 2888–2910 (2022) 43. Padmanabhan, G., Maheshwari, B.K.: Effect of shaking pattern on reliquefaction potential of sands. In: Proceedings of Indian Geotechnical Conference, Trichy Chapter, IGS (2022) 44. Maheshwari, B.K., Singh, H.P., Saran, S.: Effects of reinforcement on liquefaction resistance of Solani sand. J. Geotech. Geoenviron. Eng. 138(7), 831–840 (2012) 45. Varghese, R.M., Madhavi Latha, G.: Shaking table tests to investigate the influence of various factors on the liquefaction resistance of sands. Nat. Haz. 73(3):1337–1351 (2014)
498
G. Padmanabhan and B. K. Maheshwari
46. Padmanabhan, G., Shanmugam, G.K., Subramaniam, S.: Shaking table tests on liquefiable sand deposits treated with sand compaction piles. In: Proceedings of the Indian Geotechnical Conference 2019, pp. 523–532. Springer, Singapore (2021) 47. Padmanabhan, G., Maheshwari, B.K.: Assessment of reliquefaction behavior of solani sand specimen using 1-g shaking table experiments. Special issue in honour of Prof. D.K. Paul on Disaster Mitigation and Management in ISET Journal of Earthquake Technology (2022) Accepted 48. Padmanabhan, G., Shanmugam, G.K.: Addressing influence of prefabricated vertical drains in liquefaction resistance under multiple shaking events. In: Soil dynamics, pp. 203–212. Springer, Singapore (2021)
Inclusion of Fatigue Checks in Current IS Codes for Monopole and Stack Structures K. A. Sahakari , S. U. Talankar , and Y. K. Gaude
Abstract This paper covers the fatigue design of monopoles, spun towers, and steel stacks. Steel stacks/spun towers are among high vertical, flexible, and wind resisting structures. They help to resist cyclones, wind turbulence, and dynamic forces during earthquakes. Mostly, the cyclic stresses due to wind forces are governing in tall steel stack structures. The authors provide methodology of fatigue design for cyclic loadings in these structures. NBC and IS codes fail to provide systematic methodology for fatigue design. This study is carried out to understand the performance of a fatigue resistant design of steel structures by presenting a case study. Due to cyclic loadings, weld connections also need to be checked as per IS 1024. The paper is subdivided into two parts, former part consists of an introduction to the topic under consideration and explains in brief the methodology that will be adopted for fatigue design. And the later part consists of a case study. As part of a case study, it has been decided to analyze and design a 5 m monopole, spun towers of 15 m and 20 m and to evaluate their feasibility with respect to installation through National Cyclone Risk Mitigation Project which are under construction at Altinho, Panaji Goa from Structural safety point of view. Monopole/steel stacks are subjected to dynamic wind pressures; as a result, joints will be subjected to fatigue stresses. Hence, it is advisable to check the welded joints for these cyclic stresses. Residual stresses due to installation of bolts or welds are usually not required to be considered in statically loaded structures, but connections in cyclically loaded structures shall be designed considering fatigue as specified by this author. Fatigue assessment is required especially for steel structures supporting lifting or rolling loads, members subjected to repeated stress cycles from vibrating machinery, wind induced oscillations of many cycles in life, and members subjected to crowd induced oscillations of a large number of cycles in life etc. Furthermore, modeling and analysis of monopole of 5 m and spun towers of 15 m and 20 m will be carried out using STAAD Pro and ETABS, MIDAS, and their corresponding fatigue checks considering the above provisions. Keywords National cyclone risk mitigation project · ETABS · STAAD · MIDAS K. A. Sahakari (B) · S. U. Talankar · Y. K. Gaude Consulting Engineer, K. A. Sahakari & Associates, Ponda, Goa, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_39
499
500
K. A. Sahakari et al.
1 Introduction 1.1 General The construction of taller towers, which is the most typical tower configuration, is a result of the continuously growing demand. Spun towers and steel stacks are among the tallest, slender, and wind-resistant constructions. They provide resistance to hurricanes, wind turbulence, and dynamic forces during earthquakes. The cyclic pressures imposed by wind forces govern the design of tall steel stack structures. Recent tower catastrophes brought on by fatigue loading have put the engineering community under pressure to construct robust structures with less material [1]. The tower design shall be such that they can sustain a variety of loads, but recent tower collapses that took place under typical wind and earthquake conditions while the shell stresses were still within the elastic range draw attention to the significance of fatigue phenomena and how they impact the joints in the towers. For the manufacturing and mounting procedures utilized to build steel towers, four different kinds of welded joints have been found. Circumferential welds, longitudinal welds, circumferential welds between the tower shell and stiffening rings, circumferential welds between the bottom flange and tower shell, etc., are the four different kinds of welded connections. It has been discovered that these circumferential welds between tower, tower subparts, and connecting flanges are susceptible to failure arising due to fatigue since cracks have been observed in these areas of wind towers that have already been constructed [2]. Fatigue is the repeated application of stresses that causes microscopic cracks to progress into macro cracks. Fatigue damage is the damage and/or failure of materials under cyclic loads in engineering applications. Failure due to fatigue typically occurs at stress significantly lower than the yield stress (ultimate strength) of the materialstress considered safe by static failure analysis. The failure is primarily the result of repeated stresses from maximum to minimum. A structure is subjected to four major loads: dead, live, earthquake, and wind. The structure is always subjected to dead and live loads. However, the structure may only be subjected to the design live loads once or twice a year. The design wind and seismic loads, which are cyclic in nature, will occur once every 50 years. Structures often experience minor levels of induced cyclic stresses, which are typically caused by machinery. Steel can resist an endless number of load reversals at low stresses. As a result, fatigue is not taken into account in the design of members. Bridges, gantry girders, cranes, slender tower-like structures, offshore platforms, and structures supporting large rotating equipment are all examples of fatigue-prone structures. Verifications in the fatigue limit state are frequently more critical for these structures than in the serviceability or ultimate limit state. This implies that fatigue resistance may be more important for these structures than structural stiffness or strength [3]. Weld fatigue failure is one of the main causes of structural failure in wind turbine towers [4], and it recently caused the complete collapse of a major wind turbine
Inclusion of Fatigue Checks in Current IS Codes for Monopole …
501
tower owing to fatigue failure of circumferential welded joints. Common tower finite element models simulate the structures as full structures with no further detail provided in numerical models, although this practice must be reviewed in light of recent incidents caused by welding failure [3]. This paper discusses the methodology in the design of a monopole being used in National Cyclone Risk Mitigation Project. The methodology proposed in the paper was necessitated due to the deficiency of proper procedures for fatigue checks in IS 800 and NBC. The analysis is done using various software, and the check for fatigue is done manually using the formulae as discussed elsewhere.
1.2 Wind-Induced Fatigue Analysis Since monopole/steel stacks are subjected to dynamic wind pressures, joints are subjected to fatigue stresses. As a result, it is advisable to evaluate the welded joints for cyclic stresses. Residual stresses caused by bolt or weld installation are usually not required to be considered in statically loaded structures, but connections in cyclically loaded structures must be designed with fatigue in mind, as specified by this author. Fatigue evaluation is required for steel structures supporting rolling or lifting loads, members exposed to repeated stress cycles because of vibrating machinery, windinduced oscillations of infinite cycles, and members exposed to oscillations of a large number of cycles in life induced due to crowd. The fatigue phenomenon, which begins with the appearance of small cracks in a specific structure region of high-stress concentration, progresses to structural failure and, in the worst-case scenario, the collapse of the entire structure. According to post-collapse structure analyzes, collapses occurred without warning and with stress amplitudes lying still within the elastic range of the material. This is obvious because cyclic loading causes steel hardening, which leaves the material brittle, resulting in the formation of cracks which further expand under the cyclic loading and the material failing without the occurrence of larger deformations. The mother material rarely fails due to fatigue, whereas areas with discontinuities, thickness changes, holes, welds, bolts, and so on are more prone to damage due to cyclic loading.
1.3 Factors Affecting Fatigue Life The three factors listed below are considered to be among the most crucial of the many factors that influence fatigue life. • The total number of loading cycles that the member undergoes. • The stress range at the location • The type of member/detail at the location.
502
K. A. Sahakari et al.
Additional variables that affect fatigue behavior include material strength, stress concentration, steel residual stress, imperfections, plate thickness, stress ratio, postweld treatment, frequency of cyclic loading, environment, steel service temperature, etc.
2 Numerical Models The authors provide a methodology for wind-induced fatigue design/check for cyclic loadings in these structures. NBC and IS codes fail to provide a systematic methodology for fatigue design. This study is carried out to understand the performance of a fatigue-resistant design of steel structures by presenting a case study. Data from past literature and other country standards have been used to arrive at the proposed methodology for fatigue checks.
2.1 Case Study Model description. The use of monopoles in wireless communication is common nowadays. The steel monopoles and spun concretes monopoles are being used. In the case of concrete spun monopoles, the connection between two segments and the connection to the base is made up of mild steel, which is either welded or bolted. These connections need to be checked for fatigue. In this instance, a monopole used for Tsunami Warning Tower was to be checked for fatigue. The fatigue check is used to ensure that the structure does not fail during the high-velocity wind and that it remains functional during natural calamities. The methodology mentioned in the literature for the design of chimneys is used for the design of monopoles. However, it was found that the procedure to check the fatigue stresses is missing in the codes. The study is organized into two sections; the first part provides an overview of the topic at hand and briefly outlines the methodology that will be used for fatigue design. And a case study is included in the subsequent part. As part of a case study, it was decided to analyze, design, and assess the feasibility of installing a 5 m monopole and spun towers of 15 m and 20 m from a structural safety point of view. Moreover, the suggested design approach involves modeling and analyzing the prototype of a 5 m monopole, as well as 15 m and 20 m spun towers, using STAAD Pro, ETABS, MIDAS, and their corresponding fatigue checks have been carried out as per the proposed design procedure. The steps involved in this study include as follows: 1. Identification and theoretical calculation of loads acting on towers. 2. Modeling, analyzing, and designing the monopoles and steel towers using Staad, Midas and Etabs and comparison of the same.
Inclusion of Fatigue Checks in Current IS Codes for Monopole … Table 1 Details of structure
503
Component
Description
Type of structure
Monopoles and spun towers
Height of structure
5 m, 15 m, and 20 m, respectively
Basic wind speed
66.67 m/sec
Probability factor, k1
1.08
Return period for probability factor k1
100 years
Terrain category
2
Topography factor, k3
1
Cyclonic region Importance factor, k4
1
Grade of concrete for the spun tower
M80
Modulus of elasticity of concrete for the spun tower
4.4721 × 1010 N/m2
3. Proposing methodology for fatigue check and using the same to evaluate the above-mentioned structures. These structures are examined for fatigue analysis since they have welded steel connection joints and also to determine their structural safety. The figures below depict the structural models of spun towers and monopoles using software such as Staad Connect, Etabs 20.1.0, and Midas Gen which will be further assessed for fatigue check using the proposed methodology. The structures under consideration are situated in Goa. Table 1 presents the details of structure, and Fig. 1 shows the modeling of monopole and spun towers of 5 m, 15 m, and 20 m, respectively, using Staad Connect, Etabs, and Midas, respectively.
3 Methodology 3.1 Past Literature and Country Standards A simplified methodology has been provided to assess the wind-induced fatigue study in accordance with the data from CICIND’s “Model Code for Steel Chimneys revision 1-1999 amendment A-March 2002” [5]. From “Eurocode 1-basis of design and actions on structures-wind actions” [6], the relevant data have been obtained. The AS4100-1998 [7] Australian Steel Structures Code also provides a method for fatigue assessments. The methods of fatigue analysis have been divided into the following categories in accordance with how fatigue life is defined:
504
(a) 5m monopole in Staad Connect
(b) 15m & 20m monopole in Etabs
K. A. Sahakari et al.
(b) 15m & 20m monopole in Staad Connect
(d) 15m & 20m monopole in Midas
Fig. 1 Modeling of monopole and spun towers of 5 m, 15 m, and 20 m, respectively
• Stress method • Strain method • Crack propagation method. The total fatigue life is defined by stress and strain methods in terms of cyclic stress or strain range. These methods estimate the number of stress cycles or strain cycles required to cause fatigue failure in an originally uncracked or smooth surfaced laboratory specimen. The resultant fatigue life includes the time required for a fatigue crack to start, grow, and eventually fail catastrophically. Due to the specimen’s flat surface, the fatigue initiation life typically accounts for 90% of the total life. In fatigue-critical applications, such as the aircraft and nuclear industries, which may result in loss of human life due to catastrophic failures, the crack propagation method has been frequently adopted [3]. IS:800 [8] employs the stress approach based on S–N curves. In fatigue design, structural components are susceptible to two different types of load histories. Constant amplitude loading is the most basic load history, and it exists in machinery parts like shafts and rods during stages of the steady-state rotation.
Inclusion of Fatigue Checks in Current IS Codes for Monopole …
505
The probability of the same sequence and magnitude of stress ranges occurring over a specific time interval is significantly lower in the second load history, known as the variable-amplitude loading history, and cannot be described by an analytical function. Numerous structures are subjected to this kind of loading, which includes wind loading for aircraft, towers, wave loading for ships and offshore platforms, and truck loading for bridges. S-N curves. S-N curves (see Figs. 2 and 3), which depict the relationship between the number of cycles, stress S, or stress range f f , due to the applied cycle load, are the most frequently used method to represent the fatigue testing data. Typically, the ordinate is S, the stress or stress range f f , or the logarithm of stress or stress range, and the abscissa is the logarithm of N. The nominal stress at the detail’s location is the only stress that needs to be calculated. One can utilize a typical standard S-N curve data set from IS 800 to evaluate the number of cycles for machinery whose cyclic loading data are known or can be obtained. This methodology is also followed in the Eurocode 3-1993. However, for the evaluation of wind-induced fatigue cycles, no proper methodology is available in Indian codes. A lot of fatigue testing needs to be done in order to gather this stress– strain data. This includes experimental trials and methods to obtain the stress–strain contours to obtain the actual data. So, in this research, authors are presenting a simple and theoretical way for the computation of fatigue cycles by taking reference of various country codes available. Fig. 2 S-N curve for normal stress [8]
506
K. A. Sahakari et al.
Fig. 3 S-N curve for shear stress [8]
According to IS 800, there are two methods for designing fatigue-resistant structural elements: “fail-safe” and “non-fail-safe”. The definition of a fail-safe structural component or detail is one where the local failure of one component owing to a fatigue crack does not cause the structure to fail since an alternate load pathway is available (referred to as a redundant system). A non-fail-safe structural component or detail is one whose non-redundant frame causes local failure of one component to ultimately cause the failure of the entire structure [8]. So, based on all the above stated literature, a methodology for fatigue check has been proposed.
3.2 Adopted/Proposed Methodology A simplified approach for the evaluation of fatigue has been presented. Step 1: Calculation of basic wind speed. According to the region where the chimney/tower is to be erected, the basic wind speed V b is defined as follows: It is the mean hourly speed, measured 10 m above the ground in an open, flat area free of obstacles, at the chimney location, which occurs around once every 50 years on average. Meteorological measurements must be used to determine the value of the basic wind. This data can be obtained from Annex A or using Fig. 1 of IS 875 (Part 3):2015 [9].
Inclusion of Fatigue Checks in Current IS Codes for Monopole …
507
Step 2: Calculation of design hourly mean wind speed. For various terrains, the hourly mean wind speed at height z can be calculated from Eq. (1) V z,H = k 2,i Vb
(1)
where k 2,i = Factor for hourly mean wind speed for varying terrain categories k 2,i
z (z 0,i )0.0706 = 0.1423 ln z 0,i
The design hourly mean wind speed at height z can be obtained from Eq. (2) V z,d = V z,H k1 k3 k4
(2)
where, k 1 = Probability factor k 3 = Topography factor. k 4 = Cyclonic region importance factor. All these values can be obtained from IS 875:2015 (Part 3) [9]. Step 3: Computation of frequency due to vortex shedding. The following Eq. (3) must be used to obtain the vortex shedding frequency fs for slender structures: fs =
StVz,H b
(3)
where St = Strouhal number, V z,H = hourly mean wind speed at height z, and b = breadth or diameter of a structure or structural member normal to the wind direction in the horizontal plane. • Circular structures St = 0.20 for DV z,H less than 6 m2 /s and = 0.25for DV z,H more than or equal to 6 m2 /s. • Rectangular structures, St = 0.10 This is in reference to IS 875:2015 (Part 3) [9]. Step 4: Computation of natural/resonant frequency in the first mode. The natural/resonant frequency which occurs in the first mode of vibration can be computed from Eq. (4) f 1 = 0.2
do √ E ck to 0.3 H2 ρck t H
(4)
508
K. A. Sahakari et al.
where t o = shell thickness at bottom, in m, t H = shell thickness at top, in m, H = z = height of structure, d o = centerline diameter of the shell at bottom, in m, ρ ck = mass density of concrete, kg/m3 , and E ck = dynamic modulus of elasticity of concrete, N/m2 In most cases, frequency (f 1 ) from only the first structural mode is prominent. However, the response to second mode vibration (frequency f 2 ) should also be evaluated for chimneys slender in nature with very low critical wind speed in the first mode. Frequency in the second mode of vibration is given by Eq. (5) f2 = 6 f1
dH tH do to
0.2 (5)
This is in reference to IS 4998:2015 [10]. Step 5: Computation of Critical Wind Speed (V cr ). The critical wind speed (V cr ) can be computed from Eq. (6) Vcr =
f1d St
(6)
where f 1 = natural/resonance frequency in the first mode, d = diameter of shell, in m, St = Strouhal number, This is in reference to IS 875:2015 (Part 3) [9] and CICIND “Model Code for Steel Chimneys revision 1-1999 amendment A-March 2002” [5]. Step 6: Computation of the number of cycles. The fatigue check must ensure that the movement caused by vortex shedding does not induce cracks and gradually spread throughout the material, especially close to welds, ultimately leading to a weakened part failing. If stress–strain contour data are available for wind loads, then stress–strain cycles can be obtained directly. It is possible to obtain the number of fatigue load cycles in the direction of the crosswind by using Eq. (7) if stress–strain data are not available directly. Equation (7) is not available in any Indian code; therefore, it is obtained from CICIND “Model Code for Steel Chimneys revision 1-1999 amendment A-March 2002” [5]. N = 1.26 × 107 × T × f 1 × A × e(−A
2
)
where N = Number of load cycles, T = Required lifetime of the chimney/tower in years, f = Resonance frequency, A = Distance of nearby chimneys in row arrangements, given by Eq. (8).
(7)
Inclusion of Fatigue Checks in Current IS Codes for Monopole …
A=
4 ∗ Vcr V z,d
.
509
(8)
V cr = Critical wind speed. V z,d = Design wind velocity V (z) at the top of the chimney/tower. Step 7: Fatigue assessment. The design fatigue strength for these N cycles may be obtained from S–N curves (Figs. 2 and 3). This is given by the Eq. (9) N ≤ 5 × 106
27μc γmft f feq
3 (9)
where N = Number of load cycles as obtained from Step 6, μc = (25/t p )0.25 = Correction factor for thickness of connecting plate, t p = Thickness of thicker plate in mm, γ mft = Partial safety factor for fatigue strength. f feq = Equivalent constant amplitude stress range in MPa corresponding to the connection detail at 5 × 106 number of life cycles as obtained from S–N curves. This is in reference to IS 800:2007 [8]. If Eq. (9) is satisfied, then no further fatigue assessment is required, or the structure is safe from a fatigue point of view.
4 Numerical Example Referring to the above-stated procedure, a solved example of a fatigue check has been presented for the structures under consideration.
4.1 Data Adopted Considering spun tower of 20 m. Diameter of shell, d or b = 807 mm = 0.807 m. Basic wind speed = 66.67 m/s. Return period for probability factor/lifetime of structure = 100 years. Probability factor, k 1 = 1.08. Topography factor, k 3 = 1. Cyclonic region importance factor, k 4 = 1. Grade of concrete for spun tower = M80. Modulus of elasticity of concrete for spun tower = 4.4721 × 1010 N/m2 .
510
K. A. Sahakari et al.
4.2 Solution Step 1: Calculation of basic wind speed. Basic wind speed = 66.67 m/s. Step 2: Calculation of design hourly mean wind speed. Height of structure, z = 20 m. Equivalent aerodynamic roughness height zo,1 = 0.002. k 2,i
z (z 0,i )0.0706 = 0.845 = 0.1423 ln z 0,i
Hourly mean wind speed at height z, V z,H = k 2,i V b = 0.845 × 66.67 = 56.33 m/s. Design hourly mean speed at height z can be obtained as follows: V z,d = V z,H k 1 k 3 k 4 = 56.33 × 1.08 × 1 × 1 = 60.83 m/s. Step 3: Computation of frequency due to vortex shedding. b = 0.55 m. For circular structures, D V z,H = 0.807 × 56.33 = 45.45 m2 /s. St = 0.25 for D V z,H more than or equal to 6 m2 /s. fs =
StVz,H 0.25 × 56.33 = = 17.45Hz b 0.807
Step 4: Computation of natural/resonant frequency in the first mode. t o = 0.13 m. t H = 0.1 m. H = z = 20 m. d o = 0.807 m. ρ ck = 2500 kg/m3 E ck = 4.4721 × 1010 N/m2
do √ E ck to 0.3 H2 ρck t H 0.807 √ 4.4721 ∗ 1010 0.13 0.3 = f = 0.2 = 1.84Hz 202 2500 0.1
f 1 = 0.2
Step 5: Computation of critical wind speed (V cr ). Vcr =
1.84 × 0.807 f1 d = Vcr = = 5.93 m2 /s St 0.25
Step 6: Computation of the number of cycles. T = 100 years. f 1 = 1.84 Hz.
Inclusion of Fatigue Checks in Current IS Codes for Monopole …
A=
4∗Vcr V z,d
=
511
4∗5.93 = 0.389 60.83
N = 1.26 × 107 × T × f 1 × A × e−A
2
= 1.26 × 107 × 100 × 1.84 × 0.389 × e−0.389
2
= 775, 211, 299 cycles Step 7: Fatigue assessment. Based on S–N curves, the number of load cycles, N, is found to be less than, N ≤ 5 × 106
27μc γmft f feq
3
Since the above equation is satisfied, then no further fatigue assessment is required, and the structure is safe from a fatigue point of view.
5 Conclusions Monopoles are widely used in modern wireless communication. Any steel stack structures or towers or chimneys require to be designed to minimize wind-induced fatigue. For concrete spun monopoles, the connection between two segments and the connection to the base is both made of mild steel and is either welded or bolted together. It is important to assess these connections for fatigue. In this instance, a monopole used for Tsunami Warning Tower was to be checked for fatigue. The fatigue check is used to ensure that the structure does not fail during high-velocity winds and that it continues to function during natural disasters. In general, not much research has been carried out to advance our understanding of wind-induced fatigue damage. Neither the CICIND, Australian codes nor the Eurocode methods have very accurate calibrations against experimental data. Since steel stack structures have more complex shapes, it is essential to develop an appropriate methodology for the evaluation of the same. Data provided by IS 800:2007 are also insufficient to check the structure against fatigue. As it is previously noted, when the stresses exceed either the constant stress range limit or the cut-off limit, comprehensive fatigue calculations are necessary. To carry out this kind of analysis, it is necessary to have reliable wind data. Therefore, even though the fatigue design actions are barely within the allowable limit, a thorough inspection routine for potential fatigue cracks in future needs to be implemented. A methodology for fatigue checks has been proposed by deriving pertinent data from IS codes and other country standards since NBC and other Indian codes fail to provide a systematic detailed procedure. This methodology can be used for steel tower-like structures or structures that include steel welded connection details. This report also includes a solved numerical as part of the investigation for the structures under consideration.
512
K. A. Sahakari et al.
References 1. Stavridou, N., Efthymiou, E., and Baniotopoulos, C.: Wind induced fatigue in tubular steel wind turbine tower welded joints. In: Cesare’17 Coordinating Engineering For Sustainibility And Resilience, pp. 1–10, Dead Sea, Amman, Jordan (2017) 2. Stavridou, N., Efthymiou, E., Baniotopoulos, C.: Welded connections of wind turbine towers under fatigue loading: finite element analysis and comparative study. Am. J. Eng. Appl. Sci. 8(4), 489–503 (2015) 3. Subramanian, N.: Design of Steel Structures. Oxford University Press, Oxford (2008) 4. Khatri, D.: Structural Failures of Wind Towers and Dynamic Analysis Procedures. URS Corporation, Los Angeles, CA (2009) 5. CICIND: Model Code for Steel Chimneys revision 1-1999 Amendment A-March 2002 6. Eurocode 1-Basis of Design and Actions on Structures—Wind Actions 7. AS 4100-1998 Australian Standard—Steel Structures 8. IS 800:2007–General Construction in Steel-Code of Practice 9. IS 875 (Part 3): 2015–Design Loads (Other than Earthquake) for Buildings and Structures -Code of Practice 10. IS 4998:2015 Design of Reinforced Concrete Chimneys-Criteria
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil for Gulf of Khambhat Region R. Singh Sujawat
and R. Kumar
Abstract The FOWIND consortium performed various feasibility studies to establish initial pathways for assessing the development of offshore wind power in Gujarat and Tamil Nadu, India. It paved the way for the researchers to investigate further the viability of various offshore wind turbines (OWTs) elements. A 200 MW project titled first offshore windfarm project in India (FOWPI) is planned in Zone-B off the coast of Pipavav port in Gujarat to demonstrate the risk issues involved before the large-scale implementation of offshore wind farms. This paper presents the development of a three-dimensional finite element model to simulate the monopile foundation of OWTs subjected to monotonic loading for the soil conditions of the Gulf of Khambhat. Soil properties are considered for the clayey soil obtained from the geotechnical investigation done for the LIDAR platform established at the site. Feasibility studies under FOWIND suggested three rating turbines of 4, 6, and 10 MW. Therefore, the current study considered the structural dimensions and material properties of monopiles for these three turbines. Response of all three monopiles has been evaluated for the serviceability limit. Further, p-y curves are developed for the monopile of each turbine, which is then compared with the conventional and recently developed p-y methods. Keywords Monopile · Offshore wind turbine · Monotonic loading · Finite element modeling
1 Introduction To achieve its target of a 5 trillion economy, India is planning its enormous demand for energy accordingly. Indian government wants to diversify its energy generation sector R. S. Sujawat (B) · R. Kumar Department of Earthquake Engineering, IIT Roorkee, Roorkee, India e-mail: [email protected] R. Kumar e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_40
513
514
R. S. Sujawat and R. Kumar
in offshore wind farms, considering the need to develop clean and renewable energy sources. A feasibility study has prioritized the Gujarat and Tamil Nadu states as suitable sites for establishing offshore wind turbines (OWTs). Currently, foundation systems used for OWTs are base, suction, cassion, monopile, tripod, or jacket/lattice foundations, in which monopile foundation is the most widely used foundation for offshore wind turbines [1]. Conventional design practices [2] apply the Winkler beam method to address the lateral loads on the monopile foundation. These practices are based on the [3] and [4]which propose the p-y curves for clay and sand, respectively, derived from the limited experimental results performed on the pile foundations for oil and gas (O&G) platforms. Unlike the monopile foundation for O&G platforms, which has a considerable length to diameter ratio (L/D), larger than 30, the monopile foundation for OWTs has a ratio of around 2–6 [5]. Therefore, there is a significant difference between monopiles used for O&G structures and monopiles for OWTs. A large L/D ratio leads to less flexible behavior, limiting the application of conventional API p-y curves for the design of the large diameter monopiles. Numerous studies have been done to analyze the feasibility of the API p-y curves for building monopile foundations for the offshore wind turbine. Numerical analysis performed by Abdel-Rahman and Achmus [6] shows that the API method underestimates the pile deformations and overestimates the initial stiffness of the soil. Further, the API method considered soil stiffness linear in-depth, while finite element modeling considered it as the square root of the depth [7]. The specific behavior of laterally loaded monopile can be captured more realistically by the rigorous 3D FEM studies as compared to the API p-y curves [8]. Along with the limitations mentioned above, there are shortcomings in the formulations of the API p-y curves, which further make its utilization uncertain. Studies done to develop the API p-y curves used soil data and a corresponding constitutive model which explicitly resembles that site’s conditions. Jeanjean [9] reanalyzed the API p-y curve for soft clay by investigating the lateral load behavior of the conductor connected to a floating structure. The study undertook the real-time loading effect on the offshore structure, and it demonstrates that the p-y curves suggested by API promote conservative design in members below mudline and non-conservative design in members above mudline. Further, OWTs are subjected to repetitive cyclic loads, so ignoring the fatigue design of its monopile foundations may not be a good practice. Considering the large-scale demand for green and clean energy along with the increase in the establishments of OWTs on the European coastlines, the PISA project was initiated in 2013. The project aims to develop improved design guidelines for laterally loaded piles [10]. Large-scale project comprises of ground characterization [11], medium scale field testing [12, 13], and numerical simulations [14, 15]. From the study, an original approach has been shown in which the conventional p-y curves complemented the new soil reaction components in addition to the distributed load, i.e., distributed moment, horizontal base force, and base moment. A pathway has been represented to develop the 1D model from the 3D finite element analyzes to reduce the required computational time. New soil reaction curves obtained help in the reduction of the overall cost of the project. Despite the intensive experiments, analyzes, and
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil …
515
simulations, the project is limited to only specific soil profiles. Therefore, further research should be conducted to use these soil reaction curves for other sites. Currently, India is planning to establish its first series of OWTs in the coastal region of Gujarat and Tamil Nadu. This paper presents the applicability of the conventional and newly developed soil reaction curves for the Indian offshore site conditions, specifically to the soft clay available in the Gulf of Khambhat. The study highlights the response of the monopiles under monotonic loading. Further, the soil reaction curves obtained from the FEM study have been compared with the conventional and recently developed p-y curves.
2 Finite Element Modelling To avoid the influence of model boundaries, dimensions of model are taken as 60 m × 60 m [7], and default boundary conditions are taken into account available in numerical platform which is sufficient to address the problem statement. A homogenous layer of soft clay is modeled for depth of 60 m below seabed level (Fig. 1). Three numerical models have been developed for three different rating of wind turbine, i.e., 4, 6, and 10 MW. Pile is modeled as an embedded beam placed in soil which is modeled as 10 nodded tetrahedral elements. Monopile is having properties of the hollow tubular section with dimensions as per the suggestion of [16]. The structural dimensions of monopiles are according to the support piles for wind turbines, as in Table 1. Embedded beam follows the constitutive relation of linear elastic beam having a unit weight of γ = 78 kN/m3 , Young’s modulus, E p = 200 GPa, and Poisson’s ratio, vp = 0.3. Total number of elements and nodes generated after meshing are 12,474 and 18,863, respectively.
Fig. 1 3D FEM mesh
516
R. S. Sujawat and R. Kumar
Table 1 Monopile dimensions Parameters
Symbol
Units
4 MW
6 MW
10 MW
Outer diameter
D
m
5.42
6.59
8.78
Thickness
t
m
0.08
0.09
0.12
Total length
L+h
m
61
64
71
Embedded length
L
m
41
45
52
Load eccentricity
h
m
20
19
19
3 Soil Model Due to the very limited availability of data at the initial stage of the project, the soil model is developed using simple hardening soil constitutive model, which can catch the nonlinear soil response under the monotonic loading of the pile [17]. Parameters of soft clay have been calculated using the estimated soil profile obtained from the previous experience of site, as shown in Table 2. To obtain the other parameters for the model, ε50 and su are used. Here, ε50 is the strain at one-half of maximum deviatoric stress in laboratory undrained compression tests on undisturbed cohesive soil samples, and su is the undrained shear strength assumed to be linearly varying from the top surface at a rate of 1.5 kN/m2 /m. Stiffness of the clay can be calculated through E i = initial tangent modulus, which is related to ε50 using hyperbolic curve fitting expression Eq. (1), suggested by Kondner and Zelasko [18]. ε50 =
1 2 − Rf
σf Ei
(1)
where Rf = ratio of the deviatoric failure stress to deviatoric ultimate stress taken as 0.9; σ f = deviatoric failure stress given as 2*su. Relations for stiffness-related characteristics can be defined using equations mentioned in the PLAXIS manual. Stiffness modulus for immediate loading, E 50 depending on confining stress, is evaluated using Eq. (2). Ei =
2E 50 2 − Rf
(2)
Oedometer stiffness modulus is obtained with the help of Hooke’s law given by Brinkgreve [19]. Table 2 Indicative soil profile
Soil type
γsub (kN/m3 )
S u (kPa)
ε50
Clay
7.5
10–30
0.01
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil …
E 50 =
(1 − 2v)(1 + v) E oed 1−v
517
(3)
For addressing the loading and unloading path, load-reload stiffness, E ur is used, which is derived from relation as per PLAXIS manual. E ur = 3 × E 50
(4)
Since the soil is considered as pure cohesive soil, corresponding reference moduli Eqs. (5–7) is equal to their original moduli, which relates with the help of power function given in the PLAXIS manual. ⎛ ref E oed = E aed ⎝
⎛ ref E oed = E aed ⎝
ref E ur = E ur
cosϕ −
⎞m
σ3 Ka N C
sinϕ
cosϕ + Pa · sinϕ
cos ϕ −
σ3 Ka N C
⎠
sin ϕ
cos ϕ + Pa · sin ϕ
ccos(ϕ) − σ3 sin(ϕ) ccos(ϕ) + prefsin(ϕ)
(5)
⎞m ⎠
(6)
m (7)
The model considers a gap formation between soil and pile when the pile is laterally loaded. Interfacial strength reduction is considered between pile and soil surface to account for the slip between them. Initial soil conditions are accounted for with the over consolidation ratio obtained from the correlation given by Eq. (8) from [20] ε50 = 0.85qc + 0C R − 4.5
(8)
Here, qc is the cone tip resistance given in Eq. (9) ε50 = 0.86qc − 0.5
(9)
4 Data Processing Soil reaction curves demonstrate the soil resistance p as a function of deflection y for the pile at any depth below the ground surface. To obtain the soil reaction curves at any given depth x, a set of differential equations are used, as shown in Eqs. (10–13). Considering a particular load case, the bending moment and corresponding displacements in the direction of lateral loading of the pile at different depths are obtained
518
R. S. Sujawat and R. Kumar
from the numerical model. 5th order polynomial curve fits the bending moment trend along the depth. The fitted equation obtained is then further solved to give shear force and soil resistance along the pile depth. Similarly, the displacement profile is fitted with the polynomial of seventh order from the embedded beam deflection data, and the equation obtained can be used to evaluate the displacements at the required depth. The slope of pile deflection (S): S=
dy dx
(10)
Bending moment along the pile (M): M = EI
d2 y dx 2
(11)
Shear force along the pile (V ): V =
dM dx
(12)
p=
d2 M dx 2
(13)
Soil resistance (p):
Here, E = Pile Young’s modulus. I = Pile moment of inertia.
5 Results and Discussion The behavior of all three monopiles has been analyzed under increasing lateral loading conditions. For assessing the stability of wind turbines, specific conditions need to be considered, in which deflection and rotation at the foundation level are considered as the most crucial requirement. Serviceability limit state demands maximum allowable mudline deflection for monopile foundation which is 0.5° [16]. This lower value of rotation corresponds to the small strain behavior of soil. Therefore, the observed trend between bending moment and rotation is linear, which is true in the case of significant or ultimate displacement response. The current numerical study determines the lateral load at which the suggested monopile will reach its serviceability criteria. Figure 2 shows the relationship between the bending moment and ground-level measured rotation. Due to greater section modulus, 10 MW wind turbine’s monopile is having largest moment capacity of 19 MNm at serviceability
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil …
519
25
Fig. 2 Bending moment versus rotation of monopile at mudline level
Bending Moment (MNm)
19 MNm
20 15.2 MNm
15
12 MNm
10
5
4 MW 6 MW 10 MW
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Rotation at ground level (degrees)
limit. Similarly, the required moment demand of monopile for 4 and 6 MW wind turbines to reach rotation of 0.5° is 12 MNm and 15.2 MNm, respectively. Further, all three monopile foundations responses along the depth are obtained. Incremental lateral load is applied at the monopile head in different stages. Accordingly, the deflection and bending moment profiles of monopile foundation along the depth have been extracted from the numerical study. Figure 3 represents the responses of monopile foundation corresponding to 0.5° rotation. Figure 3a, b represents the deflection and rotation profiles of monopile foundations, respectively. The deflection profile is fitted with the 7th-order polynomial. The rotational profile is then evaluated with the help of Eq. (9). As stated, the rotation is constrained at a value of 0.5° which is self-evident from Fig. 3b. Despite the different diameters and lengths, the ground level displacement of all three monopile is very close to each other, having a value of 8.1 mm. However, the displacement profile keeps on changing its profile along the depth. This can be explained because there is difference in soil reaction along the depth which depends on monopile diameter and embedded depth which is responsible for changing the alignment of monopile in the soil. Point of rotation for 4 MW, 6 MW, and 10 MW is 24, 27, and 32 MW, respectively. Extracted bending moment profile is fitted with the fifth order polynomial, and using Eq. (12), the shear force profile along the depth is evaluated. Figure 3c, d shows the bending moment and shear force profile, respectively. The observed bending moment at the ground level is equal to the applied bending moment due to the lateral load at pile head. Similarly, the observed shear force equals the applied lateral load at the pile head. Soil reactions at a depth of 5 m are evaluated for monopile of 4 MW wind turbine from the numerical model with the help of Eqs. (10–13). Obtained soil
520
R. S. Sujawat and R. Kumar
b 0
-10
-10
-20
-20
Depth(m)
Depth(m)
a 0
-30
-30
-40
-40
-50
-50
-60 -4
-2
0
2
4
6
8
-60 -0.4
10
Displacement (mm)
-10
-10
-20
-20
Depth(m)
Depth(m)
0
-30
0.4
0.6
-30
-40
-40
-50
-50
-60 -15
0.2
d
c
-20
0.0
Rotation (degrees)
0
-25
-0.2
-10
-5
0
-60 -1.2 -0.8 -0.4 0.0 0.4 0.8 1.2
Shear Force (MN)
Bending Moment (MNm) 4 MW
6 MW
10 MW
Fig. 3 Measured displacement, rotation, bending moment, and shear force at 0.5° rotation
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil … 2000
Soil Resistance (kN/m)
Fig. 4 Comparison of FEM p-y curve with the API, ISO, and PISA for monopile of 4 MW wind turbine embedded in the soft clay at depth of 5 m
521
1500
API ISO PISA FEM
1000
500
0
0.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0.32
Displacement (m)
reaction is then plotted against the displacement of monopile for different loading stages. These curves are then compared with the conventional API and recently developed ISO and PISA curves. Figure 4 represents the comparison of all four curves, and it is observed that soil reaction curves obtained for the present FEM study have a significant difference from the other p-y curves. This difference can be explained because of the variation of soil parameters for clayey soil. API method has been developed on the slender piles embedded in the Sabine River [3]. New ISO method derived the soil reaction curves from the centrifuge test performed on the clayey soil found in the Gulf of Mexico [21]. While PISA method developed their 1D model for p-y curve using site condition of Cowden [10]. Whereas obtained parameters for clayey soil found in Indian offshore situations resemble an entirely different soil condition, parameters of which can be observed in Table 2.
6 Conclusions A preliminary numerical model has been developed to investigate the feasibility of existing design curves of the monopile foundation for OWTs in Indian offshore site situation. The site is considered one of the designated locations for establishing new offshore wind farms in India. Responses of monopiles under monotonic loading have been extracted. From the classical method, soil reaction curves are derived which is
522
R. S. Sujawat and R. Kumar
then compared with the already developed p-y curves. The following observations have been made in this numerical study: • Corresponding to the serviceability criteria mentioned in the [2], the required moment capacity at the ground level for 4 MW, 6 MW, and 10 MW wind turbines is 12, 15.2, and 19 MNm, respectively. • At any fixed rotation, performance of monopile in terms of displacement at ground level remains same irrespective of the monopile dimensions. • Soil reaction curves derived for the site under consideration show a considerable quantitative difference from the soil reaction curves in practice. Therefore, it is suggested that the recommended soil reaction curves should be reconsidered for the design of monopile foundations for the OWFs in India. It is proposed that a thorough site-specific study should be performed comprising of ground characterization and physical modeling. Accordingly, revised soil reaction curves should be developed using the site-specific behavior and already available methodologies in the literature.
References 1. O’Kelly, B.C., Arshad, M.: Offshore wind turbine foundations - analysis and design. In: Offshore Wind Farms: Technologies, Design and Operation, Elsevier Inc., pp. 589–610 (2016). https://doi.org/10.1016/B978-0-08-100779-2.00020-9 2. API: Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms—Working Stress Design (2000) 3. Matlock, H.: Correlation for Design of Laterally Loaded Piles in Soft Clay (1970). https://doi. org/10.4043/1204-MS 4. Reese, L.C., Cox, W.R., Koop, F.D.: Analysis of Laterally Loaded Piles in Sand (1974). https:// doi.org/10.4043/2080-MS 5. Beuckelaers, W.: Numerical Modelling of Laterally Loaded Piles for Offshore Wind Turbines (2017) 6. Abdel-Rahman, K., Achmus, M.: Finite element modelling of horizontally loaded monopile foundations for offshore wind energy converters in Germany. In: Frontiers in Offshore Geotechnics, ISFOG 2005—Proceedings of the 1st International Symposium on Frontiers in Offshore Geotechnics, pp. 391–396 (2005). https://doi.org/10.1201/noe0415390637.ch38. 7. Bekken, L.: Lateral Behavior of Large Diameter Offshore Monopile Foundations for Wind Turbines (2009) 8. Kim, Y., Jeong, S.: Analysis of soil resistance on laterally loaded piles based on 3D soilpile interaction. Comput. Geotech. 38(2), 248–257 (2011). https://doi.org/10.1016/j.compgeo. 2010.12.001 9. Jeanjean, P.: OTC 20158 Re-Assessment of p-y Curves for Soft Clays from Centrifuge Testing and Finite Element Modeling (2009). Accessed 17 Aug 2022. [Online]. Available: https://doi. org/10.4043/20158-MS 10. Byrne B.W., et al.: PISA: New Design Methods for Offshore Wind Turbine Monopoles (2017) 11. Zdravkovic, L., et al.: Ground characterisation for PISA pile testing and analysis. Geotechnique 70(11), 945–960 (2020). https://doi.org/10.1680/jgeot.18.PISA.001 12. Byrne, B.W., et al.: Monotonic laterally loaded pile testing in a dense marine sand at Dunkirk. Geotechnique 70(11), 986–998 (2020). https://doi.org/10.1680/jgeot.18.PISA.004
Behavior of Monopiles for Offshore Wind Turbines in Clayey Soil …
523
13. Burd, H.J., et al.: New data analysis methods for instrumented medium-scale monopile field tests. Geotechnique 70(11), 961–969 (2020). https://doi.org/10.1680/jgeot.18.PISA.002 14. Zdravkovic, L., et al.: Finite-element modelling of laterally loaded piles in a stiff glacial clay till at Cowden. Geotechnique 70(11), 999–1013 (2020). https://doi.org/10.1680/jgeot.18.PIS A.005 15. Taborda, D.M.G., et al.: Finite-element modelling of laterally loaded piles in a dense marine sand at Dunkirk. Geotechnique 70(11), 1014–1029 (2020). https://doi.org/10.1680/jgeot.18. PISA.006 16. FOWIND, “Feasibility study for offshore wind farm development in Gujarat,” 2018 17. Murphy, G., Igoe, D., Doherty, P., Gavin, K.: 3D FEM approach for laterally loaded monopile design. Comput. Geotech. 100, 76–83 (2018). https://doi.org/10.1016/j.compgeo.2018.03.013 18. R Kondner, R. L., Zelasko, J. S.: A hyperbolic stress-strain formulation of sands. In: Proceedings of the 2nd Pan American Conference on Soil Mechanics and Foundation Engineering, pp. 289– 324 (1963) 19. Brinkgreve, R.: PLAXIS 3D Reference Manual (2013) 20. Ebrahimian, B., Nazari, A., Pasha, A.Y.: Evaluating ε50 for lateral load-displacement behavior of piles in clay. Ocean Eng. 96, 149–160 (2015). https://doi.org/10.1016/j.oceaneng.2014. 12.027 21. Jeanjean, P., Zakeri, A., Zhang, Y., Andersen, K.H.: The New ISO/API p-y Curves in Clays and their Reconciliation with the PISA Framework (2022). https://doi.org/10.4043/31860-ms
Linear Spring Constants of Soil for Pile Groups for the Nuclear Power Plants Mohd Firoj and B. K. Maheshwari
Abstract The nuclear power plants are very massive and stiff structures. For such structure when founded on soft layered soil mass, the soil-structure interaction (SSI) has significant influence to the seismic response. Most of the existing nuclear power plants in India are constructed on rock which may not have the requirement of seismic soil-structure interaction analysis but some of the upcoming nuclear power plants will be founded on the alluvial soil necessitating to consider SSI. The pile foundation will be appropriate for nuclear power plants and high-rise buildings in the soft soil conditions and subjected to earthquake loading because of its effectiveness in load distribution to soil. In this research, simplified linear spring constants of soil are proposed to simulate the behavior of pile group foundation. These springs shall take care of pile-soil-pile interaction, i.e., group effect. The pile group is modeled as an embedded beam element with the finite element discretization. In order to verify the validity of the proposed linear spring constants, computed response (in terms of bending moment, shear force, and deflection) is compared with the published results, where the soil is modeled as a continuum using the finite element method. The good agreement achieved shows that the proposed method provides a simple and use-full tool for engineering design of pile groups. Keywords Bending · Deflection · Finite element method · Nuclear power plants · Pile group · Spring constant
1 Introduction The pile foundation is much used under the multistory structure, flyover, nuclear power plants, etc. In the field, pile load test is performed to estimate the pile head M. Firoj (B) · B. K. Maheshwari Department of Earthquake Engineering, IIT Roorkee, Roorkee 247667, India e-mail: [email protected] B. K. Maheshwari e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_41
525
526
M. Firoj and B. K. Maheshwari
displacement subjected to lateral loading. In addition to these field tests, numerical analysis of 1D and 3D pile group is performed by the many researcher [1–4]. For 1D model, Winkler’s spring [5] is widely used for the pile, where the soil is modeled by the linear spring. Kumar and Lalvani [6] used the p-y curve for the nonlinear modeling of pile group. The laterally loaded pile group is analyzed by the continuum elastic medium [7]. Nonlinear p-y spring is also used by the many researchers to define the soil reaction along the length of pile [8, 9]. However, finding representative p-y curves for the layered soil mass from the accessible site data can normally be challenging. The aim of present study is to develop the simplified spring constant for the pile group of large structure such as nuclear power plants so as to reduce the computation time period of the computer program. In this study, a 1D model of single pile is selected to verify the accuracy of the proposed spring constant with the well published literature. After that a 3D model of group pile is prepared by the finite element modeling of piles, cap, and soil modeling by the proposed spring constant. For the 1D single pile, the spring constant k s is calculated by the many researcher using the correlation of Young’s modulus [10, 11] based on experiential data.
2 Description of Single Pile and Pile Group The model of single pile was taken from the Rani and Prashant [12]. A single pile of 2.4 m diameter (D) and 31.5 m length of 9.58GPa Young’s modulus is considered in this study. The length of pile was considered 30 m embedded into the soil, however, 1.5 m was considered above the ground surface. For 1D modeling, Beam on Winker Foundation is used by attaching the series of linear springs along the embedded length of the pile at an interval of 0.25 m as shown in Fig. 1. The material behavior of the soil and pile is considered in the linear elastic range. To analyze the lateral behavior of pile, end bearing pile is used which is kept fixed at the base, and a horizontal force (P) is applied 0.5 m above the ground surface. In order to check the availability of the proposed spring constant for the single pile, a 3D pile group system is reproduced using the spring constant model as reported by Kumar et al. [13] with the finite-volume-based PLAXIS 3D and examined under the pseudo static horizontal loading. Figure 2 provides a schematic demonstration of the pile group presenting the location of applied load and discretized FE mesh, along with its proportions. The springs are attached at an interval of 0.5 m. A square cap of 4 m width and 1 m thickness was demonstrated as a shell element. Four end bearing piles having length of 9 m, 500 mm in diameter, and a center-tocenter spacing of 2 m were modeled with the use of beam element in the library of ABAQUS, as shown in Fig. 2. The neighboring soil was modeled by the series of proposed linear springs contents in both horizontal directions.
Linear Spring Constants of Soil for Pile Groups for the Nuclear Power …
527
Fig. 1 1D laterally load linear spring constants model of single pile
Fig. 2 Schematic illustration and finite element model of pile group
3 Verification of Single Pile Model In the present study, the single pile model was validated with the closed form solution given by Hetényi [14] and Rani and Prashant [12] for a homogenous soil profile with constant Young’s modulus (E soil = 565,000 kN/m2 ) throughout the length of the pile. The ground level deflection was calculated for the embedded pile length which is subjected to the 2 MN horizontal force at the surface level.
528
M. Firoj and B. K. Maheshwari
The shear forces and bending moments observed from the single pile model were matched with [14] closed form results and Rani and Prashant [12] and were also found to match closely as shown in Fig. 3a, b. The spring constant used by the Rani and Prashant [12] and in Present study is given in Table 1. Hetényi [14] gives the closed formed solution of beam on elastic foundation. The length of element in the proposed spring constant was calculated based on the mesh size sensitivity analysis by providing the spring constant at regular intervals along the embedded length of pile. The different intervals chosen were 2 m, 1 m, 0.5 m, and 0.25 m. The overall variation in the response was found to be about 10%. Pile deflection along the length of pile models is shown in Fig. 3c, in which spring constant k x is taken by the Young’s modulus of elasticity E soil . Zhang et al. [15] reported through a relative study that the lateral deflection of the pile is mainly precise by the spring constant chosen for the soil at the embedded length of 3D to 5D. Where D is diameter or width of pile. As it is clear from the Fig. 4 that the deflection is zero at the depth of 8 m which is showing the good acceptance of the proposed spring constant.
4 Verification of Pile Group Model In this study of group pile, the soil having Young’s modulus of 40,000 kN/m2 was modeled using the spring constant as calculated from the Table 1. The total vertical load applied at the pile cap was 5.86 MN, and the lateral load was calculated by multiplying the seismic coefficient for earthquake event to the vertical load to obtain the equivalent pseudo static lateral force, deprived of any soil amplification. Figure 4 shows the normalized horizontal displacement throughout the normalized depth of pile. In this study, linear spring constant is compared with the nonlinear finite element modeling of pile group foundation. The normalized pile head displacement calculated in linear analysis is 0.0053, while in finite element analysis, it is 0.0075. The nonlinear analysis is showing the higher displacement as compared to linear analysis, this is due to the reduced strength during the nonlinear behavior.
5 Conclusions In the present study, 1D single pile and 3D group pile of nuclear power plants were investigated using the finite element program ABAQUS under the lateral loading. It was noted during the analysis of group pile, continuum soil model taken more computation time and space as compared to proposed spring constant model. The numerical finite element study of single pile and group pile with attached spring constant is provided the good agreement with past study where the soil was modeled as continuum. For a large structure such as nuclear power plant requires the more computation time period, these linear spring constants can be a useful tool for solving
Linear Spring Constants of Soil for Pile Groups for the Nuclear Power …
(a) Shear Force
(b) Bending Moment
(c) Deflection Fig. 3 Shear force, bending moment, and deflection along the embedded depth of pile
529
530 Table 1 Spring constants from Young’s modulus of soil
M. Firoj and B. K. Maheshwari Sl. No.
Author
1
Rani and Prashant [12]
2
Present study
Correlation 0.15 soil k x = 5 × EEpile × E soil kx = E soil × Length of Element
Fig. 4 Normalized horizontal displacement of pile
large problem in short period of time. The nonlinear analysis shows the significant effect on the response of structure, i.e., linear analysis underestimates the displacement demand of group pile. Therefore, nonlinear behavior of soil has significant role in laterally loaded pile of NPP structure.
References 1. Basu, D., Salgado, R.: Elastic analysis of laterally loaded pile in multi-layered soil. Geomech. Geoeng. 2(3), 183–196 (2007) 2. Maheshwari, B.K., Truman, K.Z., Gould, P.L., El Naggar, M.H.: Three-dimensional nonlinear seismic analysis of single piles using finite element model: effects of plasticity of soil. Int. J. Geomech. 1(35), 35–44 (2005) 3. Matlock, H.M., Reese, L.C.: Generalized solutions for laterally loaded piles. Trans. Am. Soc. Civ. Eng. 127(1), 1220–1247 (1962) 4. Poulos, H.G.: Behavior of laterally loaded piles: I-single piles. J. Soil Mech. Found. Div. 97(5), 711–731 (1971) 5. Winkler, E.: Die Lehre von der Elasticitaet und Festigkeit. Dominicus, Prague (1867) 6. Kumar, S., Lalvani, L.: Lateral load–deflection response of drilled shafts in sand. Int. Eng. J. 84, 282–286 (2004) 7. Poulos, G., Davis, H.: Pile Foundation Analysis and Design. Wiley, New York (1980)
Linear Spring Constants of Soil for Pile Groups for the Nuclear Power …
531
8. Ismael, N.F.: Behavior of laterally loaded bored piles in cemented sands. J. Geotech. Engrg. ASCE 116(11), 1678–1699 (1990) 9. Reese, L.C., Van Impe, W.F.: Single Piles and Pile Groups Under Lateral Loading. CRC Press (2000) 10. Matlock, H.: Correlations for design of laterally loaded piles in soft clay. In: Proceeding, 2nd Offshore Techniques Conference, vol. 1, pp. 577–594. Houston (1970) 11. Terzaghi, K.: Evaluation of subgrade reaction. Géotechnique 5(4), 279–326 (1955) 12. Rani, S., Prashant, A.: Estimation of the linear spring constant for a laterally loaded monopile embedded in nonlinear soil. Int. J. Geomech. 15(6), 04014090–04014113 (2014) 13. Kumar, A., Choudhury, D., Katzenbach, R.: Effect of earthquake on combined pile–raft foundation. Int. J. Geomech. 16(5), 04016013 (2016) 14. Hetényi, M.: Beams on Elastic Foundation. University of Michigan Press, Ann Arbor, MI (1946) 15. Zhang, L., Zhao, M., Zou, X.: Behavior of laterally loaded piles in multilayered soils. Int. J. Geomech. 15(2), 06014017–06014027 (2013)
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static Seismic Load V. Sharma , D. Raj , and R. Gupta
Abstract In general, two-dimensional slope stability methods assume the slope material as homogeneous, isotropic, and horizontally distributed, which is rarely true in reality. When the slope has complex geometry (sharp ridges, corners, cut and fill slopes, unplanned excavations, etc.), heterogeneous distribution of materials (along with depth and in out of plane direction), and complex loading conditions (seepage and seismic loading), a three-dimensional analysis for slope stability is preferred. In this article, a numerical study was conducted to access the stability of the 3D slope under bi-directional seismic loads using the simplified pseudo-static method. The strength reduction technique is employed in a finite element framework to obtain the failure surface and factor of safety (FoS). A parametric study was performed considering four generic slopes having different complex three-dimensional geometries with similar cross sections, soil properties, and boundary conditions to understand the variation in failure surface and FoS. The FoS obtained from the present study is plotted against the horizontal seismic coefficient applied in both lateral directions. As evident, the FoS is found to be decreasing rapidly with increasing horizontal seismic coefficients. Keywords 3D slope stability · Strength reduction method · Bi-directional seismic load
1 Introduction Hilly regions in Indian Himalayas cover far north (Jammu & Kashmir) to distant east (Mizoram) India. These hilly regions have always been a center of attraction for people residing in densely populated towns and cities with relatively flat grounds. Due to a rapid increase in population and limited employment opportunities in the past few decades, the hilly regions have also witnessed a lot of construction activities to V. Sharma · D. Raj (B) · R. Gupta Department of Civil Engineering, MNIT Jaipur, Jaipur, Rajasthan 302017, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_42
533
534
V. Sharma et al.
cater residential demands including houses, residential villas and hotels; commercial demands including shopping malls, cinema halls, theme parks, zoos; public utilities including towers for telecommunication and power distribution, aerial ropeways, etc. Most of these hilly regions are densely populated and overloaded with structures built adjacent to each other. In addition, these hilly areas are also located in seismically active zones, e.g., Darjeeling (West Bengal) and Mussoorie (Uttarakhand) both are located in seismic zone IV. Figure 1a, b shows the cracks developed in foundations of the building built on the downside and upside of the slope, respectively. In the hilly terrains, the leading causes of slope instability are (a) increase in the applied stress and (b) reduction in the strength of slope materials. When the buildings/structures are constructed on a slope in a hilly area, the foundations underneath Fig. 1 Crack in the foundation of: a downside hill building; and b upside hill building, in Nainital
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static …
535
the building transfer the load to slope and increase the applied stress which in turn may cause failure of hill slope in the following three ways [1]: Firstly, a local failure may occur only under the column footing near the slope; or secondly, the slope may fail overall, including all the structures built on it; or thirdly, a mixed failure mode of the above two may be observed [2]. In the past, several researchers [3–7] have used limit equilibrium approach for analyzing the slope stability in two dimensions. Generally, in 2D slope stability analysis, the homogeneous and isotropic slope materials are assumed as horizontally distributed in out of plane direction, and slopes are subjected to planer loading (seismic load, imposed load from the structure, pore water pressure, etc.), which is hardly found in actual field condition. To deal with the above-mentioned conditions, a 3D analysis is preferred, where the slope geometry is complex (include narrow failure surfaces, ridges or corners, slopes cut by excavations, etc.) in all direction, having heterogenous and anisotropic material with significant changes in out of plane direction, and the existing 2D methods are incapacitated. From the past studies [8–14], it has been found that the factor of safety (FoS) obtained from 3D slope stability was greater than the FoS in 2D analysis for the same slope. In addition, stability analysis of multiple number of 2D cross sections of slope is required to access the stability of entire complex 3D slope geometry. Being a more realistic approach, the advantages of a 3D slope stability analysis are consideration of complex boundary conditions, geometry, loading, and inclusion of other 3D structures appropriately. This enhanced the accuracy of the results by inclusion of realistic simulation of the slope failure mechanism by considering the three-dimensional effect of seismic loading in both horizontal and vertical directions. In this article, a numerical study has been conducted to access the stability of the 3D slope under bi-directional seismic loads using the simplified pseudo-static method. The strength reduction technique is employed in finite element framework using proprietary software ABAQUS [15] to obtain the failure surface and FoS. A parametric study has been performed considering four generic slopes having different 3D geometries with similar 2D cross sections, soil properties, and boundary conditions. The results of the present study are represented as variation in FoS with the horizontal seismic coefficient applied in both lateral directions. In reality, the hilly slopes are bound to have heterogeneous soil properties; however in this article, slopes with homogeneous soil properties are analyzed, as the objective of the present study is to explore the variation in FoS with bi-directional horizontal seismic force.
2 Numerical Study In the present study, four homogeneous slopes (convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope, and concave turning arc 90˚ slope, as shown in Fig. 2) with the same dimensional properties; slope angle, β = 26.57˚ (2H:1 V) and slope height, H = 12 m, have been considered. Table 1 shows the material properties considered in this study.
536
V. Sharma et al.
Fig. 2 3D view of: a convex 90˚ slope; b concave 90˚ slope; c convex turning arc 90˚ slope; d concave turning arc 90˚ slope
Table 1 Soil properties [16]
S. No.
Property
Value
1
Cohesion, c
29 kPa
2
Friction angle (φ)
20˚
3
Slope angle (β)
26.57˚
4
Unit weight of soil (γ )
1880 kg/m3
5
Young’s modulus (E)
10 MPa
6
Poisson’s ratio (ν)
0.25
To explore the variation in failure surface and FoS, different slopes are considered under the action of gravity loading along with either varying uni-directional seismic loading (horizontal seismic coefficients, in x-direction α hx or z-direction α hz ) or varying bi-directional seismic loading (horizontal seismic coefficients, in x-direction α hx, and z-direction α hz ).
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static …
537
3 FE Modeling and Analysis In the present study, 3D finite element analysis (FEA) based on strength reduction method (SRM) has been performed to evaluate the FoS of considered slopes under bi-directional seismic loading using ABAQUS [15]. In this method, the material parameters are reduced by a strength reduction factor at each step, until a state of instability of slope is achieved [17–19]. The existing SRM has been modified and implemented in ABAQUS, based on the work of Xu et al. [20] by introducing the field variable representing an incremental step time, and controlling parameter to reduce the values of c and φ of soil in subsequent steps. The static FoS found from the current method is in good agreement with the work of Zhang et al. [16] for the slopes used in this article with similar geometry for rough-rough boundary conditions, i.e., the side faces of the slope were constrained from movement in any direction, while the only normal directional movement was restricted for the front and back faces of the slope. An elasto-plastic constitutive model based on Mohr–Coulomb failure criterion and following non-associated flow rule has been used for soil modeling in FEA. The 3D FE model of the soil mass has been discretized with 8-noded brick element with reduced integration (C3D8R) elements, as available in ABAQUS element library (Fig. 2). The lateral extent of FE model has been considered using a sensitivity study and recommendation from past studies, so that the effect of boundary conditions on the FoS is insignificant. At the base of the FE model of the slope, the movements in all directions are restrained (i.e., displacements are zero). The lateral boundary conditions of all the four slopes were considered to be rough-rough. To simulate the seismic effect on the slope, pseudo-static forces have been applied on the entire soil mass, in terms of horizontal seismic coefficients, α hx and α hz . For seismic analysis, each of the considered slope has been analyzed till under the influence of critical acceleration (α c ) [21, 22]: αc = (FoSS − 1) × g × sin β
(1)
where FoSS = static factor of safety, g = acceleration due to gravity, β = slope angle. As per IS 1893 (Part 1): 2016 [23], the combination of bi-direction seismic loading, taken as 100% in one direction and 30% in relative orthogonal direction, is used for seismic analysis. All the considered slopes have been analyzed under the action of either gravity loading and varying uni-directional seismic loading (α hx or α hz in multiple steps) or gravity loading with the bi-directional seismic load combinations (α hx + 0.3 × α hz ; α hx + α hz and 0.3 × α hx + α hz in multiple steps). A total sixty-six number of analyzes have been performed for each considered slopes.
538
V. Sharma et al.
4 Results and Discussion As mentioned earlier, the prime objective of the present study is to understand the failure surface and variation in FoS of four different complex 3D slopes (convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope, and concave turning arc 90˚ slope) subjected to combined action of gravity and seismic loading. The results of the present study, highlighting the influence of bi-directional seismic loading on slope stability, are discussed here in detail. Figure 3a–d shows the failure surface represented by strain rate (ER) profile for convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope, and concave turning arc 90˚ slope under gravity load only, respectively. Similarly, Fig. 3e–h shows the failure surface represented by strain rate (ER) profile for convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope, and concave turning arc 90˚ slope under the influence of seismic loading α hx = 0.24 g, α hz = 0.072 g, respectively. It can be noted from the figures that (comparing left column to right column of Fig. 3) the failure surface of the slope changes with increasing combination of seismic loading, as the involvement of soil mass in the failure surface also increases. Figure 4a–d shows the resultant displacement (U) profile for convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope and concave turning arc 90˚ slope under gravity load only, respectively. Similarly, Fig. 4e–h shows the resultant displacement (U) profile for convex 90˚ slope, concave 90˚ slope, convex turning arc 90˚ slope and concave turning arc 90˚ slope under the influence of seismic loading α hx = 0.24 g, α hz = 0.072 g, respectively. By comparing left column to right column of Fig. 4, it is interesting to note that that the resultant displacement (U) for the slopes increase with increasing applied seismic load combination. Figure 5a–d shows the variation in FoS for convex 90˚ slopes, concave 90˚ slopes, convex 90˚ turning arc slope, and concave 90˚ turning arc slope, respectively, with increasing bi-directional seismic load combinations (α hx + 0.3 × α hz , α hx + α hz and 0.3 × α hx + α hz in multiple steps). Figure 5a–d also shows the variation in FoS for 2D section of the 3D convex 90˚ slopes, concave 90˚ slopes, convex 90˚ turning arc slope, and concave 90˚ turning arc slope, respectively, with increasing uni-directional seismic load (α hx or α hz in multiple steps). It can be noted that in all the cases, FoS is drastically reducing with increasing horizontal seismic coefficients α hx and α hz . The FoS for 3D slope (convex and concave turning arc 90˚ slope) was found always higher than the corresponding 2D slope section.
5 Conclusions In this article, a parametric study has been conducted to understand the behavior of four 3D slopes having different 3D geometries with similar 2D cross sections, soil properties, and boundary conditions, under bi-directional seismic loads, using the simplified pseudo-static method. Modified strength reduction technique has been
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static …
539
Fig. 3 Failure surface represented by strain rate (ER) profile for: a convex 90˚ slope under gravity load only, b concave 90˚ slope under gravity load only, c convex turning arc 90˚ slope under gravity load only, d concave turning arc 90˚ slope under gravity load only, e convex 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, f concave 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, g convex turning arc 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, and h concave turning arc 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g
540
V. Sharma et al.
Fig. 4 Resultant displacement (U) profile at failure for: a convex 90˚ slope under gravity load only, b concave 90˚ slope under gravity load only, c convex turning arc 90˚ slope under gravity load only, d concave turning arc 90˚ slope under gravity load only, e convex 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, f concave 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, g convex turning arc 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g, and h concave turning arc 90˚ slope under the influence of α hx = 0.24 g, α hz = 0.072 g
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static …
2.2
2.0
2.0
1.8
1.8
FOS
2.4
2.2
FOS
2.4
1.6
1.6
1.4
1.4 0.6
0.6
1.2
1.2
0.5
2D
1.0
0.4
0.1
0.3
0.3
0.1
0.5
0.6
0.3
0.1
0.4 αhx (g)
0.0
αhz (g)
0.2
0.2
0.1
0.4 αhx (g)
0.4
0.0
αhz (g)
0.2
0.2
0.5
2D
1.0
0.3
0.0
(a)
0.5
0.6
0.0
(c)
2.4
2.2
2.2
2.0
2.0
1.8
1.8
FOS
2.4
FOS
541
1.6
1.6
1.4
1.4 0.6
1.2
0.6
1.2
0.5
2D
1.0
0.4
0.3
0.0 0.1
0.2
0.2 0.3
0.1
0.4 αhx (g)
0.5
0.6
(b)
0.0
0.5
2D
1.0
0.4
0.3
0.0
αhz (g)
0.1
0.2
0.2 0.3
αhx (g)
αhz (g)
0.1
0.4
0.5
0.6
0.0
(d)
Fig. 5 Variation in FoS with horizontal seismic coefficients α hx and α hz for: a convex 90˚ slope; b concave 90˚ slope; c convex turning arc 90˚ slope; and d concave turning arc 90˚ slope
encoded in ABAQUS finite element software to obtain FoS of the considered slopes. It was found that the shape of failure surface was changing with the horizontal seismic coefficient. As expected, the FoS was found decreasing with the increase in the horizontal seismic coefficient, in either direction or in combination, in all cases. The FoS for 2D slope section was found always lower than the corresponding 3D slope, except in case of convex 90˚ slope subjected to higher value of horizontal seismic coefficient. The present study has been conducted by assuming soil as homogeneous material, generic and simple slope geometry, and seismic force as pseudo-static;
542
V. Sharma et al.
hence, the result is limited to the considered case only. However, for realistic understanding, a more robust study is required considering dynamic analysis of slope with time varying shear strength and natural slope geometry. Acknowledgements The authors are grateful to the Department of Civil Engineering, MNIT Jaipur for providing all the necessary facilities for this investigation.
References 1. Paul, D.K., Kumar, S.: Stability analysis of slope with building loads. Soil Dyn. Earthq. Eng. 16(6), 395–405 (1997) 2. Raj, D., Singh, Y.: Effect of building loads on stability of hill slopes. In: De, A., Reddy, K.R., Yesiller, N., Zekkos, D., Farid, A. (eds) GEO-CHICAGO 2016: Sustainable Geoenvironmental Systems, pp. 638–647. ASCE GSP 271, Chicago, Illinois (2016) 3. Bishop, A.W.: The use of the slip circle in the stability analysis of slopes. Géotechnique 5(1), 7–17 (1955) 4. Morgenstern, N.R., Price, V.E.: The analysis of the stability of general slip surfaces. Géotechnique 15(1), 79–93 (1965) 5. Spencer, E.: A method of analysis of the stability of embankments assuming parallel interslice forces. Géotechnique 17(1), 11–26 (1967) 6. Janbu, N.: Slope stability computations. In: Hirschfeld, R.C., Poulos, S.J. (eds.) EmbankmentDam Engineering—Casagrande Volume, pp. 47–86. Wiley, New York (1973) 7. Sarma, S.K.: Stability analysis of embankments and slopes. Géotechnique 23(3), 423–433 (1973) 8. Baligh, M.M., Azzouz, A.S.: End effects on stability of cohesive slopes. J. Geotech. Eng. Div. 101(11), 1105–1117 (1975) 9. Giger, M.W., Krizek, R.J.: Stability analysis of vertical cut with variable corner angle. Soils Found. 15(2), 63–71 (1975) 10. Leshchinsky, D., Baker, R., Silver, M.L.: Three dimensional analysis of slope stability. Int. J. Numer. Anal. Meth. Geomech. 9(3), 199–223 (1985) 11. Cavounidis, S.: On the ratio of factors of safety in slope stability analyses. Géotechnique 37(2), 207–210 (1987) 12. Hungr, O.: An extension of Bishop’s simplified method of slope stability analysis to three dimensions. Géotechnique 37(1), 113–117 (1987) 13. Chen, Z., Wang, X., Haberfield, C., Yin, J.H., Wang, Y.: A three-dimensional slope stability analysis method using the upper bound theorem: Part I: theory and methods. Int. J. Rock Mech. Min. Sci. 38(3), 369–378 (2001) 14. Chugh, A.K.: On the boundary conditions in slope stability analysis. Int. J. Numer. Anal. Meth. Geomech. 27(11), 905–926 (2003) 15. ABAQUS. ABAQUS documentation. Dassault Systèmes, Providence, RI, USA (2016) 16. Zhang, Y.B., Chen, G.Q., Zheng, L., Li, Y., Zhuang, X.J.C.G.J.: Effects of geometries on three-dimensional slope stability. Can. Geotech. J. 50(3), 233–249 (2013) 17. Dawson, E.M., Roth, W.H., Drescher, A.: Slope stability analysis by strength reduction. Géotechnique 49(6), 835–840 (1999) 18. Griffiths, D.V., Lane, P.A.: Slope stability analysis by finite elements. Géotechnique 49(3), 387–403 (1999) 19. Raj, D., Singh, Y., Kaynia, A.M.: Behavior of slopes under multiple adjacent footings and buildings. Int. J. Geomech. 18(7), 04018062 (2018) 20. Xu, Q., Yin, H., Cao, X., Li, Z.: A temperature-driven strength reduction method for slope stability analysis. Mech. Res. Commun. 36(2), 224–231 (2009)
Three-Dimensional Slope Stability Under Bi-Directional Pseudo-Static …
543
21. Newmark, N.M.: Effects of earthquakes on dams and embankments. Géotechnique 15(2), 139–160 (1965) 22. Jibson, R.W.: Regression models for estimating coseismic landslide displacement. Eng. Geol. 91(2), 209–218 (2007) 23. BIS. IS1893: Crieteria for Eathquake Resistance Design of Structures, Part 1 General Provisions and Buildings. Bureau of Indian Standard, New Delhi (2016)
Strength of Masonry Infill RC Frame Influenced by Weak and Strong Type RC Frames Kaushal P. Patel and R. N. Dubey
Abstract Masonry is most commonly used as an infill material in RC buildings. It considerably increases RC buildings’ lateral strength and stiffness if appropriately connected with the RC frame members. It has been observed from past earthquakes that if the infill walls are severely damaged, then it may put the life of persons inside the building in danger. So, it is crucial to determine the effect of infill walls on the behaviour of RC buildings. The present study investigates the effect of varying percentages of steel reinforcement of beams and columns on the strength and damage pattern of the RC frame with and without infill. The RC frame is modelled in the Abaqus using the continuum modelling approach, and the masonry is modelled using a simplified micro-modelling method also known as discrete element modelling. It has been found that reinforcement percentage significantly affects the strength and damage pattern of the RC frame. Keywords RC frame · CDP · Infill masonry · Discrete element model
1 Introduction Masonry infill walls are used as partitions in reinforced concrete (RC) structures. Infill walls are considered non-structural elements, and their impact on the behaviour of the RC frame is generally not considered. However, past studies have shown that masonry infill interacts with the RC frame during the seismic event and enhances the RC frame’s lateral strength and stiffness [1, 2]. Mehrabi et al. [3] performed several experimental tests to identify the infill panel’s role on the RC frame’s strength, incorporating varying aspect ratios of infill, the strength of the RC frame, vertical load distribution, and loading history. The authors found a considerable increase in K. P. Patel (B) · R. N. Dubey Department of Earthquake Engineering, IIT Roorkee, Roorkee, India e-mail: [email protected] R. N. Dubey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Shrikhande et al. (eds.), Proceedings of 17th Symposium on Earthquake Engineering (Vol. 3), Lecture Notes in Civil Engineering 331, https://doi.org/10.1007/978-981-99-1579-8_43
545
546
K. P. Patel and R. N. Dubey
the strength of the RC frame due to masonry infill. Mehrabi and Shing [4] developed the numerical model for masonry infill RC frames. A good agreement was found between the numerical and experimental results. Stavridis and Shing [2] checked the accuracy of the nonlinear finite element model in capturing the various failure modes of masonry infill RC frames. The model was found to predict the strength and failure mechanism with good accuracy. Mohyeddin et al. [1] developed a discrete element model for the detailed modelling of masonry infill RC frames. It was found the developed model was able to capture the behaviour of infill frame for a wide range of drift. Calió and Pantó [5] used the macro-element model for the seismic assessment of the infill RC frame. The study aimed to develop a macro-model which can be used for the design and vulnerability assessment of infill RC frames. Nasiri and Liu [6] developed a numerical model for the nonlinear behaviour of RC frames. The effect of mortar parameters and fracture energy on the behaviour of the infill RC frame was also studied. Dhir et al. [7] proposed a novel computational modelling strategy for infill RC frames. In this study, rubber joints were used between bricks and between bricks and RC frames to minimize the damage to the bricks. Most of the past studies have focussed on the different modelling approaches and the experimental works on the infill RC frames. It has been found that micromodelling approach has better accuracy in predicting the strength, stiffness, and damage pattern of the masonry walls. In this modelling approach, the bricks are modelled using the nonlinear material model, and the mortar is modelled using the interface elements. It can predict the different failure mechanisms of infill RC frames, namely flexural failure, diagonal cracking, horizontal slip, corner crushing, and midheight horizontal cracking [8]. The infill RC frame is modelled in the study using the micro-modelling approach in the finite element software Abaqus. The bricks are modelled using the concrete damage plasticity (CDP) model, and mortar is modelled using the zero-thickness interface elements. The response of the infill RC frame is governed by various parameters such as the beam-column reinforcement ratio, strength of concrete and masonry, strength of mortar joints, aspect ratio, and vertical pre-compression acting on the infill walls. Amongst all these parameters, the present study focusses on the effect of the reinforcement ratio in the beam and columns on the response of the infill RC frame. It has gotten little attention in past research work. The influence of varying reinforcement ratios is obtained by modelling the RC frame as the strong column weak beam and strong beam weak column. In both cases, the response is obtained as a pushover curve for bare frames, and infill RC frames, and the results are compared with each other in terms of the strength and damage pattern.
2 Finite Element Modelling The RC frame is modelled using continuum elements in the finite element software Abaqus. Three-dimensional brick elements (C3D8R) with a reduced integration scheme are used for the beam and columns. The reinforcement is modelled using
Strength of Masonry Infill RC Frame Influenced by Weak and Strong …
547
3D linear beam elements (B31). The nonlinear behaviour of RC frame members is defined using the concrete damage plasticity (CDP) model. It requires compression and tension stress versus inelastic strain as well as strain versus damage as input parameters. The damage in compression and tension is modelled using linear damage evolution law. The steel is modelled using isotropic hardening with VonMises failure criteria. Reinforcement is perfectly embedded in the concrete using the “embedded element technique.” It is assumed that there is no slip between reinforcement and concrete. It may overestimate the stiffness, but it gives reasonably acceptable behaviour, as suggested by Dhir et al. [7]. The masonry infill is modelled using a simplified micro-modelling approach. The bricks are expanded up to half thickness of the mortar joint, and the zerothickness interface elements connect them. The bricks are modelled using the C3D8R elements to capture the crushing and tensile cracking of the bricks. The failures of the mortar joint in tension and shear are arrested using the interface elements. In case of compression, hard contact formulation has been used. The behaviour of interface in shear is governed by Mohr-Coulomb criterion, as shown in Eq. (1). τ = c + μσ
(1)
where c is the cohesion, τ is the shear stress, μ is the friction angle, and σ is the vertical compression stress. The damage initiation of the interface in tension and shear is defined using the quadratic damage evolution law. Further details about the model can be found in [7, 9].
3 Validation of the Modelling Approach The capability of the model in capturing the behaviour of the masonry infill RC frame is validated by considering the RC frame without and with infill from the past study [3]. The geometry of the RC frame, reinforcement details, and the dimensions of the bricks is shown in Fig. 1. The material parameters of the walls are considered by Mehrabi et al. [3, 7]. The compression and tension strength of the concrete are 30.9 and 3.29 MPa, respectively. Young’s modulus of concrete is 21930 MPa. The compression and tension strength of the brick units are 15.59 and 1.57 MPa, respectively. Young’s modulus of brick is 9520 MPa. Steel with a yield strength of 400 MPa was used in the tests. The tensile strength of the interface is 0.14 MPa. The cohesion and friction coefficient of the interface are considered as 0.2 and 0.9, respectively. The fracture energy of the interface in tension G 1f and shear G 2f is 0.015 and 0.090 N/mm, respectively. First, the bare frame is considered for the validation study. The columns are subjected to a vertical force of 146.8 kN each initially. Later, the displacement was applied to the beam to obtain the pushover curve. The pushover curve obtained from the experiment is compared with the numerical results from the present study as well
548
K. P. Patel and R. N. Dubey
Fig. 1 Geometry of RC frame and infill masonry [3, 7, 13]
as past studies, as shown in Fig. 2. It indicates good agreement; however, the higher initial stiffness is obtained due to the no-slip condition between reinforcement and concrete. The damage patterns of the bare frame obtained from the experiment and numerical simulation are compared in Fig. 3 using the tension damage contours. A good agreement has been found between them. The experimental result obtained from [3] for the infill RC frame (specimen 3) is compared with the present study’s numerical results and past study in Fig. 4 as pushover curves. The results show good agreement with each other. It represents that the numerical model used in the present study can predict the behaviour of infill RC frames with reasonably good accuracy. Further, the damage pattern of the infill RC
Fig. 2 Comparison of experimental and numerical results for the bare frame
Strength of Masonry Infill RC Frame Influenced by Weak and Strong …
549
Fig. 3 Comparison of experimental and numerical damage pattern of the bare frame
Fig. 4 Comparison of experimental and numerical results for the infill RC frame
frame obtained from the experiment and numerical simulation is compared in Fig. 5. The numerical damage pattern matches well with the experimental damage pattern.
4 Results and Discussion The RC frame with and without infill is modelled using the finite element software Abaqus, and the results are presented in this section. The RC frames are modelled by designing them as the strong column weak beam (SCWB) and strong beam weak column (SBWC). The ratios of reinforcement percentages of beam and columns for SCWB and SBWC are 0.4 and 2.4, respectively. The size of the beam and columns
550
K. P. Patel and R. N. Dubey
(a) Experimental (Mehrabi 1994)
(b) Numerical
Fig. 5 Comparison of experimental and numerical damage pattern of the infill RC frame
is 300 × 300 mm. The geometry and reinforcement details are shown in Fig. 6. The size of the brick units is 230 × 110 × 75 mm. The thickness of the mortar joint is considered 10 mm. The material parameters of the RC frame and infill walls are shown in Tables 1 and 2. The value of overstrength factor is considered as 5. The CDP model requires compression and tension stress–strain curves for concrete and masonry. In the case of concrete, the formulation given by Sima et al. [10] and Nasiri and Liu [6] has been used to get the compression and tension stress–strain curves, respectively. For masonry walls, the compression and tension stress–strain curves are obtained using the formulation given by Kaushik et al. [11] and Chen et al. [12], respectively. The damage/cracking in compression and tension for concrete and masonry is modelled using the linear damage evolution law. The reinforcement is modelled using the bar elements. The bond between reinforcement and concrete is considered as perfectly fixed. The frame is fixed at its bottom, and the incremental displacement is applied at the top during the pushover analysis, as shown in Fig. 6. The results for RC frame with and without infill for SCWB and SBWC are plotted as pushover curves as shown in Fig. 7. The strength of bare frame in SCWB and
Fig. 6 Geometry and reinforcement detailing of the RC frame
Strength of Masonry Infill RC Frame Influenced by Weak and Strong …
551
Table 1 Material parameters of the RC frame and masonry infill Mechanical properties
Concrete
Brick units
Reinforcement
Young’s modulus (MPa)
22,360
1898
200,000
Poisson’s ratio
0.2
0.15
0.3
Compressive strength (MPa)
30
3.88
–
Strain corresponding to peak compressive stress
0.002
0.0037
–
Ultimate strain
0.007
0.01
–
Tensile strength (MPa)
3.5
1.5
–
Yield strength (MPa)
–
–
400
Table 2 Properties of the joint interface
Knn (N/mm3 )
67
Kss , Ktt (N/mm3 )
29
σ t (MPa)
0.1
Cohesion, c (MPa)
0.16
Friction coefficient, μ Tension fracture energy,
0.75 GF1
(N/mm)
Shear fracture energy, GF2 (N/mm)
0.010 0.050
SBWC is 173.55 and 109.86 kN, respectively. So, in the case of SCWB, 57.97% increment in the strength has been observed compared to the SBWC case. The strength of the infill RC frame for SCWB and SBWC is 244.61 and 158.50 kN, respectively. So, a 54.33% increment in strength has been observed for the RC frame with infill in SCWB compared to the SBWC. It indicates that increment in strength due to infill is more or less similar in SCWB and SBWC cases. The initial stiffness of the RC frame is also increasing considerably due to masonry infill, as shown in Fig. 7. The damage pattern of the RC frame with and without infill is shown in Fig. 8. In the case of the bare frame, most of the damages have occurred at the bottom of the columns and at the joints. In SBWC, corners of the bare frame have shown severe damage compared to the SCWB. The RC frames with infills show damage at the corners and bottom of the columns, along with bed joints sliding in the bricks. The failure has also been observed at the connection of the RC frame with the masonry infill.
5 Conclusions The behaviour of RC frame with and without infill walls has been investigated for the strong column weak beam (SCWB) and strong beam weak column (SBWC) cases. The model was analyzed in the finite element software Abaqus, in which the concrete
552
K. P. Patel and R. N. Dubey
Fig. 7 Comparison of pushover curves for SCWB and SBWC with and without infill
SCWB
SBWC Fig. 8 Damage pattern of RC frames with and without infill for SCWB and SBWC
and masonry are modelled using the concrete damage plasticity (CDP) model, and the steel reinforcement is modelled using the beam elements. The mortar in the brick is modelled using the zero-thickness surface-based cohesive elements. The modelling approach used in the present study is able to capture the behaviour of RC frames
Strength of Masonry Infill RC Frame Influenced by Weak and Strong …
553
with and without infill with reasonably good accuracy. The main conclusions from the present study are as follows: 1. The results obtained using the selected modelling approach show good agreement with the past experimental results in strength and damage patterns. 2. The stiffness of the RC frame obtained numerically is higher than the experimental result due to the assumption of a no-slip condition between reinforcement and concrete. 3. A significant increment in the strength has been obtained for SCWB with and without infill compared to the respective SBWC cases. 4. RC bare frame with SBWC shows considerable damage near corners compared to the SCWB. 5. In the case of infill RC frame with SCWB and SBWC, the failure of infill masonry occurred primarily due to horizontal bed joint sliding and the tension failure of the interface at the connection of infill with column and beam.
References 1. Mohyeddin, A., Goldsworthy, H.M., Gad, E.F.: FE modelling of RC frames with masonry infill panels under in-plane and out-of-plane loading. Eng. Struct. 51, 73–87 (2013) 2. Stavridis, A., Shing, P.B.: Finite-element modeling of nonlinear behavior of masonry-infilled RC frames. J. Struct. Eng. 136(3), 285–296 (2010) 3. Mehrabi, A.B., Benson Shing, P., Schuller, M.P., Noland, J.L.: Experimental evaluation of masonry-infilled RC frames. J. Struct. Eng. 122(3), 228–237 (1996) 4. Mehrabi, A.B., Shing, P.B.: Finite element modeling of masonry-infilled RC frames. J. Struct. Eng. 123(5), 604–613 (1997) 5. Caliò, I., Pantò, B.: A macro-element modelling approach of infilled frame structures. Comput. Struct. 143, 91–107 (2014) 6. Nasiri, E., Liu, Y.: Development of a detailed 3D FE model for analysis of the in-plane behaviour of masonry infilled concrete frames. Eng. Struct. 143, 603–616 (2017) 7. Dhir, P.K., Tubaldi, E., Ahmadi, H., Gough, J.: Numerical modelling of reinforced concrete frames with masonry infills and rubber joints. Eng. Struct. 246, 112833 (2021) 8. Mehrabi, A.B., Shing, P.B.: Performance of masonry-infilled R/C frames under in-plane lateral loads: analytical modeling. In: Proceeding, NCEER workshop on seismic response of masonry. San Francisco (1994) 9. Abdulla, K.F., Cunningham, L.S., Gillie, M.: Simulating masonry wall behaviour using a simplified micro-model approach. Eng. Struct. 151, 349–365 (2017) 10. Sima, J.F., Roca, P., Molins, C.: Cyclic constitutive model for concrete. Eng. Struct. 30(3), 695–706 (2008) 11. Kaushik, H.B., Rai, D.C., Jain, S.K.: Stress-strain characteristics of clay brick masonry under uniaxial compression. J. Mater. Civ. Eng. 19(9), 728–739 (2007) 12. Chen, Y., Ashour, A.F., Garrity, S.W.: Moment/thrust interaction diagrams for reinforced masonry sections. Constr. Build. Mater. 22(5), 763–770 (2008) 13. Mehrabi, A.B.: Behavior of Masonry Infilled Reinforced Concrete Frames Subjected to Lateral Loadings [Ph.D]. University of Colorado at Boulder (1994)
Drained and Undrained Response of Fully Saturated Specimen in Resonant Column Tests Subjected to Large Number of Torsional Vibrations Ninad Sanjeev Shinde
and Jyant Kumar
Abstract In this paper, the drained and undrained responses of the saturated sand specimens have been investigated when subjected to small strain torsional excitation cycles using the resonant column apparatus. The sand specimens were reconstituted at an identical relative density of 40%. The fully saturated sand samples were then subjected to different effective isotropic consolidation stresses of 65, 100, and 150 kPa. For each test, thousands of vibration cycles were applied to the specimen by keeping the amplitude of cyclic driving torque constant. The response of the specimen was evaluated in both drained and undrained conditions. Beyond threshold strain, the undrained response of the saturated specimen demonstrated a considerable increase in pore water pressure and decrease in shear modulus, whereas axial strain increased substantially in case of vibrations applied to the specimen in drained conditions This type of study would be beneficial to determine deformational characteristics of fully saturated sand stratum beneath various vibratory machines which impart small stain and high-frequency vibrations. Keywords Resonant column test · Vibration cycles · Pore water pressure
1 Background The understanding of the response of soil strata subjected to different types of vibrations including earthquakes is essential for finding out the solutions to different geotechnical problems associated with soil structure interaction or studies on wave propagation in the soils. In the past, the response of the soil specimen subjected to vibration cycles has been evaluated using the conventional soil testing apparatus such as simple/cyclic shear and torsional shear apparatuses. These equipment usually operate in the lower frequency range (4.75 mm)
5
Sand in % (4.75–0.075 mm)
94
Silt in % (