Modern Geotechnical Design Codes of Practice : Implementation, Application and Development [1 ed.] 9781614991632, 9781614991625

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MODERN GEOTECHNICAL DESIGN CODES OF PRACTICE

Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

Advances in Soil Mechanics and Geotechnical Engineering Advances in Soil Mechanics and Geotechnical Engineering (ASMGE) is a peer-reviewed book series covering the developments in the key application areas of geotechnical engineering. ASMGE will focus on theoretical, experimental and case history-based research, and its application in engineering practice. The series will include proceedings and edited volumes of interest to researchers in academia, as well as industry. The series is published by IOS Press under the imprint Millpress.

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Volume 1

ISSN 2212-781X (print) ISSN 2212-7828 (online)

Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

Modern Geotechnical Design Codes of Practice Implementation, Application and Development

Edited by

Patrick Arnold Delft University of Technology, Geo-Engineering Section, Delft, Netherlands University of Manchester, Geo-Engineering Expert Group, Manchester, United Kingdom

Gordon A. Fenton Visiting Professor, Delft University of Technology, Geo-Engineering Section, Delft, Netherlands Dalhousie University, Department of Civil and Resource Engineering and Department of Engineering Mathematics, Halifax, Nova Scotia, Canada

Michael A. Hicks Delft University of Technology, Geo-Engineering Section, Delft, Netherlands

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Timo Schweckendiek Deltares, Unit Geo-engineering, Delft, Netherlands Delft University of Technology, Section of Hydraulic Engineering, Delft, Netherlands

and

Brian Simpson Arup Geotechnics, London, United Kingdom

Amsterdam • Berlin • Tokyo • Washington, DC

Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

© 2013 The authors and IOS Press. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without prior written permission from the publisher. ISBN 978-1-61499-162-5 (print) ISBN 978-1-61499-163-2 (online) Library of Congress Control Number: 2012952418 Publisher IOS Press BV Nieuwe Hemweg 6B 1013 BG Amsterdam Netherlands fax: +31 20 687 0019 e-mail: [email protected]

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Distributor in the USA and Canada IOS Press, Inc. 4502 Rachael Manor Drive Fairfax, VA 22032 USA fax: +1 703 323 3668 e-mail: [email protected]

LEGAL NOTICE The publisher is not responsible for the use which might be made of the following information. PRINTED IN THE NETHERLANDS

Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved.

v

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Preface Geotechnical design is a product of local history, engineering practice, availability of construction materials and, of course, the geology of each site. All of these factors vary from region to region, which is why a standard recipe for developing geotechnical codes of practice does not exist. It is probably fair to say that the differences in geotechnical design codes worldwide are much larger than exist between steel or concrete design codes. Steel and concrete are quality controlled materials and the uncertainty in their engineering behaviour is very similar from region to region. Thus, concrete and steel design codes have been able to take advantage of worldwide research efforts in their calibration over the decades. Modern geotechnical design codes are generally striving towards a similar harmonisation, both with their counterpart structural design codes and between regional geotechnical codes. However, harmonising geotechnical design codes is not an easy task. An excellent example of the challenges faced in harmonisation is presented by Eurocode 7. Although aiming to create common terms of reference, Eurocode 7 still required several design approaches to accommodate the needs of all member states, along with national annexes enabling each member state to define their own set of safety factors. Why was this diversity in design approaches necessary? And what do code developers have in mind when they make their choices in adopting a design approach or set of safety factors? Some answers to these questions will be given in this book. The impetus for this publication started with an international workshop on Safety Concepts and Calibration of Partial Factors in European and North American Codes of Practice, which was held on November 30 to December 1, 2011 at Delft University of Technology, the Netherlands. The aim of the workshop was to exchange experience and transfer knowledge between code developers, practitioners, and researchers on code development, safety concepts and the calibration of partial factors in modern geotechnical codes of practice. The attendees, who were leading authorities from Europe and North America, provided interesting and valuable insights into the development of their own national codes. This workshop led to the idea of collecting contributions from geotechnical code developers worldwide into a single book, providing a resource that can be referred to as a guide in the years to come. The papers collected in this book are organised into three sections: Code Implementation describes choices relating to safety concepts, target reliabilities, and design approaches; Code Application addresses their application to specific geotechnical problems; and Code Development includes papers discussing directions for future developments. The editors would like to acknowledge the support of the following committees who have substantially contributed to and supported this publication: the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) Technical Committee for Safety and Serviceability in Geotechnical Design (TC 205), Technical Committee for Engineering Practice of Risk Assessment and Management (TC 304), and the Comité Européen de Normalisation (CEN) Technical Committee for Structural Eurocodes (TC250).

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Contents Preface

v

Code Implementation Implementation and Evolution of Eurocode 7 Andrew Bond Harmonisation of Anchor Design Within Eurocode Eric R. Farrell

15

Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland Beata Gajewska

25

An Explanation of Characteristic Values of Soil Properties in Eurocode 7 Michael A. Hicks

36

Implementation of Eurocode 7 in German Geotechnical Design Practice Kerstin Lesny

46

Implementation of Eurocode 7 in French Practice by Means of National Additional Standards Jean-Pierre Magnan and Sébastien Burlon Implementing Eurocode 7 to Achieve Reliable Geotechnical Designs Trevor Orr

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3

Dealing with Uncertainties in EC7 with Emphasis on Determination of Characteristic Soil Properties Hans R. Schneider and Mark A. Schneider

60 72

87

The Safety Concept in German Geotechnical Design Codes Bernd Schuppener

102

British Choices of Geotechnical Design Approach and Partial Factors for EC7 Brian Simpson

116

Dutch Approach to Geotechnical Design by Eurocode 7, Based on Probabilistic Analyses Ton Vrouwenvelder, Adriaan van Seters and Geerhard Hannink

128

Code Application Limit State Design of the Foundations of Concrete Gravity Dams – A Case Study Laura Caldeira, Maria Luísa B. Farinha, Emanuel Maranha das Neves and José V. Lemos Using Numerical Analysis with Geotechnical Design Codes Andrew Lees

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143

157

viii

Influence of Ground Water Level on Shallow Foundation Design. Application of EC7 Probabilistic and Deterministic Methods Carlos Pereira and Laura Caldeira

171

Reliability Based Design of Drilled Shafts: LRFD and Performance Based Design Lance A. Roberts and Anil Misra

183

Application of Computational Limit Analysis in Ultimate Limit State Design Colin Smith

195

Probabilistic Assignment of Design Strength for Sands from In-Situ Testing Data Marco Uzielli, Paul W. Mayne and Mark J. Cassidy

214

Experiences with Limit State Approach for Design of Spread Foundations in the Czech Republic Martin Vaníček and Ivan Vaníček

228

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Code Development AASHTO Geotechnical Design Specification Development in the USA Tony M. Allen

243

Lessons Learned from LRFD Calibration of Reinforced Soil Wall Structures Richard J. Bathurst, Tony M. Allen, Yoshihisa Miyata and Bingquan Huang

261

Geotechnical Design Code Development in Canada Gordon A. Fenton

277

Can We Do Better than the Constant Partial Factor Design Format? Kok-Kwang Phoon and Jianye Ching

295

Target Reliabilities and Partial Factors for Flood Defenses in the Netherlands Timo Schweckendiek, Ton Vrouwenvelder, Ed Calle, Wim Kanning and Ruben Jongejan

311

Subject Index

329

Author Index

331

Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

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Code Implementation

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-3

3

Implementation and evolution of Eurocode 7 Andrew BOND Director, Geocentrix Ltd, Banstead, UK and Chairman of TC250/SC7

Abstract. The paper describes the ways in which Eurocode 7 has been implemented by National Standards Bodies in Europe. It identifies key differences between the 33 countries involved in their choice of Design Approach for different foundation types and the introduction of different factors based on the design situation being considered and the consequences of failure. Finally, the paper gives details about the plans that are in place to develop the Eurocodes as a whole and Eurocode 7 in particular. Keywords. Partial factors, material strength design, load and resistance factor design, consequences of failure

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Introduction In 1975, the Commission of the European Community (known, at the time, as the European Economic Community, EEC), decided to create an action programme in the field of construction, with the objective of promoting free trade between the member states by the elimination of technical obstacles and harmonization of technical specifications. The fruits of that programme are the suite of European Standards for structural (and geotechnical) design known as the ‘Eurocodes’. The story of the development of Eurocode 7 has been reported in detail by Orr (2008) and will not be repeated here, other than to note the immense contribution of the late Prof. Niels Krebs-Ovesen – whose ‘clear and deep understanding of geotechnical design principles, … excellent social and diplomatic skills, and … enthusiasm and ability to motivate people’ (Orr, loc cit.) were key to the successful development of Eurocode 7.

1. Implementation of Eurocode 7 The European Standard for geotechnical design, EN 1997 (better known as ‘Eurocode 7’), was published by CEN, the European Standards Organization, as a full Euronorm (EN) between 2004 and 2007, following more than 30 years of development. The standard is divided into two parts: Part 1 (designated EN 1997-1: 2004) giving General Rules for geotechnical design, and Part 2 (EN 1997-2: 2007) covering Ground Investigation and Testing. CEN’s rules regarding publication of European Standards normally require such standards to be implemented in Member States within six months of them being made available. Because of the complexity and interconnection of the 58 standards in the

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A. Bond / Implementation and Evolution of Eurocode 7

Eurocode family, these rules were relaxed, thereby allowing a phased introduction of the codes throughout Europe. A deadline of April 2010 was set for full introduction of the Eurocodes and withdrawal of any national standards that conflicted with them. This deadline has not been universally met and so the take up of Eurocode 7 into geotechnical design practice in Europe has been slower than anticipated. 1.1. Choice of Design Approach for GEO/STR ultimate limit state verifications Eurocode 7 requires ultimate limit states that involve the strength of structural materials or the ground (so-called limit states STR and GEO) to be verified using the inequality: Ed ≤ Rd

(1)

where Ed is the design effect of actions (e.g. bending moment, shear force, bearing pressure, etc.) and Rd is the corresponding resistance to that effect (bending capacity, shear capacity, bearing capacity, etc.). Reliability is introduced in a deterministic manner, by the introduction of partial factors into this expression:

γ E E { Fd , X d , ad } ≤

R { Fd , X d , ad } γR

(2)

where Fd, Xd, and ad represent design values of actions, material properties, and geometry, respectively; γE and γR are partial factors on the effects of actions and resistance; and E{…} and R{…} denote appropriate functions of the enclosed variables. The enclosed variables are themselves modified by partial factors:

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Fd = γ F Frep , X d =

Xk , ad = anom ± Δa γM

(3)

where Frep, Xk, and anom represent representative values of actions, characteristic material properties, and nominal dimensions, respectively; γF and γM are partial factors on the actions and material properties; and Δa is a tolerance or safety margin on the geometry. The particular partial factors (and their values) that must be used in a country are specified in National Annexes to Eurocode 7 published by the various National Standards Bodies. Eurocode 7 provides a choice between three Design Approaches as follows: •

•

Design Approach 1 (DA1) requires two separate verifications to be performed using different combinations of partial factors: in Combination 1, factors > 1.0 are applied to actions only; in Combination 2, factors > 1.0 are applied primarily to ground strengths (except in the case of piles and anchors, for which factors > 1.0 are applied to resistances instead) Design Approach 2 (DA2) requires a single verification using partial factors > 1.0 being applied to actions and resistances simultaneously

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A. Bond / Implementation and Evolution of Eurocode 7

•

5

Design Approach 3 (DA3) requires a single verification using partial factors > 1.0 applied to structural actions and ground strengths simultaneously

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Design Approaches 1 and 3 adopt what is known as the ‘material strength design’ (MSD) method, which was introduced into European practice by Brinch Hansen (1956). In this method, partial factors are applied (either separately or simultaneously) to loads – called actions in the Eurocode system – and material strengths. By contrast, Design Approach 2 is similar to the ‘load and resistance factor design’ (LRFD) method that will be familiar to users of modern American codes, such as the AASHTO LRFD Bridge Design Specifications. In this method, partial factors are applied simultaneously to loads and resistance.

Figure 1. Design Approaches adopted by different European countries for design of shallow foundations

Figure 1 shows the choice of Design Approach that has been made for the design of shallow foundations by the 33 countries who are members of CEN: • • • •

6 countries have chosen DA1 (Belgium, Iceland, Lithuania, Portugal, Romania, and the UK) 11 countries have chosen DA2 (Austria, Cyprus, Estonia, Finland, Germany, Greece, Hungary, Poland, Slovakia, Slovenia, and Spain) 4 countries have chosen DA3 (Denmark, Netherland, Norway, and Sweden) 1 country allows a choice of DAs 1 and 2 (Italy)

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A. Bond / Implementation and Evolution of Eurocode 7

• • •

1 country allows a choice of DAs 2 and 3 (France) 2 countries allow a choice of all three DAs (Czech Republic and Ireland) 8 countries have yet to decide – or their decision is unknown to the author (Bulgaria, Croatia, Latvia, Luxembourg, Macedonia, Switzerland, and Turkey – plus Malta, which is not shown the map)

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The division of Design Approaches indicates an almost equal number of countries favouring the MSD method as there are favouring the LRFD method. This balance changes, however, when considering the design of slopes and embankments, as Figure 2 illustrates. For these foundations, there is almost universal adoption of the MSD method (i.e. Design Approaches 1 and 3).

Figure 2. Design Approaches adopted by different European countries for design of slopes and embankments

Finally, Figure 3 shows the choice of Design Approach that has been made for the design of pile foundations by the members of CEN. A strong majority has specified the use of Design Approach 2 and – since in Design Approach 1 partial factors are applied to pile resistances and not ground properties – this means there is almost universal adoption of the LRFD method for pile foundations.

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A. Bond / Implementation and Evolution of Eurocode 7

Figure 3. Design Approaches adopted by European different countries for design of pile foundations

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1.2. Reliability discrimination based on design situation The head Eurocode, EN 1990, uses the term design situation to describe ‘physical conditions … occurring during a certain time interval for which the design will demonstrate that relevant limit states are not exceeded’. Four design situations are specified in EN 1990, as listed in Table 1. Table 1. Design situations defined in EN 1990 Design situation Persistent Transient Accidental

Seismic

Description

Normal use Temporary conditions Exceptional conditions

When subject to seismic events

Examples

Execution or repair Fire, explosion, impact, or the consequences of localized failure

Partial factors for ultimate limit state STR γG γQ 1.35 1.5 1.35 1.5 1.0 1.0

1.0

1.0

Values of the partial factors γG and γQ – which are applied to permanent and variable actions, respectively – are summarized in Table 1 for limit state STR. EN 1990 recommends one set of values for persistent and transient design situations; and a different set (all equal to 1.0) for accidental and seismic situations; i.e.:

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A. Bond / Implementation and Evolution of Eurocode 7

(γ

F , persistent

= γ F ,transient ) > ( γ F , accidental = γ F , seismic )

Two countries – Austria and Germany – have decided to specify alternative values for γG and γQ depending on the design situation being considered, with these values obeying the general relationship:

γ F , persistent > γ F ,transient > ( γ F , accidental = γ F , seismic ) For example, in Germany, the partial factor applied to variable actions is specified as γQ = 1.5 for persistent, 1.2 for transient, and 1.0 for accidental design situations. Likewise, these same countries specify alternative values for the resistance factors γR to those given in Eurocode 7 (EN 1997-1) with:

γ R , persistent > γ R ,transient > ( γ R , accidental = γ R , seismic ) For example, in Germany, the partial factor applied to vertical bearing resistance is specified as γRv = 1.4 for persistent, 1.3 for transient, and 1.2 for accidental design situations. 1.3. Reliability discrimination based on consequences The head Eurocode also allows the level of reliability used for the verification of ultimate limit states to be varied according to ‘classes of consequence’, as summarized in Table 2. Table 2. Consequence classes and their associated reliability indices, as defined in EN 1990

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Consequence Class

CC3

CC2

CC1

Description

Examples

High consequence for loss of human life, or economic, social or environmental consequences very great Medium consequence for loss of human life, economic, social or environmental consequences considerable Low consequence for loss of human life, and economic, social or environmental consequences small or negligible

Grandstands, public buildings where consequences of failure are high (e.g. a concert hall) Residential and office buildings, public buildings where consequences of failure are medium (e.g. an office building) Agricultural buildings where people do not normally enter (e.g. storage buildings), greenhouses

Associated minimum reliability index, β, for given reference period 1 year 50 years 5.2 4.3

KFI

1.1

4.7

3.8

1.0

4.2

3.3

0.9

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One way of introducing reliability discrimination is to introduce an extra partial factor KFI into the calculation of design actions, such that:

Fd = K FI × γ F × Frep

(4)

with the values of KFI given in Table 2. Five countries – Austria, Denmark, Finland, the Netherlands, and Sweden – have decided to adopt this approach. So, for example, in these countries the partial factor applied to variable actions is γQ = 1.35 for CC1, 1.5 for CC2, and 1.65 for CC3. This method of reliability discrimination does not work for the design of slopes and embankments, where the governing parameter is the strength of the ground, rather than imposed loads. Three of the five countries listed above – Austria, Denmark, and the Netherlands – have therefore extended this concept to the calculation of design strengths, by increasing or decreasing the value of γM by a factor akin to KFI: Xd ≈

Xk K FI × γ M

(5)

For example, in the Netherlands, the partial factor applied to the coefficient of shearing resistance (i.e. tan ϕ) is specified as γϕ = 1.2 for CC1, 1.25 for CC2, and 1.3 for CC3. 1.4. Summarizing reliability discrimination Figure 4 indicates which countries have chosen different values for partial factors on actions, material properties, and resistance to account for an increase or decrease in risk brought about by the either a) the design situation and/or b) the consequence of failure (KFI). In total, 7 of the 33 countries within CEN have chosen to do this (just over 20%). Copyright © 2012. IOS Press, Incorporated. All rights reserved.

1.5. Other changes to partial factors for ground properties Several countries have chosen to adopt slightly different values for the partial factors to be applied to ground properties in their jurisdiction. The motivation and justification for this is beyond the scope of this paper, but, to give an idea of the changes that have been made, Table 3 summarizes the values specified for slope design in selected countries’ National Annexes. There is a slight tendency for γϕ to be reduced from the recommended value given in Eurocode 7 and for γcu to be increased. 1.6. Some lessons learnt from implementation of Eurocode 7 The preceding review of the implementation of Eurocode 7 in various countries throughout Europe reveals considerable variation from the ‘template’ provided by the code for the level of reliability required in geotechnical design. It is clear that countries have chosen to preserve their existing national practice as far as they can and have adapted the Eurocode rules in order to do so. The challenge going forward will be to explain the reasons for the apparent differences in national practice and to reduce these differences where they are based on outdated experience.

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A. Bond / Implementation and Evolution of Eurocode 7

Figure 4. Countries where partial factors vary according to the consequence of failure and/or design situation

Table 3. Values of partial factors that differ from Eurocode 7’s recommended values

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Standard/Country

Design Approach adopted for slope design

Partial material factors for design of slopes in persistent design situation, CC2 γϕ γc γcu Eurocode 7 Values given for DA3 1.25 1.25 1.4 1.25 Austria DA3 1.1 1.15 Denmark DA3 1.2 1.8 1.2 Finland DA3 1.25 1.25 1.5 Germany DA3 1.25 1.25 1.25 Netherlands DA3 1.25 1.75 1.45 Portugal DA3 1.1 1.15 1.1 Sweden DA3 1.3 1.5 1.3 Underlined values differ from the recommended values given in Eurocode 7

2. Evolution of Eurocode 7 In May 2010, the European Commission issued a ‘Programming Mandate’ M/466 to initiate further development of the Structural Eurocodes. This Mandate invited CEN, the European Standards Organization, to submit proposals for creating new Eurocodes and evolving existing Eurocodes. Responsibility for preparing CEN’s response to the Mandate was delegated to CEN Technical Committee TC250.

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2.1. Response to the Mandate CEN’s initial response to the Commission’s Programming Mandate proposed new Eurocodes for: 1. design of structural glass 2. structural use of fibre-reinforced polymers 3. design of membrane structures1 CEN’s response also proposed various improvements to existing Eurocodes, including: 1. reducing the number of Nationally Determined Parameters (NDPs) 2. incorporating recent research on innovation (e.g. performance-based and sustainability concepts) 3. incorporating recent research on sustainability 4. simplifying rules for limited and well identified fields of application Nationally Determined Parameters allow the Member Countries of CEN to decide on their own safety levels and give national geographic and climatic data via National Annexes to the appropriate Eurocodes. The use of NDPs and the publication of supporting documents and standards (so-called ‘non-contradictory complementary information’ or ‘NCCI’) have been far more extensive than was originally envisaged. A priority for the evolution of the Eurocodes is to reduce national alternatives and thus aid simplification.

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2.2. How the evolution of Eurocode 7 is being organized At its meeting in Cambridge, UK, in March 2011, TC250/SC7 – the subcommittee that is responsible for the maintenance and development of Eurocode 7 – decided to establish a number of ‘Evolution Groups’ to prepare for the ‘second generation’ of Eurocode 7. The brief for each Evolution Group (EG) was to prepare the best possible advice to allow SC7 to make the necessary changes, additions, and/or deletions to Eurocode 7 to meet the aims set out in CEN’s response to the Mandate. The Evolution Groups that were established – with one or two amendments – are shown in Figure 4.2 As Figure 5 shows, the Evolution Groups can be divided into four broad groups. EGs 2 and 8 are concerned mainly with editorial matters, such as simplification and harmonization of rules throughout both parts of the code; EGs 4, 6, 9, 10, and 11 are concerned with generic technical subjects that are independent of foundation type; while EGs 1, 5, 7, 13, and 14 deal with specific technical subjects which generally have their own sub-section with EN 1997-1 (reinforced soil and rock mechanics are the exceptions to this – but plans are in place to change this during evolution of the code). EG3 is unusual amongst this company, since its purpose is to develop worked examples based on the current Eurocode text, to establish current best practice. This group is continuing the work of ETC10, the European Technical Committee established by the International Society of Soil Mechanics and Geotechnical Engineering to research the implementation of Eurocode 7. Finally, EG0 is an over-

1

At the time of writing, it seems likely that European Commission will only fund the creation of a new Eurocode for the first of these subjects and not for the other two 2 Creation of EG12 Tunnelling is pending; EG14 was created after the March 2011 meeting of SC7

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A. Bond / Implementation and Evolution of Eurocode 7

arching group whose task is to coordinate the work of all the other groups and to act as a single link to the main technical committee TC250/SC7.

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Figure 5. SC7’s Evolution Groups

A micro-site has been setup to support the work of these Evolution Groups at www.eurocode7.com/sc7/evolutionsgroups.html, where you will find the names of the delegates who are working in each group. 2.3. Maintenance and simplification The Structural Eurocodes have generally been regarding as complicated documents that are not easy for designers to use. In its response to Mandate M/466, TC250 stated: The Eurocodes are the result of a consensus between many European experts after enormous exposure to examination. The Eurocodes are technically advanced standards which are intended to allow the design of most structures that are likely to be needed now and in the future. Accordingly they are very comprehensive, which can lead to their appearing to be more complicated than is necessary when a limited range of types of structure is to be designed.

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A. Bond / Implementation and Evolution of Eurocode 7

In view of the above, TC250 agreed to ensure simplification in the future development of the Eurocodes by: 1. 2. 3. 4.

improving clarity simplifying routes through the Eurocodes limiting, where possible, the inclusion of alternative application rules avoiding or removing rules of little practical use in design

To date, EG2 has concentrated its efforts on improving the contents of Eurocode 7 Part 2, which covers ground investigation and testing and has been accused of including too much ‘text book’ material that would be better left out of the code. The EG is also attempting to remove as much duplication as possible between Parts 1 and 2, in order to simplify both documents. 2.4. Harmonization

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In many ways, EG8 has the most important and most difficult tasks of all the Evolution Groups – the reduction in national variation introduced via the National Annexes to Eurocode 7. This task, however, is the European Commission’s number one priority in commissioning evolution of the Eurocodes, since national variation is perceived as a barrier to trade. EG8 is investigating ways in which the need for different Design Approaches introduced in EN 1997-1 might be avoided. The almost universal adoption of material strength (MSD) design for slopes and embankments and load and resistance factor design (LRFD) for piles suggests that progress towards this goal could be achieved on a case-by-case basis, considering each foundation type in turn. There appears to be a strong case for introducing reliability discrimination into Eurocode 7, taking the best ideas from (mainly Scandinavian) practice. One proposal under consideration is to ‘build up’ the value of the partial factors applied to ground properties γM from various elements, like this: γ M = γ M ,basic × kCC × k DS

where γM,basic would be the base value for γM for consequence class CC2 in persistent design situations. The factor kCC would then modify γM for different consequence classes; and kDS would do likewise for different design situations. Table 4 gives some proposed values for these factors, based on the review of national practice described in the first part of this paper. (The values given in Table 4 reproduce to a large extent the specific values of γM already adopted in those countries which have already introduced reliability discrimination, as indicated on Figure 4.) Table 4. Some proposed values for the modifiers to be applied to basic partial material factors Modifier for…

Symbol

Specific values Case Symbol Low consequence (CC1) kCC1 kCC2 Consequence Class kCC Medium consequence (CC2) High consequence (CC3) kCC3 kpers Persistent Transient ktran Design Situation kDS Accidental kacc Seismic kseis Underlined = ‘default’ consequence class and design situation

Value 0.95 = 1/ 1.05 1.0 1.1 1.0 0.95 = 1/ 1.05 0.91 = 1/ 1.1 0.91 = 1/ 1.1

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A. Bond / Implementation and Evolution of Eurocode 7

3. Conclusion If the European Commission’s goal of free trade between member states in the field of construction is to be achieved, then technical obstacles – such as a choice of Design Approaches, a multitude of Nationally Determined Parameters, and further national rules presented as non-contradictory complementary information (NCCI) – must be reduced or eliminated. The best way to achieve this is to understand the purpose of these national variations – and to provide alternative means of satisfying that purpose.

References

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Bond, A.J. and Harris, A.J. (2008). Decoding Eurocode 7, Taylor and Francis, London. Brinch Hansen, J. (1956). Limit design and safety factors in soil mechanics, Bulletin No. 1, Danish Geotechnical Institute. Orr, T.L.L. (2008). The story of Eurocode 7, 14th European Conference on Soil Mechanics and Geotechnical Engineering.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-15

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Harmonisation of Anchor Design within Eurocode a

Eric R FARRELL a,1 AGL Consulting and Department of Civil Structural and Environmental Engineering, Trinity College, Dublin, Ireland

Abstract. The harmonisation of anchor design within the limit state framework of the Eurocode presented a challenge due to the different design and testing practices in use in the various countries. An Evolution Group (EG1) was set up by TC250/SC7 tasked with developing a standard that conformed with the limit state philosophy and which could be used in the member countries. This paper presents the basis of a draft standard that has been prepared by EG1, which considers the ULS and SLS of the restrained structure and of the anchor itself and introduces the force FServ.k which considers the effect of prestress on the anchor force. The application of the recommendations is illustrated by a design example Keywords. Anchor, Eurocode.

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Introduction The development of a European standard for anchor design presented two major challenges, namely developing a standard for the design of anchors that conformed with the philosophy of the limit state culture of the Eurocode and secondly accommodating the different approaches to anchor design which are used within the various countries. It had been recognized that Section 8:Anchorages of the current Eurocode (EN1997-1:2004) did not adequately cover the design of anchors and an Evolution Group (EG1) was set up by TC250/SC7 tasked with revising this section. The members of this group are listed in the acknowledgements and whilst the views expressed in the paper are solely those of the author, the experience and knowledge of the members was a major source of information. The Evolution Group has been very active over the last year or so and has produced a draft document for circulation within the membership of TC250/SC7. This document has been taken as the basis of this paper and will be referred to as Sec 8:July 2012 in the text. Also, the document EN1997-1 ‘Geotechnical Design-Part 1’ will be abbreviated to EC7. The design of anchors is inextricably linked to their construction (execution) and to the methods used to test the anchors. EN1537:1999 ‘Execution of special geotechnical work-Ground Anchors’, which is currently being revised by CEN/TC288 WG14, standardizes the execution procedures and the material properties required for grouted anchors. EN1537 is at the final stages of a review process and comments on prEN 1537:2011 have been received by TC288/WG14 and this execution standard will 1

Corresponding Author.

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E.R. Farrell / Harmonisation of Anchor Design Within Eurocode

be updated in the near future. No standard is currently available on the testing of anchors, however prEN ISO 22477-5 ‘Geotechnical Investigation and Testing –Testing of geotechnical structures – Part 5:Testing of anchorages’ has been circulated for comment and hopefully will be developed into an EN in the near future. This paper summarises the limit state design process set out in Sec 8:July 2012 and the adaptation of that standard to include the variety of design methods that are used in the various countries. The application of the recommendations is illustrated by a design example using the partial and correlation factors given in that draft standard.

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1

An Anchor

The term anchor is generally used to cover such installations as anchor walls (also called deadman anchors), grouted prestressed anchors, non-prestressed anchors (sometimes called passive anchors), duck-bill anchors, and rock anchors, among others. The feature that distinguishes an anchor from other tension members, such as a micropile, is that an anchor transfers a load from the anchor head to a remote stratum using a free length. In order to cover a broad range of anchors the definition adopted in Sec 8:July 2012 is an ‘Installation capable of transmitting an applied tensile load through a free length to a load bearing stratum’. Ideally all of the different types of anchors should be covered in this section of EC7, however, whilst Sec 8:July 2012 covers the basic principles of the design of all anchors it is mainly directed at ‘grouted anchors’. The designer is referred to Section 9 ’Retaining structures’ for the design of anchor walls. A grouted anchor is defined as ‘An anchor that uses a bonded length formed of cement grout, resin or similar material to transmit the tensile force to the ground.’ It should be noted that EN1537 is limited to grouted anchors only and the use of the term ‘ground anchor’ in that standard refers solely to that type of anchor. The presence of a free tendon length means that an anchor can a) be prestressed to minimize deformations in a structure or supporting structure and b) that generally it can readily be load tested using a jack, thus avoiding the need for expensive reaction beams that are required to test tension piles in order to take the reaction away from the tested element. These tests can assess, not only the load carrying capacity of the anchor tested, but also that the bonded length is correctly located by comparing the measured extension under load with that calculated using the designed free length. The maximum test load to which each anchor is subjected (Proof load) has implications on the value of the partial factors that can be adopted in design. One aspect of the anchor standardization which the author considers is poorly addressed in the current draft of Sec 8:July 2012 is the grey area between the definition of an anchor and a micropile. The requirement in Sec 8:July 2012 that all anchors be subjected to acceptance tests, including non-prestressed anchors, does not give a smooth transition with the testing requirements of micropiles and could cause confusion should the latter be given free length for a special reason, such as to prevent downdrag or to allow for ground expansion.

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17

Limit states in anchor design

This section presents a summary of the limit state design of anchors to Sec8:2012. The standardization of anchor design within the limit state framework must consider: Ultimate Limit States (ULS) and Serviceability Limit States (SLS) of the anchor, together with ULS and SLS of the supported structure.  Prestress forces and the effect of prestress forces, where relevant. 2.1

Ultimate limit state (ULS) design force to be resisted by an anchor

Anchors are required to have the capacity to resist not only the force required to prevent an ULS in the structure and supporting structures, but also, they must have the capacity to resist the maximum force that could be transferred to the anchor during its service life (FServ,k) with an adequate margin of safety. The ULS resistance of an anchor (RULS;d) must be capable of resisting the ultimate limit state (ULS) design force (E ULS,d). EULS,d is the greater of the force required to prevent any ULS in the supported structure (FULS,d) and FServ,d which is the design value of the maximum anchor force expected within the design life of the anchor, including effect of lock off load, and sufficient to prevent a SLS in the supported structure. These requirements are expressed in Eqs. (1) to (3) where γServ is a partial factor:RULS;d ≥ EULS,d

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where E ULS,d = Max(FULS,d; FServ,d) and FServ,d = γServFServ,k

(1) (2) (3)

All the load conditions that would apply during the life of the anchor must be considered when deriving the design value FULS,d, and where relevant, the limit states considered must include those that could arise from any prestressing force which may be applied. The introduction of FServ,k is a novel concept within Eurocode, but is required to ensure that an anchor has the required SLS and ULS resistance under the maximum working load likely to be experienced over its working life. It is similar to the concept of a ‘service load’ used in the French practice and to the ‘working load’ used in the UK. It is needed because anchors may well sustain in service forces that are bigger than the force required to prevent an ULS in the structure and supporting structures. Where a prestress force is required in an anchor to prevent a SLS in the structure, F Serv,k would include the effect of that prestress and any increase that may subsequently occur if staged construction is involved. Depending on the value of γServ adopted, the value of FServ,d in some design situations may exceed FULS,d. Consequently, where applicable, the anchor must be designed to resist this higher value with a sufficient margin of safety. Some countries, for example Germany, do not require FServ,d as the prestress force is considered when determining FULS,d.

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2.2

E.R. Farrell / Harmonisation of Anchor Design Within Eurocode

Serviceability limit state (SLS) design force to be resisted by an anchor

A separate validation of the SLS of an anchor is not required in some countries as it is considered to be satisfied by the margins in the ULS calculation, i.e by Eq.1. When stated in the National Annex of a country, as well as satisfying Eq.1, an anchor shall be designed to ensure that it has the required design SLS resistance (R SLS;d) such that the appropriate SLS limiting creep or load loss criteria are not exceeded at FServ,k, with an appropriate margin of safety, i.e Eq.4 must be satisfied, where γF,SLS is a partial factor (normally equally to unity). France and the UK have such requirements but this calculation is not required in Germany. RSLS;d ≥ γF,SLS FServ,k 2.3

(4)

Geotechnical ultimate limit state anchor resistance

The design value of the geotechnical ultimate limit state anchor resistance (R ULS;d) can only be obtained from values measured (RULS;m) in investigation and/or suitability tests on anchors. The assessment of measured values depends on the particular criteria used in each country and is discussed in further detail in Section 4. The design value is determined from the measured values using Eqs.5 and 6. RULS;k = RULS;m,min / ξULS

(5)

where RULS,m,min is the lowest value of RULS;m measured in investigation and/or suitability tests, for each distinct condition of the ground and structure, RULS;k is the characteristic value of the ULS anchor resistance and ξULS is a correlation factor. Also, RULS;d = RULS,k / γa,ULS

(6)

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where γa,ULS is a partial factor. 2.4

Geotechnical serviceability limit state anchor resistance

In those countries that consider the SLS of an anchor in their design, the design value of the geotechnical serviceability limit state anchor resistance (R SLS;d) can only be obtained from values measured (RSLS;m ) in investigation and/or suitability tests on anchors in a similar manner to that adopted for ULS design, which is:RSLS;k = RSLS;m,min / ξSLS

(7)

RSLS,d = RSLS,k / γa,SLS

(8)

Where RSLS;k is the characteristic value of the SLS anchor resistance, RSLS,m,min is the lowest value of RSLS;m measured in investigation and/or suitability tests, ξSLS a correlation factor and γa,SLS is a partial factor which would commonly have a value of unity.

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Determining RULS,m and RSLS,m

Sec 8:July 2012 requires that the geotechnical resistance of an anchor be determined from anchor tests, however such tests must be taken to a Proof load (PP) which confirms that the anchor has sufficient resistance under a specified load sequence and time hold periods. In order to satisfy Eq.1 using Eqs.5 and 6, the Proof load in investigation and/or suitability tests must satisfy Eq.9.

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PP ≥ ξULS γa,ULS EULS,d

(9)

The difference between investigation and suitability tests is mainly that investigation tests are carried out on a sacrificial anchor (sometimes called preliminary anchors) and are designed to be taken to a failure criterion, whereas suitability tests are carried out on working anchors and not necessarily to failure. The definition of an investigation test in the standard is ‘Load test to establish the geotechnical ultimate resistance of a ground anchor at the grout/ground interface and to determine the characteristics of the anchor in the working load range’. Such tests are typically taken to failure of the ultimate grout/ground interface, possibly using a stronger tendon than is required for a working anchor. The definition of a suitability test is ‘Load test to confirm that a particular anchor design will be adequate in particular ground conditions’. Suitability tests are not generally expected to be taken to a failure criterion of an anchor but must show that the anchor has sufficient resistance to satisfy the requirements of Eq.1. Sec 8:July 2012 requires a minimum number of investigations/suitability tests to be carried out, but the number required can be set in the National Annex. Typically an anchor design should be based on a minimum of two or three such tests. Different anchor test methods are in use in Europe and different limiting criteria are interpreted from these tests. Not all ULS criteria adopted could be said to be a true ‘pull-out resistance’ of an anchor. This has significance when it comes to the level to which an acceptance test can be taken. An acceptance test is used to verify the resistance of each individual anchor and is discussed in Section 4. The interpretation of anchor capacity from load tests is based on the relationship between load and creep rate or load loss rather than the load displacement relationship which is used for piles. The creep rate is determined from the displacement/time measurements where the load is maintained or from the loss of load/time measurements where the displacement of the anchor head is held constant. Three test methods are recognised in pr EN ISO 22477-5 and are referred to as Test Methods 1 to 3 (TM1, TM2 and TM3). An indication of the measurements to be made in these anchor tests and the type of loading regime applied can be got from those required for Investigation tests, which can be taken to failure, and which are summarised in Table 1. The definition of RULS,m and RSLS,m adopted in Sec 8:July 2012 states that the limit state values of these resistances are those complying with the relevant ULS or SLS criteria. This wording has been carefully chosen to avoid the difficult task of defining the ultimate failure or serviceability condition and allows each country to continue with current practice. The provisional limiting criteria for the three test methods in Annex 8 of Sec8:July 2012 are given in Table 1.

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E.R. Farrell / Harmonisation of Anchor Design Within Eurocode

The measured ultimate resistance is taken as that anchor load that induces the limiting condition, or the Proof load applied (PP) if that criterion has not been reached i.e. RULS;m = Min { Rm (αULS or kl ULS) and PP} Note: α and kl defined in footnote to Table 1

(10)

A similar approach is taken in the determination of RSLS;d, for those countries which consider a SLS resistance of an anchor.

Table 1. Summary of anchor test methods 1 to 3 for investigation tests. Test method

TM1

Type of loading

Cycle loading

Rest periods

Maintained loads Tendon head displacement vs applied load at end of each cycle

TM2

TM3

Cycle loading Maintained deflection Load-loss vs time at the highest load of each cycle

In steps Maintained load Anchor head displacement vs anchor load at the beginning and end of each load step.,

Measurements Tendon head displacement vs time

k1 versus anchor load

α versus anchor load

Anchor head displacement vs time for each load step. α versus anchor load or bond load, if possible.

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Displacement vs load for all cycles SLS Limiting values in Sec8:July 2012 ULS Limiting values in Sec8:July 2012

NA

k1,SLS =2% per log cycle of time

Pc

α1,ULS = 2mm

k1,ULS =2% per log cycle of time.

α3,ULS =5mm

Note:α = slope of ‘creep displacement versus logarithm of time. k1= load loss expressed as percentage of applied load; NA= Not Applicable

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Acceptance testing of anchors

The values of the partial and correlation factors used in the design of anchors is inextricably linked to the degree to which the capacity of each working anchor is verified in an acceptance test. Lower partial factors can be used in the design of anchors when the Proof load is such that RULS,d ≥ EULS,d is verified than if the test were taken to a lower proof load. Some countries relate PP of acceptance tests to the ‘service load’ or ‘working load’ and the degree to which RULS,d is verified in such cases has to be considered. Sec 8:July 2012 requires that an acceptance test is carried out on every anchor and permits countries to select whether PP is based on EULS;d or FServ,k from Eqs.11 & 12:PP ≥ ξa,acc,ULS γa,acc,ULSEULS;d

(11)

or PP ≥ ξa,acc,SLS γa,acc,SLS, γF,SLS FServ,k where

(12)

ξa,acc,ULS ; ξa,acc,SLS are correlation factors

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γa,acc,ULS; γa,acc,SLS are partial factors

Germany, for example, uses Eq.11 and requires acceptance tests to be loaded to the same PP as investigation/suitability tests and to satisfy the same criterion (α1=2mm), albeit which shorter holding periods. France on the other hand, load the anchors to a lower PP for acceptance tests which is 1.25 FServ,k for permanent anchors but requires an anchor to satisfy a creep criterion that is less than for a ULS condition. The results of tests taken to failure, which are mandatory in France, are used together with their experience of anchor performance, to be satisfied that anchors that comply with this criterion satisfy the ULS requirements. The current draft of Sec 8:July 2012 does not address the design of anchors should one of the anchors fail an acceptance test, even if only marginally. Should this anchor test be incorporated into the design process of all the anchors or should it be essentially ignored and treated as an outlier.

5

Discussion

The application of the principles of Sec 8:July 2012 can best be illustrated using an example of the design of an anchored sheetpile wall as illustrated on Figure 1. Taking an anchor spacing of 3m and using a simple limit equilibrium analysis (LEM) and the free earth anchor support method, a design value of the ULS force (FULS,d) of 270kN/anchor is determined using Design Approach 1. Interestingly, Germany uses a different calculation approach that determines a characteristic permanent (F G,k) and (FQ,k) variable anchor components and FULS,d using Eq.13. Any prestress force is included in the determination of FULS,d in Germany.

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E.R. Farrell / Harmonisation of Anchor Design Within Eurocode

FULS,d = 1.35 FG,k +1.5 FQ,k

..

(13)

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As there is no particular requirement on serviceability in this example, there is no need to apply a particular prestress into the anchor at lock-off. Typically the prestress force may be related to FServ,k in those countries which determine that force.

Figure 1. Design example of quay wall.

FServ,k must be determined in those countries which elect to consider this force in the design of anchors. In practice for the simple design situation of the Quay Wall given in Figure 1, the value of FServ,k is frequently estimated by carrying out a simple LEM analysis using characteristic values of actions and soil parameters/resistances and using the length of the sheetpile wall required for equilibrium with these forces, i.e. with a sheet pile shorter than required for ULS. For the Quay Wall example, this would give FServ,k = 158 kN/anchor, provided it is not prestressed to a higher force. The design value of this force for ULS design is obtained from Eq.3. Using γserv=1.35, then FServ,d = 213.3 kN/anchor for use in Eq.2. The SLS resistance of an anchor (RSLS,d) would be determined from Eq.4 using γF,SLS of 1.0. Note that a different value of FServ,k would be obtained from a finite element method, the actual value being dependent on the soil model and the sequence of loading adopted.

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In summary,

RULS,d ≥ EULS = Max(270 , 213.3) = 270kN/anchor

and , if required in the NA,

RSLS,d = 1.0x158kN/anchor = 158kN/anchor

As stated previously, Sec 8:July 2012 requires that anchors be designed from investigation/suitability tests, and with the provisional values given in Annex 8 of a minimum of 3 if test methods 1 & 2 are adopted or a minimum of 2 if test method 3 is used. Irrespective of the test method to be employed, and using the provisional values given in Annex 8 (γa,ULS = 1.1, ξULS = 1.0 for acceptance tests on all anchors) in order to verify the ULS resistance, the Proof load in investigation/suitability tests (I/S tests) in all test methods must be taken to be:PP (I/S tests) ≥ ξULS γa,ULS EULS,d = 1.0x1.1x270 = 297 kN The value of PP applied in acceptance tests depends on the test methods selected for use in each country. For instance, in Germany, PP is based on EULS,d (Eq.11) and TM 1 (γa,acc,ULS = 1.1, ξa,acc,ULS =1.0), which gives:PP (acceptance TM1) ≥ 1.0x 1.1x270 = 297 kN and must meet a ULS criterion

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The Proof load for acceptance tests in France is based on FServ (Eq.12) and uses TM3 (γa,acc,SLS = 1.25, ξa,acc,SLS =1.0, γF,SLS =1.0 ), which for permanent anchors gives:PP (acceptance TM3) = PP ≥1.0x1.25x1.0x158 = 198kN but must meet a creep criterion less stringent than that for a ULS condition. When using TM3 for acceptance tests, the confidence that each anchor has the required RULS,d relies on a combination of the database/experience from results at this level of Proof load, and from the results of the investigation tests which are mandatory in France. It is also a requirement that the apparent free length of a grouted anchor comply with the requirements in EN 1537. The question of differing value of PP in acceptance tests for temporary and permanent anchors has not been addressed in Sec8:July2012 but could be covered in the National Annex of each country. While a definition of a temporary anchor is given (anchor with a design life of 2 years or less), it is considered by some that this relates to corrosion protection and that the partial and correlation factors for acceptance tests would more correctly be related to the consequences of a failure and amount of monitoring employed, rather than to a time interval.

6

Conclusion

The current draft of a standard for anchor design (Sec8:July2012 ) that has been prepared for circulation with SC7 of TC250 presents a rational and comprehensive framework for the limit state design of an anchor that considers the ULS and SLS limit states of the structure and of the anchor.

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E.R. Farrell / Harmonisation of Anchor Design Within Eurocode

The preparation of the standard on anchors that harmonizes the European experience has been difficult owing to the varying practices that have developed over the years in the different countries. These differences relate to the methods used to determine the force for which the anchor design is based and on the criteria used to assess the anchor performance from testing. It was considered necessary to introduce a force, FServ,k , which considers the effects of prestress on the anchor force, as well as the anchor force required to ensure that SLS requirements of the structure and supported structure. Many of the anchor testing methods in use at present have been developed for a different design philosophy and there is scope for reviewing the practices to make them more consistent with that of a limit state design method.

Acknowledgements The author would like to acknowledge the information exchanged in EG1 with members Klaus Dietz, Yves Legendre, Caesar Merrifield, Ole Møller, Pierre Schmitt, Bernd Schuppener, Arne Schram Simonsen and Brian Simpson. The author would also like to thank his colleagues Conor O’Donnell and David Gill for their assistance.

References

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EN 1537:1999, ‘Execution of special geotechnical work – Ground anchors’ prEN 1537:2011 Execution of special geotechnical work – Ground anchors’ EN1997-1:2004 Eurocode 7:Geotechnical Design-Part 1:General Rules. prEN ISO 22477-5 ‘Geotechnical investigation and testing – Testing of geotechnical structures – Part 5:Testing of pre-stressed ground anchors.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-25

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Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland Beata GAJEWSKA1 Road and Bridge Research Institute, Poland

Abstract. In Poland, designing with the use of limit states and partial factors has been a common practice for over 30 years. However, there are many differences between Eurocode 7 and Polish practice and previous codes. The paper presents some of these differences. The state of Eurocode 7 implementation in Poland is presented in general. Eurocode gives opportunity to choose one of the three Design Approaches. The reasons of the choice of the Design Approaches in Poland are presented. The Polish National Annex to EC7, as well as the Polish EC7 guide, are discussed. Reliability issues and the National TC Geotechnics’s structure reliability approach are also raised. Keywords. Eurocode 7, Polish Standards PN-B, Polish practice, EC7 implementation, limit state design, partial factors

Introduction

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In Poland, the designing with limit states and partial factors was introduced in 1974. Foundations, retaining walls and similar structures were designed on the basis of a set of Polish Standards (PN-B) of design. The main of these standards include: • • •

PN-B 03020:1981 Shallow foundations. Geotechnical design, PN-B 02482:1983 Bearing capacity of piles and pile foundations, PN-B 03010:1983 Retaining structures. Geotechnical design.

These standards are presently not harmonized with Eurocode 7. The PN-B standards generally use the concept of limit states and partial factors. However, in practice there are exceptions for some problems (e.g. for slope stability), in which the use of global safety factor is considered more reasonable. There are also several standards which are harmonized with the Eurocodes (with the ENV EC generation). They include: • •

PN-B-02481:1998 Geotechnics. Basic terms and definitions, PN-B- 06050:1999 Geotechnics. Earthworks.

Previous Polish Standards of design include calculation models and detailed procedures.

1 Corresponding Author: Beata Gajewska, Road and Bridge Research Institute, Instytutowa 1, 03-302 Warsaw, Poland; E-mail: [email protected]

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

1. Structure of EC7 Eurocode 7 should be used for all structure-ground interaction issues, foundations and retaining structures. The Standard concerns buildings, bridges and other engineering structures. In Eurocode 7-1 (PN-EN 1997-1) the method of limit states is used. Partial factors in EN 1997-1 are analogous to the load factors (usually greater than 1) and reduction factors (usually less than 1) in the previous PN-B standards. However, the system of factors (partial and correlation) in the Eurocode 7-1 is more developed and diversified. For each of the three design approaches EC-7 gives different sets of partial factors. The recommended values of the factors are in Annex A. They can be determined nationally. Detailed rules for the design or calculation models (i.e. specific formulas or charts) are included in informative Annexes only. Eurocode 7 is a quite general document, which gives only the geotechnical design principles. It allows to calculate the geotechnical actions on the structures, as well as ground resistances. It also contains the rules and principles of good practice. Standard EN 1997-1 does not include many commonly used structures such as reinforced soil with nails or geosynthetics, or ground strengthened by columns or other inclusions. Eurocode introduces a term “geotechnical design”, which is new to the Polish practice.

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2. The main differences between PN-B and EC7 Eurocode is quite close in philosophy to the previous Polish standards. In both cases, namely EC7 and PN-B, the limit states are checked and partial safety factors are used. However, there are many significant differences. They have been reported in many papers (Kłosiński 2007, Kłosiński and Rychlewski 2009, Konderla 2008, Kotlicki 2005, Wysokiński 2002, Wysokiński 2006). This paper discusses only a few examples. Comparative calculations (Wysokiński et al. 2011, Krzyczkowska et al. 2004, Wysokiński 2008) indicate the designing according to the previous PN-B to be usually more economical than those based on Eurocode 7. Nonetheless the structures are generally safe. A few cases of failure were caused by reasons not related to used values of safety factors (Wysokiński 2007). 2.1. Design of spread foundations The provisions of Section 6 of EC7 apply to spread foundations including pads, strips and rafts. This Section contains a list of the limit states. The actions listed in 2.4.2(4) of EC7 should be considered. Informative annexes provide detailed examples of calculation models for bearing resistance calculation (Appendix D), semi-empirical method for bearing resistance estimation (Appendix E), settlement evaluation (Appendix F), deriving presumed bearing resistance for spread foundations on rock (Appendix G). The provisions of Chapter 6 concern the design of spread foundations in all possible cases. Given calculation models concern verification of basic limit states. The scope of PN-B 03020:1981 is restricted to the commonly occurring cases. Analyses were reduced to demonstrate that exceeding the elementary limit states are sufficiently improbable, i.e. loss of bearing resistance of soil under the foundation

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

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(including slip of foundation) and the settlement limit state. For these cases, the standard sets out detailed procedures to be followed. The Standard indicated that for specific cases it is needed to incorporate additional recommendations that have not been determined. Formulas for the dimensioning of the spread foundations in drained conditions are similar to those previously used. But in fact, they differ significantly from PN-B 03020:1981 due to different foundation shape factors and inclination of the load factors (according to PN-B the load inclination factors was determined from nomographs). The verification of bearing resistance limit state in undrained conditions is novel for the Polish standard.

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2.2. Design of pile foundations The provisions of Section 7 of EC7 apply to end-bearing piles, friction piles, tension piles and transversely loaded piles installed by driving, by jacking, and by screwing or boring with or without grouting. Piles should be constructed in accordance to standards: EN 1536 – Bored piles, EN 12063 - Sheet pile walls and EN 12699 Displacement piles. Eurocode 7-1 contains the general patterns and recommended values of partial safety factors and the rules for determining the resistances (correlation factors). The pile design should be generally based on load tests (static and dynamic), or the observed performance of a comparable pile foundation. Calculations based on the results of the ground tests have a supporting role, and there are no indications how to calculate resistances. EC 7 contains general requirements for the interpretation of pile tests and determination of characteristic and design resistances. In difference to PN-B, there are no numerical values to determine the resistances or displacements of piles. Extensive information about the design of steel piles and sheet piling is provided in EN 1993-5. EN 1997-1 provisions are quite significantly different from the previous Polish standards and unsatisfactory for practical design of piles. It will be necessary to use withdrawn national standards, guidelines and technical literature. However, pile standard PN-B-02482:1983 requires a substantial change, updates and complements, as well as adjustments to the requirements of Eurocode. The equation 7.9 (characteristic values of base resistance and shaft friction obtained by calculation) according to EN 1997-1 is similar to the equation in Polish standard PN-B-02482:1983. The base resistance qb;k and shaft friction qs;i;k are not entirely synonymous with resistance qi and ti in the PN-B standard. For the practical application of Eurocode 7-1 it will be necessary to supplement the National Annex and amend the previous pile standard PN-B-02482:1983. Standard PN-B-02482 is already regarded as too conservative. The application of unit base resistance and shaft friction of piles, taken directly from the PN-B-02482: 1983 to EN 1997-1, results in an additional factor of safety. Ultimate resistances in the PN-B-02482: 1983 are not true ultimate values in the meaning of EN 1997-1, but “design limit values” (i.e. reduced).

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

2.3. Design of retaining structures and anchorages. The standard distinguishes between retaining structures: gravity walls, embedded walls and composite retaining structures. Section 8 contains list of limit states (ULS and SLS), actions (inter alia weight of backfill material, surcharges, weight of water, wave and ice forces, thermal effects) and design situations, which should be considered. It describes in detail the rules for determining the earth pressure on the walls (at rest, active, passive, intermediate) The informative Annex C contains example calculation formulas and charts for analytical determination of earth pressures. The rules are generally similar to those given in the PN-B 03010:1983; however, they are substantially different in many ways. Different values of displacement needed for mobilization of earth pressure may be an example. Displacement values necessary for raising passive earth pressure are at least twice as large in EC7 (Wysokiński et al. 2011).

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2.4. Characteristic values of soil parameters In geotechnical design proper determination of geotechnical parameters, i.e. the numerical values of the ground properties, is a key issue. The rules for determining characteristic values according to EC 7-1 are significantly different from previous national standards PN-B. Till now they were equivalent to the most probable i.e. average values. The characteristic value of the parameter did not depend on the type and number of tests. The design value was determined by reducing (or increasing) the characteristic value by applying the relevant factors or their combinations. EC 7-1 states that the characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state. Further, it is said that if statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state is not greater than 5%. A cautious estimate of the mean value is a selection of the mean value of the limited set of geotechnical parameter values, with a confidence level of 95%. So these are significantly reduced (or increased) values. It is an important difference compared to the previous national practice. Design values of geotechnical parameters (according to 2.4.6.2 of EC7) can also be assessed directly (expert’s values). In this case, the values of the partial factors recommended in Annex A should be used as a guide for required level of safety.

2.5. Other design issues Eurocode 7-1 contains rules for several important design problems that have not been included in previous national standards, or were considered marginal. These are: hydraulic failure (Section 10), overall stability (Section 11) and the design of embankments (Section 12). These issues are presented in some detail, but not exhaustively. EC-7 provide lists of limit states, actions and design situations. Detailed rules for checking the resistance and overall stability may be new for Polish designers. There is no comprehensive national literature on these subjects, especially including provisions of EC 7. Instruction ITB 424/2011 concern the evaluation of overall stability of slopes.

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The design of anchorages is a new issue, which was not available in Polish standards before. Often the DIN Standard was used. Eurocode provides requirements concerning the verification of the limit states: ultimate (pull-out resistance, structural resistance, overall stability) and serviceability, calculation models, and requirements concerning tests of anchorages.

3. PL National Annex to Eurocode 7-1 The role of the National Annex, among others things, is to indicate Design Approach and to include the decision of the nationally determined values. The National Annex may also give the normative status to one or more of the informative Annexes. In this case, they become mandatory within the country. Each country may supplement Eurocode 7 general rules by national standards to clarify the calculation models and design rules used in the country. However, these standards must be consistent with Eurocode. One of the tasks of the National Annex is to provide partial coefficients and models to be used in Poland. The proper selection of safety factors values is important to ensure the durability and safety of structures, without excessive costs. In order to establish numerical values of partial factors, the research and comparison analysis with existing national standards are needed. The choices are limited because the values of partial factors for actions have already been included in the standard PN EN 1990:2004, which Poland accepted without changes. Those values are more cautious than in previous Polish Standards. In the Polish NA the following choices were made: • •

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• •

National choice of Design Approach for slopes - DA3; Other than slopes - DA2* (GEO - Design bearing resistance equation 2.7b, characteristic values and γF = 1,0); HYD Limit state – Hydraulic failure by heave - the use of equation 2.9b was recommended; Posted the scope of Ground Investigation for Geotechnical Categories.

Reasons for DA2* selection: • • • •

is the most similar to our previous (current) practice; simples calculation due to less loading combinations (checks with γG 1 are not needed); avoiding multiplying twice the eccentricity of the resultant action by partial factor; was chosen by many countries, including Germany, whose practice is most similar to ours.

Reasons for selection of DA3 for slopes: • •

it is more rational then DA2 for slopes is similar to previous (current) rules of stability verification

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

Table 1. Minimum requirements for the scope of the ground investigation (according to PL National Annex). Geotechnical category

Scope of the subsoil investigation Qualitative determination of the ground properties on the basis of:

Structures classified to the 1st geotechnical category in simple ground conditions

•

archival data analysis

•

comparable experience considered

•

field investigation

Quantitative determination of numerical values of geotechnical parameters on the basis of: Structures classified to the 2nd geotechnical category in simple and complex ground conditions

•

archival data analysis and comparable experience considered

•

field investigation results

•

laboratory investigation results

Quantitative determination of numerical values of geotechnical parameters on the basis of:

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Structures classified to the 3rd geotechnical category in simple, complex and complicated ground conditions

•

archival data analysis and comparable experience considered

•

field investigation results

•

laboratory investigation results

•

special investigation results with allowance made for direct correlations from investigation

There is a general practice that a geotechnical investigation report contains a table with geotechnical parameters values for each layer. These values were often taken from table in standard PN-B 03020:1981 – method B. The method consists of determining the value of the parameter based on the correlation between strength or physical parameters and so cold “leading” parameters (e.g. liquidity index or density index). The National Annex to EC7 states that the scope and methods of the ground investigations as well as geotechnical parameters for the structural design are determined by the author of geotechnical design report (geotechnical conditions of foundation) with cooperation with the structural designer. Minimum requirements for the scope of the ground investigation are presented in Table 1. Annex H was supplemented by the following recommendations: • •

It is recommended to verify the limit states for construction settlements on the basis of displacement and deformation values: smax, θmax, Δmax, ω. Limit displacement and deformation values for buildings: • for commonly used structures • with no special requirements referring to the settlements

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The limit values of measurements of settlements for buildings recommended in the Polish National Annex are presented in Table 2. Table 2. The limit values of measurements of settlements for buildings according to the PL National Annex. smax [mm]

θmax [rad]

Δmax [mm]

ω [rad]

50

0.002

10

0.003

Recommended limit values smax are close to the limit values according to PN-B 03020:1981. So far practice does not indicate these values to be inappropriate. The θmax value is in the range of values recommended in Annex H of EC7 for relative rotation (βmax). The Polish NA in general accepts the partial factor values recommended in EC 7-1 Annex A. In two cases the use of different values of partial factors than those given in Annex A may be justified: • •

more unfavorable values in the case of specific risk, complicated soil conditions and/or unusual loads (structures classified to the 3 rd geotechnical category); less severe values for temporary structures or transient design situations.

The use of more unfavorable or less severe values of partial factors should be justified in the design.

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4. Polish guide to EC7 In 2011 “Geotechnical design according to Eurocode 7 – Guidance” was published (Wysokiński et al. 2011). The guide explains requirements, recommendations and geotechnical design procedures provided in EC7. It describes predominantly cases of design foundations of Geotechnical Category 2. The Guide also compares Eurocode with the previous PN-B Standards, noting Polish practice and experience, especially in the case of shallow foundations and retaining structures. A great part of the publication concerns methods of ground testing and the interpretation of results. The Guide contains three comprehensive sections on foundation designing. These are: design of shallow foundations, pile foundation and design of retaining structures. Attention was also paid to the overall stability of slopes. The guide presents examples of "step by step" calculations of typical, commonly used types of foundations. The guide does not include issues related to hydraulic failure and embankments.

5. Status of Eurocodes in Poland Until 31 December 1993 the use of Polish Standards (PN-B) was mandatory. Disobedience to provisions of standard was a violation of the law. From 1 January 1994 the use of Polish standards is voluntary. However, up to 31 December 2002 it was possible, by the relevant ministers and in some cases, to impose the use of PN. From 1

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

January 2003 the use of PN-B is completely voluntary (Journal of Laws of 2002 No 169 item 1386, the Law on Standardization), beyond a few exceptions. The following rules are applied in national (Polish) standardization (Law on Standardization): • • •

transparency and public accessibility; taking into account the public interest; voluntary participation in the development and application of standards.

According to the Law on Standardization, Polish standards may be established in the law after their publication in Polish (art. 5, paragraph 4). Thus, standards may be referred to in the mandatory documents. Polish Building Law and Ministries’ regulations in many instances state that design shall be made according to standards. The Minister of Transport, Construction and Maritime Economy Regulation (2012) gives the requirements for the content of geotechnical design according to Polish standards PN-EN 1997-1: Eurocode 7: Geotechnical design - Part 1: General principles and PN-EN 1997-2: Eurocode 7: Geotechnical design - Part 2: Ground investigation and testing.

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6. Implementation of Eurocode 7 Both parts of Eurocode 7 are published in Polish. PN-EN 1997-1 was published on 6th May 2008 under the Polish title: “Eurokod 7 - Projektowanie geotechniczne - Część 1: Zasady ogólne”. PN-EN 1997-2 was published on 10th April 2009 under the Polish title: “Eurokod 7 - Projektowanie geotechniczne - Część 2: Rozpoznanie i badanie podłoża gruntowego”. The National Annex to Eurocode 7-1 PN-EN 19971:2008/NA:2011 was published on 27th October 2011. The English version of the National Annex is under preparation by the Polish Standardization Committee on Geotechnics (KT 254). The implementation of the standard EN 1997 'Geotechnical design' has long been discussed. For several years, the specific work has been undertaken in the Building Research Institute ITB (e.g. Kotlicki 2005, Wysokiński 2006) and in the Road and Bridge Research Institute IBDiM (e.g. Assumptions to NA 2002, Kłosiński 2006), as well as in the others. National practice shows that previous standards provide a sufficient (if not excessive) level of safety (Wysokiński 2002, Kotlicki 2005). Therefore, there is no reason for radical changes in the value of safety factors. In foundation design according to PN-B Standards, the total safety factor was a combination of partial factors applied to the loadings (different in the case of buildings and bridges) and to the soil parameters (material parameters), corrections factors m (additional partial factor, having no equivalent in EC7) and others. This results in large number of variables and complicates the comparison of the effects of designing according to Eurocode-7. Additionally, the values of partial factors to be applied in Poland to the actions have already been established in the National Annex to the standard PN-EN 1990. PKN Technical Committee No. 254 on Geotechnics consider that it is reasonable to complement Eurocode 7 by national standards harmonized with the EC7, complementary its provision. There is a need to clarify the rules for determining geotechnical parameters, designing spread foundations, designing pile foundations,

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designing retaining structures (including deep excavations) and checking the overall stability. Some national geotechnical standards, e.g. PN-B-03020, PN-B-02482, PN-B03010 will still be needed (as in other EU countries). However, those standards should be completely rewritten: harmonized with Eurocodes, updated and supplemented. In order to promote Eurocode numerous conferences, seminars and workshops are organized. To familiarize designers with design according to Eurocode, postgraduate studies „Geotechnical design” and courses are organized. EC7 Implementation Commission was established in the Polish Geotechnical Committee (PKG). Tasks of the Commission are as follows: • • • • •

Clarification and analysis of Eurocode 7. Opinion and advisory role in the preparation of standards. The collection of opinions. Popularization of European Standard solutions. Collection and dissemination of information on Eurocode 7.

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7. Structure reliability aproach Limit state methods, in previous Polish Standards, were methods in which an appropriate level of reliability of a structure was achieved by using a set of partial factors modifying representative values of variables deciding upon the condition of a structure. The values of safety factors have been established on the basis of previous experiences. Now Poland has adopted values of partial factors recommended in Annex A. As previously mentioned, Polish Standards were generally more economical. Calibration of current reliability measures, i.e. calibration of partial factor values recommended in the Polish NA, is needed, especially in the case of some types of foundations, e.g. piles. Simplified probabilistic methods with the use of the reliability ratio β (provided in Eurocode 1990) and probabilistic methods in Polish geotechnical practice are rather not used. After 30 years from the introduction of Polish Standards generation based on semi probabilistic method of limit states there exists a general view, that acceptance of a slight risk of failure of every structure is unavoidable, and that fundamental variables taken into account in the design process are usually uncertain (Woliński 2011). The Polish TC 254 for Geotechnics initiated action aiming at a common approach to the reliability of the structure from the loadings point of view (EC0 and EC1) and geotechnical resistances (EC7), and, consequently, a common calibration of reliability measures. In Table 3 a comparison of the safety factors in PN-B-02482 and EC7 is presented. For this comparison it was assumed (for a building) that 70% of loading is dead loads and 30 % is live loads. In this case the total safety factor obtained from applied partial factors according to EC7 is about 40 to 50 % higher than according to PN-B. The shaft and base resistances given in PN-B-02482 are design limit values, i.e. reduced (equivalent settlement of about 5% of the diameter). The EC7 limit resistance corresponds to a settlement equal to 10% of the diameter. The number of tests or profiles has a significant impact on the result. Total factor according to EC7 is even greater because of the way of determining the characteristic resistances. In the Polish

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B. Gajewska / Eurocode 7 and Polish Practice: Implementation of Eurocode 7 in Poland

Standard PN-B the characteristic value is a mean value, not a cautious estimate. And pile foundations are in general safe and rather oversized. Table 3. Comparison of the safety factors for piles in PN-B-02482 and EC7. Piles - partial factors for:

PN-B-02482 *

Eurocode 7-1

loads

(0,7 x1,1+0,3x1,2)=1,13

(0,7x1,35 + 0,3x1,5)=1,395

parameters

1/0,9 = 1,11

1,4 - 1,25

resistance

1/0,9** (0,8; 0,7) = 1,11

1,1

1,13:0,9:0,9=1,4

1,395x(1,25-1,4)x1,1=1,92-2,15

total factor Ratio * **

(1,92 – 2,15) : 1,4 = 1,37 – 1,54

70% of loadings is dead weight, 30 % is live loads m=0,9 for 3 and more piles, 0,8 for 2 piles, 0,7 for 1 pile

8. Conclusions

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Eurocode 7 is not easy to use, despite similarity to previous Polish Standards. Previous Polish Standards include calculation models and detailed procedures to be followed. They were also less extensive than EC7. The statements in EC7 are often more general than a designer (used to more detailed standards) would expect. More details on the determination of characteristic values of geotechnical parameters are needed. Parameter values should be adjusted for the type and features of a specific structure. Calibration of current reliability measures (partial factor values recommended in the Polish NA) is still needed, especially in the case of some types of foundations, e.g. piles, anchors. A common approach to the reliability of a structure, from the loadings point of view (EC0 and EC1) and geotechnical resistances (EC7), can contribute to improving the design’s economy, while providing safety of a structure.

References EN 1997-1 Eurokod 7 – National Annex NA – Assumptions. The implementation of European standards in road and bridge construction in Poland (bridges). IBDiM, Item SN-1, Stage 2002. Instruction 424/2011(author: Wysokiński, L.). Evaluation of slope stability. Rules for selection of protection. Building Research Institute ITB, Warsaw. Minister of Infrastructure Regulation, 10th of December 2010, changing the regulation on the technical requirements to be met by buildings and their location. Journal of Laws of 2010 No. 239 item 1597 Minister of Transport, Construction and Maritime Economy Regulation, 25th of April 2012, on the establishing of geotechnical conditions for the foundation of building structures. Journal of Laws of 2012 No. 0 item 463. Kłosiński, B. (2006): Perspectives for the implementation of the geotechnical Eurocodes, Inżynieria i Budownictwo No 6, p. 318-322. Kłosiński, B. (2007). Problems of implementation of EN 1997 'Geotechnical design', Inżynieria i Budownictwo No 7-8, p. 361-364. Kłosiński, B., Rychlewski, P. (2009). Characterization of new European geotechnical standards. XXIV National Workshop of Structural Designers. Wisła, 17-20 of March. Konderla, H. (2008). Slope stability in terms of Eurocode 7, Geoinżynieria drogi mosty tunele No 2, s. 26-28. Kotlicki, W. (2005). Design of spread foundations in terms of Eurocode 7. XX National Workshop of Structural Designers, Wisła-Ustroń, 1-4 of March.

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Krzyczkowska, A., Gajewska, B., Kłosiński, B. (2004). Examples of calculations of foundations according to ENV 1997-1. Seminar on "Design of bridges in European standards", IBDiM, Warsaw, 15th of November. PN-B-02481:1998 Geotechnics. Basic terms and definitions. PN-B 02482:1983 Bearing capacity of piles and pile foundations. PN-B 03010:1983 Retaining structures. Geotechnical design. PN-B 03020:1981 Shallow foundations. Geotechnical design. PN-B- 06050:1999 Geotechnics. Earthworks. PN-EN 1536 Bored piles. EN 1990 Eurocode. Basis of structural design. PN-EN 1993-5 Eurocode 3. Design of steel structures. Piling. PN-EN 1997-1 Eurocode 7. Geotechnical design. General rules. PN-EN 1997-1:2008/NA:2011 Eurocode 7. Geotechnical design. General rules. (PL National Annex to EC71). PN-EN 1997-2 Eurocode 7. Ground investigation and testing. PN-EN 12063 Sheet pile walls. PN-EN 12699 Displacement piles. Rymsza, J. (2011). Procedure of fast implementation of Eurocodes in bridge structures in Poland, Rzeszów University of Technology Scientific Papers, Civil and Environmental Engineering z 58 (3/11/I), s. 235248. The Law on Standardization, Journal of Laws of 2002 No 169 item 1386. Woliński, Sz. (2011). Probabilistic basis of contemporary design codes, Rzeszów University of Technology Scientific Papers, Civil and Environmental Engineering z 58 (3/11/I), s. 269-288. Wysokiński, L. (2002). Issues relating to the implementation of European geotechnical standards in Poland, Inżynieria i Budownictwo, No 11, p. 625-630. Wysokiński L. (2006). The implementation of European standards in the Polish geotechnical practice. International Geological Fair „Geologia-2006”, Warsaw, 6-7 of June. Wysokiński, L. (2007). Systematic errors in the ground investigation and their impact on building design. XXIII Conference of Building Failures, Szczecin-Międzyzdroje, p. 527-541. Wysokiński, L. (2008). Information of Technical Committee of Polish Committee for Standardization, TC 254 (Geotechnics) about the Eurocode 7 implementation in Poland. ITB Warsaw, 11 p. Wysokiński, L., Kotlicki, W., Godlewski, T. (2011) Geotechnical design according to Eurocode 7 – Guidance. Building Research Institute ITB, Warsaw.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-36

An Explanation of Characteristic Values of Soil Properties in Eurocode 7 Michael A. HICKS Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, Netherlands

Abstract. The paper investigates the philosophy and use of characteristic soil property values in Eurocode 7. Due to the spatial nature of soil variability, characteristic property values are shown to be problem-dependent and a function of two competing factors: the spatial averaging of properties along potential failure planes, which reduces the coefficient of variation of property values; and the tendency for failure to follow the path of least resistance, which causes an apparent reduction in the property mean. The Random Finite Element Method provides a self-consistent framework for quantifying and understanding this behaviour, and for deriving characteristic values satisfying the requirements of Eurocode 7. It is widely accepted that characteristic values may be over-conservative if they do not account for the spatial averaging of property values. Conversely, this paper argues that characteristic values based only on variance reduction techniques may be unconservative, if no account is taken of the apparent reduction of the mean along potential failure planes. Simpler probabilistic methods can be effective in guiding design through quantifying uncertainty. However, further research is needed to assess when such methods are applicable, and when they are significantly in error and require further attention.

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Keywords. Characteristic value, Eurocode 7, geotechnical design, heterogeneity, reliability, soil properties

Introduction Engineers have traditionally followed a conservative approach to geotechnical design, involving mostly subjective estimates of design soil properties and global factors of safety (Hicks, 2007; Schneider, 2010; Schneider & Fitze, 2011). Eurocode 7 (CEN, 2004) is innovative, in that it requires uncertainties in the design process to be considered more explicitly and in a consistent manner. However, it is also controversial in that it provides little guidance as to how this should be achieved, especially with respect to the determination of so-called characteristic soil property values used in design. This paper focuses on uncertainty due to soil variability and, in particular, on Section 2.4.5.2 of Eurocode 7, “Characteristic values of geotechnical parameters” (CEN, 2004). It highlights and explains selected paragraphs, clarifies the relationship between paragraphs and addresses areas of potential confusion. In particular, it clearly demonstrates the influence of soil heterogeneity and scale of fluctuation on the problem-dependency of characteristic values, and demonstrates how the Random Finite Element Method may be used for improving understanding and for deriving characteristic values satisfying the requirements of Eurocode 7 (Hicks & Samy, 2002b).

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1. Heterogeneity and Eurocode 7 Eurocode 7 states that the design value, Xd, of the soil property, X, is given by X Xd = k (1) m where Xk is the characteristic value of X and γm is the partial safety factor. The value of the partial safety factor is defined by the Code. Hence, all engineering judgement is focused on the chosen characteristic value. In terms of the mean property value, Xm, it may be represented by (2) Xk = αX Xm where αX is a factor which, for strength properties, generally lies in the range 0 to 1. Table 1 lists a selection of paragraphs on characteristic values of geotechnical parameters, taken from Section 2.4.5.2 of EC7 (CEN, 2004) which comprises twelve paragraphs in total. Firstly, Paragraph 1 asserts the principle that characteristic values be “based on results and derived values from laboratory and field tests, complemented by well established experience”; whereas Paragraph 2 asserts the principle that the characteristic value be “selected as a cautious estimate of the value affecting the occurrence of the limit state”. The apparent vagueness of the term “cautious estimate” has led to some debate; while it seems to support the continued application of previous good practice, implying “no change”, there is little specific guidance within EC7 as to how characteristic values should be derived. However, Paragraphs 3-12 present some points of reference, including Paragraph 4 which lists items to account for. In particular, “the variability of the measured property values” highlights the variable nature of soils; whereas, “the extent of the field and laboratory investigation” and “the type and number of samples” highlights the uncertainties that exist when determining property values, partly due to the variability itself and partly due to the constraints of field and laboratory testing. Meanwhile, “the extent of the zone of ground governing the behaviour of the geotechnical structure” indicates that the spatial characteristic of the variability is important. And finally, “the ability of the geotechnical structure to transfer loads from weak to strong zones in the ground” implies that the characteristic value is problem-dependent; that is, for the same ground conditions, the characteristic value will be different for different structures and different loading conditions. Paragraphs 7-8 are an attempt to simplify matters for two limiting scenarios. Firstly, Paragraph 7 considers the case when the zone of ground governing the structure performance is large, relative to the size of soil specimens tested in the laboratory and the zone of ground affected in an in situ test. It states that, in this instance, “the value of the governing parameter is often the mean of a range of values covering a large surface or volume of the ground”. However, there are two things that should be noted: (a) it is the domain size relative to the spatial scale of fluctuation of the property value that is important in assessing the relevance of the mean property value, not the domain size itself, nor its size relative to test samples and field tests although this may have an influence; (b) the mean value of a property over a potential failure surface may indeed be a reasonable choice for the characteristic value (e.g. Tang, 1993), but this value may differ significantly from the mean for the domain of influence as a whole, due to the tendency of failure mechanisms to follow the weakest path. Hence, the challenge is to identify the potential failure mechanisms and whether, and to what extent, the

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M.A. Hicks / An Explanation of Characteristic Values of Soil Properties in Eurocode 7

mechanisms and characteristic values are influenced by the spatial structure of the heterogeneity.

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Table 1. Extracts from Section 2.4.5.2 of Eurocode 7 (CEN, 2004). No.

Paragraph

Author Comments

(1)P

The selection of characteristic values for geotechnical parameters shall be based on results and derived values from laboratory and field tests, complemented by well-established experience.

No change to previous practice.

(2)P

The characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state.

No change to previous practice. But what is meant by a cautious estimate?

(4)P

The selection of characteristic values for geotechnical parameters shall take account of the following:  geological and other background information, such as data from previous projects;

Reduces uncertainty.

 the variability of measured property values and other relevant information, e.g. from existing knowledge;

Should account for soil variability.

 the extent of the field and laboratory investigation;

Affects uncertainty.

 the type and number of samples;

Affects uncertainty.

 the extent of the zone of ground governing the behaviour of the geotechnical structure at the limit state being considered;

Spatial aspect of soil variability is important.

 the ability of the geotechnical structure to transfer loads from weak to strong zones in the ground.

Characteristic values are problem-dependent.

(7)

The zone of ground governing the behaviour of a geotechnical structure at a limit state is usually much larger than a test sample or the zone of ground affected in an in situ test. Consequently the value of the governing parameter is often the mean of the range of values covering a large surface or volume of the ground. The characteristic value should be a cautious estimate of this mean value.

Important to consider the mean over potential failure surfaces; this could be very different to the mean over the domain of influence.

(8)

If the behaviour of the geotechnical structure at the limit state considered is governed by the lowest or highest value of the ground property, the characteristic value should be a cautious estimate of the lowest or highest value occurring in the zone governing the behaviour.

Extreme scenario implying local failure.

(11)

If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%.

5% refers to probability of failure of the structure; not to parameter values.

NOTE: In this respect, a cautious estimate of the mean value is a selection of the mean value of the limited set of geotechnical parameter values, with a confidence level of 95%; where local failure is concerned, a cautious estimate of the low value is a 5% fractile.

Percentages refer to parameter values; not to structure performance.

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For the special case of when the prevailing mechanism dictates a failure surface that is long relative to the scale of fluctuation, a conservative estimate of the mean may be warranted. However, the scale of fluctuation will generally be much larger in the horizontal plane than in the vertical direction. Hence for applications in which the prevailing mechanism has a significant horizontal component, the weaker material zones can have a considerable influence on geo-structural performance as has been demonstrated by Hicks & Samy (2002a, 2002b, 2004), Hicks & Onisiphorou (2005), Spencer & Hicks (2007), Hicks et al. (2008) and Hicks & Spencer (2010). Paragraph 8 considers the other limiting scenario, when a cautious estimate of the extreme value of the ground property may be appropriate. This may be applicable in the following situations: (a) when the domain of influence is small relative to the scale of fluctuation, as is the case in local failure; (b) when deposition-induced anisotropy of the heterogeneity results in semi-continuous weaker zones through which unstable failure mechanisms such as liquefaction can propagate (Hicks & Onisiphorou, 2005). Paragraphs 10-11 concern the possible use of statistics. In particular, Paragraph 11 states that “the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%”. This implies a minimum reliability of 95% for the geotechnical structure (before application of partial safety factors). It is important to realise that Paragraph 11 is not referring to a 95% confidence level for the property value itself, even though the footnote itself is. The footnote to Paragraph 11 is an attempt to explain the implication of the paragraph for the two limiting cases discussed previously in Paragraphs 7-8. Firstly, it states that “a cautious estimate of the mean value is a selection of the mean value of the limited set of geotechnical parameter values, with a confidence level of 95%”; this situation applies when the domain of influence is large compared with the spatial scale of fluctuation characterising the variability. Secondly, it states that “when local failure is concerned, a cautious estimate of the low value is a 5% fractile”; this refers to the underlying property distribution (rather than the mean) and applies when the domain of influence is small compared to the scale of fluctuation. For these special cases, it is reasonable to use the respective mean and property value distributions to satisfy the requirements of Paragraph 11. However, most practical situations require a more general approach.

2. Reliability-Based Characteristic Values Figure 1 illustrates two approaches to deriving reliability-based characteristic property values. Firstly, Fig. 1(a) shows the probability density function of a material property X, which, to simplify the illustration, is assumed to be normal. The simplest way to derive a reliability-based characteristic value of X is to proportion the areas under the distribution, as indicated in the figure. For example, for a reliability of R=95%, the characteristic value Xk is that value of X that subdivides the area under the distribution into the ratio 1:19, as illustrated in the figure. However, this simple approach is only of limited use, as, for most practical situations, Xk will merely be the value of X for which there is a 95% probability of a higher value occurring; it will generally not represent the reliability of the structure itself and will lead to an over-conservative value of Xk.

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M.A. Hicks / An Explanation of Characteristic Values of Soil Properties in Eurocode 7

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(a) Basic definition of Xk

(b) General definition of Xk Figure 1. Derivation of characteristic property values satisfying Eurocode 7

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In order to satisfy the Eurocode 7 requirement for a reliability of 95% with respect to the performance of the structure, a modified distribution of X is required that takes account of the problem being analysed. Figure 1(b) shows that this distribution is different to the underlying property distribution in two respects: it is narrower, to account for the averaging of property values over potential failure surfaces within the soil mass; and its centre of gravity is shifted, to account for failure being attracted to weaker zones. In other words, with respect to the underlying distribution of X, the new “effective” distribution has a reduced variance and a lower mean; this is in contrast to traditional variance reduction techniques, in which no change in the mean is assumed, thereby raising the possibility of an un-conservative value of Xk. The reliability-based value of Xk satisfying EC7 is found by proportioning the area under the effective distribution of X, as indicated in the figure. Note that the distribution of effective X has two limits. When the scale of fluctuation  is very small relative to the size of the domain of influence D, failure mechanisms pass through weak and strong zones alike and there is much averaging of soil properties. This leads to a very narrow distribution and, in the limit when /D tends to zero, to a distribution with a variance of zero. Moreover, due to the assumption of a normal distribution of X, it leads to a mean that is equal to the mean of the underlying distribution. In this case, the characteristic value is indeed a cautious estimate of the mean, as advocated by EC7. Conversely, when the scale of fluctuation is large relative to the domain of influence, there is a wide range of possible solutions and, in the limit when /D tends to infinity, the distribution of effective X tends to the underlying distribution of X. In this case, the characteristic value can be taken directly from the underlying distribution, also in line with EC7. However, for intermediate values of /D the distribution is as shown in Fig. 1(b), with an intermediate variance and lower mean. In this case, the distribution is a function of the point statistics of the soil property, the horizontal and vertical scales of fluctuation of the soil property and the problem being analysed, as demonstrated by Hicks & Samy (2002a, 2002b, 2004) and Hicks & Spencer (2010). It is also a function of the degree of knowledge about a site. Whereas the underlying property distribution quantifies the actual variation in soil property values, the distribution of effective X is the result of uncertainty in the structure response, which, in turn, results from uncertainty in the property values across the domain. This implies that, regardless of spatial variability, if the real value of X is known at every point in the domain the distribution of effective X would become very narrow and, in the limit when all information is known, tend to a single representative value. So, the choice of characteristic value is as much a function of the site investigation as of the spatial variability itself.

3. Stochastic Approach to Eurocode 7 Hicks & Samy (2002b) described a stochastic approach for deriving reliability-based characteristic values satisfying EC7 and demonstrated its use for a simple 2D slope stability problem. The approach uses the Random Finite Element Method (Fenton & Griffiths, 2008), which links random field theory for generating spatially varying property distributions with finite elements for analysing structural response. This section summarises the main features of the approach and, through reference to Hicks

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M.A. Hicks / An Explanation of Characteristic Values of Soil Properties in Eurocode 7

& Samy (2002b), summarises how the modified property distribution illustrated in Fig. 1(b) may be derived. 3.1. Statistical Definitions The geotechnical problem domain is subdivided into distinct material layers (or zones). In traditional deterministic analysis, each layer is represented by a single representative soil property value, thereby leading to geotechnical performance being defined in terms of a single factor of safety for which there is no information regarding probability of failure. In contrast, stochastic analysis may be used to quantify the uncertainty that arises in geotechnical performance, partly (but not exclusively) due to the variability of property values within the layer. In this case, the soil property variability is represented most simply by the property mean Xm and standard deviation SD, and by a probability density function such as the normal distribution used for illustrative purposes in Fig. 1. However, many researchers have demonstrated the importance of including the spatial nature of soil variability in geotechnical analysis. This is often represented by the scale of fluctuation , which is a measure of the distance over which property values are significantly correlated (Vanmarcke, 1983). In the vertical direction the scale of fluctuation v is generally small and often less than one metre (Hicks & Samy, 2002a; Hicks & Onisiphorou, 2005). In the horizontal direction, the scale of fluctuation h is generally much larger, due to the natural or engineered process of deposition (Hicks & Onisiphorou, 2005; van den Eijnden & Hicks, 2011; Lloret-Cabot et al., 2012). 3.2. Summary of Stochastic Process

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Hicks & Samy (2002b) outlined the following three-stage strategy for the stochastic analysis of geotechnical problems: •

The pre-analysis stage involves the determination of statistical properties for the site; for example, the point statistics, Xm and SD, the probability density function, and the vertical and horizontal scales of fluctuation, v and h, taking account of any depth-dependent trends in the statistics.

•

The analysis stage involves a Monte Carlo simulation. It uses the material property statistics to generate multiple predictions (i.e. random fields) of the spatial variability of soil properties over the whole problem domain (Fenton & Vanmarcke, 1990) and, for each prediction, the problem is analysed, for example using finite elements as in the Random Finite Element Method (Fenton & Griffiths, 2008). Hence the result is multiple predictions for the response of the geotechnical problem, in which each prediction of geotechnical performance is based on a different prediction of the spatial variability at the site.

•

The post-analysis stage involves expressing the results of the Monte Carlo simulation probabilistically. This generally involves defining geotechnical performance in terms of probability of failure; or in terms of reliability, the probability of failure not occurring.

Note that, while it may seem counter intuitive to generate numerical predictions of spatial variability for a site based on site-specific statistics determined from field data

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obtained for the same site, it should be remembered that the statistics will have been derived from data obtained at discrete (e.g. CPT) locations. In contrast, the numerical simulations predict soil property values at every location. Hence the purpose of the stochastic analysis is to quantify the uncertainty in the response of a geotechnical structure, not due to the heterogeneity itself, but due to the uncertainty that arises due to having incomplete knowledge about the nature of the spatial variability of material properties (as mentioned earlier). This, in turn, leads to two obvious questions (van den Eijnden & Hicks, 2011; Lloret-Cabot et al., 2012): (a) what is the required intensity of in situ testing to give reasonable estimates of the soil property statistics; and (b), how may the uncertainty in geotechnical performance be reduced through the optimal use of available data?

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3.3. Derivation of Characteristic Values Hicks & Samy (2002b) conducted detailed analyses of a simple slope stability problem, characterised by a spatially varying undrained shear strength, to illustrate how the above stochastic framework can be utilised to derive characteristic soil property values. This involved tackling the problem from two different (albeit equivalent) directions. In the first case, the statistical properties of undrained shear strength for the slope were used to analyse the problem using the Random Finite Element Method. Specifically, for each realisation of the spatial variability of undrained shear strength, the factor of safety of the slope was found by using finite elements and the strength reduction method, so leading to a distribution of factors of safety for the slope. The results demonstrated that, for most realisations, the factor of safety was lower than the factor of safety of the slope based on the mean undrained shear strength, due to the influence of the weaker zones. Using this type of analysis, the distribution of effective property values may easily be backfigured from the distribution of factors of safety (e.g. by using a stability chart). That is, for any realisation, the effective value of X is that single value giving the same factor of safety as the analysis based on the random property field. The result of such a simulation is the effective property distribution illustrated in Fig. 1(b) and, as stated previously, the characteristic value satisfying EC7 is then the value corresponding to the 5% fractile. In the second case considered by Hicks & Samy (2002b), the value of Xk is found by first deriving a relationship between reliability and factor of safety based on the mean property value. This involves the following calculation steps: •

The undrained shear strength corresponding to the slope at the point of failure, for the special case of no spatial variability, is determined; either directly, for example using a stability chart, or numerically, for example using finite elements and the strength reduction method.

•

The influence of heterogeneity for F = 1.0 based on the mean property value is quantified by generating multiple realisations of the spatial variation of X, based on the mean , and on the site statistics V, v and h, in which V is the coefficient of variation and  is equal to the value of undrained shear strength that would just cause the slope to fail in the absence of heterogeneity (i.e. as computed in the previous step). For each random field, the slope is analysed by finite elements to see if it remains standing under its own self weight. The reliability is then the percentage of realisations in which the slope remains stable.

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M.A. Hicks / An Explanation of Characteristic Values of Soil Properties in Eurocode 7

•

The process is repeated for a range of values of F, to enable the complete reliability versus F relationship to be determined. For a given value of F, the mean undrained shear strength is the value of the mean derived in the first step, multiplied by F, whereas V, v and h are the same (i.e. site) statistics as used for all other values of F.

•

For the site in question, the characteristic value for a given level of reliability may be obtained by dividing the mean property value Xm by the appropriate reliability-based value of F (i.e. the value of F corresponding to the required level of reliability).

Note that, for both of the above cases, the derived value of Xk does not correspond to a reliability of the structure of 95%. Rather, it corresponds to the characteristic value that should be used in the geotechnical design. If the structure is calculated to be safe using this value, then the reliability (before additional factoring) will be at least 95%. Conversely, if the structure is calculated to be unsafe the reliability will be less than 95%.

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4. Conclusions Some researchers have reasonably postulated that failure is approximately governed by the mean property value along the failure plane and that the uncertainty regarding property values along the plane is reduced due to local averaging. This leads to the use of variance reduction techniques that reduce the variance of property values as a function of the ratio between the failure plane length and scale of fluctuation, thereby leading to an apparent reduction in uncertainty. However, other researchers have noted that failure mechanisms follow the path of least resistance. Hence the mean property value along a failure plane will generally be lower than the mean property value in the immediate vicinity of the failure zone, with the scale of this reduction depending on the nature of the soil heterogeneity as has been demonstrated in numerous studies. The author supports the view that the mean strength along a failure plane is important, as is the local averaging of properties to reduce uncertainty. However, due to heterogeneity there may be considerable uncertainty in the mean along potential failure planes; so, the use of variance reduction techniques could lead to unconservative estimates of the characteristic value if no account is taken of the apparent reduction in the mean. In summary, due to the heterogeneous nature of soil variability, characteristic property values are shown to be problem-dependent and a function of two competing factors: the spatial averaging of properties along potential failure planes, which reduces the coefficient of variation of property values; and the tendency for failure to follow the path of least resistance, which causes an apparent reduction in the property mean. The Random Finite Element Method provides a self-consistent framework for quantifying and understanding this behaviour, and for deriving characteristic values satisfying the requirements of Eurocode 7. It is widely accepted that characteristic values may be over-conservative if they do not account for the spatial averaging of property values. Conversely, this paper argues that characteristic values based only on variance reduction techniques may be un-conservative if no account is taken of the apparent reduction of the mean along potential failure planes.

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References

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CEN (2004). Eurocode 7: Geotechnical design. Part 1: General rules, EN 1997-1, European Committee for Standardisation (CEN). Eijnden, A.P. van den & Hicks, M.A. (2011). Conditional simulation for characterizing the spatial variability of sand state, Proceedings of the 2nd International Symposium on Computational Geomechanics, Dubrovnik, Croatia, 288–296. Fenton, G.A. & Griffiths, D.V. (2008). Risk assessment in geotechnical engineering, John Wiley and Sons. Fenton, G.A. & Vanmarcke, E.H. (1990). Simulation of random fields via Local Average Subdivision, Journal of Engineering Mechanics, ASCE 116 (8), 1733–1749. Hicks, M.A. (2007) (editor). Risk and variability in geotechnical engineering, Thomas Telford, London. Hicks, M.A., Chen, J. & Spencer, W.A. (2008). Influence of spatial variability on 3D slope failures, Proceedings of the 6th International Conference on Computer Simulation Risk Analysis and Hazard Mitigation, Kefalonia, Greece, 335–342. Hicks, M.A. & Onisiphorou, C. (2005). Stochastic evaluation of static liquefaction in a predominantly dilative sand fill, Géotechnique 55 (2), 123–133. Hicks, M.A. & Samy, K. (2002a). Influence of heterogeneity on undrained clay slope stability, Quarterly Journal of Engineering Geology and Hydrogeology 35 (1), 41–49. Hicks, M.A. & Samy, K. (2002b).Reliability-based characteristic values: a stochastic approach to Eurocode 7, Ground Engineering 35 (12), 30–34. Hicks, M.A. & Samy, K. (2004). Stochastic evaluation of heterogeneous slope stability, Italian Geotechnical Journal 38 (1), 54–66. Hicks, M.A. & Spencer, W.A. (2010). Influence of heterogeneity on the reliability and failure of a long 3D slope, Computers and Geotechnics 37, 948–955. Lloret-Cabot, M., Hicks, M.A. & Eijnden, A.P. van den (2012). Investigation of the reduction in uncertainty due to soil variability when conditioning a random field using Kriging, Géotechnique Letters 2 (in press). Schneider, H.R. (2010). Characteristic soil properties for EC7: Influence of quality of test results and soil volume involved, Proceedings of the 14th Danube-European Conference on Geotechnical Engineering, Bratislava, Slovakia. Schneider, H.R. & Fitze, P. (2011). Characteristic shear strength values for EC7: Guidelines based on a statistical framework, Proceedings of the 15th European Conference on Soil Mechanics and Geotechnical Engineering, Athens, Greece. Spencer, W.A. & Hicks, M.A. (2007). A 3D finite element study of slope reliability, Proceedings of the 10th International Symposium on Numerical Models in Geomechanics, Rhodes, Greece, 539–543. Tang, W.H. (1993). Recent developments in geotechnical reliability, Balkema, Amsterdam. Vanmarcke, E.H. (1983). Random fields: Analysis and synthesis, The MIT Press, Cambridge, Massachusetts.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-46

Implementation of Eurocode 7 in German Geotechnical Design Practice Kerstin LESNY,1 Institute of Geotechnical Engineering, University of Duisburg-Essen, Germany

Abstract. For a long time the framework of geotechnical design in Germany was provided by the basic code DIN 1054 and various specific design and construction codes together with code-like recommendations for specific geotechnical structures. All these regulations were based on a global safety concept. This design philosophy was commonly supported by long-term experience and was understood to be not only safe but also economical. Under these circumstances the transition to the new design philosophy of Eurocode 7 and the Limit State Design was accompanied by a lot of discussions and adjustments until finally a broad acceptance was achieved. This contribution highlights the long tradition of geotechnical design in Germany based on the global safety concept. It shows the difficulties involved in the transition to the Eurocode 7 design principles and illustrates the current status of German Limit State Design in geotechnical engineering. Keywords. Limit State Design, Eurocode 7, global safety factor, partial factor, design approach, shallow foundation, pile foundation

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Introduction Germany has a comparably long history of codified design in geotechnical engineering. The basic German geotechnical design code used for a long period of time was DIN 1054. In addition to this code, a set of specific design and construction codes completed the standardization in this field. Furthermore, various recommendations, e.g. those for excavation pits or waterfront structures, were used for design, which were just as binding as standards. This system of regulations formed the framework for geotechnical design in Germany. It was originally based on a global safety concept with an overall factor of safety which included possible sources of uncertainties related to actions or their effects, to material parameters as well as to the calculation model in use. Minimum values of the overall safety factors for the respective design problems were defined as experience values in the relevant design codes depending on three so called load cases. These load cases were a typical feature of German geotechnical design. The intention of this concept was to introduce different levels of safety depending on the character of actions and the design situation. Because of their long-term experience with this design concept and its related design philosophy, German geotechnical engineers were convinced that geotechnical design was not only safe, but also economical. Hence, the implementation of the 1

Corresponding Author.

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probability based Limit State Design (LSD) was accompanied by a lot of doubts and criticism from the very beginning. In the end it was concluded that the use of probabilistic methods, e.g. for deriving partial factors, was not acceptable for code development, but it was agreed that the Limit State Design and the partial factor concept should be adopted. In the following, the traditional concept of German geotechnical design is highlighted briefly. Afterwards, the procedure of implementing LSD in Germany parallel to the European developments and the final transition to Eurocode 7 is outlined. Some resulting principles of geotechnical design are introduced for shallow and pile foundations and the consequences are discussed on the basis of two design examples.

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1. Traditional Structure of German Geotechnical Design Codes In Germany standards and codes are developed in various committees and published by the “Deutsche Institut fuer Normung” (DIN), which is the German institution for standardization. In geotechnical engineering the standardization goes back more than 70 years. Since then it has been continuously optimized, reaching a very high quality till now (Vogt et. al, 2008). Correspondingly, DIN 1054 was the basic design code for a very long period of time. A first version of it was published already in 1934. Its edition of 1976 was used till the end of 2007 with a transition period of about two years after the LSD-based DIN 1054:2005 came into effect (Weißenbach, 2012). DIN 1054 made reference to various specific design codes such as those for bearing resistance (DIN 4017) or slope stability (DIN 4084) or to construction codes such as the DIN-code for bored piles (DIN 4014). In addition to the DIN-codes, various recommendations e.g. for excavation pits (EAB, 2006), piles (EAP, 2012) or waterfront structures (EAU, 2004) were used in the design, which were just as binding as the codes published by the DIN. These codes and recommendations formed the framework for geotechnical design in Germany. The design in geotechnical engineering was traditionally based on the global safety concept, i.e. on an overall factor of safety K defined as the ratio between the resultant resistance R and the effect of actions E for the system in question. In the design it had to be verified that the existing safety did not fall below a certain minimum value Kmin:

R tEœK K

R t Kmin E

(1)

R and E were so-called deterministic values. Consequently, the inequality in Eq. (1) often led to the assumption that failure could not occur, i.e. that the design is safe in all cases, but the actual safety level was unknown and could only be estimated. Within a design based on the global safety concept actions usually were considered with their highest value or on the safe side. The safety level to be achieved was applied to the resistance only and was supposed to cover all kinds of uncertainties concerning e.g. load assumptions, the calculation model, the design procedure etc. Different safety levels were introduced in a normative way by the definition of load cases depending on the duration of an action and the frequency of its occurrence as defined in Table 1. The global safety factors for various structures according to DIN 1054:1976 and other standards are given in Table 2.

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Table 1. Definition of load cases according to DIN 1054:1976 Load Case LC1 LC2 LC3

Definition Permanent actions and regularly occurring variable actions Actions of LC1 plus irregular variable actions possibly occurring at the same time or actions during construction or repair Actions of LC2 plus extraordinary actions possibly occurring at the same time

There were no standardized regulations for the definition of the deterministic values of E and R. In a former version the recommendations for waterfront structures (EAU) included a procedure for the definition of soil parameters: x x x

Deterministic values had to be derived directly from the results of soil mechanics tests; Basic values had to be defined as reduced arithmetic averages from n tests; Appropriate additions or deductions had to be applied, which considered the inhomogeneity of the ground and uncertainties during soil sampling and testing in the laboratory.

The following so-called cal-values were recommended for the shear strength parameters:

cal c u

cu 1,3

cal cc

cc 1,3

cal tan Mc

tan Mc 1,1

(2)

Table 2. Global safety factors for various geotechnical structures

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Type of Structure Shallow foundations: Bearing resistance Sliding Compression piles (total resistance, one load test) Slopes (global stability analysis)

Safety factor LC1

LC2

LC3

2 1,5

1,5 1,35

1,3 1,2

2

1,75

1,5

1,4

1,3

1,2

2. Implementation of Limit State Design 2.1. Development In Germany, first attempts at implementing the use of probabilistic methods and later the LSD in civil engineering already started in the early 1980s and accompanied the progress on European level from the very beginning. These developments stimulated critical and controversial discussions among the geotechnical engineering community, which felt quite comfortable with the traditional design concept. In the early years, several attempts were made to derive partial factors from probabilistic methods. In various research projects probability-based partial factors were derived e.g. for the bearing resistance of shallow foundations (Schultze & Pottharst, 1981) or for retaining structures (Gaessler & Gudehus, 1983). On the other

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hand, further analyses showed that the reliability level achieved was not consistent in all relevant design situations. Ongoing discussions in various publications and on national conferences (a summary is given in Schuppener & Heibaum, 2011) finally led to the conclusion that probabilistic methods should not be explicitly used for code development, but it was agreed that LSD and the partial factor concept should be adopted (Weißenbach, 2012). As a consequence, a LSD concept was developed in Germany parallel to the development of Eurocode 7 as a new version of the basic design code DIN 1054, supplementing the work on Eurocode 7 and conserving traditional German experience. After several pre-standards had been issued and discussed within the geotechnical engineering community, DIN 1054 was officially introduced and approved by the building authorities in 2003 and shortly afterwards revised in 2005. Schuppener & Heibaum (2011) as well as Weißenbach (2012) outline the development of LSD in Germany, which was directly connected to the redevelopment of the basic design code DIN 1054. This process was called the “German Way” as several aspects of the old German design concept, e.g. the concept of load cases or the design approach later named as DA2* (see section 3.1) were retained. The most important reason for following a separate way, however, was to maintain the safety level of the global safety concept, which was commonly considered by geotechnical engineers to be not only safe but also economical. This means that the dimensions of a geotechnical structure designed with the new DIN 1054:2005 should be roughly the same as if designed using the old DIN 1054:1976. National standardization committees were worried that a different safety level (which may have been the result if partial factors would have been derived from probabilistic analyses) would impact the acceptance of Eurocode 7, leading to a significant delay in the transition process (Vogt et al., 2008). Based on this prerequisite, the partial factors on the resistance were derived from the former global safety factors (see section 3.1). After some years of experience German geotechnical engineers were familiar with the LSD. The design according to DIN 1054:2005 together with its set of design and construction codes was broadly accepted, because DIN 1054:2005 still included regulations representing traditional German design experience, e.g. allowable values for the base pressure of shallow foundations or experience values for pile resistances. On the other hand, DIN 1054:2005 included various regulations which were also specified in the final version of Eurocode 7 published in 2009 (see Figure 1). 2.2. Current Situation After end of the implementation process geotechnical design in Germany is now based on three codes, i.e. Eurocode 7 (DIN EN 1997-1:2009), its National Annex (DIN EN 1997-1/NA:2010) and DIN 1054:2010 as a supplement to Eurocode 7. The National Annex (NA) and DIN 1054:2010 are not independent and can therefore only be used together with Eurocode 7, which is inconvenient. Hence, an edited summary of these codes was published in 2011 as a standard-handbook which includes Eurocode 7 as the basic text supplemented by the regulations of the NA and of DIN 1054:2010, visible by a shade of grey (Normenhandbuch Eurocode 7, 2011).

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DIN EN 1054:2005

Eurocode 7

not adopted design approaches and informative annexes

joint regulations: e.g. limit states, partial factors, geotechnical categories

particular German experiences: e.g. allowable base pressures, pile resistances

Figure 1. Extent of regulations of Eurocode 7 and DIN 1054:2005 (after Schuppener & Ruppert, 2007)

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In addition to this, the framework of codes for geotechnical engineering still includes further design and construction codes as well as recommendations which have been or still need to be revised as necessary. Schuppener (2010a) illustrates the resulting system of geotechnical design codes relevant for waterway engineering (see Figure 2).

Figure 2. New system of geotechnical design codes for waterway structures (Schuppener, 2010a)

German authorities decided on a fixed deadline for the final implementation of the new standards. In most states this was July 1st, 2012. By this date DIN 1054: 2005 has been withdrawn and most of the Eurocodes and their National Annexes have officially been approved and introduced by the state building authorities. For geotechnical engineers this means that they again have to adjust to a new code system including not only new and sometimes unclear regulations, but also new definitions and terminologies, which prevents the acceptance of such codes. The most important changes are discussed in the following section 3. In section 4 the new design procedure will be compared to the old design philosophy based on some of the design examples circulated by the European Technical Committee 10 (ETC10).

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3. New Regulations for Geotechnical Design According to Eurocode 7 3.1. General In the version of DIN 1054:2005 the concept of load cases was still maintained, but the load cases were attributed to combinations of actions depending on their occurrence frequency and safety classes depending on the particular condition of the structure relevant for specific time periods. With the new DIN 1054:2010 the concept of load cases has finally been abandoned and partial factors are now defined for several design situations to adjust to DIN EN 1990:2010. However, the design situations mostly coincide with the traditional load case definitions as shown in Table 3.

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Table 3. Design situations defined in DIN 1054:2010 compared to the load cases of DIN 1054:2005 Design Situation

Denotation

Permanent design situation Transient design situation Accidental design situation Design situation for earthquake

BS-P BS-T BS-A BS-E

Load Case acc. to DIN 1054:2005 LC1 LC2 LC3 LC3

In DIN 1054:2005 three limit states 1A, 1B and 1C were differentiated in the Ultimate Limit State (ULS). With the final implementation of Eurocode 7 a new terminology has been introduced and the classification of the limit states is to some extent different than in DIN 1054:2005. The main differences refer to limit state 1A (problems dealing with a loss of equilibrium), which was split up into the limit states EQU (general equilibrium problems such as overturning), UPL (failure due to vertical forces acting in upward direction) and HYD (failure caused by flow gradients, e.g. hydraulic heave). Limit state 1B which was formerly regarded as the limit state that usually determines the dimensions of a geotechnical structure was split up into the limit states STR (internal failure of the structure) and GEO-2 (failure of the ground). A comparison of the former and the new definition of the limit states in the ULS is given in Table 4. The National Annex DIN EN 1997-1/NA:2010 states that the use of design approach 1 (DA1 – partial factors on actions or on material parameters, two combinations have to be checked) according to Eurocode 7 is not permitted in Germany. For usual design situations within limit state GEO, which have formerly been assigned to limit state 1B, design approach 2 (DA2, i.e. GEO-2) is now used whereas design approach 3 (DA3 - partial factors on actions and material parameters) has to be applied to overall stability analyses (GEO-3). DA2 is used with the “German” modification (commonly known as DA2*), in which the partial factors are applied not until the very end of the calculation. This means the whole calculation is performed using characteristic values of the effects of actions and the resistance. The partial factors are applied finally when the limit state equation Ed d Rd has to be checked. If the resistance is load-dependent, the results of a calculation using DA2* are not the same as the results of a calculation using DA2. This applies especially to the bearing resistance of shallow foundations in case of combined loading caused by permanent as well as variable actions.

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K. Lesny / Implementation of Eurocode 7 in German Geotechnical Design Practice

Table 4. Comparison of Limit States according to DIN 1054:2005 and Eurocode 7/DIN 1054:2010 Limit State Eurocode 7/ DIN 1054:2005 DIN 1054:2010

Definition Loss of equilibrium of the structure or of the foundation ground, where the strength of the structural material or the ground is not decisive for the resistance Loss of equilibrium of the structure or of the foundation ground due to uplift or by the effect of other vertical forces Hydraulic heave, inner erosion and piping in the ground caused by flow gradients Internal failure of the structure where the strength of the structural material is decisive for the resistance failure or very large deformations of the structure, where the strength of the foundation ground is decisive for the resistance

EQU 1A UPL HYD STR

1B

GEO-2 GEO-3

1C

As mentioned in section 2.1 the partial factors in the ULS are based on the condition that the safety level of the former global safety concept is maintained. With Eq. (1) the resistance factors JR have been derived in the following way:

Ed d R d œ E ˜ J E d

R JR

(3)

with E d R/K following from Eq. (1) it is:

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E ˜ JE d

R R œEd J E ˜ J R JR

Ed

R œ JR K

K JE

(4)

In Eq. (3) and Eq. (4) JE is a weighted mean of the partial factors for the effects of permanent and variable actions which have been adopted from structural engineering. The aim was to use a common factor in all disciplines of civil engineering instead of specific values for geotechnical engineering (Vogt et al., 2008). Factors of JG = 1,35 and JQ = 1,5, for example, lead to a mean value of JE of 1,40. Tables 5 and 6 show some partial factors for actions and resistances defined in DIN 1054:2010 for the different design situations. It can be seen that for BS-P they coincide with the recommended values of Eurocode 7, Annex A. In the Serviceability Limit State (SLS) no partial factors are applied. With DIN 1054:2010 combination factors are introduced in geotechnical design for the first time to adjust to DIN EN 1990:2010. The consequences of the occurrence of more than one variable action were formerly incorporated in the concept of load cases (see section 1). With DIN 1054:2010 the combination factors defined in DIN EN 1990:2010 (\0 = 0,8, \1 = 0,7, \2 = 0,5) are adopted to maintain the same level as in structural engineering. Consequently, in case of more than one independent variable action the relevant combination in the respective limit state has to be determined by checking all possible combinations of actions with interchanging leading action and corresponding accompanying actions.

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In the following specifically German geotechnical design requirements for shallow and pile foundations are highlighted. Table 5. Some partial factors for the effects of actions in the limit states GEO-2 and STR according to DIN 1054:2010 (recommended values of Eurocode 7, Annex A in parentheses) Actions or Effect of Actions

Symbol

Effects of actions from permanent actions, general Effects of actions from favourable permanent actions Effects of actions from unfavourable variable actions

JG JG,inf JQ

Design Situation BS-P BS-T 1,35 1,20 (1,35) (1,35) 1,00 1,00 (1,00) (1,00) 1,50 1,30 (1,50) (1,50)

BS-A 1,10 (1,35) 1,00 (1,00) 1,10 (1,50)

Table 6. Some partial factors for resistances in the limit states GEO-2 and STR according to DIN 1054:2010 (recommended values of Eurocode 7, Annex A in parentheses) Resistance Soil resistances Passive earth pressure and bearing resistance

Symbol

Design Situation BS-P BS-T

1,40 (1,40) 1,10 Sliding resistance JR,h (1,10) Pile resistance from static and dynamic pile load tests 1,10 Base resistance Jb (1,10) 1,10 Shaft resistance (compression) Js (1,10) 1,10 Total resistance (compression) Jt (1,10) JR,e, JR,v

BS-A

1,30 (1,40) 1,10 (1,10)

1,20 (1,40) 1,10 (1,10)

1,10 (1,10) 1,10 (1,10) 1,10 (1,10)

1,10 (1,10) 1,10 (1,10) 1,10 (1,10)

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3.2. Shallow Foundations A specific feature of German geotechnical design of shallow foundations is the verification of the allowable eccentricity of the resultant vertical loading. In DIN 1054:2005 this proof was attributed to the ULS, but not to a specific limit state and all partial factors were set to 1,0. The allowable eccentricity was defined as 1/3 of the foundation width, i.e. under eccentric loading a maximum gap may occur in the footing base up to its center of gravity. The aim of this proof was to guarantee that a significantly large portion of the foundation base participates in the load transfer to the ground. In DIN 1054:2010 this requirement is maintained but is now part of the proof of the SLS to limit the rotation of eccentrically loaded foundations. As a new requirement according to DIN 1054:2010 overturning of a foundation around the foundation edge additionally has to be checked for limit state EQU in the ULS. This verification may become relevant in the design situation BS-P compared to the proof of the allowable eccentricity in the SLS (for details see Schuppener, 2010b). The foundation edge is the true rotation axis only in case of foundations on rock. In case of foundations on or in soils it is assumed to be a fictitious rotation axis. DIN 1054 traditionally included a specific German design procedure that substitutes the proof of ULS and SLS for regular design cases by providing tables with allowable base pressures for shallow foundations for certain geometric and soil

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conditions. This procedure, which is very familiar in Germany, has been maintained as well, but in DIN 1054:2010 design values of base pressures are given instead of allowable values. The design base pressure has to be compared with the design value resulting from the current foundation loading. The tabulated values are valid for BS-P and are assumed to be on the safe side for BS-T and BS-A.

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3.3. Pile Foundations Following Eurocode 7 the pile resistance according to DIN 1054:2010 and the recommendations for piles (EAP, 2012) can be determined by static or dynamic pile load tests. Another method is the determination of the pile resistance based on ground test results. In comparison to DIN 1054:2005 the partial factors for pile resistances from pile load tests have been reduced, because the use of the scattering factors is more differentiated than before. The aim is to better reward the performance of pile load tests. In DIN 1054:2010 all scattering factors are increased, but they decrease with the number of load tests. A maximum of five load tests is rewarded, whereas in DIN 1054:2005 only two load tests have been considered. Despite these changes in the design methodology the former safety level is still maintained (see Kempfert, 2012). In the traditional German design it was also permitted to calculate the resultant pile resistance using fixed characteristic values for the base resistance and the shaft resistance depending on the type of pile and the soil characteristics. These values were considered as experience values which were based on an evaluation of numerous pile load tests. In the methodology of Eurocode 7 this procedure represents a method of determining the pile resistance based on ground test results. As these values represent long-term national experience this traditional concept has been maintained in DIN 1054:2010 as well. The experience values are tabulated in EAP (2012) together with detailed regulations for their application. For this method increased partial factors are to be applied according to DIN 1054:2010 which already include a model factor of about 1,3 as it is required according to Eurocode 7. This model factor roughly coincides with the scattering factors [1 and [2 for static pile load tests (Kempfert, 2012).

4. Consequences for Practical Design The consequences of LSD according to the new set of standards for geotechnical engineering problems shall be illustrated on the basis of two out of six design examples which were distributed by ETC10 together with a questionnaire among the European Member States to gain information on the progress of harmonization as well as to analyse the national differences in the implementation of Eurocode 7. This was the second survey after a first survey with ten design examples had been conducted in 2005 (Orr, 2005). The results of the second survey were presented in a workshop in Pavia in 2010 (ETC10, 2010) and have been discussed frequently since (e.g. Orr, 2011 and Orr et al., 2011). The two examples presented in the following are a square pad foundation (Example 2.2 in the survey) and a pile group of bored piles (Example 2.6 in the survey). In both cases the characteristic soil parameters for the design have to be derived from site investigations results, which are provided with the examples.

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The design examples are calculated here by applying all three design approaches as far as possible using the specific German design approach. Based on the results of the design overall factors of safety are given as well which are compared with the global safety factors according to DIN 1054:1976. 4.1. Example of a Shallow Foundation The square pad foundation of the ETC10 Example 2.2 is illustrated in Figure 3. characteristic loads: Gv,k = 1000 kN Gh,k = 0 Qv,k = 750 kN Qh,k = 500 kN soil: boulder clay site investigations: 5 SPTs, water contents and index tests bulk weight of soil: J = 21,4 kN/m³ ground water level: 1,0 m below subsurface

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Figure 3. Example 2.2 – square pad foundation (www.eurocode7.com/etc10)

For the design approaches DA1 and DA3 the partial factors according to Eurocode 7, Annex A are used. The bearing resistance of the pad foundation is calculated according to the German DIN 4017:2006. The evaluation of the SPT test results to determine the shear strength of the foundation in drained and undrained conditions reveals some problems as the relevant German DIN EN ISO 22476-3:2005 does not include any correlations of SPT NValues to the shear strength of the respective soils. SPTs are not very common in Germany in contrast with dynamic probing and separate boring with soil sampling. Consequently, there are no well established correlations available. After analyzing various correlations documented in the literature (see e.g. Bowles, 1996), the following experience values for the shear strength of the boulder clay adopted from von Soos & Engels (2008) are finally assumed to be applicable for this problem:

c u ,k

300 kN m²

cck

15 kN m²

tan Mck

30q

(5)

The analysis shows that the bearing resistance determines the relevant dimensions of the square pad foundation. Table 7 includes the resultant pad widths and the overall factors of safety for the different design approaches. Accordingly, the pad width in case of undrained conditions determined with DA2* is only minimally smaller compared to the other design approaches. The overall factor of safety achieved in this case is K 1,90 , which is less than the global safety factor formerly required in DIN 1054:1976 for LC1 of K 2 and is therefore not acceptable. However, undrained conditions often represent transient situations (e.g. during construction) which were formerly attributed to LC2 with a minimum global safety factor of Kmin 1,5 (see

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Table 2). Hence, the design according to the new generation of standards leads to a sufficient safety level. Table 7. Results of the square pad foundation design (Example 2.2)

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DA1 (Comb. 1) DA1 (Comb. 2) Pad width [m] Undrained 2,53 2,63 conditions Drained 3,44 3,45 conditions Overall factor of safety (K K = Rd/Nd or K= Rk/Nk) Undrained 1,01 1,02 conditions Drained 1,02 1,03 conditions

DA2*

DA3

2,89

2,53

4,69

3,44

1,90

1,01

2,11

1,02

For drained conditions the pad width designed with DA2* is much greater than the one according to the other design approaches which result in more or less the same widths. This can be attributed to the comparably high partial factor for bearing resistance of JR,v = 1,4. The design represents an overall factor of safety of 2,11 which is slightly greater than the global safety factor in LC1 of Kmin 2 (see Table 2). In general, the safety level achieved for this example is indeed comparable to the former global safety concept. However, the analysis shows that the evaluation and interpretation of site investigation results depends on national design traditions as well as on the experience of the designer. These uncertainties are not included in the partial factors of DIN 1054:2010 derived from the former global safety factors in the way illustrated in section 3.1. They have to be considered within the determination of the characteristic soil parameters instead. Several recommendations how to evaluate site investigation results (e.g. Ruppert, 2012) as well as statistical methods to determine characteristic soil parameters from test results which implicitly account for such uncertainties are available (e.g. Baudin, 2001; Pohl, 2011). However, especially statistical methods are often not applied in the daily design practice. The main reason for this can be found in the usually small sample sizes together with a lack of experience in the use of statistical methods. Hence, design experience along with knowledge of the local subsoil conditions is usually essential for the determination of the characteristic soil parameters by qualitatively taking into account uncertainties related to the interpretation of site investigation results. 4.2. Example of a Pile Foundation The pile group of ETC10 Example 2.6 is depicted in Figure 4. The pile length is designed according to the procedure described in DIN 1054:2010 and the recommendations of the committee for piles (EAP, 2012) using DA1 combination 1 and DA2*. DA1 combination 2 and DA3 are not considered as the calculation model used here is based on experience values for the resultant characteristic pile base and shaft resistances tabulated in EAP (2012), see section 3.3. So, the material factor approach of DA1, combination 2 and DA3 cannot be used.

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bored piles: D = 450 mm, a = 2 m characteristic loads for each pile: Gk = 300 kN Qk = 150 kN soil: pleistocene fine and medium sand covered by Holocene layers of loose sand, soft clay and peat site investigations: 1 CPT performed and evaluated according to DIN 4094:2002, 1 bore profile ground water level: 1,4 m below subsurface

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Figure 4. Example 2.6 – pile group of bored piles (www.eurocode7.com/etc10)

As the soil in the upper 15 m was very inhomogeneous and shows comparably small CPT tip resistances, only the soil deeper than 15 m is considered as the bearing layer. An average value of the cone tip resistance of this layer which is considered as fine sand of q c 11,18 MN m² is derived from an evaluation of the CPT results. The results of the pile design are summarized in Table 8. According to EAP (2012) the minimum embedment depth in the competent layer (fine sand) is 2,5 m. This results in a final pile length of 17,5 m. According to Table 8, the overall factor of safety is only 1,55 which is significantly less than the global safety factor of K 2 required in DIN 1054:1976 for LC1. Hence, the old safety level is not maintained in this example, which was the prerequisite of implementing Eurocode 7 in Germany. Table 8. Results of the pile design (Example 2.6) Total pile length L [m] Overall factor of safety K>@

DA1 (Comb. 1)

DA1 (Comb. 2)

DA2*

DA3

17,45

-

17,25

-

1,01

-

1,55

-

On the other hand, some uncertainty is related to the evaluation of the CPT results, i.e. in defining representative CPT tip resistances for the bearing layer in this example. As already mentioned in section 4.1 such uncertainties are not covered by the partial factors defined in DIN 1054:2010. In this case they have to be accounted for by a

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reasonable definition of the characteristic values of the base and shaft resistance from the tabulated values in EAP (2012). These values themselves are based on mean values of the cone tip resistance for a realistic soil profile indicating relevant sublayers to be derived from the CPT measurements (see also Ruppert, 2012). In the end, it is obviously difficult to give a general assessment of the success of the implementation of Eurocode 7 as it depends very much on the type of example, its boundary conditions as well as on the calculation methods used for comparison.

5. Conclusions

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The implementation of the Limit State Design with Eurocode 7 represented a radical change in the German design philosophy which was based on long-term experience and which was commonly considered to be very reliable. Engineers had to adjust to the new concept of limit states and partial factors and the new terminology with the introduction of DIN 1054:2003/2005 parallel to Eurocode 7 (the “German way”). However, after some years of experience it can be concluded that the LSD is broadly accepted among geotechnical engineers. With the deadline of July 2012 DIN 1054:2005 can no longer be used and engineers again need to adjust to changes accompanied by the final implementation of Eurocode 7. These changes not only include new and sometimes unclear regulations but again new definitions and terminologies as well as a completely new structure of the basic design codes. In the near future three codes - Eurocode 7, its National Annex plus a fully revised DIN 1054:2010 as a supplement to Eurocode 7 - will be used in geotechnical design together with other design and construction codes. A standard-handbook has been published to make the practical use of these design codes easier. The safety level included in these codes is not based on probabilistic calculations, but has been derived from the former global safety concept. It can be assumed that the achieved safety level is at least comparable to the traditional design concept in most cases, but the actual reliability of geotechnical structures remains unknown.

References Baudin, C. (2001): Determination of Characteristic Values, in: Geotechnical Handbook - part 1, ed. U. Smoltczyk, 6th edition, Ernst & Sohn, Berlin Bowles, J.E. (1996): Foundation analysis and design, 5th Edition, McGraw-Hill, New York DIN 1054 (1976): Baugrund; Zulaessige Belastung des Baugrunds, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN 1054 (2003): Baugrund - Sicherheitsnachweise im Erd- und Grundbau, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN 1054 (2005): Baugrund - Sicherheitsnachweise im Erd- und Grundbau, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN 1054 (2010): Baugrund - Sicherheitsnachweise im Erd- und Grundbau - Ergaenzende Regelungen zu DIN EN 1997-1, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN 4014 (1990): Bohrpfaehle - Herstellung, Bemessung und Tragverhalten, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German – withdrawn in 2003) DIN 4017 (2006): Baugrund - Berechnung des Grundbruchwiderstands von Flachgruendungen, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN 4084 (2009): Baugrund – Gelaendebruchberechnungen, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German)

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DIN EN 1990 (2010): Eurocode: Grundlagen der Tragwerksplanung, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) DIN EN ISO 22476-3 (2005): Geotechnische Erkundung und Untersuchung – Felduntersuchungen, Teil 3: Standard Penetration Test, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) EAB (2006): Empfehlungen des Arbeitskreises Baugruben der DGGT – EAB, 4th edition, Ernst & Sohn, Berlin (in German) EAP (2012): Empfehlungen des Arbeitskreises Pfaehle der DGGT – EA-Pfaehle, 2nd edition, Ernst & Sohn, Berlin (in German) EAU (2004): Recommendations of the Committee for Waterfront Structures, Harbours and Waterways of the DGGT – EAU, 8th edition, Ernst & Sohn, Berlin (translated from German) ETC10 (2010): Proceedings of the 2nd International Workshop on the Evaluation of Eurocode 7, April 12-14 2010, Eucentre, Pavia, Italy, http://www.eurocode7.com/etc10/Pavia/proceedings.html Eurocode 7 (2009): German version DIN EN 1997-1: Entwurf, Berechnung und Bemessung in der Geotechnik - Teil 1: Allgemeine Regeln, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) Eurocode 7/NA (2010): German version DIN EN 1997-1/NA: Nationaler Anhang - National festgelegte Parameter - Eurocode 7: Entwurf, Berechnung und Bemessung in der Geotechnik - Teil 1: Allgemeine Regeln, Normenausschuss Bauwesen im DIN e.V., Beuth Verlag, Berlin (in German) Gaessler, G.; Gudehus, G. (1983): Das neue statistische Sicherheitskonzept am Beispiel der Standsicherheit verankerter Waende und vernagelter Waende, Fraunhofer IRB Verlag (in German) Kempfert, H.-G. (2012): Pfahlgruendungen, in: Kommentar zum Handbuch Eurocode 7 – Geotechnische Bemessung: Allgemeine Regeln, chapter B7, ed. B. Schuppener, Ernst & Sohn, Berlin (in German) Normenhandbuch Eurocode 7 (2011): Handbuch Eurocode 7 - Geotechnische Bemessung, Band 1: Allgemeine Regeln, 1st edition, Beuth Verlag, Berlin (in German) Orr, T.L.L. (2005): Evaluation of Eurocode 7, Proceedings of the 1st International Workshop on the Evaluation of Eurocode 7, Dept. of Civil, Structural and Environmental Engineering, Trinity College, Dublin Orr, T. (2011): Experiences with the Implementation of Eurocode 7 in Europe, Proceedings of the Workshop on Safety Concepts and Calibration of Partial Factors in European and North American Codes of Practice, Nov. 30 to Dec. 1 2011, Delft, The Netherlands, pp. 175-185 Orr, T.L.L.; Bond, A.J.; Scarpelli, G. (2011): Findings from the 2nd Set of Eurocode 7 Design Examples, Proceedings of the 3rd International Symposium on Geotechnical Safety and Risk (ISGSR 2011), eds. N. Vogt, B. Schuppener, D. Straub, G. Braeu, Bundesanstalt fuer Wasserbau, pp. 537-547 Pohl, C. (2011): Determination of Characteristic Soil Values by Statistical Methods, Proceedings of the 3rd International Symposium on Geotechnical Safety and Risk (ISGSR 2011), eds. N. Vogt, B. Schuppener, D. Straub, G. Braeu, Bundesanstalt fuer Wasserbau, pp. 427-434 Ruppert, F. (2012): Geotechnische Unterlagen, in: Kommentar zum Handbuch Eurocode 7 - Geotechnische Bemessung: Allgemeine Regeln, chapter B3, ed. B. Schuppener, Ernst & Sohn, Berlin (in German) Schuppener, B. (2010a): Eurocode 7 Geotechnical Design – Part 1: General rules and its latest developments, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 4 (1), 32-42 Schuppener, B. (2010b): Das Normenhandbuch zu DIN EN 1997-1 und DIN 1054, 7. Kolloquium der Technischen Akademie Esslingen, „Bauen in Boden und Fels“, eds. H. Schad and C. Vogt Schuppener, B.; Heibaum, M. (2011): Reliability Theory and Safety in German Geotechnical Design, Proceedings of the 3rd International Symposium on Geotechnical Safety and Risk (ISGSR 2011), eds. N. Vogt, B. Schuppener, D. Straub, G. Braeu, Bundesanstalt fuer Wasserbau, pp. 527-536 Schuppener, B.; Ruppert, F. (2007): Zusammenfuehrung von europaeischen und deutschen Normen – Eurocode 7, DIN 1054 und DIN 4020, Bautechnik, 84 (9), 636-640 Schultze, E.; Pottharst, R. (1981): Versagenswahrscheinlichkeit und Sicherheit von Flachgruendungen als Grundlage für Bauvorschriften, parts 1-3, Fraunhofer IRB Verlag (in German) Vogt, N.; Schuppener, B.; Weißenbach, A. (2008): Implementation of Eurocode 7-1 in Germany – Selection of Design Approach and Values of Partial Factors, Proceedings of the 11th Baltic Sea Conference – Geotechnics in Maritime Engineering, September 15-18, Gdansk, Poland, pp. 1035-1042 Von Soos, P.; Engels, J. (2008): Eigenschaften von Boden und Fels – ihre Ermittlung im Labor, in: Grundbau-Taschenbuch, Teil 1: Geotechnische Grundlagen, ed. K. J. Witt, 7th edition, Ernst & Sohn, Berlin Weißenbach, A. (2012): Die Entwicklung von DIN 1054, in: Kommentar zum Handbuch Eurocode 7 Geotechnische Bemessung: Allgemeine Regeln, chapter A2, ed. B. Schuppener, Ernst & Sohn, Berlin (in German)

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-60

Implementation of Eurocode 7 in French practice by means of national additional standards a

Jean-Pierre MAGNAN a,1 and Sébastien BURLON a Université Paris–Est, IFSTTAR, GER, F–75015, Paris, France

Abstract. This paper deals with the implementation of Eurocode 7 in French practice by means of national additional standards. The architecture of French geotechnical design standards is presented. In particular, principles of safety management and of determination of characteristic value are explained. Then, for each geotechnical structure type, the values of the partial factors used are summarized and the methodology of their calibration is briefly discussed. Keywords. Eurocodes, safety factor, geotechnical structures, calibration

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Introduction French engineers in charge of the standardization process for geotechnical design consider Eurocode 7 (2004 and 2006) as an umbrella code which defines the fundamental principles of geotechnical structures design. It cannot be used on a daily basis for projects. Some sections of it must be developed to reach the level of standards and regulations which existed before (Documents Techniques Unifiés DTU which were included in the series of French standards for buildings and Fascicule 62-V for public works such as roads, bridges, etc.) and which were more detailed. French engineers are facing a situation where all parts of geotechnical design are not covered by an existing standard (in particular slopes). Moreover, different rules can be applied according to whether the structure is a bridge or a building, especially in the case of foundations, whereas Eurocode 7 does not make such distinction. The first part of this paper deals with the new architecture of French geotechnical standards and discusses the management of safety and the determination of characteristic values as recommended by Eurocode 7. The second part of the paper presents the seven national standards defining the requirements and the recommendations to design each type of geotechnical structures (slopes, spread foundations, deep foundations, etc.)

1

Corresponding Author: E-mail: [email protected].

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1. The new architecture of French geotechnical design standards 1.1. Principles

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The new French design standards include: • Eurocode 7 (NF EN 1997-1 and 2) (2004 and 2006) and the French National Annex of Eurocode 7 – Part 1(NF EN 1997-1/NA) (2006); • seven application standards for shallow foundations (NF P94-261, under preparation), pile foundations (NF P 94-262, published in 2012), retaining walls (NF P 94-281, under preparation), embedded retaining walls (NF 94-282, published in 2009), reinforced earth structures (NF P 94-270, published in 2009) and earth structures (NF P 94-290, still not undertaken). Other recommendations have been published or are being prepared as the final result of “national projects”, funded by the ministry in charge of construction (buildings and infrastructures) and by the National Research Agency. They deal with micropiles (FOREVER), raft foundation design in terms of ultimate capacity and displacements (ASIRI) and the effects of cyclic loads on piles (SOLCYP). The most important French choices are as follows: 1. Adopt Design Approach 2 (or 2*) as a quasi general rule, some situations being referred to a distributed safety factor (Design Approach 3). 2. Do not rely on statistical concepts and analyses, but rather on experience and case histories. 3. Yet accept methods strongly referred to in Eurocode 7, such as the model pile approach to pile design, but try to make them equivalent to concurrent (competing) alternative methods in all cases when they should be equivalent (typically only one or two tests or test profiles). 4. Rely on proven methods used in our country (such as the use of pressuremeter). 5. Open the list of accepted design methods to classical methods used in other countries. 1.2. Safety management The general format for safety in Design Approach 2 is based on actions, resistances and methods of evaluation. Partial factors are applied to actions A (γAA), to resistances R (R/γR) and to models (γMA for action model or γMR for resistance model) (see e.g., Frank et al., 2004 and Bond & Harris, 2008). In the basic case of one action and one resistance, this leads to an equation such as:

γ MAγ A A
30%, the log-normal distribution should be used. COVtotal < 0.3 COVtotal ≥ 0.3

→ →

normal distribution is possible log-normal distribution should be used

The log-normal distribution can be used in any case but, if applicable the normal distribution is much easier to handle for practical applications. Table 1 shows the range of typical coefficients of variation for different soil properties. Therefore the cohesion, the undrained shear strength and the compressibility modulus of a soil layer often should be evaluated using the log-normal distribution. Due to variance reduction in case of large soil volumes involved in the governing limit states, it is often possible that

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91

the above mentioned soil properties can also be determined using the normal distribution. The angle of internal friction and the density on the other hand can usually be derived by using the normal distribution. Table 1. Range of typical values of coefficients of variation for soil Soil property

࢏࢔ࢎࢋ࢘ࢋ࢔࢚

Density

1  10 %

Angle of internal friction

5  15 %

Cohesion

30  50 %

Undrained shear strength

30  50 %

Compressibility modulus

20  70 %

3.2. Mathematical concept for COVtotal < 0.3 (normally distributed soil values) Used abbreviations: xm

= mean value

Sx

= standard deviation

β

= factor for 5%-fractile (β ≈ 1.65 for normally distributed soil values)

COV = coefficient of variation

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Figure 3. Definition of normal distribution and used abbreviations

The characteristic values of soil properties can be derived with the following equation. (Note: Equation (2) is also valid for any other man-made-material, for example concrete, if its values are normally distributed)      ·    · 1   ·   

(2)

The total coefficient of variation COVtotal accounts for the combined overall variability and uncertainties as well as the spatial extent of the governing failure or deformation mechanism. Tang (1984) and Phoon & Kulhawy (1999) proposed an additive model to take account of the combined effects of aleatory and epistemic uncertainties.



COV  Γ,

 COV COV COV COV

(3)

The variance reduction function Γ ,   considers the influence of the spatial extent (averaged length L, area A or volume V) of the governing failure mechanism. Although

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H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

there exist several approaches to mathematically describe the variance reduction function, Vanmarcke (1977) proposes to use the following simple form: Γ  Γ  Γ  Γ 

೔

೔

·೔

with Γ   ೔ · 1 

Γ  Γ  Γ  Γ  Γ  Γ  Γ

 if L  δ and Γ  1 

೔ ·೔

Γ  Γ  Γ · Γ

 if L # δ $ %  , ', (

(4)

in which δ )*+ is the scale of fluctuation and L )*+ is the length of the governing failure mechanism in the considered direction x, y or z. The scale of fluctuation estimates the distance within which soil properties show relatively strong correlation. Instead of the scale of fluctuation often the autocorrelation distance is used in literature. The autocorrelation distance R defines the separation distance at which the covariance function decays to a value of Sx/e and the correlation between the soil properties can be considered relatively weak (Sx stands for the standard deviation and e for the base of the natural logarithm). Generally the scale of fluctuation is about twice the value of the autocorrelation distance (exponential correlation model: δ  2 · R; Gaussian correlation model δ  √/ · R 0 1.8 · R). In the following considerations only the scale of fluctuation is used. 3.3. Mathematical concept for COVtotal ≥ 0.3 (log-normally distributed soil values) If the total coefficient of variation becomes larger than about 0.3 the log-normal distribution should be used to avoid unrealistic negative values. Equation (6) to determine the characteristic values can be derived as follows:   3 .·

456

7  ln   

9 2

456

 9  :;5 1 <  

(5)

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   ·

. ^  

(6)

4. Simplification of general equations according to section 3 4.1. Simplifications for soil properties with COVtotal < 0.3 (normally distributed) Substitution of the coefficient of total variation COVtotal leads to equation (7).      x  x  1  β  Γ,   COV    COV   COV    COV   

(7)

With a 5%-fractile value of β ≈ 1.65 (normal distribution) and the assumption that the coefficients of variations covering the influences of measurement, transformation and statistical errors can be neglected (see Table 2) compared to the dominating COV inherent, equation (7) can be rewritten as: x > x  ?1  1.65  COV

!"!#

· :Γ, %  E

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(8)

93

H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

Table 2. Assumptions referring to coefficients of variation of different sources of uncertainty and variability  Measurement errors Strictly adhering to testing standards with sufficiently accurate measuring devices should largely reduce these uncertainties. Transformation errors Applying well established transformation models should reduce these uncertainties to fairly small values. Statistical errors In geotechnical engineering the mean value as well as the standard deviation is usually known with reasonable accuracy from experience with similar soils.



   small

 ! 





  "#

 small

 small

   0

  ! 

 



 "#

0

0

The values of the proposed variance reduction function Γ,   depend, as previously seen on the spatial extent of the governing failure mechanism (averaged length L or area A or volume V) as well as on the scale of fluctuation δ. Fenton and Vanmarcke (1991) reasoned that the scale of fluctuation is largely dependent on the geotechnical process of layer deposition rather than on the specific soil property being studied. Therefore it is not surprising that the scale of fluctuation in horizontal direction (in general: parallel to soil layering) is generally more than one order of magnitude larger than in vertical direction (in general: perpendicular to soil layering).

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Table 3. Summary of typical values of scale of fluctuations in horizontal and vertical direction within layers of relatively uniform soils

Typical range

Vertical direction

Horizontal direction

δv = δz [m]

δh = δx = δy [m]

1÷6

40 ÷ 60

Source of data

Phoon and Kulhawy (1999)

for different soil properties

≈2÷6

≈ 20 ÷ 80

(R = 1 ÷ 3)

(R = 10 ÷ 40)

El-Ramly et al. (2003)

In Rackwitz et al. (2002) typical values for in situ soil properties from many different authors have been summarized. They fall all within the above mentioned range and are therefore not listed separately. Recommended design values

2

50

Schneider and Fitze (2011)

With the given information a general approach to determine characteristic soil values can be worked out. In the following equations the x- and y- directions are always referred to as the horizontal ones and the z-direction as the vertical one.

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H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

General approach for soil properties with COVtotal < 0.3 (normally distributed) x > x  F1  1.65  COV

:

 

!"!#

· :Γ&, · Γ&, · Γ', G







from experience or test results ,see section 5-

 !".





from experience or test results ,see section 5-

 Γ$,%





Γ$    4

Γ",&

 Γ",'





Γ"    5

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Figure 4. Variance-Reduction-Function in vertical direction

Figure 5. Variance-Reduction-Function in horizontal direction

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(9)

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H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

4.2. Simplifications for soil properties with COVtotal ≥ 0.3 (log-normally distributed) In case the log-normal distribution should be used (COVtotal ≥ 0.3) the characteristic value of a certain soil property can be determined according to equation (10). General approach for soil properties with COVtotal ≥ 0.3 (log-normally distributed)

 0  ·

:

0.2^

 () *+,-, ·-, ·-, ·./  

01

· Γ&, · Γ', ·  *&2%2* :1 < Γ&,







from experience or test results ,see section 5-

 !".





from experience or test results ,see section 5-

Γ$,% 





Γ$    4

Γ",&

 Γ",'





Γ"    5

(10)

5. Simplified approach for design practice In the following section a diagram that allows a fast and easy determination of characteristic soil values is presented.

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5.1. General considerations Spatial averaging is only possible if the governing failure mechanism is capable of redistributing forces or stresses along the failure surfaces. True cohesion is often not ductile, i.e. brittle (is lost after small strains) and is mobilized on the failure surface depending on stress history and stress level. Cohesion can therefore not generally be averaged because the strains acting on the failure surface generally vary along the failure surface. Many engineers are well aware of this fact and will consequently neglect cohesion in most stability calculations. To estimate the characteristic values of cohesion and the angle of internal friction for strain-softening soils it is advised to use the critical state angles of friction and no cohesion along the entire failure surface. 5.2. Diagram for practical applications For typical geotechnical problems the horizontal extension of the governing failure mechanism is usually small compared to the scale of fluctuation in its direction. Furthermore the scale of fluctuation in vertical direction is much smaller than in horizontal direction and therefore dominates the averaging process. Within reasonable accuracy it can be assumed that the variance reduction function is only a function of the vertical extension of the failure mechanism and its corresponding scale of fluctuation. The assumption of perfect correlation in horizontal direction Γ&  Γ  Γ  1 and the

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H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

recommended design value for the vertical scale of fluctuation according to Table 3 (δ v = 2m) leads to the diagram presented below (Figure 6). To evaluate the characteristic value of a certain soil property only the mean (xm), the coefficient of variation (COVinherent) as well as the vertical extension of the considered failure mechanism (L z) are required. The required input values xm, COVinherent and Lz are outlined in the next section. Since the lognormal distribution and the normal distribution are almost identical for small coefficients of variation it is advised to use the black lines (lognormal distribution) to determine characteristic values.

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Figure 6. Diagram to evaluate characteristic soil properties

In case the governing failure mechanism extents only in horizontal direction, for example sliding of a foundation, the characteristic values can be obtained using Figure 6 for Lz = 0m. The black dots assume a log-normal distributed and the grey dots a normal distributed soil property. Note: For failure mechanisms with large horizontal extensions (Lh > 30m) it is possible to further reduce the variance reduction function resulting in higher characteristic values and more economical design. In such a case the design values can be determined using the general design approach as presented in section 4. 5.3. Required input parameters xm, COVinherent and Lz As seen by inspection of Figure 6 only three input parameters are required for the assessment of the characteristic value xk. These input parameters are the mean value xm, the coefficient of variation COVinherent (alternatively the standard deviation) and the vertical extent of the considered failure mechanism Lz. The mean value and the coefficient of variation of a soil property are either known from experience or can be evaluated trough field- or laboratory testing. It has been found on a worldwide data

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basis (e.g. that the coefficient of variation is approximately constant for a certain soil property. Table 4 presents typical and recommended values for different soil properties. Table 4. Range of typical values and recommended values of coefficients of variation Range of typical values COVinherent

Recommended values COVinherent

Density

0.01  0.10

0.0

Angle of internal friction

0.05  0.15

0.1

Cohesion

0.30  0.50

0.4

Undrained shear strength

0.30  0.50

0.4

Compressibility modulus

0.20  0.70

0.4

Soil property

If a priori knowledge (experience, personal judgment) as well as a certain number n measured test values is available Bayes` theorem can be used to combine the information. Table 5. Bayes theorem to combine a priori knowledge (experience, personal judgment) with test values

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Estimated a priori values (1)

Test values (2)

Combined information (3)

∑ !௜  #

!௠ଷ 

!௠௜

!௠ଵ

&௫௜

&௫ଵ

∑)!௜  !௠ଶ *ଶ &௫ଶ  ( #1

௫௜

௫ଵ  &௫ଵ ⁄!௠ଵ

௫ଶ  &௫ଶ ⁄!௠ଶ

!௠ଶ

!௠ଵ &௫ଶ ଶ ·% ' # &௫ଵ 1 &௫ଶ ଶ 1 ·% ' # &௫ଵ

!௠ଶ 

&௫ଷ  &௫ଶ ·

1 + & ଶ #  % ௫ଶ ' &௫ଵ

௫ଷ  &௫ଷ ⁄!௠ଷ

6. Illustrative examples 6.1. Example 1: Slope stability Slope stability - Input values: JK  30°;  3  0.1 O  30*; O  20*; O  10* General approach, Equation (9) JK P 28.2° (normal distribution) Simplified approach, Figure 6 Figure 7. Example 1: Slope stability

JK P 27.9°

(normal distribution)

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H.R. Schneider and M.A. Schneider / Dealing with Uncertainties in EC7

6.2. Example 2: Pile foundation a) Skin friction – Input values Note: For illustration purposes only the friction angle is considered JK  30°;  3  0.1 O  20* General approach, Equation (9) JK P 28.4° (normal distribution) Simplified approach, Figure 6 JK P 28.5°

(normal distribution)

b) Tip resistance – Input values: Note: For illustration purposes only the cohesion is considered T 4   20 UV4;  5  0.4 O  4*; O  2* General approach, Equation (10) TK P 10.9 UV4 (log-normal distribution)

Figure 8. Example 2: Pile foundation

Simplified approach, Figure 6 TK P 10.6 UV4

(log-normal distribution)

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6.3. Example 3: Earth pressure and sliding a) Earth pressure – Input values: JK  30°;  3  0.1 O P 6*; O  10* General approach, Equation (9) JK P 27.9° (normal distribution) Simplified approach, Figure 6 JK P 27.9°

Figure 9. Example 3: Earth pressure and sliding

(normal distribution)

b) Sliding – Input values: JK  30°;  3  0.1 O P 10*; O  40* General approach, Equation (9) JK P 25.9° (normal distribution) Simplified approach, Figure 6 JK P 25.5°

(normal distribution)

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7. Summary Geotechnical performance of a structure is usually governed by spatial average soil properties, such as the average shear strength along a potential slip surface or the average compressibility of a volume of soil beneath a footing. It becomes clear that the characteristic value cannot be quantified by a field- and laboratory investigation alone, but is dependent on the spatial extent of the governing failure mechanism to be designed for. In EC 7 the characteristic value xk is the fundamental soil value. Despite its important safety relevance, the definition and determination of the characteristic value is far from clear. An attempt is made to develop a simplified approach to determine characteristic soil values. It is based on the mean value, the standard deviation (or coefficient of variation) of a certain soil property and the extent of the governing failure mechanism. It has been proposed that for most geotechnical problems it is sufficient only to consider the vertical extent of the failure mechanism. Based on this assumption a simplified approach for practical applications has been developed, and the examples included in section 6 confirm that this approach is valid. The presented simplified approach is easy to use and the results correspond well with more rigorous methods. Examples to illustrate the approach as well as guidelines of typical input parameters are provided.

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References Baecher, G.B. (2003). Reliability and Statistics in Geotechnical Engineering. John Wiley and Sons. Ltd, England. Baker, J. and Calle, E. (2006). JCSS Probabilistic Model Code, Section 3.7: Soil Properties, Joint Committee on Structural Safety, Updated version Aug. 2006, Zürich, Switzerland. Bond, A. and Harris, A. (2008). Decoding Eurocode 7, London: Taylor and Francis, 616 pp. Brinch Hansen, J. (1956). Limit State and Safety Factors in Soil Mechanics, Danish Geotechnical Institute, Copenhagen, Bulletin No. 1. Butler, H.C. (2001). Spatial autocorrelation of soil electrical conductivity, M.Sc.-Thesis, Iowa State University, Ames, Iowa. Christian, J.T. and Ladd, C.C. and Baecher, G.B. (1994). Reliability Applied to Slope Stability Analysis, J Geotech Eng-Asce 120, 2180-2207. Craig, R.F. (1992). Soil Mechanics, Chapman and Hall. Denver, H. and Ovesen, N.K. (1994). Assessment of Characteristic Values of Soil Parameters for Design, Proc. XIII ICSMFE. New Delhi, India. Elkateb, T. and Chalaturnyk, R. and Robertson, P.K. (2003). An overview of soil heterogeneity: quantification and implications on geotechnical field problems, Can. Geotech. J. 45, 1-15. El-Ramly, H. (2001). Probabilistic analyses of landslide hazards and risks: Bridging theory and practice, Ph.D. thesis, University of Alberta, Edmonton, Alta. El-Ramly, H. and Morgenstern, N.R. and Cruden, D.M. (2003). Probabilistic stability analysis of a tailings dyke on presheared clay-shale, Can. Geotech. J. 40, 192-208. El-Ramly, H. and Morgenstern, N.R. and Cruden, D.M. (2006). Lodalen slide: a probabilistic assessment, Canadian Geotechnical Journal 43, 956-968. Eurocode 7. (1994). Part 1: Geotechnical Design, General Rules, Final Version of ENV 1997-1, Oct 3., produced by CEN. Fellenius, W. (1936). Calculation of the stability of earth damn, Transactions of the 2nd Congress on Large Dams, Washington, D.C., 445-462. Fenton, G.A. and Vanmarcke, E.H. (1991). Spatial variation in liquefaction risk assessment, Geotechnical Engineering Congress 1991, Boulder, Colorado, 10-12 June. Geotechnical Special Publication No. 27, American Society of Civil Engineers, Reston, Va. Volume 1, 594-607.

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Harr, M.E. (1987). Reliability-based design in civil engineering”, McGraw Hill. Kay, J.N. and Krizek, R.J. (1971). Estimation of the Mean for Soil Properties. Int. Conf. on Applications of Statistics and Probability to Soil and Strucutral Engineering, Hong Kong. Lacasse, S. and Nadim, F. (1997). Uncertainties in characterizing soil properties, NGI Publ. No. 201. Lumb, P. (1974). Application of Statistics in Soil Mechanics, Chapter 3 in Soil Mechanics-New Horizons, ed. by I.K. Lee. Mantoglou, A. (1987). Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method, Mathematical Geology 19, 129-149. Mostyn, G.R. and Li, K.S. (1993). Probabilistic slope analysis – state-of-play. Probabilistic Methods in Geotechnical Engineering, Li and Lo (eds), 1993 Balkema, Rotterdam, ISBN 90 5410 303 5, pp. 89 – 109. N.R.C. (1995). Probabilistic methods in geotechnical engineering, National Academy Press, Washington, D.C. Orr, T. (1993). Use of Partial Factors in Eurocode 7. Paper presented at 6th meeting of SC7, Berlin. Orr, T.L.L. and Breysse, D. (2008). Eurocode 7 and reliability based design, in: Phoon, K.-K. (Ed.), Reliability-based design in geotechnical engineering; computations and applications, Taylor and Francis, London, 2008, 298-343. Phoon, K.K. and Kulhawy F.H. (1999). Evaluation of geotechnical property variability. Canadian Geotechnical Journal 36, 625 – 639. Phoon, K.K. and Kulhawy F.H. (1999). Characterization of geotechnical variability. Canadian Geotechnical Journal 36, 612 – 624. Rackwitz, R. and Denver, H. and Calle, E. (2002). JCSS probabilistic model code, section 3.7: Soil properties, 5th (final) version. Joint Committee on Strucutral Safety, Zürich, Switzerland. Rethati, L. (1988). Probabilistic solutions in geotechnics. in: Developments in geotechnical engineering 46, Elsevier, Amsterdam. Schneider, H.R. (1990). Die Wahl der Baugrundkennwerte. in: Anwendung der neuen Tragwerksnormen des SIA im Grundbau – Referate der Studie Schweizerische Gesellschaft für Boden- und Felsmechanik, Mitteilungen der Schweizerischen Gesellschaft für Boden und Felsmechanik, Zürich. Schneider, H.R. (1997). Definition and determination of characteristic soil properties, XIV ICSMFE, Hamburg, Balkema. Schneider, H.R., (2010). Characteristic Soil Properties for EC7: Influence of quality of test results and soil volume involved, Proc. 14th Danube-European Conference on Geotechnical Engineering, Bratislava. Schneider, H.R., (2011). Safety Concepts and Calibration of Partial Factors in European and North American Codes of Practice, Workshop Nov. 30 – Dec. 1, Delft University of Technology, Delft, The Netherlands. Schneider, H.R. and Fitze, P. (2009). Charakteristische Baugrundwerte: Erfahrung, Versuchswerte und Statistik, Herbsttagung SBGF, 6. Nov., EPFL Lausanne. Schneider, H.R. and Fitze, P. (2011). Characteristic shear strength values for EC7: Guidelines based on a statistical framework, XV European Conference on Soil Mechanics & Geotechnical Engineering, Athens, Greece, Sept. 2011 Schneider, H.R. and Tietje, O. and Fitze, P. (2010). Charakteristische Werte nach Swisscode: Definition, Bestimmung und Anwendung in der Geotechnik-Praxis, Jan.18, HSR Hochschule für Technik, Rapperswil, Switzerland. Sivakumar Babu, G.L. and Dasaka, S.M. (2007). The Effect of Spatial Correlation of Cone Tip Resistance on the Bearing Capacity of Shallow Foundations, Department of Civil Engineering, Indian Institute of Science, India Soulié, M. and Montes. P. and Silvestri. V., (1990). Modeling spatial variability of soil parameters. Canadian Geotechnical Journal 27, 617 – 630. Tang, W.H. (1993). Recent developments in geotechnical reliability, Balkema, ISBN 9054103035. Tang, W.H. (1971). A Bayesian Evaluation of Information for Foundation Engineering Design, Int. Conf. on Applications of Statistics and Probability to Soil and Structural Engineering, Hong Kong. Taylor, D.W. (1948). Fundamentals of soil mechanics, John Wiley and Sons, Inc., New York. Terzaghi, K. (1940). Sampling, Testing and Averaging. Proceedings, Purdue Conference on Soil Mechanics and its Applications, Purdue University, West Lafayette, USA. Thorne, C.P. and Quine, M.P. (1993). How reliable are reliability estimates and why soils engineers rarely use them. Probabilistic Methods in Geotechnical Engineering, Li and Lo (eds), (1993). Balkema, Rotterdam, ISBN 90 5410 303 5, 325 – 332. Tietje, O. and Richter, O. (1992). Stochastic modeling of the unsaturated water flow using auto-correlated spatially variable hydraulic parameters, Modeling Geo-Biosphere processes 1, 163-183. Tietje, O. and Fitze, P. and Schneider, H.R. (2011). Slope stability based on autocorrelated shear strength parameters, XV European Conference on SMGE. Sept., Athens.

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Uzielli, M. (2008). Statistical analysis of geotechnical data, in: Geotechnical and Geophysical Site Characterization, Huang and Mayne (eds), Taylor and Francis Group. Vanmarcke, E.H. (1977). Probabilistic modeling of soil profiles. Journal of the Geotechnical Engineering Division, ASCE, 103 (GT11), 1227 – 1246. Vanmarcke, E.H. (1977). Reliability of earth slopes. Journal of the Geotechnical Engineering Division, ASCE, 103 (GT11), 1247 – 1265. Vanmarcke, E.H. (1983). Random fields: analysis and synthesis, MIT Press, Cambridge. White, W. (1993). Soil variability: characterization and modeling. Probabilistic Methods in Geotechnical Engineering, Li and Lo (eds), 1993 Balkema, Rotterdam, ISBN 90 5410 303 5, 111 – 120. Wu, T.H. (2009). Reliability of geotechnical predictions, in: Geotechnical risk and safety, Honjo et. al (eds), Taylor and Francis Group. Zhang, L.L. and Zhang, L.M. and Tang, W.H. (2008). Similarity of soil variability in centrifuge models, Can. Geotech. J. 45, 1118-1129.

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The Safety Concept in German Geotechnical Design Codes Bernd Schuppener Federal Waterways Engineering and Research Institute, Karlsruhe, Germany

Abstract. The Eurocodes were officially adopted in Germany on 1st July 2012. Since then, application of the partial safety concept has been mandatory in all areas of structural engineering. The partial safety concept creates the impression that partial factors based on probability theory are applied to actions or effects of actions and resistances depending on the degree of uncertainty in each case. This is hardly possible in geotechnical engineering. European geotechnical engineers have therefore decided that the partial factors for the permanent and variable actions from the ground should be the same as those used in other areas of structural engineering for the sake of consistency in the field of construction. In Germany, the partial factors for the resistances from the ground have been selected so that the safety level is more or less the same as the tried-and-tested global safety level. In other words, the application of the partial safety concept results in approximately the same dimensions for foundations and geotechnical structures as those obtained with the global safety concept in the past. Thus, on closer inspection, the partial safety concept in its present form is, in geotechnical engineering at least, a modified global safety concept. Users are faced with the challenge of having to apply a concept which in some respects is new and more complex. However, this is reasonable when one considers the important contribution that has been made to placing European construction standards on an urgently needed common basis, thus promoting the unification of Europe.

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Keywords. Safety, reliability, partial factor, geotechnical design, standards

1. The probabilistic safety concept The traditional global safety factor concept has the serious disadvantage that the actual variability of the soil strength is not directly taken into account, and consequently a particular conventional safety factor does not necessarily have the same meaning for all soils. It is not easy to compare different designs with different soil types or even different designs with the same soil type. A probabilistic approach instead of the traditional global concept is therefore a fascinating vision for geotechnical engineers as it not only provides a rational basis for the quantification of geotechnical safety but also a meaningful and consistent basis for comparison (Lumb, 1970). By defining a probability of failure, a direct comparison is possible whereas global safety factors are related to every single verification format which cannot be compared with each other. The probabilistic safety concept, i.e. a safety concept based on probability theory, which was meant to replace the global safety concept upon implementation of the Eurocodes in Europe, is based on the following considerations: • If it is assumed that the actions on a structure and the resistances of that structure are randomly dispersed quantities and that both the actions on a structure and the

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resistances of structural elements and components can be described in a rational manner by means of statistics, • then it must also be possible to use probability theory to define a common safety level which is independent of the design and construction materials. The probabilistic safety concept is thus based on the assumption that the actions and resistances can be described statistically by an appropriate statistical distribution, in simple cases by a normal distribution. As it is generally not the actions themselves but the internal forces, moments or stresses caused by the actions that are of relevance, the term “effects of actions” as defined in current standards is used below instead of “actions”.

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Figure 1. Distribution densities of effects of actions and resistances.

If, as shown in Figure 1 (left), the probability distributions of the effects of actions S and the resistances R overlap (i.e. the resistance R is lower than the effects of actions S) failure may be expected to occur. If the difference Z between the resistance R and the effects of actions S is then calculated, the result is another probability distribution describing the random variable Z. The area under the distribution curve in the negative part of Z corresponds to the probability of failure pf. The probability of failure pf, where the resistance R is lower than the effects of actions S, is shown by the hatched area to the left of the ordinate. By contrast, the reliability of a structure is indicated by the area to the right of the ordinate (p s=1 - pf) where the resistance R is greater than the effects of actions S. The greater the mean value mz and the lower the standard deviation σz of the random variable Z, the greater the reliability of the structure will be. A safety index β was therefore defined as mz/σz as a measure of reliability. At that time, the aim was to achieve a safety index β equal to 4.7 for a reference period of one year. This corresponds to a probability of failure of around 10-6 for the one-year reference period, in other words the likelihood of similar structures failing in a single year is one in a million. So far the pure theory, which was very unfamiliar to structural engineers. However, it was also clear to convinced statisticians at the time that it would not be possible to perform such time-consuming and complex statistical safety analyses when designing structures in practice. The theory therefore had to be radically simplified in order to facilitate its application. The partial safety concept, in which it is demonstrated that the design value of the effects of actions to which a structural element or component is subjected does not

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exceed the design value of the resistances, was shown to be highly suitable. Eurocode 7 Geotechnical design - Part 1: General rules (CEN, 2004) (EC 7-1) proposes 3 design approaches as options which are later presented in detail. For Design Approach 2 of EC 7-1 the design value Ed of the effects of actions is calculated in one of two ways: • either by multiplying the characteristic value Fk of the actions by the partial factor γF to obtain the design value Fd of the actions which is then used to determine Ed, • or by determining the characteristic value Ek of the effects of actions from the characteristic value Fk of the actions and multiplying the resulting value by the partial factor γF to obtain Ed. The design value Rd of the resistances (as used in Germany) is obtained by dividing the characteristic value Rk of the resistances by the partial factor γR. The resulting limit state condition is therefore:

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Ed ≤ Rd = Rk /γR The principle of the simplified method, referred to by various authors as the “semiprobabilistic method”, consisted of determining the partial factors in extensive statistical studies performed with the verification methods usually applied in soil mechanics. The values of the partial factors had to be such that the required safety level β of 4.7 would be achieved. The standards writers who began drafting the Eurocodes in the 1970s were fascinated by this combination of probability theory and the partial safety concept for two reasons: • On the one hand, the theory provided an opportunity to define a common safety level irrespective of the design and construction materials, in other words, for all types of construction; • on the other hand, the theory could serve as a common European safety concept for the design of structures. It was a new approach with which each of the Member States would have to familiarize themselves and which would need to be a compromise to enable agreement on it to be reached. The reliability theory had been adopted as the common safety concept for the future Eurocodes (Joint Committee on Structural Safety, 1976). As a consequence, a special committee was established in Germany which lay down the principles for the application of the reliability theory in future structural standards (Arbeitsausschuss “Sicherheit im Bauwesen” (Committee for Safety in Structural Design), 1981).

2. The scientific discussion on the safety concept among geotechnical engineers For geotechnical design, the reliability theory using a probabilistic approach was officially introduced at the German National Geotechnical Conference in 1978. The concept was presented by G. Breitschaft (Breitschaft and Hanisch, 1978) who was president of the DIBt (Deutsches Institut für Bautechnik, an institute of the German Federal and Regional (Laender) Governments for a uniform fulfilment of technical tasks in the field of public law) and later became chairman of the technical committee of CEN in charge of the structural Eurocodes (TC 250). Their lecture intended to

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promote the ideas among German geotechnical engineers and to lay the basis for future standardization work in Europe and Germany. In the following years numerous research studies on the application of the reliability theory were conducted and published for the various geotechnical verifications (e.g. Rackwitz and Peintinger, 1981). Moreover, a revised guidance paper was drawn up by the Committee for Safety in Structural Design (Arbeitsausschuss “Sicherheit im Bauwesen”, 1981) which was intended to serve as a mandatory basis for all future structural design standards. The probabilistic safety concept was brought up again in a special session held during the National Geotechnical Conference in 1982. Five papers dealt with the subject and its application to • the verification of the safety of spread foundations against failure by heave (Pottharst, 1982), • anchored or nailed walls (Gässler, 1982) • the evaluation of test results (Peintinger, 1982; von Soos, 1982) and • the application of previously available information (Rackwitz, 1982). The most interesting part of the special session was a panel discussion. Most of the arguments for and against the probabilistic safety concept, which have been repeated over and over again in discussions since then, were put forward there. They were as follows: • The probabilistic approach does not take account of human error in design and execution although it is one of the main causes of damage (Blaut, 1982). • The possibilities of collecting statistical data on soil are severely limited in practice (Vollenweider, 1982). • The differences between geotechnical engineering and other areas of structural engineering are not only the higher coefficients of variation in the former – soil cannot be produced with clearly defined characteristics according to a set formula – but also that the geotechnical engineer only ever sees a limited part of the structure he is designing (Vollenweider, 1982). Most prominent German geotechnical engineers took rather a critical view of the probabilistic approach (in favour: 3; undecided: 5, against: 4). However, it was generally agreed that greater effort was required during soil investigations, there was a definite need for databases for information on soil to be set up and that more extensive checks and inspections of geotechnical engineering work were necessary. In the following years the probabilistic approach was a research topic at nearly all geotechnical engineering departments at German universities and nearly all analyses in geotechnical design were examined to establish whether they were suited to the application of the probabilistic approach. Eder recalculated the failure of a rock slope (Eder, 1983), Heibaum examined the stability of anchored retaining walls at deep slip surfaces (Heibaum, 1987), Genske and Walz (Genske and Walz, 1987) as well as Smoltzcyk and Schad (Smoltczyk and Schad, 1990) considered the application of the probabilistic safety philosophy to calculations of the bearing capacity of soil, Reitmeier researched the possibility of applying a stochastic approach to quantifying differential settlements (Reitmeier, 1989) while Hanisch and Struck applied the method to evaluate pile loading tests (Hanisch and Struck, 1992). In addition, there were a number of publications dealing with the evaluation of soil investigations in terms of how the results could be used in connection with the probabilistic approach (Hanisch and Struck, 1985, von Soos, 1990, and Alber, 1992) as

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well as papers in which the new concept was clearly set out and explained to colleagues with the intention of promoting it (Gudehus, 1987 and Franke, 1990). Even though the future direction of standardization work in geotechnical engineering seemed to have been firmly established by a decision of the steering committee of the national committees in charge of drafting geotechnical engineering standards in 1982, the “Principles for the specification of safety requirements for structures” (Arbeitsausschuss “Sicherheit im Bauwesen”, 1981) were repeatedly the subject of fundamental criticisms in the years that followed. Thus Franke (Franke, 1984) demonstrated the problems that occur when the probabilistic safety concept is applied to piles, commenting scathingly that the possibility (of applying the probabilistic approach) was viewed most optimistically by those colleagues who were least involved in conducting soil and rock investigations and describing soil and rock on a daily basis in practice. He went on to say that, in his view, the observation method was a far superior aid even though it is not mentioned in the “Principles for the specification of safety requirements for structures”. Furthermore, it was also shown that, for a constant safety level, the partial factors depend on the magnitude and number of parameters involved and in particular on the coefficient of variation (Heibaum, 1987). For Germany at that time it was seldom possible to obtain more than only a rough estimate of the coefficient of variation of geotechnical parameters. Fundamental criticism of the new safety concept was voiced above all by Swiss colleagues. After analysing 800 cases of structural damage that had been described by means of the same criteria and evaluated in different ways, Matousek and Schneider concluded that random deviations of the material properties, the resistances of structures or the loads on structures from the expected values are evidently well covered by the conventional safety concept. The vast majority of cases of damage occur during execution. Matousek and Schneider went on to state that while every care is taken at the design stage, the construction conditions are often viewed as of secondary importance although they require greater attention (Matousek and Schneider, 1976). Schneider considered the probability of serious errors generally to be far greater (ten- to a hundredfold) than the theoretical probabilities of failure (Schneider, 1994). Vollenweider expressed similar doubts about the safety goal of a very low probability of failure. He questioned whether the statistical data for this range of values, if available at all, was sound and whether the correct distribution laws were applied. Vollenweider spoke out in favour of applying the hazard scenario approach instead to enable the risk potential to be managed more reliably (Vollenweider, 1983 and 1988). Summing up the scientific studies and the debate up until around 1990 it can be seen that the probabilistic approach in geotechnical engineering yielded a great number of interesting scientific research results and findings in Germany but that it was not yet possible to develop a convincing standardization concept for application in everyday practice. Although the partial safety concept had won through, the probabilistic approach no longer had any part to play during discussions between standards writers on the issue of which parameters partial safety factors should be applied to and what the values of those factors should be. There were only a few isolated voices who continued to advocate taking the probabilistic approach into account in geotechnical engineering standards (Hanisch, 1998). Although the probabilistic approach was finally abandoned in German geotechnical design standards, the subject continued to be attractive in scientific research. Thus Hartmann and Nawari attempted to discover new ways of evaluating uncertainty and risk with the aid of fuzzy logic and the fuzzy set theory (Hartmann and

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Nawari, 1996), Pöttler et. al. examined the application of the probabilistic approach to tunnel construction (Pöttler et. al., 2001), Ziegler considered the possibilities of risk simulation calculations (Ziegler, 2002), Katzenbach and Moormann used the data collected for Frankfurt clay over many decades to examine the structural performance of piled raft foundations (Katzenbach and Moormann, 2003), Stahlmann et. al. employed probabilistic methods to simulate the inhomogeneities in the soil properties of a railway embankment (Stahlmann et. al., 2007) and Russelli compared various probabilistic methods as applied to investigations of the bearing capacity of soil, demonstrating the great influence of the combination of friction and cohesion and their correlation (Russelli, 2008). So far, none of these studies has been taken into account in geotechnical standards or recommendations.

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3. Eurocode 7 Geotechnical design Work on the Model Code for Eurocode 7 “Geotechnical design” started in 1981 and was headed by Krebs Ovesen (Orr, 2007) who chaired the subcommittee (SC 7) in charge of the work for 18 years. One of the fundamental ideas was that the Eurocode should only contain qualifying rules, in other words, should require the bearing capacity to be verified but would not specify which method of calculation should be used. Naturally, this improved the likelihood of reaching a consensus on the rules. There were intense discussions on the applicability of the statistical safety concept in the European committee as the original enthusiasm for the probabilistic approach had vanished. It was agreed that, should the probabilistic safety concept be introduced in geotechnical engineering, a great number of difficulties would still need to be overcome and that the partial factors would initially have to be based on experience but would have to be confirmed by probabilistic analyses at a later date (Sadgorski, 1983). The drafts of the Eurocode differentiated between the core text and supplementary comments. Initially there was no intention of specifying numerical values for either the loads or the partial factors in the core text of the Eurocodes (Sadgorski, 1983); the values were to be set in National Annexes instead. In 1987, the “Draft Model for Eurocode 7 – Common unified rules for Geotechnics, Design” was published (Representatives of the Geotechnical Societies within the European Countries, 1987) as a report prepared for the European Communities. The annex of the draft model specified partial factors after all. Reference was made to the relevant loading codes for structures above ground level for variable actions while a partial factor, γg, of 1.0 was specified for permanent actions from the structure, ground and groundwater. The following partial factors were given for geotechnical parameters: γϕ = 1.2 on the tangent of angle of internal friction, γc1 = 1.8 on the cohesion when verifying the load-bearing capacity of foundations and γc2 = 1.5 on the cohesion when verifying the stability and earth pressure. Moreover, partial factors were stated for the load bearing resistance of piles and anchors and for structures under construction. In 1989 “Eurocode 7 Geotechnics” was published as a Preliminary Draft for the European Communities on the basis of the December 1987 version of the Model Code produced by the ISSMFE (EC 7 Drafting Panel, 1989). A chapter 7 for piles and a chapter 8 for retaining structures had not yet been prepared. This version now gave numerical values for partial factors in the core text and it was emphasized in the

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preface that “they represented the best estimate of the drafting panel. In geotechnical engineering limited experience has been gained until now on a European basis on the use of limit state design and partial safety factors. Consequently there is a strong need for calibration of all safety elements introduced into the draft before it is issued for use”. In Section 2 “Basis of Design” it was stated as a fundamental requirement that: “A structure shall be designed and constructed in such a way that with acceptable probability, it will remain fit for the use …., and with appropriate degrees of reliability, it will sustain all actions ....”. However, neither principles nor application rules were given for the derivation of partial factors on actions and ground parameters by means of reliability theory. A first complete version of Eurocode 7 was published in 1994 as pre-standard ENV 1997-1:1994 “Geo-technical design - Part 1 General rules” (EC 7-1). Three cases were introduced. Case A covered the loss of static equilibrium of a structure as a rigid body where the strength of the construction material of the ground is not governing. For the verification of ultimate limit states in the ground two combinations of partial factors had to be investigated: Case B and Case C. • Case B aimed to provide safe design against unfavourable deviations of the actions from their characteristic values. Thus, in Case B, partial factors greater than 1.0 were applied to the permanent and variable actions from the structure and the ground, the factors being the same as those used in other fields of structural engineering. By contrast, the calculations of the ground resistance were performed with characteristic values, i.e. the partial factors for the shear parameters, γϕ, γc and γcu, were all set at 1.00. • Case C in the pre-standard aimed to provide safe design against unfavourable deviations of the ground strength properties from their characteristic values and against uncertainties in the geotechnical calculation model. It was assumed that the permanent actions corresponded to their expected values and the variable actions deviated only slightly from their characteristic values. Thus, the partial factors for the characteristic values of the ground strength parameters were γϕ= 1.25 γc = 1.6 and γcu = 1.4 while the characteristic values of the permanent actions from the structure (with γG set at 1.00) were used in the verification. This concept for the verification of two cases, B and C, was strongly opposed in Germany. The philosophy for Cases B and C was not convincing because it could not guarantee a sufficient safety level for the combination or superposition of the uncertainties of the material properties (soil and other material) and the actions. Furthermore, there were strong objections to the mandatory application of partial factors to the ground strength properties ϕ´, c´ and cu in order to determine the design values of the resistances of the soil. Although this corresponded to German practice for the verification of slope stability, in which the Fellenius method was applied, it was not the case for the verification of the design of shallow foundations and retaining walls. The application of partial factors to the ground strength properties would have resulted in some cases in larger dimensions and in others in smaller dimensions than would have been obtained if the former global safety concept had been applied (Weißenbach, 1991). Moreover, with factored shear strength parameters, the relevant verification would be based on failure geometries in the ground which might not be realistic. A more detailed critical review and a proposal for an improvement of the pre-standard of EC 7-1 can be found in Schuppener et. al. (1998) and Weißenbach (1998).

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These fundamental criticisms were shared by many other European countries. As a compromise, the final version of EC 7-1 of 2004 (CEN, 2004) gives three design approaches (DA) as options. Each Member State has to establish in its National Annex to EC 7-1 which of the three DAs is mandatory for which limit state verification. In Design Approach 1 (DA 1), two combinations of partial factors have to be investigated. Combination 1 aims to provide safe design against unfavourable deviations of the actions from their characteristic values. Thus, in that combination, partial factors greater than 1.0 are applied to the permanent and variable actions from the structure and the ground. The recommended factors are γG = 1.35 for unfavourable permanent actions, γG;inf = 1.00 for favourable permanent actions and γQ = 1.50 for variable actions. The factors are the same as those used in other fields of structural engineering and they are consistent with those specified in EN 1990: Basis of structural design. By contrast, the calculations for the ground resistance are performed with characteristic values, i.e. the partial factors γϕ, γc and γcu, which are all set at 1.00, are applied to the shear parameters; the partial factor of the ground resistance, γR, is also 1.00. Combination 2 of DA 1 aims to provide safe design against unfavourable deviations of the ground strength properties from their characteristic values and against uncertainties in the calculation model. It is assumed that the permanent actions correspond to their expected values and the variable actions deviate only slightly from their characteristic values. Thus, in this verification, the partial factors γϕ´, γc' and γcu with numerical values of 1.25 or 1.40 are applied to the characteristic values of the ground strength parameters whereas the characteristic values of the permanent actions from the structure (with γG set at 1.00) are used. The partial factors are applied to the representative values of the actions and to the characteristic values of the ground strength parameters at the beginning of the calculation. Thus the entire calculation is performed with the design values of the actions and the design shear strength. Of the two combinations, the one resulting in the larger dimensions of the foundation will be relevant for designs according to Design Approach DA 1. In Design Approach 2 only one verification is ever required unless different combinations of partial factors for favourable and unfavourable actions need to be dealt with separately in special cases. The partial factors applied to the geotechnical actions and effects of actions are the same as those applied to the actions on or from the structure, i. e. γG = 1.35, γG;inf = 1.00 and γQ = 1.50. There are two ways of performing verifications according to Design Approach 2. In the design approach referred to as “DA 2”, the partial factors are applied to the characteristic actions at the very start of the calculation and the entire calculation is subsequently performed with design values. By contrast, in the design approach referred to as “DA 2*”, the entire calculation is performed with characteristic values and the partial factors are not introduced until the end when the ultimate limit state condition is checked. As characteristic internal forces and moments are obtained in the calculation, the results can generally also be used as a basis for the verification of serviceability. Similarly, only one verification is required for Design Approach 3 (DA 3). The partial factors applied to the actions on the structure or coming from the structure are the same as those used in Design Approach DA 2. However, for the actions and resistances of the ground, the partial factors are not applied to the actions and resistances but to the ground strength parameters, ϕ´, c´ or cu instead. The recommended values of γϕ', γc' and γcu are 1.25 and 1.40. The partial factors are applied to the representative values of the actions at the beginning of the calculation and to the

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characteristic values of the ground strength parameters. Thus, in DA 3, the entire calculation is performed with the design values of the actions and the design shear strength.

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4. DIN 1054 Safety in Earthworks and Foundation Engineering The steering committee of the German national committees in charge of drafting geotechnical engineering standards decided in 1982 to gradually incorporate the new safety concept into the standards for that field (Gudehus, 1987). It was even decided to prepare a Guidance Paper on Reliability in Geotechnical Design. A new standardizing committee “Safety in Earthworks and Foundation Engineering” was established. Its aim was to act as a mirror committee for the European subcommittee drafting Eurocode 7 “Geotechnical Design” and revise the German standard DIN 1054 with the new title “Safety in Earthworks and Foundation Engineering” to make it compatible with the principles and application rules of the future Eurocode 7. The idea behind revising DIN 1054 at the same time as Eurocode 7 was to familiarize German geotechnical engineers with the new design concepts as early as possible and to enable them to make technically sound contributions to the discussions held during the process of writing the Eurocode. With the implementation of EC 7-1 in the Member States all conflicting national standards had to be withdrawn after a coexistence period. DIN 1054 was a conflicting standard as it partly covered the same items as EC 7. So the current version of DIN 1054 (2010) therefore only contains specific German rules, which are not given in EC 7-1 (CEN, 2004). The title of the DIN standard has been amended accordingly to “Subsoil – Verification of safety of earthworks and foundations – Supplementary rules to DIN EN 1997-1”. During the process of revising DIN 1054 a design concept was developed which was later adopted as Design Approach 2 in the final draft of EC 7-1 (CEN, 2004). In order to eliminate the discrepancies in EC 7-1 described above, the following proposals were included in the revised version of DIN 1054-100 (1996): • as a first step, the characteristic values of the actions and the resistances are determined with the aid of the characteristic soil parameters, • as a second step, the characteristic effects of actions, such as the reactions at supports and bending moments, are determined and • only at the end of the verification are the resulting characteristic effects of actions increased and the characteristic resistances reduced by applying partial factors in order to obtain the design values. These are then used to demonstrate that the limit state conditions have been satisfied. This design approach, referred to as “the Weißenbach Approach” during the discussion phase, was then incorporated into the drafts of 2004 and 2005. It was also included in EC 7-1 of 2004 as Design Approach DA 2*. The approach is used in DIN 1054:2010-12 for the structural analysis of retaining walls, spread and pile foundations and anchors.

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5. Partial safety factors Germany has a tradition of standards for geotechnical engineering that dates back more than 70 years. The first edition of DIN 1054, entitled “Guidelines for the permissible loads on ground in building construction”, was published in 1934. Since then, geotechnical standards have continuously been optimized and have reached an outstanding quality. The safety level of the former global safety concept proved successful and the specified safety factors made safe and economic geotechnical designs possible. The Advisory Board of the Standards Committee for Building and Civil Engineering of the German Standards Institute, DIN, therefore decided in 1998 that any increase in cost as a result of new standards had to be justified. As the existing standards were well tried and tested, it was decided that the safety level of the former global safety concept should be maintained when the geotechnical standards were adapted to accommodate the partial safety factor concept of the Eurocodes. This meant that the design approaches and the partial factors had to be selected in such a way that a foundation designed according to EC 7-1 would have roughly the same dimensions as a design in accordance with the previous standards. This was a prerequisite as serious problems regarding the acceptability of the Eurocodes would otherwise have arisen. For example, a structure undergoing modification might need strengthening or even underpinning according to the new safety concept, although this may not have been necessary under the previous one. As reliability theory was not considered to provide partial factors for ground resistance and ground properties, maintaining the safety level of the former global safety concept was also a necessary assumption for the determination of the partial factors for geotechnical actions and resistances. In order to maintain that safety level in the concept of partial factors in Design Approach 2 (DA2*) of EC 7-1 the equation

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γR ⋅ γG,Q ≈ ηglobal must be fulfilled, where γR is the partial factor for the resistance of the ground, γG,Q is a weighted mean partial factor for the effects of permanent and variable actions and ηglobal is the global safety factor used hitherto. The values recommended in Annex A of “Eurocode - Basis of structural design” (CEN, 2002), which are γG = 1.35 and γQ = 1.50 for the permanent and variable effects of actions respectively, were adopted in EC 7-1 and in German geotechnical design standards as they had been in the other fields of structural engineering. As the permanent actions are generally greater than the variable actions in geotechnical engineering, a weighted mean value, γG,Q, of 1.40 was used to calculate the partial factor for the ground resistance, γR, for the various verifications. Thus the following partial factor, γR, for the resistance is obtained from γR ≈ ηglobal / γG,Q. For the ground bearing resistance, where a global safety factor ηglobal, of 2.00, was used in Germany we then arrive at a partial factor of γR,v = 2.00/1.40 ≈ 1.40. The partial factors for the ground resistance in each limit state and design situation were determined in this way. The numerical values of the partial factors for actions have been specified by structural engineers and it is therefore certainly debatable whether they provide a

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realistic description of the uncertainties in geotechnical engineering. Yet EC 7 and the national German standards committee for geotechnical engineering considered it more important for common partial factors to be used in all fields of civil engineering in future than for specific partial factors to be laid down for geotechnical design, especially as selecting the values would also have given rise to endless discussions. Design Approach 3 (DA 3) of EC 7-1 is used in Germany for the verification of overall and slope stability. The approach specifies that partial factors must be applied to the shear strength of the ground as well as to the loads from the structure and the variable loads. Reducing the shear strength conforms to the Fellenius method which was already an option for verifying overall stability in Germany. The reduction in shear strength leads to an increase in the actions from the ground and a decrease in the ground resistance. In order to maintain the safety level of the global safety concept it was decided in Germany that the characteristic values of the permanent actions from the structure would be used and only the variable actions would be increased by a partial factor greater than unity. Generally speaking, their effect on the safety of slopes is very slight anyway as it is the self weight of the soil that is the predominant factor. Further details of the implementation of EC 7-1 in Germany can be found in Lesny (2012).

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6. Summary and outlook The introduction of the partial safety concept provided a common format for analysis in structural design for different types of construction and construction materials. However, a common safety level, in terms of a common probability of failure, has not been achieved, even if very similar partial factors have been introduced for the actions in all areas of structural design. As explained above, these partial factors have also been adopted in geotechnical engineering, with no attempt being made to develop separate partial factors for geotechnical actions. Thus they are not – as was originally planned – a measure of the reliability with which the magnitude of geotechnical actions can be determined. The same applies to the partial factors for the resistances as they were derived on the basis of the condition that approximately the same dimensions for foundations should be obtained for designs in accordance with the partial safety concept as for those performed with the former global safety concept. Thus, in fact the partial safety concept in German geotechnical design is a global safety concept. The incorporation of the new concept into all German geotechnical engineering standards and recommendations has meant that these have been harmonized and thus become more user-friendly. Any technical progress was only an indirect consequence owing to the fact that the German standards and recommendations were, of course, brought up to date and improved as they were being revised to include the partial safety concept. Eurocodes do not take account of human errors, nor are such errors mentioned in the definitions of the partial factors. Instead, all Eurocodes have a list of assumptions which define and make sure that everything is planned, executed, supervised and maintained according to the plans by personnel having the appropriate skill and experience. Although human error was never explicitly referred to in the standards based on the global safety concept it was implicitly assumed that it was covered, at least to a certain extent, by the safety factors. The objective was always to achieve a robust yet economic design that would not fail just because of a few minor errors. The

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adoption of the safety level of the previous standards has thus meant that “minor” human errors are now included in the partial factors. There is general agreement amongst geotechnical experts that human errors and insufficient knowledge of the soil conditions present the greatest risk in geotechnical engineering. It is for this reason that, from now on, greater attention should be paid above all to raising the requirements for soil investigations and introducing stricter controls during execution instead of refining the stability analyses. The author therefore believes that, in future, the incorporation of the hazard scenario approach (Vollenweider, 1983, SIA 260:2003 and SIA 267:2003) or risk simulation calculations (Ziegler, 2002) into geotechnical engineering standards would be more appropriate, especially as the theories behind them are closer to engineering practice. In Germany, there are various views on the technical benefits of applying the partial safety concept in geotechnical engineering. This issue was discussed at length at a meeting of the Steering Committee of the Geotechnical and Earthworks Engineering Section of the Building and Civil Engineering Standards Committee (NABau) of DIN. Irrespective of the technical points of view, the Steering Committee agreed that the partial safety concept should be retained, not least for political reasons. It presents a common language for structural design in Europe which now needs to be simplified and developed further in order to work towards the political aim of eliminating technical barriers to trade and harmonizing technical tendering procedures. A return to the global safety concept would therefore not be desirable.

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References Alber, D. (1992): Überlegungen und Verfahren zur Schätzung statistischer Parameter von Bodenkennwerten, Bauingenieur 67 (1992), S 39 - 45. Arbeitsausschuss „Sicherheit im Bauwesen“, (1981): Grundlagen für die Festlegung von Sicherheitsanforderungen für bauliche Anlagen (Principles for the establishment of safety requirements for structures), Beuth Verlag, Berlin Blaut, H. (1982): Diskussionsbeitrag bei der Podiumsdiskussion zur Spezialsitzung „Sicherheit im Grundbau“ Vorträge der Baugrundtagung, Braunschweig Breitschaft, G. and Hanisch, J. (1978): Neues Sicherheitskonzept im Bauwesen aufgrund wahrscheinlichkeitstheoretischer Überlegungen – Folgerungen für den Grundbau unter Einbeziehung der Probennahme und der Versuchsauswertung, Vor-träge der Baugrundtagung in Berlin, Deutsche Gesellschaft für Erd- und Grundbau, Eigenverlag, CEN (2002) Eurocode: Basis of structural design. European standard, EN 1990: 2002. European Committee for Standardization: Brussels. CEN (2004) Eurocode 7 Geotechnical design - Part 1: General rules. Final Draft, EN 1997-1:2004 (E), (F) and (G), November 2004, European Committee for Standardization: Brussels, 168 pages (E). DIN 1054 (2010): Subsoil – Verification of the safety of earthworks and foundations – Supplementary rules to DIN EN 1997-1, Beuth Verlag, Berlin EC 7 Drafting Panel (1989): Eurocode 7 Geotechnics, Preliminary Draft for the European Communities, Geotechnik 13 (1990), S 1-40 Eder, F. (1983): Erläuterung des Statistischen Sicherheitskonzepts am Beispiel einer Rutschung, Buchkapitel in: Mitteilungen des Instituts für Bodenmechanik, Felsmechanik und Grundbau, TU Graz, Nr.6 Franke, E. (1984), Einige Anmerkungen zur Anwendbarkeit des neuen Sicherheitskonzepts im Grundbau, geotechnik, Jg.7, Nr.3, S.144-149 Franke, E. (1990): Neue Regelung der Sicherheitsnachweise im Zuge der Europäischen Bau-Normung - Von der deterministischen zur probabilistischen Sicherheit auch im Grundbau? Bautechnik 7/1990 Gässler, G. (1982): Anwendung des statistischen Sicherheitskonzeptes auf verankerte Wände und vernagelte Wände, Vorträge der Baugrundtagung, Braunschweig, S 49 – 81

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Genske, D.D. und Walz, B. (1987): Anwendung der probabilistischen Sicherheitsphilosophie auf Grundbruchberechnungen nach DIN 4017, geotechnik 10, S 53 – 66 Gudehus, G. (1987): Sicherheitsnachweise für Grundbauwerke , Geotechnik 10, S. 4-34 Hanisch, J. und Struck, W. (1992): Betrachtungen zur Ermittlung der Sicherheitsbeiwerte für Pfahlbelastungen aus Stichprobenergebnissen und zusätzlichen Informationen, Geotechnik 1992, S 138 ff Hanisch, J. und Struck, W. (1985): Charakteristischer Wert einer Boden- oder Materialeigenschaft aus Stichprobenergebnissen und zusätzlicher Information, Bautechnik 10/1985 Hanisch, J. (1998): Ist der EUROCODE 7 noch zu retten? - Wird der EC 7 zur Hilfe oder zur Bremse bei der Beurteilung der Zuverlässigkeit neuer Bauarten? Bautechnik 9/1998 Hartmann, R., Nawari, O. (1996): Ansatz der Fuzzy-Logik und –Set Theorie in der Geotechnik – neue Wege zur Unsicherheits- und Risikobewertung. Vorträge der Baugrundtagung in Berlin, Deutsche Gesellschaft für Erd- und Grundbau, Eigenverlag Heibaum, M. (1987): Zur Frage der Standsicherheit verankerter Stützwände auf der tiefen Gleitfuge, Darmstadt; Mitteilungen des Instituts für Grundbau, Boden- und Felsmechanik, Heft 27 Joint-Committee on Structural Safety (1976): Common unified Rules for Different Types of Construction and Material, Comité-Euro-International du Beton (CEB), Bulletin d´ínformation No 116 E Katzenbach, R., Moormann, C. (2003): Überlegungen zu stochastischen Methoden in der Bodenmechanik am Beispiel des Frankfurter Tons, Heft 16 der Gruppe Geotechnik, Technische Universität Graz, pp 255282 Kramer, H. (1982): Diskussionsbeitrag bei der zur Spezialsitzung „Sicherheit im Grundbau“ Vorträge der Baugrundtagung 1982, Braunschweig Lesny, K. (2012): Implementation of Eurocode 7 within German Geotechnical Design Practice, Geotechnical Special Publication „Modern Geotechnical Design Codes of Practice – Development, Calibration & Experiences“ Lumb, P. (1970): Safety factors and the probabilistic distribution of soil strength, Canadian Geotechnical Journal, 7, 225-242 Matousek, M. und Schneider, J. (1976): Untersuchungen zur Struktur des Sicherheitsproblems bei Bauwerken, Bericht Nr. 59 aus dem Institut für Baustatik und Konstruktion ETH Zürich, Basel und Stuttgart: Birkhäuser Verlag Orr, T. (2007): The Story of Eurocode 7, Spirit of Krebs Ovesen Session, European Conference on Soil Mechanics and Geotechnical Engineering, Madrid, 2007 Peintinger, B. (1982): Auswirkung der räumlichen Streuung von Bodenkennwerten, Vorträge der Baugrundtagung Braun-schweig,1982, S 105 – 117 Pöttler, R.; Schweiger, H.F.; Thurner, R. (2001): Probabilistische Untersuchungen für den Tunnelbau – Grundlagen und Berechnungsbeispiel, Bauingenieur - Ausgabe 03-2001, S. 101 Pottharst, R. (1982): Erläuterung des statistischen Sicherheitskonzepts am Beispiel des Grundbruchs, Vorträge der Baugrundtagung, Braunschweig, S 9 – 47 Rackwitz, R. und Peintinger, B., (1981), Ein wirklichkeitsnahes stochastisches Bodenmodell mit unsicheren Parametern und Anwendung auf die Stabilitätsuntersuchung von Böschungen, Bauingenieur 56, 215 – 221 Rackwitz, R. (1982): Können Vorinformationen über den Baugrund quantifiziert werden? Vorträge der Baugrundtagung 1982, Braunschweig, S 83 – 104 Reitmeier, W. (1989): Quantifizierung von Setzungsdifferenzen mit Hilfe einer stochastischen Betrachtungsweise, Lehrstuhl und Prüfamt für Grundbau, Bodenmechanik und Felsmechanik der Technischen Universität München, Schriftenreihe Heft 13 Representatives of the Geotechnical Societies within the European Countries (1987): Draft Model for Eurocode 7 – common unified rules for Geotechnics, Design. Russelli, C. (2008): Probabilistic methods applied to the bearing capacity problem, Mitteilung 58 - Institut für Geotechnik, Universität Stuttgart Sadgorski, W. (1983): Neues vom Eurocode 7, Geotechnik 6, S 107 – 110 Schneider, J. (1994): Sicherheit und Zuverlässigkeit im Bauwesen, B. G. Teubner Verlag, Stuttgart Schuppener, B., Walz, B., Weißenbach, A. and Hock-Berghaus K. (1998): EC7 – A critical review and a proposal for an improvement: a German perspective, Ground Engineering, Vol. 31, No. 10 Smoltzcyk, U. und Schad, H. (1990): Zur Diskussion der Teilsicherheitsbeiwerte für den Grundbruchnachweis, Geotechnik 13 (1990) S 41-43 Stahlmann, J.; Schmitt, J.; Fritsch, M. (2007): Anwendung probabilistischer Methoden zur Simulation der stofflichen Inhomogenitäten des Untergrunds in der Geotechnik, Bauingenieur - Ausgabe 5/2007, S. 214-223 Vollenweider, U. (1982): Diskussionsbeitrag bei der zur Spezialsitzung „Sicherheit im Grundbau“ Vorträge der Baugrundtagung, Braunschweig

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Vollenweider, U. (1983): Denkanstöße im Grundbau oder die Lösung grundbaulicher Probleme mittels Gefährdungsbildern, Schweizer Ingenieur und Architekt, 7/83 Vollenweider, U. (1988): Gedanken zur Sicherheit im Grundbau, Schweizer Ingenieur und Architekt Nr. 39, S 1069-1075 von Soos, P. (1982): Zur Ermittlung der Bodenkennwerte mit Berücksichtigung von Streuung und Korrelationen, Vorträge der Baugrundtagung 1982, Braunschweig, S 83 – 104 von Soos, P.: (1990), Die Rolle des Baugrunds bei der Anwendung der neuen Sicherheitstheorie im Grundbau, geotechnik 13 (1990), S, 82-91 Weißenbach, A. (1991): Diskussionsbeitrag zur Einführung des probabilistischen Sicherheitskonzepts im Erd- und Grundbau, Bautechnik 68, Heft 3 S 73-83 (1991) Weißenbach, A. (1998): Umsetzung des Teilsicherheitskonzepts im Erd- und Grundbau, Bautechnik 9/1998 Ziegler, M. (2002): Risikosimulationsrechnung – eine Möglichkeit zur Quantifizierung von Sicherheit und Risiko in der Geotechnik, Vorträge der Baugrundtagung in Mainz, Deutsche Gesellschaft für Erd- und Grundbau, Eigenverlag

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-116

British choices of geotechnical design approach and partial factors for EC7 Brian SIMPSON 1 Arup Geotechnics

Abstract. The Eurocode system allows each nation to specify, for designs to be constructed on its territory, which of its three geotechnical “design approaches” are to be used and what values are to be given to partial factors. These are published in the National Annex to Eurocode 7 (EC7). This paper reviews the choices made by British engineers working under the auspices of BSI to produce the UK National Annex. The UK has chosen to use Design Approach 1, judging that it has the potential to provide the best balance between safety and economy over a wide range of design types, while allowing broad compatibility with previous designs. It also facilitates use of finite element analysis, a feature not shared with Design Approach 2. At this stage in development, values for the partial factors have been selected on the basis of calibration against past experience; probabilistic calculations have not been used to a significant extent in this process. Particular difficulties have been encountered in providing for pile design to EC7, for which the code gives separate requirements for design based on load testing and design based on calculation using ground properties. In practice in the UK, these are often used in combination, and it was found necessary to vary the factors offered for calculations by EC7 as a function of the amount and type of testing undertaken.

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Keywords: Eurocode 7; National Annex; Design Approach; piling

Introduction The Eurocodes have been developed as a compatible system of standards for the design of buildings and civil engineering structures. The Basis of design is provided by EN1990 (BSI 2002). EN1991 Actions on structures is a loading code and EN1992 to EN1996 are concerned with design of structures using various types of materials. Eurocode 7 is concerned with Geotechnical design; Part 1 (EN1997-1, BSI 2004) gives General rules for design and Part 2 (EN1997-2) covers Ground investigation and testing. This paper is concerned with EN1997-1, which will be referred to here as EC7. The Eurocodes are first prepared by international committees for the European standards body Comité Européen de Normalisation (CEN). The system allows each nation to provide “National Annexes” giving values for partial factors, and some other “nationally determined parameters”, to be used for construction on its territory. For EC7, one of three “Design Approaches” can be chosen, which indicates the system of partial factors to be applied for ultimate limit state (ULS) design. The United Kingdom 1

Corresponding Author: Brian Simpson, Arup Geotechnics, 13 Fitzroy Street, London W1T 4BQ, UK; Email: [email protected]. Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

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National Annex (UKNA, BSI 2007) for EC7 requires the use of Design Approach 1 (DA1); the reasons for this are discussed in this paper. For design of piled foundations, the code gives separate requirements for design based on load testing and design based on calculation using ground properties. In practice in the UK, these are often used in combination, and it was found necessary to vary the factors offered for calculations by EC7 as a function of the amount and type of testing undertaken.

1. Design approaches for ULS calculations Table 1 shows the values of partial factors for the three design approaches, which can be varied nationally. Table 1 shows the UK values for DA1 and the CEN values for DA2 and DA3. Values for piled foundations will be considered later. Table 1. Values for the partial factors in EC7. DA1 Comb 1 Actions

Permanent

unfav

Variable

unfav

DA2

DA3

1.35

1.35(1.0)*

1.5

1.5(1.3)*

Comb 2

1.35

fav

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Soil

1.5

1.3

tan φ'

1.25

1.25

Effective cohesion

1.25

1.25

Undrained strength

1.4

1.4

Unconfined strength

1.4

1.4

Spread

Bearing

1.4

footings

Sliding

1.1

Retaining

Bearing capacity

1.4

walls

Sliding resistance

1.1

Earth resistance

1.4

Note: Blanks in the table indicate that factors are 1.0. * 1.35 and 1.5 for structural loads (1.0 and 1.3 for loads derived from the ground).

Design Approach 1 requires two separate calculations using two “combinations” of factors. The entire design, geotechnics and structure, has to accommodate both combinations. The action factors in Combination 1 of DA1 are generally applied to the actions themselves, but in some cases EC7 2.4.7.3.2(2) is followed, applying the factors to action effects; this applies particularly to the structural action effects (bending moments etc) caused by earth and water pressures. Design Approach 2 (DA2) includes factors to be applied to actions; it is similar to the LRFD method favoured in the USA. Originally the factors were to be applied to actions themselves, meaning the basic pre-defined loads acting on a structure at the start of the equilibrium calculations; this form of DA2 is used by some countries. However, some developments, particularly in Germany, have specified that equilibrium and compatibility calculations are carried out in terms of unfactored characteristic

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values, applying the factors to derived action effects (such as bending moments, bearing pressures or active earth forces). This approach, called DA2*, is considered by its developers to follow EC7 2.4.7.3.2(2). In Design Approach 3, factors are generally applied to actions, not to action effects. The calculations are performed using design values for loads and material strengths, rather than characteristic values. It is generally recognised that DA2 is not suitable for problems such as slope stability and for the use of finite element analysis. As a result, most countries that have adopted DA2 as their basic approach use it in combination with DA3 for specific cases. The use of DA1 is not very different from the combined use of DA2 and DA3, except that DA1 requires checking of two calculations, whereas combined use of DA2 and DA3 could imply acceptance of a design that passes according to one DA but fails according to the other. The legal implications of such a situation might be debatable.

2. British choice of Design Approach 1 2.1. UK National Annex

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The British choice, represented by the UK National Annex published by BSI, is to use DA1. This is the original approach published in the earlier ENV version of EC7, and it is considered to have important advantages noted below. The main objections to DA1 have been (a) that it requires two calculations and (b) that it is not consistent with previous practice using global factors of safety. It is sometimes also argued (c) that strength factoring leads to the “wrong” failure mechanism. In response to objection (a), it is argued that carrying out a second calculation is in most cases trivial in comparison with other tasks required in the process of design, such as ground investigation and determining the characteristic values of soil strengths and other parameters to be used. This is particularly the case when computer software is used for the calculations. 2.2. Compatibility with previous practice In relation to objection (b), the partial factor format of the Eurocodes was set up with the intention that it could give a more rational basis of design than the former global safety factors. While the benefits of past experience must not be lost, in the author’s view it is regrettable that attempts are made simply to replicate the past, as has been done to a large degree by the development of approach DA2*. Previous UK practice used single factors of safety, which in some cases were applied in calculations as factors on soil strength. For example, in design of embedded retaining walls factors on soil strength have been in common use since they were introduced as an option in CIRIA Report 104 (Padfield and Mair 1984). Although the values were little changed, these were interpreted as “mobilisation factors”, associated with both serviceability and ULS in the British Standard on retaining structures, BS8002 (BSI 2001). CIRIA Report C580 (Gaba et al 2003) recommended the use of the factor values from BS8002 but considered them as strength factors; this approach differed little from DA1 Combination 2 of EC7, which is usually the dominant combination for embedded retaining walls.

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For slope stability, UK practice, in common with most others, uses factors of safety applied to soil strength. For both spread and piled foundations, however, resistance factors were commonly used. Use of factors on pile resistance is retained in DA1. It can be seen, therefore, that approaches using factors on soil strength were already familiar in the UK, so its adoption on DA1 was not inconsistent with previous practice. The factors adopted in DA1 are not identical with those of previous UK practice and therefore designs may differ slightly. Nevertheless, comparisons have shown broad compatibility with previous designs, and this is considered acceptable (eg Gaba et al 2003, Simpson 2005, Bond and Simpson 2010-11). 2.3. The wrong failure mechanism? In relation to objection (c), the author questions whether there is such a thing as the “right” failure mechanism. Failure is not the “right” outcome of design, and so EC7 is concerned more about proving success than studying failure. The purpose of partial factoring, therefore, is to show that even in extreme circumstances failure will not occur, or at least that the system could only be on the very point of failure, by the most critical mechanism.

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3. Consistent levels of reliability DA1 is intended to provide a reasonable balance of safety and economy over the full range of geotechnical problems, and to provide a system consistent with structural design. This means, for example, that if a retaining wall is used to stabilize a slope that supports foundations, the wall, slope and foundations can all be designed in consistent geotechnical calculations, which pass seamlessly into the structural designs of the wall and foundations. The connection between geotechnical and structural designs was a noted weakness of existing UK codes, particularly for retaining structures. These issues were considered by Simpson (2007) and by Simpson et al (2009). One of the aims of design is to achieve roughly constant reliabilities irrespective of how actions, strengths and resistances combine in particular situations. In Annex C of EN1990, reliability is represented by the target reliability index β, which represents the number of standard deviations between the characteristic state and the ULS design state. EN1990 discusses how the values of partial factors might be selected in order to achieve a target reliability index, proposing that factors could be applied simultaneously to actions and strengths (or action effects and resistances). In effect it proposes that the action effects for ULS design should be 0.7β standard deviations from their characteristic values, and the margin on resistances should be 0.8β (the symbol used for the factors 0.7 and 0.8 is α). But EN1990 places an important limit on this approach: it is only applicable if the ratio of the standard deviations of the action effect and resistance, σE/σR, lies within the range 0.16 to 7.6. The implication of this is that a different approach is to be used if the uncertainty of one of variables – actions or resistances – is much more important to the design than is the other one. For such a situation, the margin on the more critical variable is required to be 1.0β, with a lower margin, 0.4β, on the less critical variable.

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σ /σ E R = 0.16

1.2

SAFETY RATIO.

1.1 1

σ /σ E R = 7.6

Ratio of β achieved to β required Less economic

0.9 αE=-0.7, αR=0.8

0.8 Less safe

0.7 0.6 0

0.2

0.4

0.6

0.8

1

σE/(σR+σE)

Figure 1. Reliability achieved using (0.7, 0.8) combination for α.

SAFETY RATIO

.

1.2 Typical foundations

1.1 1

αE=-0.7, αR=0.8

0.9 0.8 Slope stability

0.7

Tower foundations

0.6

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0

0.2

0.4

0.6 σE/(σR+σE)

0.8

1

Figure 2. Reliability for some typical geotechnical situations.

The result of this approach is shown in Figure 1, in which the reliability achieved (in terms of number of standard deviations of the design point from the characteristic state) is plotted against the ratio of the standard deviations expressed as σE/(σE+σR). The result is plotted as a “safety ratio” by dividing by the required reliability, β standard deviations, so that the desired value is 1.0. Over the range in which both σE and σR are of similar, significant magnitude, the result is reasonably close to the desired value. However, as either σE and σR becomes small compared to the other, the reliability achieved drops substantially, indicating an unsafe design with inadequate reliability. This explains why EN1990 limits the range of applicability of the approach to σE/σR = 0.16 to 7.6. Figure 2 shows that in geotechnical design it is important to consider the full range of σE/σR values. Conventional foundations may have σE and σR of similar magnitude, but other situations may be dominated by either σE or σR. For example, in slope stability problems there is often very little uncertainty about the loading and

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uncertainty of soil strength is dominant, as shown by the fact that factors of safety are normally applied to soil strength. At the other extreme, designs for foundations of tall towers may have loading as the dominant uncertainty. In geotechnical design, these problems often occur together, so the approach adopted must be able to accommodate the full range of σE/σR. Figure 3 shows the result of an approach using two “combinations” in which the margin on the more critical variable is required to be 1.0β, with 0.4β on the less critical variable. Much greater consistency is achieved, with none of the resulting values falling substantially lower than required (ie 1.0). This illustrates the benefit of the use of two combinations: a very wide range of design situations can be covered without change in the design approach. In common with other design approaches, the factors used in DA1 have not been deduced by probabilistic calculation. Nevertheless, they do reflect the principles propounded in EN1990, illustrated in Figure 3, and the lessons that may be learnt by considering a probabilistic framework. Although the concept of “combinations” is relatively new to geotechnics, it is familiar to structural engineers who frequently design for several combinations of actions. The background to DA1 is essentially the same as that of combinations of actions, giving a severe value to the lead variable in combination with less severe values of other variables, but in DA1 the method is extended to include resistances or material strengths, as suggested by EN1990. The fundamental principle of DA1 is that “All designs must comply with both combinations in all respects, both geotechnical and structural”. I this context, the word “design” means “that which will be built”.

Ratio of β achieved toβ required 1.2

Uneconomic αE=-0.4, αR=1.0

αE=-1.0, αR=0.4

SAFETY RATIO

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.

1.1 1 0.9 0.8

Unsafe

0.7 0.6 0

0.2

0.4

0.6

0.8

1

σE/(σR+σE)

Figure 3. Reliability achieved using (1.0, 0.4) combinations for α

4. Apply the factors where the uncertainties lie EN1990 [6.3.2(4)] refers to “non-linear analysis”, by which it means situations where an action effect changes disproportionately as the action changes. Figure 4 shows the requirements of EN1990 when there is a non-linear relationship between actions and

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Ac tio n effect

Factor the resistance

Resistance Factor the action effect

Factor the material strength

Factor the action Ac tio n

Figure 4. Non-linear relationship between actions and action effects

Material strength

Figure 5. Non-linear relationship between material strengths and resistance

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action effects. If the changes in the effect are disproportionately large compared with those in the action, then it is important that safety factors are applied to the action, not the action effect. EN1990 does not consider the possibility of a similar disproportionate relationship between material strength and resistance, and this may not be very important in structural engineering. In soils, however, where the strength is essentially frictional, such disproportionality is often significant. For example, passive resistance and bearing capacity both increase disproportionately with angle of shearing resistance ϕ′ (Simpson et al 2009); in some cases, when ϕ′ is large, a small change in ϕ′ has a very large effect on the resistance. The author suggests that similar thinking should therefore be applied to strengths and resistances as to actions and action effects. Figure 5 shows situations where there is a non-linear relationship between material strength and resistance. The author submits that if the changes in the resistance are disproportionately large compared with those in the strength, then it is important that safety factors are applied to the strength, not the resistance.

5. Apply factors before combining variables Disproportionate effects may occur simply due to the addition of actions which tend to cancel. Interest in partial factoring methods in the United Kingdom was encouraged by the study of the collapse of the Ferrybridge cooling towers (for more detail see Simpson et al 2009). The stress in the concrete was derived from the addition of compression due to the weight of the towers and tension due to wind loading, which tended to cancel each other. Using a working state approach, this resulting stress was then compared with a factored strength. Unfortunately, the wind loading was underestimated and this led to a disproportionately large increase in the resulting tension, which caused a very serious collapse. The disaster might have been avoided if the two actions, weight and wind load, had been factored separately before being combined into a single action effect. In view of this, parameters are factored before they are combined in DA1, as far as it is reasonably possible, and generally factors are applied to soil strength rather than to “resistances”. Difficult situations for combining actions occur in earth pressure calculations for design of retaining walls, affecting DA1 Combination 1 and also DA2.

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These are considered in EN1997-1 in 2.4.7.3.2(2) which says “In some design situations, the application of partial factors to actions coming from or through the soil (such as earth or water pressures) could lead to design values which are unreasonable or even physically impossible. In these situations, the factors may be applied directly to the effects of actions derived from representative values of the actions.” The author submits that this approach is acceptable for DA1 Combination 1, where factors are applied to actions, provided that Combination 2 is also checked, factoring the soil strength before using it to calculate resistances. The absence of an equivalence of this in DA2 is considered by the author to be a shortcoming of DA2. One additional benefit of this approach is that it coincides with conventional structural design, indirectly applying a factor to ground water pressure for the calculation of structural forces and bending moments.

6. Compatibility with numerical analysis Numerical methods can be used relatively easily for ULS computations if this merely requires using factored values for the input to the program, or simply factoring the structural action effects resulting from the geotechnical program. Design Approach 2 requires factors to be applied to quantities that are internal to the geotechnical analysis such as active and passive forces or pressures, and bearing resistance for spread foundations. So it is generally accepted that full numerical analyses of ultimate limit states, in which resistances are internal to the numerical computation, cannot be undertaken for DA2. Most countries that use DA2 require use of DA3 for numerical analysis. Design Approach 1 was the only approach in the ENV version of EC7 published in 1995. In its development, the possible use of numerical methods was considered, so they can be used relatively easily with DA1.

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7. Distinction between ULS and SLS As adopted in the UKNA, DA1 is used to prevent exceedance of ultimate limit states and it is assumed that serviceability will be considered separately. An exception occurs for piled foundations, as discussed below. For spread foundations, it will often be the case that design is governed by settlement criteria, and no attempt has been made to adjust the DA1 factors for ULS so as to cover this. It could well be that spread foundations designed only checking DA1 factors for ULS would have unacceptably high bearing pressures in service and so would settle too much. For spread foundations on clays, EC7 allows the possibility that settlement could be limited by providing a larger overall factor of safety (6.6.2(16)), but this is seen clearly as a serviceability requirement. For retaining structures, if displacement is critical a separate assessment of it is required, using a combination of experience, case histories and calculation. In practice, this assessment is most likely to affect the choice of type of wall rather than the details of its geometry or strength. It is usually found that walls that are adequate for ULS using DA1 factors do not need modification for serviceability, apart from the reinforcement needed for crack width control in reinforced concrete.

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8. Reliability calculations and “calibration” in deriving values for partial factors It was noted above that principles of reliability theory underlie the general form of DA1. However, values of partial factors have been checked by calibration with past experience, and generally reliability calculations have not been attempted. It is not clear whether use of reliability analysis could provide a more rational basis for selection of factor values, but it is thought that an extremely high level of expertise would be needed to handle the very wide variety of data, often quite sparse, typically involved in geotechnical design. This issue was considered further by Simpson (2011) in relation to the use of reliability theory in the design process itself. The Eurocodes provide partial factors on a small number of leading parameters. However, in order to achieve robust designs sufficient to protect public safety, it is necessary to accommodate unexpected events and variations in other, secondary parameters; these could include, for example, minor accidents or vandalism, small errors or changes in construction, minor deterioration, etc. Calibration of new formats against existing experience is seen to be the best way to achieve this. Derivation of factor values from existing experience is problematic, however, when there is a desire to separate ULS and SLS calculations. Successful existing designs have usually satisfied both criteria, but it may be unclear which of them governed the need for particular factors of safety. The process followed has therefore been to check the use of the factor values proposed in the CEN version of EC7 against design results from previous experience, noting the relevance of serviceability calculations and assessments. These values have been found to be appropriate for general use, but for piling the factors in the UK national annex have been changed significantly from teh CEN values.

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9. Piling Design of pile foundations is the subject of Section 7 of Eurocode 7. Clause 7.4.1 says that design shall be based on: a) the results of static load tests, which have been demonstrated, by means of calculations or otherwise, to be consistent with other relevant experience; or b) empirical or analytical calculation methods whose validity has been demonstrated by static load tests in comparable situations. Design may also be based on dynamic tests or observed behaviour of other piled foundations. However, in the UK most piles are designed using a combination of load testing and calculation. Method (a) above emphasises load tests and method (b) emphasises calculations, but both methods rely to some extent on both load tests and calculations. However, in the remainder of Section 7 design procedures based on load testing and calculation are dealt with separately, and it is not clear how they are to be combined. In the default values of partial factors given in the CEN version of EC7, factors greater than unity are allocated to pile resistances in Combination 1, but these are all taken as unity in the UKNA, thus providing a simple system. Combination 1, with load factors as shown in Table 1, may govern structural design of piles, but Combination 2 generally governs the geotechnical design. Table 2 shows the values of resistance factors for ULS in the CEN version of EC7 and in the UKNA. These are to be applied to characteristic resistances, defined by EC7 (2.4.5.2(2)) as “a cautious estimate of the

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125

value affecting the occurrence of the limit state”. Paragraph 2.4.5.2(11) adds that “If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%”. This gives an indication of the meaning of “cautious estimate” in the definition of characteristic value. It implies that the result of a single pile loading test or of a “best estimate” calculation is unlikely to be sufficiently cautious to comply with the definition. For design based primarily on load testing – method (a) above – EC7 (7.6.2.2) provides a method of deriving characteristic pile resistance from the results of one or more tests, using the mean and minimum of the test results and dependent on the number of tests. In the UK, however, the industry has judged that the method used is primarily based on calculation – method (b) above – using ground test results as input and supplemented by load testing. For this, 7.6.2.3 says in a note “the values of the partial factors γb and γs recommended in Annex A may need to be corrected by a model factor larger than 1,0. The value of the model factor may be set by the National annex.” It is considered that the biggest uncertainty in calculating pile resistances is in the calculation model, rather than in the parameters used to characterize the ground mass. The UK approach is therefore to calculate shaft and base resistance from measured ground parameters (“using methods whose validity has been demonstrated by static load tests in comparable situations”), and to apply a model factor to the result of the calculation in order to derive characteristic (ie cautious) values of resistances. The complete process is illustrated in Figure 6. The value of the model factor depends on whether there has been a trial pile tested at least to a load equivalent to the calculated unfactored ultimate resistance. If such a trial has been carried out the model factor is 1.2; otherwise it is 1.4. Characteristic soil strengths (cu,k, tanφk, etc)

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Calculation model – accurate or erring on the side of safety Calculated shaft and base resistance γRd=1.4 or 1.2

sĂůƵĞĚĞƉĞŶĚƐŽŶ ƚƌŝĂůƉŝůĞƚĞƐƚƐ

Characteristic shaft and base resistance γs and γb

sĂůƵĞĚĞƉĞŶĚƐŽŶ ǁŽƌŬŝŶŐƉŝůĞƚĞƐƚƐ

Design shaft and base resistance (ULS) Figure 6. Process of pile design required by the UKNA.

Having derived the characteristic resistance of the pile, the design ULS resistance is found by dividing the shaft and base resistances by further factors γs and γb; alternatively, the total resistance may be divided by γt. As for the model factor, the

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values of these partial factors are dependent on the amount of testing undertaken. In this case, a reduction is allowed if at least 1% of the piles is loaded tested to at least 1.5 times the representative load; these are generally working piles. The UKNA also allows this reduction in γ-values if settlement in service is explicitly predicted by some other reliable means, or if settlement at the serviceability limit state is of no concern. Table 2 shows that the partial factor values adopted in the UK are bigger than the default values recommended in the CEN version of the code. Most other countries have also increased these factors, either directly or indirectly through the use of model factors. The previous British foundations code, BS8004 (BSI 1986), recommended that piles be designed to an overall factor of safety between 2 and 3, depending whether “ultimate bearing capacity has been determined by a sufficient number of loading tests or where they may be justified by local experience”. In a more detailed paper on pile design to EC7, Bond and Simpson (2009-10) have shown that the factors included in the UKNA are reasonably consistent with previous practice. For shaft controlled bored piles, overall factors of safety may be slightly lower than previously; in the case of a pile with negligible base resistance and carrying only permanent compression loads, the overall factor of safety could be as low as 1.68 with maximum testing, increasing to 2.24 if the design relies on calculation alone with no testing. Slightly lower values are allowed for driven piles. The values are higher for base-controlled piles, being close to 3 for base-controlled bored piles with no load testing. Table 2. Values for the partial factors in piling – DA1 Combination 2. CEN Base

1.3

UKNA 1% tested 1.5

10. Concluding remarks The UK National Annex for Eurocode 7 requires the use of Design Approach 1. The reasons for this choice have been given: essentially it is considered that DA1 covers the widest range of design types, balancing of economy and safety, and also allows the use of all appropriate forms of calculation, including the finite element method. The default values for partial factors given by CEN have generally been accepted, except in the case of pile design, for which values have generally been increased. A model factor is included in the derivation of characteristic pile resistances, and all the factors are adapted to suit the combination of calculation and testing typically used in the design process.

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References

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Bond, AJ and Simpson, B (2009-10) Pile design to Eurocode 7 and the UK National Annex (2 parts). Ground Engineering, Dec 2009 and Jan 2010. BSI (1986) BS 8004:1986, Code of Practice for Foundations. BSI, London. BSI (2001) BS 8002:1994, Code of Practice for Earth Retaining Structures. BSI, London. BSI (2002) BS EN 1990:2002. Eurocode: Basis of design. BSI, London. BSI (2004) BS EN 1997:1: 2004. Eurocode 7: Geotechnical design - Part 1: General rules. BSI, London. BSI (2007) UK National Annex to Eurocode 7: Geotechnical design - Part 1: General rules. BSI, London. Gaba, AR, Simpson, B, Powrie, W,& Beadman, DR (2003) Embedded retaining walls: guidance for economic design. CIRIA Report C580. Padfield, C.J. & Mair, R.J. (1984) Design of retaining walls embedded in stiff clay. CIRIA Report 104. Simpson, B (2005) Eurocode 7 Workshop – Retaining wall examples 5-7. ISSMGE ETC23 workshop, Trinity College, Dublin. Simpson, B (2007) Approaches to ULS design - The merits of Design Approach 1 in Eurocode 7. ISGSR2007 First International Symposium on Geotechnical Safety & Risk pp 527-538. Shanghai Tongji University, China. Simpson, B (2011) Reliability in geotechnical design – some fundamentals. Proc 3rd Int Symp on Geotechnical Safety and Risk, Munich. Simpson, B, Morrison, P, Yasuda, S, Townsend, B, and Gazetas, G (2009) State of the art report: Analysis and design. Proc 17th Int Conf SMGE, Alexandria, Vol 4, pp. 2873-2929.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-128

Dutch approach to Geotechnical design by Eurocode 7, based on probabilistic analyses Ton VROUWENVELDERa, Adriaan van SETERSb and Geerhard HANNINKc a Delft University of Technology, TNO, Delft b Fugro Geoservices, Leidschedam c Public Works Rotterdam

Abstract. In the Netherlands, due to the large infrastructure and waterway projects from the 1980’s onwards, much experience was developed using probabilistic design. Due to the vast extent of e.g. the Eastern Scheldt Storm Surge Barrier, these structures could not have been designed economically using conventional engineering. The probabilistic approach is reflected in the building and geotechnical standards which were introduced in the early 1990’s. These standards were based on a target probability of failure or reliability index β. Probabilistic analyses (Monte Carlo) were undertaken to determine the partial load and material factors. These analyses were also performed for geotechnical structures, leading to a large set of material factors for soil properties. The old method of Ultimate Limit State analysis consisting of overall resistance factors was then replaced by partial factors. Consequently, when Eurocode 7 was established around 2000, Design Approach 3 adopting partial load and material factors was preferred in the Netherlands as its philosophy is similar to the 1991 Dutch building codes.

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Keywords. Partial factors, Eurocodes, Limit state design, Geotechnics

Introduction The first Dutch geotechnical design codes appeared around 1990. They have been developed in the same period as part 1 of Eurocode 7. The need for the geotechnical codes became imminent by new legislation for the Dutch building industry, that was approved in 1991. The new Dutch geotechnical design codes consisted of one general part and two specific parts for the design calculations of foundations on piles and of shallow foundations respectively. They were the result of a discussion of more than 15 years about the use of an overall safety factor or the use of partial factors on loads and strength of materials. The content of the Dutch code on the design of pile foundations in the Netherlands has been reported during a seminar of the European Regional Technical Committee 3 ‘Piles’ in Brussels (Everts & Luger, 1997). Because of the presence of Holocene peat and clay layers at the top, pile foundations are, especially in the western part of the Netherlands, installed since the medieval ages. The Royal Palace in Amsterdam, that was built from 1648 to 1665, has been founded on 13,659 wooden piles. The length of the piles was mainly assessed by experience. For important buildings and constructions a test pile was driven to be sure that the pile base reached the bearing sand layer.

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The experimental way of realizing pile foundations in the Netherlands lasted until the invention of the Dutch cone penetrometer test (CPT) around 1930. The first relations between the results of CPT’s and the bearing capacity of a pile were proposed by Koppejan & Van Mierlo (1952). Since that time the CPT’s were used to predict the ultimate load on a specific type of pile. In the Netherlands generally low factors are used for driven prefabricated concrete piles, and relatively high factors for in situ made piles. This resulted in overall safety factors varying from 1.7 to 2.5 for displacement piles and from 2.5 to 3.5 for nondisplacement piles. The current safety for driven piles in the Netherlands is made up of a number of partial factors: the partial factor on actions γF (1.3 – 1.5), the partial resistance factor γR on compression (1.2), and the correlation factor ξ3 to derive characteristic values from ground test results (1.25 – 1.40). This can be compared with an overall safety factor of 1.4 * 1.2 * 1.3 ~ 2.2. The ultimate bearing capacity of a shallow foundation is found when a potential slip pattern or a continuous plastic zone has developed. In the past Prandtl’s approach was followed in the Netherlands with an overall safety factor between 2 and 3. Sheet pile walls are usually installed in undisturbed soils and afterwards excavation at one side takes place. A number of failure modes needs to be considered, such as rotation of the wall, slip of the anchor, buckling of the strut, excessive bending of the wall, excessive settlement behind the wall, bottom heave and slip failure. In the past Blum’s design approach was followed in the Netherlands, where the required quality of the wall is determined by the maximum bending moment. Usually a safety factor of 2 was applied. Slopes were generally analyzed according to the Bishop method of analysis using low characteristic values for the soil parameters. The resulting overall factor of safety should be at least 1.3 for the permanent situation and 1.1 for the building phase. The present paper will deal with the general theory behind the development of partial factors. Examples will be given for shallow foundations and sheet pile walls.

1.

The partial factor method

In partial factor design a structure is considered as safe enough if, for all relevant limit states, the following inequality is fulfilled: Z ( Xd1,Xd2, ..) > 0

(1)

Here Z( X1, X2, ..) is the so called limit state function, indicating for which values of the basic variables Xi (loads, material properties, etc) the limit state is exceeded and for which it is not. Negative values of Z correspond to the failed situation and positive values of Z to the non-failed situation. The design Xdi values are obtained from: Xdi = γi Ski (for loads) and Xdi = Rk / γm (for resistance)

(2)

where Ski is the representative value of load number i, Rk is the representative value of the resistance and γ are the partial factors. In the American standards 1/γm is normally referred to as φ, but that is no essential difference. In practice it may be difficult to choose the characteristic values and partial factors. Obviously design values equal to mean values will lead to too many failures. But which

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margins should be taken? Two basic notions are of importance: the scatter or uncertainty present in the variables on the one hand and the desired reliability on the other. The latter one may depend on the consequences of failure and the costs necessary to obtain more safe solutions. Using the theory of reliability (ISO/TC98, 1994) the following formula for γm may be derived: γm =

(3)

(1 − 1 . 64 V ) (1 − αβ V )

where α is a sensitivity coefficient (0q@ MI >(N1)60@>q@ 0.001 -4.4 -5.1 0.005 -3.7 -4.3 0.01 -3.3 -3.9 0.05 -2.3 -2.7 0.10 -1.8 -2.1

MIVs1 >q@ -6.2 -5.2 -4.7 -3.3 -2.6

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M. Uzielli et al. / Probabilistic Assignment of Design Strength for Sands from In-Situ Testing Data 225

The investigation on the uncertainty in effective friction angle of sands illustrated in this paper highlights the relevance of uncertainty in widely used geotechnical procedures, such as the derivation of design values from in-situ testing. The significant magnitudes of the model factors calibrated herein attests for the importance and convenience of addressing uncertainty in geotechnical analysis in order to attain a target reliability level expressed in probabilistic terms, thereby pursuing safety and performance in a way which is as rigorous as possible. The results of the analyses presented in this paper are directly applicable only to design problems in which friction angle is the single dominant uncertainty. Nonetheless, the quantitative information regarding the model factors can be used in cases in which other design parameters are modeled as random variables. For instance, in a multivariate design case, distribution parameters of the model factors allow the probabilistic description of friction angle in a second-moment sense (e.g., for implementation in a FOSM framework) by considering the deterministic value as the central tendency parameter and by quantifying the second central moment (i.e., standard deviation) based on the distribution parameters of the model factor as obtained herein. In a higher-level analysis relying on probabilistic simulation, the distribution parameters of model factors allow the direct generation of simulation input samples of friction angle, possibly including statistical dependence among random variables using copula theory or other multivariate distribution modeling techniques. Another important aspect of reliability-based design which is not explicitly addressed herein is the selection of the “physically characteristic” value of the field measurement which servers as input to the uncertainty-based estimation of friction angle, e.g. the “representative” value of cone resistance over a soil volume in which the measured parameter is spatially variable. Formally, the acknowledgment of this source of epistemic uncertainty entails the increase in the epistemic uncertainty associated with the independent variable. The magnitude of such an increase is extremely variable and difficult to quantify aprioristically, as it is largely case- and site-specific. As has been shown in the paper, there exists an inverse relationship between the magnitude of epistemic uncertainty in field measurement and the standard deviation of the model factor. By not considering this additional epistemic uncertainty explicitly, (a)

(b)

(c)

50

50

45

45

45

40

40

40

35

I[°]

50

I[°]

I[°]

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5. Concluding remarks

35

35

30

30

30

25

25

25

20

0

200 qt1

400

20

0

20 40 (N1)60

60

20

140 160 180 200 220 Vs1[m/s]

Figure 3. Source data points, deterministic regressions and design curves for: deterministic case (black); pt=0.005 (dark gray) and pt=0.050 (light gray)

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226 M. Uzielli et al. / Probabilistic Assignment of Design Strength for Sands from In-Situ Testing Data

unconservatism in the characterization of model factors is avoided. As any output of a statistical/probabilistic analysis, the quantitative results obtained and presented herein depend from the source datasets, and are likely to vary to some extent if new data become available to update them. Model factors are thus not static quantities; rather, the progressive increase in high-quality data would allow updating of quantitative estimates. The calibration procedure shown herein demonstrates the possibility of making available the results from complex probabilistic methods in a simple format for practical implementation in routine design. The proposed format is compatible with a “full reliability-based” approach which bypasses the necessity to assign a “characteristic value”. The progressive compilation of sets of model factors derived through rigorous procedures would be beneficial in the drafting and refinement of design codes based on probability and reliability concepts.

Acknowledgments

The first Author is grateful to Dr. Alessandro Bessi for his assistance in performing the MCMC calculations.

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References American Petroleum Institute API RP2A (2011). ANSI/API Recommended Practise 2 Geo. Geotechnical and Foundation Design Considerations, Modified version of ISO 19901-4:2003. Bureau Veritas (2004). Classification of mooring systems for permanent offshore units. Guidance Note NI 493. Ching, J., Chen, J.-R., Yeh, J.-Y., Phoon, K.-K. (2012). Updating uncertainties in friction angles of clean sands, Journal of Geotechnical and Geoenvironmental Engineering 138 (2), 217-229. Christian, J.T., Baecher, G.B. (2011). Keynote lecture: Unresolved problems in geotechnical risk and reliability, Proceedings of Georisk 2011 – Geotechnical Risk Assessment and Management, GSP 224, Atlanta, USA, ASCE Press, Reston, Virginia, 50-63. EC1 (1994). Eurocode 1: Basis of design and actions on structures (Part 1: Basis of design). European Committee for Standardisation, ENV 1991-1:1994. EC7 (1995). Eurocode 7: Geotechnical Design – Part 1: General rules, together with the United Kingdom National Application Document, DD ENV 1997-1:1995. British Standards Institution, London. Gelman, B.A., Carlin, B.P., Stem, H.S., Rubin, D.B. (1995). Bayesian data analysis, Chapman & Hall, London. Geman, S., Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Transactions on Pattern Analysis of Machine Intelligence 6, 721-741. Ghiassian, H., Jalili, M. (2008). Empirical relationships between internal friction angle and modulus of elasticity of sandy soils based on in-situ and checking triaxial tests, Proc., 3rd Int. Conf. on Site Characterization (ISC-3, Taipei), Taylor & Francis, London, (CD-ROM). Gilbert, R.B., Tang, W.H. (1995). Model uncertainty in offshore geotechnical engineering, Proc. of 27th Annual Offshore and Technology Conference, Houston, USA, OTC7757, 557-567. Goble, G. (1999). Geotechnical related development and implementation of load and resistance factor design (LRFD) methods, NCHRPSynthesis276, Transportation Research Board, Washington, D.C., USA. Green, R., Becker, D. (2001). National report on limit state design in geotechnical engineering: Canada, GeotechnicalNews 19 (3), 47-55. Hatanaka, M., Uchida, A. (1996). Empirical correlation between penetration resistance and internal friction angle of sandy soils, Soils and Foundations 36 (4), 1–9. Honjo, Y. (2011). Keynote lecture: Challenges in geotechnical reliability based design, Proceedings of the International Symposium on Geotechnical Safety and Reliability ISGSR 2011, Vogt, Schuppener, Straub & Bräu (eds.), Munich, Bundesanstalt für Wasserbau, CD-ROM.

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M. Uzielli et al. / Probabilistic Assignment of Design Strength for Sands from In-Situ Testing Data 227

Kulhawy, F.H., Mayne, P.W. (1990). Manual on estimating soil properties for foundation design, Report EL6800, Electric Power Research Institute, Palo Alto, USA, 306p. Kulhawy, F.H., Birgisson, B., Grigoriu, M.D. (1992). Reliability-based foundation design for transmission line structures: transformation models for in-situ tests, Report EL5507(4), Electric Power Research Institute, Palo Alto, USA, 113 p. Kulhawy, F.H., Trautmann, C.H. (1996). Estimation of in-situ testing uncertainty, Uncertainty In the Geologic Environment: From Theory to Practice, ASCE Press, Reston, USA, 269-286. Kulhawy, F.H., Phoon, K.K. (2002). Observations on geotechnical reliability-based design development in North America, Proc. of the Int. Workshop on Foundation Design Codes and Soil Investigation in view of International Harmonization and Performance. Tokyo, 31-48. Mayne, P. W., Christopher, B. R., Berg, R. R., DeJong, J. (2002). Subsurface investigations—Geotechnical site characterization, FHWA-NHI-01-031, National Highway Institute, Federal Highway Administration, Washington, D.C., 301p. Mayne, P.W. (2006). The 2006 James K. Mitchell Lecture: Undisturbed sand strength from seismic cone tests, Geomechanics and GeoEngineering 1 (4), Taylor & Francis Group, London, 239-257. Mayne, P.W. (2007). Invited Overview Paper: In-situ test calibrations for evaluating soil parameters, Characterization & Engineering Properties of Natural Soils, Vol. 3 (Proc. 2nd Singapore Workshop), Taylor & Francis Group, London, 1602-1652. Metropolis, N., Rosenblueth, A.W., Rosenblueth, M.N., Teller, A.H., Teller, E. (1953). Equation of state calculations by fast computing machines, Journal of Chemical Physics 21, 1087-1092. Meyerhof, G.G. (1994). Evolution of safety factors and geotechnical limit state design. 2nd Spencer J. Buchanan Lecture. Texas A&M University, College Station, USA. Moss, R.E.S. (2008). Quantifying measurement uncertainty of thirty-meter shear-wave velocity, Bulletinof theSeismologicalSocietyofAmerica98ȋ͵Ȍǡͳ͵ͻͻȂͳͶͳͳǤ Osborne, J.J., Teh, K.L., Houlsby, G.T., Cassidy, M.J., Bienen, B., Leung, C.F. (2010). “InSafeJIP” Improved guidelines for the prediction of geotechnical performance of spudcan foundations during installation and removal of jack-up units, RPS Energy Report Number EOG0574-Rev1. Final Guielines of the InSafe Joint Industry Project. 124p. Phoon, K.K., Kulhawy, F.H. (1999). Characterisation of geotechnical variability. Canadian Geotechnical Journal 36(4), 612-624. Phoon, K.K., Kulhawy, F.H. (1999). Evaluation of geotechnical property variability. Canadian Geotechnical Journal 36(4), 625-639. Phoon, K.K., Becker, D.E., Kulhawy, F.H., Honjo, Y., Ovesen, N.K., Lo, S.R. (2003). Why consider reliability analysis for geotechnical limit state design, Proc. of LSD2003: International Workshop in Limit Stet Design in Geotechnical Engineering Practice. Phoon, Honjo and Gilbert (eds). World Scientific Publishing Company, Cambridge, USA. Phoon, K.-K. (2008). Numerical recipes for reliability analysis – a primer, Reliability-Based Design in Geotechnical Engineering, Phoon, K.K. (ed.), Taylor and Francis, London, 1-75. Pillai, V.S., Stewart, R.A. (1994). Evaluation of liquefaction potential of foundation soils at Duncan Dam, Canadian Geotechnical Journal 31 (6), 951-966. Plewes, H.D., Pillai, V.S., Morgan, M.R., Kilpatrick, B.L. (1993). In-situ sampling, density measurements, and testing of foundation soils at Duncan Dam, Proceedings 46th Annual Canadian Geotechnical Conference, Saskatoon: 223-235. Re-published in Canadian Geotechnical Journal 31 (6), 927-938. Taylor, B.B., Lewis, J.F., Ingersoll, R.W. (1993). Comparison of interpreted seismic profiles to geotechnical borehole data at Hibernia, Proc. 4th Canadian Conference on Marine Geotechnical Engineering, Vol. 2, St. John’s, Newfoundland: 685-708. Thompson, G.R., Long, L.G. (1989). Hibernia geotechnical investigation and site characterization, Canadian Geotechnical Journal 26 (4), 653-678. Whitman, R.V. (1984). Evaluating calculated risk in geotechnical engineering, Journal of Geotechnical and Geoenvironmental Engineering 110 (2), 145-188. Zhang, J., Tang, W.H., Zhang, L.M., Huang, H.W. (2012). Characterising geotechnical model uncertainty by hybrid Markov Chain Monte Carlo simulation, Computers and Geotechnics 43, 26-36.

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Experiences with Limit State Approach for Design of Spread Foundations in the Czech Republic Martin VANÍEK a,1 and Ivan VANÍEK a Czech Technical University in Prague

a

Abstract. The first experience with limit state design approach was introduced in the Czech Republic already 45 years ago for shallow foundations. However just the experiences with the second version which was implemented in 1987 (25 years ago) will be discussed here in more detail. The paper describes both limit states Ultimate and Serviceability limit states. Mainly the focus will be on: - definition and distinction of the design into 3 geotechnical categories - demands on the site investigation - nominal values of soil properties for different geotechnical categories - design approaches within limit states - definition of material partial safety factors - design calculations for both limit states - evaluation of up to date experience with respect to probability of failure. Keywords. Spread foundations, Limit state approach, bearing capacity, settlement

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Introduction Limit state approach was for the first time introduced for the geotechnical design in the Czech Republic in 1966 when the standard SN 73 1001 (Foundation of structures. Subsoil under shallow foundations) was published. Only the basic principles will be defined as new standard with the same number and name was published in 1987. There were several reasons why the standard was redrafted. The most important are as follows: x The classification system for foundation subsoil suggested in 1966 showed itself as insufficient, as for example for cohesive soils used only 3 classes based on the plasticity index, while for sandy soils it used 7 classes. However in the Czech Republic there are not so many non-plastic sandy soils. Moreover for cohesive soils there were defined parameters for undrained shear strength required for bearing capacity calculation based on soil consistency and hence the values were very close. x Suggested approaches for the total settlement analysis were generally giving significantly higher values than those measured afterwards in reality.

1

Corresponding Author.

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229

Therefore higher attention is devoted to the standard from 1987, which adopted most of the principles from the original standard from 1966, however it differs from the original version mainly in those 2 above mentioned points and though in other points certain corrections were also made. Just before the issue of the new version in 1987 the drafters were informed by Prof. Krebs Ovesen about the first proposal of the Eurocode 7.

The standard distinguishes 3 fundamental approaches for the design of shallow foundations with respect to the severity of the superstructure and complexity of the subsoil conditions: a) For modest superstructures in simple subsoil conditions it is possible to use values of derived nominal bearing capacity (which are published in the standard for each soil class). b) For demanding superstructures in simple subsoil conditions or for modest superstructures in complex subsoil conditions limit states calculations are required. The calculations are performed for nominal mechanical parameters of subsoil, which are tabulated for each soil class in the standard. c) For demanding superstructures in complex subsoil conditions limit state calculations are required. However, the calculations are performed for statistically evaluated mechanical properties from performed tests for given subsoil. Simple subsoil conditions were defined as: smooth terrain, subsoil within the site is not changing significantly and the strata are more or less of the same thickness and roughly horizontal. Modest superstructures from foundation engineering point of view are defined as follows: houses up to 5 storeys and other buildings up to 3 storeys, which are not affected by differential settlement of foundation elements up to the range of 20 to 30mm. Ultimate state (limit state of bearing capacity) for homogeneous subsoil and centric loading (Fig. 1) was calculated from the equation: qf = n1(r) B/2 Nr + n2(r) D Nqr + c(r) Ncr

(1)

where values of the design bearing coefficients Nr, Nqr, Ncr are defined for undrained u(r), resp. drained ’(r) values of the angle of internal friction. Note: for u = 0: Nr = 0, Nqr = 1 and Ncr = 5.1. The limit value of bearing capacity was finally compared with the extreme value of contact pressure (for extreme loading).

D

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1. First standard from the 1966

B Figure 1. Sketch of the situation for the basic equation of the bearing capacity

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For design values of shear parameters applies: (r) = (n) · k

(2)

c(r) = c(n) · k

(3)

where k is the standard value of the coefficient of uniformity and (n) and c(n) are recommended table nominal values for the design approach ad b) or evaluated values after statistical analysis for the design approach ad c). For design values of weight density applies: n(r) = n1(n) · n

(4)

where n = 0.9 is a coefficient of loading The last coefficient - coefficient of calculation reliability m - was applied on bearing capacity factors, when m = 0.5 was applied for (r) > 30° and was linearly increasing with lower value of (r) up to m = 1 for (r) = 0. A short note can be made to the selection of coefficient of uniformity k for the angle of internal friction for the design approach ad c). The minimum of tested samples is N = 5. During the statistical analysis of the measured values it is assumed that the basic set of examined values is close to the normal distribution – Gauss-Laplace. Hence the corresponding coefficient of uniformity k is determined from the equation (5): k=1 - 

(5)

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where  is determined from the Fig. 2 for the probability of 0.999, namely with respect to the amount of samples N and variability of the measured values v. Value of  = 0.3 and the corresponding value of coefficient of uniformity k = 0.7 are limiting. If for the given number of measured values N and its variability v the value of  > 0.3 it is necessary to either increase the number of samples N or to divide the measured values more concisely to statistically more homogeneous sets.

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Number of measured values N

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Coefficient of variability v Figure 2. Determination of the coefficient of uniformity k = 1 –  as function of the number of measured values N and coefficient of variability v for probability of 0.999 (according to SN 731001:1966)

For the calculation of the total settlement two equations were recommended, one based on the theory of elasticity and a second one based on the stress-strain method. For both methods the coefficient of calculation reliability m = 1.25 was applied and for the first one as well correction factor m1 for different types of soils (m1 is in the range of 0.5 – 0.8) and for the second method correction factor m2 which is different for normally consolidated soils (m2 = 0.8) and for over-consolidated soils (m2 = 0.5).

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2. Second standard from the 1987 Firstly new soil classification system was applied for this standard. This new system is in principle based on US Bureau of Reclamation System with some modifications, as we have had very good experience with this system from the view of small earth fill dams design. In more details this new system is described in Šimek et al. (1990) and in shorter version in Vaní ek I. and Vaní ek M. (2008). Also a new equation for the total settlement calculation was recommended and which is based on large in situ experiments, e.g. Havlí ek (1978), or Sey ek (1995). Numerous application problems show that in most cases the calculated settlements and deformations are greater than the real measured values (Vaní ek, 1982). This difference is most often attributed to some type of sample failure during the process of sample extraction and/or sample handling before testing. In order to explain the abovementioned difference, extensive laboratory and on-site tests were carried out. Highprecision sensors registering vertical deformations were mounted under modelled reallife spread foundations. The results manifested that only negligible vertical movements were measured in subsoil despite the fact that according to the theory of elastic halfspace there should be stress increase and hence also deformation. The differences in results were also determined for different types of soils. The differences found were

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attributed to the structural strength of soil, i.e. the bond between individual grains, which develops in time for long-term acting initial stress. It is becoming evident that additional bonds arise in soils exposed to long-term action of geostatic stress, which are manifested by the appearance of over-consolidation stress even in normally consolidated soils or by its increase in over-consolidated soils. This fact is attributed to secondary consolidation, or the appearance of additional diagenetic bonds (such as cementation). These bonds, sometimes also referred to as "cold welding“, are of relatively fragile nature, and they may easily be broken even by mere sample unloading to zero external load. Therefore the recommendation regarding settlement calculation will be shown hereinafter. 2.1. Principles for the spread foundation design The approach to the design of shallow foundations is in principle the same as the approach suggested in 1966. There are also 3 design approaches, even so the specification on the complexity of structures is not as detailed, it only specifies that a modest superstructure is not sensitive to differential settlement and has sufficient safety margin within plastic deformation area. Here for the first time the term – design according to the 1st, 2nd or 3rd Geotechnical Category – is used, when: x

For the 1st Geotechnical Category the effects of the supposed service design loading for basic combinations d,s are compared with tabled nominal values of the bearing capacity of ground Rd,t: d,s Rd,t

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x

x

(6)

nd

For the 2 Geotechnical Category the effects of the supposed extreme loading d,e for the most dangerous combination are compared with the design bearing capacity of the ground Rd, which is calculated from tabulated nominal mechanical properties recommended for different types of soils or are based on mechanical properties, which are very well known for a certain region (local standard characteristics). For the 3rd Geotechnical Category the effects of the supposed extreme loading d,e for the most dangerous combination are compared with the design bearing capacity of the ground Rd, which is calculated from standard mechanical properties determined via tests.

In principle the procedure of calculation for 2nd and 3rd Geotechnical Category is the same. d,e Rd

(7)

2.2. Soil classification system and indicative nominal soil characteristics Czech standard SN 73 1001 (1987) distinguishes 5 types of gravel soils (G1 – G5), 5 types of sandy soils (S1 – S5) and 8 types of cohesive soils (F1 – F8), according to the Figures 3 and 4. Selected indicative nominal soil characteristics are presented in Tables 1 and 2, where  is Poisson’s ratio,  unit weight and is the coefficient expressing the ratio between Eoed and Edef , when Eoed = 1/ · Edef.

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Figure 3. Classification of soils with grains smaller than 60 mm (according to SN 731001:1987)

Figure 4. Plasticity chart (according to SN 731001:1987)

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Table 1. Indicative nominal soil characteristics for cohesive soils F1 – F4 (according to SN 731001:1987) Soil type Symbol

MG

CG

MS

CS

Property

Consistency Firm Stiff Hard Sr < 0.8 Sr > 0.8 Sr < 0.8 – Sr > 0.8  = 0.35; = 0.62;  = 19.0 5–10 10–20 12–24 15–30 determined by tests 40 70 70 70–80 0 0 10 12–15 4–12 8–16 16–32 16–24 determined by tests 26–32  = 0.35; = 0.62;  = 19.5 4–8 7–15 10–12 18–25 determined by tests 30 60 60 60–70 0 0 10 12–15 6–14 10–18 18–36 18–26 determined by tests 24–30  = 0.35; = 0.62;  = 18.0 3–6 5–8 8–12 15–15 determined by tests 30 60 60 60–70 0 0 10 12–15 8–16 12–20 20–40 20–28 determined by tests 24–29  = 0.35; = 0.62;  = 18.5 2.5–4 4–6 5–8 8–12 determined by tests 30 50 70 70–80 0 0 5 8–14 10–18 14–22 22–44 22–31 determined by tests 23–27 Soft –

, , [kNm-3] Edef [MPa] cu [kPa] u [°] cef [kPa] ef [°] , ,  [kNm-3] Edef [MPa] cu [kPa] u [°] cef [kPa] ef [°] , ,  [kNm-3] Edef [MPa] cu [kPa] u [°] cef [kPa] ef [°] , ,  [kNm-3] Edef [MPa] cu [kPa] u [°] cef [kPa] ef [°]

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Table 2. Indicative nominal soil characteristics for sandy soils S1 – S5 (according to SN 731001:1987) Soil type Symbol





 [kNm-3]

SW SP S–F SM

0.28 0.28 0.30 0.30

0.78 0.78 0.74 0.74

20 18.5 17.5 18

SC

0.35 0.62

18.5

Edef [MPa]

ef [°]

ID = ID = ID = ID = 0.33–0.67 0.67–1.0 0.33–0.67 0.67–1.0 30–60 50–100 34–39 37–42 15–35 30–50 32–35 34–37 12–19 17–25 28–31 30–33 5–15 28–30 4–12

26–28

Factors to be cef considered when [kPa] determining the values in the range ID, w, % of gravel, particle shape, angularity Amount of fine particles and soil 4–12 consistency 0 0 0 0–10

Table 3. Values of the bearing capacity Rd,t for F soils – valid for foundation depth D = 0.8 – 1.5 m and width B 3m (according to SN 731001:1987) Soil type Symbol MG CG MS CS ML, MI CL, CI MH, MV, ME CH, CV, CE

Soft 110 100 100 80 70 50 50 40

Tabulated design bearing capacity Rd,t [kPa] Consistency Firm Stiff 200 300 175 275 175 275 150 250 150 250 100 200 100 200 80 160

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Hard 500 450 450 400 400 350 350 300

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2.3. Tabulated values of the bearing capacity Rd,t for different types of soils Tabulated design values of the bearing capacity Rd,t, which are used for the design of spread footings falling under the 1st Geotechnical Category, are shown in Tables 3 and 4. Table 4. Values of the bearing capacity Rd,t for S soils – valid for foundation depth D = 1.0 m and for dense sands (S1 – S3) or for consistency stiff to firm for S4 and S5 (according to SN 731001:1987). Soil type Symbol SW SP S-F SM SC

0.5 300 250 225 175 125

Tabulated design bearing capacity Rd,t [kPa] Width of foundation B [m] 1 3 500 800 350 600 275 400 225 300 175 225

6 600 500 325 250 175

2.4. Determination of the design bearing capacity Rd The following general equation is used for the design bearing capacity Rd determination for foundations with horizontal footing bottom, for both undrained and drained conditions:

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Rd = cd Nc sc dc ic + 1 d Nd sd dd id + 2 b/2 Nb sb db ib

(8)

where: 1 and 2 – effective unit weight above or below footing bottom [kNm-3]. Note: For drained conditions the ground water level should be taken into consideration b – effective width or diameter of foundation [m] Nc, Nd, Nb – bearing capacity coefficients [-] d – foundation depth [m] cd – design value of cohesion [kPa], sc, sb, sd – shape factor [-] dc, db, dd – depth factor [-] ic, ib, id – load inclination factor [-] The bearing capacity coefficients are determined from following equations: valid for d > 0 Nc = (Nd – 1) / tan d valid for d = 0 Nc = 2 +

Nd = tan2 (45° + d / 2). exp ( tan d) Nb = 1.5 (Nd – 1) tan d

(9)

where d is the design value of the angle of the internal friction. The shape factors are calculated from the following equations: sc = 1 + 0.2 b/l sd = 1 + b/l sin d sb = 1 - 0.3 b/l

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(10)

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where b and l are the dimensions of a rectangular footing. For square or circular footing b = l. Depth factors are calculated from the following equations: dc = 1+0.1 (d/b) dd = 1+0.1 (d/b · sin 2d) db = 1

(11)

where b is the width or diameter of the footing. Inclination factors are calculated from the following equations: ic = id = ib = (1 – tan )2

(12)

where  is the angle of inclination of the forces resultant from vertical. Note: For this case also resistance in footing bottom should be taken into account. For  > 30° an individual approach is needed. Note: For eccentric loading an effective footing area Aef = bef · lef is applied for the design bearing capacity as well as for the shape and depth factors. Design values of the angle of internal friction d and cohesion cd are determined from the nominal values or local values (for 2nd GC) or from recommended values after measured statistical data evaluation (for 3rd GC) divided by the material partial factor for subsoil m . d =  / m,

cd = c / m,c

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Material partial factor for  is m, = 1.5 m, =  / ( – 4) Material partial factor for c is m,c = 2

valid for  12° valid for  > 12°

(13) or

2.5. Determination of the serviceability limit state – limit state of deformation The serviceability limit state calculations of deformation are used to prove that service design loading of subsoil would not exceed allowable deformation of subsoil. Hence, the superstructure settlement, either uniform or differential, would not cause inadmissible superstructure deformation or such change of superstructure location that would cause significant difficulty of the superstructure ordinary usage. For the 1st geotechnical category the serviceability limit state is not assessed. For the 2nd geotechnical category the settlement analysis is performed using the tabled nominal values of subsoil properties (see e.g. Tables 1 and 2). If available, local nominal values should be used instead. For the 3rd geotechnical category the settlement analysis is performed using nominal values of deformation characteristics determined during ground investigation. The equation for the total settlement analysis fall in the “stress-strain” method category, it assumes 1D deformation along with structural strength:

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s

n

V z ,i  mi ˜ V or ,i

i 1

Eoed ,i

¦

˜ hi

237

(14)

where: s – total settlement n – total number of layers z,i – vertical component of stress (surcharge) in the middle of layer i caused by the bearing pressure overload at foundation level ol mi – corrective coefficient of surcharge, which is for layer i determined based on soil type from Tab. 5. and represents the influence of structural strength or,i – original vertical geostatic stress in the middle of layer i hi – thickness of layer i Eoed,i – design oedometric modulus of subsoil layer i Table 5. Values of corrective coefficient of surcharge m (according to SN 731001:1987)

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Type of subsoil Highly compressible fine-grained soils with deformation modulus Edef < 4 MPa normally consolidated soft or firm consistency (all 3 conditions must be fulfilled) Embankments and other bulk soils, subsoils subsequently surcharged and up to now unconsolidated Rocks within classes R1, R2; sound Mesozoic and Cainozoic sedimental rocks within classes R4, R5 Fine-grained soils within F classes, whereby does not belong other coefficient m Sands and gravels within types SW, SP, GW, GP under the groundwater level Rocks within class R3 Sands and gravels within types SW, SP, GW, GP above the groundwater level Sands and gravels within types S-F, SM, SC, G-F, GM, GC Rocks within classes R4, R5 – except sound Mesozoic and Cainozoic sedimental rocks Rocks within class R6 (eluvia) Loess and loess loams above groundwater level, if it is possible to avoid their water saturation

m

0.1

0.2

0.3 0.4 0.5

In the above mentioned calculation model the vertical surcharge z is reduced for each layer just to its effective component (z – m·or), which contributes to the deformation. Note: SN 731001:1987 takes great care of the determination of the vertical surcharge component z. Therefore it allows determining of this component under selected point of flexible or rigid foundation. Reducing the vertical surcharge just to its effective component the settlement analysis is limited only to the real deformation zone. Deformation zone under the foundation is limited area within which indispensable deformations are generated from superstructure surcharge (see Fig 5). The Czech standard SN 731001:1987 also defines limiting values for settlement, that is, both for final total average settlement (60 – 200 mm) and relative differential settlement (0.0015 – 0.006).

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ex isting Gr ound l ev el pr oposed

F oundation l ev el

Vol

h1

h2 e.g.

Ground water lev el

m =0,3 m =0,1

Vor

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m·Vor

Vz

Deformation zone depth zz

Figure 5. Calculation model for the determination of total settlement (effective surcharge is hatched). According to SN 731001:1987

3. Conclusion The article summarises the approaches used in the Czech Republic for the design of shallow foundations according to limit states in the period of last 45 years. It is obvious that the focus is on partial safety factors for material (m), because from the limit states point of view the probability approach to the subsoil properties is preferred. This partial

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239

safety factor is however applied directly on the angle of internal friction and not on the tan as it is now suggested in Eurocode 7. Thus, this approach allows direct use for shape and depth coefficients calculations for the limit bearing capacity. The described approach is therefore most similar to the Design Approach 3 (DA3) in current Eurocode 7. The most meaningful way forward would hence be to propose to used further the DA3, however in the newest proposal of National annex (yet not approved) it is proposed to follow Design Approach 1. DA1 allows the use of not only the already used principle, but also allows to design the foundation structure itself in compatible way with structural Eurocodes. The calculation model suggested for the bearing capacity of shallow foundations is closest to the model proposed by B. Hansen (1970) with the modification to simplify the calculation namely for inclination factors. The calculation model proposed in SN 731001:1987 for the settlement analyses is based on actual in-situ measurements and correspondence between analysis and follow up monitoring and is much better compared to those valid in between 1966 and 1987. The current version of described standard SN 731001:1987 was officially cancelled in 2010 when Eurocode 7 was fully implemented, however the calculation models described here are still applicable in accordance to EN SN 1997-1 (Eurocode 7). Even thought the original idea was to guarantee the design safety with probability of about 10-4 up to now experience shows that this safety (probability of failure) is rather in the range of 10-6. Since 1987 only 2 foundation failures are known to the authors even if during this period about 1-2 million of spread foundations were constructed. Discussion to the level of this indemnity is therefore possible, especially if we know that probability of failure of other geotechnical structures is significantly higher (e.g. for earth fill dams the probability of failure is 1:100).

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References SN 73 1001 (1966). Foundation of structures. Subsoil under shallow foundations, (In Czech – Základová pda pod plošnými základy), ÚNM Praha, 64 p. SN 73 1001 (1987). Foundation of structures. Subsoil under shallow foundations. (In Czech). ÚNM Praha, 75 p. SN EN 1997-1 (2006). Eurocode 7: Geotechnical design – Part 1: General rules. (In Czech). NI Praha, 138 p. Hansen, B. (1970). Bearing capacity, Danish Geot. Inst., Bull. No 28. Havlí ek, J. (1978). Foundation settlement. (In Czech). Final Report of the Research Project C 52-347-018, SG Praha. Sey ek, J. (1995). Calculation of 2nd Limit State of Shallow Foundations. (In Czech), PhD thesis, Czech Technical University in Prague. Šimek, J., Jesenák, J., Eichler, J. and Vaní ek, I. (1990). Soil Mechanics. (In Czech). SNTL Praha, 388 p. Vaní ek, I. (1982). Soil Mechanics. (In Czech). Publishing company of the Czech Technical University in Prague, 331 p. Vaní ek, I. and Vaní ek, M. (2008). Earth Structures in Transport, Water and Environmental Engineering. Springer. 637 p.

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Code Development

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AASHTO Geotechnical Design Specification Development in the USA Tony M. ALLEN,1 Washington State Department of Transportation, USA

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Abstract. A complete, formal geotechnical design code of practice addressing all aspects of geotechnical engineering really does not exist in the USA at the national level. However, a geotechnical design code has been developed at the national level in response to the needs of the structural engineers as part of the American Association of Highway and Transportation Officials (AASHTO) specifications, primarily focusing on structure foundations, buried structures, and retaining walls. Since 1994, AASHTO began migrating from Allowable Stress Design (ASD) to Load and Resistance Factor Design (LRFD), the USA equivalent to Limit States Design (LSD). AASHTO fully adopted LRFD, at least in the transportation Sector, in 2007, and ceased updating their Allowable Stress Design and Load Factor Design specifications in 2002. A key issue for the USA geotechnical community regarding geotechnical design code has been to strike a balance between prescriptive minimum design requirements and levels of safety (i.e., load and resistance factors) and the flexibility needed by geotechnical engineers to apply engineering judgment to address site specific issues and local experience. Summarized is the historical development of geotechnical foundation design code in the USA for transportation applications. With regard to the geotechnical portions of the current AASHTO LRFD Bridge Design Specifications, the development and selection of load and resistance factors is discussed. Key considerations for geotechnical design specification development are identified. Finally, gaps and future development needs for USA geotechnical design codes of practice are presented. Keywords. foundation design, limit states, LRFD, resistance factors, calibration.

Introduction A complete, formal geotechnical design code of practice addressing all aspects of geotechnical engineering really does not exist in the USA at the national level. However, a geotechnical design code has been developed at the national level in response to the needs of the structural engineering community as part of the American Association of Highway and Transportation Officials (AASHTO) specifications, primarily focusing on structure foundations, buried structures, and retaining walls in transportation applications. While other national design codes contain limited geotechnical specification guidance (e.g., the International Building Code – IBC), the AASHTO LRFD design specifications, which are focused on the transportation sector, contain the most complete geotechnical design specifications and are the most widely 1

State Geotechnical Engineer, Washington State Department of Transportation, P.O. Box 47365, Olympia, WA, 98504-7365, USA; E-mail: [email protected] Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

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used. AASHTO began migrating in 1994 from Allowable Stress Design (ASD) to Load and Resistance Factor Design (LRFD), using the Ontario bridge Limit States Design (LSD) code, which was first developed in 1979, as a starting point. The LRFD approach fits within the broader framework of LSD. The foundations portion of the AASHTO LRFD Bridge Design Specifications was completely rewritten and published in 2005 through a task force of Federal Highway Administration, State Transportation Department, and consultant experts. AASHTO fully adopted LRFD in 2007, and ceased updating their Allowable Stress Design and Load Factor Design specifications in 2002. State transportation agency specific geotechnical design codes are also becoming available. These agency specific design codes are developed to provide state agency specific implementation of the AASHTO LRFD specifications, to address areas of geotechnical practice not covered in the AASHTO specifications, and to define geotechnical practice for use in contracting methods such as design-build. Examples of such state transportation geotechnical manuals that augment the AASHTO specifications include the Washington State Department of Transportation (DOT) Geotechnical Design Manual (WSDOT 2011), the Florida DOT Soils and Foundations Handbook (FDOT 2012), and the KDOT Geotechnical Manual (KDOT 2007). A complete listing of state DOT geotechnical design manuals is provided by FHWA (2007). A key issue for the USA geotechnical community regarding geotechnical design code has been to strike a balance between prescriptive minimum design requirements and levels of safety (i.e., load and resistance factors) and the flexibility needed by geotechnical engineers to apply engineering judgment to address site specific issues (Goble 1999). Another key issue is whether or not to maintain levels of safety used in past successful practice versus the level of safety that theoretically should be used based on reliability theory analysis. Finally, past geotechnical design practice has not clearly separated the geotechnical limit states (e.g., service and strength) in a way that is compatible with the categories of limit states used by the structural engineering community. Moving from ASD to LRFD requires these limit states to be separated so that the level of safety used in the design is properly matched with the limit state under consideration. This paper summarizes the development of geotechnical foundation design code in the USA, focusing on transportation applications. With regard to the geotechnical portions of the current AASHTO LRFD Bridge Design Specifications, the development and selection of load and resistance factors is discussed, as well as how past ASD geotechnical design procedures were adapted to LSD. Finally, gaps and future development needs for USA geotechnical foundation design codes of practice are presented.

1. Overview of AASHTO Design Code Development in the USA The AASHTO specifications are intended to be a comprehensive design code for the design of bridges, walls, underground structures, and other transportation sector structures. The primary focus of the committee and the design code it produces is structural design, and most of the committee members are structural engineers. The design specifications are organized to be most efficient for the structural design of bridges. However, geotechnical design specifications are included for foundations,

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walls, and underground structures, primarily in chapters 10 (foundations) and 11 (abutments and walls). Portions of Chapter 3 (loads and load factors) and Chapter 12 (buried structures and tunnel liners) also include geotechnical design provisions, both for static and seismic loads. Beginning in 1997, geotechnical engineers from the state departments of transportation were added to the committee as members, primarily on the technical committee that specifically focuses on development of the foundation and wall design chapters (i.e., chapters 10 and 11, and part of Chapter 3) of the AASHTO LRFD Bridge Design Specifications. For those state transportation departments that do not have geotechnical engineers specifically appointed to the committee, the state’s structural engineering representative on the committee is expected to get input from their respective geotechnical departments to help review the specifications and recommend voting decisions when changes to the geotechnical portions of the specifications are proposed. New design specifications, and any changes made to existing specifications, are developed by or through the technical committee responsible for the subject area (in the case of foundations and walls, the T-15 Technical Committee is the one responsible for this subject area) and then submitted by that technical committee to the full Bridge and Structures Subcommittee. Note that a two-thirds majority of the voting members (one vote per state) of the full Subcommittee is required to approve changes to the design specifications. For additional information regarding the subcommittee, its structure, and its activities, see the website for the AASHTO Bridge and Structures Subcommittee (AASHTO 2012b). The AASHTO LRFD specifications (AASHTO 2012a) include mandatory design code in the left column of each page and commentary in the right column of each page. The AASHTO design specification provisions (referred to as “articles”) and associated commentary are typically developed from what is considered widely accepted design practice. For example, geotechnical design methodologies found in national design manuals (e.g., FHWA manuals), textbooks, and peer reviewed journal publications and research reports are typically used as the basis of the provisions included in the AASHTO specifications. In some cases, research specifically targeted at development of the AASHTO LRFD specifications is used to develop the design specifications, subject to review and revision conducted by the responsible AASHTO Bridge and Structures technical committee, in this case T-15, and the subcommittee as a whole. The technical committee will also typically obtain input from a wide range of private sector organizations that would have an interest in the design specifications being considered, as well as academia, before finalizing the specification changes to be sent on to the full subcommittee for final review and voting. The AASHTO design specifications are intended to represent what the state departments of transportation engineering leadership consider to be the standard of practice. However, due to the political structure of the USA, being made up of individual states, each state can decide how it will implement the AASHTO design specifications in their state. That adoption is usually addressed through state bridge and/or geotechnical design manuals or design policy memorandums that explain and augment how the AASHTO design specifications will be applied for transportation projects in their respective states. State geotechnical design manuals and other documents may also include design requirements for issues not specifically addressed in the AASHTO manual. Therefore, it is the combination of the AASHTO LRFD Bridge design specifications with the bridge and geotechnical design manuals or policy memorandums in each state transportation department that define the standard of

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practice for the transportation sector. Note that this description is not intended to be a legal definition of “standard of practice,” but is simply a general description of what is typical of state transportation department engineering practice. State transportation departments may also directly use national manuals produced, for example, by the Federal Highway Administration (FHWA) to augment the AASHTO LRFD Bridge Design Specifications. Detailed geotechnical design specification development has been slower than the development of the structural design specifications. Geotechnical engineers in the USA have been reluctant to develop codes to govern their design practice due to fear of being too prescriptive and inflexible to apply engineering judgment to adapt the design practices available to site-specific conditions (Goble 1999; DiMaggio, et al., 1999). This reluctance is especially strong with regard to the selection of the level of safety to use (i.e., the factor of safety, or load and resistance factors), as well as how to apply ASD geotechnical design procedures to LSD based design (Goble 1999; Christian 2003). Furthermore, national design codes may not be able to accommodate the design practices successfully used locally. Practicing geotechnical professionals typically rely heavily upon past successful practices. These past practices have defined the levels of safety needed to have a successful design. Furthermore, these past ASD practices tended to combine multiple limit states into one calculation. LSD based design codes require a clear separation between the various limit states so that the level of safety used can be more accurately targeted to the consequences of failure and the likelihood a given load combination will occur. Because of these issues, geotechnical engineers have been slow to accept and use LSD based design codes such as the AASHTO LRFD Bridge Design Specifications, though at this point, LSD based design has become more widely accepted and used.

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2. Design Approach Used to Achieve Desired Level of Safety in the AASHTO LRFD Bridge Design Specifications The AASHTO specifications use load and resistance factors (i.e., LRFD) to account and design for the various sources of variability in the applied loads and the resistance to those loads available when designing structures such as bridges and walls. The general approach used to address the level of safety needed and how the North American (e.g., USA) approach differs from the European approach is illustrated in Figure 1. In the LRFD approach, individual loads within a given load group are increased using a load factor to account for the uncertainty in each load. Then the total resistance available to resist the applied loads is reduced using a resistance factor to account for uncertainty in the resistance available. Figure 1 also illustrates the difference between the LRFD and ASD approaches. Eq. (1) illustrates the North American LSD approach.

¦ Q i

ni

d I Rn

(1)

where, Ji is a load factor applicable to a specific load type Qni; the summation of JiQni terms is the total factored load for the load group applicable to the limit state being considered; I is the resistance factor; and Rn is the nominal unfactored resistance available (either ultimate or the resistance available at a given deformation).

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C/fc, Isfc

C, Is (a)

Design Model

Rd Qd

247

Q Q x Jf

European LSD approach (Design Models 1 and 3)

(b)

North American LSD approach

Rn Design Model

Rn/FS Safety Factor, FS

C, Is (c)

Q

>

North American ASD approach

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Figure 1. Approaches to address level of safety needs in design.

For geotechnical design, three categories of limit states are typically considered. These limit state categories include service, strength, and extreme event. Of these, there are several subcategories of limit states that affect which specific set of loads (i.e., load groups) are considered. For geotechnical design, the primary subcategories within the AASHTO design specifications include Service I, Strength I (most common for geotechnical design) and IV (used for long span bridges where dead load dominates), and Extreme Event I (seismic) and II (vessel or vehicle collision and scour). The details of these load groups for these limit states are provided in AASHTO (2012a), specifically Article 3.4.1, and especially tables 1 and 2 in that article. Properly combining these groups of loads for design purposes can be complicated, as some loads require the use of either a maximum or minimum value. The selection of the maximum or minimum value depends on whether the load is contributing to the instability of the element or feature being designed (in this case the maximum load factor is used) or contributing to the stability of the element or feature being designed (in this case the minimum load factor is used). The principle is to select combinations of maximum and minimum load factors to produce the most extreme factored force effect. Many of the geotechnical load factors provided in the AASHTO specifications have both maximum and minimum values. For examples of how maximum and minimum load factors have been combined for specific geotechnical design situations, see WSDOT (2011) and Berg, et al. (2009). As illustrated in Figure 1 and Eq. 1, each load typically has its own load factor associated with it to address the uncertainty in each load. For application of load factors, forces are not broken down into vertical and horizontal components to apply maximum and minimum load factors to the components of the single load that contribute to instability or stability of the element, respectively – only a single load factor is applied to the single resultant force for each source of load. For resistance, a

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single resistance factor is typically applied to the available resistance to address uncertainty, though there are cases where different resistance factors are applied to different components of the resistance. An example of this is drilled shaft design, in which the side resistance has a different resistance factor from the base resistance. Phoon, et al. (2003) discuss the various approaches to applying resistance factors and the advantages and disadvantages of each approach. It is the combination of load and resistance factors that determines the level of safety in the design. For LRFD, the level of safety is captured through a reliability index, E, which can also be represented by a probability of failure, Pf. For a given category of limit states (e.g., the strength limit state), the target reliability index, EW, used to establish the load and resistance factor combination is consistent for all limit states within that category. The various categories of limit states (e.g., service, strength, extreme event) represent differences in both the consequences of failure and differences in the probability that a given loading will occur within the specified design life of the structure. For example, the strength limit states consider loads that have a high probability of occurring (e.g., static loads due to structure weight) and a failure consequence that is high due to the potential for collapse, since strength limit state design is focused on the ultimate strength of the component or supporting soil. The consequences of a service limit state failure (e.g., excessive deformation, but no collapse and subsequent loss of life) may be less than the consequences of a strength or extreme event limit state occurrence. However, for extreme events, the consequences of failure are high and similar to those associated with the strength limit state, yet the load combination (e.g., combinations that include earthquakes) may have a very low probability of occurrence in comparison to the strength limit state load combination. Because of the low probability of occurrence of the load combination, more severe consequences of failure and a less stringent failure criterion can be acceptable for extreme event limit states. The AASHTO Bridge Subcommittee has determined that the strength limit states should target a E value of 3.5 (approximately 1 in 5,000 probability of failure), not considering redundancy. The level of safety in the foundation units supporting the bridge piers or other structures must be at that level. However, foundation units may contain multiple foundation elements that provide some redundancy in the foundation. The foundation elements (e.g., an individual pile or shaft in multiple pile or shaft foundation units) do not necessarily need to be designed to the 1 in 5,000 probability of failure, since it is the level of safety in the foundation unit as a whole that is most important to be consistent with the level of safety in the structure the foundation unit supports, assuming that the load in the foundation elements has the ability to redistribute should one of the elements not perform as expected. The AASHTO LRFD Bridge Design Specifications (specifically AASHTO 2012a – Article C10.5.5.2.1) allow individual elements within a foundation unit to be designed for a higher probability of failure than the 1 in 5,000 the structure must meet for the strength limit state. For service and extreme event limit states, the target level of safety to use is under development. Currently, load and resistance factors for service and extreme event limit states are near 1.0 to reflect differences in failure consequences or probability of occurrence of the load combination relative to the strength limit state. Additional information on the selection of a EW for various limit states is provided in Allen, et al. (2005). Additional perspectives on this issue are also provided by Phoon, et al. (2003). Recommendations on the effect of failure consequences on the

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selection of the target reliability level are also provided by ISO (1998) and Santamarina, et al. (1992). Reliability levels needed for various types of limit states are also discussed by Meyerhof (1994). In general, there appears to be agreement that EW for service and extreme event limit states should be lower (i.e., higher Pf) that what is used for the strength limit state, but how much lower is yet to be determined. Allowance of a higher Pf (lower EW) for service and extreme event limit states will result in load and resistance factors that are closer to 1.0 than is the case for the strength limit state.

3. Historical Development of Geotechnical LRFD Foundation Design With regard to the AASHTO specifications, a fairly complete history of the development of geotechnical load and resistance factors for foundation design up through 2005 is provided in Allen (2005). Key points from that historical development summary are provided herein. Geotechnical LRFD, or Limit States Design, was developed in the USA with consideration to three main issues: 1) the separation of geotechnical design procedures into clearly defined limit states, 2) definition of what is a load and what is a resistance, especially when dealing with geotechnical elements contained within a continuum and soil-structure interaction problems, and 3) the establishment of load and resistance factors to meet a level of safety that is consistent with the rest of the AASHTO LRFD Bridge Design Specifications yet consistent with past design practice. Not all of these issues have been completely resolved, but sufficient progress regarding each of these has been made to develop a useable design code.

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3.1. Definition of Geotechnical Limit States The combination of more than one limit state into a single design procedure is fairly common in US geotechnical engineering practice. For example, Peck, et al. (1974) provide spread footing design charts that are partially based on the limit to prevent shear failure of the soil in bearing and partially on excessive settlement. Similarly, presumptive footing bearing capacities for various common soil or rock conditions are typically based on settlement limited maximum values. Because of this past practice, the typical geotechnical engineer had little experience with bearing resistance values greater than these settlement limited values. Though well accepted bearing capacity theory such as described in Munfakh, et al. (2001) could be used to calculate much higher bearing resistance values that are representative of ultimate conditions, geotechnical engineers rarely took advantage of higher bearing values. It is important to keep in view the definition of each limit state when attempting to address this issue. For example, for the strength and extreme events limit states, definition of the limit state is typically exceedance of the maximum resistance available by the applied loads (ISO 1998). Exceedance of this limit state usually results in collapse of the considered structure or structure components, or at least large uncontrolled and unpredictable deformation which contributes to the collapse of the structure. For the service limit state, definition of the limit state is exceedance of a defined acceptable deformation to insure functionality of the considered structure or structure component. Exceedance of this limit state usually does not result in collapse

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of the structure but may require eventual repair or replacement of the considered structure due to reduced life or functionality (ISO 1998). Considering these limit state definitions, past design practices must be refitted to accommodate the separation of the limit states contained within LSD based design procedures. For example, in past ASD practice, for very dense foundation soil, the allowable bearing resistance would be typically limited to 500 to 600 kPa. However, bearing capacity theory, which is used to estimate the bearing resistance at shear failure of the foundation soil, a calculation applicable to the strength limit state, could result in a maximum bearing resistance value of 2,500 to 5,000 kPa. Even using typical LRFD resistance factors for bearing resistance at the strength limit state (i.e., 0.50 as specified in AASHTO 2012a, Article 10.5.5.2.2), the strength limit state bearing resistance allowed for the strength limit state is much higher than previous geotechnical experience would allow. To provide the needed separation, settlement limited bearing resistance design methods have been included in the service limit state articles of the specifications, and ultimate bearing capacity methods such as described in Munfakh, et al. (2001) have been included in the strength limit state articles, as the load and resistance factor combination for the strength limit state would result in excessively conservative designs if applied to settlement limited bearing resistance design methods. A related issue with regard to the blurring of the limit states in geotechnical design is how ultimate values are defined. For the strength limit state, failure is defined by the ultimate resistance, which typically results in shearing of the soil whereas for the service limit state, failure is defined by a maximum allowed deformation (ISO 1998). However, in a number of cases, the ultimate geotechnical resistance of a foundation element is defined by a deformation criterion. In such cases, is the ultimate geotechnical resistance really a deformation limited resistance and therefore appropriate for a service limit state design and not a strength limit state design? For example, for pile foundations, ultimate bearing resistance of a pile is often defined using a criterion such as that proposed by Davisson, as shown in Figure 2. In the figure, Qf is the failure load, F is the total pile settlement at failure, Lp is the pile length, A is the pile cross-sectional area, and E is the pile modulus. The current AASHTO LRFD specifications specifically refer to this method (AASHTO 2012a). For a 300 mm diameter pile, this criterion would define ultimate bearing resistance as the resistance at approximately 33 mm of vertical displacement for a typical bearing resistance for a pile of this diameter. Yet for service limit state design, the resistance allowed would typically be defined at a vertical displacement of 25 mm. Therefore, in this example, the strength limit state ultimate bearing resistance would occur at almost the same displacement as the service limit state resistance. It can be observed from Figure 2 that the deformation based failure criterion does not capture the true ultimate bearing resistance of the pile, in that there is significant reserve capacity beyond the bearing value defined as failure (i.e., Qf). However, current design practice assumes that this value is an ultimate resistance, and any additional resistance available beyond this point is assumed to not be reliable or useful. A similar problem occurs with the design of drilled shafts for bearing resistance. Ultimate end bearing resistance for drilled shafts is typically defined as the resistance at a deformation of 5 percent of the shaft diameter (Brown, et al., 2010). However, drilled shaft bearing resistance is complicated by the fact that side resistance reaches its ultimate value at a much smaller deformation (e.g., approximately 0.5 percent of the shaft diameter). These deformation based ultimate bearing resistance definitions

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0.0

PILE SETTLEMENT, MM

5.0

ELASTIC COMPRESSION OF PILE QL p



10.0 15.0 20.0

AE Qf

X

F FAILURE CRITERION (X = 3.8 + B/36,600 B = Pile Dia., MM)

25.0 30.0 35.0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 APPLIED LOAD, Q, KN

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Figure 2. Davisson criteria for pile foundation load test interpretation (adapted from Davisson 1972).

complicate the determination of ultimate shaft bearing resistance for the strength and extreme event limit states. For deep foundations, full scale load tests are the most common way of obtaining measured ultimate bearing resistance values. While a plunging failure, which comes closest to a true ultimate bearing resistance, can occur, more commonly the load test is considered to have reached its ultimate value once a predefined deformation limit has been exceeded, such as shown in Figure 2, as the foundation resistance will continue to increase as the deformation increases, though at a decreasing rate. It has been decided by the AASHTO specification writers to continue with these deformation based definitions of ultimate foundation bearing resistance to be consistent with past design practice and to keep the ultimate resistance practical to achieve and determine. Furthermore, the foundation load test results used in the calibration of resistance factors have used these deformation based definitions of ultimate resistance. Therefore, the strength limit state resistance factors have been derived using deformation based definitions of ultimate resistance.

3.2. Separation of Loads from Resistance in Geotechnical LSD For some aspects of geotechnical design, it is not always clear how to separate and separately factor the applied loads and available resistance (Goble 1999), or to separate destabilizing forces from restoring forces when considering when to use maximum versus minimum load factors. DiMaggio, et al. (1999) found that this issue has

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affected the development of LSD in Europe as well as in the USA, and that the solution to this problem is neither simple nor forthcoming. Handling slope stability analysis in LSD is one of the most problematic examples of this. Furthermore, most slope stability programs in use in the USA are designed to conduct the analysis in a way that produces a slope stability safety factor. The AASHTO specifications have accommodated this problem by having slope stability analyses conducted within the service limit state, even though in concept, slope stability analysis and design are really strength limit or extreme event limit state activities. The reason this has been done is that for the service limit state, at least currently, all load factors applicable in the slope stability analysis situation are 1.0. This eliminates the need for maximum and minimum load factors and the need to differentiate destabilizing forces from restoring forces. Furthermore, for slope stability design, a resistance factor significantly less than 1.0 is used to provide the level of safety needed, and the inverse of the safety factor produced by the slope stability analysis program is equated to the target maximum resistance factor needed. Essentially, this is a “work-around” until a better approach to address this issue in the context of LSD is developed. Monte Carlo simulation can be applied to slope stability analysis, which can account for variability in the input parameters. The Monte Carlo technique does not specifically account for any model uncertainties, though it is likely that model uncertainties will be fairly small for typical slope stability situations. The exception to this is slopes (or walls) with reinforcement elements, as limit equilibrium based methods may poorly model such situations (Rowe and Ho 1993; Allen and Bathurst 2002). The Monte Carlo approach could be used to more directly evaluate the reliability of a slope stability design (WSDOT 2011), at least without reinforcement elements, though not in the format currently used in AASHTO’s version of LSD. Soil-structure interaction problems can also be problematic with regard to their application to LSD. In such cases, the soil loads and stiffness affect the structure loads, making it difficult to decide how to factor the applied loads and available resistance to produce a safe result. Lateral loading and analysis of deep foundations is an example of this. The geotechnical portion of lateral load analysis includes the determination of the soil springs used in the structural modeling. Soft soil springs allow more deformation in the structure, whereas stiff soil springs attract more load into the structure. Either case can produce the critical design case, depending on the limit state being considered and the structure details. This has hindered the development of a soil strength limit state for lateral loading of foundation elements, an issue that is currently under discussion. For structural design of the foundations and the structure the foundations support, the distribution of loads between the foundations and above ground structure is assessed by not factoring the loads applied to the foundations (AASHTO 2012a; WSDOT 2011). Once the load distribution is determined, then the loads applied to each structural element are factored and equated to the factored resistance in each structural element (see WSDOT 2011, specifically Section 8.6.1).

3.3. Establishment of Load and Resistance Factors for Geotechnical Design Early development work to determine load the resistance factors for geotechnical design heavily relied upon a technique known as calibration by fitting to ASD. Essentially, this technique provides a way to determine load and resistance factors that will produce the same level of safety as has been used in ASD past practice.

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Calibration by fitting to ASD conducted for the case where two load sources are considered uses the following equation:

I





J DL DL LL  J LL

DL LL  1 FS

(2)

where, I the resistance factor, JDL is the load factor for the dead load, JLL is the load factor for the live load, DL/LL is the dead load to live load ratio, and FS is the allowable stress design factor of safety. As can be seen from this equation, there is no consideration of the statistical parameters associated with the loads and the resistance, and therefore no consideration of the margin of safety inherent in the FS. Note that this equation simply provides a way to obtain an average value for the load factor considering the use of two different load factors from two different sources, and considering the relative magnitudes of each load. In the most basic terms, the ASD FS is simply the average load factor divided by the resistance factor. There is no consideration of the actual bias or variability of the load or resistance prediction methods when “calibration” by fitting to ASD is used, nor is there any consideration to the probability of failure, Pf. All that is being done here is to calculate the magnitude of a resistance factor, for a given set of load factors, that when combined with the load factors, provides the same magnitude of FS as is currently used for ASD. The key benefit of this technique is that it is useful for providing benchmark load and resistance factors that are representative of past design practice. Problems with this technique include the following: x x Copyright © 2012. IOS Press, Incorporated. All rights reserved.

x

Past practice may vary widely across the USA (i.e., when establishing national specifications, which past practice should be used to establish load and resistance factors?), The actual level of safety remains unknown and is not likely to be consistent for the various aspects of design, and Perception may have a role in defining the level of safety implied by successful past practice. Factors affecting this perception include the potential for built-in conservatisms in how the design procedures are applied that are not captured by the ASD safety factor used (e.g., some practices may base “ultimate” values using severely limited deformations), and use of design procedures that have a bias toward producing excessively conservative predictions.

The preferred approach is to use reliability theory to establish load and resistance factors if adequate data are available to establish statistical input parameters. Through reliability theory calibrations, load and resistance factors can be established that provide a consistent level of safety. The general process used to perform calibration using reliability theory is to: x

Gather the data needed to statistically characterize the key load and resistance random variables, developing parameters such as the mean, COV, and distribution type (e.g., normal, lognormal),

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x x

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x

Estimate the reliability inherent in current design methods using statistical data gathered that are characteristic of the variability and bias in the design methods and input parameters used, Select a target reliability based on the margin of safety implied in designs used in previous practice, considering the need for consistency with the reliability used in the development of the rest of the AASHTO LRFD specifications, and considering levels of reliability for geotechnical design as reported in the literature, and Determine load and resistance factors consistent with the selected target reliability.

Two basic calibration approaches have been used to develop the load and resistance factors for the geotechnical portions of the AASHTO specifications. The calibrations conducted by Barker, et al. (1991) are an example of one approach, in which they developed statistics for key input parameters such soil friction angle, soil unit weight, and other parameters, attempting to characterize inherent spatial variability, systematic error, and design model error. Design model error is usually obtained from measurement of the performance of full scale structures, or possibly bench scale laboratory model data, and represents the ability of the design model to make accurate predictions of load or resistance (i.e., how well does theory match reality?). However, it is not usually straight-forward to separate the other sources of error from the model error, as the model error may also contain error from spatial and systematic sources (Phoon 2005). The calibrations conducted by Paikowsky, et al. (2004) are an example of the other approach, in which these three sources of error are considered to be contained with the statistics used. Allen, et al (2005), Allen (2005), and Phoon (2005) provide additional details regarding these two approaches and how they are carried out, and examples that illustrate these two approaches and the pitfalls that can occur, as well as the application of the calibration results to the determination of the load and resistance factors provided in the AASHTO LRFD specifications. Load factors were established through the original calibration work done for the overall LRFD bridge design specifications (Nowak 1999; Kulicki, et al. 2007). They were in general not modified for adoption to geotechnical design; instead, the calibration effort focused on modifying the resistance factors needed to meet overall level of safety requirements (Allen 2005). Barker, et al. (1991) also investigated the probability of failure, Pf, implied by the safety factors used in past design practice, with consideration to the statistical data gathered. They discovered that the Pf was higher for foundation systems with many elements (e.g., pile foundations) than for systems with fewer elements, such as shaft and footing foundations. This was considered when establishing the target reliability index, EW, to use for the various foundation types to determine the resistance factors needed (Isenhower and Long 1997; Allen 2005; Allen, et al. 2005; AASHTO 2012a). Allen (2005) summarized the historical progression of resistance factor development for footings, drilled shafts, and driven piles, considering both calibration by fitting to ASD and reliability theory calibrations. Initially, the available data suitable for conducting reliability theory calibrations were rather limited. Since those initial calibrations, additional database development and calibrations were conducted for some foundation types and design methods. Also note that initial LRFD calibrations conducted by Barker, et al. (1991) used load factors from an older

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AASHTO design code. Allen (2005) updated those calibrations using the newer LRFD load factors (described in the table as “current practice”). A portion of the resistance factor development for drilled shafts as reported by Allen (2005) is summarized in Table 1. The load factors used in the initial calibrations as well as the calibrations used to determine the resistance factors currently provided in the AASHTO specifications are summarized in Table 2. See Allen (2005) for additional calibration result summaries for various foundation types. While reliability theory calibrations have the potential to produce more accurate and consistent results, the final resistance factors selected in the AASHTO LRFD specifications for the various foundation types and limit states did not necessarily fully rely on the reliability theory calibration results. In general, estimation of geotechnical resistance, and loads, can involve considerable engineering judgment, and this judgment is difficult to quantify statistically. Furthermore, the available data upon which the needed input statistics were based were limited in terms of quantity and quality in some cases. In other cases, considerable high quality data were available to develop the needed statistics for reliability theory input. Therefore, the final selection of resistance factors considered both the statistical reliability of the method and the level of safety implied by past successful design practice. The degree of reliance on past successful design practice depended upon the quality of the database available, and how well that data modeled reality. In addition, the calibration studies summarized by Allen (2005) were conducted over a considerable period of time, and changes and upgrades in design procedures have occurred since those studies were conducted. Judgments were made regarding how the available calibration results apply to the newer design methods. There is some inherent reliability in past successful design practice and the safety factors used in those design practices. Therefore, if it is decided to deviate from those past successful design practices, there must be a strong reason for doing it. A large and reliable database coupled with reliability theory could be an adequate reason for deviating from past practice, especially if it is recognized that past practice has been excessively conservative, or if past practice has resulted in a higher than acceptable failure rate. This philosophy was used in the establishment of the resistance factors for design in the AASHTO LRFD Bridge Design Specifications. In summary, the AASHTO LRFD design specifications load and resistance factors were determined using calibration by fitting to ASD, reliability theory in cases where adequate data to develop statistics were available, or a combination of the two (Allen 2005; AASHTO 2012a), primarily based on the original work by Barker, et al. (1991) and Paikowsky, et al. (2004). For those cases where the selected resistance factor was developed through strong reliance on the reliability theory calibration results, average measured soil properties were used to determine predicted values in those calibrations. This means that theoretically, average soil/rock property values could be used in combination with those reliability theory derived resistance factors to achieve the desired level of safety. However, if the amount of property data is not adequate to reliably establish average design parameters, more conservative property values should be considered.

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Table 1. Summary of calibration results for drilled shaft bearing resistance (after Allen 2005). I from Calibration by fitting to ASD (NCHRP 343)

I from Reliability Theory (NCHRP 343)

I RecomASD FS mended Current in Practice NCHRP 343

I from Calibration by fitting to ASD (Current Practice)

Strength Limit State

Condition and Location

Design Method

Bearing

Side Resistance in clay

D-method (Reese and O’Neill 1988)

Bearing

Base Resistance in clay

Total Stress (Reese and O’Neill 1988)

2.75*

0.55

0.55

2.75*

0.50

Bearing

Side Resistance in sand

E-method (Reese and O’Neill 1988)

2.5

0.612

-

2.5

0.55

Bearing

Base Resistance in sand

Reese and O’Neill 1988

2.75*

0.55

-

2.75*

0.50

ASD FS Used

2.5

0.61

2

0.65

2.5

I from Reliability Theory (NCHRP 343 Stats.), Updated to Current J’s

0.55

0.72 (0.674)

0.604

-

-

I from Reliability Theory, Recommended in NCHRP 507 0.24 to 0.28, depending on constr. method for clay (0.30 recommended) 0.24 to 0.28, depending on constr. method (0.30 recommended) 0.25 to 0.73, depending on constr. method (0.40 recommended) 0.25 to 0.73, depending on constr. method (0.40 recommended)

New Recommended I

0.455

0.405

0.555

0.505

Side and Base 0.52 to 0.69, 0.55 for Resistance Reese and depending on constr. side, Bearing 2.5 0.55 (sand/clay O’Neill 1988 method (0.50 to 0.70 0.50 for mixed recommended) base5 profile) *Implied in NCHRP 343, due the logic that there is greater uncertainty in the base resistance due to the need for greater deformation to mobilize base resistance. 2 The value shown in the table is slightly lower than the value shown in Appendix A of Barker, et al. (1991). The difference appears to be the result of using a DL/LL ratio of 2.0 rather than 3.0 when performing the calibration by fitting to ASD. 4 Comparitive or other calibrations conducted by the writer using reliability theory (Monte Carlo Method). 5 The recommended resistance factor is applicable to both the Reese and O’Neill (1988) and the O’Neill and Reese (1999) methods.

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Table 2. Load Factor Design (LFD) and LRFD load factors used in resistance factor calibration (after Allen 2005).

Dead load, JDL Live load, JLL

LFD Load Factors (Used in the NCHRP 343 Calibrations) 1.30 2.17

2004 LRFD Load Factors 1.25 1.75

Since 2005, additional resistance factor evaluations were conducted for driven piles. One reason for this was that the resistance factors for pile design, which were based in part on the work by Paikowsky, et al. (2004), were more conservative than had been used in many years of past practice. Pile foundation design using that past practice have performed very well with virtually no failures or even poor performance. Therefore, some of the resistance factors for pile foundation design were increased somewhat to be more consistent with that past successful practice.

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4. Future Geotechnical Development Activities and Needs for the AASHTO LRFD Specifications Since the AASHTO LRFD Bridge Design Specifications became mandatory in 2007, a number of research projects to develop load and resistance factors have been funded and several of them completed. Several of these have been funded by state transportation departments in an effort to determine how to adopt the LRFD specifications to local practices. Others have been funded at the national level to fill gaps in the AASHTO specifications with regard to geotechnical load and resistance factors. Examples include Allen (2007), Smith, et al. (2011), Basu and Salgado (in press), Paikowsky, et al. (2010), Paikowsky, et al. (2005), Schneider (2009), Yang and Liang (2009), TRB E-Circular E-C136 (2009), and Long, et al. (2009). A key hindrance to continued development of load and resistance factors as new data become available or as new methods are developed is that the information contained in the databases developed is not complete, making the data less useful for conducting future calibrations. In most cases, foundation design calibration work and the databases generated and published have not included enough detail for each case history to allow the calibrations to be updated once new or improved design methods are developed. This creates the need to re-gather the details of the case histories used in previous calibrations to accomplish calibrations of new or updated design procedures, as model uncertainty and bias for each design methods is unique. The AASHTO Bridge Subcommittee, at least informally, adopted a recommended practice for conducting calibrations, the development and documentation of the databases generated used as the basis for these calibrations, and the selection of load and resistance factors based on such work. It should be anticipated that most future calibration efforts will follow these recommended practices, especially for research funded through the AASHTO Bridge Subcommittee, which will help to improve the database completeness problem. Those recommended practices are contained in NCHRP Report 20-07/186 (Kulicki, et al., 2007). This report heavily references TRB Circular E-C079 (Allen, et al. 2005) for the details of calibration procedures and database content. Since those documents were produced, Bathurst et al. (2008) and

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Bathurst et al. (2011) provided some refinements to the reliability theory calibration approach that should be used, and they should be considered as an update to the TRB Circular. Another important issue that is yet to be addressed is how to give credit to the amount and quality of the site specific data available when selecting load and resistance factors. This issue is partially addressed for pile foundation design, in that higher resistance factors can be used if dynamic pile tests or pile load tests are conducted (AASHTO 2012a, Zhang 2004, Allen 2005). This issue is not adequately addressed for other foundation systems or situations. Most of the calibration effort has focused on the strength limit state. Efforts for other limit states (e.g., service, extreme event – seismic) are on-going and needed.

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5. Concluding Remarks The development of LSD in USA geotechnical practice has come far in the last 15 years since it was first implemented in 1994. Even 10 years after LRFD was first adopted, at least in the transportation sector, geotechnical engineers were reluctant to move forward with LSD (Goble 1999; Christian 2003). However, since that time, most state transportation departments as well as the Federal Highway Administration have adopted LSD, termed LRFD in the USA, for their geotechnical design practices. While initially, load and resistance factors were developed to provide a level of safety that was consistent with past practice, reliability based approaches have been used to start developing load and resistance factors that better reflect a level of safety that is consistent with the structures the foundations support. Geotechnical engineers are now gaining the confidence they need to start using load and resistance factors that may be more or less conservative than the equivalent level of safety they have used in past practice, educating themselves using what is available in the literature or in university level classes on the subject that are now becoming available, or having research conducted that demonstrates how LRFD should be applied to their local geotechnical practices. As indicated herein, a significant number of studies to develop load and resistance factors for use in LRFD have already been published, and the amount of research being conducted on this subject is growing, both for public and private sector application. What is most important now is to make sure that the databases created to accomplish this work are consistent in the level of detail included, so that future calibration efforts can build on the previous efforts. Not only can these databases be used to improve the effectiveness and consistency of the load and resistance factors developed, but they can also be used to improve the accuracy of the design methods themselves (Bathurst, et al. 2011; Huang, et al. 2012 – in press). Development and maintenance of these databases is expensive and requires a long-term commitment. Furthermore, they have to be updated to keep up with the rapid development of computer software. The recommended practice described by Kulicki, et al. (2007) and Allen et al. (2005) provides an excellent starting point to accomplish this. Finally, the use of statistics and reliability theory techniques is new to most of the geotechnical engineering community (Christian 2003). It is important for those who develop design specifications as well as those who do the reliability based research to be able to communicate to the average geotechnical engineer what this all means to them and how it relates to their current design practice. Once this is accomplished, only then can LSD move forward in geotechnical practice unhindered.

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References AASHTO (2012a). AASHTO LRFD Bridge Design Specifications, American Association of State Highway and Transportation Officials, 6th Edition, Washington, D.C., USA. AASHTO (American Association of State Highway and Transportation Officials) (2012b). Subcommittee on Bridges and Structures, http://bridges.transportation.org/Pages/default.aspx. Allen, T.M., and Bathurst, R.J. (2002). “Soil Reinforcement Loads in Geosynthetic Walls at Working Stress Conditions,” Geosynthetics International, Vol. 9, Nos. 5-6, pp. 525-566. Allen, T. M. (2005). Development of Geotechnical Resistance Factors and Downdrag Load Factors for LRFD Foundation Strength Limit State Design, Publication No. FHWA-NHI-05-052, Federal Highway Administration, Washington, DC, 41 pp. Allen, T.M. (2007). “Development of a New Pile Driving Formula and Its Calibration for Load and Resistance Factor Design,” Transportation Research Record 2004, Washington, DC, pp. 20-27. Allen, T.M., Nowak, A.S. and Bathurst, R.J. (2005). Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design, Transportation Research Board Circular E-C079, Washington, DC, 93 p. Bathurst, R.J., Allen, T.M., and Nowak, A.S. (2008). “Calibration Concepts for Load and Resistance Factor Design (LRFD) of Reinforced Soil Walls,” Canadian Geotechnical Journal, Vol. 45, pp. 1377-1392. Bathurst, R.J., Huang, B., and Allen, T.M. (2011). “Load and Resistance Factor Design (LRFD) Calibration for Steel Grid Reinforced Soil Walls,” Georisk, Vol. 5, Nos. 3 and 4, pp. 218-228. Barker, R. M., Duncan, J. M., Rojiani, K. B., Ooi, P. S. K., Tan, C. K. and Kim. S. G. (1991). Manuals for the Design of Bridge Foundations. NCHRP Report 343, TRB, National Research Council, Washington, DC. Basu, D., and Salgado, R. (2012 - in press). “Load and Resistance Factor Design of Drilled Shafts in Sand,” ASCE Journal of Geotechnical and Geoenvironmental Engineering. Brown, D.A., Turner, J.P., and Castelli, R.J. (2010). Drilled Shafts: Construction Procedures and LRFD Design Methods – Geotechnical Engineering Circular No. 10, FHWA NHI-10-016. National Highway Institute, Federal Highway Administration, U.S. Department of Transportation, Washington, DC. Berg, R. R., Christopher, B. R., and Samtani, N. C. (2009). Design of Mechanically Stabilized Earth Walls and Reinforced Slopes, No. FHWA-NHI-10-024 Vol I and NHI-10-025 Vol II, Federal Highway Administration, 306 pp (Vol I) and 378 pp (Vol II). Christian, J. T. (2003). “Geotechnical Acceptance of Limit State Design Methods,” LSD2003: International Workshop on Limit State Design in Geotechnical Engineering Practice, Phoon, Honjo, & Gilbert (eds), World Scientific Publishing Company, pp. 1-7. Davisson, M. T. (1972). “High Capacity Piles.” Proceedings Lecture Series, Innovations in Foundation Construction, Illinois Section, American Society of Civil Engineers, Reston, VA. DiMaggio, J., Saad, T., Allen, T., Christopher, B., DiMillio, A., Goble, G., Passe, P., Shike, T., and Person, G. (1999). Geotechnical Engineering Practices in Canada and Europe, Report No. FHWA-PL-99-013, Washington, DC, 74 pp. FHWA (Federal Highway Administration) (2007). Geotechnical Technical Guidance Manual, http://flh.fhwa.dot.gov/resources/manuals/pddm/Geotechnical_TGM.pdf#2.6. Florida State Department of Transportation (2012). Soils and Foundations Handbook, Gainesville, FL, 188 pp. Goble, G. (1999). Geotechnical Related Development and Implementation of Load and Resistance Factor Design (LRFD) Methods, NCHRP Synthesis 276, Transportation Research Board, Washington, D.C., 69 pp. Huang, B., Bathurst, R.J., and Allen, T.M. (2012 - in press). “Load and Resistance Factor Design (LRFD) Calibration for Steel Strip Reinforced Walls,” ASCE Journal of Geotechnical and Geoenvironmental Engineering. International Standards Organization (ISO) (1998). ISO 2394 – General Principles on Reliability of Structures, Annex E. Isenhower, W. M., and Long, J. H. (1997). “Reliability Evaluation of AASHTO Design Equations for Drilled Shafts,” Transportation Research Record 1582, Transportation Research Board, Washington D.C., pp. 60-67. Kansas State Department of Transportation, 2007, KDOT Geotechnical Manual. Meyerhof, G. G. (1994). Evolution of Safety Factors and Geotechnical Limit State Design, the Second Spencer J. Buchanan Lecture, Texas A&M University, College Station, TX, 32 pp. Kulicki, J. M., Prucz, Z., Clancy, C.M., Mertz, D.R., and Nowak, A.S. (2007). Updating the Calibration Report for AASHTO LRFD Code, NCHRP 20-07/186, Transportation Research Board, Washington D.C., 156 pp.

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Long, J.H., Hendrix, J., and Baratta, A. (2009). Evaluation/Modification of IDOT Foundation Piling Design and Construction Policy, Research Report FHWA-ICT-09-037, Illinois Center for Transportation, 58 pp. Munfakh, G., Arman, A., Collin, J. G., Hung, J. C.-J., and Brouillette, R. P. (2001). Shallow Foundations Reference Manual. Publication No. FHWA-NHI-01-023, Federal Highway Administration, Washington, D.C. Nowak, A. S. (1999). Calibration of LRFD Bridge Design Code, NCHRP Report 368, Transportation Research Board, Washington, DC. O’Neill, M. W. and Reese, L. C. (1999). Drilled Shafts: Construction Procedures and Design Methods. Report No. FHWA-IF-99-025, Federal Highway Administration, Washington, D.C. Paikowsky, S. G., C. Kuo, G. Baecher, B. Ayyub, K, Stenersen, K. O’Malley, L. Chernauskas, and M. O’Neill (2004). Load and Resistance Factor Design (LRFD) for Deep Foundations, NCHRP Report 507, Transportation Research Board, Washington, DC. Paikowsky, S.G., Fu, Y., and Lu, Y. (2005). LRFD Design Implementation and Specification Development, NCHRP 20-07/183, Transportation Research Board, Washington, D.C., 30 pp, plus Microsoft Access Database. Paikowsky, S.G., Canniff, M. C., Lesny, K., Kisse, A., Amatya, S., and Muganga, R. (2010). LRFD Design and Construction of Shallow Foundations for Highway Bridge Structures, NCHRP Report 651, Transportation Research Board, Washington D.C., 140 pp. Peck, R. B., Hansen, W. E., and Thornburn, T. H. (1974). Foundation Engineering. Second Edition, John Wiley and Son, Inc., New York, 514 pp. Phoon, K.K., Kulhawy, F. H., and Grigoriu, M.D. (2003). “Development of a Reliability-Based Design Framework for Transmission Line Structure Foundations,” ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 129, No. 9, pp. 798-806. Phoon, K.K., (2005). “Reliability-Based Design Incorporating Model Uncertainties,” 3rd International Conference on Geotechnical Engineering Combined with 9th Yearly Meeting of the Indonesian Society for Geotechnical Engineering, Samarang, Indonesia, pp 191-203. Rowe, R. K. and Ho, S. K. (1993). “Keynote Lecture: A Review of the behavior of reinforced soil walls.” Earth Reinf. Practice, Balkema, Rotterdam, pp. 801-830. Reese, L. C., and O’Neill, M. W. (1988). Drilled Shafts: Construction Procedures and Design Methods. FHWA Publication No. FHWA-HI-88-042, 564 pp. Santamarina, J. C., Altschaeffl, A. G., and Chameau, J. L. (1992). “Reliability of Slopes: Incorporating Qualitative Information,” Transportation Research Board, TRR 1343, Washington, D.C., pp. 1-5. Schneider, J.A. (2009). “Uncertainty and Bias in Evaluation of LRFD Ultimate Limit State for Axially Loaded Driven Piles,” Deep Foundations Institute Journal, Vol. 3, No. 2, pp. 25-36. Smith, T., Babas, A., Gummer, M., and Jin, J. (2011). Recalibration of the GRLWEAP LRFD Resistance Factor for Oregon DOT, Final Report – SPR 683, FHWA-OR-RD-11-08, 92 pp. Transportation Research Board (2009), Implementation Status of Geotechnical Load and Resistance factor Design in State Departments of Transportation, E-C136, Transportation Research Board, Washington, D.C., 42 pp. Washington State Department of Transportation (2011). Geotechnical Design Manual M46-03.06, Olympia, WA, USA. Yang, L., and Liang, R. (2009). “Incorporating Setup into Load and Resistance Factor Design of Driven Piles in Sand,” Canadian Geotechnical Journal, Vol. 46, pp. 296-305. Zhang, L. (2004). “Reliability Verification Using Proof Pile Load Tests,” ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 130, No. 11, pp. 1203-1213.

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261

Lessons learned from LRFD calibration of reinforced soil wall structures Richard J. BATHURST1, Tony M. ALLEN2, Yoshihisa MIYATA3 and Bingquan HUANG4

Abstract. This paper reports lessons learned from reliability theory-based LRFD calibration for internal limit states for reinforced soil walls subjected to soil selfweight under operational conditions. The example of the ultimate pullout limit state for steel strip reinforced soil walls is used to demonstrate key issues. A unique feature of the general approach is the use of bias values that include the influence of model error and other sources of variability in input parameters on nominal load and resistance values. The paper shows how bias values can be used to: a) develop analytical load and resistance models that are statistically more accurate and avoid unwanted dependencies; b) select load factors satisfying a target exceedance value, and; c) compute resistance factors meeting a target probability of failure (reliability index value). The general approach has application to rigorous LRFD calibration of a wide range of geotechnical soilstructure design problems. Keywords. LRFD calibration, reliability theory, bias, reinforced soil walls, steel strip, pullout

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1. Introduction Design practice for reinforced soil walls in the USA, Canada and Japan is moving to load and resistance factor design (LRFD). This has generated renewed interest in procedures to calibrate limit state equations based on reliability theory. The objective of LRFD design is to select or size a component (element) so that the probability of failure does not exceed a target value that is based on experience, project requirements, system redundancy and/or dictated in codes. The objective of LRFD calibration is to compute load and resistance factors that are consistent with an acceptable target probability of failure. Issues related to LRFD calibration are the focus of this paper. The authors have carried out LRFD calibration for simple limit states for a number of different wall systems including steel strip and steel grid walls (Huang et al. 2012; Bathurst et al. 2011a), multi-anchor steel walls (Bathurst et al. 2011c) and geosynthetic 1

Corresponding Author: Professor and Research Director, GeoEngineering Centre at Queen’s-RMC, Department of Civil Engineering, Royal Military College of Canada, Kingston, Ontario, K7K 7B4 CANADA; Email: [email protected] 2 State Geotechnical Engineer, Washington State Department of Transportation, State Materials Laboratory, Olympia, Washington, 98504-7365, USA; E-mail: [email protected] 3 Associate Professor, Department of Civil and Environmental Engineering, National Defense Academy, 110-20 Hashirimizu, Yokosuka 239-8686, JAPAN: E-mail: [email protected] 4 AMEC Earth & Environmental, 5681-70th St, Edmonton, Alberta, T6B 3P6 CANADA; E-mail: [email protected]

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reinforced wall systems (Bathurst et al. 2011b). A common feature of these calibration exercises is the use of bias values and their associated statistics to perform calibration of simple limit state functions. The limit state for ultimate steel strip pullout in conventional reinforced soil walls is used in this paper to demonstrate how bias values can be employed to: a) b) c) d)

Develop analytical load and resistance models that are statistically more accurate; Avoid and test for unwanted dependencies; Select load factors satisfying a target exceedance value, and; Compute resistance factors meeting a target probability of failure (reliability index value).

This paper summarizes the lessons learned which will benefit other researchers, engineers and code developers engaged in LRFD calibration for a wide range of other simple geotechnical soil–structure interaction problems.

2. General approach This paper is restricted to linear limit state functions having only one load term which can be expressed as:

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g  φR   γ Q

(1)

Here, Qn = nominal (calculated) load; Rn = nominal (calculated) resistance; γQ = load factor; and ϕ = resistance factor. The nominal values are assumed to be computed using closed-form equations which are deterministic. The expectation is ϕ ≤ 1 and γQ ≥ 1, and these limits are imposed on calibration outcomes. True probability of failure for a given limit state (i.e. probability that g < 1) should be based on the distribution of measured load (Qm) and measured resistance (Rm) values for the simple (single load) limit state introduced earlier rather than the nominal (calculated) values. The reason is that it is rarely the case that calculated values and measured values are the same in geotechnical practice. The ratio of measured value to nominal (calculated) value is called bias. Bias values are used to adjust calculated values from deterministic theory-based, semi-empirical or empirical equations to better match observed (measured) values. Bias values can be understood to capture model bias (i.e. the intrinsic accuracy of the deterministic theoretical, semi-empirical or empirical model representing the mechanics of the limit state under investigation), random variation in input parameter values, spatial variation in input values, quality of data and, consistency in interpretation of data when data are gathered from multiple sources, which is the typical case (Allen et al. 2005). The transformation from nominal load and resistance values to measured values is made by multiplication of each nominal load and resistance value by the corresponding bias value (i.e. Qm = QnXQ and Rm = RnXR). Algebraic manipulation leads to the limit state function Eq. (1) expressed in terms of load and resistance bias values as (e.g. Huang et al. 2012): g

ೂ 

X  X

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(2)

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263

This transformation is only strictly valid if there are no dependencies between load and resistance bias values and their corresponding nominal load and resistance values (i.e. they are uncorrelated). Simple statistical tests introduced later in the paper are used to check that this criterion is satisfied. Clearly, the use of bias values to perform LRFD calibration using Eq. (2) requires a sufficient database of measured loads and a related database of measured resistance values. The accumulation and interpretation of quality measurement data from monitored reinforced soil structures and laboratory testing of reinforcement components has been a major effort of the authors.

3. Selection of probability of failure The objective of LRFD calibration for a limit state function is to select values of resistance factor and load factor such that ϕ ≤ 1, γQ ≥ 1 and a target probability of failure (Pf (g < 1)) is satisfied. The choice of probability of failure (or equivalently, reliability index β) is prescribed by codes, experience and system redundancy. Past geotechnical design practice has led to a probability of failure for foundations, in general, of approximately 1 in 1000. However, reinforced soil walls are highly redundant systems with multiple layers of reinforcement. Hence, the tensile failure (or pullout) of a single reinforcement layer will not result in failure of the wall. This redundancy concept is similar to pile groups that are designed to a target reliability index value of β = 2.0 to 2.5 because of potential load shedding from a failed pile to other piles in the group (Barker et al. 1991; Paikowsky et al. 2004; Allen 2005). A value of β = 2.33 corresponds to a probability of failure of 1 in 100 (Pf = 0.01). This is the reference value that has been used for the internal limit states calibration for reinforced soil wall systems by the authors in previous related work.

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4. Load and resistance models The LRFD calibration procedure described in this paper is based on load and resistance bias statistics. As demonstrated later in this paper, the magnitude and frequency distribution of these values will be sensitive to the accuracy of the underlying deterministic models adopted for the limit state. Many load and resistance equations in reinforced soil wall design codes include empirical coefficients that were originally selected for allowable stress design (ASD) practice (classical factor of safety approach). These equations, when first developed, typically over-predicted load values when compared to measured loads (where available) and under-predicted resistance values (tensile or pullout capacity) from laboratory tests on reinforcement elements. This may be expected since initial model development with limited data was purposely conservative to encourage safe ASD outcomes. However, the amount of conservatism was often subjective, and excessive conservatism often led to design curves that did not capture the measured trends in the data or qualitative expectations based on the mechanics of the soil-structure interaction mechanism. Furthermore, in some cases, the original model development and calibration for ASD practice was carried out two or three decades ago, and re-examination of the accuracy of the underlying load and resistance models has not kept pace.

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R.J. Bathurst et al. / Lessons Learned from LRFD Calibration of Reinforced Soil Wall Structures

5. Example In this paper, LRFD calibration issues are referenced to the example of the ultimate pullout limit state function for a steel reinforcement strip found in a conventional mechanically stabilized earth wall. This example is used because there is a large database of quality load data available from full-scale instrumented wall structures (Miyata and Bathurst 2012a). A large database of pullout tests is also available for steel strip reinforcement in combination with a wide range of frictional soils (Miyata and Bathurst 2012b). Some features of the details of the implementation of the underlying deterministic equations used here are simplified and the range of measurement data is purposely broad to maximize the number of data points in each data set. For example, the pullout data are exclusively from Japanese sources while the load data are from monitored walls in the USA, Japan and Europe. Some soils used in Japan are not recommended in USA specifications for the same type of wall structure. As another example, no distinction is made between pullout test results using different pullout test methodologies. 5.1. Load models Figures 1 and 2 compare calculated load data using two different load models and measured load data from a database of steel strip reinforced soil walls. The database is comprised of 93 measurements taken from 16 different structures constructed with granular backfill soil having a friction angle in the range of 35 ≤ φ ≤ 45o (Miyata and Bathurst 2012a). The maximum tensile load (Tmax) in a reinforcement layer is expressed as:

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T  KS σ

(3)

where: Sv = reinforcement spacing; K = coefficient of earth pressure; σv = vertical pressure at the elevation of the reinforcement strip; and, z = depth of layer below the crest of the wall. In current codes (e.g. PWRC 2003; AASHTO 2012; BSI 2010) a bilinear distribution for coefficient K is recommended which can be expressed as:



౥

౥

K  K 1    K   

for z ≤ zo = 6m

(4a)

K = Ka

for z > z o = 6 m

(4b)

and

Here Ka = (1 − sinφ)/(1 + sinφ) and Ko = 1 − sinφ. The earth pressure coefficient K is normalized with Ka in Figure 1a and it can be seen to vary slightly as a function of friction angle. Superimposed on the figure are back-calculated values of K/K a using Eq. (3) and measured reinforcement loads. The bilinear model results in larger K/K a values with decreasing z < zo which is also the visual trend in the back-calculated values. There are four data points that may be treated as outliers. Using the φ = 40o design curve as a reference, the exceedance level (i.e. fraction of measured load values greater than calculated values) is about 58%. Applying a multiplier to the bilinear reference

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R.J. Bathurst et al. / Lessons Learned from LRFD Calibration of Reinforced Soil Wall Structures

a)

a)

b)

b)

c)

c)

d)

d) Figure 1. Bilinear load model

Figure 2. Exponential load model

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R.J. Bathurst et al. / Lessons Learned from LRFD Calibration of Reinforced Soil Wall Structures

curve reduces the exceedance value as illustrated in the inset table. Miyata and Bathurst (2012a) concluded that, when bilinear load models of this type were originally proposed in the late 70’s, the exceedance rate for ASD design practice was about 37%. Since that time there is now more data (n = 93 viz n = 34 based on original documents). The larger data set with the same original model now gives an exceedance value of 58%. This observation illustrates that load factors based on exceedance values should be re-examined periodically as the amount of measured data increases over time. To the best knowledge of the authors, this is seldom if ever done. Also shown in Figure 1a is the design curve with load factor γQ = 1.75 which corresponds to an exceedance rate of about 4%. This value is close to the 3% exceedance rate that was adopted by bridge engineers during the development of modern LRFD for bridge superstructure elements in North American codes (Nowak 1999; Nowak and Collins 2000; Allen et al. 2005). The applicability of this low exceedance rate to reinforced soil structures is discussed at the end of the paper. Figure 1b shows that that measured load values increase in a generally linear manner with calculated values. This indicates that, at least qualitatively, the bilinear load model is accurate. However, the mean load bias value μQ = 1.12, which means that on average measured load values are 12% higher than calculated values based on the currently available measured load data. Load bias values are plotted against depth z and nominal (calculated) load values in Figure 1c and 1d, respectively. If the outlier points are removed (i.e. the data is filtered), the visual impression is that the bias values are independent of z and T max (calculated). In fact, a regressed linear line fitted to all data points in both plots includes a zero slope within 95% confidence limits on the estimate of slope. The Spearman’s rank coefficient test, which is a measure of the strength of a monotonic relationship between data pairs, showed that there was no relationship between independent and dependent parameters at a level of significance of 5%. Hence, at this point the current bilinear load model is judged to do reasonably well regardless of whether or not the visual outliers are removed from analyses. Furthermore, there is no evidence in the source documents why these data are anomalous. The quantitative effect of removing the four outlier points is a small improvement in bias values (i.e. μQ decreases from 1.12 to 1.07, and COVQ decreases from 0.332 to 0.271). An alternative model for coefficient K is an exponential function of the form: K  K  a 





  

(5)

This function has the following advantages: a) It is smoothly continuous; b) The independent parameters remain depth z and soil friction angle φ; c) There are three constant coefficients (a, b and c) – this is the same number of coefficients found in the current bilinear expressions (i.e. Eq. (4a)), and; c) The maximum value of K occurs at z = 0 and the minimum value is strongly asymptotic with increasing z. Hence, maximum and minimum values for K are a function of soil friction angle as is the case with bilinear expressions found in current codes. The accuracy of this model can be referenced to the plots in Figure 2. The constant coefficients in this model were computed using the non-linear optimization utility (Solver) in Excel. The objective function was μQ = 1 and solutions were constrained to a > 1, b > 1 and c = 1. The coefficients were adjusted slightly to give convenient values of a = 1.14 and b = 3.36. Hence, z = 0 gives K = 4.5×Ka and z →∞ gives K = 1.14×Ka.

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The corresponding load bias statistics are μQ = 1.00 and COVQ = 0.316. The need to remove the outlier points identified earlier is visually less compelling using this model. However, if these data points are removed, the bias statistics improve slightly to μQ = 1.00 and COVQ = 0.283. The independence of load bias values with depth z and Tmax (calculated) is visually apparent in Figures 2c and 2d and confirmed using the quantitative tests described earlier. 5.2. Resistance (pullout) models The ultimate pullout capacity of a reinforcement strip in a soil retaining wall is computed as: P  2f σ bL

(6)

where: f is a dimensionless empirical interface shear coefficient; σv = vertical pressure at elevation of the reinforcement strip; b = strip width; and, L e = anchorage (pullout) length. The value of f in this example is computed using the default model for frictional soils in the range of 35 ≤ φ ≤ 45o. Japanese, USA and UK design codes use bilinear equations to compute coefficient f . The Japanese equations for different soil and reinforcement types have the following format:



౥

౥

f  f  1    tan ψ  

for z ≤ zo

(7a)

f  tan ψ

for z > z o

(7b)

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and

In this example, the default values for the three constant coefficient terms are taken from the Japanese (PWRC 2003) design code for ribbed steel strips in granular soils, i.e. f  = 1.5, zo = 6 m and ψ = 36o. Figure 3a shows back-calculated values of coefficient f using Eq. (6) and measured Pmax values from pullout test results. Superimposed on the plot is Eq. (7) with different multipliers. In LRFD terminology, these multipliers are equivalent to resistance factors (ϕ). A review of Japanese past practice shows that the original design curve (multiplier = 1) adopted in the 1980’s corresponded to a minimum exceedance rate of 78% (Miyata and Bathurst 2012b). The exceedance rate using available data today is about 57%. Figure 3b shows measured versus calculated Pmax values. The general trend is that measured values increase with calculated values. However, resistance (pullout) bias statistics show that the measured values are on average 39% greater than calculated values (μR = 1.39) and the spread in bias values is high, as indicated by COVR = 0.559. Pullout bias values are visually correlated with depth z and calculated Pmax values as shown in Figures 3c and 3d, respectively. The 95% confidence limits on the slope of the linear regressed lines shown in the figures confirm these dependencies, as does the Spearman’s rank correlation test at a level of significance of 5%. The accuracy of load predictions in terms of mean bias and coefficient of variation of bias values can be improved using an exponential function of the same general form as Eq. (5) but adapted to the pullout case as (Miyata and Bathurst 2012b):

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a)

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a)

b)

b)

c)

c)

d)

d) Figure 3. Bilinear pullout model

Figure 4. Exponential pullout model

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R.J. Bathurst et al. / Lessons Learned from LRFD Calibration of Reinforced Soil Wall Structures

f 

‫כ‬౥  ౟    

 tan ψ

269

(8)

This equation has the following advantages: a) The equation has three constant coefficients which is the same number of coefficients as the bilinear models currently recommended by PWRC (2003); b) The minimum value of interface shear coefficient remains f  tan ψ , and; c) The function is smoothly continuous with depth z. The constant coefficient terms were selected after minor adjustment from the results of optimization (i.e. same method used to fit the exponential function for maximum tensile load). The final values are, f  = 7.0, Ψi = 33o and d = 0.420. The value for coefficient Ψi is within a few degrees of the default value (36o) currently recommended in the Japanese code for the case of granular soil in combination with ribbed steel strips. Back-calculated f values using Eq. (6) and measured pullout capacity test data are shown in Figure 4a, and measured versus calculated Pmax values are plotted in Figure 4b. The visual impression is that the exponential model is more accurate than the bilinear model. This is confirmed quantitatively by the matching bias statistics which have a mean μR = 1.00 and COVR = 0.475. Figures 4c and 4d show no visual indication of bias dependency with depth and calculated pullout capacity values, respectively. This was confirmed quantitatively using the zero slope test as before and Spearman’s rank correlation test at a level of significance of 5%.

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6. Calculation of resistance factors The probability of failure using bias values is notionally related to the area of overlap between the load bias (XQ) and resistance bias (XR) frequency distribution curves illustrated in Figure 5. Load and resistance factors (γQ, ϕ) are selected to shift the two curves apart along the horizontal axis so that the probability of failure (overlap) does not exceed an acceptable value. As noted earlier, a value of Pf = 0.01 has been recommended for highly strength redundant systems such as reinforced soil walls with multiple reinforcement layers. If the load and resistance bias frequency distributions can be closely fitted to lognormal distributions over many standard deviations from the mean, then the bias statistics for the entire data sets can be used to compute Pf. However, this is not always the case. In fact, it is very common that deviations from idealized log-normal distributions will occur in the tails of these distributions for soil-structure problems such as reinforced soil walls. Because it is the overlap between the upper tail of the load frequency distribution and the lower tail of the resistance frequency distribution that will largely influence the true probability of failure, it may be necessary to select other log-normal distributions to capture the data in the tails (Allen et al. 2005). Figure 6a shows bias values for reinforcement load using the bilinear load model plotted as a cumulative distribution function (CDF) plot. Log-normal approximations have been fitted to the entire data set (n = 93) and to the upper tail comprised of the four data points previously identified as possible outliers. In Figure 6b the four outliers

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Figure 5. Idealized frequency distribution curves for unfactored and factored load and resistance bias values Table 1. Load and resistance bas statistics a) Bilinear models Load bias Figure 6a Column → Parameter

1

Figure 6b 2

Fit to all data

3

Fit to all data upper tail

4

Fit to all data

Fit to all data upper tail

Resistance bias* Figure 8 5 6 Fit to all Fit to all data data lower tail

n 93 93 89 89 70 Mean 1.12 0.900 1.07 1.49 1.45 COV 0.332 0.556 0.271 0.027 0.577 *Resistance bias values are correlated with nominal (calculated) pullout (resistance) values

70 0.750 0.267

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b) Exponential models Load bias Figure 7a Column →

1

Parameter

Fit to all data

n Mean COV

93 1.00 0.316

Figure 7b 2

Fit to all data upper tail 93 1.00 0.316

3 Fit to all data 89 1.00 0.283

4 Fit to all data upper tail 89 1.20 0.108

Resistance bias Figure 9 5 6 Fit to all Fit to all data data lower tail 70 70 1.00 1.00 0.475 0.50

at the upper tail are removed (n = 89) and again a log-normal approximation fitted to the entire distribution and through the upper tail. Figure 7a shows similar data using the exponential load model to compute the load bias values. In this case, the log-normal approximation to the entire data set (n = 93) is judged to be an acceptable fit to the upper tail of the load bias distribution. The four possible outliers in the original data set are removed in Figure 7b and log-normal approximations fitted to the entre data set (n = 89) and the upper tail. Figures 8 and 9 show a similar log-normal fitting exercise applied to the pullout bias data sets. However, the fit-to-tail is now at the bottom of the CDF plots. No

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a)

271

a)

b) Figure 6. Bilinear load model

b) Figure 7. Exponential load model

outliers have been removed in these two plots. The possible outlier identified in Figure 9 has been ignored in the fit-to-lower tail. The difference in bias statistics for the two approximations is negligible in the figure. It is clear from the fit-to-tail approximations shown in Figures 6 through 9 that judgment plays a role in the choice of approximation to the distribution tails.

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Load and resistance bias statistics are summarized in Table 1. Resistance factors can be computed for a target probability of failure by trial and error using Monte Carlo simulation and combinations of the bias mean and COV in Table 1. For demonstration purposes, it is more convenient to compute resistance factors to sufficient accuracy using the following closed-form solution: γQ ϕ =

{

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exp β

μR μQ

(1+COV ) (1+COV ) 2 Q

⎣(

2 R

LN ⎡ 1+COVQ

2

)(1+COV )⎤⎦ } 2 R

(9)

This equation is applicable to load and resistance bias values having log-normal distributions, which is the case in this example. The derivation of this equation can be found in the paper by Bathurst et al. (2011c). The results of calculations for β = 2.33 (Pf = 0.01) and using all permutations of bias statistics in Table 1 for bilinear and exponential load and resistance models are plotted in Figure 10a and 10b, respectively. The figure inset legends identify the combinations of bias statistics from Table 1 used to generate the ϕ-γQ lines. The two figures show that the bilinear models, which are generally less accurate than the exponential models, give a wider range of possible resistance factors (i.e. the vertical spread in ϕ-γQ lines is greater). Two fit-to-tail curves are identified by the heavy lines in each figure. Since the choice of fit-to-tail is subjective, the choice of which ϕ-γQ line should be used for calibration requires judgment. For each calibration line, the resistance factor can be computed using an appropriate load factor. For example, Japanese past practice has shown that an exceedance value of 37% of the calculated load is acceptable. This corresponds (by interpolation) to a load factor (multiplier) γQ = 1.20 using the bilinear load model (Figures 1a and 1b). The same exceedance value using the exponential load model gives a lower value, i.e. γQ = 1.10. The resulting resistance factor using the bilinear load and pullout models is ϕ = 0.28 to 0.32 and for the exponential load and resistance models is ϕ = 0.27. Other load factors could be used. For example, the current AASHTO (2012) code recommends a load factor of γQ = 1.35 for the calculation of reinforcement load due to soil self-weight plus any permanent surcharge loading. This value leads to slightly higher resistance factors using the same ϕ-γQ lines in Figure 10. However, the corresponding exceedance values are much lower than the 37% value identified earlier (i.e. 24% and 11% in Figures 1a and 2a using currently available load data).

7. Discussion and conclusions This paper has demonstrated a number of key steps and issues related to LRFD calibration of a simple linear limit state function with a single load term. The example used to develop these points is the ultimate pullout limit state for steel strips used in reinforced soil walls. Bias values have been used to quantify the accuracy of current steel strip reinforcement load and resistance (pullout) models found in design codes. Bias values

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Figure 8. Bilinear pullout model

273

Figure 9. Exponential pullout model

computed for the current bilinear resistance (pullout) model used in practice today show that this model has variable accuracy with depth. Furthermore, it violates the criterion that bias values should be independent of nominal (calculated) pullout values. This criterion must be satisfied in order to transform the original limit state function expressed in terms of nominal load and resistance values to a linear function in terms of load and resistance bias values. The paper shows how bias statistics can guide the development of load and resistance models that are more accurate on average and ensure that the model predictions are uncorrelated with depth. In this paper exponential models are used, but the authors have demonstrated in other related papers that multi-linear formulations may be adequate (Bathurst et al. 2011a; Huang et al. 2012). The example problem demonstrates that LRFD calibration requires special attention be paid to the upper tail of the load bias CDF plot and the lower tail of the resistance CDF plot since it is the region of tail overlap that strongly influences the true probability of failure. The sensitivity of LRFD calibration outcomes on bias statistics (mean and COV values) extracted from approximations to unfiltered and filtered CDF data plots, and best-fit-to-tail in CDF plots has been demonstrated quantitatively. The selection of the load factor(s) used in limit state equations should reflect current accepted levels of load exceedance as a practical strategy to link current practice to LRFD calibration outcomes. In the development of current LRFD equations for bridge superstructure design, the load factor for dead load was based on a load exceedance rate of 3%, which corresponds to two standard deviations below the mean of measured loads. An important difference between measured loads in steel structures and measured reinforcement loads in soil-structures (such as soil retaining walls) is that the spread in measured loads for the latter is much larger (i.e. higher COV values).

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a)

Bilinear load and resistance (pullout) models

b)

Exponential load and resistance (pullout) models Figure 10. Computed resistance factors for probability of failure Pf = 0.01 (β = 2.33)

Hence, load factors based on small exceedance values common in structural engineering applications are not practical for some limit states for reinforced soil retaining walls. Whether consciously or not, larger exceedance values are acceptable in

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geotechnical engineering as demonstrated by comparison of measured loads with design curves originally developed for pullout ASD practice. Nevertheless, as demonstrated in this paper, the same acceptable target probability of failure (reliability index β) can be achieved using different combinations of load and resistance factor. Hence, there is no compelling reason to impose the load factor based on 3% exceedance in structural engineering practice on soil-structure limit states. The most important outcome from LRFD calibration is that an acceptable target probability of failure is satisfied and the computed resistance factor and load factor satisfy ϕ ≤ 1 and γQ ≥1, respectively. It is clear that large databases of quality measured load and resistance data are required for LRFD calibration of simple linear limit state functions. Sufficiently large and high quality databases of the type compiled by the authors for steel strip reinforced soil walls may not be available for similar limit state function calibration in other systems. Judgment in the selection of data from multiple sources and fitting to frequency distribution plots is an unavoidable feature of LRFD calibration. Additional discussion on these issues can be found in the TRB Circular E-C079 (Allen et al. 2005). Finally, it is prudent to remind design engineers that limit state functions that are empirically adjusted and calibrated against physical data should only be used for design when project-specific conditions fall within the physical data envelope that was used to calibrate the underlying deterministic models and to compute the load and resistance factors.

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Acknowledgments The authors are grateful for the financial support from the following departments and agencies: Natural Sciences and Engineering Research Council (NSERC) of Canada; Department of National Defence (Canada); Japan Ministry of Education, Culture, Sports, Science and Technology; Japan Ministry of Defense; JSPS Invitation Fellowship Program for Research in Japan; Ministry of Transportation of Ontario and the following US State Departments of Transportation - Alaska, Arizona, California, Colorado, Idaho, Minnesota, New York, North Dakota, Oregon, Utah, Washington and Wyoming.

References Allen, T.M. (2005). Development of Geotechnical Resistance Factors and Downdrag Load Factors for LRFD Foundation Strength Limit State Design, Publication No. FHWA-NHI-05-052, Federal Highway Administration, Washington, DC, 41 pp. Allen, T.M., Nowak, A.S. and Bathurst, R.J. (2005). Calibration to Determine Load and Resistance Factors for Geotechnical and Structural Design. Circular E-C079, Washington, DC: Transportation Research Board, National Research Council. American Association of State Highway and Transportation Officials (AASHTO) (2012). LRFD Bridge Design Specifications. 6th edition. AASHTO: Washington, DC, USA. Barker, R.M., Duncan, J.M., Rojiani, K.B., Ooi, P.S.K., Tan, C.K. and Kim. S.G. (1991). Manuals for the Design of Bridge Foundations. NCHRP Report 343, TRB, National Research Council, Washington, DC.

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Bathurst , R.J., Huang, B. and Allen, T.M. (2011a). Load and resistance factor design (LRFD) calibration for steel grid reinforced soil walls, Georisk, 5(3-4): 218-228. Bathurst, R.J., Huang, B. and Allen, T.M. (2011b). Interpretation of installation damage testing for reliability-based analysis and LRFD calibration, Geotextiles and Geomembranes, 29(3): 323-334. Bathurst, R.J., Miyata, Y. and Konami, T. (2011c). Limit states design calibration for internal stability of multi-anchor walls, Soils and Foundations, 51(6): 1051-1064. British Standards Institution (BSI) (2010). Code of Practice for Strengthened/Reinforced Soil and Other Fills. BSI, Milton Keynes, BS 8006. Huang, B., Bathurst, R.J. and Allen, T.M. (2012). Load and resistance factor design (LRFD) calibration for steel strip reinforced soil walls, ASCE Journal of Geotechnical and Geoenvironmental Engineering, 138(8): 922-933. Miyata, Y. and Bathurst, R.J. (2012a). Measured and predicted loads in steel strip reinforced c-φ soil walls in Japan, Soils and Foundations, 52(1): 1-17. Miyata, Y. and Bathurst, R.J. (2012b). Analysis and calibration of default steel strip pullout models used in Japan, Soils and Foundations, 52(3): 481-497. Nowak, A.S. (1999). Calibration of LRFD Bridge Design Code. NCHRP Report 368, National Cooperative Highway Research Program, Transportation Research Board, Washington, D.C. Nowak, A.S. and Collins, K.R. (2000). Reliability of Structures. McGraw-Hill, New York. Paikowsky, S.G. (2004). Load and Resistance Factor Design (LRFD) for Deep Foundations. NCHRP Report 507, National Cooperative Highway Research Program, Transportation Research Board of the National Academies, Washington, D.C. 126 pp. Public Works Research Center (PWRC) (2003). Design Method, Construction Manual and Specifications for Steel Strip Reinforced Retaining Walls. 3rd revised Edition. Public Works Research Center, Tsukuba, Ibaraki, Japan, 302 pp. (in Japanese).

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-277

Geotechnical Design Code Development in Canada Gordon A. FENTON Visiting Professor, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands, and Professor, Department of Engineering Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada; email: [email protected] Abstract. Canada has two national codes of practice which include geotechnical design provisions: the National Building Code of Canada and the Canadian Highway Bridge Design Code. Both of these codes have been using a load and resistance factor format for about two decades now, but are still in the process of adopting a reliability-based design framework. This paper describes the advances planned for these codes. Keywords. geotechnical code development, reliability-based geotechnical design, load and resistance factor design, Canadian codes, code comparison

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1. Background Geotechnical design codes have been migrating towards reliability-based design concepts for several decades now. Prior to 1979, geotechnical design in Canada was based on working stress design (WSD) which involved satisfying an equation of the form Rˆ ≥ Fs ∑ Fˆi

(1)

i

where Rˆ is the characteristic (nominal or design) resistance, Fs is a factor of safety, and Fˆi is the ith characteristic (nominal or design) load effect. The factor of safety was traditionally used to account for all sources of uncertainty. However, in recent decades, it has been recognized that not all sources of uncertainty are equal. For example, usually live loads are less certain than dead loads, concrete strengths are less certain than steel strengths, and soil strengths are less certain than most other engineering properties. It has thus made sense to break up the global factor of safety, Fs , into a sequence of partial factors, one for each source of uncertainty in the design. In most modern code implementations, the resulting set of partial factors has been separated into two distinct groups (which are nevertheless inversely related). These are the load and resistance factors which lead to a design methodology referred to as Load and Resistance Factor Design (LRFD). The partial factors are individually related to the variability of the quantity that they are factoring and are used to scale the characteristic design values to more conservative values such that the overall probability of design fail-

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G.A. Fenton / Geotechnical Design Code Development in Canada

ure is acceptably small. In general, this means that loads are scaled up (so long as they are acting in a way that reduces overall system safety) and resistances are scaled down so that the final factored design values are acceptably conservative. Under the LRFD approach in most codes, designs must satisfy an equation of the following generalized form (although the right hand side is often expressed more precisely as a series of possible load combinations),

ϕg Rˆ ≥ ∑ Ii ηi αi Fˆi

(2)

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i

where ϕg is a geotechnical resistance factor, Rˆ is the characteristic geotechnical resistance (based on characteristic ground parameters), and, for the ith load, Ii is a structure importance factor, ηi is a load combination factor, αi is the load factor, and Fˆi is the characteristic load effect. In this paper the word characteristic is used because it suggests a value which characterizes (in some sense) a design parameter which is uncertain, e.g. a load or resistance, having a random distribution. The words nominal or design have also been commonly used to equivalently describe such design parameters, but these words do not carry the suggestion of the underlying random distribution of the design parameter, and so will not be used here. Some design codes (e.g. the Eurocode) provide a specific statistical definition of the word characteristic as the 5th or 95th percentile, whichever is worst. Most other geotechnical design codes provide only vague definitions for the characteristic value. For example, probably the most popular definition is “a conservative estimate of the mean.” In Canada, the LRFD approach is embedded within a Limit State Design (LSD) framework, where the LRFD formulation is satisfied for each of a sequence of possible failure modes, or limit states. Typically the load and resistance factors are specifically selected for the limit state under consideration. For example, designing against the limit state of bearing capacity failure would usually involve different factors than designing against the limit state of excessive settlement. The load and resistance factor method typically appears in one of two forms in geotechnical design codes around the world; 1) the partial resistance factor approach, in which the individual components of ground strength, e.g. cohesion and friction, are factored separately. The rational behind this approach is that the components of strength have different levels of uncertainty – for example, cohesion is generally deemed to be more uncertain than friction angle. This is analogous to how live and dead loads are factored separately. 2) the total resistance factor approach, in which the geotechnical resistance is computed in the traditional way using best estimates of the ground parameters (i.e. characteristic values) and then the final result is factored. This approach is more analogous to how resistances are factored in structural engineering where each engineering material (e.g. concrete, steel, and wood) has its own resistance factor. The ground is then viewed as just another engineering material. In 1979 and then again in 1983 the Ontario Highway Bridge Design Code (OHBDC) adopted the partial resistance factor approach from Danish practice, in which components of ground strength (e.g., cohesion and friction angle) were individually factored. In 1983, the LSD approach became mandatory in the bridge code. Unfortunately, the partial factor format did not lead to design consistency with the working stress design approach

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and so was not readily accepted by geotechnical engineers. Another complaint levied against the partial resistance factor approach is that by modifying the ground properties away from their characteristic values, the resulting predicted failure mechanism was sometimes significantly different than the actual failure mechanism in the ground. Many geotechnical engineers found that the myriad of resistance factors that the approach involved made it difficult to retain a clear understanding of the geotechnical problem being considered. In addition, the 1983 edition of OHBDC applied both a partial factor to soil properties along with a load factor to active and passive earth pressures. This double factoring of the ground led to increases of approximately 30% in footing widths for cantilever retaining walls (Green and Becker, 2000) beyond what traditional designs called for. In 1991, the OHBDC switched to the total resistance factor approach, where the characteristic (nominal) geotechnical resistance was computed using traditional (working stress design) methods and then factored at the end. In general, this approach was preferred by the geotechnical community because it was simpler and more familiar (similar to the traditional factor-of-safety approach, Eq. 1), because it more closely preserved the best estimate of the failure mechanism, and because it seemed to be in better harmony with the approach taken by structural engineers of factoring each engineering material. The 1991 edition of the Ontario Highway Bridge Design Code (OHBDC) was the third and last edition of the OHBDC. In 2000, the 9th edition of the CAN/CSA-S6 code, renamed the Canadian Highway Bridge Design Code (CHBDC) became a national standard and was largely modeled on OHBDC 1991. The most recent edition of CHBDC was published in 2006 (10th Edition). The geotechnical design code provisions in the current CHBDC are little changed from the 1991 OHBDC. The National Building Code of Canada (NBCC) permitted both working stress and limit states design in their 1995 edition. In the next edition, 2005, limit state design became mandatory for geotechnical designs, although the geotechnical resistance factors themselves are still not part of the Building Code, even in the most recent edition (National Research Council, 2010). In other words, the NBCC is still lagging well behind the CHBDC with respect to geotechnical design.

2. Present Status At this time, geotechnical design in Canada follows the total resistance factor approach within a Limit State Design framework, as do most other geotechnical design codes in North America, e.g., American Association of State Highway and Transportation Officials (AASHTO, 2007). The resistance factors to be used in Canada appear in the CHBDC (Canadian Standards Association, 2006) and in the User’s Guide to the NBCC (National Research Council, 2010), with the latter being nearly identical to those specified in the CHBDC. It is of interest to compare the resistance factors specified in the CHBDC to those specified in other codes from around the world. To this end, a very simple example in which the required area of a spread footing designed against bearing failure is considered. Characteristic dead and live loads of FˆD = 3700 kN and FˆL = 1000 kN, respectively, are to be supported by a weightless soil having characteristic soil properties cˆ = 100 kPa and φˆ = 30 ◦ (note that the distinction between drained and undrained parameters is not

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G.A. Fenton / Geotechnical Design Code Development in Canada

made here since this is not important to the illustration being made – either condition can be assumed). The resulting required areas are shown in Table 1. The design must satisfy the following equation (which also corresponds to Design Approach 2 in the Eurocode);

ϕgu Rˆu ≥ αL FˆL + αD FˆD

(3)

where the importance factor and load combinations factors appearing on the right hand side of Eq. (2) are both 1.0 for this simple load combination, and the subscript u on the left hand side (resistance side) denotes that this is an ultimate limit state (ULS). For a weightless soil, the characteristic ultimate geotechnical resistance, Rˆu , is equal to the footing area, A, times the characteristic ultimate soil bearing capacity, cˆNˆ c , i.e., Rˆu = AcˆNˆ c

(4)

The characteristic bearing capacity factor, Nˆ c , is given by (e.g. Prandtl, 1921, and Meyerhof, 1951, 1963), as   ˆ exp{π tan φˆ } tan2 π4 + φ2 − 1 (5) Nˆ c = tan φˆ so that the minimum required footing area is computed from Eq. (3) as A=

αL FˆL + αD FˆD ϕgu cˆNˆ c

(6)

For the given problem, Nˆ c = 30.14, so that cˆNˆ c = 100(30.14) = 3014 kPa and

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A=

1000αL + 3700αD 3014ϕgu

(7)

In the case of the partial factor approach, where the components of the ground shear strength are factored separately, it can be seen that the Nˆ c term involves both tan(φˆ ) and φˆ . Thus, applying partial factors yields a ‘factored’ Nˆ c value which will be referred to here as Nˆ f and which is computed as

Nˆ f =

exp{πϕφ tan φˆ } tan2



π 4

+

φˆ f 2



−1

ϕφ tan φˆ

(8)

where ϕφ is the partial factor applied to tan(φ ) and φ f is the ‘factored’ friction angle defined as   φ f = tan−1 ϕφ tan φˆ

(9)

so that the minimum footing area required for the partial factor approach becomes A=

αL FˆL + αD FˆD ϕc cˆNˆ f

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(10)

G.A. Fenton / Geotechnical Design Code Development in Canada

281

where ϕc is the partial factor associated with the cohesion component of shear strength. In Table 1, where a range in factors is given, the midpoint of the range is used. Table 1 Values of load and resistance factors suggested by various sources along with the footing area each would require in a bearing capacity design example assuming similarly defined characteristic loads. All factors are applied in a multiplicative fashion. Source

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Dead Load Factor CFEM (1992) 1.25 NCHRP 343 (1991) 1.3 NCHRP 12-55 (2004) 1.25 Denmark (1985) 1.0 AASHTO (2007) 1.25 AS 5100 (2004b) 1.2 CHBDC (2006) 1.2 AS 4678 (2002b) 1.25 EC 7 DA 1 (2004) 1.0 EC 7 DA 2 (2004) 1.0

Live Load Factor 1.5 2.17 1.75 1.3 1.75 1.8 1.7 1.5 1.3 1.3

tan(φ ) Factor 0.8

c Bearing Factor Factor 0.5-0.65 0.35-0.6 0.45 0.83 0.56 0.45-0.55 0.35-0.65 0.5 0.75-0.95 0.5-0.9 0.8 0.8 0.71

Area (m2 ) 5.22 4.88 4.70 4.13 4.23 4.14 4.07 3.89 3.06 3.04

Table 1 illustrates that a range in conservatism apparently exists across this selection of codes under the above assumptions. The 1992 Canadian Foundation Engineering Manual (CFEM, Canadian Geotechnical Society, 1992) is perhaps the most conservative, with a required bearing area of 5.22 m2 . The least conservative (apparently) are the two Design Approaches (DA 1 and 2) of Eurocode 7 (2004) with required bearing areas of about 3.05 m2 . However, Table 1 also assumes that the characteristic design parameters are the same for all codes. A more complete comparison of the levels of safety inherent in each design code involves a more careful consideration of how all of the parameters entering the design process are defined and factored, particularly with respect to characteristic values. Such a comparison is considered next. 2.1. Characteristic Loads and Bias Factors Some codes specify that the characteristic load is equal to the mean, others suggest using a ‘cautious estimate of the mean’, while others specify the use of an upper (or lower) quantile. Similarly, the characteristic resistance may be computed using mean strength parameters, or using quantiles of the strength parameters. In general, the difference between the characteristic design value and its mean is usually captured by a bias factor usually defined as the ratio of the mean to characteristic value, i.e., kR =

μR , Rˆu

kL =

μL , FˆL

kD =

μD FˆD

(11)

where k is the bias factor and μ is the mean of the subscripted variable. Introducing the dead to live load ratio, RD/L = μD / μL , allows Eq. (3) to be re-expressed as

μR ≥ Fs (μL + μD )

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(12)

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where Fs is a global factor of safety, defined as 

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Fs =

kR ϕgu



αL αD RD/L + kL kD



1 1 + RD/L

 (13)

Note that Eq. (12) is seen to take on a similar role (and definition as ratio of mean resistance to mean load) as does the traditional factor of safety used in working stress design approaches. If the coefficients of variation of the loads and resistances are approximately the same worldwide, then the global factor of safety provides a simple measure of the relative safety of a code design which then allows the safety level of various codes to be compared. Ellingwood (1999) notes that probability models for loads collected in research programs in North America and Europe agree reasonably well, and so the assumption that coefficients of variation are similar, at least between North America and Europe, is deemed to be reasonable. In this paper the global factor of safety provided by the following design codes are compared for shallow foundations at the bearing capacity ultimate limit state; 1) The National Building Code of Canada (NBCC) published by the National Research Council of Canada (2010), 2) The Canadian Highway Bridge Design Code (CHBDC) published by the Canadian Standards Association (2006), 3) AASHTO LRFD Bridge Design Specifications (AASHTO), published by the American Association of State Highway and Transportation Officials (2007), 4) The Eurocode, in particular Eurocode 0 (Basis of Structural Design, British Standard, 2002a), Eurocode 1 (Actions on Structures – Part 1-1: General Actions, British Standard, 2002b) and Eurocode 7-1 (Geotechnical Design – Part 1: General Rules, British Standard, 2004), 5) Australian Standard AS5100 (Bridge Design, Standards Australia, 2004) To compare the level of safety between each of these codes, a hypothetical geotechnical system will be considered which has dead to live load ratio RD/L = 3.0. The Eurocode is reasonably specific as to how characteristic loads are defined. With respect to dead loads, the Eurocode 0 (British Standards, 2002a) states that the variability of permanent actions (i.e. dead loads) may be neglected if they do not vary significantly over the design working life. In other words, if the coefficient of variation of dead loads, vD , is less than about 10%, then the dead loads can be considered to be non-random and FˆD = μD so that kD = 1.0. The other codes considered are less specific about the definition of characteristic dead loads, but generally indicate that FˆD is to be estimated using mean structural component weights. Bartlett et al. (2003) suggest that some dead load components are often forgotten or missed in the estimation process, so that in practice the characteristic (design) dead load is generally somewhat less than the true mean dead load and the dead load bias factor is more like 1.05 (see also Ellingwood et al., 1980). Since this error is probably common to all localities, it will be assumed here that kD = 1.05 for all codes considered. With respect to live loads, the North American codes define the characteristic live load as the mean maximum live load exerted on the structure over its design lifetime – for example, Clause 4.3.1 of ASCE-7 (2010) states that uniformly distributed live loads are the mean of the maximum load over the design lifetime. Although the NBCC does not specifically define the characteristic live load, Bartlett et al. (2003) implies that it has

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the same definition as ASCE-7. Both codes specify acceptable characteristic live load values which are typically somewhat higher than the actual mean maximum live load. For example, both the Canadian and US codes specify a uniform live load for office space of 2.4 kPa. Bartlett et al. (2003) suggest that, after reductions for influence or tributary area, the code specified characteristic live load is typically about 10% higher than the actual mean value, so that kL = 0.9 was adopted by Bartlett et al. in their calibration efforts for the 2005 edition of the NBCC. As also reported by Bartlett et al., this bias value is in reasonable agreement with ASCE-7. The Eurocode 0 (British Standard, 2002a) states in Clause 4.1.2(7) that, for variable actions, the characteristic value shall correspond to one of; an upper value with an intended probability of not being exceeded or a lower value with an intended probability of being achieved, during some specific reference period; or a nominal value, which may be specified in cases where a statistical distribution is not known. This is a fairly vague definition, but Clause 4.1.2(4) suggests that an “upper value” (which would be of interest for loads) corresponds to a 5% probability of being exceeded (95% fractile). Clause 4.1.2(4) further states that the action may be assumed to be Gaussian. If this is assumed, then the 95% fractile is given by

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FˆL = μL (1 + 1.645vL)

→

kL = 1/ (1 + 1.645vL)

(14)

where vL is the coefficient of variation of the maximum lifetime live load. Both Allen (1975) and Bartlett et al. (2003) use vL = 0.27. The author is not sure what value of vL was assumed in the Eurocode, but Ellingwood (1999) suggests that Europe uses a similar value to that used in North America. If this is the case, then the Eurocode is using kL = 0.69, which is very close to Allen’s (1975) suggested bias of 0.7. Another approach to estimating the live load bias factor employed in Europe is to consider the characteristic office occupancy uniform live load specified in the European and North American codes, which are 3.0 and 2.4 kPa, respectively. If the live load bias factor of kL = 0.9, adopted by Bartlett et al. (2003), is assumed true for North America, then μL = 0.9(2.4) = 2.16 kPa. If it is further assumed that this mean live load is at least approximately true in Europe, then the European live load bias factor is kL = 2.16/3.0 = 0.72. On the basis of both of the above approximate calculations, it appears likely, then, that the Eurocode uses a live load bias factor of approximately kL = 0.70. The Australian Standard AS5100.1 (Standards Australia, 2004a) specifically defines load actions for ultimate limit state as “an action having a 5% probability of exceedance in the design life” in Clause 6.5. This is the same as used in the Eurocode (albeit more clearly specified). In addition, since the Australian- New Zealand “Structural Design Actions” Standard AS/NZS 1170 (Standards Australia, 2002a) specifies that the characteristic uniform live load for office buildings is 3.0 kPa, which is the same as the Eurocode, it appears that the live bias factor for Australia is also kL = 0.70. 2.2. Characteristic Resistance and Bias Factors The estimation of the resistance of the ground to imposed loads is generally a multi-step process: 1) take measurements of the ground properties, 2) correlate the measurements with characteristic engineering parameters (e.g. cohesion and friction angle), and 3) use the characteristic parameters in a prediction model. Each step introduces errors, and so

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G.A. Fenton / Geotechnical Design Code Development in Canada

the characteristic resistance and associated resistance factor (discussed later), along with the loads and load factors, must be found in such a way to ensure a safe design. Eurocode 7-1, Clause 2.4.5.2 (British Standard, 2004) provides a number of requirements for the selection of characteristic properties, such as “The characteristic value of a geotechnical parameter shall be selected as a cautious estimate of the value affecting the occurrence of the limit state” and “If statistical methods are used, the characteristic value should be derived such that the calculated probability of a worse value governing the occurrence of the limit state under consideration is not greater than 5%. NOTE: In this respect, a cautious estimate of the mean value is a selection of the mean value of the limited set of geotechnical parameter values, with a confidence level of 95%; where local failure is concerned, a cautious estimate of the low value is a 5% fractile.” The Eurocode 0 (British Standard, 2002) states that “where a low value of material or product property is unfavourable, the characteristic value should be defined as the 5% fractile value.” According to Schneider (2012), the characteristic ground parameters should be selected as a 5% fractile value of the sample mean, using the distribution of the sample mean, rather than √ that of the samples directly (the sample mean having standard deviation s/ n, where s is the sample standard deviation, and n is the number of samples used to estimate s). The author notes that a 5% fractile value based on the sample mean will generally be quite a bit less conservative than a 5% fractile based on the samples themselves. Hicks (2012) interprets Clause 2.4.5.2 of Eurocode 7-1 as meaning that the characteristic soil parameters are to be selected so as to ensure a 95% confidence in the geotechnical system being designed. While this is a reasonable interpretation, it will involve both the distribution of the applied maximum lifetime load and an appropriate spatial averaging of geotechnical parameters over the actual failure surface (or failure domain). The author feels that it is probably easier to develop a design code using characteristic soil parameters based on fractiles of the soil parameter distribution at this point in time. In any case, the above discussion about characteristic values used in the Eurocode refers to the selection of characteristic strength parameters (e.g. cu or φ ) rather than to the characteristic resistance appearing in Eq. (3). The characteristic geotechnical resistance, Rˆu , would then be computed employing a (probably non-linear) model which uses these characteristic ground parameters. Thus, the final bias of the characteristic resistance depends not only on the distribution of the ground properties, but also on the model used to predict Rˆu . It will be assumed here that the coefficient of variation, vR , of Rˆ u is approximately equal to the coefficient of variation of the ground parameters used in the model, which are typically in the range of 0.1 to 0.3 (e.g., Meyerhof, 1995 and Phoon and Kulhawy, 1999). Note that geotechnical resistance often involves an average of ground properties, e.g. along a failure surface, which will have a smaller variability than the point variability suggested in the literature. Thus, a reasonable value for the resistance variability is deemed to be about vR = 0.15, which will be assumed here. Similar to Eq. (14), the resistance bias factor assumed in the Eurocode can be computed from Rˆ u = μR (1 − 1.645vR)

→

kR = 1/ (1 − 1.645vR)

(15)

which for vR = 0.15 gives kR = 1.33. The Australian Standard AS5100.3 (Standards Australia, 2004b) states that “the characteristic value of a geotechnical parameter should be a conservatively assessed value of the parameter.” Although the author was unable to find a more precise defini-

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tion, the wording here suggests that the Australians are following the Eurocode approach. Thus, a bias factor of kR = 1.33 will be assumed for Australia as well. In North America, Commentary Clause C10.4.6.1 of AASHTO (2007) says that “For strength limit states, average measured values were used to calibrate the resistance factors”, which suggests that kR = 1.0. However, the commentary goes on to say that “it may not be possible to reliably estimate the average value of the properties needed for design. In such cases, the Engineer may have no choice but to use a more conservative selection of design properties” which suggests that in practice, kR > 1.0. Clause 8.5 of the Canadian Foundation Engineering Manual (Canadian Geotechnical Society, 2006) states that “Frequently, the mean value, or a value slightly less than the mean is selected by geotechnical engineers as the characteristic value.” Commentary K of the NBCC User’s Guide (National Research Council of Canada, 2011) says that “the [characteristic] resistance is the engineer’s best estimate of the ultimate resistance.” Becker (1996a) claims “The design values do not necessarily need to be taken as the mean values, although this is common geotechnical design practice.” All of these statements suggest that kR = 1.0, or perhaps slightly greater than 1.0. However, Becker (1996a) later argues that the characteristic resistance is typically selected to be somewhat below the mean, due to sampling uncertainties, and he subsequently uses kR = 1.1 in his NBCC development paper (Becker, 1996b). Based on Becker’s reasoning, the value of kR = 1.1 will be assumed to apply to all of the North American design codes considered here. 2.3. Load Factors

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Load factors are designed to reflect uncertainty in the lifetime loads experienced by a structure or foundation. The basic idea is to set the factored loads, αL FˆL and αD FˆD , to values having sufficiently low probability of being exceeded by the true (random) lifetime loads. Considering, for example, live loads (with dead loads following the same reasoning), the factored live load which has probability ε of being exceeded by the true live load over the design lifetime can be approximated as

αL FˆL = μL (1 + zε vL )

(16)

in which zε is the standard normal point with exceedance probability ε , i.e. the point such that Φ(−zε ) = ε , where Φ is the standard normal cumulative distribution function. Note that Eq. (16) assumes that the live load is (at least approximately) normally distributed. Rearranging Eq. (16) leads to an expression for the load factor, which is 

αL =

μL FˆL

 (1 + zε vL ) = kL (1 + zε vL )

(17)

ASCE-7 (American Society of Civil Engineers, 2010) found that their load factors are well approximated by Eq. (17) when they set zε = ωL β , where β is the target reliability index and ωL = 0.8 when L is a principle action or ωL = 0.4 when L is a companion action. Equation (17) can be used for other load types simply by changing the subscript. Note that Eq. (17) suggests that load factors are independent of the resistance distribution. It also states that the load factors are very dependent on how the characteristic load is defined, i.e. on the load bias factor, k. If designs have a common target

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G.A. Fenton / Geotechnical Design Code Development in Canada

reliability index, β , and kL = 0.9 in North America and kL = 0.7 in Europe and Australia, as suggested above, then one would expect the load factors in Europe and Australia to be lower than those used in North America if Eq. (17) is accurate. As will be seen, the European and Australian load factors are generally higher than those used in North America – the European and Australian codes compensate for their higher load factors through higher resistance factors. In other words, Eq. (17) cannot be used as a general formula for load factors. The magnitude of the resistance factors (and bias factors) must still be considered. Table 2 gives the load factors as specified by the various design codes considered here. The last column of the table gives the total load factor, αT , for a given mean dead to live load ratio, which scales the total mean load, μL + μD , to be equal to the sum of factored live and dead loads. The total load factor can be seen in Eq. (13) and is defined by 

αT =

αL αD RD/L + kL kD



1 1 + RD/L

 (18)

Table 2 Load and bias factors for various design codes.

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Source NBCC 2012 CHBDC 2006 AASHTO 2007 Eurocode 7 AS5100.3

kL 0.9 0.9 0.9 0.7 0.7

kD 1.05 1.05 1.05 1.05 1.05

αL 1.50 1.70 1.75 1.50 1.80

αD 1.25 1.20 1.25 1.35 1.20

αT 1.31 1.33 1.38 1.50 1.50

The dead load factor for the Eurocode (1.35) is larger than the dead load factors used in North America (1.2 to 1.25) which, when combined with the smaller value of kL , yields a final αT value which is significantly larger than that appearing in the Canadian codes and in AASHTO. The Australian Standard AS5100 has the second highest αT value because of their relatively high live load factor, αL , and low live load bias factor, kL . Table 3 shows the total effective load factor, the resistance bias, the resistance factor, and the global factor of safety for the five design codes considered with respect to shallow foundation bearing capacity (assuming Design Approach 2 and the GEO limit state for the Eurocode). Table 3 Global factor of safety for various design codes. Source NBCC 20121 CHBDC 2006 AASHTO 2007 Eurocode 72 AS5100.3

αT 1.31 1.33 1.38 1.50 1.50

kR 1.1 1.1 1.1 1.33 1.33

ϕgu 0.50 0.50 0.45 − 0.5 0.71 0.35 − 0.65

Fs 2.88 2.93 3.04 − 3.37 2.81 3.07 − 5.70

1

the NBCC itself does not specify resistance factors.The resistance factors shown above appear in Appendix K of the NBCC User’s Guide (National Research Council, 2011). 2 based on Eurocode 7 Design Approach 2 for the GEO limit state. Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

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Perhaps unsurprisingly, and despite the considerable variation in implementation details, the five codes considered here all arrive at quite similar global factors of safety, Fs , as seen in the last column of Table 3. Many assumptions were made in arriving at Table 3 about how characteristic values are actually defined in the various codes, and so there may actually be more discrepancy between the codes for this particular limit state. However, it appears likely that codes are calibrated for much the same target failure probability regardless of the implementation details. The author notes that, if this is the case, there seems to be little justification in codes being different – we might as well all adopt the same model and work in common towards a safer and more economical design code. The model adopted worldwide should be the simplest and easiest to define.

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3. Future Directions Geotechnical engineers are, of course, well aware of the fact that their designs depend on one of the most uncertain of all engineering materials. Unlike wood, concrete, steel, and other quality controlled engineering materials, it is not even known how the natural variability of soil properties should properly be characterized. In addition, geotechnical engineers are also aware that their uncertainty about the resistance of a geotechnical system decreases with increased site understanding and site modeling effort. Thus, there is a real desire amongst the geotechnical community that their designs reflect the degree of their site and modeling understanding. In other words, geotechnical designs should become more economical as site and model understanding increases. To accomplish this, it makes sense to have a resistance factor which is adjusted as a function of site and model understanding. There are at least two advantages to such an approach: 1) overall safety can be maintained at a common target maximum failure probability, and 2) the direct economic advantage to having site and model understanding can be demonstrated. For example, the current Canadian design codes specify a single resistance factor for bearing capacity design (0.5). It doesn’t matter how confident one is in one’s prediction of the bearing capacity of a foundation, the same resistance factor must be used. Thus, there is no direct advantage to improving the geotechnical response prediction if only a single resistance factor can be used – one might as well spend the least one can on the site investigation and modeling since the resistance factor cannot currently be increased. The resulting desire for a resistance factor which depends on site and model understanding is not new. In 1991, the Institution of Civil Engineers (1991) made the classic observation that “You pay for a site investigation whether you have one or not,” which is, as we all know, entirely true. Recognizing this fact, it is of real economic value to have a sliding resistance factor to reflect the true lifetime cost of the lack or presence of a site investigation. The Australian Standard for Bridge Design, Part 3: Foundations and Soil-Supporting Structures (AS 5100.3, Standards Australia, 2004b) has provided a range in “geotechnical strength reduction factors” since 2004 with worded guidance as to which end of the scale should be used. For example, AS 5100.3 suggests that the lower end of the resistance factor range (more conservative) should be used for limited site investigations, simple methods of calculation, severe failure consequences, and so on. It is of interest to note that the Australian Standard recommendations for the resistance factor considers both site and model understanding and failure consequence in their single factor.

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As is well known, the overall safety level of any design should depend on at least three things: 1) the uncertainty in the loads, 2) the uncertainty in the resistance, and 3) the severity of the failure consequences. These three items are all basically independent of one another and in most modern codes are thus treated separately, as is reasonable. In most codes, uncertainties in the loads are handled by load and load combination factors, failure consequences are handled by applying a multiplicative importance factor to the more uncertain loads (e.g. earthquake, snow, and wind), and uncertainties in resistance are handled by material specific resistance factors (e.g. ϕc for concrete, ϕs for steel, etc). Because the ground is so highly uncertain, similarly to earthquake, snow, and wind loads, it makes sense to apply a partial safety factor to the ground that depends on both the resistance uncertainty and consequence of failure. This would be analogous to how wind load, for example, in the NBCC (NRC, 2010) has both a load factor associated with wind speed uncertainty as well as an importance factor associated with failure consequences. Figure 1 illustrates the basic idea, where the overall partial factor applied to the geotechnical resistance varies with both uncertainty and failure consequence. The numbers in the figure are relative to the default central partial factor (i.e. relative to 1.0) and it is assumed that current geotechnical design approaches in Canada lead to typical or default levels of site and model understanding so that, for typical failure consequence geotechnical systems, the central value is what is currently used in design. From this value, increased site investigation and/or modeling effort leads to lower uncertainty and a higher resistance factor (and a more economical design). Similarly, for geotechnical systems with high failure consequences, e.g. failure of the foundation of a major multi-lane highway bridge in a capital city, the resistance factor is decreased to ensure a decreased maximum acceptable failure probability. Of particular note in Figure 1 is the fact that if a geotechnical system with high failure consequences is designed with high site and model uncertainty, the designer is penalized by a low partial factor.

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HIGH Consequence 1.0

0.8

0.6

TYPICAL

1.2

1.0 (default)

0.8

LOW Consequence

1.4

1.2

1.0

LOW TYPICAL HIGH Uncertainty Uncertainty Figure 1. Floating partial safety factor, relative to the default, applied to geotechnical resistance (numbers are for illustration only). Figure 1 suggests that for each limit state (e.g. bearing, sliding, overturning, etc.) a 3 x 3 matrix of resistance factors would have to be provided. Rather than introducing the resulting myriad tables, the multiplicative approach taken in structural engineer-

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G.A. Fenton / Geotechnical Design Code Development in Canada

289

ing (where the load is multiplied by both a load factor and an importance factor) will be adopted for geotechnical resistance as well. In other words, the overall safety factor applied to geotechnical resistance is broken into two parts; 1) a resistance factor, ϕgu or ϕgs , which accounts for resistance uncertainty. This factor basically aims to achieve a target maximum acceptable failure probability equal to that used currently for geotechnical designs for typical failure consequences (e.g. lifetime failure probability of 1/5,000 or less). The subscript g refers to ‘geotechnical’ (or ‘ground’), while the subscripts u and s refer to ultimate and serviceability limit states, respectively. 2) a consequence factor, Ψ, which accounts for failure consequences. Essentially, Ψ > 1 if failure consequences are low and Ψ < 1 if failure consequence exceed those of typical geotechnical systems. For typical systems, or where system importance is already accounted for adequately by load importance factors, Ψ = 1. The basic idea of the consequence factor is to adjust the maximum acceptable failure probability of the design down (e.g. 1/10,000) for high failure consequences, or up (e.g. 1/1,000) for low failure consequences. The geotechnical design would then proceed by ensuring that the factored geotechnical resistance at least equals the effect of factored loads. For example, for ultimate limit states, this means that in Canada the geotechnical design will soon need to satisfy an equation of the form Ψϕgu Rˆ ≥ ∑ Ii ηi αui Fˆui

(19)

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i

which is almost identical to Eq. (2), with the exception that the overall geotechnical resistance factor is expressed as the product of the consequence factor, Ψ, and the ultimate geotechnical resistance factor, ϕgu , and the loads and load factors appearing on the righthand-side are also those specific for the ultimate limit state under consideration (and, hence, the subscript u). An entirely similar equation must be satisfied for serviceability limit states, with the subscript u replaced by s. The serviceability geotechnical resistance factors, ϕgs , will be closer to 1.0 than ϕgu , since serviceability limit states can have larger maximum acceptable probabilities of occurrence. In Eq. (19), the value of Ψ is shown as being independent of the ultimate or serviceability limit states (not subscripted by u or s). It is currently not known if this is true. It is known that the target maximum failure probabilities for serviceability limit states are greater than those for ultimate limit states. For example, a typical geotechnical system might have a target maximum lifetime failure probability of 1/5, 000 for ultimate limit states, but only 1/500 for serviceability limit states. If the geotechnical system has high failure consequences, the lifetime maximum acceptable failure probability might decrease by the same fraction, i.e. to 1/10, 000 for ULS and to 1/1, 000 for SLS. Thus, it is suspected that the same (or similar) consequence factor can be used to scale the target maximum acceptable failure probability for both ULS and SLS designs, since the probabilities scale by the same amount. This is a topic of further investigation. The geotechnical resistance factor, ϕgu or ϕgs , depends on the degree of site and prediction model understanding. Three levels will be considered in the future editions of the building and highway codes in Canada;

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• High understanding: Extensive project-specific investigation procedures and/or knowledge are combined with prediction models of demonstrated (or proven) quality to achieve a high level of confidence in performance predictions, • Typical understanding: Usual project-specific investigation procedures and/or knowledge are combined with conventional prediction models to achieve a typical level of confidence in performance predictions, • Low understanding: Understanding of the ground properties and behaviour are based on limited representative information (e.g. previous experience, extrapolation from nearby and/or similar sites, etc.) combined with conventional prediction models to achieve a lower level of confidence with the performance predictions. The resulting table for ULS geotechnical resistance factors to appear in future Canadian codes will look something like Table 4. NOTE: the numerical values appearing in Table 4 are purely illustrative and have yet to be determined.

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The SLS geotechnical resistance factors will appear in a very similar table, an example of which appears in Table 5. Again, all numbers are for illustration only. The consequence factor, Ψ, adjusts the maximum acceptable failure probability of the geotechnical system being designed to a value which is appropriate for the consequences. Three failure consequence levels will be considered in future Canadian geotechnical design codes; • High consequence: the geotechnical system is designed to be essential to postdisaster recovery (e.g. hospital or lifeline bridge), and/or has large societal and/or economic impacts. • Typical consequence: the geotechnical system is designed for typical failure consequences, e.g. the usual office building, bridge, etc. This will be the default failure consequence level. • Low consequence: failure of the geotechnical system poses little threat to human or environmental safety, e.g. storage facilities, temporary structures, very low traffic volume bridges, etc. Table 4 Example table of ultimate limit state geotechnical resistance factors (static loading), ϕgu . All numbers are for illustration only – factors have not yet been determined. Limit State Shallow Foundations Bearing resistance Passive resistance Horizontal resistance (sliding) Ground Anchors Static Analysis – tension Static Test – tension Deep Foundations – Piles Static Analysis Compression Tension etc.

Degree of Understanding Low Typical High 0.45 0.40 0.75

0.50 0.50 0.80

0.60 0.60 0.85

0.30 0.55

0.40 0.60

0.50 0.65

0.35 0.35

0.40 0.40

0.50 0.45

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Table 5 Example table of serviceability limit state geotechnical resistance factors (static loading), ϕgs . All numbers are for illustration only – factors have not yet been determined. Limit State

Degree of Understanding Low Typical High

Shallow Foundations Settlement Embankments Settlement Lateral displacement Deep Foundations – Piles Settlement Lateral displacements etc.

0.70

0.90

1.00

0.70 0.60

0.80 0.70

0.90 0.80

0.80 0.70

0.90 0.80

1.00 0.90

Table 6 illustrates how the consequence factor table will appear in future Canadian geotechnical design codes. As with Tables 4 and 5, the factors are not finalized and are for illustration only. Table 6 Example consequence factor table for the Canadian Highway Bridge Design Code. Numbers are for illustration only. Consequence Level High Typical Low

Example Lifelines, Emergency Highway Bridges Secondary Bridges

Consequence Factor, Ψ 0.9 1.0 1.1

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4. Conclusions The evolution of geotechnical design codes, from traditional working stress design (factor of safety) to reliability-based design approaches, has been lagging well behind structural design codes. There is no question that this lag is due to the much larger uncertainty about the ground than exists with most other engineering materials. A batch of 30 MPa concrete will have pretty much the same distribution in strength properties whether ordered in Calgary or in Tokyo. On the other hand, the ground properties at sites in these two cities will almost certainly be significantly different – in fact, ground properties will usually differ from point to point within the same site. In general, all sources of uncertainty entering into the LRFD equation (e.g. Eq. 2) are factored to arrive at an acceptably safe design solution. The factors applied are related to the magnitude of the uncertainty in the parameter being factored. For example, the uncertainty associated with steel reinforcing is less than that with concrete and so the steel resistance factor is closer to 1.0 than is the concrete resistance factor. Reduced uncertainty about an engineering material results in an increased resistance factor. The ground is simply another engineering material and the resistance factor associated with the ground should be related to its site specific uncertainty. Since the distribution of the

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ground strength varies from site to site and even within a site, it makes sense to relate the geotechnical resistance factor to the magnitude of the residual uncertainty, i.e. the uncertainty remaining after site investigation and modeling efforts have been accounted for. The structural design codes in Canada also recognize the fact that some of the parameters in the LRFD equation are highly variable and so need to be treated with special consideration in the event that the system being designed is of higher or lesser importance, i.e. if the failure consequences are higher or lower than usual. Because earthquake, wind, and snow load are highly variable and have site specific distributions, both the NBCC and the CHBDC apply importance factors to these loads. The importance factors increase with increasing system importance. Similarly, ground properties are both highly variable and site specific, and so the application of a factor to account for system importance is appropriate on the resistance side. With the above thoughts in mind, the next editions of the Canadian Highway Bridge Design Code and the National Building Code of Canada will include several philosophical changes to their geotechnical design provisions. These include; • the introduction of three levels of site and model understanding – high, typical, and low – through the ULS and SLS resistance factors. These factors are intended to account for site and modeling uncertainties and are aimed at producing a design with a target maximum acceptable failure probability for typical geotechnical systems (i.e. systems having typical failure consequence levels). For example, ULS and SLS maximum acceptable lifetime failure probabilities might be 1/5,000 and 1/500, respectively, and so these resistance factors would be targeted at these values. • the introduction of three levels of failure consequence – high, typical, and low – through a consequence factor which multiplies the factored resistance. The basic idea of the consequence factor is to allow the target maximum acceptable lifetime failure probability provided by the resistance factor to be adjusted up or down depending on whether the failure consequences are lower or higher than typical. Research into the determination of the required resistance and consequence factors for the Canadian codes is ongoing. The consequence factor is a new idea and work is still needed to determine when it should and should not be applied. For example, whether both the consequence factor and importance factors should be applied simultaneously is unknown, but initially, they will not be.

References Allen, D.E. (1975). Limit States Design – A probabilistic study, Canadian Journal of Civil Engineering 2(1), 36–49. American Association of State Highway and Transportation Officials (2007). LRFD Bridge Design Specifications, Washington, DC. American Society of Civil Engineers (2010). Minimum Design Loads for Buildings and Other Structures, ASCE Standard ASCE/SEI 7-10, Reston, Virginia. Bartlett, F.M., Hong, H.P. and Zhou, W. (2003). Load factor calibration for the proposed 2005 edition of the National Building Code of Canada: Statistics of loads and load effects, Canadian Journal of Civil Engineering 30(2), 429–439. Becker, D.E. (1996a). Eighteenth Canadian Geotechnical Colloquium: Limit states design for foundations. Part 1. An overview of the foundation design process, Canadian Geotechnical Journal 33(6), 956–983.

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Becker, D.E. (1996b). Eighteenth Canadian Geotechnical Colloquium: Limit states design for foundations. Part II. Development for the National Building Code of Canada, Canadian Geotechnical Journal 33(6), 984–1007. British Standard BS EN 1990 (2002a). Eurocode – Basis of Structural Design, CEN (European Committee for Standardization), Brussels. British Standard BS EN 1991-1-1 (2002b). Eurocode 1: Actions on Structures – Part 1-1: General Actions – Densities, Self-weight, Imposed Load for Buildings, CEN (European Committee for Standardization), Brussels. British Standard BS EN 1997-1:2004 (2004). Eurocode 7: Geotechnical design – Part 1: General rules, CEN (European Committee for Standardization), Brussels. Canadian Geotechnical Society (1992). Canadian Foundation Engineering Manual, 3rd Ed., Montreal, Quebec. Canadian Geotechnical Society (2006). Canadian Foundation Engineering Manual, 4th Ed., Montreal, Quebec. Canadian Standards Association (2006). Canadian Highway Bridge Design Code, CAN/CSA-S6-06, Mississauga, Ontario. Danish Geotechnical Institute (1985). Code of Practice for Foundation Engineering, DGI-Bulletin No. 36, Copenhagen. Ellingwood, B.R. (1999). A Comparison of General Design and Load Requirements in Building Codes in Canada, Mexico, and the United States, Engineering Journal 2, 67–81. Ellingwood, B.R., Galambos, T.V., MacGregor, J.G. and Cornell, C.A. (1980). Development of a Probability Based Load Criterion for American National Standard A58: Building Code Requirements for Minimum Design Loads in Buildings and Other Structures, National Bureau of Standards, U.S. Dept. of Commerce, NSC Special Publication 577, Washington, D.C.. Green, R. and Becker, D. (2000). National report on limit state design in geotechnical engineering: Canada, in LSD2000: International Workshop on Limit State Design in Geotechnical Engineering, ISSMGE, TC23, Melbourne, Australia. Hicks, M.A. (2012). An explanation of characteristic values of soil properties in Eurocode 7, in Modern Geotechnical Design Codes of Practice - Development, Calibration & Experiences, edited by Arnold, P., Fenton, G.A., Hicks, M.A., Schweckendiek, T. and Simpson, B., IOS Press, Amsterdam, The Netherlands. Institution of Civil Engineers (1991). Inadequate Site Investigation, Thomas Telford, London. Meyerhof, G.G. (1951). The ultimate bearing capacity of foundations. G´eotechnique 2(4), 301–332. Meyerhof, G.G. (1963). Some recent research on the bearing capacity of foundations, Canadian Geotechnical Journal 1(1), 16–26. Meyerhof, G.G. (1995). Development of geotechnical limit state design. Canadian Geotechnical Journal 32(1), 128–136. NCHRP (1991). Manuals for the Design of Bridge Foundations, Report 343, National Cooperative Highway Research Program, Transportation Research Board, NRC, Washington, DC. NCHRP (2004). Load and Resistance Factors for Earth Pressures on Bridge Substructurs and Retaining Walls, Report 12-55, D’Appolinia and the University of Michigan, National Cooperative Highway Research Program, Transportation Research Board, NRC, Washington, DC. National Research Council (2011). User’s Guide – NBC 2010 Structural Commentaries (Part 4 of Division B), 3rd Ed., National Research Council of Canada, Ottawa. National Research Council (2010). National Building Code of Canada, 13th Ed., National Research Council of Canada, Ottawa.

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Phoon, K-K., and Kulhawy, F.H. (1999). Characterization of geotechnical variability, Canadian Geotechnical Journal 36(4), 612–624. Prandtl, L. 1921. Uber die Eindringungsfestigkeit (Harte) plastischer Baustoffe und die Festigkeit von Schneiden, Zeitschrift fur angewandte Mathematik und Mechanik 1(1), 15–20. Schneider, H.R. 2012. Dealing with uncertainties in EC7 with emphasis on determination of characteristic soil properties, in Modern Geotechnical Design Codes of Practice - Development, Calibration & Experiences, edited by Arnold, P., Fenton, G.A., Hicks, M.A., Schweckendiek, T. and Simpson, B., IOS Press, Amsterdam, The Netherlands. Standards Australia (2002a). Structural Design Actions, Part 1: Permanent, imposed and other actions, Australian/New Zealand Standard, AS 1170.1:2002, Sydney, Australia. Standards Australia (2002b). Earth-Retaining Structures, Australian Standard AS 4678– 2002, Sydney, Australia. Standards Australia (2004a). Bridge Design, Part 1: Scope and General Principles, Australian Standard AS 5100.1–2004, Sydney, Australia. Standards Australia (2004b). Bridge Design, Part 3: Foundations and Soil-Supporting Structures, Australian Standard AS 5100.3–2004, Sydney, Australia.

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295

Can We Do Better Than the Constant Partial Factor Design Format? a

Kok-Kwang PHOONa,1 and Jianye CHING b Department of Civil and Environmental Engineering, National University of Singapore, Singapore b Department of Civil Engineering, National Taiwan University, Taiwan

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Abstract. A partial factor format involves multiplying a nominal resistance such as the mean bearing capacity by a resistance factor or dividing a characteristic strength such as the lower 5% undrained shear strength by a partial factor. The purpose of a partial factor format is to implement reliability-based design without requiring the engineer to perform reliability analysis. Hence, the performance of a partial factor format must be measured by its ability to produce designs achieving a desired target reliability index within an acceptable error margin. It is an article of faith that it is possible to achieve an approximately consistent reliability index by recommending a single numerical value for a single resistance factor. This practice is widely adopted in the form of the Load and Resistance Factor Design (LRFD) approach. Based on the examples studied in this paper (pile installed in homogeneous clay and pile installed in clay and sand), it is demonstrated numerically that the deviation from the target reliability index can be so large, particularly on the unconservative side, that the purpose of reliability calibration becomes nearly meaningless. In other words, the partial factor format may not perform significantly better than an uncalibrated format in achieving the prescribed target reliability index. In our opinion, it is difficult to provide a compelling reason to engineers to go through the hassle of changing a code format in this case. If a design guide is insistent on recommending a single numerical value in association with a partial factor format, it is more sensible to recommend a constant quantile value, rather than a constant resistance factor. Keywords. Partial factor format, reliability calibration, LRFD, MRFD, piles.

Introduction Reliability-based design is presently implemented in the form of familiar “look and feel” code formats such as the partial factor format, Load and Resistance Factor Design (LRFD) format, and Multiple Resistance Factor Design (MRFD) format (Phoon et al. 2003b), among others. The common feature of these formats involves multiplying a nominal resistance such as the mean bearing capacity by a resistance factor or dividing a characteristic strength such as the lower 5% undrained shear strength by a partial factor. For brevity, we broadly term these code formats as partial factor formats. From the perspective of an engineer, there is no difference between applying partial factor formats and the prevailing factor of safety format, other than adopting a different numerical value or more commonly, a set of numerical values for different 1

Department of Civil and Environmental Engineering, National University of Singapore, Block E1A, #07-03, 1 Engineering Drive 2, Singapore 117576, Singapore; Email: [email protected]. Modern Geotechnical Design Codes of Practice : Implementation, Application and Development, IOS Press, Incorporated, 2012.

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resistance and load components mandated in such codes. The key difference lies with the design goal. In partial factor formats, the numerical values of these factors are not based purely on experience or precedents, but calibrated by the code developer using reliability analysis to achieve a desired target reliability index. It is clear that partial factor formats are meant to implement reliability-based design without requiring the engineer to perform reliability analysis. The obvious limitation associated with replacing reliability analysis with a simple multi-factor algebraic design check is that the target reliability index cannot be achieved exactly. The performance of a partial factor format must be measured by its ability to produce designs achieving a desired target reliability index within an acceptable error margin. When the partial factor format is first introduced into a design code, it should preferably produce designs comparable to those produced by the factor of safety method for continuity with past practice and experience. In fact, the target reliability index is commonly prescribed to comply with this judicious continuity principle. However, the primary goal must be to maintain a uniform level of reliability – this is the key basis for switching to reliability-based design in the first place. For a partial factor format, the ability to maintain a uniform level of reliability is primarily related to the range of design scenarios covered by the code and the number of available partial factors that can be “tuned” during the reliability calibration process. A partial factor format should reveal the maximum deviation from the target reliability index among the range of design scenarios appearing in the calibration domain. In principle, application of a partial factor format to a design scenario lying outside the calibration domain can produce a reliability index far from the target value. Hence, it is important to state the salient features of the underlying calibration domain explicitly in association with any partial factor format to avoid conveying the impression that it can be applied to any design scenario, which is unlikely to be true. One noteworthy feature of this calibration domain that is distinctive to geotechnical engineering is that coefficients of variation of geotechnical parameters can vary over a wide range, because of diverse evaluation methodologies to cater for diverse practice and site conditions. It is easy to envisage that a single partial factor is unable to achieve a uniform reliability index if the range of coefficients of variation is sufficiently large, say between 10% and 70% for undrained shear strength estimated using different methods as shown in Table 1. There are three ways to respond to this issue. One, the code developer accepts a large error band in the actual reliability indices produced by the partial factor format. Nonetheless, this paper shows that the error can be so large, particularly on the unconservative side, that the purpose of reliability calibration becomes nearly meaningless. In other words, the partial factor format may not perform significantly better than an uncalibrated format in achieving the prescribed target reliability index. In our opinion, it is difficult to provide a compelling reason to engineers to go through the hassle of changing a code format in this case. Second, the range of coefficients of variation is fortuitously narrow for the design scenarios commonly found in a particular locale. This is an unlikely situation for large countries with diverse geologic conditions and diverse local practice. Third, the range of coefficients of variation is divided into sufficiently small segments during reliability calibration such that a constant partial factor can assure a reasonably uniform reliability level over each segment. The third method is probably the most realistic approach currently. Phoon et al. (1995) proposed a simple three-tier scheme (low, medium, high) for coefficients of variation (Table 1) and calibrated LRFD and MRFD factors for each variability tier. In

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other words, three numerical values are associated with each LRFD/MRFD factor, rather than recommending a single numerical value for each LRFD factor (a practice commonly adopted in most structural design codes). The main drawback with this approach is that the reliability index may be affected by other deterministic/statistical parameters such as the mean value of a strength parameter. If the mean value of a strength parameter also varies over a wide range (not unusual in geotechnical engineering), then it must be considered in the calibration domain. Hence, the calibration domain involves two dimensions (coefficient of variation and mean of strength parameter). It is clear that there are nine calibration subdomains if each dimension is segmented into three parts as shown in Figure 1. There is a potential practical problem here associated with unwieldy proliferation of reliability-calibrated factors as the dimension of the calibration domain increases. It is possible to mitigate this problem slightly by deleting subdomains deemed unrealistic in practice, but the fundamental proliferation problem remains. Table 1. Ranges of soil property variability for reliability calibration (Phoon et al. 1995, updated Phoon & Kulhawy 2008). Property variability Coefficient of variation (%) Lowa 10 - 30 Mediumb 30 - 50 c 50 - 70 High Effective stress friction angle Lowa 5 - 10 Mediumb 10 - 15 c High 15 - 20 30 - 50 Horizontal stress coefficient Lowa Mediumb 50 - 70 Highc 70 - 90 a - typical of good quality direct lab or field measurements b - typical of indirect correlations with good field data, except for the standard penetration test (SPT) c - typical of indirect correlations with SPT field data and with strictly empirical correlations

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Geotechnical parameter Undrained shear strength

Fig. 1 Segmentation of 2D parameter space into 9 subdomains for reliability calibration (Phoon et al. 1995).

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There are two objectives in this paper. First, the degrees of deviation from the target reliability index produced by existing partial factor formats are demonstrated for piles in homogeneous and layered soils. It will be demonstrated that the performance of existing partial factor formats in the context of achieving the target reliability index can be poor under some fairly common circumstances. Second, the quantile value method proposed by Ching & Phoon (2011) is able to mitigate this poor performance associated with stretching one numerical value/partial factor to cover diverse calibration design scenarios on the one hand and proliferation of numerical values/partial factor arising from segmentation of calibration design scenarios on the other hand. It is accurate to say that considerable practical challenges remain in the development of a simplified reliability-based design format suitable for realistic application in geotechnical engineering, even for fairly routine pile design.

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1. Piles Installed in Homogeneous Clay Consider a pile installed in homogeneous clay with an average undrained shear strength = Su as shown in Figure 2. It is subjected to a dead load (DL) and a live load (LL). The diameter (B) of the pile is 1 m and the length is L. The loadings DL and LL are lognormally distributed with mean values (μDL, μLL) and coefficients of variation (c.o.v.) (δDL, δLL). Suppose that μLL/μDL = 0.5, δDL= 10%, and δLL = 20%. The undrained shear strength Su is lognormally distributed with mean value μsu and c.o.v. δsu. In this example, it is assumed that the pile is long and hence, it is reasonable to estimate the pile capacity based on the side resistance alone. The side resistance is computed using the α method = αSuπLB, in which the adhesion factor, α = 14.88 × εα × Su-0.7, 14.88 is an empirical coefficient for the correlation, and εα characterizes the model error. It is assumed that ln(εα) is normally distributed with mean = 0 and standard deviation = 0.3. This probabilistic model for the adhesion factor is obtained from calibration with instrumented load test data as shown in Figure 3 (Chen et al. 2012). It is important to note that the undrained shear strength is referenced with respect to the direct simple shear test (DSS). Failure is defined as the state in which the total load (DL+LL) exceeds the side resistance (tip resistance assumed to be minor) or the safety ratio is less than one:

SR(Y, θ) =

α(Su , εα )Su πLB (14.88εαS−u0.7 )Su πLB =

μ δ P⎜ 1 | , , L Su Su ⎜ 14.88 × Su−0.7 × ε α × Su × πLB ⎟ ⎜ ⎟ DL + LL ⎝ ⎠

(11)

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Because the mean dead load appears in the numerator and denominator of Eq. (11) (note that DL = μDL exp{-0.5ln(1+δDL2)-[ln(1+δDL2)]0.5ZDL} in which ZDL is a standard normal variable), it is not necessary to compute the critical mean dead load in this example. The average of the 1000 η values is the recommended quantile for design and it is denoted by η* in Tables 2 and 3. It suffices to note here that the optimization method requires the solution of Eq. (5) to obtain the resistance factor γR, while QVM requires the solution of Eq. (7) to obtained the average quantile η*. The reliability indices associated with 1000 randomly selected independent validation points, βV, can be computed via Monte Carlo simulation once the critical mean dead load is obtained from Eq. (10) with η = η*. The statistics of βV are reported in Tables 2 and 3. For this simple example, the following observations are clear: 1. It is better to calibrate a single value of η rather than a single value of γR. 2. QVM is less sensitive to the potentially wide range of resistance coefficients of variation in domain D. 3. QVM satisfies mean βV – minimum βV < 0.5 or standard deviation of βV < 0.5 without dividing D into subdomains. 4. In Table 2, QVM actually outperforms the resistance factor approach even when it is calibrated locally in each subdomain. The partial factor format based on QVM [i.e., Eq. (9)] and the partial factor format based on γR [i.e., Eq. (4)] are the same if we set: μsu−0.7

μ su = (Sηu ) −0.7 × εηα × Sηu γR

(12)

or γ R = exp ⎡0.15ln (1 + δsu2 ) − 0.3 ln (1 + δsu2 ) × Φ −1 ( η) − σln( εα ) × Φ −1 ( η)⎤ ⎣⎢ ⎦⎥

(13)

Based on Eq. (13), it is clear that the resistance factor implied by the QVM format is not a constant. The superior performance observed above can be attributed to this variable QVM-based resistance factor.

3. Piles Installed in Clay and Sand Consider a pile installed in a layer of clay with an average undrained shear strength = Su overlying a layer of sand with an average SPT N-value = N60 as shown in Figure 4. The side resistance in sand is correlated to the Standard Penetration Test (SPT) as 2.71×εN×N60×πLsB (kN/m2), in which Ls (m) is the shaft length supported in sand, 2.71

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is an empirical coefficient for the correlation, ln(εN) is normally distributed with mean = 0 and standard deviation = 0.63, and N60 is lognormally distributed with mean value μN and c.o.v. δN (Ching & Phoon 2012). This probabilistic model for the SPT N model is obtained from calibration with instrumented load test data as shown in Figure 5 (Chen et al. 2012).

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Fig. 4 Pile installed in clay and sand.

Fig. 5 fs-N correlation for drilled shafts in sand (Chen et al. 2012).

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The safety ratio for this example is:

SR(Y, θ) =

(14.88εαS−u0.7 )Su πLc B + 2.71ε N N 60 πLs B DL + LL

(14)

in which Lc = shaft length supported in clay. The safety ratio depends on a vector Y consisting of six lognormal random variables (Su, εα, N60, εN, DL, LL) and a vector θ consisting of five design parameters (μsu, δsu, μN, δN, Lc/L, L). The domain D is defined by the following representative ranges of values: 50 ≤ μsu ≤ 200 kN/m2, 0.1 ≤ δsu ≤ 0.5, 10 ≤ μN ≤ 50 blows/30 cm, 0.1 ≤ δN ≤ 0.5, 0 ≤ Lc/L ≤ 1, and 10 m ≤ L ≤ 50 m. The rest of the assumptions are identical to those adopted in the previous example: (a) shaft diameter (B) is 1 m and shaft length is L = Lc + Ls, (b) ln(εα) is normally distributed with mean = 0 and standard deviation = 0.3, (c) Su is lognormally distributed with mean value μsu and c.o.v. δsu, (d) DL and LL are lognormally distributed with mean values (μDL, μLL) and coefficients of variation (c.o.v.) (δDL, δLL), and (e) μLL/μDL = 0.5, δDL= 10%, and δLL = 20%. The optimization method [Eq. (5)] is applied to calibrate two partial factor formats for this example: 1.

Load Resistance Factor Design (LRFD)

[(14.88μ su−0.7 )μ su πLc B + 2.71μ N πLs B] / γ R ≥1 1.35μ DL + 1.5μ LL 2.

Multiple Load Resistance Factor Design (MRFD) (Phoon et al. 2003b)

(14.88μ su−0.7 )μ su πLc B / γ c + 2.71μ N πLs B / γ s ≥1 1.35μ DL + 1.5μ LL Copyright © 2012. IOS Press, Incorporated. All rights reserved.

(15a)

(15b)

The difference between LRFD and MRFD is that the former factors the overall resistance with a resistance factor γR, while the latter factors each resistance component separately with a factor γc for side resistance in clay and a factor γs for side resistance in sand. For both partial factor formats, optimization can be performed over the entire domain D (50 ≤ μsu ≤ 200 kN/m2, 0.1 ≤ δsu ≤ 0.5, 10 ≤ μN ≤ 50 blows/30 cm, 0.1 ≤ δN ≤ 0.5, 0 ≤ Lc/L ≤ 1, and 10 m ≤ L ≤ 50 m) or restricted to subdomains. As mentioned previously, the latter strategy will produce a table of values for each resistance factor, rather than a single value. As shown in Table 2, the c.o.v. of the undrained shear strength (δsu) has a minor effect on the resistance factor. Hence, the range of δsu is not segmented into two smaller parts. Rather than segmenting the ranges of values for μsu, μN, and Lc/L individually, a combined parameter called the mean resistance ratio is segmented into two smaller parts: 0 ≤ Rc ≤ 0.5 and 0.5 ≤ Rc ≤ 1. The parameter Rc is defined as:

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Rc =

(14.88μsu−0.7 )μsu πLc B (14.88μsu−0.7 )μsu πLc B + 2.71μ N πLs B

(16)

It is clear that Rc denotes the ratio of the nominal side resistance in clay to the total nominal side resistance. When Rc ≤ 0.5, the total side resistance is dominated by sand (Ls large and/or μN large) and vice-versa. Based on the above considerations, it is possible to define four concise subdomains: 1. 2. 3. 4.

0 ≤ Rc ≤ 0.5 and 0.1≤δN≤ 0.3 0.5 ≤ Rc ≤ 1 and 0.1≤δN≤ 0.3 0 ≤ Rc ≤ 0.5 and 0.3≤δN≤ 0.5 0.5 ≤ Rc ≤ 1 and 0.3≤δN≤ 0.5

For the quantile value method (QVM), the following partial factor format is calibrated:

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η 14.88 × (Sηu ) −0.7 × εαη × Sηu × πLc B + 2.71 × εηN × N 60 × πLs B ≥1 1.35μ DL + 1.5μ LL

(17)

It is worth emphasizing that the average quantile (η*) is computed over the entire domain D, i.e. the subdomain strategy is not implemented for QVM. The same calibration and validation approaches are adopted. The only computational difference is that the reliability indices for the calibration points are computed using the First-Order Reliability Method (FORM), rather than Monte Carlo simulation. The target reliability index in Eq. (5) is 3.8. The reliability indices for the validation points, βV, are computed using Monte Carlo simulation. Table 4 compares the performance of QVM with LRFD. It is clear that a layered soil profile poses considerable challenges to partial factor formats in general. If one adopts the more relaxed criterion requiring the standard deviation of βV to be less than 0.5, the performance of QVM can be considered to be reasonable. The standard LRFD that attempts to cover all design scenarios (which include piles supported in varying proportions of clay and sand) with a single resistance factor taking a single numerical value is not satisfactory, which is hardly unexpected. It is rather interesting that the four subdomains adopted in this study are not satisfactory as well, particularly for the subdomains where sand is dominant (0≤Rc≤0.5). A likely reason is that the model uncertainty associated with the evaluation of side resistance in sand using SPT-N is large. Obviously the subdomain strategy can be refined to perfection if one is willing to reduce the size of subdomains indefinitely. Table 5 compares the performance of QVM with MRFD. It is useful to note that the numerical values for γc and γs are distinctly different. This example nicely demonstrates in a concrete numerical way what many practitioners may have already suspected, namely a single resistance factor is too simplistic for design scenarios involving significantly different resistance components (in the statistical sense). For this example, MRFD is comparable to QVM. MRFD with subdomains is most effective in achieving a consistent reliability index across domain D.

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309

Table 4. Performance of optimization (LRFD) and quantile value methods for a single pile installed in clay and sand. Quantile value method (QVM)

Optimization method

η* = 0.043

No subdomains 0.1≤δN≤0.5 0≤Rc≤1 γR = 2.84

0.1≤δN≤0.3 0≤Rc≤0.5 γR = 3.45

0.1≤δN≤0.3 0.5≤Rc≤1 γR = 2.35

0.3≤δN≤0.5 0≤Rc≤0.5 γR = 3.82

0.3≤δN≤0.5 0.5≤Rc≤1 γR = 2.42

βV mean βV COV βV max βV min

3.81 0.10 4.42 2.51

3.74 0.21 4.42 1.67

3.74 0.19 4.42 2.22

3.91 0.04 4.17 3.40

3.68 0.21 4.42 2.02

3.91 0.05 4.17 3.39

mean - min std deviation

1.30 0.38

2.07 0.79

1.52 0.71

0.51 0.16

1.66 0.77

0.52 0.20

γR or η*

Four subdomains

Table 5. Performance of optimization (MRFD) and quantile value methods for a single pile installed in clay and sand. Quantile value method (QVM)

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γc, γs or η*

η* = 0.043

Optimization method No subdomains 0.1≤δN≤0.5 0≤Rc≤1 γc = 1.91 γs = 5.84

0.1≤δN≤0.3 0≤Rc≤0.5 γc = 1.44 γs = 6.95

0.1≤δN≤0.3 0.5≤Rc≤1 γc = 2.26 γs = 2.65

0.3≤δN≤0.5 0≤Rc≤0.5 γc = 1.47 γs = 9.13

0.3≤δN≤0.5 0.5≤Rc≤1 γc = 2.26 γs = 3.06

Four subdomains

βV mean βV COV βV max βV min

3.81 0.10 4.42 2.51

3.86 0.10 4.42 2.60

3.93 0.05 4.26 3.19

3.91 0.04 4.17 3.28

3.90 0.06 4.42 3.10

3.90 0.04 4.17 3.29

mean - min std deviation

1.30 0.38

1.26 0.39

0.74 0.20

0.63 0.16

0.80 0.23

0.61 0.16

4. Conclusions A partial factor format involves multiplying a nominal resistance such as the mean bearing capacity by a resistance factor or dividing a characteristic strength such as the lower 5% undrained shear strength by a partial factor. The purpose of a partial factor format is to implement reliability-based design without requiring the engineer to perform reliability analysis. Hence, the performance of a partial factor format must be measured by its ability to produce designs achieving a desired target reliability index within an acceptable error margin. Based on the concept of a reliability class proposed in BS EN1990:2002, two yardsticks for an acceptable error margin are recommended: (1) mean βV – minimum βV < 0.5 and (2) standard deviation of βV < 0.5, in which βV refers to the actual reliability index produced by a partial factor format design. The recommendations imply that a sufficiently large sample of representative designs should be evaluated. Fundamental to this performance evaluation is the explicit definition of the range of design scenarios covered by a partial factor format called the design domain. The error margin should be acceptable within this design domain.

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Two partial factor formats are studied. They are distinguished by the nature of the factor associated with the resistance or strength. The first format factors the overall resistance (LRFD) or factors each resistance component separately (MRFD). The second format factors the strength indirectly using a quantile. These factors can be calibrated over the entire design domain or within subdomains. It is obvious that the deviation from the target reliability index must be smaller in a subdomain, because the design scenarios are more uniform. The former strategy will produce a single numerical value for each factor. The latter strategy will produce a table of values – the number of values is equal to the number of subdomains. Based on the examples studied in this paper (pile installed in homogeneous clay and pile installed in clay and sand), one may venture to conclude that: 1. If a design guide is insistent on recommending a single numerical value in association with a partial factor format, it is more sensible to recommend a constant quantile value, rather than a constant resistance factor. 2. If a design guide is willing to recommend more than one numerical value, it is worthwhile evaluating MRFD and subdomain calibration. The former recommends a different resistance factor for each resistance component. The latter recommends different numerical values for the LRFD/MRFD factors in different subdomains

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References British Standards Institute (2002). Eurocode: Basis of Structural Design. BS EN 1990:2002, London. British Standards Institute (2004). Eurocode 7: Geotechnical Design – Part 1: General Rules. BS EN 19971:2004, London. Chen, J.R., Chuang, B.Y., Ching, J., Yang, Z.Y. & Shiau, J.Q. (2012). “Axial behavior of dilled shafts in multiple strata – Taipei database”, Soils and Foundations, under review. Ching, J.Y. & Phoon, K. K. (2011). “A quantile-based approach for calibrating reliability-based partial factors”, Structural Safety, 33(4-5), 275-285. Ching, J. Y. & Phoon, K. K. (2012). “Quantile value method versus design value method for calibration of reliability-based geotechnical codes”, Structural Safety, under review. Phoon, K.K., Kulhawy, F.H. & Grigoriu, M.D. (1995). “Reliability-based design of foundations for transmission line structures”, Rpt. TR-105000, Electric Power Research Inst., Palo Alto (CA), 380 p. [available online at EPRI.COM] Phoon, K.K., Kulhawy, F.H. & Grigoriu, M.D. (2003a). "Development of a reliability-based design framework for transmission line structure foundations", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129(9), 798-806 Phoon, K. K., Kulhawy, F. H. & Grigoriu, M. D. (2003b). "Multiple Resistance Factor Design (MRFD) for spread foundations", Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129(9), 807 – 818. Phoon, K.K. & Kulhawy, F.H. (2008). “Serviceability limit state reliability-based design”, Chap. 9 in Reliability-Based Design in Geotechnical Engineering: Computations & Applications, Ed. K.K. Phoon, Taylor & Francis, London (U.K.), 344-384. Sørensen, J. D. (2002). Calibration of partial safety factors in Danish Structural Codes. Workshop on Reliability Based Code Calibration, Swiss Federal Institute of Technology, ETH Zurich, Switzerland, March 21-22, 2002.

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Modern Geotechnical Design Codes of Practice P. Arnold et al. (Eds.) IOS Press, 2013 © 2013 The authors and IOS Press. All rights reserved. doi:10.3233/978-1-61499-163-2-311

311

Target Reliabilities and Partial Factors for Flood Defenses in the Netherlands Timo SCHWECKENDIEKa,b,1, Ton VROUWENVELDERa,c,, Ed CALLEb, Wim KANNINGa and Ruben JONGEJANa,d a Delft University of Technology b Deltares, Unit Geo-engineering c TNO Built Environment and Geosciences d Jongejan Risk Management Consulting

Abstract. Modern codes of practice such as Eurocode strive to provide design rules including partial factors with an appropriate level of safety for a wide range of applications. The target reliability levels and partial factors in such codes are not equally efficient for all applications, since they are calibrated to work well in both typical and unusual situations. For large engineered systems like flood defense systems with large potential consequences and substantial investments in improvement and maintenance, it is worthwhile to develop tailor-made solutions. This paper describes the approach adopted in the Netherlands to develop safety requirements to flood defenses such as partial factors for dikes within an acceptable risk framework accounting for system reliability aspects. The main steps herein are to define a risk-informed target reliability for the whole system (i.e., including all elements and failure modes), to derive target reliabilities for specific elements (e.g., dike sections) and failure modes and to calibrate partial factors on the latter. After describing those steps, the paper provides an application example for the uplift and piping failure mode (i.e., internal erosion).

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Keywords. flood defenses, LRFD, dikes, failure modes, system reliability, lengtheffect, spatial variability, partial factors, code calibration, target reliability

Introduction Modern codes of practice such as Eurocode use consequence or reliability classes to assign target reliabilities and corresponding partial factors to different types of structures or structural members. Flood defense systems are large engineered systems protecting flood-prone areas from inundation. Since the consequences of failure of flood defenses can be significant as are typically the investments in increasing the reliability of such systems, it is worthwhile define tailor-made target reliabilities instead of using the reliability classes from general geotechnical codes of practice, which may be inefficient (i.e., either too low or too high) for a given flood defense system. Furthermore, system reliability aspects need to be paid special attention. Flood defenses are typically long linear structures, for the so-called length-effect is significant. That is the effect that the reliability of a linear structure decreases with increasing length. The paper describes the proposed steps to derive partial factors for geotechnical failure mechanisms of linear flood defenses from high level risk-based safety requirements.

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Figure 1. Outline Step-wise Procedure and Corresponding Sections

As outlined in Figure 1, sections 1 to 4 describe the steps from high level risk and reliability targets to partial factors for individual dike reaches. Section 1 illustrates how risk-informed target reliability values at the highest level, that is for a flood defense (sub-)system with relatively homogeneous consequences in case of failure (i.e. where the consequences are of similar magnitude regardless of the mode or position of failure in the (sub-)system), can be chosen. Individual risk, group risk and economic risk provide valuable input, however, the ultimate decision remains a political one. A flood defense (sub-)system is composed of different types of structures, which are prone to different failure modes. Section 2 describes how target reliabilities for a particular failure mode and structure can be derived or motivated. The so-called length effect is treated in section 3, in which we account for the spatial variability in load and resistance, especially in ground properties. The final step from target reliability per dike section to a set of calibrated partial factors is elaborated in section 4. Furthermore, it will be shown that it is more efficient to take the last two steps together by using an alternative calibration criterion. Section 5 illustrates the workings of the approach for the derivation of safety factors for an assessment rule for the piping failure mode. It is emphasized that the described method and example are based on a safety assessment framework, rather than on a design situation (i.e., design of a new structure). For design situations, the changes of loading conditions and resistance properties during the system’s lifetime should be taken into consideration. The overall approach remains the same, however.

1. From Acceptable Risk to System Target Reliability Target reliabilities for engineered systems or structures are often risk-informed. The higher the potential consequences of failure, the higher the target reliability. Below we discuss three widely used types of criteria for evaluating the risks related to floods and major industrial hazards. From such acceptable risk-criteria, we can derive an acceptable probability of failure or a target reliability for a given system.

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1.1. Economic Criteria Economically optimal protection levels can be obtained from cost-benefit analyses. In such analyses, risk is typically defined as (valued at) the expected value of economic damage (which is the actuarially fair insurance premium). The economically optimal reliability of an engineered system can be found by equating marginal costs with marginal benefits, or by minimizing the sum of the present value of the cost of strengthening flood defenses and the present value of the economic risk, see e.g. Van Dantzig (1956) for an application to a major levee system (a present value is today’s value of future cash-flows). This optimization procedure is shown schematically in Figure 2. Cost

total cost

cost of increasing system reliability

expected loss (present value) optimal reliability

System Reliability

Figure 2. The optimization of a system’s reliability: total cost equals the cost of increasing the system reliability plus the present value of expected loss (PV = present value)

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1.2. Individual Risk Criteria Individual risk criteria are reference levels for evaluating individual exposures. These are often defined as a maximum allowable probability of death. The stringency of individual risk criteria is often related to considerations regarding the voluntariness of exposure, and the degree to which an exposed person benefits from the hazardous activity (e.g. Vrijling et al., 1998), for Western countries typically ranging from a probability of 10-2 per year for voluntary activities with relatively high direct benefit like mountaineering to 10-6 for involuntary activities without direct benefit, the latter being frequently used in industrial safety. 1.3. Societal Risk Criteria When individual exposures are low, there is still a chance that disaster strikes affecting a vast population. Psychometric studies have shown that risk perception is strongly influenced by “dread”, or catastrophic potential (e.g. Slovic, 1987). The assessment of multi-fatality disasters often involves societal risk criteria. One common type of societal risk criterion is the FN-criterion (e.g. Jonkman et al., 2003). An FN-curve shows the exceedance probabilities (F) of different numbers of fatalities (N), plotted on double logarithmic scale. The FN-curve should not cross the criterion line, see Figure 3.

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For the definition and motivation of FN-acceptance criteria, the reader is referred to e.g. Jongejan (2008) , Ball and Floyd (1998) and Stallen et al. (1996). Exceedance probability (F) on log scale

FC/nD FN-criterion exceeded

Number of fatalities (N) on log scale Figure 3. Schematic overview of different types of FN-criteria..

2. Target Reliabilities per Failure Mode The first step in going from system target reliabilities (previous section) towards concrete safety requirements is to break down the system in terms of elements and failure modes as discussed below.

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2.1. Failure Modes of Flood Defense Systems

Figure 4. Fault tree for Flood Defense Failure Modes

A flood defense system is a series of dikes, dunes, retaining walls, higher grounds, storm surge barriers, sluices and so on, protecting a flood-prone area. Dikes and dunes are usually subdivided into statistically homogeneous sections in terms of relevant geometrical, material and loading parameters. They are typically between, say, 100 meters to several kilometers long. The most common failure mechanisms for dike sections are shown in Figure 4. For detailed descriptions of these mechanisms in terms of limit state functions, reference is made to Steenbergen and Vrouwenvelder (2003). For dune sections usually only dune erosion is considered and for structural components (sluices, locks, quay walls) a set of mechanisms such as overflow, piping, structural integrity and incorrect closure operations may be relevant.

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2.2. System Reliability In order to calculate the inundation probability for a protected area, one needs a set of mathematical models to describe the various failure mechanisms as well as the statistical properties for all basic random variables involved. A proper statistical model requires the distribution type and parameters (e.g., mean and standard deviation) and descriptions of the mutual as well as auto-correlations in space and time. Note further that it is essential to include all uncertainties, not only the natural variability in dike heights, soil properties or water levels, but also epistemic uncertainties like the inaccuracies in resistance and load models as well as the uncertainties in the statistical parameters as well as distribution types. The first step in estimating the failure probability of a flood defense system is to calculate the failure probability for each individual failure mode of each individual element or section:

Pf ,i , j

P Z i , j ( X )  0

³[ f

X Z i , j ( )0

([ ) d [

(1)

where Zi,j is the limit state function for failure mode i (1..m) and element or section number j (1..n) (i.e., Zi.j < 0 corresponds to failure), X is the vector of stochastic variables and fx([) their n-dimensional probability density. The frequently used reliability index is related to the probability of failure by:

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E

) 1 Pf



(2)

in which  is standard normal distribution. The second step is to aggregate the failure probabilities of all modes and sections or elements to the probability of (sub-)system failure. In the case of a simple series system of m independent modes and n independent components, the failure probability of the system may (for small probabilities) be written as: m n

Pf , sys

¦ ¦ Pf ,i j

(3)

i 1j 1

This equation holds equally for summation over sections, mechanisms, wind directions or time periods, provided that the contributing probabilities of failure, Pf,i,j, are small and mutually independent. In reality, however, the contributing probabilities are (slightly) mutually dependent, due to (spatial) correlation of the random variables involved in the computation of the failure probabilities (see section 3) and due to common random variables in the limit state models (e.g. hydraulic load). Eq. (3) is therefore an (upper bound) approximation.

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2.3. Target reliabilities per failure mode Assume that acceptable risk considerations have led to an acceptable annual probability of system failure expressed in terms of PT,,sys (T = target). The task of the engineer is to design (and maintain) the flood protection system in such a way that it meets this reliability target in the most efficient way. For the sake of practicability one may start by allocating failure probabilities to each failure mode and each section or element in such a way that the top (system) requirement is met. The simplest way is to set:

PT ,i. j

PT , sys mn

(4)

This, however, maybe very inefficient as we ignore correlations between failure modes and sections, as well as differences between cost functions. In principle, an economic optimum could be determined using the philosophy described in section 1.1. A more pragmatic way would be to allocate ‘failure probability space’ to different elements/failure modes based on current practice, as one may assume that in decades or centuries of trial and error have led to more or less efficient designs. An advantage of such an approach would be that new approaches are aligned with current practice. It is well known that introducing too many changes at a time is error-prone and unlikely to be easily accepted. Another important aspect in allocating target probabilities of failure (PT,i,j) is to account for the spatial variability. This will be discussed in the next section.

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3. The Length-Effect Spatial variability or statistical dependence between random variables (load and/or resistance properties), between and within a system’s components (e.g. dike sections) have significant impact on its reliability. When it comes to flood protection systems, the main aspect to consider is the so-called length-effect. 3.1. What is the length-effect? The length-effect refers to the increase of the failure probability with the length of a dike due to imperfect correlations and/or independence between different cross sections and/or elements. The underlying reason is a lack of full correlation between the different load and resistance variables as a result of spatial variability. Typically, the load variables are highly correlated over different dike sections, whereas resistance properties of dike sections exhibit little correlation due to the small horizontal correlation distances. This results in a partially correlated limited state function in the length direction and thus an increase of failure probability in the length direction. It must be noted that only horizontal correlation distances are affecting the length-effect, the effect of vertical spatial variability is assumed to be incorporated in the analytical models. As a general rule one may say that the smaller the correlation distances (see 3.2) of important random variables, the higher the increase of the probability of failure with the length. Two types of spatial variability contribute to the length-effect: continuous fluctuations and discontinuities (e.g. anomalies).

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For flood defenses, the uncertain soil conditions relevant to geotechnical failure modes are normally the main contributors to the length-effect. This is because the uncertainties are often considerable and correlation distances are relatively short. The spatial correlation (lengths) of load parameters (e.g., typically water levels or wave conditions) are relatively high. Below we explain and illustrate the length-effect due to continuous fluctuations in soil properties. 3.2. Outcrossing Approaches Spatial variability can be modeled by random fields (e.g. Vanmarcke, 1977). A Gaussian autocorrelation function can be used to describe the decay of spatial correlation with distance x:

U ( x) U x  1  U x e

§ x · ¨ ¸ © G0 ¹

2

(5)

in which x models the part of the variance that does not decay in space (non-ergodic, see Vrouwenvelder, 2006) and 0 is the correlation distance. In order to incorporate the length of the dike (L) in the reliability calculation, we are interested in the probability of the limit state function Z being less than 0 in the domain [0, L], for which outcrossing approaches (or first passage see e.g. Vanmarcke (1975)) provide the following generic solution: L

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P (0, L) 1  e

³

 h ([ )d [ 0

(6)

where h() is the conditional failure rate. For long L, h() can be approximated by the mean crossing rate (see Rice, 1952), which is the mean rate at which level  is crossed by the considered random variable. If we make several assumptions (Pcs is small, L is long, the upcrossings, which are the crossing from below to above the threshold, are independent, the crossing rate is constant), the probability of failure P(0,L) can be approximated by eqn. (7), (see e.g. Calle, 2010). These assumptions are valid failure probabilities are in the order of 10-3 or lower and dike section lengths are larger than horizontal correlations distances, which is usually the case.

§ L· P (0, L) | Pcs ¨1  ¸ l¹ ©

(7)

Where P(0) is the probability of failure of a cross-section and l is the independent equivalent length (for ”(0)>0 and thus for one of x,i < 1) according to:

l|

2S

ET ,cs

1  U ''(0)

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(8)

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where ”(0) is the second derivative of the autocorrelation function (Eq. 5): N

¦

U "(0)

2D i2 (1  U x ,i )

(9)

G 0,2 i

i 1

where  is the FORM sensitivity factor, which is the result from a reliability analysis (forward analysis) or an average of several dike analyses for the derivation of safety factors. 3.3. Accounting for the length effect In order to account for the length-effect, we have to find the target reliability of the cross-section (ET,cs) as a function of the dike ring characteristics for the considered failure mechanism. Hence, we need to use Eq. (8) in an inverse way where P(0) corresponds to PT,cs and P(0,L) to PT,sec, as discussed in section 2.3. So we end up with:

PT ,sec

PT ,cs

(10)

(1  L / l )

6 Cross Section Target Reliability ET,cs

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Several assumptions have to be made to solve equation (11), notably to find a representative value of l, which can be found by taking the average of several dike rings determined in (forward) reliability analyses. Furthermore, one needs to realize that L should actually be interpreted as the dike length of sections in the system that contribute significantly to the failure probability. For example, if only 10% of the system contributes to the probability of piping (e.g., some dikes may not have a piping sensitive layer), only 10% of the system length should be taken into account. In fact, this is part of the determination of target reliability per failure mode and dike section; see e.g. equation (4).

5.5

5

4.5

ET,sys = 4.26 ET,sys = 4.06

4

ET,sys = 3.89 ET,sys = 3.78

3.5

0

20

40

60 80 100 120 140 Contributing Dike Ring Length L [km]

160

180

200

Figure 5. Relation between Target Reliability and Contributing Dike Length L (l = 282 m)

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319

Figure 5 shows an example for piping with l = 282 m (based on a statistical analysis of results for three Dutch dike rings from the VNK2 project (Lopez de la Cruz et al., 2010); the values of ET,sys correspond to a failure probability that equals 10% of the Dutch safety standard. For typical contributing lengths of between 10 and 100 km, the difference between ET,sys and ET,cs (i.e., length effect) is about 0.5 to, which corresponds to ratios of approximately 10 to 100 of the respective target probabilities of failure. It is important to realize that the length-effect has implications for the allocation of target reliabilities for dike sections or elements, as well as for translating these into requirements for individual cross sections.

4. Derivation of Partial Factors

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Load and resistance factors for geotechnical failure modes of flood defenses (e.g., slope instability, uplift & piping etc.) are typically derived in an iterative fashion. First preliminary factors are determined using standardized FORM sensitivity factors D. Subsequently, their effect on the resulting reliability is investigated by reliability analyses for a variety of representative cases, before final values are chosen. Partial factors typically apply to loads and resistances, the uncertainty of which can be modeled as random variables. Some uncertainties involved in geotechnical engineering, however, lack the possibility of being adequately modeled this way. For example, schematizations of the stratification of the subsoil, based on limited soil investigation or assessment of the type of response to external actions (e.g., drained or un-drained), may be highly uncertain. Uncertainties involved in this schematizations are at least as important as uncertainties of resistances due to uncertain soil parameters (Terzaghi, 1929). Yet, these type of uncertainties are not (explicitly) addressed in codes of practice. It is trusted that they are adequately handled by professional judgment. Only recently, Schweckendiek & Calle (2010) suggested more explicit ways of handling this type of schematization uncertainties. However, in the present paper, the focus is on partial factors for loads and resistances, which can adequately be modeled as random variables, having normal distributions. 4.1. From Target Reliability to Partial Factors To get a first impression of the partial factors, needed to fulfill the target reliability concerning some potential failure mechanism, use can be made of the ISO standardized sensitivity factors (Table 1). Table 1. Standardized FORM-sensitivity factors (ISO 2394) Random Variable Xi

Di

Dominant resistance parameter

0.8

Other resistance parameters

0.8 x 0.4 = 0.32

Dominant load parameter

- 0.7

Other load parameters

- 0.7 x 0.4 = - 0.28

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The idea is based on the design point notion in FORM type reliability analyses (ISO 2394). In such a first-order framework, the required partial safety factors for load S and resistance R, assuming Gaussian probability distributions, can be expressed as:

JS

1  ET D S VS 1  1.65VS

JR

1  1.65VR 1  E T D R VR

(11)

where VS and VR are the respective coefficients of variation and the factors are used with 5% and 95%-characteristic values (i.e., Sd = Sk JS and Rd = Rk / JR). 4.2. Calibration Using Representative Test Sets

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In order to produce more accurate partial factors one may use representative data sets and work in a trial and error fashion. A recent example for piping is given by Lopez et al. (2011). The test set members are realistic cases, for example, draft designs of dike cross sections, representative for the envisaged range of application. The line of thought is that the test set members are first “designed”, using preliminary partial factors, based on the target index of reliability. Next, probabilistic analyses of the designs yield a set of actually ‘realized’ probabilities of failure and, equivalently the actually realized indices of reliability. These are then compared with the target reliability. This way an appropriate set of partial factors can be found iteratively. Since a set of partial factors will not perform equally well on all test set members, one needs to adopt a calibration criterion. An example would be that 95% of the designs need to satisfy the target reliability, which, however, is a rather strict criterion that would often be economically suboptimal. Somewhat more relaxed criteria have been suggested in the literature (e.g., Ciria, 1977; Sørensen, 2001; Faber and Sørensen, 2002). For example, for a single safety factor, the calibration criterion may read (Sørensen, 2001):

J : min W( J )

N

¦w

k

( Pf , cs ,i ,k ( J )  PT ,cs , i )2

(12)

k 1

where  is the safety factor to be determined, Pf, cs, i, k () is the realized probability of cross section failure (considering failure mechanism i) of test set member k (k=1…N), when applying the safety factor , and PT, cs, i is the target probability of failure. The wk are weights, reflecting relative frequencies of occurrence of design situations in practice, represented by each of the test set members. The weights sum up to 1. Instead of probabilities of failure, actually realized and target reliability indices may be used in eq. (13). So far, these criteria refer to safety requirements for individual test set members. For (flood defense) systems the calibration criterion may be related to the system target reliability as discussed in section 4.3. 4.3. Calibration Criterion at System Level An alternative way to determining local target reliabilities first (i.e., for a section or element) is to calibrate partial factors directly on the basis of the system target reliability, in this case of a (part of a) dike ring. From now on we consider an annual

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321

target probability of failure for one mechanism for all elements in the system PT,i Combining Eq. (3) and Eq. (8) yields the following approximation for the system probability of failure of mode i (e.g., piping):

P

f , sys, i

|

m

§

·

¦ P f , cs, j ¨1  L j / l j ¸ © ¹ j 1

(13)

where Lj are the lengths of the individual sections and lj the independent equivalent lengths of the failure mode, the latter often being assumed an average value per failure mode in calibration analyses. The calibration criterion is based on the premise that the average probability of flooding over all consequence systems should be lower than the safety standard (in practice, the probability of flooding is evaluated for each system separately). This is approximately the case when the following condition is met:

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P d cs, avg

P T , sys, i

§¨1  L ·¸ n /l avg © avg avg ¹

(14)

where Pcs,avg = average failure probability of cross sections, Pt,sys,i = target failure probability for mode i on system level, navg = average number of sections per system, Lavg = average section length and lavg = average equivalent independent section length (mode-dependent). Hereafter, the criterion defined in Eq. (15) will be referred to as calibration criterion type 1. When the test cases do not cover entire systems, this calibration criterion may yield overly optimistic results. To deal with such situations, another type of calibration criterion was developed, hereafter referred to as type 2. When the reliability indices per section (that are designed according to a specific set of partial factors) are normally distributed with a standard deviation of 0.5, it can be shown that in order to meet the requirement stated by Equation (14), the following condition has to be met:

E

cs, 20%

t )

1

§ · P ¨ ¸ T , sys, i ¨ ¸ ·¸ ¨¨ n §¨1  L /l ¸¸ avg avg ¹ ¹ © avg ©

(15)

where cs,20% = 20th percentile of the reliability indices per cross section. Note that both calibration criteria yield the same results when N is sufficiently large and the reliability indices per cross section are normally distributed with a standard deviation of 0.5. Furthermore, both calibration criteria assume sections to be independent. In case of strong correlations (e.g. greater than 0.85), calibration criterion type 1 will yield conservative design values, while the opposite holds true for calibration criterion type 2. After all, when sections (and their cross-sections) are perfectly correlated, the

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reliability index of a system will be equal to the lowest cross-sectional reliability index, which is less than the 20th percentile.

5. Application Example: Semi-probabilistic Assessment Rule for Piping 5.1. Introduction The example concerns the calibration of a semi-probabilistic safety assessment rule for piping, an internal erosion mechanism elsewhere also referred to as under-seepage or backward erosion. The calibration was carried out within the WTI2017-project, which has the objective to develop a new framework for statutory safety assessments in the Netherlands based on acceptable probabilities of flooding (i.e., dike ring system failure). The underlying limit state function is a revised version of the well-known Sellmeijer model (Sellmeijer, 1988) and is given by (see e.g. Lopez de la Cruz et al. 2010; Sellmeijer et al. 2012): Z

i L  §¨ h  h  0.3d ·¸ in c p © ¹

(16)

where ic = critical (average) gradient for piping [-]; Lp = seepage length [m]; h = water level [m+REF]; hin = hydraulic head at the exit point [m+REF] (i.e., h-hin is the hydraulic head difference over the levee); and d = thickness of the impervious blanket layer [m]. Notice that the product ic,p Lp represents the critical head difference [m].

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5.2. Target Reliability The system target reliability in the Netherlands were based on the present-day Dutch flood safety standards, see Table 2 and Figure 6. For calibration purposes, these target reliabilities had to be broken down to the different failure mechanisms. Based on experience from the VNK2-project (Jongejan et al., 2013), a nation-wide flood risk analysis, the so-called failure probability budget for piping (i.e. the allowable contribution of the piping mechanism to the system’s overall probability of failure) for all dike sections in a dike ring was set to 35% (see Table 2). Table 2. Target Reliabilities (levees only), all probabilities are on an annual basis.

Safety standard/ acceptable probability of flooding1 PT 1/500 1/1,250 1/2,000 1/4,000 1/10,000

Failure probability budget 35% 35% 35% 35% 35%

Target Probability of Failure PT,pip

Target reliability index ET,pip

1/1,400 1/3,600 1/5,700 1/11,400 1/28,600

3.20 3.45 3.58 3.75 3.98

1 The numbers in the Dutch safety standard actually refer to frequencies of the load events used in the safety assessment. These, however, are frequently necessarily interpreted as acceptable probabilities of flooding or system (i.e., dike ring) failure for sake of calibration of semi-probabilistic assessment rules.

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5.3. Partial Factor and Safety Format In semi-probabilistic safety assessments, characteristic values (subscript k) are used and a partial factor is applied to the critical head difference:

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Figure 6. Safety Standards for Flood Defenses in the Netherlands Interpreted as Acceptable Probabilities of Flooding1

1

J



ic , k L p , k t h  h

p

k

in, k

 0.3d

k



(17)

where p = partial resistance factor. Note that ic,k is defined as the critical gradient from Lopez de la Cruz (2010) with characteristic values for all input variables. A single partial resistance factor was chosen in order to stay close to the currently used rule. 5.4. Test Set and Probabilistic Analyses Table 3. The test set for the preliminary calibration exercise.

Levee system No. 5 Texel island No. 17 IJsselmonde No. 36 Land van Heusden/de Maaskant

Safety standard/ acceptable probability of flooding PT (a-1) 1/4,000 1/4,000 1/1,250

No. of sections 13 21 33

Total length (m) 16,626 23,984 25,345

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The test set members were obtained from the VNK2-project (see Jongejan et al., forthcoming for more details on the VNK2-project). At the time of analysis, reliable results were available for three levee systems (see Table 3). It contains a wide range of characteristics in terms of water level (i.e., load) distributions, substrata thicknesses, and grain size distributions etc. The test set members were analysed in an iterative fashion as discussed in section 4.2. The squared FORM sensitivity factors in Figure 7 indicate that the total uncertainty in the limit state function was dominated by geotechnical uncertainties (mainly the permeability together with other ground-related variables) in levee systems no. 5 and 17 whereas the load uncertainty is much more important in no. 36. To avoid inconsistencies with past performance, the inputs were modified with respect to the original prior input from the VNK2 project. While this was done somewhat arbitrarily, by reducing the variance of the permeability to raise the design point values of the water level, Schweckendiek et al. (2012) demonstrate how Bayesian Inference can be used to use actual data about past performance in a more formal and systematic fashion. For each section, the required length of the seepage path was determined with the semi-probabilistic assessment rule, for different values of p (Eq. 17). FORM analyses (Hasofer & Lind 1974) were then carried out using the required seepage length to analyse the “assessment reliability”. The results of these calculations as shown in Figure 8.

Squared FORM-influence coefficient

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Dike ring no.5

Dike ring no.17

Dike ring no. 36

1 0,8 Other stochastic variables Outer water level Permeability

0,6 0,4 0,2 0 1

11

21

31

41

51

61

Testcase no.

Figure 7. Squared FORM-sensitivity factors per section after modifications based on past performance.

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325

2.0 1.8

p

1.6 1.4 1.2 1.0 4

5

6

7

8

cs Figure 8. Reliability index per cross-section (cs) as a function of the partial factor (R). The distinction between the different levee systems, represented by the symbol shapes, is not elaborated in this figure, for it is not essential to the example.

5.5. Calibration Criterion

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According to calibration criterion type 1 (Equation 14, the ratio Pcs,avg/PT,,cs should be equal to one 2 . If Pcs,avg/PT,,cs>1, the partial factor is too optimistic (too low); if Pcs,avg/PT,,cs