Experimental and Numerical Investigation of Soil

VERÖFFENTLICHUNGEN des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiana in Karlsruhe Herausgeber: G. Gudehus

Heft 166

Experimental and Numerical Investigation of Soil-Foundation–Structure Interaction during Monotonic, Alternating and Dynamic Loading

von Michael Max Bühler

Karlsruhe 2006

ISSN 0453-3267

Dissertation genehmigt von der Fakultät f¨ ur Bauingenieur-, Geo- und Umweltwissenschaften der Universität Karlsruhe (TH)

Tag der m¨ undlichen Pr¨ ufung: 8. Februar 2006 Referenten: o. Prof. Dr.-Ing. Dr.h.c. G. Gudehus Univ.-Prof. Dr.-Ing. J. Grabe, Hamburg

Der Autor dieses Heftes ist: Michael Max B¨ uhler aus Karlsruhe Wissenschaftlicher Angestellter am Institut f¨ ur Bodenmechanik und Felsmechanik der Universität Karlsruhe bis Februar 2006.

Preface of the editor Faced with the title of a dissertation over 3 lines I am used to reduce it to at most 1.5 lines, but this would be inadequate in the present case. Actually Mr. B¨ uhler treated the comprehensive field of his correctly entitled dissertation with a unified methodology and obtained convincing results. The theoretical base for it is hypoplasticity, with intergranular strain for clay with soft particles including viscosity. This constitutive theory is described in detail in other publications and has already been validated by various lab tests and field observations. Now Mr. B¨ uhler presents a further series of validations for his subject area. For decades the evolution of soil mechanics was rather separate in statics and dynamics, in particular for the interaction of ground and structure. Even now the latter is often captured in calculations by simplifying assumptions which where never verified, more so in soil dynamics than in statics. Based on the present dissertation this is no more necessary, this can be verified by interested readers up to details. As can be expected hypoplasticity fails at the transion from grain skeletons to suspension, one could say that we are not responsible for mud flow. At the end of this publication it is also shown that this new state of knowledge has certainly consequences for design and construction methods. The research work of Mr. B¨ uhler was supported by the German Research Community (DFG) within the Centre of Excellence SFB 461 (Strong Earthquakes) and within an Indo-German Cooperation Project (combined with a DAAD Master Sandwich Program). This is gratefully acknowledged.

G. Gudehus

Vorwort des Herausgebers Wenn mir ein drei Zeilen langer Titel einer Dissertation vorgelegt wird, pflege ich diesen auf höchstens eineinhalb Zeilen zu verk¨ urzen, in diesem Falle wäre dies aber verfehlt. Herr B¨ uhler hat tatsächlich in seiner nun vorliegenden Doktorarbeit das mit dem langen Titel korrekt beschriebene umfangreiche Gebiet mit einer einheitlichen Methodik bearbeitet und u ¨ berzeugende Ergebnisse erzielt. Die theoretische Basis dazu bildet die Hypoplastizität mit intergranularer Dehnung, bei bindigen Böden mit weichen Partikeln einschließlich Viskosität. Diese Stofftheorie ist in anderen Publikationen ausf¨ uhrlich beschrieben und wurde bereits durch verschiedenste Laborversuche und Geländebeobachtungen validiert. Nun legt Herr B¨ uhler f¨ ur seinen Themenkreis eine weitere Serie von Validierungen vor. Die Bodenmechanik hat sich u ¨ ber Jahrzehnte in der Erdstatik und der Bodendynamik ziemlich getrennt entwickelt, auch und gerade bei der Anwendung auf die Wechselwirkung von Baugrund und Bauwerk. Noch immer wird letztere oft mit vereinfachenden Annahmen rechnerisch erfasst, die keiner Pr¨ ufung standhalten, in der Bodendynamik noch mehr als in der Erdstatik. Damit braucht man sich aufgrund der nun vorliegenden Dissertation nicht mehr abzugeben, wovon sich interessierte Leser bis ins Detail u ¨berzeugen ¨ können. Erwartungsgemäß funktioniert die Hypoplastizität erst beim Ubergang von Kornger¨ usten zur Suspension nicht mehr, f¨ ur Schlammbewegungen sind wir sozusagen nicht mehr zuständig. Wie am Schluss der Arbeit aufgezeigt wird, hat dieser neue Kenntnisstand selbstverständlich auch Konsequenzen f¨ ur Entwurfsverfahren und Bauweisen. Die Forschungstätigkeit von Herrn B¨ uhler wurde von der DFG im Rahmen des Sonderforschungsbereichs 461 (Starkbeben) und im Rahmen eines deutsch-indischen Kooperationsprojekts (kombiniert mit einem DAAD-Master-Sandwich-Programm) gefördert. Daf¨ ur sei hier ausdr¨ ucklich gedankt.

G. Gudehus

Preface of the author The interaction of soil with structures built in and on the ground is an important field in geotechnical engineering. Its investigation represents a demanding task for the engineer. In the scope of two interdisciplinary research projects in cooperation with scientists from India and Romania, I investigated experimentally and numerically the behaviour of piles and pile foundations during strong earthquakes. The presented PhD thesis was developed during my tenure as a scientific associate at the Institute of Soil and Rock Mechanics at the University of Karlsruhe (IBF). I am deeply indebted to my doctoral supervisor and teacher Professor Gerd Gudehus. I would like to express my gratitude to him. The extraordinarily collegial atmosphere that he promoted at his Institute played a large role in the successful outcome of my work. I would also like to convey my thanks to Professor J¨ urgen Grabe for being the second examiner. Furthermore, I would like to thank my former colleagues and friends Sven Augustin, Konrad N¨ ubel, and Christian Karcher for their continuous support and encouragement during my time at the IBF. My friend and teacher Roberto Cudmani has supported me professionally and as a friend in difficult periods long before I started to bring this work to a close. I will treasure the memories of the eventful times we spent during workshops and conferences in India and Canada. Czesary Slominski and Michael K¨ ulzer have enriched my time at the Institute over the last years. I also would like to express gratitude to Ana Libreros for the close collaboration in the field of earthquake engineering. I would like to thank Thomas Meier, not only for countless philosophical discussions but also for a good collaboration. I am very grateful to Gerhard Huber, Martin Jentsch, Helmut Schnepf, Holger Wienbroer and Daniel Rebstock who supported me untiringly with the experimental part of the presented dissertation. The support of Sophia Horzel, Ilona Sauter, Brigitte Meininger, Ruth Poslowski and Magdalena Gödel is highly appreciated. I also would like to thank the soccer team of the Institute, the workshop with Robert Runk and Ralf Hill as well as the student assistants. In particular, I would like to single out my parents. I owe it all to them and therefore would like to dedicate this doctoral dissertation to them. I deeply thank my partner, Anke Sieb for her patience, her joie de vivre and her support in all situations in life. Michael Max B¨ uhler

Vorwort des Verfassers Die Beschreibung der Interaktion des Bodens mit Strukturen im und auf Böden ist ein wichtiges Gebiet der Geotechnik und stellt eine anspruchsvolle Aufgabe f¨ ur den Ingenieur dar. Im Rahmen von zwei interdisziplinären Forschungsprojekten in Kooperation mit indischen und rumänischen Wissenschaftlern wurde mir ermöglicht, das Verhalten von Pfählen und Pfahlgr¨ undungen während Starkbeben im Experiment und im Modell zu untersuchen. Diese Arbeit entstand während meiner Zeit als wissenschaftlicher Angestellter am Institut f¨ ur Boden- und Felsmechanik der Universität Karlsruhe (IBF). Mein außerordentlicher Dank gilt meinem Doktorvater und Lehrer Herrn Professor Gerd Gudehus. Die einzigartige Arbeitsatmosphäre am IBF und das Gelingen der Arbeit sind vor allem ihm zu verdanken. Bei Herrn Professor J¨ urgen Grabe bedanke ich mich f¨ ur die ¨ Ubernahme des Korreferates. Bei allen Mitarbeiterinnen und Mitarbeitern des IBF möchte ich mich f¨ ur die gute Zusammenarbeit bedanken. An meine ehemaligen Zimmerkollegen und Freunde, die Herren Dr. Sven Augustin, Dr. Konrad N¨ ubel und Dr. Christian Karcher, geht ein besonderer Dank. Sie haben mich während meiner Zeit am IBF immer unterst¨ utzt und ermutigt. Hervorheben möchte ich auch meinen Freund und Lehrer Dr. Roberto Cudmani. Er hat mich in den manchmal nicht einfachen Zeiten auf dem Weg zum Abschluss meiner Arbeit fachlich wie auch als Freund unterst¨ utzt. In guter Erinnerung wird mir die ereignisreiche Zeit mit ihm auf Workshops und Konferenzen in Indien und Kanada bleiben. Die Herren Dipl.-Ing. Czesary Slominski und Dipl.-Ing. Michael K¨ ulzer sind mir in den letzten Jahren ans Herz gewachsen und haben meine Zeit im Nebengebäude sehr bereichert. Frau Dr. Ana-Bolena Libreros Bertini danke ich f¨ ur die herzliche Zusammenarbeit bei Erdbeben und sonstigen Problemen. Nicht nur unzählige philosophische Denkanstöße verdanke ich Dipl.-Ing. Thomas Meier, der mich schon seit dem Gymnasium begleitet. Den Herren Dr. Gerhard Huber, Martin Jentsch, Helmut Schnepf, Dipl.-Ing. Holger Wienbroer, Dipl.-Ing. Daniel Rebstock danke ich f¨ ur ihre unerm¨ udliche Unterst¨ utzung im experimentellen Bereich. Auch war die edle Unterst¨ utzung aus dem Sekretariat von Frau Sophia Horzel, Frau Ilona Sauter und neuerdings auch Frau Meininger nicht selbstverständlich. Dies gilt auch f¨ ur Frau Poslowski und Frau Gödel. Danken möchte ich auch meinen IBF-Fußballern, der Werkstatt, vor allem den Herren Robert Runk und Ralf Hill, sowie den Hiwis. Im besonderen Maße wertschätzen möchte ich meine Eltern, denen ich alles zu verdanken habe. Ihnen widme ich diese Arbeit. Meiner Lebensgefährtin Anke Sieb danke ich f¨ ur Ihre Geduld, Ihre Lebensfreude und Ihre Unterst¨ utzung in allen Lebenslagen. Michael Max B¨ uhler

For my parents Elfriede and Max Dieter

Contents

1 Introduction

1

1.1

Overview and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Problem Description, Objectives and Methods . . . . . . . . . . . . . . . .

5

2 Theoretical Framework

9

2.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2

Experimental Investigation of SFSI . . . . . . . . . . . . . . . . . . . . . . 11

2.3

9

2.2.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.2

Full-Scale Field Tests with Piles . . . . . . . . . . . . . . . . . . . . 12

2.2.3

Model-Scale Pile Tests on shake tables . . . . . . . . . . . . . . . . 12

2.2.4

Centrifuge Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Computational Investigation of SFSI . . . . . . . . . . . . . . . . . . . . . 14 2.3.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.2

Winkler’s Approach . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.3

Non-linear Winkler Approach . . . . . . . . . . . . . . . . . . . . 19

2.3.4

Elasticity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.5

Finite Element Method (FEM) . . . . . . . . . . . . . . . . . . . . 22

2.4

Principal Mechanisms of the dynamic SFSI . . . . . . . . . . . . . . . . . . 26

2.5

Problems occurring with FEM

. . . . . . . . . . . . . . . . . . . . . . . . 28

2.5.1

Numerical Accuracy and Stability . . . . . . . . . . . . . . . . . . . 28

2.5.2

Soil-Foundation Interface Modelling . . . . . . . . . . . . . . . . . . 30

i

2.6

Current State-of-Practice Design and Seismic Building Codes . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3 Used Models and their Parameter Determination

39

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2

Parameters of the Hypoplastic Relation . . . . . . . . . . . . . . . . . . . . 41

3.3

3.2.1

Critical Friction Angle ϕc . . . . . . . . . . . . . . . . . . . . . . . 41

3.2.2

Granulate Hardness hs . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.3

Exponent n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.4

Characteristic Void Ratios at Zero Pressure ed0 , ec0 , and ei0

3.2.5

Exponent α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2.6

Exponent β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

. . . . 43

Parameters of the Visco-hypoplastic Relation . . . . . . . . . . . . . . . . . 50 3.3.1

Compression Coefficient λ and Swelling Coefficient κ . . . . . . . . 50

3.3.2

Critical Friction Angle ϕc . . . . . . . . . . . . . . . . . . . . . . . 52

3.3.3

Viscosity Index Iv . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3.4

Shape Parameter of the Yield Surface βR . . . . . . . . . . . . . . . 53

3.3.5

Determination of the Reference Isotach by means of ee0 , pe0 , and ε˙e0 55

3.3.6

Definition of OCR . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.4

Parameters of Intergranular Strain . . . . . . . . . . . . . . . . . . . . . . 60

3.5

Determination of the Initial State Variables . . . . . . . . . . . . . . . . . 61

3.6

Soils and other Materials used in the Experiments . . . . . . . . . . . . . . 63

3.7

3.6.1

Parameters of the Soils . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.6.2

Materials used for the Model Piles

. . . . . . . . . . . . . . . . . . 66

Preparation of the Model Soils . . . . . . . . . . . . . . . . . . . . . . . . . 70

4 Experimental Investigations of SFSI

75

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2

Small Shake Box without SFSI

. . . . . . . . . . . . . . . . . . . . . . . . 75

4.2.1

Dry Granular Soil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.2.2

Saturated Granular Soil . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2.3

Saturated Soft Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.2.4

General Remarks on Small Shake Box Experiments . . . . . . . . . 83

4.3

Model Piles used in the Experiments . . . . . . . . . . . . . . . . . . . . . 85

4.4

Barrel Experiments with Model Piles . . . . . . . . . . . . . . . . . . . . . 88

4.5

4.6

4.4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.4.2

Test Setup of the Barrel Experiments . . . . . . . . . . . . . . . . . 88

4.4.3

FE Models used to simulate the Experiments

4.4.4

Results of the Barrel Experiments and their Simulation . . . . . . . 93

4.4.5

General Remarks on the Barrel Experiments . . . . . . . . . . . . . 95

. . . . . . . . . . . . 90

Large Shake Box and Shake Table . . . . . . . . . . . . . . . . . . . . . . . 98 4.5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.5.2

Experimental Setup of the Shake Table . . . . . . . . . . . . . . . . 100

4.5.3

Laminar Box and Soil Preparation . . . . . . . . . . . . . . . . . . 108

4.5.4

Experimental Programme . . . . . . . . . . . . . . . . . . . . . . . 110

4.5.5

Visual Observations during the Experiments . . . . . . . . . . . . . 115

4.5.6

Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 118

4.5.7

General Remarks on the Large Shake Box Experiments . . . . . . . 145

Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

5 Numerical Investigation of SFSI

149

5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

5.2

Simulation of the Shake Box Experiments . . . . . . . . . . . . . . . . . . 149 5.2.1

Modelling with FE mesh . . . . . . . . . . . . . . . . . . . . . . . . 150

5.3

5.4

5.5

5.2.2

Results and their Discussion . . . . . . . . . . . . . . . . . . . . . . 152

5.2.3

General Remarks concerning the Simulation of the Shake Box Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Large-Scale Field Tests with Piles

. . . . . . . . . . . . . . . . . . . . . . 161

5.3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

5.3.2

Site Investigation and Laboratory Testing . . . . . . . . . . . . . . 165

5.3.3

Pile Loading Program and Instrumentation . . . . . . . . . . . . . . 169

5.3.4

Numerical Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 170

5.3.5

Results and Observations . . . . . . . . . . . . . . . . . . . . . . . . 177

5.3.6

General Remarks concerning Numerical Modelling of Large-Scale Pile Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Seismic SFSI Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5.4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

5.4.2

The Seismic SFSI Model . . . . . . . . . . . . . . . . . . . . . . . . 191

5.4.3

Results and their Discussion . . . . . . . . . . . . . . . . . . . . . . 193

5.4.4

General Remarks on the Seismic SFSI Analysis . . . . . . . . . . . 205

Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

6 Recommendations

213

6.1

Mitigation of Liquefaction Susceptibility . . . . . . . . . . . . . . . . . . . 213

6.2

Failure Modes and their Prevention . . . . . . . . . . . . . . . . . . . . . . 214

7 Summary and Perspectives

217

8 Zusammenfassung

223

A Diagrams - Shake Table Experiments

251

A.1 Laminar Box Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 A.2 Protocols of Shake Table Experiments

. . . . . . . . . . . . . . . . . . . . 255

A.3 Shake Table Displacements during the Experiments . . . . . . . . . . . . . 259

A.4 Evolution of Pore Pressures during the Experiments . . . . . . . . . . . . . 264 A.5 Evolution of Vertical Displacements during the Experiments . . . . . . . . 269 A.6 Maximal Strains in Model Pile during the Experiments . . . . . . . . . . . 274 A.7 Pore Water Pressure during Event B4 . . . . . . . . . . . . . . . . . . . . . 279 A.8 Pile Head Deflection during Event B4 . . . . . . . . . . . . . . . . . . . . . 282 A.9 3D Pile Bending Moments vs. time during Event B4 . . . . . . . . . . . . 285 A.10 3D Lateral Soil Displacements vs. time during Event B4 . . . . . . . . . . 289 A.11 3D Lateral Pile Deflections vs. time during Event B4 . . . . . . . . . . . . 293

Chapter 1 Introduction In the last years, many methods have been proposed to deal with the analysis of the dynamic response of structures founded on soft or liquefiable soils, in which soil-foundationstructure interaction (SFSI) is crudely simplified or even totally neglected. Worldwide, the anti-seismic structural design is based on standard procedures, in which the ground is oversimplified and the type of foundation and its interaction with the soil and the structure is not taken into account. Neglecting SFSI has often been assumed to be beneficial for the seismic response of the supported structure because its consideration is said to improve the safety margins. While this assumption may be true for buildings founded on very stiff soils and rock, it cannot be extended carelessly to soft or liquefiable soils where, especially in case of strong earthquakes, there is still a lack of understanding the influence of the foundation type and the role of SFSI. Figure 1.1 shows a prominent case of damage due to soil liquefaction. The superstructures were not damaged during the earthquake. An inadequately compacted sandy fill caused a liquefaction induced ground failure exhibiting a dramatic relevance of the supporting soil. Within this dissertation, experiments in-situ as well as in the laboratory are presented and explained to investigate the behaviour of deep foundations under monotonic, alternating as well as dynamic loading. Concomitantly, approaches based on the Finite Element Method (FEM) are applied to simulate the experiments showing the tremendous capabilities of the constitutive relations used to simulate the soil behaviour and to validate the used methods. Subsequently, the FEM is employed to predict and investigate the behaviour of structures with different types of foundations, which shows the practicability of the presented methods in geotechnical engineering.

1

2

Chapter 1. Introduction

Figure 1.1: Kawagishi-cho apartment buildings during the 1964 Niigata earthquake (after [Ste92])

1.1

Overview and Motivation

The interaction between the soil and the foundation under earthquake loading is essentially affecting the performance of the structures built above. Observations of pile foundations during earthquakes have shown that piles in firm soils generally perform well. However, the performance of piles in soft or liquefied ground can range from excellent to poor resulting in structural damage or excessive deformations [Bou97]. Figure 1.2 shows a harbour structure after the 1989 Loma Prieta earthquake in Oakland and San Francisco where numerous marine and port facilities experienced moderate to extensive damage. Lateral movements of the liquefying soil as well as the relatively high stiffness of inclined pile systems, viz. batter piles, led to failures at the pile caps. The batter piles were installed in loose fill slopes along the coastline. During the earthquake the loose fill settled, liquefied as well as spread laterally resulting in additional down-drag and lateral forces on the piles. Thus, the piles failed near their pile caps due to shearing and at the transition where the piles came out of the ground due to exhausting bending stresses. The softening of cohesive soils can also lead to a loss of bearing capacity of pile foundations. This was observed during the 1985 Mexico City earthquake resulting in heavy settlements, tilting, as well as damage to the superstructures. Figure 1.3 shows a combined 9-floor

1.1. Overview and Motivation

3

Figure 1.2: Damaged batter piles at the port of Oakland (left) and port of San Francisco (right) after the devastating 1989 Loma Prieta earthquake (after [SEA91])

residential and commercial building, which sank more than one metre into the softened soil. Medium-height buildings were the most vulnerable structures and among the buildings that either collapsed or incurred serious damage; about 60% were in the 6-15 story range. The resonance frequency of such buildings coincided with the frequency range with strongest amplification in the subsoil. Other buildings whose pile foundations rested on a hard layer of soil protruded from the surrounding terrain after the ground around the buildings subsided more than the buildings themselves [NGD05]. State-of-the-art analysis and design procedures exist for evaluating pile behaviour under earthquake loading, but their application to cases involving soft or liquefiable ground is uncertain due to the lack of physical data, against which they can be evaluated. Thus, physical modelling with detailed instrumentation has to be used to obtain the required physical data to reproduce the mechanisms involved [Bou97]. Therefore, within this work small-scale experiments have been carried out to investigate the behaviour of single piles and pile groups under quasi-static as well as earthquake loading. Numerical analysis has to be applied to predict the performance of foundations in soft or liquefiable ground during earthquakes. The most common design approach in practice is to avoid inelastic behaviour of piles and their connections below the ground surface where damage would be difficult to detect and repair [Bou97]. Many reported case histories of earthquakes round the world stated that liquefaction is the major phenomenon, which is responsible for the damage of deep founded structures. When liquefaction takes place in sandy deposits during earthquakes, the ground often undergoes a large amount of permanent deformation. This is a result of lateral flow even if the ground is nearly flat, resulting in damage of the foundation while liquefaction may result in loss of bearing

4


Figure 1.3: Pile supported building founded on soft soil after the 1985 Mexico City earthquake, foundation and soil profile (left) and heavy settled structure (after [MA88])

capacity, excessive settlement, and tilting of foundations. Lateral spread and flow of liquefied soils have also caused significant damage to pile foundations. Pile foundations are common all over the world in areas where thick layers of alluvial and underconsolidated soils are present. Such soil layers may undergo partial or complete liquefaction once a strong earthquake occurs in the vicinity. The piles driven through such soil layers may lose a significant portion of their lateral soil support. Instead, large lateral soil forces may be imposed on pile foundations if the ground experiences lateral movements. The performance of piles in liquefied as well as soft ground is not clearly understood at present.

The mentioned mechanisms observed during earthquakes, viz. liquefaction and softening of cohesive soils, can be well reproduced by using advanced constitutive models presented in this dissertation. The developed methods applied to realistic large-scale boundary value problems show the potential to predict soil-structure interaction behaviour, so these methods can be used for an optimised design of the foundation.

1.2. Problem Description, Objectives and Methods

1.2

5

Problem Description, Objectives and Methods

The objective of this thesis is to better understand the mechanisms of soil-foundationstructure interaction (SFSI) during monotonic, alternating, and dynamic loading. Experiments as well as numerical methods are presented to successfully investigate the SFSI behaviour. Unfortunately, there is a lack of well-documented seismic soil-pile response case histories, and very few of these cases include piles that have been instrumented to record dynamic response. This limited database of measured pile performance during earthquakes does not provide a good basis for calibration and validation of the numerical methods developed for seismic soil-pile-superstructure interaction problems presented in this dissertation. Accordingly, quasi-static small-scale laboratory tests and shake table model tests carried out on single piles as well as pile groups have to be used to augment the field case history data with laboratory data obtained under controlled conditions. The vast majority of shake table model tests in the literature has shown soil-pile seismic response in cohesionless soils with liquefaction potential. Anyway, many pile foundations supporting critical structures are sited on soft clays, which have the potential for cyclic strength degradation during seismic loading. This dissertation starts with an extensive literature review on laterally loaded piles in terms of experimental as well as computational investigation of soil-foundation-structure interaction (SFSI, Chapter 2). In this regard, an overview is given over the methods applied in the following chapters dealing with model-scale experiments as well as numerical modelling. At this juncture, the emphasis is placed on the finite element method (FEM) and problems occurring with it. Chapter 3 gives a brief introduction to the applied constitutive relations used for the investigated soils, namely hypoplasticity and visco-hypoplasticity. The bigger part of this chapter deals with the determination of the parameters of these constitutive laws. This determination is required for the numerical simulation of the experiments presented in the next chapter, and the numerical investigation of piles in a large-scale pile test as well as the investigation of foundations under earthquake excitation. The experimental investigation presented in Chapter 4 deals with liquefiable and soft soils and model piles subjected to monotonic, alternating as well as dynamic loading. A detailed simulation of the experiments is presented along with the experimental investigation. The numerical simulation of an in-situ large-scale pile test is shown in Chapter 5. The same chapter also presents the investigation of different types of foundations with consideration of their performance under earthquake excitation.

6


Conclusions are drawn, including a summary of the dissertation and its findings, their relevance to design procedures as well as an outlook and recommendations for future work in Chapter 6 and 7.

Chapter 2 Theoretical Framework 2.1

Introduction

In the international literature, the investigation of the behaviour of soil-foundationstructure interaction (SFSI) is carried out by means of a vast number of experimental (Chap. 4) as well as analytical, semi-empirical, and numerical methods, which can be summarised as computational methods (Chap. 5). Emphasis will be put in particular on the finite element method (Chap. 2.3.5), which is applied within this thesis in order to numerically investigate SFSI. Problems, which occurred during the application of the FEM, are presented in chapter 2.5. In the following sections, an overview will be given about the most common procedures applied in practice and science to describe and to analyse SFSI. The state-of-practice and the international building codes (Chap. 2.6) are still dominated by the application of oversimplified procedures [Whi03] [Whi97] [WL196] [WL200] [(NT92] [McG93] [Paz95] [Day02] [Paz95] [API82] [API93], which are, subsequently, presented including their assumptions, their limitations, and their most important shortcomings. In both, the experimental as well as the computational investigation of SFSI, the type of foundation and the type of loading are distinguished. This thesis places its emphasis on deep foundations, namely pile foundations, where experiments as well as calculations mostly make the difference between single piles and pile groups. In terms of pile loading, a large difference has to be made between a load applied at the pile head, including its rate of loading in terms of inertia (static, quasi-static, and dynamic), and a pile or pile group subjected to a dynamic excitation from the ground. The duration as well as the rate of loading also affects the shear strength, stiffness, and damping behaviour of the soil as well as pore water dissipation behaviour, viz. undrained, coupled, and fully drained conditions.

9

10

Chapter 2. Theoretical Framework

Figure 2.1 gives an overview over the influence of the loading types, rates, and duration distinguished in literature which support the right choice of an appropriate experiment or an applicable computational method. As can be seen, an important influencing variable is the inertia of the investigated system. For dynamic loading, the influence of inertia is high whereas for static loading it can be neglected. Soil mechanical numerical calculations distinguish between fully drained, coupled, and undrained computations. Prior to the calculations, the engineer has to decide, in which way and to what extent the velocity of loading, the duration of loading, the number of cycles, the permeability of the soil, and inertial effects, do affect his simulations. influence of the inertia

influence of the pore water flow undrained

computation

fast

velocity of loading

high

low

permeability of the soil

long

short

duration of the loading

few

number of cycles

fully drained E dynamic loading A quasi-static loading

M

slow

M

M

A

E

A few

static M loading

coupled

E many A

E

examples M slow monotonic loading A alternating loading due to wind & sea E strong earthquake excitation

Figure 2.1: Overview of the effect of type and rate of loading of piles in soil-foundationstructure interaction (SFSI) analysis

2.2. Experimental Investigation of SFSI

2.2 2.2.1

11

Experimental Investigation of SFSI Overview

In order to validate and investigate soil-foundation-structure interaction (SFSI), field and laboratory experiments have been performed all over the world. In most cases, the objectives are to provide parameters for constitutive models and to validate analytical methods with respect to SFSI. The lack of SFSI data recorded during earthquakes, the possibility of making parametric studies under controlled boundary conditions, known physical properties and state of the used soils, forced researchers to develop experimental methods for • soil-pile systems with single piles or pile groups, • different types of loading (static, cyclic, dynamic, free vibration, seismic), • different boundary conditions (excitation of head or soil mass, including different head restraints) • small or large strains during the experiments, • different pile types, soil types and conditions. Much research is carried out by performing tests with cyclic loads applied to the pile head. In these tests, the degradation of the lateral stiffness with an increasing number of loading cycles, compared to the stiffness under monotonic deflection, is investigated. Procedures have been developed for coupling the monotonic stiffness reaction with semiempirical degradation factors to derive an equivalent pile foundation stiffness to be used in numerical modelling. However, the extension of cyclic pile head loading tests to seismic loading conditions has several limitations. With pile head loading, the soil remains a passive resistor, while in seismic events the soil is applying load to the pile as will be shown later. Experiments are performed in different scales and at different places, namely: • full-scale in-situ pile tests with single piles, pile groups lateral loaded, quasi-statically or dynamically (field tests, Chap. 5.3), • model-scale pile tests with lateral head loading, • model-scale pile tests on shake tables (1-g model tests, Chap. 4.5)

12


• small-scale pile tests with geotechnical centrifuges. Sand is by far the most commonly used soil; however, more rarely silt and clay soils are used as well. A variety of techniques is used to place the soil and install the piles. In some studies, the soil is placed first and the piles are subsequently driven, pushed or bored into place. In other cases, the piles are held in place and soil is placed around them. In order to place the soil, techniques are used including dropping and tamping for soft fine-grained soils, pluviation, raining, and flooding for hard-grained soils.

2.2.2

Full-Scale Field Tests with Piles

The full-scale tests with piles identified during the literature review include a wide variety of pile types, installation methods, soil conditions, and pile-head boundary conditions but only few of them are completely presented to the public so that they can be used for a numerical simulation [Mok99]. Full-scale pile load tests offer the distinct advantages of utilising real soil, piles, and soil-pile stress conditions. Nevertheless, their limitation lies in their type of loading applied from the top. Thus, the effects of inertial interaction due to the superstructure cannot be taken into account, and the effects of wave interaction from below due to an earthquake excitation are ignored. Famous full-scale pile tests, which also have been codified in API [API82] [API93] design recommendations, were performed by Matlock [Mat70] in soft ground, Reese et al. [RCK75] in stiff clay, and Reese et al. [RCK74] in sands. Lateral head loading tests in flooded and partially saturated San Francisco Bay Mud were conducted by Gill [Gil68]. Feagin [Fea37] performed the first field test on a group of driven timber piles in sandy soil in 1937. The pile group, consisting also of some inclined piles, was loaded horizontally in different directions. Further tests on pile groups with sand and clay can be found in [KB76] [KSB79] [HMFG82] [BRO87] [BMR88] [ABA05b] [RPW98] [WRP98].

2.2.3

Model-Scale Pile Tests on shake tables

In order to understand and to validate SFSI, shake table tests with model piles and pile groups are conducted in the worldwide literature. The majority of experiments performed on piles fall under the category of 1-g model tests. Model tests are relatively inexpensive and can be conducted under controlled laboratory conditions. This provides an efficient means of investigation.

2.2. Experimental Investigation of SFSI

13

The primary shortcomings of 1-g model testing are related to scaling and edge effects. Scaling effects limit the applicability of model tests in simulating the performance of prototypes, which is not the objective of the experiments presented in the following experimental chapters (Chap. 4). 1-g models are useful in performing parametric studies to examine relative effects. Caution is required in extrapolating results obtained from model tests to full-scale dimension. The experiments presented within this dissertation are modelled by means of the finite element method under consideration of exactly the same stress levels and dimensions used in the experiments. A direct extrapolation of the results to full-scale dimensions is not favourable since soil pressure distribution, soil particle movements, and at-rest stress levels are all factors influenced by scaling. However, the applied constitutive relations (cf. Chap. 3) are valid for a wide range of stress conditions with the same set of parameters, this allows a numerical up-scaling towards full-scale problems. Edge effects become significant if the size of the test tank is too small relative to the size of the model pile. Prakash and Sharma [PS90] propose to keep a minimum zone of influence to be at a distance of 8 to 12 times the pile diameter or width in the direction of loading and three to four times the pile diameter normal to the direction of loading. Experimental containers, e.g. laminar boxes that do not meet these guidelines, would involve edge effects, which are not easily quantified. The ratios of container width to pile diameter given in the experiments presented within this dissertation in order to consider edge effects are in a range between 70 for the barrel tests (Chap. 4.4) and 120 for the shake box tests (Chap. 4.5), which is well above the minimum zone of influence proposed by [PS90]. Most of the shake table tests presented in the literature are intended to investigate the seismic response of single piles or pile groups in hard-grained soils, only very few have been carried out with respect to piles in soft fine-grained soils. Most of the input motion in the literature consisted of sinusoidal waves, only few used an earthquake excitation record, and to date no shake table test on model piles in soft fine-grained soils with a high level earthquake base excitation in a flexible model container has been reported [Mey98]. Kubo [Kub69] conducted first experiments with single model piles in 1969 investigating soil-pile interaction and pile bending. Groups of aluminium pipes in silty clay under static lateral loading as well as shake table loading were tested by Yao in 1980. Kagawa and Kraft [KK81] carried out shake table tests with piles in saturated sand. Mizuno and Iiba [MI82] applied the first earthquake time history base excitation using a setup with model piles of rectangular cross-section in a polyacrylamide-bentonite mixture as a model soil. Using the same testing equipment Korgi [Kor86] tested different soils and different pile head restraint conditions. Using a realistic pile installation process Liu and Chen [LC91]

14


investigated pile groups in liquefiable sand. Nomura et al. [NST91] used a laminar box container in order to study SFSI behaviour of piles during liquefaction. Lateral spreading of the soil and its effects on piles and pile groups were investigated by Sasaki et al.[STMS91], Tokida et al. [KT92], Ohtomo [OH94], and Hamada [Ham91]. Further tests were carried out by Tao et al. [TTKA98], Makris et al. [MTXY97], Yamamoto [YUM92], and Yan et al. [YBD91].

2.2.4

Centrifuge Tests

Similar to 1-g model testing, a geotechnical centrifuge provides a relatively rapid method for performing parametric studies. The advantage of centrifuge modelling lies in the ability to reproduce prototype stress-strain conditions in a reduced size model. An extensive introduction pertaining to centrifuge mechanics and its principles is given in [Sch80]. Both head loading and base-shaking boundary conditions can be simulated in a centrifuge. In order to reduce parasitic boundary effects of the soil containers, laminar and hinged boxes are used. The pioneers in testing model piles in the centrifuge were Scott et al. [SLT77]. They used instrumented steel rods in dry sand and let the rods freely vibrate. Improvements were carried out, and saturated sand was used [STST82] in order to provide cyclic lateral loading. Ting and Scott [TS84] investigated pile groups in saturated sand. First earthquake-like tests on piles were conducted by Zelikson et al. [ZLP82], Oldham [Old84] was the first who installed piles during a centrifuge experiment, called in-flight installation, and Finn and Gohl [GF87] were the first who used a base-shaking device in order to simulate earthquake motion. The first earthquake experiment in a centrifuge with clay was conducted by Hamilton et al. in 1991 [HDMP91]. An extensive overview over centrifuge modelling on model piles and pile groups can be found in [Mey98].

2.3 2.3.1

Computational Investigation of SFSI Overview

The computational prediction of the behaviour of piles and pile groups in the ground during monotonic, alternating, and most notably earthquake loading remains a difficult task, especially when the soil supporting the piles experiences liquefaction. Current design practice for structures subjected to earthquake loading regards dynamic soil-foundationstructure interaction (SFSI) to be mainly beneficial to the behaviour of structures. By the state-of-practice, the flexibility of the foundation is said to reduce the overall stiffness of

2.3. Computational Investigation of SFSI

15

the soil-foundation-structure (SFS) system and, therefore, reduces peak loads caused by a given ground motion. Even if this may be true in many cases, there is the possibility of resonance occurring because of a shift of the natural frequencies of the SFS system. This can lead to large inertial forces acting in and near the structure. As a result of these large inertial forces, caused by the structure oscillating in its natural frequency, the structure as well as the soil surrounding the foundation can undergo plastic deformations. Note that the natural frequency of the SFS system changes incessantly since the state of the surrounding soil changes during the dynamic loading and afterwards. Plastic deformations in turn further modify the overall stiffness of the SFS-system and make any prediction on the behaviour very difficult. Quasi-static alternating as well as dynamic SFSI gain importance in the design of large geotechnical projects. In the last years, the concept of performance-based design has been introduced to the engineering community [Ham00], hence more sophisticated models are needed. A good numerical model of a soil-foundation-structure system can not only prevent the collapse or damage of a structure. It can also help to save money by optimising the design in order to withstand alternating loading by wind, sea, or an earthquake with a certain return period. A variety of methods of different levels of complexity is currently being used by engineers. In the following, an overview over the most important ones is presented. A more thorough discussion on methods and specific aspects of SFSI is available in Wolf [Wol85] [Wol88], and more recently in [WS02]. Various approaches have been developed for the SFSI analysis of single piles and pile groups. These approaches can be applied to predict lateral deflection, rotations, and stresses in the piles throughout the loading history. Approaches that are more sophisticated are also capable to predict changes of state of the surrounding soil during loading. The following is a shortcut of different types of SFSI approaches, which are currently pursued. Without SFSI, the ground motion is applied directly to the base of the building. Alternatively, instead of applying the ground motion directly to the base of the structure, effective discrete earthquake forces proportional to the base acceleration are applied to the structure distributed over its levels. This is the so-called push-over method. This procedure is at best reasonable for very flexible structures on very stiff soil or rock. In this case, the displacement and the state of the soil do not get modified by the presence of the structure. For stiffer structures on soil, the ground motion has to be applied to the soil. The model has to incorporate propagation of the motion through the soil, its interaction with the structure and the radiation away from the structure. The response of pile-structure systems is highly dependent on frequency, which calls into question the applicability of pseudo-static analyses to such problems. Unfortunately, this state-ofpractice approach without SFSI is assumed to be on the safe side, which can be crudely

16


wrong. In case of analytical methods, the soil around the pile can be modelled analytically as a homogeneous elastic continuum by means of the linear elasticity theory [Pou71]. Analytical approaches are often restricted to simplified boundary conditions and can hardly be modified in order to consider variations in geometry, geology, complexity, and non-linearity. Substructure methods infer the principle of decomposition, i.e. if linearity is presumed. Generally, the SFS-system is subdivided into a structure part and a soil part. Both substructures are analysed separately, and the total displacement can subsequently be obtained by adding the calculated contributions at the interfacing nodes. This method reduces the size of the problem considerably. As the time needed for an analysis does not increase linearly with an increasing number of equations, the substructure method is much faster than the direct methods presented below. However, a big drawback of the method is the fact that linearity for all single parts has to be assumed. For non-linear systems, the substructure method cannot be used. Thus, an application is only justifiable in cases of structures built on very stiff soils which are subjected to small loading amplitudes. Correspondingly, substructure methods are rarely suitable to consider strong earthquake excitation. Direct methods treat the SFS-system as a whole. The numerical model incorporates the spatial discretisation of the structure and the soil. The analysis of the entire system is carried out in a single step. This method provides the widest generality as it is capable of incorporating any non-linear behaviour of the structure, the soil, and the interface between those two. For the direct method, different levels of sophistication are possible. • In the foundation stiffness approach, the behaviour of the soil is accounted for by simple mechanical elements such as springs, masses, and dashpots. Different configurations of the subsoil can be taken into account by connecting several springs, masses, and dashpots whose parameters have to be determined by a curve fitting procedure [Wol94]. This approach is very popular among structural engineers as it is easily integrated in commonly used finite element codes. Variants use frequency dependent springs and dashpots and, therefore, require an analysis in the frequency domain. Relatively complex configurations of layered subsoil and embedded foundations can be modelled with reasonable accuracy if the state of the soil does not change considerably by replacing the (elastic) soil by a sequence of conical rods [WS02] [WP03]. • Different stages of development can be associated to p-y methods


17

– The Winkler or the so-called subgrade reaction approach is the oldest method for the prediction of pile deflections and bending moments. It can be seen as the predecessor of the p-y method. – The quasi-static non-linear Winkler or the so-called p-y method of analysis. In this approach, the lateral pile support is modelled by a series of uncoupled springs that are either linearly elastic or non-linear. The load-deformation relationship is usually described by p-y curves, where p is the soil resisting force per unit length of the pile at a given lateral pile displacement y. – The dynamic non-linear Winkler approach. Attempts have been made to apply the static p-y approach for evaluating lateral loading on pile foundations to dynamic problems. Mostafa et al. [MN02] list several references and provide a parametric study of single piles and pile groups in different soil types under simplified loading cases. Even if p-y curves are widely used for estimating lateral loading on piles, they are rarely used in full dynamic soil-structure interaction analyses. Current work trying to implement these methods into structural finite element codes is likely to make them more popular within the engineering community. However, changes of state of the soil cannot be taken into consideration by p-y methods. • Full non-linear 3D-methods of SFSI can be regarded as an overall approach. The pile and the soil can be modelled numerically using finite element, boundary element or finite difference techniques. It is desirable to use non-linear constitutive representations of the soils’ stress-strain relation. This thesis concerns the latter. Displacements and forces can be obtained not only for the structure as in the abovementioned methods, but also in any location of the soil. For all of the computational resources and modelling effort required for an analysis, it is the only method that remains valid for all kinds of problems involving material non-linearities, contact problems, different loading cases, and complex geometries.

2.3.2

Winkler’s Approach

The Winkler approach (1867), also called subgrade reaction theory [Win67], is the oldest method. It uses a modulus of subgrade to model the soil by a series of unconnected linear springs with a stiffness ks expressed in SI-units by [kN/m3 ]. The modulus of horizontal soil reaction (or soil modulus) is defined as: def

ks =

−p , y

(2.1)

18


where p is the lateral soil reaction per unit length of the pile, and y is the lateral deflection of the pile [MR60]. The negative sign indicates that the direction of soil reaction is opposite to the direction of the pile deflection. Terzaghi [Ter55] introduced a coefficient (or modulus) of horizontal subgrade reaction kh . kh = αk

ks , D

(2.2)

where D is the diameter or width of the pile and αk is an empirical factor, which was initially suggested by Terzaghi as αk = 0.74. However, αk depends on the type and the state of the soil, the stiffness of the pile as well as the applied boundary conditions. Consequently, a large number of authors proposed different values for αk , depending on their application. In this manner, Matlock [Mat70] found αk = 1.8 for a deflection at 50% of the ultimate capacity. Poulos [PD80] compared the Winkler and elastic continuum approaches by equating the displacement obtained by modelling a stiff fixedheaded pile and found αk = 0.82. Pyke [PB84] found αk = f (ν) to be a function of the Poisson’s ratio ν by applying the plane strain problem of a rigid disk moving through an infinitely elastic medium, also allowing for the build-up of gaps, resulting in αk between 1.8 and 2.3. The behaviour of a single pile can be analysed using the equation of an elastic beam supported on an elastic foundation, which is represented by the forth order differential equation of a bending beam:

Ep Ip

d2 y d4 y + Q + ks y = 0, dz 4 dz 2

(2.3)

where Ep is the modulus of elasticity of the pile, Ip is the moment of inertia of the pile section, Q is the axial force in the pile, z is the vertical depth, and y is the lateral deflection of the pile at point z measured along the length of the pile. Making simplifying assumptions, viz. neglecting the axial component (Q has very little effect on the deflection and the bending moment), and applying variation techniques, viz. the minimisation of potential energy leads to the governing equation for the deflection of a laterally loaded pile, d4 y ks + y = 0. dz 4 Ep Ip

(2.4)


19

The soil stiffness modulus for sand and normally consolidated clay is often assumed to vary linearly with depth as follows:

ks = kz

(2.5)

where k is in units of force per volume. For various pile-head boundary conditions, and for the assumed linear variation of ks with depth, non-dimensional coefficients are given in the literature that can be used to calculate pile deflections, rotations, and bending moments [MR60] [PD80]. Non-linear soil modulus distributions versus depth such as step functions for layered soils, hyperbolic as well as exponential functions are given in [GD70]. The Winkler subgrade reaction method has to be handled with care because of its obvious shortcomings. The modulus of subgrade reaction ks is not an objective property of the soil, but it depends intrinsically on the interaction behaviour with the pile, i.e. pile stiffness, magnitude of the deflection, and the state in terms of stress and density of the soil. Thus, ks depends neither on physically justifiable parameters nor can it be assumed to be constant even during a single monotonic loading step. The method to determine ks is semi-empirical in nature, and the soil model used in the method is discontinuous, viz. the linearly elastic Winkler springs behave independently and, thus displacements at a certain point are not influenced by displacements and stresses at other points along the pile.

2.3.3

Non-linear Winkler Approach

In most cases in literature, a lateral pile analysis is conducted using a beam on an elastic foundation model with non-linear p-y curves, also named Beam on Non-linear Winkler Foundation (abbr. BMWF). The method was developed by Reese and coworkers [RCK74] [RCK75]. The soil is represented by a series of non-linear p-y curves that vary with depth and soil type. Figure 2.2 shows a pile considered as a beam with attached discrete non-linear springs whose p-y reaction is given at the right-hand side. These models were established and matched by means of field tests with fully instrumented piles in uniform soils, in particular hard-grained [RCK74] and soft fine-grained [Mat70] [RCK75]. Subsequently, the results were adjusted by using empirical parameters with the aim to utilise these models for a large variety of soil conditions. The early models by Matlock [Mat70] and Reese [RCK74] work with independent non-linear springs (Winkler springs) at discrete locations. These simplified models do not account for the interaction of one layer with another, and they are not capable to model changes of pile properties with boundary condition, i.e. of pile bending stiffness, pile shape, and pile

20


head fixity [ANP98]. The most widely used analytical expression for p-y curves is the cubic parabola represented by [Ree77]: p = 0.5 pult

y y50

1/3 ,

(2.6)

where pult is the ultimate soil resistance per unit length of the pile and y50 is the deflection at one-half the ultimate soil resistance. In order to convert from strains measured in laboratory triaxial tests to pile deflections, y50 is calculated by means of the following equation:

y50 = Aε50 D,

(2.7)

where A is a constant that varies in a range from 0.35 to 3.0 [RCK74], and ε50 is the strain at 50% of the maximum principal stress difference, determined in a laboratory triaxial test, and D is the pile width or diameter. lateral load p

y

z1

y

z2

y

z3

y

z4

y

z5

y

pile

z

non-linear springs

p-y curves

Figure 2.2: The non-linear Winkler approach by means of p-y curves, the pile is subdivided in 5 parts with attached non-linear springs


21

Deflections, rotations, and bending moments in the pile can be calculated by solving the bending beam equation using numerical techniques, e.g. the finite difference or the finite element method, where the pile is subdivided into small increments and, subsequently, analysed using assigned p-y curves to represent the soil resistance. Boundary conditions at the top and at the pile bottom have to be taken into account to solve the bending beam equation correctly. In most cases where piles are slender, a zero moment can be assumed at the bottom of the pile. The experiments presented in the following chapters show that this is not a necessity. The boundary conditions at the pile top can be categorised by

free-head conditions, which are given when the pile is not restrained against rotation, i.e. Q(z0 ) =const. and M (z0 ) =const. or zero. moment loading conditions, which are satisfied when vertical eccentrical loads are applied at the ground surface, i.e. Q(z0 ) = 0 and M (z0 ) =const. partially restrained conditions, which are fulfilled when the pile head extends into a superstructure or is partially restrained against rotation, i.e. ratio M (z0 )/w (z0 ) =const. and Q(z0 ) =const. fully restrained conditions or the so-called fixed-head conditions, which are given when the rotations are kept constant, i.e. usually w (z0 ) = 0 and Q(z0 ) =const.

Even if the p-y method is an improvement on the linear subgrade reaction approach because it accounts for the non-linear behaviour of the soil, the method has plenty of limitations. The continuous nature of the soil along the pile is not explicitly modelled by the p-y method, where its curves are assumed to be independent of each other. The determination of p-y curves is at best acceptable when full-scale instrumented lateral load tests are performed. Even then, tremendous difficulties exist in choosing appropriate p-y curves for a given combination of pile size and soil type. Standard curves, i.e. the socalled default curves, must not be used for untested conditions as default curves are at best limited to the soil types, in which they are developed. Thus, their application is not universal. The replacement of the soil continuum by discrete springs, when applying the non-linear Winkler approach, restricts the extension of the analysis to pile groups since interaction between the neighbouring piles may not be taken into account when determining the p-y curves. Furthermore, the non-linear Winkler approach cannot work with reversals in case of soil degradation or self healing.

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2.3.4


Elasticity Theory

To determine soil-foundation-structure interaction behaviour by means of the elasticity theory, the piles are assumed to be thin vertical strips of length L, diameter D, and flexural stiffness Ep Ip . The piles are divided into n + 1 elements, between each element a horizontal stress p is assumed as a function of the axial coordinate z. It is assumed that the horizontal displacements of the pile are equal to the horizontal displacements of the soil. The soil is assumed to be ideally elastic, homogeneous, isotropic and semi-infinite, defined by the elastic parameters Es and νs . The soil displacements ys can be expressed as {ys } =

D [Is ]{p} Es

(2.8)

where {ys } is the column vector of the soil displacements, {p} is the column vector of the horizontal loading between the soil and the pile, and [Is ] is the n + 1 by n + 1 matrix of soil-displacement influence factors determined by the integration of Mindlin’s equation (details how to solve the Mindlin’s equation can be found in Appendix B of [PD80]) using the boundary element method [Pou71]. Afterwards, the finite difference form of the bending beam equation has to be used to determine the pile displacements. The form of the equation varies, depending on the applied pile-head boundary conditions. For a number of different soil and loading conditions, expressions for free-head and fixed-head piles can be found in the literature [PD80]. Some authors tried to adapt the method to account for the non-linear behaviour of the soil, others applied it for analysing battered piles, pile groups of any shape and dimension, layered systems, and systems, in which the soil modulus varies with depth. The elasticity theory is a limited method as well: The biggest limitation appears from the difficulty in determining an appropriate soil modulus Es , which is far away from being a soil parameter because it can even change within a single loading step. Furthermore, the handling of the Mindlin equation and its adaption to non-linear soil behaviour and complicated boundary conditions is very complex.

2.3.5

Finite Element Method (FEM)

Overview The finite element method (FEM) potentially provides the most powerful means for conducting SFSI analysis. The advantages of a finite element (FE) approach include the


23

capability of performing the SFSI analysis of single piles and pile groups in a fully coupled manner, i.e. without resorting to independent calculations of site or superstructure response, or application of empirical pile group interaction factors. It is principally possible to model any arbitrary soil profile and to study 3D effects. Challenges to a successful implementation of this technique lie in providing appropriate constitutive soil models that can model small to very large strain behaviour, rate dependency and degradation of resistance, and still prove practicable (cf. Chapter 3.1). Special features can also be implemented to account for pile installation effects (cf. Chapter 2.5.2) and soil-pile gapping (cf. Chapter 2.5.2). Typically, FE approaches model the soil as a continuum. In most of them, the pile displacements and stresses are evaluated by solving the bending beam equation (Eq. 2.3) with standard numerical methods. Interface elements are often used to model the soil-pile interface. Interface elements can allow friction behaviour when there is contact between the pile and the soil, and exclude transition of forces across the interface when the pile is separated from the soil. Within the general framework of the finite element methods, several variations are again possible: • total stress approaches based on equivalent linear soil properties, • partly coupled effective stress approaches, • fully coupled approaches. The discretisation of the model can be either • one-dimensional idealised, which is applicable in plane shear wave propagation problems where the interaction with structures in the soil is not of importance. • two-dimensional calculations suitable for long geotechnical structures. In order to take into account the appropriate SFSI behaviour, the stiffness of the foundation per unit length into the plane has to be determined. • three-dimensional calculations, which in a dynamic analysis are still CPU-intensive but indispensable for an adequate modelling. FE techniques can be used to analyse complicated loading conditions, i.e. any combination of axial, torsional, and lateral loads on the pile. The capability of considering the nonlinear behaviour of the structure and the soil and the potential to model the pile-soilstructure interactions appear to be satisfactory. Time-dependent results can be obtained,

24


and more intricate conditions such as battered piles, inclined soil layers, and different types of soils can be modelled. The method is used in the literature with a variety of soil stress-strain relationships, and is capable for analysing pile group behaviour. Until now performing a three-dimensional finite element analysis requires considerable engineering time for generating input and, subsequently, interpreting the results. For this reason, the finite element method has predominantly been used for research but rarely for design. Verification and Validation Process in FEM discretisation & solution error

constitutive modelling

mathematical model

idealisation

verification

Implementation physical system

experimental database

EXPERIMENTS

FEM idealisation & discretisation

discrete model

equation solver

discrete solution

solution error simulation error

verification

validation

Figure 2.3: The FEM analysis process in terms of verification and validation of the discrete solution, after [Sar03] (modified)

Processes using the finite element method involve carrying out a sequence of steps in order to simulate physical systems by means of a so-called model-based simulation. A detailed overview can be found in [Sar03]. The process is illustrated in Fig. 2.3. The centrepiece is the modelling of the physical system, i.e. here the SFSI model. The processes of idealisation and discretisation are carried out concurrently to produce the discrete model. The solution step is handled by an equation solver customised to FEM, which delivers a discrete solution or solutions. The concept of error search arises in the FEM in two ways. These are known as verification and validation, respectively. Verification is done by replacing the discrete solution into the discrete model to get the solution error. Validation tries to compare the discrete solution against observation of reality by computing the simulation error, which combines modelling and solution errors. As the latter can principally be neglected, the simulation error in practice can be identified with the modelling error. One way to adjust the discrete model in a manner that it represents the physics is better called model updating. Then the discrete model is given free


25

parameters, these are determined by matching the discrete solution against experiments, as shown in Fig. 2.3.

Historical review of SFSI and FEM The non-linear lateral pile response of single piles and pairs of piles to static loading using FEM and a radial soil-pile interface element was first presented by Yegian and Wright in 1973 [YW73]. Based on Kausel’s work [KRW75], Blaney et al. [BKR76] used a finite element formulation with a consistent boundary matrix to represent the free-field, subjected to both pile head and seismic base excitations, and derived dynamic pile stiffness coefficients as a function of the dimensionless frequency. Desai and Appel [DA76] presented a three-dimensional FE solution with interface elements for the laterally loaded pile problem. Emery and Nair [EN77] studied an axisymmetric FE model that incorporated non-symmetric free-field acceleration boundary excitations from wave propagation analyses. Randolph and Wroth [RW78] modelled the linear elastic deformation of axially-loaded piles. Kuhlemeyer [Kuh79a] offered efficient static and dynamic solutions for an elastic lateral soil-pile response. Kuhlemeyer [Kuh79b] used an FE model of dynamic axially loaded piles to verify Novak’s solution [Nov77] and a simplified method presented by the same author. Angelides and Roesset [AR81] extended Blaney’s work with an equivalent linearisation scheme to model the non-linear soil-pile response. Force-deflection relations were developed and compared favourably with p-y curves suggested by Stevens and Audibert [SA79]. Randolph [Ran81] derived simplified expressions for the response of single piles and groups from a finite element parametric study. Dobry et al. [DVOR82] made a parametric study of the dynamic response of head loaded single piles in uniform soil using Blaney’s method, and proposed revised pile stiffness and damping coefficients as a function of Es and Ep . Kay et al. [KKvH83] promoted a site-specific design methodology for laterally loaded piles consisting of pressuremeter test data as input to an axisymmetric FE programme. Lewis and Gonzalez [LG85] compared field test results of drilled piers to a 3D FE study that included non-linear soil response and soil-pile gapping. Koojiman [Koo89] described a quasi-3D FE model that substructured the soil-pile mesh into independent layers with a Winkler type assumption. Brown et al. [BSK89] obtained p-y curves from 3D FE simulations that enabled only a fair comparison to field observations. Wong et al. [WKI89] modelled soil-drilled shaft interaction with a specially developed 3D thin layer interface element. Bhowmik and Long [BL91] devised 2D and 3D FE models that used a bounding surface plasticity soil model and provided for soil-pile gapping. Brown and Shie [BS91] used a 3D FE model to study group effects on modification of p-y curves.

26


Urao et al. [UMKF92] contrasted results from a dynamic 3D FE analysis of a composite pile-diaphragm wall foundation with an axisymmetric model. Cai et al. [CGD95] analysed a 3D non-linear FE subsystem model consisting of substructured solutions of the superstructure and soil-pile systems. In companion papers, Wu and Finn [WF97a] [WF97b] presented a quasi 3D FE formulation with relaxed boundary conditions that permitted a dynamic non-linear analysis of pile groups in the time domain and dynamic elastic analysis of pile groups in the frequency domain. These methods showed good comparison to techniques with reduced computational cost, which are more rigorous. Fujii et al. [FCTH98] compared the results of a fully coupled 2D effective stress SSI model to measure the performance of a pile-supported structure in the Kobe earthquake. Maheshwari et. al published several papers showing 3D non-linear seismic analysis of single piles as well as pile groups using FEM and elasto-plastic constitutive models in the time domain [MTGEN03] [MTMP03] [MTENG03] [MTM03]. Ross et al. [RBW+ 04] compared FE non-linear dynamic analyses with results of dynamic centrifuge model tests of pile-supported structures in liquefying sand profiles. Their FE models utilised soil spring elements that connect pile elements to 1D or 2D meshes of a soil profile. Liu et al. [LLY04] describe the formulation and validation of a new FE model for the 3D analysis of pile-soil interaction problems. The proposed element is designed by wrapping four slip elements around a 2-noded flexural element.

2.4

Principal Mechanisms of the dynamic SFSI

Generally, it has been accepted as a conservative seismic design assumption for a spectral analysis approach to ignore or simplify the influence of pile foundations on the ground motions applied to the structure. Routinely deep foundations are employed to transfer axial structural loads through soft soils down to stronger bearing strata at depth. Nevertheless, these foundation elements may also be subject to transient or cyclic lateral loads arising from earthquake, wind, impact, or machine operation. The occurrence of major pile-supported structures sited on soft soils in areas of earthquake hazard (e.g. 1985 Mexico City Earthquake) results in significant demands on deep foundations. Liquefaction and/or strain-softening potential in these soft soil sites can impose additional demands on pile foundation systems. Observations of pile performance during earthquakes show that pile foundations do affect the ground motions. The superstructure experiences and piles can suffer extreme damage and failure under earthquake loading. Figure 2.4 illustrates schematically the principal characteristics of seismic soil-foundationstructure interaction (SFSI). The system components include the superstructure (SS), the

2.4. Principal Mechanisms of the dynamic SFSI

27

SS nonlinear response PC

hysteretic damping

Seismic Energy S

P

kinematic

Shear Waves

physical

kinematic

Surface Waves

P material damping radiation

Near Field Domain kinematic radiation Shear Waves Far Field Domain

Figure 2.4: Principal Mechanisms of the seismic soil-pile-superstructure interaction, SS superstructure, PC - pile cap, P - piles

pile cap (PC), the piles (P), the soil idealised into near field and far field domains, and the seismic energy source. The modes of system interaction in general are often described as kinematical, inertial, physical, and radiation interaction: The mode of the so-called kinematical interaction accounts for the kinematical coupling between the individual domains (far field soil, near field soil, foundation, superstructure) transmitting the motion from the seismic source up to the pile foundation and structure. In that way, the pile surrounding soil attempts to deform more or less, i.e. if the soil-pile gapping does not dominate the interaction together with the pile resulting in the superstructure experiencing a different ground motion than the soil at the free-field surface. The so-called inertial interaction accounts for structural inertial forces being transferred to the pile foundation imposing lateral loads concentrated near the pile head, but also additional axial loads due to a rocking mode of the pile-structure system. The degree of inertial interaction is dependent of the type of head fixity (fully constrained, partially constrained, free-head conditions), the static loads but also the pile cap embedded resistance. The so-called physical interaction is dependent on the installation process influencing

28


the state of the surrounding soil, the loading history of the soil-pile-interface, and possible down-drag of the surrounding soil. It depends on the behaviour of the soil-pile interface like friction, the soil-pile gapping behaviour on the properties of soil, and the pile itself influencing the axial and lateral response of the pile-soil system. During seismic loading, gaps may open between the soil and the pile near the ground surface. In hard-grained soils, the gap between the soil and the pile may instantly fill and may be compacted before being opened. However, in soft soils the gap may stand open resulting in a reduction of soil-pile lateral stiffness. When the gap is submerged, water alternately draws in and ejects from the gap during each load cycle; it may scour the soil adjacent to the pile resulting in a further reduction of stiffness. The so-called radiation interaction occurs when the pile-structure system is vibrating at much higher frequencies than the surrounding soil due to the large stiffness difference between the soil and the piles [Mey98]. This results in the transition of high frequency kinetic energy away from the pile into the surrounding soil. In most cases, radiation interaction can be neglected because it is restricted to extremely low soil damping, high frequencies being dissipated by the hysteretic behaviour of the soil preventing their propagation, and cannot propagate through gaps between soil and pile. For systems with a strong non-linear response, a fully coupled analysis technique may be desirable. Figure 2.4 shows the extremely high degree of system coupling between the kinematical, inertial, physical, and radiation modes and their components of interaction illustrating the complexity of seismic soil-pile-superstructure interaction.

2.5 2.5.1

Problems occurring with FEM Numerical Accuracy and Stability

The accuracy of a numerical simulation of dynamic SFSI is controlled by two main parameters: a) the spacing of the nodes of the finite element model ∆h and b) the duration of the time step ∆t. Assuming that the numerical calculation converges towards the exact solution as ∆h and ∆t go towards zero the desired accuracy of the solution can be obtained as long as sufficient computational resources are available. In order to provide sufficient numerical accuracy and stability for every numerical model, a study has to be carried out to verify convergence of the solution. For this reason, in the shake table simulations (cf. Sect. 5.2) as well as in the seismic SFSI analysis (see Sect. 5.4) the time increments have been reduced from ∆t = 0.001 seconds to ∆t = 0.0005 s. The solutions have been

2.5. Problems occurring with FEM

29

compared and proved to fit exactly. In addition, the meshes have been refined in order to show that any refinement of the model won’t have any influence on the solution. In order to represent a travelling wave of a given frequency accurately, about 10 nodes per wavelength λ are required. Fewer than 10 nodes can lead to numerical damping as the discretisation misses certain peaks of the wave. In order to determine the appropriate maximum grid spacing, the highest relevant frequency fmax that is present in the model needs to be found by performing a Fourier analysis of the input motion. Typically, for seismic analyses fmax is about 10 Hz. By choosing the wavelength λmin = v/fmax , where v is the wave velocity to be represented by 10 nodes, the smallest wavelength that can still be captured partially is λ = 2∆h corresponding to a frequency of 5 fmax . The maximum grid spacing should not exceed

∆h ≤

λmin 10v , = 10 fmax

(2.9)

where v is the lowest wave velocity that is of interest in the simulation. Generally, this is the shear wave velocity. For the seismic SFSI analysis in Sect. 5.4, the grid spacing has to be smaller than ∆hmax = 1 metre according to Eq. 2.9. The same assumption is fulfilled for all shake table simulations in Sect. 5.2 where all node spacings in the FE meshes are smaller than 5 cm. For full-scale simulations, the grid spacing is chosen to fit exactly the requirements of Eq. 2.9 in order to reduce CPU costs. The time step ∆t, used for numerically solving non-linear vibration or wave propagation problems, has to be limited for two reasons. The stability requirement depends on the numerical procedure in use and is usually formulated in the form ∆t/Tn < value. Tn denotes the smallest fundamental period of the system. Similar to the spatial discretisation Tn needs to be represented by about 10 time steps. While the accuracy requirement provides a measure, on which higher modes of vibration can be represented with sufficient accuracy, the stability criterion needs to be satisfied for all modes. If the stability criterion is not satisfied for all modes of vibration, then the solution may diverge. In many cases, it is necessary to provide an upper bound to the frequencies that are present in a system by including a frequency dependent damping to the model. The second stability criterion results from the nature of the finite element method. As a wave front progresses in space, it reaches one node after the other. If the time step in the finite element analysis is too large, the wave front can reach two consecutive nodes at the same moment. This violates fundamental properties of wave propagation and subsequently can lead to instability. Therefore, the time step needs to be limited to

30


∆t
1) than for normally consolidated soils (OCR ≈ 1). In the visco-hypoplastic constitutive relation, OCR is defined as def

OCR =

pe , p+ e

(3.40)

where pe is the equivalent stress determined by Butterfield’s approximation (Eq. 3.22) with regard to the reference state (ee0 , pe0 )

1 pe = pe0 exp ln λ

1 + ee0 1+e

,

(3.41)

and the value of p+ e is given by 2 p+ , e = p 1+η

(3.42)

with η from Eq. 3.37 as a function of the current stress, i.e. η has to be updated during the simulations.

3.3. Parameters of the Visco-hypoplastic Relation

59

Table 3.2: Overview of the parameters of the visco-hypoplastic constitutive relation and required laboratory tests parameter required laboratory tests λ

coefficient of virgin compression

triaxial isotropic compression tests, oedometric CRSNcompression tests, or conventional oedometric compression tests using Eq. 3.22 and conversion by Eq. 3.26 triaxial isotropic compression tests and Eq. 3.23, oedometric CRSN-compression tests using conversion by Eq. 3.24, or from conventional oedometric compression tests using conversion Eq. 3.26 undrained triaxial tests or shear box tests at limit state from Eq. 3.27 oedometric CRSN-compression tests, isochoric shear tests, isotropic compression tests with variation of the deformation rate (Eq. 3.28), isotropic or oedometric creep tests (Eq. 3.29). Crude estimation by empirical correlation (Eq. 3.30)

κ

swelling coefficient

ϕc

critical friction angle

Iv

viscosity index

βR

shape parameter

fit of stress paths of undrained tests for normally consolidated samples (Fig. 3.7), with constant deformation rate

ee0

reference void ratio

from the determination process of the reference isotach, i.e. λ-line described in Section 3.3.5

pe0

reference pressure

arbitrarily chosen, e.g. pe0 = 100 kPa

e0 ˙

reference deformation rate

arbitrary or according to the deformation rate ε˙1 used in experiments, e.g. for isotropic compression Eq. 3.31

60

3.4

Chapter 3. Used Models and their Parameter Determination

Parameters of Intergranular Strain

In nearly all cases, boundary value problems in geotechnical engineering exhibit changes of the direction of stress and deformation paths in soil elements during the loading history. This is obvious for cyclic and dynamic loading, but also static problems, i.e. slow horizontal loading and unloading of a pile show this feature. A change of path direction leads to a sudden change of the stiffness. Experimental investigations show that soils with the same density and effective stress behave much stiffer after a monotonic deformation [ARS90]. However, a continued monotonic deformation after the changed direction again leads to an asymptotic approach of the original deformation path also reached without change of direction. This condition was called swept out of memory state (SOM, [GGW77]) because the memory of the soil with respect to their previous deformation paths is wiped out. In case of soft fine-grained soils, Krieg [Kri00] introduces so-called extended SOM states (ESOM ). Physically the intergranular strain behaviour can be explained by a change of the contact shapes and the contact forces between the soil particles without any significant change of the grain skeleton assembly [Gud01]. A disregard of small strain phenomena in numerical calculations results in an overprediction of total displacements for given external forces. Soils loaded with very small strain cycles (amplitudes smaller than about 10−5 ) tend to behave nearly elastically. A numerical simulation using the hypoplastic constitutive relation without allowance for the mentioned small strain behaviour of the soils, shows a gradual accumulation of strains by stress cycles, especially very small ones [BW92], [NH97]. The excessive accumulation of deformations, as well as the excessive decrease of stresses, are called ratcheting. A similar effect is given when shear cycles under undrained conditions exhibit an overestimated increase of the pore water pressure. A more detailed description is given in [NH97]. In order to overcome the noted disadvantages, the hypoplastic constitutive relation is extended by an additional state variable, the so-called intergranular strain δ. The five parameters of the intergranular strain (Rmax , mT , mR , βχ , χ) control the increase of the stiffness after a change of the direction of deformation. Rmax defines a strain range, for which the granular material behaves practically elastic immediately after the direction of deformation changed. mR and mT , respectively, are the ratios of the stiffness directly after and before a change of direction by 90◦ and 180◦ . βχ and χ are exponents in the evolution equation for the intergranular strain tensor. They control the transition from quasi-elastic behaviour in case of small strains to hypoplastic behaviour for larger strains. For the determination of the parameters either resonant column, cyclic triaxial or cyclic shear tests are needed. For quartz sand, the following parameters have often been used [NH97]: R = 1 · 10−4 , mR = 5.0, mT = 2.0, βχ = 0.1, and χ = 1.0. For cohesive soils,

3.5. Determination of the Initial State Variables

61

there is no exact data available so far, but the increase of stiffness after a change of the direction of the deformation is higher (mR = mT > 10). Provided that experimental data is available, a practical approach would be to carry out a parameter study starting with the values shown above. The evolution equation is very sensitive with respect to the value of R, hence its determination has to be examined carefully. Subsequently, mR and mT should be varied. Then if necessary βχ and χ.

3.5

Determination of the Initial State Variables

The initial state variables of a soil element are the effective stress prior a simulation σ 0 , the initial void ratio e0 , and the initial value of the intergranular strain tensor δ 0 . They have to be determined from in-situ data by means of suitable procedures, or they have to be assumed when there is a lack of field data. For a homogeneous layer with a free horizontal surface, the initial effective stress tensor field σ 0 can be determined by the overburden soil pressure, which increases linearly with depth σz = γ z using the effective specific weight γ and the depth z below ground level. The horizontal pressure at rest can be calculated by σy = K0 σz . The coefficient of earth pressure at rest K0 can be estimated by several approaches (Fig. 3.9). For hard-grained ´ky [Ják44] formula K0 = 1 − sin ϕc is sufficiently accurate. For soft finesoils, the Ja grained soils, Niemunis [Nie03] proposes an upper bound of the lateral earth pressure coefficient K0U P as a function of a(ϕc ) (determined by Eq. 3.19) from oedometric creep tests by

K0U P

=

−2 − a2 +

√

36 + 36a2 + a4 . 16

(3.43)

Another approach in order to estimate the lateral earth pressures at rest is proposed by Mayne and Kulhawy [MK82] taking into account the influence of the over-consolidation ratio OCR: K0 = (1 − sin ϕc )OCRsin ϕc

(3.44)

Figure 3.9 compares the presented approaches in order to determine the initial stress state for soft and hard-grained soils prior to the numerical simulation. Assuming a fully saturated soil the initial void ratio e0 can be estimated by e = wγs /γw from the water content w determined in the laboratory, the specific weight of water γw = 10 kN/m3 , and a specific solid weight, which can be estimated to be about γs =

62


1 K0 [Mayne & Kulhawy]

K 0 [-]

0.8

OCR = 1.1 OCR = 1.3 OCR = 1.5 UP

K0 [NIEMUNIS]

0.6 K0 [JAKY] 0.4

0.2 10

20

30 ϕc [˚]

40

50

Figure 3.9: Determination of K0 -values in order to estimate initial stress conditions in a ´ky formula, i.e. for hard-grained soils or an upper boundary after simulation using the Ja Niemunis for soft fine-grained soils. Mayne and Kulhawy propose K0 -values, which depend on OCR.

26.5 kN/m3 for most the soils. Close to the water level, partially saturated soils are taken wγ into consideration by e = S γs , where Sr is the degree of saturation. r w

The initial intergranular strain δ 0 depends on the deformation history of the soil. In many instances, the genesis of the soil may be assumed to be a sedimentation process. This means that the intergranular strain δ 0 is assumed to be maximal and to have δ1 /δ2 = σ 1 /σ 2 initially. In cases, where soil layers were compacted dynamically, or when the ground water level is variable, the assumption of δ 0 = 0 is more adequate.

3.6. Soils and other Materials used in the Experiments

3.6

63

Soils and other Materials used in the Experiments

For the experimental investigation of the soil-foundation-structure interaction behaviour well known soils are used, namely Karlsruhe sand, Stuttgart sand, and Konstanz lacustrine clay. The model piles consist of a S235JR steel plate of 20 mm × 2 mm section and a silicon rubber sealing of 25 mm in diameter. The numerical simulation of the presented experiments as well as a large-scale pile test and a dynamic SFSI analysis requires material parameters for the respective soils and pile materials which are given below.

3.6.1

Parameters of the Soils

In order to simulate undrained conditions in the soil in a numerical simulation, the influence of gas bubbles in the grain skeleton has to be taken into account. The gas in the soil is strongly influencing its compressional behaviour. Liquefaction and softening mechanisms of the soil depend on the bulk modulus of the water-gas-mixture, which has to be determined for the simulation. Figure 3.10 shows the bulk modulus of the fluid, e.g. in the voids of a grain skeleton, depending on the degree of saturation Sr and the ambient pressure p. In particular, soil close to the water level can be partially saturated. Even in deeper layers, trapped air was often detected in the grain skeleton. Nevertheless, with increasing pore pressure the gas is increasingly dissolved in the void fluid. Figure 3.10 gives an example how to determine the bulk modulus Df for an 98% saturated water-gas-mixture. Table 3.3 shows the hypoplastic parameters used for hard-grained soils, viz. sandy fill and silty sand layers, in the dynamic SFSI analysis presented in Chap. 5.4. The viscohypoplastic parameters of the soft fine-grained soil layer D, viz. young bay mud, is given in Tab. 3.4. Further parameters like intergranular strain parameters, density or initial state variables are given in Tab. 3.5. In the presented experiments with model piles in a barrel (Chap. 4.4), and with the shake table experiments in the small (Chap. 4.2) or in the large laminar box (Chap. 4.5), for the hard-grained soils Karlsruhe as well as Stuttgart sand were used. The hypoplastic parameters of these materials are well known; they are presented in Tab. 3.6. For the presented experiments with clay or a covering clay layer, beneath a Karlsruhe sand layer a Konstanz lacustrine clay is used. Its visco-hypoplastic parameters are determined following the procedures including examples of its determination given in Sect. 3.3.

64


D

1000

water =

2140 MPa p

gas

Df [MPa]

100 10

p= p=

Df=10 MPa

1

p=

1 00

10

1k

=1 000 kP a

kPa

kPa

(atm osp

he r

Pa

ic p res sur e

)

0.1 0.01 -1

Df = (1/Dwater+(1-S)/pgas)

0.001

Sr=0.99 1e-05

0.0001

0.001

0.01 1-Sr [-]

0.1

1

Figure 3.10: Bulk modulus of the water-gas-mix in the voids of a grain skeleton depending on the degree of saturation

Table 3.3: hypoplastic parameters for the SFSI analysis in Chapter 5.4 layer A

soil

depth [m]

sandy fill

0.0 ÷2.0 sandy fill 2.0 ÷8.0 silty sand 8.0 ÷15.0

B C

ϕc [ /rad]

hs [MPa]

n [-]

ed0 [-]

ec0 [-]

32.1◦ 0.56rad 32.1◦ 0.56rad 32.9◦ 0.575rad

4000

0.25

0.55

0.95

1.05 0.07 1.0

4000

0.25

0.55

0.95

1.05 0.07 1.0

750

0.45 0.831 1.281 1.41 0.05 1.0

◦

ei0 [-]

α [-]

β [-]

Table 3.4: visco-hypoplastic parameters for the SFSI analysis in Chapter 5.4 layer D

soil

depth [m]

young 15.0 bay mud ÷30.0

λ [-]

κ [-]

0.20 0.02 0.56rad

ϕc [ /rad] ◦

25◦

Iv [-]

βR [-]

ee0 [-]

0.04 0.85 1.2

pe0 [kPa]

ε˙e0 [◦ ]

100

1 · 10−7


65

Table 3.5: further parameters, intergranular strain, density, initial conditions for the SFSI analysis in Chapter 5.4 layer

ρs [g/cm3 ]

Rmax [-]

mT [-]

A B C D

2.65 2.65 2.65 2.65

1 · 10−4 1 · 10−4 1 · 10−4 1 · 10−4

mR [-]

5.0 5.0 5.0 5.0 5.0 5.0 20.0 20.0

1)

βχ [-]

χ [-]

e0 OCR2)

Df [MPa]

0.05 0.05 0.05 0.05

1.0 1.0 1.0 0.9

0.71) 0.71) 1.11) 1.42)

2 · 103 2 · 103 2 · 103 2 · 103

Table 3.6: hypoplastic parameters for hard-grained soils used in the barrel and shake table experiments described in Chapter 4 soil

ϕc [◦ /rad]

hs [MPa]

Karlsruhe 30◦ sand 0.524rad Stuttgart 33◦ sand 0.576rad

n [-]

ed0 [-]

ec0 [-]

ei0 [-]

α [-]

β [-]

5800

0.28 0.53 0.84 1.00 0.13 1.05

2600

0.3

0.6

0.98 1.15

0.1

1.00

During the experiments with piles under alternating or dynamic loading, the strain paths in the soil surrounding the piles are subjected to multiple changes of load direction. This behaviour is accompanied by a sudden change in stiffness of the soil, which highly influences the results of the calculations. In order to take these effects into account, the constitutive relations are extended by the intergranular strain as described in Sec. 3.4. Its parameters are given in Tab. 3.8. The parameters of intergranular strain have been

Table 3.7: visco-hypoplastic parameters for soft-grained soils used in the barrel and shake table experiments described in Chapter 4 soil Konstanz lacustrine clay

λ [-]

κ [-]

0.03 0.012

ϕc [ /rad] ◦

Iv [-]

βR [-]

ee0 [-]

35◦ 0.015 0.95 0.49 0.611rad

pe0 [kPa]

ε˙e0 [-]

100

1 · 10−7

66


estimated according to the determination by Niemunis and Herle [NH97]. Table 3.8: Parameters of the intergranular strain for the soils used in the experiments described in Chapter 4 soil

ρs [g/cm3 ]

Rmax [-]

mT [-]

Karlsruhe sand Stuttgart sand Konstanz lacustrine clay

2.65 2.65 2.65

1 · 10−4 1 · 10−4 5 · 10−4

mR [-]

βχ [-]

χ [-]

2.0 5.0 0.5 1.0 2.0 5.0 0.3 1.0 20.0 20.0 0.1 1.5

Table 3.9: Hypoplastic parameters of the large-scale field test described in Chapter 5.3 soil

ϕc [ /rad] ◦

fine silty sand

hs [MPa]

37.2◦ 1.2 · 103 0.649rad

n [-]

ed0 [-]

ec0 [-]

ei0 [-]

α [-]

β [-]

0.27 0.53 0.864 0.996 0.127 1.05

Table 3.10: Visco-hypoplastic parameters of the large-scale field test described in Chapter 5.3 soil silty clay

3.6.2

λ [-]

κ [-]

0.125 0.02

ϕc [◦ /rad]

Iv [-]

βR [-]

ee0 [-]

18◦ 0.031 0.85 0.941 0.314rad

pe0 [kPa]

ε˙e0 [-]

100

1 · 10−7

Materials used for the Model Piles

Aluminium is the most frequently used material for model piles. Small diameter aluminium pipes, bars, or tubes as well as piles from other materials such as steel and synthetic materials are used for 1-g model tests. For the experiments carried out within this thesis, model piles are used made out of a thin steel plate coated with silicon rubber. In order to simulate the behaviour of the silicon rubber SI-5 in the numerical models, the elastic properties of the rubber material were determined by a one-axial compression test


67

Silicon SI-5 faces unlubricated Silicon SI-5

σ1 [kPa]

200

measured unlubricated

lubricated unlubricated

best fit for large strains ε1 E = 150 kPa ν = 0.5

100

measured lubricated

Detail A

0 0

10

20

30

40

50

6

8

10

ε1 [%]

50

Silicon SI-5 faces lubricated

Detail A

40

Silicon SI-5 lubricated unlubricated

σ1 [kPa]

30

best fit for small strains ε1 E = 300 kPa ν = 0.5

20

10

0 0

2

4 ε1 [%]

Figure 3.11: One-axial compression tests with (bottom) and without (top) lubricated end faces carried out with silicon rubber SI-5 used for the model pile coating

68


with lubricated and unlubricated end faces. Figure 3.11 shows the measured and subsequently calculated compressive behaviour of the silicon rubber for small (top diagram) and large (bottom diagram) strains, respectively. The experiments exhibit shortening under nearly constant volume. Thus, for the calculations a Poisson ratio ν = 0.499 is assumed. A numerical simulation of the compression tests was conducted with both unlubricated and lubricated faces of the sample showing the far softer behaviour of the lubricated samples. In all simulations with model piles, relatively small strains of the silicon rubber coating (below 10%) can be presumed. Thus, the parameter set (cf. Tab. 3.11) for small strains is used in the FEM models. Table 3.11: Elastic properties and dimensions of the silicon rubber coating used in the experiments of Chapter 4 material silicon rubber

E [kN/m2 ] 300

ν ρ [-] [g/cm3 ] 0.499 0.495

shore ∅ hardness [mm] 5.0 25

Table 3.12 shows the material properties used for the steel plate, which is instrumented with strain gauges in eight positions applying at each position a full stain gauge bridge in order to measure pure bending strains along the pile. The bending strains can be easily converted into bending moments assuming pure bending, small inclinations (w2 1) of the pile, and the Bernoulli assumptions [SGH95]. The curvature of the pile neutral axis can be calculated as

κB =

w (1 − w2 )2/3

≈ w = −

M EI

(3.45)

Assuming a linear elastic behaviour of the steel plate and using the geometric and elastic properties of Tab. 3.12 leads to a direct conversion of the measured strains µε into a bending moment M [Nm] by

M [Nm] =

1.4 µε[-] 1000

(3.46)

To protect the strain gages on the steel plate from being damaged, the permitted strains in the steel are restricted to the elastic range. For this reason, only elastic material behaviour is assumed for the steel in the numerical model. The silicon rubber is originally designed as a casting material to withstand very large deformation without any plastic


69

deformation by applying the material properties of Tab. 3.12 and Tab. 3.11, the model pile is modelled in three dimensions using the FEM. Within the FE mesh, the steel core is modelled by means of 3D beam elements. The silicon coating is added by using continuum elements using the beam nodes. The successful application of the 3D model is presented in Chap. 4.3 together with the calibration of the model pile. The FE model is able to satisfactory simulate the calibration procedure presented in Figure 4.9. In addition, the test pile calibration under changed boundary conditions, i.e. a fully restraint at the pile toe is used to validate the FE model (Fig. 4.10). Table 3.12: Elastic properties and dimensions of the steel core sealed in the model pile material

E [kN/m2 ]

ν [-]

ρ [g/cm3 ]

d [mm]

steel

2.1 · 108

0.3

7.2

2.0

b Iy [mm] [mm4 ] 20

13.3

70

3.7


Preparation of the Model Soils

In order to assemble the soil in the experimental containers, e.g. barrel container and laminar box container, hard- and soft fine-grained soils are placed by means of special techniques to provide sufficiently homogeneous soil conditions. To obtain a loose state for dry sand, the sand is placed using a funnel with a long ending tube, which is refilled instantly while lifting it. The sand is close to its critical state while coming out of the funnel by rolling and sliding along the surface of the built sand cone. Thus, a density of the sand close to ec can be assumed. A loose state for saturated sand is obtained by filling the respective containers with water and by continuously pouring dry sand by means of a sieve onto the water surface. Thus, the sand grains sink through the water and assemble in a relatively loose state. A high void ratio e ≈ ec is obtained. In order to obtain dense sand, dry grains are poured through a set of several perforated metal plates. In this way, the grains are dropped with a constant height to the soil surface, resulting in a dense assembly with void ratios e ≈ ed . The densities of soft fine-grained soils are controlled by means of mixing with suitable water content. For the experiments, the clay was placed by hand in lumps in the experimental containers close to the liquid limit w ≈ wL . The air is released by using a stick in order to tumble the soil surface. Experiments are carried out either shortly after the soil is put into the container, or after given the soil time to consolidate under its weight. In order to accelerate the consolidation process, vertical cotton drains were installed according to a grid as presented in Figure 3.12. A preliminary design of the drain grid was carried out according to an analytical solution of the consolidation by drain wells [Bar48]. The drains are installed using a specially fabricated installing device, driving them with steel rods vertically into the soil. The guiding is shown in Figure 3.14, and the installation procedure in order to place the cotton drains exactly vertical is illustrated in Figure 3.13. The efficiency of the vertical cotton drains was investigated by means of a preliminary test comparing a clay column with and without a single drain. The test indicated an acceleration of the settlements due to consolidation of around 400 times. After twenty hours, secondary consolidation can be observed (see Fig. 3.15). Figure 3.16 shows the vertical displacements of the soil surface during an experimental period. The first experiments were carried out with unconsolidated clay. Prior to the experiment, a relatively large gradient of settlements can be observed (A). Experiment

3.7. Preparation of the Model Soils

71

vertical drain grid PG-C

80 cm

80 cm

4 cm

4 cm

60 cm

60 cm

vertical drain grid SP-C

4 cm

4 cm

Figure 3.12: Grid of vertical drains installed to accelerate the consolidation process of the fully saturated clay experiments with single pile, photography of the soil surface (top), drain grid for the single pile case (left), and grid for the pile group case (right)

PG-C1L is carried out under unconsolidated conditions, i.e. with relatively soft soil. Subsequently, the vertical cotton drains are installed resulting in tremendous settlements (B). The shaking events of experiment PG-C2D using the fully consolidated clay are leading to further settlements, whereas the last series of experiments (PG-C3D) do not affect the evolution of further settlements.

72


Figure 3.13: Installation procedure in order to place the cotton drains exactly vertical

Figure 3.14: Fabrication of the vertical drains by means of a positioning device

3.7. Preparation of the Model Soils

73

settlement [mm]

0 without vertical cotton drain

10

with vertical cotton drain

20 0

20

40 time [h]

settlement [mm]

0

60 without drain

with vertical cotton drain 10

se co con ns da ol ry id at io n

20 0.01

0.1

1 time [h]

10

100

Figure 3.15: Comparison of the settlements with and without vertical cotton drains

zeit_setzung_ges.txt

0

A

PG-C1L pile group in clay

10

Installation of vertical drains

∆s [mm]

20

B PG-C2D

30

PG-C3D

pile group in clay

pile group in clay

40

50 0

200

400

600

t [h]

Figure 3.16: Vertical displacements of the soil surface during the experimental period of the pile group test due to consolidation. Accelerated settlements due to the vertical drains can be observed

Chapter 4 Experimental Investigations of SFSI 4.1

Introduction

In the last decades, different model-testing devices – so-called shake boxes – have been developed to investigate the dynamic behaviour of soils and embedded geotechnical foundations and structures under seismic excitation in the laboratory. Experiments with shake boxes are usually performed in a normal laboratory environment (so-called 1-g condition), or in a centrifuge where the magnitude of the acceleration field is n times bigger than by gravity (Sect. 2.2.4). Shake boxes differ in the construction of their walls. Basically, the walls of a box can be rigid (“rigid box”) or consist of movable segments (“laminar box”). Most of the laminar boxes consist of rigid rectangular frames that are permitted to translate relatively to each other. Although such a laminar box is an improvement against a rigid box for the modelling of plane waves, the strain field in it still differs from that of plane wave propagation since shear strains are localised – as in a conventional shear box test – in thin zones between the rigid frames. The influence of the type of the wall kinematics on the shear behaviour of the soil specimen is clearly outlined by means of a numerical simulation presented in Figure 4.1. Only with hinged walls, a plane wave propagation can be achieved.

4.2

Small Shake Box without SFSI

In order to investigate the dynamic response of soil under dynamic earthquake-like excitation, model tests have been carried out with a novel small 1-g hinged laminar box shown in Figure 4.2 (length 400 mm, width 300 mm, height 500 mm) [BCO+ 03] [Wie03].

75

76

Chapter 4. Experimental Investigations of SFSI

Figure 4.1: Numerical simulation of the behaviour of shake boxes during the propagation of a shear wave (colours indicate Mises stresses) using different types of walls. (a) shake box with hinged translatable and rotatable walls (b) shake box with translatable and not rotatable wall segments

To overcome the limitations of existing laminar boxes, the lamellas of this laminar box are hinged so that they can translate and rotate simultaneously. Opposite lamellas are constrained to undergo exactly the same motion by hinged bar connectors, allowing the specimen to transmit a free shear wave motion from the excitation source at the base to the top surface of the soil. Parallel to the shaking direction, the box consists of a pair of smooth rigid steel walls, which are rigidly connected to the base of the specimen, and provide a nearly friction-free lateral boundary to the soil specimen. The dynamic base excitation is generated by means of six spiral springs attached to the base of the box. Initial spring forces are activated by enforcing a certain initial displacement to the base and fixing it by means of a steel wire in the desired position. Shaking is initiated by a manual release mechanism cutting through the steel wire. Thus, the dynamic excitation takes place by the spiral springs releasing their tensional energy and, subsequently, inducing the soil specimen to oscillate freely. After the moment of release, a damped oscillation of the soil and the laminar box is observed. The change of state of the soil is observed until rest. Displacements of the lamellas, settlements of the surface, and pore pressures at the bottom are recorded, processed and consequently analysed. In most of the experiments, fine quartz sand (d50 =0.25 mm, emax = 0.975, emin =0.595, U =2.35, ρs = 2.65 g/cm3 ) was used in both dense and loose initial state. A few experiments were also made with soft, nearly water saturated silty clay. In case of silty clay, the lateral wall adhesion was mitigated

4.2. Small Shake Box without SFSI

77

by means of a water film produced by electrophoresis. Its efficiency was investigated in preliminary tests.

4.2.1

Dry Granular Soil

In the first test series, loose dry sand was investigated for different intensities of excitation of the base by applying initial deflections of the base of 2, 4, and 8 mm. These deflections cause peak acceleration values of slight, moderate and strong earthquakes, respectively. Figure 4.3 shows the horizontal displacements of the lamellas versus time. As can be seen, damping of the soil-laminar-box system increases with increasing shaking intensity and decreases with increasing initial density. This demonstrates the hysteretic nature of soil damping, and indicates that the assumption of viscous damping in elastic models is not realistic for moderate and strong earthquakes. During the shaking, the free soil surface settles due to densification. After about five test series, the further settlement of the surface became negligibly small. In order to simulate the experiments by means of the small laminar box with dry initially loose sand, a 3D FE model using hypoplasticity was developed by [LB06]. The soil specimen was modelled with C3D8 elements [ABA05b] obtaining the real scale dimensions of 0.30 m in length, 0.30 m in width, and a height of 0.4 metres. The initial excitation was applied by means of ABAQUS spring elements, i.e. SPRING1 elements, which are prestressed at the base and released in the dynamic simulation step. The weight of the shake box and the lamellas were modelled using MASS elements. The measure of the damping coefficient of the ABAQUS DASHPOT1 elements as well as the coefficient of the SPING1 elements have been determined by means of free oscillation experiments with the empty box [Wie03]. During the dynamic step, the horizontal displacements along the lamellae, the vertical displacements at the surface, and in case of saturated sand, the pore water pressure at the base of the soil specimen were recorded. Fig. 4.4 shows the damped oscillation of the laminar box versus time with a frequency of about four Hertz. Together with the horizontal displacements at the base, the surface of the soil specimen settles about five millimeters after one second. The calculated evolution of settlements and horizontal displacements exhibit a good agreement with the recordings during the experiment.

78


photo 3D view laminar segments 350

u 386

386

340

distance keeping rods

spiral springs

360

460

680

front view

side view

780

plan view

300

360

u

220

680

spiral springs for excitation

spiral springs for lateral guidance

isometry

Figure 4.2: Photography, 3D-layout and technical drawings of the small shake box


79

u[mm]

u[mm]

1st test series (loose), Amplitude 2 mm

2.0 1.0

4.0 2.0

0.0

0.0

-1.0

-2.0

-2.0

-4.0

Loose dry sand

base top

Loose dry sand

base

3.0

2.0

1.0

0.0


top

0.0

t[s]

1.0

2.0

3.0 t[s]

u[mm]

u[mm]


8.0 4.0

8.0 4.0

5th test series (dense), Amplitude 8 mm

0.0

0.0

-4.0

-4.0

-8.0 -8.0

Loose dry sand

base top

2.0

1.0

0.0

Dense dry sand

base

3.0

top

0.0

t[s]

1.0

2.0

3.0 t[s]

Figure 4.3: Experimental results of the small shake box filled with dry sand

calculated measured

calculated measured

0 u 3 [mm]

u 2 [mm]

8

3

-5

-2 0

0,5

1,0 t[s]

1,5

0

0,5 t[s]

1,0

Figure 4.4: Simulation of the small laminar box experiments with dry initially loose Stuttgart sand. Measured and calculated [LB06] horizontal displacements (left) and vertical displacements at the surface (right)

80


u[mm] 2.0

u[mm]



4.0 2.0

1.0

0.0 0.0

-2.0

-1.0

-4.0

Loose saturated sand

-2.0 base top

0.0

1.0

3.0

2.0


base top

0.0

t[s]

1.0

2.0

3.0 t[s]

u[mm]

u[mm]


8.0 4.0

8.0 4.0

0.0

0.0

-4.0

-4.0

-8.0


base top

0.0

1.0

2.0

3.0 t[s]


-8.0

Dense saturated sand

base top

0.0

1.0

2.0

3.0 t[s]

Figure 4.5: Experimental results of the small shake box filled with saturated sand

4.2.2

Saturated Granular Soil

Subsequent experiments have been carried out with saturated sand (Fig. 4.5) where the soil showed higher energy dissipation than in a dry state even for small amplitudes. Liquefaction, which is assumed to occur when the measured excess pore water pressure at the base equalled the initial effective stress, took place already for an initial base deflection of 4 mm. Since the upper half of the soil specimen moves as a rigid body (Fig. 4.5), it is deduced that liquefaction must have occurred underneath. By contrast, for an initial deflection of 8 mm, skeleton disaggregation extends to the whole specimen since the observed dynamic response of the material resembled that of a viscous suspension (Fig. 4.5). Excess pore pressure dissipates and subsequent settlements of the surface develop about ten times faster than calculated by means of the conventional consolidation theory taking the permeability of the material into account. Observation of the surface during the experiment reveals a system of fine vertical water channels allowing faster drainage. After repeating the test, the sample densifies quickly and, thus the liquefaction susceptibility


81

was reduced. Fig. 4.6 shows the horizontal displacements (left) as well as the evolution of the pore water pressures (right) in case of fully saturated sand during the experiments under exactly the same boundary conditions. During the excitation phase, the pore water pressure increased up to about 7.0 kPa. The calculation [LB06] shows the pressures kept constant after the excitation whereas the experiments shows a relatively fast decrease of the pore pressure with time due to the build up of channels allowing a fast drainage. Despite the successful results of the small shake box, the test set up has three essential shortcomings: 1. The type of excitation can be described as an undefined impact-like wave, which is not reproducible and is too far away from the characteristics of a real earthquake motion. 2. Due to the small dimensions of the small shake box, layers of soils with different properties cannot be installed. 3. For the same reason structures installed in the soil and/or on the surface of the soil would interact heavily with the boundaries of the small box and have to be excluded therefore. Subsequently, a larger shake box presented in 4.5 has been designed and constructed to overcome these restrictions.

4.2.3

Saturated Soft Clay

The experiments in the small laminar box with saturated clay (Fig. 4.7) show only small settlements during and after the base excitation. After the decrease of the excess pore water pressure, the experiments were nearly reproducible. This was not the case with the experiments with hard-grained soils presented before. This behaviour can be explained by a nearly unchanged state of the clay after the previous experiments. The mode of motion was also repeatable at least for amplitudes smaller than 4 mm. In all four cases, i.e. for 1, 2, 4, and 8 mm, respectively, a very strong amplification of the base-shaking signal could be observed at the surface of the soil specimen. The increase of the pore pressure ratio ∆pw /σv versus time at the base of the saturated clay specimen is given in Fig. 4.8. Numerical simulations [LB06] also provide a good agreement with the measured values.

82


calculated measured

5

calculated measured

8 p w [kPa]

u2 [mm]

10

0

4

-5 0 -10

0

1

2 t [s]

3

4

1

0

2 t [s]

4

3

Figure 4.6: Simulation of the small laminar box experiments with fully saturated initially loose Stuttgart sand. Measured and calculated [LB06] horizontal displacements (left) and evolution of the pore pressure at the bottom of the soil specimen (right)

u[mm] 1.0

u[mm]

5th test series (loose), Amplitude 1 mm


2.0 1.0 0.0 -1.0 -2.0

0.0 -1.0

Silty clay

Silty clay

base top

0.0

1.0

2.0

base

t[s]

top

0.0

1.0

2.0 t[s]

u[mm]

u[mm]


4.0 2.0

8.0 4.0

0.0

0.0

-2.0

-4.0

-4.0


-8.0

Silty clay top

0.0

1.0

2.0

Silty clay

base

base

t[s]

top

0.0

1.0

2.0 t[s]

Figure 4.7: Experimental results of the small shake box filled with saturated silty clay


83

saturated silty clay

8

1.0

4 Initial displacement 1 ... 8 mm 2

1

0

1

saturated sand

0 -1 ∆pw / σv' [kPa / kPa]

∆pw / σv' [kPa / kPa]

1

1 0 -1

2

1

4

0 -1 1

1

∆t [s]

8

0 -1 1

∆t [s]

Figure 4.8: Increase of the pore pressure ratio ∆pw /σv versus time at the base of the saturated clay specimen applying 8, 4, 2 and 1 mm base deflection amplitude, respectively

These test results are also confirmed by high-speed video recordings of tracer columns in transparent model clay in the hinged laminar box [Zee02]. The high-speed videos visualise the shear waves propagating from the base of the model clay specimen to the surface without generating substantial parasitic waves along the laminar box boundaries.

4.2.4

General Remarks on Small Shake Box Experiments

In order to overcome limitations, viz. shear localisation and parasitic waves from the wall boundaries, a novel shear box type experimental container for soils has been designed and constructed to better simulate earthquake-like excitation. The lamellas are allowed to undergo translational as well as rotational motion of opposite lamellas arranged in pairs. The horizontal displacements of the lamellas in case of dry sand exhibit that the damping of the whole freely oscillating soil-container-system increases with increasing shaking intensity and decreases with increasing initial density. Already after one single experimental series of five experiments with the same specimen, further settlements of the soil surface became negligibly small. In case of fully saturated sand, the soil showed significantly higher energy dissipation even for small amplitudes due to liquefaction, when the soil turned in a turbulent soil-water suspension. The measurements demonstrate that the pore pressure dissipates about ten

84


times faster than observed by means of the conventional consolidation theory due to fine vertical water channels. Experiments with saturated Konstanz lacustrine clay show a reproducible repetition of the experiments due to a nearly unchanged state of the soil. In addition, the mode of motion is very similar independent from the magnitude of excitation. Numerical simulations [LB06] show a good agreement with the measured values for all experiments. In order to overcome restrictions like the type of excitation and the small dimensions of the container, a large laminar box is presented in Chap. 4.5.

4.3. Model Piles used in the Experiments

4.3

85

Model Piles used in the Experiments

The 700 mm long model pile consists of a steel plate being 2 mm thick and 20 mm wide and is sealed with silicon rubber [REC03] (shore hardness 5) with a circular cross section. Thin foil strain gages of the series DMS LG11/3/350 (resistance of 350 Ω) manufactured by [Hot05b] are used for the pile instrumentation in order to determine bending moments versus time and depth. The strain gages are attached to the polished steel plate at eight positions at a distance of 80 mm on both sides along the pile. Thermal drift is minimised by means of a full strain gage bridge since the strain gages in the piles would be electrically excited causing a continuous heating of the gages and change their resistance, thus affecting voltage output. Calibration was accomplished by placing the piles horizontally on supports and loading them as simple beams using a four point loading configuration. The gages were subjected to both tension and compression by turning the pile 180 degrees after the first set of loadings was completed, and by repeating with the other side up, thus reversing the stress state. Figure 4.9 shows the calibration configuration. The four point loading test configuration uses two equal concentrated loads symmetrically spaced with respect to the supports. Loading in this manner gives different moment values for the gages between the supports and the loads according to the beam equation: M = P x, again with P as the load magnitude and with x as the distance from the support to the strain gage. Therefore, the symmetrically spaced loads are applied outside the supports. Between the supports, the moment would be a constant value given by the equation: M = P a, where a is the distance from the support to the position of the load. Care was taken to keep the gages at least 80 mm away from the supports, and the loads so that Saint Venant’s effects would not be read by the gages. A four point loading test was performed with the model pile simply suspended from steel wires near its ends, and equal static loads were applied at the pile ends (Fig. 4.9). This loading pattern results in a zone of constant moment being applied across the central section of the member. The bending strains measured by the foil strain gages, mounted to the compression and tension faces of the steel plate inside the test pile, are read at each loading increment. From the measured bending strains, the moment, the curvature, and the pile displacements are calculated. The measured moment-curvature relation for the model pile is shown in Fig. 4.9 superimposed on the theoretical plot, both at model scale. The agreement in the range of elastic response is excellent. These results proved the composite of steel plate and silicon rubber sealing to be an adequate model pile for the model-testing programme. The equipment consisted of frames to support the piles, calibration weights and the means

86


a = 190

a = 190

62

62

m [Nm]

700

constant length [m]

FE model

1000

µε [-]

calculated measured

500

0 0

0.2

0.4

0.6 length [m]

Figure 4.9: Calibration load configuration to calibrate the model pile with and without silicon rubber sealing using a 3D FEM model with beam elements for the steel core and continuum elements for the silicon coating

4.3. Model Piles used in the Experiments

87

to hang them from the piles, a pile alignment or orientation device, and the data acquisition system and computer.

a [mm]

100 measured calculated

0

2

1

3

-100 measured calculated

F [N]

1 0

2

1

3

-1 0

200 a [mm]

400

600 t [s]

F [N]

measured calculated

0.6 2 3 2

0.4

1

0 -1 -2

-100

0

100

pile length [m]

F [N]

1

measured calculated

1

0.2

2

3

a [mm] 0 0

200 400 µε [-]

Figure 4.10: Calibration of the test pile applying the clamped restraint at the pile toe and realistic loading at the pile head used in the barrel experiments as well as the shake table experiments

Figure 4.10 shows the results of a calibration test of the model pile installed in the barrel testing facility. The model pile is clamped at the bottom of the barrel. The expected linear moment distribution vs. pile length is confirmed exactly by the FE calculation.

88

4.4 4.4.1


Barrel Experiments with Model Piles Introduction

Within this dissertation, experiments with instrumented model piles in a barrel have been carried out. The work is addressed to the investigation of the non-linear interaction behaviour of a single pile with the surrounding cohesive soil (Konstanz lacustrine clay) during the alternating pile head deflection. Firstly, the pile head is moved force-controlled to deflect the pile in one direction. Subsequently, the pile head is moved distance-controlled cyclically in both directions. Key components, i.e. the soil, the type of foundation system, the structure, and the type of loading, have to be observed in detail to analyse the non-linear soil-pile interaction behaviour in general. The objectives of a soil-pile interaction analysis are the evaluation and estimation of the total performance of the complete soil-foundation-superstructure system to provide a robust, efficient, and realistic numerical description of system and material response for a performance-based design. In order to validate proposed methods, it is essential to develop and refine 1-g laboratory experiments, which provide an invaluable resource for calibrating existing numerical codes to reduce inherent modelling uncertainty. The improvement of state-of-the-art methods to estimate the performance of deep foundations, in particular the design of pile foundations in seismic zones, in soft and liquefiable soils is extremely important. Hypoplastic constitutive relations are capable to describe the soil behaviour realistically, from small to large strains, with non-linear response and damping characteristics, which correspond well with measured soil behaviour. The determination of parameters and the initial state for the constitutive relations is also well established.

4.4.2

Test Setup of the Barrel Experiments

The finite element method potentially provides the most powerful means for conducting soil-pile interaction analysis but it has not yet been fully accepted as a practical tool. Appropriate constitutive models, here hypoplasticity, and suitable FE-meshes are required. In contrast to conventional 1-g modelling techniques, an FE-modelling in model scale does not require laws of similarity. At first, the behaviour of the model must be reproduced successfully by a finite element model using hypoplasticity. The second step is the upscaling of this model under consideration of changed boundary and initial conditions to dimensions relevant for geotechnical problems. The successful application of this method

4.4. Barrel Experiments with Model Piles

deflection of pile head

quasi-static loading (very slow cycles) deflection controlled

89

deflection controlled

force controlled

time

load steps for initial pile deflection load cell shaking table

force controlled

g.l.

soil clay/sand balance weight for initial pile deflection

counterweight for rod pretension

clamped support

Figure 4.11: Test setup of a model pile in a barrel and deflection of the pile head versus time

implies that the constitutive model is able to reproduce realistic results for a wide range of pressures. After a successful validation, more complex boundary value problems can be solved. A validation of the presented method is also accomplished by means of selected examples of well-documented case histories for monotonic, cyclic (only a few cycles), and dynamic loading of pile or pile-like structures. Boundary value problems cover rather complex strain and stress paths whereas element tests usually work with rather simple paths. A need for the validation process is the knowledge about soil properties and the initial state of the soil. The better information is available about the state and the properties of the soil the more precise a prediction or validation can be carried out.

90


magnetic sensor

pile head displacement pointer

1038

62

69

308

pile head mass

force transducer

730

700

silicon coating

steel plate side view

front view 250 0

25

base

plan view

3D view

pile clamping

Figure 4.12: Instrumented single pile used in barrel tests as well as in large shake box tests

4.4.3

FE Models used to simulate the Experiments

In order to simulate the barrel experiments, the 3D pile configuration presented in Section 4.3 was used. The surrounding soil was modelled with about 9000 continuum 8noded elements considering the barrel margins as a lateral rigid boundary, while the soil is allowed to settle frictionless along the barrel walls. The visco-hypoplastic and the hypoplastic parameters can be taken from Section 3.6.1. Between soil and pile, contact interaction is taken into account applying a soft contact definition (refer to Chap. 2.5.2). Friction between the silicon rubber and the sand is also taken into consideration according to the friction angle between rubber and sand.


91

35

62

460

side view

front view

25

37

460

0

38

3D view

plan view

Figure 4.13: Displacement transducer to record the pile deflection at the top of the pile, also used in the shake box experiments

Gapping between soil and pile is allowed for. The FE-model is presented in Fig. 4.15. The initial stress tensor field in the model is applied according to the density of the soil and the resulting overburden pressure under K0 -conditions. The void ratio is derived by the measured mass of the soil and the known volume of the barrel container. The intergranular strain is assumed to be maximal and to have δ1 /δ2 = σ 1 /σ 2 initially. Symmetry enables to take only half of the soil specimen and model pile into account. The symmetry plane spans in vertical and in direction of the lateral pile movement. In order to avoid positive effective pressures (tension), in particular close to the free surface during the simulation, a slight isotropic capillarity pressure of 0.1 kPa throughout the soil specimen has to be applied. An additional small capillarity pressure is also necessary to allow a free-standing gap between soil and pile during the simulation. The numerical simulation procedure of the barrel experiments starts with a geostatic step, i.e. gravity is imposed. In the calculation with saturated sand, the initial effective pressures resulting from overburden load under K0 -conditions are taken into account. In the second step, the quasi-static loading of the pile head applying the deflection history of the shake table record has been applied to the FE-model as a time-dependent boundary condition. In case of the free-head experiments, the pile tip is allowed to rotate, whereas in case of the restrained head condition the rotational degree of freedom of the latest beam node has been confined in rotation.

92


74

349

480

505

678

1042

8

balancing weight

front view

350

side view

traverse with position transducer

roller

pointer

shake table

load cell

250

645

480

350

model pile 505 plan view barrel balancing weight

3D view

Figure 4.14: Technical drawings of test setup of a model pile in a barrel


93

Figure 4.15: FE model to simulate the experiments with model piles carried out in the barrel

4.4.4

Results of the Barrel Experiments and their Simulation

Figure 4.16 presents the experimental results compared with the finite element simulation of the barrel experiments with loose dry sand. The diagrams at the left side of Fig. 4.16 show the free-head test whereas the right side diagrams show the results of experiments with a restrained head. The diagrams at the top visualise the deflection-force relation of the experiments. The void ratio of the sand is taken as e = 0.70. As can be seen from the gradients in the plot, there is an obvious deviation of stiffness in the numerical simulation during each loading cycle. This can be explained by the evolution of a gap between the soil elements and the pile elements due to the introduction of a small isotropic capillarity pressure. A small capillarity pressure is necessary to stabilise the free surface in the calculation: The more the pile is in contact with the soil along its shaft, the more the stiffness increases; whereas the stiffness reaches a minimum when the pile is in the neutral, i.e. vertical, position (a = 0). This contact non-linearity due to gapping leads to an S-shaped load-deflection curve. The experiments show a different behaviour: In case of experiments with dry sand (or fully saturated sand), i.e. if the capillary cohesion vanishes, the gap along the pile shaft will be

94


steadily closed by a longitudinal flow of sand along the pile shaft filling the gap between the pile and the soil. The closing of the gap results in a reduction of the contact nonlinearities, which in return changes the shape of the load-deflection curve. This behaviour is not simulated by means of the presented FE models. It has to be noted that the incremental stiffness exactly coincides after a certain deflection in both the calculation and the measurements. The two diagrams at the bottom of Fig. 4.16 show the distribution of bending strains along the pile versus depth during a maximal deflection of a = ±5 mm. The fact that the stiffness in the calculations fits quite well with the experimental results at the end of every half cycle, i.e. when a = amax , also leads to realistic distributions of the strains along the pile. The free-head experiments exhibit a zero moment at the tip of the pile and a field maximum at 0.55 m above the bottom clamping of the pile. By contrast, the restrained head experiments indicate an end moment at the pile head. Measured values are higher since the lateral force also get higher for deflections of a = ±5 mm. However, in particular the measured strains show a clearly unsymmetrical distribution due to the mixed boundary conditions on the one hand and due to the irregular state of the soil caused by the interaction process starting asymmetrically on the other hand. The measured strains are slightly higher than the calculated ones as also the horizontal force F is higher. Compared to the barrel experiments with loose sand the experiments with dense sand (Fig. 4.17) display a rather stiffer behaviour. The F -a relation evidences around double the system stiffness due to the stiffer lateral soil reaction on the one hand, and due to the shortening of the effective pile length since the dry sand was compacted. For dense sand, the simulation calculated with a void ratio of about e = 0.53. In case of the restrained head, a large gap is marked in Fig. 4.17, diagram top right. As in the experiments with loose sand, the experiments with dense sand show the same differential stiffness at maximal deflection, but forces are higher due to the filling of the gap in the experiments. This results in higher bending strains at least at the top of the pile. Due to the compacted soil the range of field moments shifts towards the soil surface, and the moment diminishes far earlier with depth. Further experiments in the barrel are carried out with Konstanz lacustrine clay. As can be seen from the F -a relations, the system stiffness is significantly softer compared to the experiments with hard-grained soils. The bending strain distribution indicate that the deflection of the pile reaches larger depths while the bending strains are predictably far lower compared to the previous experiments.


95

10 pile in loose sand

pile in loose sand

free-head

restrained head

e = 0.70

e = 0.70 F [N]

F [N]

10

0

0

measured calculated

measured calculated

-10 -10

-5

0

5

10

a [mm]

a [mm] -10 F [N]

0.6

0.4

0.4

a = ±5 mm pile in loose sand

0.2

0 -400

-200

200

400

0 -400

5

10

a [mm]

a = ±5 mm restrained head

e = 0.70 0 µε [-]

0

pile in loose sand

measured calculated

free-head

-5

M [Nm]

0.6

0.2

-10

-200

measured calculated

e = 0.70 0 µε [-]

200

400

Figure 4.16: Experimental results compared with numerical simulations of the barrel tests with loose sand

4.4.5

General Remarks on the Barrel Experiments

In order to investigate the SFSI behaviour under quasi-static conditions, experiments with piles in a barrel with clay and dry sand under loose and dense conditions have been carried out. The pile head has been defected on the one hand under free-head conditions and on the other hand under restrained head conditions. The experiments clarify the interaction behaviour between a single pile and different soils. The properties of the soils and their state as well as the pile material are well defined. The simulations by means of the FEM show that the numerical results suit the experimental results since the state and the properties of the soil are known.

96


10

10 e = 0.53

pile in dense sand

free-head gapping

F [N]

F [N]

e = 0.53 0

0 measured calculated pile in dense sand

measured calculated

restrained head

-10 -10

-5

0

5

10

a [mm]

a [mm] F [N]

-10 -10

0.6

0.4

0.4

a = ±5 mm pile in dense sand

0.2 measured calculated

free-head 0 -400

-200

200

5

measured calculated

restrained head 400

0 -400

10

a = ±4 mm pile in dense sand

e = 0.53 0 µε [-]

0 a [mm]

M [Nm]

0.6

0.2

-5

-200

e = 0.53 0 µε [-]

200

400

Figure 4.17: Experimental results compared with numerical simulations of the barrel tests with dense sand

A negligibly small fictitious capillarity cohesion has been introduced in order to stabilise the simulation, in particular for zones where the effective pressures become very small, viz. close to the free surface and in the gap. Nevertheless, the simulations also show that the evolution of a gap between soil and pile is rather complex. The longitudinal flow of soil refilling the gap should be taken into account, which is not possible with the present FE models, in order to more realistically simulate the force-deflection behaviour. On the other hand, the load-deflection relationship presented in Figs. 4.16 to 4.18 show an excellent agreement of the incremental stiffness with increasing deflection.


97

2

2

pile in clay

pile in clay

free-head

restrained head

1 F [N]

F [N]

1

0

0

-1

-1

measured calculated

measured calculated

a [mm]

-2 -4

-2

0 2 a [mm]

-2

4

-4 F [N]

M [Nm]

0.6

0.4

0.4

pile length [m]

0.6

0.2

a = ±2 mm pile in clay

free-head 0 -80

-40

0.2

40

80

0 2 a [mm]

4

a = ±2 mm pile in clay

restrained head

measured calculated

0 µε [-]

-2

0 -80

-40

measured calculated

0 µε [-]

40

80

Figure 4.18: Experimental results compared with numerical simulations of the barrel tests with soft lacustrine clay

98

4.5 4.5.1


Large Shake Box and Shake Table Introduction

Soil-foundation interaction under seismic excitation was investigated experimentally as well as numerically. An experimental method, which was developed for the investigation of the shear wave propagation during strong earthquakes, was adapted to the investigation of selected cases of soil-foundation interaction during earthquake excitation. The gained test data was used to verify numerical models. In an extensive series of tests, single piles and pile groups both with pile caps simulating the mass of a superstructure lying above were installed in a laminar box, which was mounted on the shake table. Subsequently, the shake box system was excited at its base. Using the mentioned experimental setup the soil-pile-superstructure interaction under seismic excitation was studied. The magnitude of the surficial settlements of the soil specimens, the change of the distribution of the bending moment versus depth and time during the simulated earthquake, the permanent deformation of the piles, and the displacement of the superstructure were quantified. The objective of this dissertation is the development and improvement of experimental and analytical methods for a more reliable assessment of ductility and serviceability of ductile geotechnical structures, namely deep foundations under seismic excitation. Within the scope of the presented work, the behaviour of structures embedded in granular soils, e.g. sand, as well as cohesive soils, e.g. clay, subjected from weak up to strong earthquake motion were investigated experimentally as well as numerically. Suitable constitutive laws have been developed in the past [Nie03] [Kol00] [Kol91] [Kol87] [Kol88] [KHvW95] [Gud96] [Bau96] [Wol96] and adapted and enhanced to describe the rate-dependent non-linear behaviour of soft fine-grained soils under alternating loading. Based on these constitutive laws numerical methods and three-dimensional finite element models have been developed to simulate realistically the non-linear ground response as well as soil-foundation-structure interaction during earthquakes. In earlier times, numerical simulations, as for instance the propagation of plane waves during earthquakes in hard-grained soils, were extended to soft fine-grained soils. Hard-grained soils, e.g. sand and gravel, were described before by a hypoplastic constitutive law. For soft fine-grained soils, a novel visco-hypoplastic law was successfully applied to boundary value problems modelling geotechnical structures embedded in fine-grained soils, which makes it possible to realistically simulate soil-foundation interaction also for soft soils. Seismically triggered decay of grain skeleton, i.e. liquefaction, was proved to occur with hard-grained soils, but not for soft fine-grained soils where merely a slight decrease of effective pressures can be observed in both experiments and calculations with visco-

4.5. Large Shake Box and Shake Table

99

hypoplasticity. The experiments show also that the seismic decay of soft soils can be accelerated by the presence of air bubbles, which can be taken into account in numerical simulations by the compressibility of the pore fluid. Further validation of these methods and their subsequent transferability for different regions of high earthquake risk has been proven. The validation of the numerical methods to predict ground response and liquefaction susceptibility is supported by experiments and well documented cases from strong earthquakes. Furthermore, numerical analysis of models including geotechnical structures, e.g. models simulating foundations of structures during strong earthquakes, has been carried out to investigate soil foundation structure interaction as well as the dynamic behaviour of geotechnical structures. Numerical investigations have been carried out mainly by means of the finite element method. Experiences from past investigations of the behaviour of soil systems and structures under plane and anti-plane base shaking have been considered. The presented concepts have been verified in many cases by means of data gained by laboratory tests and in-situ measurements. Small-scale experiments in the lab have been investigated to prove wave-induced non-linear phenomena characteristic for strong earthquakes. Typical model soils (granular as well as soft fine-grained soils) are used to carry out the proposed experiments. Newly developed wave propagation models have been verified by means of a novel 1-g-shake-box allowing its opposing wall segments to translate and rotate freely but synchronously. Consequently, the passage of a plane wave is enabled unhindered nearly without reflections. This has been proven by means of a high-speed camera. Despite the successful experiments with a small shake box in earlier times, three substantial limitations of the testing device have been pointed out: earthquake-like excitation was not realised, small dimensions neither allowed to model different soil layers nor embedded structures. As a result, a larger laminar box of 2m height including a servo-hydraulic shake table was designed and constructed. The tests were carried out to evaluate liquefaction susceptibility depending on the magnitude of base excitation and density of the soil samples. Data acquired by own experiments were used to validate the theoretical models, e.g. by tests in the improved laminar shake box as well as well documented data from foreign sources. Former tests were carried out by means of the small laminar box with samples of dry sand, saturated sand and saturated clay. The following mechanisms were observed during the tests: Dry sand samples were compacted due to induced dilatancy waves. Increasing initial amplitude leads to an increased damping of the dry sand. Repeated tests showed a decrease of damping with increased compaction while at the surface amplified motions were observed. Specimens consisting of saturated sand showed softening due to an increase of pore water pressure followed by layer separation and total liquefaction. Tests on

100


saturated sand of different densities were compared and showed liquefaction for critical amplitudes where maximal damping, i.e. total dissipation of kinetic energy, was reached. Repeated tests also showed increasing compaction followed by a decrease of damping. However, tests with homogenous soft fine-grained soil showed moderated softening due to relatively slight increase of the pore water pressure. After dissipation of the excess pore water pressure through drainage, repeated experiments with saturated clay showed a similar behaviour because the state of the soil, i.e. void ratio, remained nearly unchanged. For all the tests with clay, a strong amplification of the surface motion was observed. Based on results from experimental and numerical investigation, tools to evaluate and calculate the influence of the soil on foundations and structures will be provided to the cooperating partners within the project to realistically simulate damage scenarios.

4.5.2

Experimental Setup of the Shake Table

Shake Table and its Actuation The shake table consists of a welded base frame and a welded table frame of high distortional stiffness. The table frame is mounted on the base frame and guided uni-directionally by two parallel pairs of ball rail systems. The table footprint measures 2.45 m by 1.0 m and has a payload capacity of 28 kN allowing for moments when the centre of gravity of the soil specimen is up to 1 metre over the edge of the table. Table motions are produced by an actuator, which is attached to the base frame, performing maximum displacements of +/- 100 mm when frequencies lesser than 0.3 Hz are applied. For frequency contents, which are typical for earthquake motion, i.e. frequencies between 0.3 and 10 Hz, the maximal velocity of the table motion can reach 0.19 m/s. The maximal velocity is restricted by the discharge-flow-through of the hydraulic oil passing the hydraulic generator. Producing frequencies greater than 10 Hz accelerations of the shake table of about 1.1g are possible, being provided by the highest possible hydraulic oil pressure in the hydraulic system. The limit frequency is designed for about 30 Hz, covering the complete range of common earthquake frequency spectra. The guide rail is encapsulated totally to guarantee a dust-free ambience protecting the bearings from damage.

Shake Table Motion Shake table motions are controlled by a self-made state-of-the-art vibration control software, which performs closed-loop control of the shaker and is capable of reproducing recorded earthquake motions or motions with numerous prescribed waveforms of very

948

101

side view


800

1131

870

2470

969

1100

2880

1977 plan view 1017 1217

2880

tr ins

la

1017

1115 front view

3D view

Figure 4.19: technical drawing of the shake table, laminar box and its instrumentation in plan view, side view, front view and 3D view, respectively

102


high accuracy. The shake table motion can be configured to produce either arbitrary stored displacement histories (with a maximal 12-bit resolution, a maximal sampling rate of 40MSa/s, and a 16,000-point deep arbitrary waveform storage) or periodic functions (e.g. sine, triangle, square, ramp, noise), both by means of a 15 MHz Function/Arbitrary Waveform Generator (Agilent 33120A, [Agi04]). A sinusoidal input motion with variable frequency and amplitude as well as a Loma Prieta 1989 earthquake signal configuration were used to conduct all the tests in this study (Fig. 4.21). The earthquake motion applied by the hydraulic actuator is attained by twofold numerical integration versus time of the acceleration signal of the Loma Prieta earthquake. The double-integrated displacement history is used as the input data (set-point value signal) of the superposed displacement closed-loop control, collecting the displacements of the hydraulic actuator (actual value signal) by a linear magnetostrictive non-contact position sensor.

PS_pile

L

L m FT

control

03

02

SG08 SG07 SG06 SG05 SG04 SG03 SG02 SG01

actuator

non-contacting intelligent laser displacement sensor (optoNCDT 1400) - surfacial settlements of the soil specimen force transducer (Z8)

FT PS01

02

PPT02

01

PPT03 PPT01 PPT02

hydraulic pump

L

water cooling

PS08 PS07 PS06 PS05 PS04 PS03 PS02 PS01 PS_table

linear magnetostrictive non-contact position sensors (novotechnik TLM series) - horizontal displacement (lamellea, pile head, table) ceramic pressure transmitter (VEGABAR 14) 15 MHz function/arbitrary waveform generator (Agilent 33120A) amplifier type ... data acquisition, analoque-digital convertion, calibration (Hottinger MGCplus) data storage and interpretation (PC, Matlab)

Figure 4.20: test setup of shake table tests


103

1 acc a [m/s2]

0.5 0 -0.5

Max. acceleration: 0.66 m/s2 at t=11.32 s

-1 0

10

20

30

40

time [s] 0.2 vel Max. velocity: 0.15 m/s at t=11.18 s

v [m/s]

0.1 0 -0.1 -0.2 0

10

20

30

40

time [s] 40

disp

u [mm]

20 0 -20 -40 0

10

20

30

40

time [s]

Figure 4.21: Time history of the earthquake record during the M7.1 Loma Prieta earthquake at Yerba Buena Island in 1989. Horizontal (90DEG) acceleration (top), velocity (middle) and displacements (bottom), which are used for the shake table experiments and the dynamic SFSI analysis

104


Laminar Test Box The model tests were carried out in the novel hinged laminar box type (cf. Fig. 4.19) to investigate the behaviour of hard-grained and soft fine-grained soils with embedded piles under dynamic earthquake excitation. The soil specimen has a cubic shape with a footprint of 600 × 800 mm. The height of the storage facility can be chosen as 700, 1400, and 2100 mm. The excitation of the prismatic soil column is applied horizontally at their bottom face. Along the height of the soil specimen, laminar segments are able to translate and rotate freely in moving direction while conserving the footprint in all horizontal sections of 600 × 800 mm constant. Instrumentation of Laminar Box, Soil and Piles The test piles consist of a 2 mm thick and 20 mm wide steel plate core instrumented with eight pairs of full-bridge strain gages. The steel plate is coated with soft silicon rubber [REC03] protecting the gages from water and subsequent corrosion. The configuration in the laminar box was either single pile (Fig. 4.12) or pile group (Fig. 4.24). Soil movements are recorded indirectly by means of eight linear magnetostrictive non-contact position sensors [nov04] measuring the horizontal displacements of the lamellae of the laminar box. Superficial settlements of the soil specimen are acquired using two non-contacting laser displacement sensors [mic04] covering a measuring range of about 50 mm providing a resolution of about 5 µm. In three different depths in the soil, the pore water pressure is measured using a stainless steel tube finished by a filter gauze at the one end within the soil, passing the base of the soil specimen and a pore pressure transducer [VEG05] at the other end outside the laminar box. The displacements of the pile head are recorded by means of a linear magnetostrictive non-contact position sensor [nov04] and inertial forces at the pile head resulting from the mass inertia of the pile head mass are measured by a force transducer [Hot05a] with a double bending beam and strain gauge measuring system. For details refer to Figures 4.19 and 4.20.

105

side view


645 600

590

300

2470 800

800

97

110 100

60

785

488

364

520

1017

plan view 182

displacement transducers (horizontal pile head deflection)

492

laser displacement transducers (soil settlements)

1977

488

520

instrumented pile

60

load cell

pore pressure filter

600 1017 1115 front view

traverse for instrumentation

shake table

3D view pore pressure transducers

Figure 4.22: Instrumentation of the soil specimen (e.g. laser transducers, pore pressure transducers, displacement transducers) used in the shake box experiments

106


110 100

200

785

110

210

200

800

910

100 100

590

side view

3D-view

364

1017

520

plan view

front view

3D-view detail

Figure 4.23: Pore pressure transducer used in the shake box experiments to record the pore pressures in different heights of the soil specimen


107

239

pointer

load cell

236

position transducer

62

pile mass

model pile w.l.

w.l. g.l.

670

25 silicon coating

736

g.l.

973

98

60 front view clamping base plate

side view 60 position transducers (pile head deflection)

250 magnetic sensor

pointer pile head mass

25

0

load cell

460

model piles

38 plan view base plate

3D view clamping

Figure 4.24: Mechanical drawing of the pile group used in the shake table experiments

108

4.5.3


Laminar Box and Soil Preparation

Prior to the experiments, the laminar box is mounted on the shake table. To allow experiments with a water saturated soil specimen, the laminar box is sealed by means of a polyethylene foil. The foil is tailored and glued to fit the inner dimensions of the laminar box (80 cm in shaking direction, 60 cm perpendicular to it, and 75 cm in height, see for example Fig. 4.25), and is placed and clipped to the upper edge of the laminar box. Three gasket openings at the bottom of the sealing allow passing through pore pressure tubes ending with filter stones in different depths of the soil specimen. The instrumented pile (Fig. 4.25) and the instrumented pile group (Fig. 4.26), respectively, are screwed to a massive clamping and, subsequently, fixed centrically to the bottom of the laminar box. The clamping at the toe of the pile and at the toes of the piles, respectively, simulates the embedding of the piles in a very stiff soil layer, which is the most desirable case in practice. Afterwards, the sealed laminar box is filled with water covering the filters. The pore water tubes and filter stones are rinsed thoroughly with deaerated water to release trapped air bubbles preventing a malfunction of the pore pressure transducers. To obtain a loose and fully saturated sand layer, Karlsruhe sand is assembled by means of the pluviation method where the grains fall through sieves on the water surface and, subsequently, sink to the ground arranging in a grain assembly, which is close to the critical void ratio. To obtain a homogenous clay layer, Konstanz lacustrine clay is homogenised in a compulsory mixing machine. Water is added until a designated water content is achieved. To ease the assembling of the soil in the laminar box, a water content close to the liquid limit of the soil is established. The clay is assembled in 5 cm thick layers and, subsequently, stamped to release trapped air. A layer of water of about 2 cm covers the assembled soil specimen to prevent the soil to desiccate. A first series of experiments is carried out a day after the installation, i.e. with unconsolidated clay with a water content close to the liquid limit. After the first experiment in case of thick clay layers, the consolidation process is accelerated by means of vertical cotton wool drains. The setup of all experiments carried out is depicted in Appendix A.1. In the first series of experiments, a single pile was installed in fully saturated sand. Experiment SP-S1L (Fig. A.1) shows the initial state of the Karlsruhe sand prior to the experiment, whereas SP-S2D (also Fig. A.1) shows the state of the soil prior to the last experiment of the


109

vane shear test #1to10

single pile with clay


SP-C2D single pile with clay

single pile

64.5 cm

PWD1 h=52cm PWD2 h= 45cm

Konstanz lacustrine clay cu = 2.4 kPa w = 0.290

11

20 cm 30 cm 40 cm

75 cm ∆s=5.6cm

60 cm

60 cm

PWD1 h=52cm 58.9cm

80

single pile

m

c 80

cm

75 cm

SP-C1L

PWD2 h=45cm


PWD3 h=6cm

m 1c

cm 2

11

cm 21

cm

20 cm 30 cm 40 cm

Figure 4.25: Experimental setup of the single pile installed in saturated clay before (first experiment SP-S1L) and after (last experiment SP-S2D) the experimental programme

experimental series with fully saturated sand. A fast drainage up to the soil surface can be observed. In order to confine the superficial drainage, a clay layer was placed on top of the sand in two tests. The Karlsruhe sand layer is about 50 cm high and is covered with about a 10 cm layer of Konstanz clay. This configuration allows the increase of pore water pressure in the fully saturated sand during the simulation of strong earthquakes. This behaviour is investigated in the experiments SP-SC1L and SP-SC2D (Fig. A.2). During strong shaking, the evolution of sand boils between the clay layer and the polyethylene foil could be observed. The interface between pile shaft and surrounding clayey soil opens and closes during the quake. Thus, the outflow of water and sand along the open gap between pile shaft and clay was observed as well. The soil-pile interaction in clay was investigated in experiments SP-C1L and SP-C2D, respectively (Fig. 4.25). Due to the total height of about 65 cm, the clay layer was drained rapidly by means of vertical cotton wool drains in experiment SP-C2D. Experiments with fully saturated sand covered by a clay layer were also carried out with a pile group consisting of four single piles (Fig. 4.26). The first experiment was initiated with loose Karlsruhe sand and unconsolidated Konstanz lacustrine clay (PG-SC1L), while the last experiment was terminated with dense sand and consolidated clay (PG-SC2D). The experimental programme was closed with an experiment investigating the behaviour



PG-SC1L pile group sand & clay

pile group sand & clay

pile group

m

c 80

m 0c

PWD1 h= 52cm PWD2 h=45cm

e = 0.84 γs = 26.5 KN/m³ γ' = 8.7 KN/m³ γd = 14.4 KN/m³ V = 0.252 m³

6c cm 20 cm 30 cm 40 cm

11

cm

21

cm

75 cm

49.8 cm 10.5 cm

10.5 cm 52.5 cm

Karlsruhe sand

∆s=2.7 cm

8

60 cm Konstanz lacustrine clay cu = 2.5 kPa w = 0.29


PG-SC2D

water 60 0 cm c Konstanz lacustrine clay cu = 4.4 kPa w = 0.24 PWD1 h=52cm PWD2 h=48,8cm

pile group sand sand boils sand

75 cm

110

Karlsruher sand e = 0.74 γs = 26.5 KN/m³ γ' = 9.45 KN/m³ γd = 15.2 KN/m³ PWD3 h=6cm V = 0.239 m³ m cm 21 c 1 1 20 cm 30 cm 40 cm

Figure 4.26: Experimental setup of the pile group installed in saturated sand covered by a clay layer before (first experiment PG-SC1L) and after (last experiment PG-SC2D) the experimental programme

of a pile group installed in a homogenous clay layer (Fig. A.5). The experiment PG-C1L enabled the investigation of the pile group in Konstanz clay with water content close to the liquid limit, whereas in the experiment PG-C3D the Konstanz clay was fully consolidated using vertical drains to fasten the consolidation process.

4.5.4

Experimental Programme

Several shake table experiments with different soil and pile configurations were carried out in the laminar box to investigate soil-pile-structure interaction in soft and liquefiable soils during strong earthquakes. The complete experimental programme was presented in Tab. 4.1 for the single pile experiments and in Tab. 4.2 for the pile group experiments. In the first experiment, a single pile was installed in loose fully saturated sand covered with a 10 cm thick clay layer (Fig. A.6). A second test was carried out using the single pile in dense fully saturated sand with a covering clay layer (Fig. A.7). Further experiments were conducted with a single pile in homogenous clay shortly after assembling the soil, i.e. unconsolidated clay experiment (Fig. A.8), and after a sufficient time permitting the clay to consolidate (Fig. A.7). The pore water dissipation was accelerated significantly in the second case by means of the vertical cotton wool drains. The behaviour of a pile group


111

consisting of four single piles was investigated in the laminar box using loose saturated sand with a covering clay layer (Fig. A.10), dense sand with a clay layer (Fig. A.11), unconsolidated homogenous clay (Fig. A.12), and fully consolidated clay (Fig. 4.27). In all tests, a displacement history was imposed by the table excitation, which was obtained by the twofold numerical integration of an acceleration record at Yerba Buena Island during the 1989 Loma Prieta Earthquake (M=7.1). Only the strong phase of the earthquake was required in the experiments. An arbitrary waveform generator [Agi04] was used to store the earthquake record together with a phase of zero displacement before and after the quake. The complete signal has a length of about T = 71 seconds, which is equivalent to a total frequency of about f = 14 mHz. For every experiment, the earthquake signal was used several times. The table excitation was scaled within the experiments in amplitude and in frequency in order to better investigate the influence of small, medium and strong earthquakes. The first quake of the first series (A-series) of every experiment (refer to displacement A1 in Fig. A.6) was scaled down to an eighth of the displacement of the original quake, which corresponds to a voltage of about 0.375 V provided by the control system. The second quake was double the displacement which is 0.75 V (A2). The third (A3) and fourth (A4) quake were induced by applying 1.5 V and 3.0 V, respectively. In order to increase the effect on the interaction behaviour, the frequency was doubled in a second series (B-series) of quakes. In the B-series, the amplitude was doubled four times from 0.375 V (B1) up to a maximum of 3.0 V (B4). The most impressive effects could be observed in case of B4 where the maximal frequency and the maximal amplitude are driven. In a C-series, the earthquake was scaled again with 28 mHz and 1.5 V (C1), and, subsequently, twice repeated with the full amplitude of 3.0 V (C2 and C3, see Fig. A.8). After applying the earthquake motion and a pause of a few minutes a sinusoidal base excitation was employed to the laminar box. The sinusoidal excitation started with low frequencies of 100 mHz or even less, and was increased after some cycles incrementally up to frequencies of around 1200 mHz (see for example Fig. A.9 S1 and S5, respectively). For every frequency increment, the amplitude is initially half the maximal amplitude of 3.0 V.

112


Table 4.1: Summary of - single pile (SP)- shake table experiments SP-S1L

installation removal drainage date start end total time A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 S1 S2 S3 S4 S5 S6 S7 S8 S9 T1 T2 T3

SP-SC1L

SP-SC2D

SP-C1L

SP-C2D

16.05.2005 24.05.2005 25.05.2005 09.06.2005 12.06.2005 17.05.2005 25.05.2005 25.05.2005 10.06.2005 13.06.2005 10.06.2005 17.05.2005 25.05.2005 25.05.2005 10.06.2005 13.06.2005 13:44 16:00 11:41 12:09 14:16 16:21 12:12 12:40 31 min 21 min 31 min 31 min 11:41 12:10 11:42 12:12 13:51

13:55 13:57 14:11 14:11

11:45

16:00 16:04

16:18 16:19 16:20

11:48 11:49

12:18 12:19 12:20

11:51 11:53

12:25 12:27

12:10

12:37 12:38


113

S050715A.mea.asc

S5

S4

400 800 1200 mHz

S3

200

S2

S1

C3

100

C1

C2

pile group in clay

B1 B2 B3 B4

A3

A4

40

PG-C3D

A2

Loma Prieta *real time

20

frequency

28 mHz

60

A1

sinus wave

0 20

80 0

500

1000

1500

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

3.0 V 3.0 V

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V

0.375 V

60

1.5 V

40

3.0 V

amplitude

0.75 V

table displacement [mm]

80

14 mHz*

2000

2500

time [s]

Figure 4.27: Displacements vs. time of a shake table experiment investigating a pile group installed in fully consolidated clay

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Table 4.2: Summary of - pile group(PG)- shake table experiments PG-SC1L

installation removal drainage date start end total time A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 S1 S2 S3 S4 S5 S6 S7 S8 S9 T1 T2 T3

PG-SC2D

PG-C1L

PG-C2D

15.06.2005 16.06.2005 20.06.2005 23.06.2005 16.06.2005 17.06.2005 21.06.2005 24.06.2005 21.06.2005 17.05.2005 25.05.2005 25.05.2005 10.06.2005 14:12 16:34 10:36 11:02 15:18 17:14 10:56 12:02 66 min 40 min 20 min 60 min

13:51

14:24 14:25 14:38 14:45 14:54

16:40

10:43

11:06 11:07

16:43 16:43

10:47 10:48 10:51

11:09 11:10 11:11

16:46 16:47

10:54 11:53

11:14 11:15

17:02 17:04 17:06

12:10

11:53

15:15 11:56


115

Table 4.3: Amplitude and frequency of Loma Prieta type wave oscillations

4.5.5

experiment

amplitude

frequency

A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 S1 S2 S3 S4 S5 S6 S7 S8 S9 T1 T2 T3

0.375 0.75 1.5 3.0 0.375 0.75 1.5 3.0 1.5 3.0 3.0 1.5/3.0 1.5/3.0 1.5/3.0 1.5/3.0 1.5/3.0 from 0.375 to 3.0 3.0 3.0 3.0

14 14 14 14 28 28 28 28 28 28 28 100 200 400 800 1200 800 800 800 800 from 200 to 1200

Visual Observations during the Experiments

During the experiments, several different phenomena were observed. The most noticeable ones are the generation of a gap between the soil and the pile, the generation of small cracks in the soil surface in vicinity of the pile, and the evolution of sand boils during the shaking.

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Generation of Gap between Soil and Pile

In the experiments with fully saturated clay or with saturated sand including a covering clay layer during the experiments, the build up of a gap between soil and pile could be observed shortly after the first excitation. Figure 4.28 illustrates the formation of gaps during the experiments. Initially, the pile and the soil is in contact. Slight shaking is not able to separate the pile from the soil. An increasing intensity in shaking generates the first gap, which is closed shortly after the excitation. Residual deformation is observed in case of long lasting strong shaking. After some events, the gap is filled with clay slurry in case of unconsolidated clay experiments, and filled with turbid water in case of fully consolidated clay experiments. Figure 4.29a shows the gapping pile group during strong motion, whereas Fig. 4.29b shows the single pile in unconsolidated clay with a slurry-filled gap.

Figure 4.28: Formation of gaps during the experiments


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Figure 4.29: Gaps observed during and after the experiments with (a) pile groups and (b) single piles in clay or in sand with a covering clay layer

Generation of Cracks in the Soil Surface Figure 4.30 presents the formation of cracks releasing small gas bubbles during the experiments with the single pile in clay. The cracks build a regular pattern around the pile which points in radial direction from the pile. This pattern sometimes changes during the experiments since some cracks close and heal while others appear. Figure 4.31 demonstrates this change in the cracks pattern.

Evolution of Sand Boils In all experiments with a saturated sand layer in combination with a covering clay layer, the evolution of sand boils could be observed. Most of the sand boils arise along the boundary of the soil container, i.e. between sealing foil and soil. Figure 4.32 shows a sand boil arisen in a corner of the laminar box, while Fig. 4.33 shows several sand boils generated along the laminar box boundary observed during the experiments with fully saturated sand with a covering clay layer.

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Figure 4.30: Initial formation of cracks with gas bubbles during the experiments

Figure 4.31: Further formation of cracks during the experiments

4.5.6

Experimental Results

Evolution of Pore Water Pressures during the Experiments In order to investigate and assess the liquefaction susceptibility of the granular soils and the softening of soft fine-grained soils used in the experiments, three pore water pressure transducers were installed in the laminar box. A detailed technical description of the three installed Vegabar 14 pore pressure transducers can be found in [VEG05].


119

Figure 4.32: A sand boil arisen in a corner of laminar box boundary, observed during the experiments with fully saturated sand with a covering clay layer

The evolution of pore water pressure vs. time of the first shake table experiment SPSC1L is depicted in Fig. 4.34. A single pile was installed in initially loose saturated sand. All three pore water pressure filters were installed in the sand layer. To allow the increase of pore water pressure during the shaking, the sand was covered with a sealing clay layer. Figure 4.34 shows an incremental increase of the pore pressure from initially 6.8 kPa to 7.1 kPa, 7.2 kPa, and 7.4 kPa after the events A1, A2, and A3, respectively. The residual pore pressures decrease only slightly due to the undesirable drainage along the laminar box walls. After the earthquake event A4, which is the real scaled 1989 Loma Prieta earthquake, post-quake pore water pressure reached 8.1 kPa. Nevertheless, it decreased rapidly due to the build up of sand boils and water conductivity along the laminar box boundaries and along the pile shaft. The subsequent events B1, B2, B3 and B4, accordingly, indicate pore pressures coming down to 7 kPa and less for the reason that a direct connection to the surface is already established. The distinctively high peaks during the earthquake events can be explained by the inertia of the water column in the pore pressure tubes. Highest peaks are recognised during events B4 and C2. After around 1000 s, the initial pore water pressure was reached, even shortly after the events C1 and C2 due to the water conductivity to the surface.

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Figure 4.33: Sand boils along the laminar box boundary, observed during the experiments with fully saturated sand with a covering clay layer

SB050525.mea.asc

14

frequency = 28 mHz

Loma Prieta real time

SP-SC1L

12

3.0 V initial pore pressure 1.5 V

3.0 V

1.5 V

6

pwd01 pwd02 pwd03

B1 B2

A4

7

A3

A2

0.75 V

8

A1

9

pore pressure increase

3.0 V 0.375 V 0.75 V

10

B3

11

C1

single pile in sand & clay

0.375 V

pore pressure [kPa]

C2

B4

14 mHz*

13

amplitude

5 0

500

1000 time [s]

1500

2000

Figure 4.34: Evolution of pore water pressure vs. time of the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer


121

The evolution of pore pressure in case of dense saturated sand with a covering fully consolidated clay layer is shown in the appendix (Fig. A.16). The pore water pressure transducer PWD01 shows a greater increase of the pressure because its filter is embedded at the bottom of the clay layer. Nevertheless, the decay of pore pressure is relatively fast after event B4 due to rapid diffusion of pore water along the clay layer margin. PWD02 and PWD03 measure in the sand layer in different depth but, subsequently, show the same pore pressure. After about 600 s, the excitation mode is shifted to a sinusoidal wave. A noticeable increase of the pore pressure in the clay layer was observed whereas the post-shaking pore pressure in the sand layer still coincides with the initial value. The increase of pore water pressure in the soft soil coincides with the softening of the clayey soil. In experiment SP-C1L (Fig. A.17), the laminar box was filled with Konstanz lacustrine clay with its water content close to the liquid limit. Shortly after the assembly of the soft soil, the experiment was carried out. Thus, the initial pore water pressures nearly correspond to the total pressures. PWD03 located at the bottom of the soil specimen displayed a pore pressure of about 12 kPa, which is an excess pore water pressure of about 5 kPa. After the application of earthquake series A, B, and C, the transducer PWD03 shows a pressure of 12.8 kPa. Even the series of sinusoidal shaking was not able to increase this value. In addition, PWD01 and PWD02 recorded constant post-quake pressures. A partial consolidation of the soil specimen led to a partial vanishing of the excess pore pressures (experiment SP-C2D in Figure 4.35). Subsequently, the pore water pressures of PWD01 to PWD03 nearly came down to 7 kPa. An incremental increase of the pore water pressures due to softening of the soil can be clearly identified. Earthquake event B4 shows a remarkable increase of pore pressure from 8.2 kPa up to 10 kPa. After the sinusoidal shaking programme, the initial state by means of shear resistance of the soft soil was obtained (compare Fig. A.17). In experiment PG-SC1L (Fig. A.19), a pile group installed in initially loose saturated sand with a covering clay layer was investigated. The evolution of pore water pressures vs. time shows a slight increase in case of the events A1, A2, and A3, respectively. However, the following earthquake events led to a gradual decrease of pore water pressure. Compared to the single pile case (Fig. 4.34), the existence of four piles aggravated the effect of leakage along the pile shafts, which made the incremental build up of pore water pressure nearly impossible. The slight inclination of the mean pore pressure evolution can be explained by the settlement of the surface, while the position of the filters was kept constant and the surficial water was removed during the experiments. Hence, at the end of the sinusoidal excitation the PWD01 record is differing due to the penetration of the PWD01 filter into

122


S050613A.mea.asc

16

S3

S4

S5

pwd01 pwd02 pwd03 S2

sin

B1 B2 B3 B4 sin

A4

A2 A3

A1

10

C1 C2 C3

single pile in clay

12

8

1.5 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

1.5 V 3.0 V 3.0 V

3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V

1.5 V

4

3.0 V

amplitude

6 0.375 V 0.75 V

pore pressure [kPa]

SP-C2D

S1


14

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

2 0

500

1000 time [s]

1500

2000

Figure 4.35: Evolution of pore water pressure vs. time of a shake table experiment investigating a single pile installed in fully consolidated clay

the clay layer, which comprises an increase of pore pressure (compare also Fig. A.16). The same phenomenon can be observed in experiment PG-SC2D (Fig. A.20) after the sinusoidal excitation is accomplished. Due to the densification of the Karlsruhe sand, the largest peaks are negative, i.e. pore water suction occurred because of the dilative behaviour of the dense granular soil. Figure A.21 shows the evolution of pore water pressure vs. time of the PG-C1L experiment investigating a pile group installed in unconsolidated clay. PWD02 and PWD03 lie in the same depth and increase slightly due to the earthquake events. Transducer PWD03 measured the pore pressures close to the bottom of the specimen. The results are comparable to the measurements in experiment SP-C1L (Fig. A.17). Consolidation of the soil specimen led to the same pore water pressures prior to test PG-C2D (Fig. A.22). Shortly after the earthquake test programme (after event C3), a maximal pore pressure of about 10 kPa could be attained. Vertical cotton wool drains allowed a continuously decrease of pore pressure down to 8 kPa within 1500 seconds. The sinusoidal excitation programme increased the pore pressure until total softening of the Konstanz lacustrine clay was observed. The last experiment PG-C3D (Fig. A.23) used the same experimental setup. Consolidation comprising a subsequent creeping period allowed the soil specimen to solidify completely. The same shaking programme as in PG-C2D (Fig. A.22) was applied. However, this time after the earthquake events, only pore water pressures of about


123

7.5 kPa were reached, which is 2.5 kPa less than in the previous experiment. After extensive sinusoidal shaking, PWD03 pressure came as well up to the maximal value of about 11 kPa (compare Fig. A.22). It is concluded that the pore water pressure measurements in granular soils (here: Karlsruhe sand) can be used to assess liquefaction susceptibility. During the strong shaking events, mostly event B4, total liquefaction could be observed. Very fast drainage through water channels along the laminar box boundaries and along the pile shafts could be observed. The build up of sand boils is a self-evident consequence. Further build up of excess pore water pressure was prevented when a heavily increased water conductivity through channels is allowed. Accordingly, further liquefaction was aggravated but locally possible during strong shaking. In case of cohesive soils (here: Konstanz lacustrine clay), a softening due to heavy shaking and subsequent pore water pressure build up could be observed. Even long lasting consolidation processes were accelerated by means of vertical cotton wool drains. Strengthening was observed after a few days. Sinusoidal excitation was able to soften the soil specimen completely, behaving then like the initial state of the clayey soil prior to consolidation.

Evolution of Vertical Displacements during the Experiments Vertical displacements of the soil surface in the laminar box were measured by means of two Laser Displacement Transducers installed at a crossbar above the shake box. A detailed description of the laser sensors can be found in [mic04]. In order to provide a suitable target surface, two white PVC beams were firmly located at two opposite positions upon the top of the soil layer. The largest settlements during the shaking events were observed in case of experiments with a loose sandy layer. The evolution of vertical displacements vs. time of the first shake table experiment SPSC1L, investigating a single pile installed in loose saturated sand with a covering clay layer, is shown in Figure 4.36. In case of small earthquake events, and of course in case of a well-working clay layer sealing, the settlements are still negligible (A1 to B2). Event B3 generated vertical displacements of about 2 mm. However, the strong earthquake event B4 led to nearly 20 mm subsidence in total. A repetition of the same earthquake in C2 comes up with another 10 mm of displacements. Even in case of the dense sand experiment SP-SC2D (Fig. A.25), the vertical displacements are quite remarkable, e.g. about 5 mm after event B4. Additional subsidence of between 15 mm (Laser01) and 40 mm (Laser02) could be observed when the sinusoidal frequency is about f = 1.2 Hz.

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SB050525.mea.asc

10

14 mHz* B4 B3

B1 B2

A4

A2

A1

A3

Loma Prieta real time e = 0.84

0

SP-SC1L single pile in clay

e = 0.83

-40 0

500

1.5 V

3.0 V

3.0 V

0.375 V 0.75 V 1.5 V

0.375 V

-30

1.5 V

e = 0.76 e = 0.72

C2

-20

3.0 V

e = 0.79

C1

laser01 laser02

-10

0.75 V

settlement [mm]

frequency = 28 mHz

amplitude

1000 time [s]

1500

2000

Figure 4.36: Evolution of vertical displacements vs. time of the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer

The evolution of vertical displacements vs. time in case of a pile group installed in loose saturated sand (experiment PG-SC1L, Fig. 4.37) exhibits a result comparable to the experiment SP-SC1L (Fig. 4.36). Largest subsidence was displayed from event B4 (about 20 mm). Subsequent events triggered a stepwise increase of the vertical displacements: C1 additional 8 mm, C2 10 mm, C3 6 mm, and, finally, the S5 event, which was a sinusoidal shaking with a frequency of f = 1.2 Hz, led to subsidence of around 5 mm. The experiment PG-SC2D (Fig. A.29) investigated the behaviour of a pile group embedded in dense saturated sand. The settlements observed in the earthquake events A1 to C3 were negligible but an applied sinusoidal frequency of f = 1.68 Hz produced incremental subsidence of 1 mm for S2 and 2 mm for S4.

In all other shake table experiments dealing with a clay specimen, settlements due to shaking were negligible. Sometimes subsidence was recorded by mistake due to softening of the clayey soil and the subsequent penetration of the PVC beam into the soil (see S5 in experiment SP-C2D Fig. A.27 or PG-C2D Fig. A.31, C1, C2, C3 in PG-C1L Fig. A.30). In other cases, heave was observed due to local surficial deformation (event S4 in experiment SP-C1L Fig. A.26).


S050616A.mea.asc

10 B4

∆e = 0.12

B3 B2

e = 0.65

C2

B1

1.5 V 3.0 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

3.0 V

S5

S4

S3

S2

C3

sinus wave

e = 0.57 3.0 V

e = 0.60 1.5 V

-40

0.375 V 0.75 V 0.7 1.5 V 3.0 V

-30

S1

A1

e = 0.63

1.5 V 3.0 V

A4

laser01 laser02

PG-SC1L pile group in sand & clay

A2

A3

-10

0.375 V 0.75 V 1.5 V 3.0 V

settlement [mm]

e = 0.71


C1

0

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

-20

125

e = 0.54

amplitude

-50 0

1000

2000 time [s]

3000

4000

Figure 4.37: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in loose saturated sand with a covering clay layer

Maximal Strains in the Model Pile during the Experiments The bending behaviour, observed by means of bending strains along the pile shaft, is presented here. The amplitude and the position of maximal bending strains depend on a huge variety of influencing variables. It is quite evident that the pile head mass, the pile support conditions and the magnitude and frequency content of the shaking event have a significant influence on the bending strains. During the experiment, the state of the soil is changing. In case of sand, liquefaction can occur, and in case of clay, the soil softens due to the shaking. While liquefaction and softening are observed, the bending strains must change in both, magnitude and position of zero points. Cohesive soils allow the development of a gap between the pile shaft and the soil, especially close to the surface. Thus, bending moments increase and migrate into deeper soil layers. Figure A.33 shows the maximal bending strains occurring in the SP-SC1L experiment. At the beginning of the experiment, only small strains were measured in the model pile (events A1 to B2), but an increase in magnitude led to a disproportionate increase in bending moments (events B3 and B4 with maximum strains of nearly 200 µε and 400 µε, respectively). The evidence of a change in the soil state is given by the increase of bending strains due to a repetition of the events, i.e. event C1 (300 µε) and C2 (500 µε). Both the liquefaction in the sand and the gapping in the covering clay layer are accountable

126


for the increase. In case of a single pile installed in dense saturated sand (experiment SP-SC2D Fig. A.34), the maximal bending moments are located at a higher position of the pile because it is embedded in a stiffer soil. Due to the large shaking of the previous experiments (SPSC1L), the sand layer and its covering clay layer settled, which leads to an increase of the free length between pile head mass and ground surface. In this way, the maximal strains of event B3 and B4 reached values of about 280 µε and 620 µε, respectively. During the sinusoidal shaking, the strains rose incrementally up to 650 µε. Experiments with a single pile installed in clayey soil show a similar behaviour. In case of unconsolidated clay in Fig. 4.38, the bending strains increased apparently with increasing magnitude (event B1 50 µε, B2 100 µε, B3 170 µε, and B4 nearly 400 µε). Nevertheless, in case of unconsolidated clay, the repetition of the events only led to a slight increase of bending strains (cf. Fig. 4.38 event B4, C2, and C3). The application of a sinus-wave shows maximal strains far lower than 300 µε for frequencies of f = 800 mHz. S050609B.mea.asc

S4

C3

B4

800 mHz

S3

S2

S1

C1

single pile in clay

B2

B3

200 400

SP-C1L

B1

A1 A2 A3

A4

200

µε [-]

frequency = 28 mHz


C2

14 mHz*

400

100

sinus wave

0

0

1000

3.0 V

3.0 V 1.5 V 3.0 V 1.5 V 3.0 0V

amplitude

1.5 V

3.0 V

3.0 V

0.375 V 0.75 V 1.5 V

1.5 V

3.0 V

-400

0.75 V

0.375 V

-200

2000 time [s]

Figure 4.38: Maximal strains measured in the model pile during a shake table experiment investigating a single pile installed in unconsolidated clay

The consolidation process of the clay leads to a significant increase of stiffness. Thus, the position of the maximal strains migrated to the upper region of the pile. Initially, the strains were relatively small (experiment SP-C2D in Fig. 4.39). The earthquake event B3 and B4 generated maximum strains in the pile of about 150 µε and 350 µε, respectively, which is a 12% reduction compared to the unconsolidated conditions. However, this time


127

the repetition of the experiments came along with a softening of the soil in the vicinity of the pile shaft and a subsequent gapping between pile and the softened clay. Hence, the strains clearly increased, reaching even higher values (C1 280 µε, C2 600 µε, C3 650 µε) than in the experiment SP-C1L in Fig. 4.38. S050613A.mea.asc

1500

SP-C2D

0

S4

S3

S2

S1

sin

sin

B1 B2 B3

A4

A2 A3

A1

B4

C1 C2 C3

single pile in clay

500 µε [-]

S5


1000

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

1.5 V 3.0 V 3.0 V

3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V

3.0 V

0.375 V 0.75 V

-500

1.5 V

amplitude

-1000 0

500

1000 time [s]

1500

2000

Figure 4.39: Maximal strains measured in the model pile during a shake table experiment investigating a single pile installed in fully consolidated clay

Maximal strains measured in one of the model piles of the pile group experiments are presented in Figures A.37 to A.40. Figure A.37 shows the maximal strains in case of loose saturated sand with a covering clay layer. It has to be pointed out that the increase of pile strains due to a change of earthquake magnitude is much higher than in the comparable single pile case. Especially, the jump between B3 (about 100 µε) and B4 (about 450 µε) is remarkable. The repetition of the earthquake event in C1 and C2 only leads to a slight increase of the bending strains. The repetition in event C3 shows a significant decrease (see C2 and C3 in Fig. A.37). In case of a dense sand layer (Fig. A.38), the bending strains during the strongest earthquake events B4, C2, and C3 remained more or less constant (around 500 µε). A subsequent experiment with frequency dependent sinusoidal shaking is giving the maximal bending strains of about 1700 µε when a frequency of f = 1.68 Hz is applied. The experiments involving pile groups installed in unconsolidated clay (Fig. A.39) and fully consolidated clay (Fig. A.40), respectively, show similar bending strains for both cases. Maximal strains of about 1000 µε were reached by event B4, C2, and C3 in both

128


experiments indicating that the system behaviour predominates the change of the soil state, which was also observed in the experiment. It can be concluded that maximal strains in the pile shafts are obtained when a sinusoidal wave is applied to the system. In case of the single pile and the pile group, the frequency has to be around f = 1.68 Hz and f = 1.2 Hz, respectively, but is has to be noticed that the frequency shifts towards lower values with a change of the state of the soil, i.e. liquefaction and softening.

Evolution of Pore Water Pressures during Event B4 The previous diagrams presented an overview of the experiments. During the experiments, the earthquake event B4 can be identified in most cases as the event with the greatest impact with regard to the state of the soil as well as the pile-soil interaction behaviour. To better understand the observed mechanisms, a detailed view on event B4 is presented by means of the following diagrams. It was already shown that in case of piles in saturated sand covered by a clay layer, the pore water pressure increases rapidly during the shaking event. Due to an insufficient sealing by the covering clay layer a very fast drainage could be observed through water channels along the laminar box boundaries as well as along the pile shafts. Thus, the excess pore water pressure decreases rapidly even if further moderate shaking takes place. Further build up of excess pore water pressure is prevented when very big water conductivity is allowed through channels. Figure 4.40 compares the experiment investigating a single pile installed in saturated loose sand (SP-SC1L) and dense sand (SP-SC2D) covered by a clay layer, respectively. In case of loose sand, the increase of pore water pressure during the event is noticeably higher (7.0 kPa instead of 5.1 kPa). Due to observed high water conductivity through large water channels, a residual excess pore water pressure was not measured in SP-SC1L but in the events before. Compared to the dense sand case, the increase occurred immediately, and all three transducers show the same results because their filter stones altogether ended in the sand layer. By contrast, experiment SP-SC2D shows different pore water sequences versus time. The pore water pressure at the bottom (pwd03) of the soil specimen increased about by the double amount as the pore pressure at the top of the specimen (pwd02), which coincided after about 10 seconds. The filter stone of pwd01 penetrated into the clay layer after its gradual settlement. Thus, the pore water pressure increase was conserved for a longer period in the dense sand experiment, which is not observed for the loose sand experiment because at that time the clay layer position was still higher.


129

20 pwd01 pwd02 pwd03

15

pwd01 pwd02 pwd03

SP-SC1L 10

SP-SC2D single pile in sand & clay

7.0 KPa


5.1 KPa

pore pressure [kPa]

B4

5

0 250

260

250

260

time [s]

Figure 4.40: Evolution of pore water pressure during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

20

pore pressure [kPa]

B4

pwd01 pwd02 pwd03

pwd01 pwd02 pwd03

15 A

10 A'

5

SP-C1L

SP-C2D

single pile in clay

0 680

single pile in clay

690

680 time [s]

690

Figure 4.41: Evolution of pore water pressure during event B4 for the shake table experiments, investigating a single pile installed in saturated clay

130


Figure 4.41 compares the behaviour of a single pile installed in unconsolidated clay (SPC1L) and fully consolidated clay (SP-C2D), respectively. Prior to the unconsolidated clay experiment, the initial pore pressures were higher for deeper locations in the soil specimen (SP-C1L). Due to the consolidation process, the excess pore pressures vanished and, thus pore pressures coincide with those, which could be observed in SP-C2D. In case of consolidated clay, a residual increase of pore water pressure was observed. It can also be seen that the displacement of the pore water curves are significantly higher (more than 30%) in case of unconsolidated clay (see grey realm A and A , respectively). 14

B4


pore pressure [kPa]

12

pwd01 pwd02 pwd03

dissipation A Inc

10

dissipation B dissipation C

8

6

PG-SC2D pile group in sand & clay

790

Dec

800

810 time [s]

Figure 4.42: Evolution of pore water pressure during event B4 for the shake table experiments, investigating a pile group installed in saturated sand covered by a clay layer A fast increase of pore water pressure at pore pressure transducers pwd02 and pwd03 by about 6.5 kPa is shown in Fig. 4.42 for pile group experiment PG-SC1L (see arrow inc). Even during the shaking, a rapid decrease of pore water pressure had to be realised (see dissipation A). Close to the surface, the increase is less impressive (see pwd01). After around 10 seconds, the pore water pressures decrease calms down for pwd02 and pwd03 and, finally, coincides with pore water curve pwd01 (dissipation B). After the shaking, the decrease accelerates again (dissipation C) and the initial pore pressures were reached within the following 5 seconds. By contrast, in case of loose sand, the largest influence of the event B4 led to a sudden increase of the pore water pressure (arrow Inc). In case of dense sand, exactly the same earthquake history leads to a rapid decrease of the pore water pressure (arrow Dec). This


131

behaviour can be explained by the dilatation of the grain skeleton due to shear wave propagation in case of dense sandy soil, and its collapsible behaviour during the shaking in case of a loose granular soil. Three different states of pore water dissipation can be observed in general as well as in Fig. 4.42: • A very fast decrease of the pore water pressure is observed shortly after a heavy impact (dissipation A). The sandy soil is liquefied and the pore pressure transducers record the pore pressures of a heavy liquid, i.e. a soil-water-suspension. In depth, where liquefaction does not take place, the increase and the subsequent decrease is comparably slower. Fast drainage is made possible through large channels permitting a high conductivity. At some sites, e.g. along the pile shaft and close to the laminar box boundary, suspension flow is possible due to the large mobility of the soil (build up of sand boils). • After the excitation attenuates and a large amount of pore water is already released to the surface, the compacted grain skeleton restarts to bear its overlying loads as well as the dynamic loads. Most of the soil grains are again in contact and, thus the water flow through the grain skeleton is impeded, which leads to a slower decrease of the pore water pressures (dissipation B). • When the shaking stops, the shearing of the soil specimen is interrupted, and with it also the rearrangement of the grains in their skeleton. At rest, the pore water dissipation takes place with an initially higher velocity (dissipation C) and approaches an asymptotical value, viz. the hydrostatical pore water pressure distribution in the soil specimen. The evolution of pore water pressure vs. time during event B4, investigating a pile group installed in saturated clay, is shown in Fig. 4.43. Three cases are presented comparing unconsolidated clay, partially consolidated clay, and fully consolidated clay, respectively. The pore pressures at the bottom of the soil specimen (transducer pwd03) show the most noticeable residual increase. In case of unconsolidated clay, the increase ∆u1 is negligibly small, but in case of partially consolidated and fully consolidated clay it reaches values of about ∆u2 = 2.1 kPa and ∆u3 = 0.9 kPa, respectively. During the shaking, the pore water pressure displacement is much higher in case of unconsolidated clay (compare A1, A2, and A3 in Fig. 4.43, respectively). Large negative excess pore water pressures, viz. ∆u = −4.5 kPa, can be observed in case of experiment PG-C2D (see peak p∗ ).

132


20

pore pressure [kPa]

B4

pwd01 pwd02 pwd03

pwd01 pwd02 pwd03

pwd01 pwd02 pwd03

15 A1

PG-C2D pile group in sand & clay

10

∆u2

∆u1

∆u3

A2

A3

5

PG-C1L

p*

PG-C3D

pile group in sand & clay


0 850

860

870

time [s]

Figure 4.43: Evolution of pore water pressure during event B4 for the shake table experiments for investigating a pile group installed in saturated clay

In summary, it may be noticed that the observation of the pore water pressure evolution may be used for a better understanding of the pore pressure and pore water flow mechanisms in the grain skeleton of hard-grained soils as well as soft soils. The dissipation of water through the soil depends in particular on the actual structure of the solid particle skeleton during the shaking. This allows very fast drainage during strong shaking including suspension transport as well as slowed down drainage after the grain skeleton settles until contact between the grains is obtained. Dense sand as well as consolidated clay show remarkably large peaks of negative excess pore water pressures when subjected to strong shaking. After a long shaking period, soft soils are able to weaken and can reach a state and mechanical behaviour comparable to that observed in the experiments with unconsolidated clay.

Pile Head Displacements vs. Time during Event B4 In the following diagrams, absolute horizontal pile head displacements vs. time during event B4 are presented. The horizontal displacements vs. time of the shake table are also indicated in the diagram by means of a dashed line. In this way, the displacement response of the foundation-structure system in comparison to the excitation at the base is clearly outlined.


100

B4 ∆s

133

head table

amp

head displacement [mm]

∆satt

0

SP-SC1L single pile in sand & clay

-100 100

∆samp

SP-SC2D

∆satt


0 head table

-100 250

260

270

280

time [s]

Figure 4.44: Pile head displacements vs. time during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

Figure 4.44 shows the pile displacements in case of the shake table experiments for investigating the behaviour of a single pile installed in saturated sand covered by a clay layer for both cases, the loose sand experiment SP-SC1L and the dense sand experiment SPSC2D, respectively. It can be seen that the frequency content as well as the phase change significantly. The single pile in loose sand swings in approximately the same frequency as the shake table. Initially, an amplification of the pile movement with respect to the base movement of about 80% can be observed (see ∆samp ). After the liquefaction of the sandy soil, the movement of the pile head is decelerated and, finally, leads to an attenuation of the pile head displacements of about 30% (see ∆satt ). In case of a dense sand layer, the pile displacement vs. time behaves completely different. The frequency content shifts to higher frequencies, i.e. up to six times higher frequencies. This can be primarily explained by the much deeper constraint by the compacted sand. Furthermore, the amplification of the pile head displacements are apparently larger than in the loose sand case, which is an amplification of about 350%. After 7 seconds, the amplification vanishes and only a slight high frequency oscillation can be observed in experiment SP-SC2D. Figure 4.45 presents the results of single pile experiments in saturated clay. The amplification of the pile head displacements is higher in case of unconsolidated clay (about 200%) compared to consolidated clay (about 150%). Thus, the stiffening of the soft soil due to consolidation is also accompanied with a moderated displacement response. Nevertheless,

134



100

B4

∆samp

head table

0

SP-C1L single pile in clay

-100 100

∆samp

head table

0

SP-C2D single pile in clay

-100 580

590

600

610

time [s]

Figure 4.45: Pile head displacements vs. time during event B4 for the shake table experiments investigating a single pile installed in saturated clay

the frequency content changes as well by a slight increase of frequency in case of the stiffer soil (experiment SP-C2D). The pile head displacements vs. time for the shake table experiments for investigating the pile groups are presented in the appendix A.8. The amplification of the pile head is partially spoiled on account of the changed static system, i.e. the pile group behaves much stiffer than the single pile. In case of the pile group installed in saturated sand and covered by a clay layer (cf. Fig. A.47), the amplification is relatively small (about 20%). Compared to the compacted sand layer the amplification is even less (about 10%). As already observed in the single pile experiments, the frequency content shifts to higher frequency, especially in case of the dense soil specimen. Comparable results can be observed in the experiments with a pile group installed in saturated clay (Fig. A.48).

Pile Bending Moments vs. Time and Depth during Event B4 In the following three sections, the evolutions of bending moments M , pile displacements w, and lateral soil displacements s are illustrated by means of three-dimensional diagrams. The length of the pile and the depth of the soil layer z, respectively, are depicted in vertical direction. The time line t showing a period of about 10 seconds points from the


135

foreground section into the background. The variable to display spans a wavelike surface which oscillates to the left and to the right depending on their actual values M = f (z, t). In order to evaluate the pile bending moments versus time and location M (z, t), the strains ε(z, t) measured by means of eight strain gauges along the test pile were stored in a two-dimensional data array. The curvature w (z, t) of the pile is easily determined by the relation ε(z, t) = w (z, t)zs (z), where zs (z) is the distance from the neutral axis of the pile section to the strain gauge. From the differential equation of the deflection curve M (z, t) w (z, t) = − , a two-dimensional data array containing the bending moment E(z)I(z) M (z, t) can be calculated. t [s]

t [s] 10.0

10.0 8.0 8.0

6.0 6.0

zero-moments 4.0

m]

4.0

m]

M

[N

2.0

2.0

en mo m ze ro-

-2.

0

ts

0

sta bil

iza

tio n

-1.

-2.

0.0

1.0

2.0

∆MFd

0

0 -1.

0.0

1.0

2.0

M

[N

∆MFl

∆ME

loose B4 SP-SC1L single pile in sand

dense B4 SP-SC2D single pile in sand

Figure 4.46: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer Figure 4.46 depicts the pile bending moments vs. time and depth for the shake table experiments for investigating a single pile installed in saturated sand covered by a clay

136


layer for both cases loose sand and dense sand. In case of loose sand, the maximal field bending moments were significantly smaller (∆MF l = 0.75 Nm) than in the dense sand case (∆MF d = 1.3 Nm) due to the softer soil reaction. However, in case of loose saturated sand, liquefaction occurred and the pile behaved like standing in a soil-water suspension. Thus, the lateral bedding of the pile got lost and, subsequently, an end moment at the clamped base appeared immediately. The first impact produced a maximal end moment of about ∆ME = 0.8 Nm, which is even slightly larger than the field moment. During the proceeding cycles, the end moments decreased rapidly and, finally, vanished after 2 seconds. This can be explained by a stabilisation process (cf. Fig. 4.46 experiment SPSC1L) initiated by water filtration preventing further liquefaction. In Fig. 4.46, a dashed grey line highlights a realm where the bending moments disappear (zero-moments). It can be noted that this realm grows visibly with reduced intensity of shaking as well as a denser state of the sandy soil. In Fig. 4.47, pile bending moments evaluated from experiments for investigating a single pile installed in unconsolidated clay and consolidated clay, respectively, are compared. In case of unconsolidated clay, an end moment of about ∆ME = 0.85 Nm is observed as well. At the other end of the pile, the moment is slightly smaller (∆MF l = 0.8 Nm). The consolidation process led to an increase of the field moment to a maximal value of about ∆MF d = 0.9 Nm. Nevertheless, the characteristic feature can be seen in the large difference in disappearing bending moments with time and depth (see realm with zeromoments). While the pile in the loose clay specimen is still bent over the whole time and the whole depth, a significant calming can be observed in the unconsolidated clay case. Thus, the clay in experiment SP-SC1L behaved like a soft slurry allowing the pile to bend along its complete length. The consolidation led to a stiffening of the soil. Particularly in the deeper layers, consolidation tightens the lateral bedding of the piles. This effect can also be observed in Fig. 4.48. Pile groups in loose sand (PG-SC1L) show moments evolving down to the bottom of the piles. A compaction of the sand causes a significant end moment at the tips of the piles but not at their toes (PG-SC2D). In case of loose sand, the maximal end moment at the toe of the piles reached ∆ME = 0.7 Nm. In case of dense sand, the maximal end moment at the tip of the piles increased to about ∆ME = 2.0 Nm, and the field moments mounted up to ∆MF d = 0.6 Nm. Simultaneously, with the change of state in terms of void ratio, the increasing compaction led to an increase of frequency from about f = 1.6 Hz, in case of loose saturated sand to about f = 3.8 Hz in case of dense sand. Figure 4.49 shows the pile bending moments vs. time and depth during event B4 for investigating the pile group installed in saturated clay with different void ratio. In case of unconsolidated clay, the end moments at the tip of the piles were smaller, i.e. end


137

t [s] 10.0

t [s] 10.0 8.0

8.0 6.0

6.0 4.0

[N m] M

2.0

ts

0 ze ro

-m

om

en

-2.

-2.

0

-1.

0.0

1.0

2.0

∆MFd

0 -1.

0.0

∆MFl

1.0

2.0

M

2.0

0

[N m]

4.0

∆ME

B4

loose SP-C1L single pile in clay

B4

dense SP-C2D single pile in clay

Figure 4.47: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

moments of about ∆ME = 1.6 Nm instead of ∆ME = 2.0 Nm and ∆ME = 1.8 Nm. The decrease of the end moment in case of dense clay (PG-C3D) can be explained by a softening and gapping of the soil-pile interface after numerous experiments. For the same reason, the field moment in PG-C3D vanished nearly completely. An end moment of around ∆ME = 0.3 Nm at the pile toes developed due to a deep gap and the subsequent loss of the lateral bedding along the pile shaft. Thus, the field moments initially increased from ∆MF d = 0.25 Nm to about ∆MF d = 0.3 Nm and, afterwards, decreased to nearly zero values due to the missing lateral bedding.

138


t [s

]

10

.0 8.0

6.0

M

6.0

4.0

m [N

2.0

M

0 2.

4.0

] m [N

2.0

0 2.

0

1.

0 1.

0

0.

0

. -1

]

.0

8.0

]

t [s

10

.0

∆ME ∆MFd

0 0.

.0

-1

-2

.0

-2

ts

en

om

m o-

r ze n

tio

b

a iliz

a st ∆ME

loose B4 PG-SC1L pile group in sand

dense B4 PG-SC2D pile group in sand

Figure 4.48: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

Lateral Soil Displacements vs. Time and Depth during Event B4 Along the height of the laminar box, the lateral displacements versus time and versus depth were measured. It is assumed that the soil specimen moved layerwise in the same manner. In the following diagrams, the experiments with single piles are presented. The diagrams show relative displacements with respect to the base of the laminar box, which is set to zero. The decrease of lateral soil displacements due to the compaction of the sand layer can be observed in Fig. 4.50. The decrease is more than 50% from initially about s = 20 mm to less than s = 10 mm at the end. The evolution of soil displacements versus depth shows a non-linear distribution with an increasing rate of lateral soil displacements from the middle of the soil specimen to its surface. Thus, a slight amplification of the surficial


139

t [s

]

10

[N

m

8.0 6.0

4.0

]

M

0

2.

∆ME

0 1.

0

0.

m

[N

2.0

0

-

ts

en

0 2.

-

om

B4

loose PG-C1L pile group in clay

∆ME

0

1.

0

0.

0 1.

-

0 2.

s nt

-

.0

-2

om

m

o-

r ze

B4

.0

-1

e

-m

o

r ze

2.0

0

∆MFm

0

[N

2.

∆ME

0 1. 0.

0 1.

M

2.

∆MFl

4.0

]

m

2.0

]

.0

6.0

4.0

t [s

10

8.0

6.0

M

]

.0

8.0

]

t [s

10

.0

medium PG-C2D pile group in clay

∆ME

B4

dense PG-C3D pile group in clay

Figure 4.49: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments for investigating a pile group installed in saturated clay

soil movements with respect to the base can be recognised. A quite different behaviour is shown in case of single piles in clay in Fig. 4.51 where the distribution of the lateral soil displacements versus depth is exactly linear, i.e. the soil specimen was subjected to simple shear, also exhibiting smaller maximal displacements of around s = 15 mm in case of unconsolidated clay. Due to the stiffening of the clay specimen within the consolidation process, the lateral displacements decreased strongly to values less than s = 5 mm.

Lateral Pile Displacements vs. Time and Depth during Event B4 M (z, t) , a twoE(z)I(z) dimensional data array containing the bending moment M (z, t) was calculated and presented in section 4.5.6. The double-integration by parts of the curvature distribution w (z, t) with respect to the depth results in a stored data array of the pile displacements w(z, t) versus time and versus depth, namely w(z, t) = w (z, t)(dz)2 = w (z, t)dz, where w (z, t) is the deflection angle of the pile. From the differential equation of the deflection curve w (z, t) = −

140


t [s

]

10

8.0

6.0

s

[m

s[

2.0

.0

20

. 10

6.0

4.0

]

20

0 0

0.

-

. 10

0

]

.0

8.0

m

t [s

10

.0

m

m

4.0

]

2.0

.0 10

.0 0.

0

0

-

0

0.

-1

. 20

-2


0.

0


Figure 4.50: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments for investigating a single pile installed in saturated sand covered by a clay layer

The boundary values are quite different in the two cases of single pile and pile group, respectively. In case of the single pile, the deflection angle at the base is zero versus time w (zbase , t) = 0 due to the rotational restraint at the piles’ toe, whereas the pile at the tip of the pile is free. In case of the pile group, the pile top is confined due to the boundary value condition w (zbase , t) = w (ztop , t) = 0. This leads to a very different behaviour for the two cases. A validation of the double-integration is presented in Fig. 4.52 comparing calculated and measured lateral pile tip displacements versus time, respectively. At the tip of the model pile, the displacement was measured by means of a position transducer. It is known that for large angles the curvature of the pile axis has to be determined exactly, w (z, t) namely κB (z, t) = . Thus, the direct double-integration of the curvature (1 + w (z, t)2 )3/2 w (z, t) is only an approximation for small angles, i.e. w (z, t)2 1. As presented in Fig. 4.52, the approximation κB (z, t) ≈ w (z, t) is applicable as that the error can be neglected for displacements less than about ±50 mm. By comparing the errors in detail A and detail B, respectively, it is evident that the calculation of the pile tip displacement


141

t [s

]

10

8.0

6.0

s[

m

6.0

4.0

]

s[

2.0

.0

20

20

0

. 10

0.

0

m

m

-

4.0

]

2.0

.0 .0

10

0

0.

0

. 10

]

.0

8.0

m

t [s

10

.0

0

-

0

0.

-1

. 20

0

0.

-2

loose SP-C1L

B4

B4

single pile in clay


Figure 4.51: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

100


head deflections [mm]

measurement calculation 0

-100 100


0 detail A

-100 730

measurement calculation

detail B

740

750

760

t [s]

Figure 4.52: Validation of the calculations by Comparison of the calculated (twofold integration of the pile shaft strains) and measured lateral pile tip displacements (position transducer at the pile head) versus time

142


slightly underestimates the measured values for displacements significantly greater than ±50 mm. This was taken into account for the following diagrams. t [s ] 10. 0

t [s ] 10. 0 8.0

8.0 6.0

6.0 4.0

] mm

mm

]

4.0

0

s[

2.0

0


-1

00

.0

-5

0.

0

0.

50

.0

0. 10 -1

00

.0

-5

0.

0

0.

0

.0 50

10

0.

0

s[

2.0


Figure 4.53: Relative lateral pile displacements vs. time and vs. depth during event B4 from the shake table experiments for investigating a single pile installed in saturated sand covered by a clay layer

Figure 4.53 shows the lateral pile displacements versus time and versus depth during event B4 for single piles installed in loose and dense saturated sand, respectively. It is noticed that in case of loose sand (SP-SC1L) the displacement came far closer to the clamping at the base. By contrast, in the dense sand case (SP-SC2D), the displacements were smaller in deeper layers, but the increase is more pronounced closer to the surface. The liquefaction process of the sandy sand dissipated the energy stored by spring tension in the test pile during the experiments, leading to reduced maximal displacements, i.e. smax = 65 mm for the loose sand case instead of smax ≥ 65 mm in the dense sand case. Figure 4.54 compares results from single pile experiments with saturated clay. The be-


143

t [s ] 10. 0

t [s

]

10.

0 8.0

8.0 6.0

6.0 4.0

s[ mm

]

s[ mm

]

4.0 2.0

.0

.0 00

-1

00

-1

.0

-5

0.

0

-5 0.

0

50

0. 0

0. 0

.0 50

10 0

.0

10 0

.0

2.0

B4


B4


Figure 4.54: Relative lateral pile displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

haviour is quite different to the pile in saturated sand. For both, the unconsolidated and the consolidated clay maximal displacements lie in a range of about smax = ±50 mm. Of course, the lateral bedding of the pile goes deeper in case of consolidated clay but the differences are not as obvious as in Fig. 4.53. As already mentioned in the beginning of Section 4.5.6, the boundary conditions are different for the pile group where the piles are confined as are the pile toes, leading to w (zbase , t) = w (ztop , t) = 0. Hence, all the piles of the pile group experiments show a vertical inclination at their tips and their toes leading to far smaller displacements in total compared to the free-head case. Figure 4.55 shows in total displacements for the head-restrained case of fewer than 10 mm, which is a fifth of the free-head case. The difference between the loose sand experiment with very deep displacements and the dense sand case with a very stiff and efficient lateral

144


t [s ] 10. 0

t [s ] 10. 0

8.0

8.0 6.0

6.0

2.0

s[ mm

s[ mm

2.0

-1

0. 0 -1 0.

0.

0

0

0.

0

10 .

0

0 10 .

4.0

]

]

4.0

loose B4 PG-SC1L single pile in clay

dense B4 PG-SC2D single pile in clay

Figure 4.55: Relative lateral pile displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

bedding is also remarkable. The maximal displacement for the loose sand is found in the middle of the soil, whereas for dense sand the maximal displacement is at the pile tip. Due to the compaction of the saturated sand specimen, the displacement frequency rises from f = 1.6 Hz (PG-SC1L) to 3.7 Hz (PG-SC2D). Especially in the cohesive soil, the gapping also modifies the lateral pile displacements versus time and versus depth. At the beginning of experiment PG-C1L (Fig. 4.56), maximal displacement comes to about 20 mm. The influence of the lateral pile displacements versus depth is relatively high. This effect is reduced in the second experiment after the consolidation process (PG-C2D) with maximal displacements at the top of about half the amount, i.e. smax = 10 mm. After some experiments, a residual gap was generated, which could not be closed again by a self-healing process even after a long lasting consolidation, viz. creep towards the pile shaft. This leads to an increase of maximal displacement of


145

t [s ] 10. 0 8.0

8.0 6.0

mm ]

4.0

s[

2.0


B4


0. 0

0. 0

-2

-1

0. 0

.0 10

0. 0

0. 0

-2

-1

0. 0

10

.0

20

.0

s[

2.0

.0 20 0. 0

-2

-1

0. 0

.0 0. 0

6.0

4.0

mm ]

mm ] s[

.0 10

20

B4

8.0

6.0

4.0 2.0

t [s ] 10. 0

t [s ] 10. 0

B4


Figure 4.56: Relative lateral pile displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated clay

about smax = 25 mm, which is far more than even in the unconsolidated clay experiments.

4.5.7

General Remarks on the Large Shake Box Experiments

In a hinged laminar box mounted on a shake table, piles and pile groups were investigated. Piles were installed in dry or saturated loose to dense sand, with or without a covering clay layer, as well as in saturated clay, unconsolidated and fully consolidated, respectively. The piles and the soils were loaded horizontally and dynamically from the base with sinusoidal as well as earthquake loading records. The extensive instrumentation of the experimental setup rendered it possible to record time-dependent soil displacements, vertical displacements at the soil surface, test pile bending strains, the lateral force and the lateral displacement at the pile tip, and pore water pressures in the soil specimen during the experiment. Thus, the state of the soil and the piles can be evaluated at any

146


time. The shake table experiments comprise an excellent database in order to validate numerical models. In this way, shortcomings of numerical models can be discovered by means of the experiments and even vice-versa if the numerical models had been validated. Accordingly, improvements can be realised. Some experimental results show that the increase of pore water pressure is prevented by the lateral drainage between soil and laminar box. In other experiments, the results show a total loss of effective pressures, i.e. liquefaction, where the saturated grain skeleton transforms into a suspension.

4.6

Summary and Conclusions

In order to investigate systematically soil-foundation interaction behaviour, single piles firstly were loaded horizontally under quasi-static conditions. For this purpose, smallscale experiments in a 60-litres-barrel were carried out. The single piles were installed in dry loose sand, dry dense sand, and saturated silty clay. The piles were deflected at their pile heads load-controlled as well as displacement-controlled. The instrumentation of the model piles allows an insight beneath the ground surface: into the distribution of the time dependent bending moments along the pile, the inclination angle along the pile by integration as well as the time dependent displacement of the pile double-integration. These results are conformed by comparison with the recorded time dependent displacements of the pile tip, which coincide perfectly for displacements of ±50 mm. In a second part, single piles and pile groups were loaded dynamically. In a laminar box mounted on a shake table, piles and pile groups were investigated installed in dry loose sand, dry dense sand, saturated loose sand, saturated dense sand, with and without a covering clay layer, and in saturated clay, unconsolidated and fully consolidated, respectively. The piles and the soils were loaded horizontally and dynamically from the base with sinusoidal as well as earthquake loading records. The extensive instrumentation of the experimental setup rendered it possible • to record time-dependently soil displacements in eight heights, • vertical displacements of the soil surface at two positions, • test pile bending strains at eightfold over the pile length, • the lateral force at the pile tip, • the lateral displacement of the pile tip,

4.6. Summary and Conclusions

147

• and pore water pressures at three positions in the soil specimen during the experiment. Thus, the state of the soil, the pile bending moments, the pile inclination angle along the pile length, and the pile displacement curves could be evaluated for any time. The shake table experiments constitute an excellent database in order to validate numerical models. Shortcomings in the numerical models can be discovered by means of the experiments and vice-versa as far as the numerical models are conformed. Accordingly, improvements can be realised. For the very fast drainage in the experiments, the lateral filtration between soil and laminar box should be reduced.

Chapter 5 Numerical Investigation of SFSI 5.1

Introduction

The following chapter describes first the numerical simulation of the shake box experiments presented in Section 4.5. Experiments with single piles as well as pile groups in clay and sand of different density are also investigated numerically, and the results are compared with those from the measurements. The subsequent section presents a full-scale field test [Ert83] with piles and its numerical simulation. Site investigation, laboratory testing, pile loading programme and instrumentation are shown in detail. The numerical modelling is carried out by means of a direct FEM approach. Results and further observations are given at the end of the section. Finally, complete seismic SFSI analyses demonstrate the capabilities of the FEM models validated in the preceding chapters. In the analysis, different types of foundations are compared, regarding their behaviour under strong earthquake excitation.

5.2

Simulation of the Shake Box Experiments

Within the following section, the results from dynamic FEM analysis with single piles as well as pile group foundations are presented in detail. The geometry and the physical properties of the piles and the used soils are taken from the model tests presented in Chapter 4. The analyses are performed in two stages. The first stage comprises a selfweight loading up to a static equilibrium. The second stage is the dynamic shaking in one direction.

149

150

5.2.1

Chapter 5. Numerical Investigation of SFSI

Modelling with FE mesh

Figure 5.1 shows a scheme of the single pile with soil being investigated by the shake table experiments (left), and the discretisation by means of the FEM (right). In order to reduce calculation time, the system is simplified by concentrating the masses of the magnetic pointer m1 , the load cell m2 , and the pile head mass m3 along the pile length in their respective centres of gravity. In order to further simplify the FE model, only half of the system is taken into account by using the symmetry plane passing through the centre of the pile in the direction of the shaking. The steel core of the model pile, and its superstructure consisting of pile head mass, load cell and pointer are modelled by means of beam elements. By contrast, the silicon coating of the pile and the soil is modelled with continuum elements. Between the pile shaft, i.e. the silicon coating element surfaces, and the adjacent soil continuum surface elements working like a master (pile) and a slave (soil) are applied, this is to simulate the contact interaction. The thickness of the sand layer h1 , and its covering clay layer h2 in case of loose (SP-SC1L) and dense sand experiments (SP-SC2D), is chosen as in the experiments. In case of the single pile experiments with unconsolidated (SP-C1L) and fully consolidated clay (SPC2D), respectively, the thickness of the clay layer h1 + h2 is taken from the experiments as well. The boundary condition of the pile embedded in the bedrock is modelled by a constrained rotational degree of freedom at the base of the lowest soil layer. The model pile was installed before the soil. Thus, the FE modelling does not take into account compaction or dilating of the soil due to the installation process, and the initial stress conditions are assumed to be the self-weight pressures in the vertical direction and the earth-pressures at rest in the horizontal directions. The calculation is carried out in two simulation steps. The first step comprises a selfweight loading up to a static equilibrium. The second step simulates the dynamic excitation at the base nodes of the model applying the displacement versus time of the B4 event in the experiments, which is the Loma Prieta Earthquake motion. The time step for the beginning of the dynamic phase is 0.0001 s and is slowly increased to a maximum time increment of 0.001 seconds. In order to simulate the behaviour of the laminar box, which allows the propagation of plane shear waves including its boundaries, a periodic boundary condition is applied to the opposing nodes at the left and right boundary of the FE mesh, allowing the respective nodes to translate in the same manner. Figure 5.2 presents the system with the pile group and its discretisation by means of the FEM. The pile group is modelled quite similarly as the single pile model. However, as a

5.2. Simulation of the Shake Box Experiments

151

Displacement transducers Pointer

m1=100 g

270

m1=100 g

Load Cell m2=120 g m3=400 g

m2=120 g

60.5

62

62

single pile (symm.)

m3=400 g

Pile head Mass

h2

1030

Single Pile

Clay

h1

700

m4=500 g

Sand Bedrock

Figure 5.1: Scheme of the single pile investigated in barrel tests as well as shake table experiments with dimensions and masses used to model by means of FEM

group of piles is much stiffer, the pile head mass m3 is drastically increased in order to cause sufficient relative displacements between soil and pile. In contrast to the free-head conditions in case of the single pile experiments, the four piles of the pile group are fully restrained at their heads, thus preventing any pile rotation at the tips of the piles.

152


218

m1=100 g

m2=11500 g m3=400 g

150

Pointer

80

m1=100 g

62

Displacement transducer

Pile head Mass

70

m2=11500 g m3=400 g

Load Cell

group of 4 piles (symm.)

m4=4x500 g

h1

700

Clay

1030

h2

Pile group

Sand Bedrock

60

Figure 5.2: Scheme of the pile group investigated in barrel tests as well as shake table experiments with dimensions and masses used to model by means of FEM

5.2.2

Results and their Discussion

In this section, the results obtained with the FE models are compared with the measurement data of the respective experiments. The load cell records the horizontal inertial forces due to the pile head mass and the mass of the pointer versus time. The numerical simulation provides the shear force versus time in each beam element. The head displacements were recorded by means of a magnetic sensor at the pointer beam moving contact-free along a displacement transducer installed above. In order to compare these recordings, the top-most node of the substitute pile beam is taken. In case of the single pile experiments with loose and dense sand, respectively, the evolution of the pore water pressure at the base of the soil specimen versus time is evaluated by means of a continuum


153

element lying at the base of the FE model. Figure 5.3 shows the simulation of the effective pressures of the single pile test with clay (SP-C2D) during the dynamic excitation at the base after a period of 3 seconds. Due to the dynamic impact, the effective pressure field in the soil shifts from a hydrostatic distribution towards curved isobars with maximal pressures of 14.0 kPa in the bottom right corner of the soil. Depending on the direction of shaking, this distribution shifts completely towards the other corner in the next moment due to the inertia of the soil mass. The pile deflects to the right causing an increase of effective pressures up to 10 kPa at the neighbouring soil on the right-hand side, causing a decrease of the effective pressures behind the pile. A gap opens behind the pile each time it bends away from the soil. It has to be noted that effective pressures were not measured in the experiments. Single Pile in Saturated Sand Fig. 5.4 presents the calculated and measured pile head deflections versus time for two cases: loose saturated sand with a covering clay layer (SP-SC1L, left) and dense saturated sand with a covering clay layer (SP-SC2D, right). The calculation with loose sand shows an overestimation of the pile head deflections versus time. This can be explained by a fast increase of calculated pore pressures and the concurrent liquefaction of the sand layer, causing the decay of the grain skeleton and with it the loss of the embedding of the pile shaft. It can be observed as well that in the calculations after one second the pile initially moves to the opposite side, but showing exactly the same frequency response. After two seconds, the pile drifts to one side indicating the same main frequency but also showing overtones in double the base frequency. Due to the large displacements, an amplification of the pile oscillation and a reduction of the effective pressures nearly to zero, the calculations break down after four seconds. In Fig. 5.4 right (dense sand), the answer in terms of pile head deflections versus time fits well during the very first three seconds. It should be noted that the measurements show head displacements exceeding the measuring range of ±150 mm at an elapsed time of 2 seconds causing distinct errors. Plastic deformations of the soil cause a significant shift of the calculated values with respect to the recorded values after three seconds. Higher frequencies can be recognised in the simulation during the first five seconds as well. Figure 5.5 compares measured and calculated forces in the load cell during the SP-SC1L (left) and SP-SC2D (right) experiments, respectively. In both diagrams, it can be detected that the predicted range fits very well. The dominant frequency is also well simulated by the FE model. Nevertheless, an exact evolution of the force versus time is only obtained at some parts of the plot.

154


-1.0 kPa

3 2

1

-3.6 kPa -4.6 kPa -5.6 kPa -6.2 kPa -8.2 kPa -9.8 kPa -11.0 kPa -14.0 kPa

Figure 5.3: Evolution of effective pressures in the clay specimen during the dynamic excitation (after 3 seconds)

The evolution of the pore water pressure at the base of the soil specimen versus time by measurement and simulation is given in Fig. 5.6 for loose (left) and dense sand (right), respectively. As the dynamic calculation is carried out under undrained conditions, the calculated pore pressures rise very fast whereas the measured pore pressures rise more moderately. This can be explained by the opening of water channels, allowing the pore pressure to decrease as can be seen in Fig. 5.6 (right). The calculated values reach a maximum pore pressure of nearly 10 kPa, whereas the measured values only reach up to 6.1 kPa. However, apart from the reduction due to channels, the calculated curves fit


155

200

SP-SC1L



200 measured calculated liquefaction


B4

100

0

-100

measured calculated

B4 100

0

-100 SP-SC2D single pile in sand & clay

-200 0

1

2

3

4

0

2

time [s]

4

6

time [s]

Figure 5.4: Measurement and simulation of the pile head deflection versus time during the dynamic excitation for loose sand (left) and dense sand (right) 4 measured calculated

2 force [N]

force [N]

single pile in sand

B4

2

measured calculated

B4

4

SP-SC1L

0

0 -2

-2

SP-SC2D

-4 0

1

2 time [s]

3

4

single pile in sand

0

2

4 time [s]

6

Figure 5.5: Measured and simulated evolution of shear forces versus time in the pile head during the dynamic excitation for both cases loose sand (left) and dense sand (right)

rather well to the measured ones. Single Pile in Clay The simulation of the pile head deflections versus time of the experiments with clay show a satisfactory agreement in terms of frequency both for unconsolidated (Fig 5.7 left) and fully consolidated clay (Fig 5.7 right). However, in particular for small shaking in the beginning the damping of the calculated system is much smaller than the measured one.

156


B4

8

B4

8

SP-SC2D ∆u [kPa]

∆u [kPa]


4

measured calculated

4


measured calculated

0 0

1

2 time [s]

0 3

4

0

2

4

6

time [s]

Figure 5.6: Measured and simulated evolution of pore water pressure at the base of the soil specimen versus time in the pile head during the dynamic excitation for loose sand (left) and dense sand (right)

The increasing displacements in the soil cause an abortion of the calculation shortly after two seconds. It can be assumed that in contrast to the calculation with sand, where the hysteretic behaviour of the soil decelerates the pile head movement, the damping of the silicon rubber of the test pile plays a significant role. Nevertheless, the silicon rubber as well as the steel plate in the piles core is modelled by means of an ideally elastic material. The introduction of material damping would lead to an attenuation of the pile head motion. Figure 5.8 shows measured and calculated shear forces versus time during the dynamic excitation, again both for unconsolidated (left) and fully consolidated clay (right). It can be clearly seen that, in particular for small force amplitudes, the damping in the experiments is much higher than the calculated one. However, with increasing amplitude the calculated behaviour fits quite well to the experiment. In order to stabilise the calculation, the periodic boundary condition is replaced by a rigid boundary condition. Figure 5.9 shows the experiment SP-C1L and its simulation for the pile head deflections (left) and the shear forces in the load cell (right). The rigid boundary condition is applied by constraining all boundary nodes to undergo the earthquake motion. This prevents the propagation of a plane wave from the bottom to the surface of the soil specimen. Compared to the periodic boundary conditions the calculations underestimate the pile head displacements as well as the shear forces grossly in the first four seconds, whereas the calculated motion is overestimated for small excitation at the end of the calculation due to the insufficient damping in the pile.


157

B4

SP-C1L



100 single pile in clay

50

0

-50 measured calculated

measured calculated

B4 100

0


-100

-100 0

2

4

0

6

2

4

6

time [s]

time [s]

Figure 5.7: Measurement and simulation of the pile head deflection versus time in the pile head during the dynamic excitation for unconsolidated (left) and fully consolidated clay (right)

4

measured calculated

B4

2 force [N]

force [N]

2

measured calculated

B4

4

0 -2

0 -2

SP-C1L


single pile in clay

-4

-4 0

2

4 time [s]

6

0

1

2

3 4 time [s]

5

6

Figure 5.8: Measurement and simulation of the evolution of shear forces versus time in the pile head during the dynamic excitation for unconsolidated (left) and fully consolidated clay (right)

158


The simulations by means of rigid box boundary conditions always lead to a soil-pilestructure interaction, which is overestimated in terms of stiffness; this leads to a higher frequency response of the whole system. In general, the calculation is more stable compared to the calculations incorporating the more complex periodic boundary conditions. It can be assumed that the correct solution will be situated somewhere between the two cases, rigid boundary and fully periodic boundary. In order to improve the results of the calculation, the system friction of the laminar box should be taken into account, as well as additional suspension spring forces applied in the experiment, in order to keep the laminar-box in its upright position. 4

B4

measured

B4 calculated "rigid box"

2 force [N]

100 disp [mm]

measured calculated "rigid box"

0


0

SP-C1L

-2

single pile in clay

-100 -4 0

4

8 time [s]

12

0

4

8 time [s]

12

Figure 5.9: Measurement and simulation of the pile head deflection (left) and shear forces in the pile head versus time (right) during the dynamic excitation for unconsolidated clay, applying a rigid shake box boundary condition

Pile Group in Clay and Sand Figure 5.10 left shows measurement and simulation of the pile head deflection for a pile group installed in saturated loose sand. The observed deflections are somewhat underestimated, but the calculated evolution is far more realistic than in the single pile case. The experiments with pile groups in dense saturated sand also show that the simulation slightly underestimates the pile deflection (Fig. 5.10 right). After some cycles, the calculation terminates due to a divergent numerical solution. Quite satisfactory results are obtained by the simulation of the pile head deflection versus time when investigating a pile group in saturated clay. The curves of the calculation and of the measurement nearly coincide.


B4


40

0

-40

PG-SC1L pile group in sand



80

159

B4

measured calculated

40

0

-40

PG-SC2D pile group in sand

-80

-80 0

4

8

0

5

time [s]

10

15

20

time [s]

Figure 5.10: Measurement and simulation of the pile head deflection versus time during the dynamic excitation for loose saturated sand (left) and dense saturated sand (right) 80

B4

measured calculated

disp [mm]

40

0

-40

PG-SC1L pile group in sand

-80 0

5

10 time [s]

15

20

Figure 5.11: Measurement and simulation of the pile head deflection versus time during the dynamic excitation for fully consolidated clay

5.2.3

General Remarks concerning the Simulation of the Shake Box Experiments

There is still a need of further research with respect to the dynamic simulation of the shake table experiments. Some results show that the calculated increase of pore water pressure is too fast, which could be improved by means of coupled instead of undrained conditions. For the very fast drainage in the experiments, either the opening of channels has to be taken into consideration, or the lateral filtration between soil and laminar box

160


has to be reduced. In other experiments and their numerical calculations, the results attain the total loss of effective pressures, i.e. liquefaction. The grain skeleton transforms into a suspension, which cannot be described by the used constitutive relations, i.e. a crossover from soil mechanics towards fluid mechanics. In the numerical models, the contact formulation between soil and pile has to be improved in order to stabilise and accelerate the analysis. The laminar box boundary conditions are rather complex and not easy to implement, thus for the time being a periodic boundary condition is used. The numerical calculations demonstrate that by means of the applied constitutive relations and known soil parameters and state of the soils, and known boundary conditions, single piles as well as pile groups can be realistically simulated under dynamic and horizontal loading. Simultaneously, important information is obtained by the calculations about the change in the state of the soil, in particular liquefaction potential, and plastic deformation. Correspondingly, the application of the presented models appears to be justified in order to design or assess pile foundations under dynamic load conditions.

5.3. Large-Scale Field Tests with Piles

5.3 5.3.1

161

Large-Scale Field Tests with Piles Introduction

Within this section, numerical investigations are presented on static and cyclic lateral load tests on instrumented piles in silty fine sand under different head restraint conditions. In order to analyse the non-linear soil-pile interaction behaviour in general, key components, i.e. the soil, the type of foundation system, the structure, and the mode of loading have to be observed in detail with care. The objective of a soil-pile interaction analysis is the evaluation and estimation of the total performance of the whole soil-foundationsuperstructure system to provide a robust, efficient and realistic numerical description of system and material response for a performance-based design. In order to validate simulation methods, it is essential to develop and improve large-scale field tests, thus providing an invaluable resource for calibrating existing numerical codes in order to reveal and to reduce the inherent modelling uncertainty. In this work, the non-linear soil-pile-foundation interaction during monotonic and alternating loading was studied numerically using the finite element method. It was possible to reproduce the behaviour of a single pile and the surrounding soil under the loading given in a well-documented field test with respect to deflection and bending moments, wherein the subsoil behaviour was modelled with hypoplastic and viscohypoplastic relations [Nie03]. These relations made it possible to model the response of cohesionless and cohesive soils under alternating and dynamic loading for drained and undrained conditions. The improvement of state-of-the-art methods to estimate the performance of deep foundations, in particular the design of pile foundations in seismic zones in soft and liquefiable soils, is extremely important. Hypoplastic constitutive relations are apt to describe the soil behaviour from small to large strains with non-linear response and damping characteristics, which correspond very well to the measured soil behaviour. The feasibility of determination of soil parameters and of initial state quantities for the constitutive relation is also well established. This work is addressed to the investigation of the non-linear interaction of a single pile with surrounding silty sand and a silty clay layer (boring 2 in Fig. 5.12) during the alternating pile head deflection under different pile head restraint conditions (Fig. 5.13). In April 1982, Prof. Hudson Matlock and Dr. Lino Cheang from Earth Technology Corporation (Ertec) carried out monotonous and cyclic lateral load tests on instrumented piles in mainly sand (Fig. 5.12) at the southern city limits of Seal Beach, Orange County,

162


Figure 5.12: Cross section of the test set-up at Seal Beach, Orange County, California [Ert83] and soil profile of the test site determined from boring 2 [Ert81]


163

California [Ert83]. The programme was funded by eight American oil companies (among them Chevron Oil Field Research Company, Conoco Inc., Exxon Production Research Company, Gulf Oil Exploration and Production Company) and the Minerals Management Service (MMS) of the United States Department of the Interior. The respective piles were previously installed in the scope of pile vibration tests sponsored by the National Science Foundation (NSF), in July 1981. These vibration tests were carried out jointly by Ertec and Professor Ronald F. Scott from the California Institute of Technology. A final report was submitted to NSF in December 1981 [Ert81]. Two piles were installed but only one was actually instrumented and used in the vibration testing. The existence of these two piles provided an excellent opportunity to pursue further experimental studies of pile behaviour. Accordingly, a proposal to do additional lateral testing was issued in October 1981, subsequently a series of tests was carried out in September 1982, and a final report, which was the basis of the calculations presented herein, was published in October 1983 [Ert83]. symmetry planes

zero restraint (free head) Fup = 0 δup, Fup

δup

0.30 m

δlow, Flow

3.96 m

dpile = 0.61 m tpile = 12.7 mm

partially restraint

fully restraint

δup = 1.44 δlow

δup = 0

δup, Fup

δlow, Flow

δlow, Flow

FH test

PRH test

Fup

δlow, Flow

Ground surface

9.75 m

FRH test

Figure 5.13: Sections of the test pile under different restraint conditions

164


Originally, the purpose of the study was to evaluate the validity of some aspects of former API recommended practice [API82]. Soil characterisation for offshore lateral pile foundation design for sand was based at that time largely on the results of a single research programme conducted by Reese in 1974 [RCK74]. His data were obtained for constructing characteristic curves of soil resistance p versus pile deflection y (called p − y curves) for either monotonous or cyclic loading. Since the criteria are based on only one set of soil and pile parameters, the uncertainty of applicability to other sites and to other typical conditions of pile-head restraint (Fig. 5.13) provided strong justification for additional testing. Nevertheless, Matlock’s report [Ert83] most notably provides an excellent database of monotonous quasi static and slow cyclic lateral load tests for checking and calibrating advanced numerical codes in order to reduce inherent modelling uncertainty. Thus, appropriate constitutive models, here hypoplasticity, and a suitable FE-mesh were applied to simulate the mentioned field tests. Laboratory tests and soil properties given in the report [Ert83] were used to determine the parameters required for the applied constitutive relations. Consecutively, the determined parameters to calculate with were verified by means of numerical element tests (Fig. 5.18).

Figure 5.14: Plan view of piles, CPT sounding and soil boring locations [Ert81], [Ert83]


5.3.2

165

Site Investigation and Laboratory Testing

profile interpretation from CPT sounding

CPT sounding 04

Figure 5.15: Seal Beach profile of CPT soundings (friction ratio and cone resistance) [Ert81], [Ert83]

The site at Seal Beach, California, is subjected to regular tidal flooding of the eastern end of Anaheim Bay. Elevation of high tide varies from 0 to 1.7 m with respect to the elevation of the ground surface at the location of the piles. The previous NSF pile vibration tests were carried out at this specific site, which exhibited a rather uniform, mainly cohesionless soil deposit with the water table very close to the ground surface, apt to study the effects of possible liquefaction on the soil-pile system during vibration. Two separate site investigation programmes were conducted. One of them was carried out prior to the pile penetration tests approx. 10 m from the nearest pile and the other

166


profile interpretation from boring

boring 01

Figure 5.16: Seal Beach profile of water content and submerged unit weight [Ert81], [Ert83]

before the lateral loading tests but this time immediately adjacent to the piles. In total, seven electric friction cone penetrometer tests (CPT) and four continuous standard penetration tests (SPT) with the standard split-spoon sampler, viz. piston soil sampling, were conducted (Fig. 5.14). The tests indicated that the soil at the pile locations consisted mainly of medium dense uniform silty fine sand with scattered shell fragments and gravel (see Fig. 5.12), characterised by a critical friction angle ranging from 35◦ to 37◦ . From a depth of 6.1 m, a thin strata of silt, clayey silt, sand, and siltstone were found in the silty fine sand layer. Scattered seashells, interbedded thin silty clay, and clayey silt layers were detected by the deeper penetrations (Fig. 5.12). From the CPT results (Fig. 5.15), a silty clay layer, which was not apparent in the earlier investigation, was


167

percent finer by weight [%]

100

80

60 sample depth [m] 40

20 0

100

10

1

0.1 grain size [mm]

0.01

0.001

Figure 5.17: Results of particle size analysis for sample depths between 0.82 and 8.72 m [Ert81], [Ert83]

detected at a depth of about 1.5 m to 2.5 m below the ground surface. The thickness of this silty clay layer was less than 1.5 m, this was indicated by the cone soundings (cf. soil profile interpretation for CPT soundings in Fig. 5.15), which must be the result of local soil variation (compare boring 1 and 2 in Fig. 5.12 and Fig. 5.16). The vane shear strength of the clay in the upper clay layer was 10.3 kPa. The presence of the clay layer provides an ideal opportunity to investigate experimentally and numerically the effect of a layered soil system on the lateral pile behaviour under different pile head restraints. Soil identification and classification tests including grain size analyses (Fig. 5.17), specific weights and water contents (distributions versus depth in Fig. 5.16) were conducted alongside with an isotropically consolidated drained (ICD) triaxial test on the sand sample (results and element test calculations in Fig. 5.18) and an unconsolidated undrained (UU) test on a clay sample. For the cohesive soils, Atterberg limit tests were performed. The ICD test was performed in three stages at three different cell pressures (10.3, 20.7 and 41.4 kPa, Fig. 5.18). The volume change plot shows some compaction in the beginning of the test in both experiment and hypoplastic calculation. The rather high angle of internal friction at the peak obtained from the test was about 42◦ , which can be explained by the angular sea shells. The confining pressure used in the UU test was 6.9 kPa, and the shear strength, as interpreted from the magnitudes of confining pressure and failure stress, is about 10.3 kPa. The same shear strength can be interpreted from the cone soundings by using an average measured cone tip resistance of 96 kPa and an assumed bearing capacity factor Nc of 10, which is empirically justified for this type of soil (Fig. 5.15). The soil

168


Deviatoric Stress σ1- σ3 [kPa]

200 σ3 = 41.4 kPa

160

120

measured

σ3 = 20.7 kPa

80 σ3 = 10.3 kPa

calculated

40

0 0

2

4

6

8

10

Axial Strain ε1 [%] 2.5 σ3 = 41.4 kPa

Volumetric stain ε v

2 1.5

σ3 = 10.3 kPa

1

σ3 = 20.7 kPa

measured 0.5

σ3 = 41.4 kPa

calculated

0 0. 5 0

2

4

6

8

10

Deviatoric Stress (σ1- σ3)/2 [kPa]

Axial Strain ε1 [%] 100 σ3 = 41.4 kPa

80 60

σ3 = 20.7 kPa

40

σ3 = 10.3 kPa

measured calculated

20 0 0

20

40

60

80

100

120

140

Mean Pressure ( σ1- σ3 )/2 [kPa]

Figure 5.18: Numerical calculations of the isotropically consolidated drained (ICD) triaxial test on the sand sample


169

parameter profile, selected for use in the numerical analysis of the pile load test, is shown in Fig. 5.12. For the numerical analysis, the layers below 3 m depth were combined to a single layer because their influence on the deflection behaviour of the pile can be neglected for lateral pile top loading. A critical friction angle of 37◦ was determined and used for the surficial and at-depth silty sand layers. The derivation of the critical friction angle was based on the numerical element test calculations leading to a peak friction angle of about 42◦ (Fig. 5.18). For the calculation, a constant submerged mean unit weight of 1.8 kN/m3 for the silty sand as well as for the cohesive soil was used. A detailed description of the determination of the used hypoplastic and visco-hypoplastic parameters is given in Section 5.3.4.

5.3.3

Pile Loading Program and Instrumentation

The loading system (Fig. 5.12), consisting of a telescoping unit assembled from 13 cm and 15 cm heavy wall standard pipes mounted horizontally between the vertical test piles and supported near the ground surface, was developed by Matlock and Cheang [Ert83] to provide various combinations of free and restrained pile-head conditions (Fig. 5.13). The centre-to-centre spacing of the two piles was 3.66 m. One of the objectives of the test programme was to study the behaviour of laterally loaded piles with head restraints covering a range typical of real offshore piles, which was considered as a requirement in the design of the loading system and the test piles. Four hydraulic rams, acting through the telescoping unit and providing the push-and-pull actions needed for arbitrary loading paths and simulation of head-restraint, were used to apply both monotonous quasi-static and slow cyclic lateral loading at 0.3 m above the ground surface. Another 15 cm pipe was connected across the two pile tops. Part of this strut consisted of a threaded rod. Two large threaded bearing wheels were used to rotate as nuts to control the pile top movement and, thus the boundary restraint (cf. the upper load strut in Fig. 5.12). Ten tests in total were performed under three different sets of boundary conditions (Tab. 5.1). The three boundary conditions are artificial to a certain degree, but they cover the full range of conventional pile-structure connections. The initial and the last tests were realised under a condition where lateral pile deflection at the pile tops was adjusted progressively. This kind of test designated as a partially restrained head (PRH) test was also used for the present numerical simulation. Further tests were cyclic free-head (FH) and fully restrained head (FRH) tests. These tests were cyclic, and a lateral movement of the pile tops was unrestricted in case of FH tests, and were not allowed to displace laterally for FRH tests. The two test piles of 13.7 m length were 61 cm in outside diameter with a uniform wall thickness of 1.3 cm. The penetration in the soil was 9.8 m. Both piles were instrumented

170


test series

pile head condition

1 partially restrained (PRH) 2 to 6 free (FH) 4 to 9 fully restrained (FRH) 10 partially restrained (PRH)

total type of numerical duration loading simulation 2.4 17.3 3.0 1.5

h h h h

static cyclic cyclic static

Fig. 5.24, 5.25 Fig. 5.26, 5.27, 5.28 Fig. 5.29, 5.30 no Fig.

Table 5.1: Summary of the total test programme [Ert83] under consideration of the pile head restraint conditions by a chain of strain gages to monitor the strains for subsequently evaluating the bending moment along the pile length. The strain gages were encapsulated in sections of square steel tubes and, subsequently, the prefabricated steel tubes were welded into the inside of the pile wall. Pile-head loads were measured by strain-gage load cells welded and wired in a full Wheatstone bridge arrangement to the top and bottom struts so as to form a continuous section of each pipe strut. Deflections were measured electronically by the use of four LVDTs at two different elevations above the ground surface. Pore pressure measurements were also attempted by four piezometer tubes installed at locations outside of each pile, placed to measure pore pressure changes down to a depth of about 3 m below the ground surface. The pile inclination was monitored periodically by a precise levelling device. Transducers were installed to monitor pore pressures in the soil during the pile loading, and pile-head inclination was measured periodically with a precise level.

5.3.4

Numerical Modelling

The finite element method potentially provides the most powerful means for conducting soil-pile interaction analysis, but it has not yet been fully realised as a practical tool. Appropriate constitutive models, here in the framework of hypoplasticity, and suitable FE-meshes were provided to model the soil profile and an embedded foundation system. In contrast to conventional scale modelling techniques, an FE-modelling in model scale does not require laws of similarity or other comparable procedures to up-scale to a prototype configuration. At first, the behaviour of a soil-pile system in model scale, which was in this regard well observed in the described large-scale test, was reproduced successfully by a finite element model using hypoplasticity (cf. Section 4.4). The second step, indispensable for engineering purposes, was the validation of the model under highly variable boundary conditions, e.g. in our case, the change of pile head restraints. A final step would be the up-scaling of this model towards the dimensions and the complexity of a practical


171

geotechnical problem. This can also be done under consideration of a completely changed material behaviour, as well as boundary and initial conditions. The successful application of this method implies that the constitutive model is capable of reproducing realistic results for a wide range of deformations and pressures. After the successful validation, which is presented in this work, more complex boundary value problems can be solved. A verification of the presented method was already accomplished by means of other selected examples of well-documented case histories for monotonic, cyclic (only a few cycles) and dynamic loading of pile or pile-like structures. Boundary value problems cover rather complex strain and stress paths whereas element tests consider quite simple paths. A need for the verification process is the knowledge about soil properties and the initial state of the soil. The better information about the state and the properties of the soil is available the more precise a prediction or verification can be carried out. Verification has also been earlier conducted by means of some appropriate small-scale experiments, which demonstrated the capability of the numerical model to be scaled freely as well as experiments documented in the literature [Zie86] [Wol97] [May00] [H¨ ug95] [N¨ ub02] [Sik92] [Cud01] [CO01] [Kar02] [Tej97] [Fel00] [Nie03] [Lou02]. The test pile problem was modelled using the hypoplastic constitutive relations described briefly in Section 4 and the finite element programme ABAQUS [ABA05b]. The material parameters of both constitutive models can be determined or estimated from granulometric properties. The hypoplastic parameters were estimated based on the laboratory tests given in the report [Ert83], and the therein-presented granulometric description of the predominant two soils. A non-cohesive granular material, like silty sand, is characterised by eight hypoplastic parameters. Five of them can be determined from index tests. In this way, the critical friction angle ϕc is determined corresponding to the angle of repose, the void ratios ed0 and ec0 coincide with the minimum and maximum void ratio emin and emax , respectively, and the granulate hardness hs , which is linked with an exponent n, is obtained by an oedometer test with an initially loose specimen. The remaining three parameters can be determined from a single triaxial and an oedometer test with initially dense specimens. Alternatively, the parameters can also be estimated; the exponent α depends on a peak friction angle, the exponent β can be found from a compression index of a dense specimen, and the void ratio ei0 at the minimum isotropic density has a constant ratio to ec0 . The entire method to evaluate hypoplastic parameters from granulometric properties of granular soils, i.e. grain size distribution, shape, and material of the grains, is given in detail in [Her97] [HG98] and summarised in Section 3. Curves provided from laboratory tests were calculated numerically using an element test programme (Fig. 5.18) together with the hypoplastic parameters for the silty sand given

172


in Tab. 5.2. ϕc [◦ ]

hs [kPa]

n [1]

ed0 [1]

ec0 [1]

ec0 [1]

α [1]

β [1]

37.2 1.2E+06 0.27 0.530 0.864 0.996 0.127 1.05 Table 5.2: Hypoplastic parameters for the silty sand determined by means of the laboratory results [Ert83] and applied to the finite element model For the visco-hypoplastic constitutive model [Nie03] seven material parameters have to be determined. For the critical friction angle ϕc , shear tests with disturbed or undisturbed specimens have to be performed either in a triaxial cell or in a direct shear box. Both drained and undrained triaxial tests can be used. However, a drained test needs larger deformations to reach the critical state. To determine the viscosity index Iv either an undrained triaxial compression test with changes of the axial strain rate, oedometric creep tests, or an empirical correlation between Iv and the liquid limit wL can be evaluated. βR describes the shape of the Cam Clay yield surfaces and can be taken as constant for many practical cases. The three material parameters λ, κ and e100 are defined using results from an isotropic compression test carried out with a constant deformation rate D, which is preferably used in the model as the reference deformation rate ε˙e0 . The determination of visco-hypoplastic parameters is described in detail in Chapter 3, [Pun04], or [Kar02]. The visco-hypoplastic parameters used in the finite element model are given in Tab. 5.3. λ [1]

κ [1]

ϕc [◦ ]

βR [1]

0.125 0.020 18.0 0.850

Iv [%]

pe0 [kPa]

3.1

100

ee0 [1]

ε˙e0 [1/s]

OCR [1]

0.941 1E-7

1.05

Table 5.3: Visco-hypoplastic parameters for the silty clay determined by means of the laboratory results [Ert83] and applied to the finite element model The state variables in the beginning of the calculation, i.e. initial stress and void ratio, must be well defined because they influence the solution significantly. In case of cyclic tests, the initial state variables of the intergranular strain vector do not play a dominant role due to the loss of the soils memory after one or two cycles. The initial void ratio can be determined directly from undisturbed soil samples or estimated indirectly from in-situ penetration tests. For this purpose, a procedure for the interpretation of cone penetration and pressuremeter tests based on a hypoplastic cavity expansion model can be applied [CO01]. The initial state of the soil was estimated using the description of the


173

site investigation. Based on the cavity expansion theory Cudmani [Cud01] developed an evaluation procedure, which enables the determination of the initial density in-situ from the results of cone penetration or pressuremeter tests. The initial stress state is determined from the overburden pressure of the soil and assumed earth pressure coefficients at rest. For dynamic problems or quasi-static problems with alternating loads, the initial value of the intergranular strain tensor does not play any significant role since the influence of its value vanishes after one or two cycles.

Figure 5.19: Abaqus 3D FE-model used for the calculations

From the given geometry, several 3D FE-models were developed and tested, one of them is shown in Fig. 5.19. The influence of the second pile operating as an abutment was also verified using a three-dimensional FE-mesh. Hence, as was anticipated, the two piles were influencing each other. An objective was also to investigate the influence of the far field boundaries. For this reason, the two symmetry boundaries were kept fixed whereas the two outer boundaries were varied to find out the margin of influence where displacements in the far field can be neglected. The test results of the first test series from the report [Ert83] were used to verify the 3D computer model results by a comparison with the

174


measurements. A detailed evaluation and comparison of the state and the movements of the soil in the first partially restrained head test were carried out using the 3D FEmodels. The time consuming calculations carried out by means of the three-dimensional FE-mesh made it necessary to simplify the model for further considerations. Especially the cyclic tests had to be investigated with a much faster and numerically robust model. For this reason, a two-dimensional section of the problem was taken (Fig. 5.20). The width s of the soil perpendicular to the section plane of the 2D problem has been chosen (see small figure bottom left of Fig. 5.22) while holding the pile section constant as a pipe beam section of r = 0.305 m and t = 0.0127 m until the same pile-soil system response was obtained. The best fit for the first at least five cycles was achieved with a 2D-model width of s = 1.07 m (a perfect agreement of the 2D and 3D calculation results is depicted in Fig. 5.22). Subsequent considerations and investigations were carried out with a 2D-model of this specific width. The used two-dimensional finite element model (Fig. 5.20) had 2600 nodes and 1805 elements in total. Two types of soil were defined using CPE4 type first-order bilinear, fully-integrated, and 4-noded plane strain continuum elements. The pile was defined using B22 type beam elements, which are 3-node quadratic Timoshenko beams in a plane of exactly the pipe section used in the large-scale test in combination with negligible soft type CPE4I incompatible mode continuum elements. These first-order elements are enhanced by incompatible modes to improve their bending behaviour and to fill the continuum gap between beam and soil (Fig 5.20). Two reference nodes, which are shared nodes of the beam and the above-mentioned pile continuum elements, were used to apply the deflections at 0.30 m and 3.96 m above ground level, respectively. An element surface was defined between the soil continuum elements, called slave surface, and the first row of soil continuum elements, called master surface, attached along the pile shaft to allow gapping between the pile and the soil. Subsequently, a contact pair was defined between the slave and the master surfaces setting a surface friction such as the critical friction angle of the silty sand and an exponential pressure-overclosure relationship (Fig. 5.21) to allow the separation of the opposing surfaces. This contact definition is a softened contact relationship, in which the contact pressure is an exponential function of the clearance between the surfaces. In this relationship, the surfaces begin to transmit contact pressure once the clearance between them, measured in the contact (normal) direction, reduces to c0 . The contact pressure transmitted between the surfaces then increases exponentially as the clearance continues to diminish. Fig. 5.21 right diagram illustrates this behaviour, which is implemented in ABAQUS/Standard. The silty sand was defined to behave hypoplastically, whereas the silty clay layer was defined to behave like a visco-hypoplastic material. In the 2D model, the width in sec-


175

Figure 5.20: Abaqus 2D FE-model used for the calculations

tion space of the soil continuum elements was varied as long as the results of the threedimensional numerical model could be approached. For this iterative process, the section properties of the beam elements were kept constant. Prior to the simulation, the initial stress conditions of the soil elements were defined to grow linearly with depth using a K0 value of about 0.396 for the silty sand and K0 = 0.67 for the clay layer. The nodes along the model boundaries to the bottom and the right side of the model were held in both vertical and horizontal translational displacement direction. The symmetry plane

176


slave master

contact pressure

soil elements

pile elements

kmax ABAQUS default penalty stiffness

first row of soil continuum elements

exponential pressureoverclosure relationship p0 = 10 kPa clearance 2D Model

overclosure c0 = 0.1 mm

Figure 5.21: Exponential pressure-overclosure contact relationship defining contact between pile and soil and allowing separation (gapping)

was taken into account by restraining the horizontal translation of the boundary nodes while allowing the other degrees of freedom. A tabular displacement-controlled amplitude boundary condition versus time was applied on the reference nodes at the strut positions to exactly retrace the deflection-controlled measuring programme given in [Ert83]. In the first simulation step, gravity loads of the pile and the soil were applied to achieve equilibrium. Equilibrium was found in all calculations after one iteration, indicating that the initial conditions had been exactly applied. In a second simulation step, the tabular amplitude boundary conditions were applied within the next 150 minutes, as it was done in the large-scale test under partially restrained head test conditions. For the calculations, a maximal increment of one second was allowed, starting with an increment of 0.01 s, which was achieved in most cases in only one iteration. From the degrees of freedom and Lagrange multiplier variables, the total number of equations in the model was about 4800. The total CPU time necessary to complete the calculation in case of the two-dimensional model was 42 min using a PC. For the three-dimensional model, the required total CPU time was about 6 days for the partially restrained head problem using the same PC be-


177

cause the total number of equations rose up to about 100,000. The 3D model (Fig. 5.19) consisted of 36,600 nodes connected by around 15,600 elements. Material definitions and initial boundary conditions were applied in the same manner. The pile was modelled using a full section with equivalent stiffness compared to the pipe section in the prototype. The model boundaries were fixed in translation in all directions for the bottom nodes, the right side nodes, and the nodes from behind the model. Symmetry planes were defined by only suppressing the translation into their planes (x-symmetry plane at the left boundary and y-symmetry plane at the front boundary) and letting the other translational components of these boundary nodes be released. The simulation steps were carried out according to the 2D model described above. comparison of 2D and 3D results

300

3D Model

load Flow [kN]

s = 1.07 m s = 1.5 m

200

100 s = 0.7 m

0

calculated 3D calculated 2D

s=? -100 0 2D Model

4 8 12 16 deflection of lower strut δlow [mm]

Figure 5.22: Numerical calculations obtained by the 3D FE-model and by a modified 2D model with a variable width s

5.3.5

Results and Observations

During the displacement-controlled cyclic loading tests, a gradual reduction in soil resistance (degradation) was measured. Grain migration, the process by which soil moves down at the back of the pile during loading and soil compaction, are also thought to have occurred during cyclic loading. Degradation and soil compaction were also observed in the numerical simulation, whereas grain migration along the pile cannot be modelled with the finite element method. However, it was indicated by the test results within the complete test programme that the effect of grain migration on lateral pile response was small

178


Figure 5.23: Displacement magnitude and deformed FE-mesh of the numerical partially restrained head test after five cycles (displacements 1000 times heightened) and detail (right) with gapping along the pile to the left and dilatation of the sand (red zones) to the right side of the pile

and, therefore, the mechanism can be neglected in the calculation. However, on the other hand, the numerical models, 2D as well as 3D, were able to reproduce gapping along the pile shaft, which is demonstrated clearly in Fig. 5.23. By displaying the volumetric strain (right plot of Fig. 5.23), dilatation (red areas) of the silty sand near the pile at the surface can be observed, while the whole soil stratum beneath this zone was compacted (green areas). The deflection curve of the pile is depicted in the left contour plot of Fig. 5.23. The lower bound pile-head load-deflection obtained for the cyclic tests produced a good agreement when comparing the calculated and measured values (Fig. 5.24). Bending moment distributions over the length of the pile were leading to a very good agreement (Fig. 5.25). The influence of far field boundaries was verified by comparing two plane strain models. The Seal Beach tests were primarily a sand-dominated experiment. Viscous and pore pressure effects due to the clayey layers were not observed. The maximum rate of loading during cyclic testing was about 1 minute per cycle. This slow loading rate,


179

together with the relatively high permeability of the soil, resulted in no observable change of pore water pressure during testing. Therefore, the observed changes in soil resistance during cycling can be considered to be primarily due to volume changes and movements of the soil. The numerical calculations exactly confirm these observations. Three different boundary restraints, which cover a wide range of possible foundation engineering conditions, were used in this study. The pile-head responses and bending moment distributions were totally different for these three cases. As expected, the stiffness from the load-deflection relationship measured at the lower load strut elevation increased with additional pile-head restraint. The shape of the bending moment distribution was similar for the partially and the fully restrained head tests. The maximum bending moment generally occurred at the height of the lower load strut level. For the free-head tests, the bending moment is zero at the lower load strut level, and the maximum value measured occurred at about 5 times the pile diameter below the ground surface. In the numerical simulation of the free-head tests, the maximum bending moment occurred at a depth of about three to four times the pile diameter. The experimental as well as the numerical results demonstrate the importance of proper assignment of boundary condition in lateral pile analysis. In engineering practice, there are only a few cases where pile heads are completely free, i.e. unrestrained, above the ground level. However, for most foundation systems some kind of restraint always exists and should be properly modelled in any analysis. The method for soil characterisation in a pile foundation solution may be important, but the physical modelling of the boundary condition, which dominates the bending moment response, is of primary significance for a reliable design.

Partially Restrained Head Test One partially restrained head test was performed prior to the cyclic test programme by applying a load increment at the bottom load strut followed by an adjusting step at the top load strut to achieve a prescribed ratio of about 1.4 of lateral deflection over the two strut levels. A saw-tooth-type force-displacement curve resulted from this loading procedure. The maximum lower strut load and deflection were about 360 kN and 17 mm, respectively. A permanent offset of about 8 mm was measured at the lower strut level at the end of the test. The permanent offset, which was also taken into account in the succeeding numerical calculations, remained stable throughout the subsequent tests and was thought to be caused by the falling-in of soil at the back of the pile, i.e. granular flow, during initial loading and compaction of the soil when the pile was unloaded in the opposite direction. Thus, the behaviour of piles in sandy soils is strongly affected by the initial loading direction, i.e. the loading history of the virgin test.

180


partial restraint δup = 1.44 δlow δup, Fup

partially restrained head test

300

load Flow [kN]

reference for moment distribution plots 1 2

δlow, Flow

6

7

200 5

100

4 2

3

1


-100

PRH test

0

4

8

12

16

deflection of lower strut δlow [mm]

Figure 5.24: Calculated versus measured load-displacement relationship of initial partially restrained head test

test no. lower limit [mm] 1 10

0 8

upper limit [mm]

no. of cycles [1]

17 36

monotonic monotonic

Table 5.4: Incremental deflection limits of the partially restrained head tests The measured and the numerically calculated lower strut load-deflection relationships are shown in Fig. 5.24 for the initial partially restrained head test. Considering that there was no trial-and-error process involved in selecting the (visco)hypoplastic soil parameters after determining them by means of the element tests, the match is surprisingly close. A discrepancy is only observed between the measured and calculated curves after the sixth cycle, which can have several reasons. One reason may be granular flow occurring after the sixth cycle, which cannot be simulated with the presented numerical model. All seven sets of bending moment distribution are presented in Fig. 5.25 where the upper right plots are showing the calculated results down to a depth of 8 m and the lower right plot is showing the measured values only down to a depth of 4 m. The pile head conditions, at which these measurements and calculations were recorded, are marked in


181

the load-deflection plot as the points marked 1 to 7 (Fig. 5.25 left). Qualitatively as well as quantitatively, the curves agree satisfactorily. Unfortunately, the measurements of the strains along the pile shaft ended in about 4 metres depth. The calculated maximal field bending moment is about 5 pile diameters below the ground surface, whereas the measured maximal bending moment appears to be about 5 to 7 diameters below the surface. The results also indicate that the agreement improved when the applied load increased so that a very good agreement is obtained for a maximum lower strut load of about 250 kN. δup, Fup

-4


-2

δlow, Flow

1

2

4 3

5

7

6

depth [m]

0 Ground surface

2

partially restrained-head test 1

300

7

load Flow [kN]

MEASURED

01 02 03 04 05 06 07

9.75 m

4

CALCULATED

6

6

200

8 -100

5

100

4 2

3 reference for moment distribution plots 1 2

4

8

12

deflection of lower strut dlow [mm]

16 depth [m]

0

100

200

δup, Fup

-4

1

0

0


-2

δlow, Flow

0 Ground surface

2

MEASURED 7

01 02 03 04 05 06 07

3 9.75 m

4

6

5

4

2

1

6 8 -100

0

100

200

bending moment [kNm]

Figure 5.25: Bending moment distributions measured and calculated by pile 1 during initial partially restrained head test

182


As already mentioned above, after the initial test loading, i.e. the partially restrained head test, a permanent deflection of the pile near the ground surface of about 8 mm was measured. The permanent deflection can be explained by sand flow into a gap upon loading. For the numerical calculation, this resistance to deflection was taken into account by means of a constant correction shift. This procedure was inevitable to provide satisfactory numerical results. Negligibly small permanent changes of the pile deflection were noted throughout the remainder of the test programme.

Free-Head Tests zero restraint (free head) δup

δlow, Flow Ground surface

300 lower strut load Flow [kN]

Fup = 0

test 2 (free-head)

200

1 0 to 23 mm

100 0

cyclic degraded curve

calculated measured

-100 reference for moment distribution plots 1 2

-200 -20

0

20

40

60

lower strut deflection δlow [mm]

FH test

Figure 5.26: Lower strut load-deflection relationship for the first free-head test

Fup = 0

δup

δlow, Flow Ground surface

FH test

300 lower strut load Flow [kN]

zero restraint (free head)

200 100

test 6 (free-head)

5

-8 to 53 mm cyclic degraded curve

0 -100


-200

calculated measured

-20 0 20 40 60 lower strut deflection δlow [mm]

Figure 5.27: Lower strut load-deflection relationship for the fifth free-head test


183

Five series of free-head tests were performed and, subsequently, calculated by imposing deflection at the lower strut. The total number of cycles performed for each of the five tests was 7, 23, 14, 12 and 22, respectively. The loading rate varied from about 1 to 8 minutes per cycle. test no. lower limit [mm] 2 3 4 5 6

0 -3 -3 -5 -8

upper limit [mm]

no. of cycles [1]

23 36 41 43 53

7 23 14 12 22

Table 5.5: Incremental deflection limits and number of cycles of the free-head tests The following discussion of the soil resistance variation during cyclic loading is based on the data collected during the displacement-controlled free-head tests and their simulation by means of finite elements. For a typical free-head pile connection, if this exists at all, most of the non-linear soil response and variation under cyclic loading occurs up to a depth of 3 pile diameters below the ground surface. Selected numerical calculations here presented as a load-deflection relationship are depicted in Fig. 5.26 for the first and in Fig. 5.27 for the fifth free-head test. The calculated test in Fig. 5.26 shows seven deflection-controlled cycles between 0 and 23 mm as it was carried out in the field. The calculated degradation is relatively large as compared to the measurements (see cyclic degraded curve in Fig. 5.26). Almost the same affinity for degradation can be seen in case of larger amplitudes. Fig. 5.27 shows a deflection-controlled free-head test from -8 to 53 mm with a large decrease of the lower strut load Flow . Plots of the bending moment distributions for all tests are shown in Fig. 5.28. The plots depicted in Fig. 5.26 and Fig. 5.27 are referenced for moment distribution plots (refer to No. 1 and No. 5, respectively). Under the free-head boundary condition, the maximum bending moment occurred consistently at depths of about 3.4 m or 5.5 times the pile diameter below the ground surface, whereas the calculated position of the maximum bending moment occurred in around 2.0 m or 3.2 times the pile diameter. The bending moment plots showed a good agreement down to this depth, but the results differ up to maximal 50% below that depth. The effect of cyclic loading is illustrated in Fig. 5.28 in the bottom right diagram by showing the bending moment curve for the first cycle (marked point No. 5) and the last cycle (marked point No. 6) of the fifth free-head test.

184


5

test 2 to 6 (free-head) measured

3

0

4 6

200 100 0 -100 -200 -20

cyclic degraded curve


0 20 40 lower strut deflection δlow [mm]

2 5 6

3

2 1

4 -600

60

-400

-200

0

0 Ground surface

2 depth [m]

2 4 1

measured calculated begin calculated end

4 6 8

8

5

6 measured begin measured end calculated begin calculated end

test 2 (free-head)

-800

FH 1 FH 2 FH 3 FH 4 FH 5


Ground surface

depth [m]

4

3

FH 1 ( 0 to 23 mm) FH 2 (-3 to 36 mm) FH 3 (-3 to 41 mm) FH 4 (-5 to 43 mm) FH 5 (-8 to 53 mm)

0

6

Ground surface

test 2 to 6 (free-head) measured

1

1

depth [m]

lower strut load Flow [kN]

300

-600 -400 -200 bending moment [kNm]

test 6 (free-head)

0

-800

-600

-400

-200

0


Figure 5.28: Bending moment distributions measured and calculated during free-head tests

As shown in the figures, cyclic loading under imposed deflection limits tends to relax the bending moment along the pile length.

Fully Restrained Head Tests Three fully restrained head tests were performed applying a loading rate of about 2 minutes per cycle. Plots of the measured and calculated load-deflection behaviour for the


-4

Fup

185

δup = 0

δup = 0


-2

δlow, Flow

-2 δlow, Flow

0

2

depth [m]

depth [m]

0

measured test 1 measured test 2 measured test 3

Ground surface

2 4

1 measured calculated begin calculated end

6 8

4 3

2

FRH test

1

fully restrained-head 1 to 3

fully restrained-head test 1

0 400 800 bending moment [kNm]

-400

0

400

800


Figure 5.29: Bending moment distributions measured and calculated by pile 1 during fully restrained head tests

three tests are shown in Fig. 5.30 (left diagrams). In case of the measured results, only the first cycle of each test is presented in the diagram to avoid congestion. The change in the head-restraint from free to full was increasing the slopes of the loaddeflection curve significantly. In contrast, the variation of soil resistance during cyclic testing was smaller in the experiment as well as in the numerical calculations. Under freehead test conditions, at each new load level some amount of progressive load reduction before final stabilisation was observed with cycling whereas with the fully restrained head loading very little progressive change was noted during cycling. test no. lower limit [mm] 7 8 9

6 4 1

upper limit [mm]

no. of cycles [1]

13 19 26

7 7 12

Table 5.6: Incremental deflection limits and number of cycles of the fully restrained head tests In lateral pile foundation design, the bending moment distribution along the pile length is an important characteristic curve, which is influenced by the pile-head boundary condition

186


δup = 0

400

δlow, Flow

4 to 19 mm

measured calculated

0

2

Ground surface

1

200

6 to 13 mm


-2

depth [m]


fully restrained-head test 1 and 2

1

0

2 4 2 measured calculated begin calculated end

6 -200 8


0

10 20 lower strut deflection δlow [mm]


30

-400

400

800


δup = 0

3



-2

400

δlow, Flow

measured calculated

0 Ground surface

200

depth [m]


0

1 to 26 mm

0

2 4 3 measured calculated begin calculated end

6 -200 8

reference for moment distribution plots 3

0

10

20

lower strut deflection δlow [mm]


30

-400

0

400

800


Figure 5.30: Bending moment distributions measured and calculated by pile 1 during fully restrained head tests

as well as the type of lateral loading. The magnitude and location of the maximum bending moment along the pile length varied highly under the three different boundary conditions for both monotonous quasi-static and cyclic loadings.


5.3.6

187

General Remarks concerning Numerical Modelling of LargeScale Pile Tests

Monotonous quasi-static and slow alternating loads were applied on instrumented piles under different head restrained conditions [Ert83]. Subsequently, the tests were simulated using the finite element method applying a hypoplastic constitutive relation. The piles in the test were embedded in a predominantly silty sand deposit with a silty clay layer occurring from about 1.5 to 2.4 m below the ground surface, which was also considered in the FE-model by means of a visco-plastic layer. The piles were 61 cm in outside diameter with a wall thickness of 1.3 cm, which was taken into account by an ideal-elastic material behaviour. The piles were driven in place to a final depth of 9.8 m below the ground surface. No changes of the soil state were assumed for the driving process. The piles used in the large-scale tests were instrumented to measure the bending moment along the shaft. The displacements of the pile nodes in the numerical model were evaluated to obtain a deflection curve versus depth along the shaft. The curvature of the pile was analysed to assess the bending moment. Pile-head load and deflection were also recorded and calculated. No significant pore pressure variations were observed during loading. Altogether ten tests were performed and, subsequently, recalculated successfully. All tests were displacement-controlled. The numerical model was capable to reproduce satisfyingly all types of boundary conditions at the pile head, i.e. partially restrained head, free-head, and fully restrained head conditions. The very significant influence of the pile-head restraint was demonstrated both experimentally and numerically. Generally, the results were stronger influenced by boundary conditions than by soil variations. The numerical calculations appear to be quite adequate for analysing the test results, and are yielding realistically the principal load deflection behaviour and bending moments. Thus, the finite element method can be adopted for a lateral pile foundation design under static or quasi-static loading. The computer model is able to simulate appropriately the different restrained head cases. Since the field measurements as well as the numerical solutions were observed to be dominated by the sand, conclusions drawn from this study are more a justification of sand criteria than soft clay criteria. The numerical models are working very well for calculations with a low up to a moderate number of cycles. All results fit very well and when differing slightly they are always lying on the save side. For a huge number of cycles, the loss of soil resistance is overestimated, but failure mechanisms can be simulated perfectly. The numerical calculations presented here are suitable to investigate the mechanisms of progressive failure. Therefore, they are

188


useful for foundation design and engineering and, hence can be used as a practical tool by the geotechnical engineer. Two contradictory mechanisms can be outlined in general: on the one hand the mechanism of stabilisation and self-stabilisation due to compaction, and on the other hand, destabilisation due to dilation and increase of pore water pressure. In a few cases, shake-down to nearly elastic behaviour could be observed even after a few cycles. These considerations can be extended to any kind of offshore applications and structures subjected to traffic loads and machine foundations. Stationary ratcheting would inevitably lead to a failure of the embedded structure. However, self-stabilisation and self-healing effects can be observed and exploited. The behaviour of the soil can be reproduced for monotonic and alternating horizontal loading of piles by means of the finite element method and an implemented hypoplastic constitutive model.

5.4. Seismic SFSI Analysis

5.4

189

Seismic SFSI Analysis

In the last years, many methods have been proposed to deal with the analysis of the dynamic response of structures founded on soft or liquefiable soils, in which soil-foundationstructure interaction is crudely simplified or even totally neglected. Worldwide, the antiseismic structural design is based on standard procedures, in which the ground is oversimplified and the type of foundation and its interaction with the soil and the structure is not taken into account. Neglecting soil-foundation-structure interaction (SFSI) has often been assumed to be beneficial for the seismic response of the supported structure because its consideration is said to improve the safety margins. While this assumption might be true for buildings founded on very stiff soils and rock, it cannot be extended inconsiderately to soft or liquefiable soils where, especially in case of strong earthquakes, there is still a lack of understanding the influence of the foundation type and the role of SFSI. The constitutive laws employed in the present investigation have been developed and enhanced to describe the rate-independent and rate-dependent non-linear behaviour of hard-grained and soft soils under alternating and dynamic loading (Chap. 3). On this basis, advanced numerical models of SFSI during strong earthquakes have been proposed to investigate SFSI of reinforced concrete (RC) buildings founded on shallow foundations [CC04]. Within this present study, a similar numerical approach is used to evaluate comparatively the seismic response of a (RC) building frame on deep and shallow foundations during strong earthquakes. The approach is based on the Finite Element Method (FEM) in the time-domain and considers the non-linearity of soil and structure as well as its interaction with the foundation, and is presented in detail in [BC05] [Bue05].

5.4.1

Introduction

In the 1950s, many studies about the implications of soil-structure interaction (SSI) for the dynamic seismic response of structures have been published. However, the majority of these contributions has been restricted to linear behaviour of the soil and the structure without considering the SSI. Modelling and analysing dynamic SSI during earthquakes began with the development of the FEM in the 1960’s. In the seventies, other works established that dynamic SSI effects might not be important for regular flexible buildings founded on rock or very stiff soil, but they could be very significant for structures embedded in soft or liquefiable soil [SI69], [Waa72]. Although considerable efforts have been made in the last twenty years to develop adequate prediction methods, conceptual and computational difficulties remain primarily due to the three-dimensional, semi-infinite and non-linear nature of the soil medium and to the embedding of the foundation.

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Currently, there are basically two methods to deal with non-linearity in the analysis of SFSI: the direct approach, also referred to as the ’Complete Finite Element’ approach, which is presented here (Fig. 5.32), and the substructure method. In the substructure method [Wol85],[Wol88], the soil-structure system is divided into at least two substructures: a structure that may include a portion of soil adjacent to it and the surrounding soil. The surrounding soil region is usually represented by an impedance matrix, which may be attached to the dynamic stiffness matrix of the structure. Numerical models based on the substructure method are not capable to consider some of the decisive non-linear properties of the system. Although numerical models based on the direct approach can deal with the non-linearities of the surrounding soil and the structure, the mentioned difficulties associated with the description of the soil, foundation, and structure material behaviour as well as the unbounded nature of the surrounding soil, the FE simulations of SFSI remain a challenge [MG00][GM98]. One of the non-linear soil effects, which are most difficult to consider in the simulation of SFSI is the phenomenon of soil liquefaction. During strong earthquakes, liquefaction can cause large ground displacements, which can have devastating effects on structures as it is known from many structural failures in past earthquakes. The scientific investigation of soil liquefaction was initiated after the Niigata and the Alaska earthquake, both in 1964. Although careful observations and systematic studies in the past decades have produced a deeper understanding of the underlying mechanisms, most constitutive models available nowadays have not yet achieved the stadium of development required to predict soil liquefaction reliably. In order to model the dynamic SFSI in soft and liquefiable soils realistically, it is necessary to take some essential aspects into account: 1. the non-linearity of soil, foundation and structure, 2. the hysteretic nature of soil damping, 3. the radiation of energy through the model boundaries (geometric damping), 4. the contact between the soil and the structure, and 5. the development of excess pore water pressure and the associated decay of effective pressure for undrained conditions. Due to the complexity of the problem, there have been so far only few attempts to address all these effects in one model. In this study, the non-linear seismic SFSI of a reinforced concrete building frame founded on a shallow foundation, a pile group consisting of six single piles, and a rather academic


191

foundation consisting of (more likely investigated for scholastic reasons) a monopile subjected to strong earthquakes is analysed with the FEM. The numerical models, which are based on those proposed by [CC04] for the case of RC buildings on shallow foundations are capable to address the five aspects listed above. In order to quantify the influence of SFSI, the ground motion under free field conditions is compared with the ground motion obtained from the simulations, which take the foundations and the structure into account. For this comparison the same same seismic excitation was applied. The calculated dynamic responses of the structure, the soil and the foundation are analysed and compared in the time and frequency domain. The presented study compares the displacements of the structure, the foundation, the soil (Fig. 5.35 and 5.37 to 5.38), and the tilting of the structure for the different foundations (Fig. 5.36). A Response Spectrum Analysis (RSA) of a single degree of freedom (SDoF) system applying the soil motion adjacent to the foundation is carried out and compared to the free-field response (Fig. 5.42). The liquefaction potential of the surrounding subsoil is investigated by regarding the decay of effective pressure in the soil (Figs. 5.43-5.48). With the aid of the presented non-linear seismic SFSI analysis, it is possible to investigate: • the influence of local site effects on the ground response considering the soil type, soil state (density, pressure) and earthquake characteristics as well as geological and hydrogeological particularities, • the susceptibility for liquefaction of the soil in the vicinity of the foundation and its consequence for the behaviour of the foundation and the dynamic response of the structure, • which type of foundation and structure adjusts better to the local site conditions, • the stability (via maximal bending moments and normal forces, formation of plastic hinges in the RC sections) and serviceability (via permanent displacements and tilting, large soil movements in vicinity) of different type of structures and foundations, and • the success of soil improvement and structural retrofitting measures.

5.4.2

The Seismic SFSI Model

Plane strain conditions are assumed for the soil elements and the structure elements. The soil and the foundation elements are modelled using linear four-node isoparametric

192


a/2 sec A

free-field response hysteretic damping Shear Waves

reflections

radiation

acceleration record applied on base nodes (bedrock)

Figure 5.31: Dynamic 2D-SFSI model with a periodic boundary. A part of the waves radiated from the embedded part of the structure is dissipated due to hysteretic damping. A critical distance a/2 has to be found by comparing the numerical results in section A close to the boundary with the expected free-field response.

plane strain elements. Each node has two translational degrees of freedom, i.e. in the x and y coordinate direction as shown in Fig. 5.32. Eight-node-elements may be better for dynamic analyses, especially for modelling the response of a system dominated by bending deformations (e.g. the piles). In the current analysis, four-node-elements were selected for simplicity since the study does not focus on the evaluation of internal pile forces. It is assumed that the structure is founded on a layered ground from Treasure Island, San Francisco Bay [SDI91]. An acceleration record at Yerba Buena Island during the 1989 Loma Prieta Earthquake (M=7.1) is used as bedrock excitation. A seismic motion parallel to the plane of the RC frames is considered. Only the strong phase of the earthquake is considered in the FE-calculations. The seismic bedrock excitation is applied as a velocity boundary condition (velocity history) by constraining all the nodes on the bottom boundary of the model to undergo the same motion. The subsoil behaviour is modelled with hypoplastic and visco-hypoplastic constitutive equations [Nie03], which are able to simulate the response of cohesionless and cohesive soils under alternating and dynamic loading, for drained and undrained conditions [BCLB+ 02] [BCO+ 03] [BCG04a] [Bue04] [BCG04b] [BC05] [Bue05] [CBLBG04] [COBG03] [GCLBB04] [KDGB03]. By using a Finite Difference Algorithm proposed by Osinov [Osi03] and the hypoplastic and visco-hypoplastic constitutive relations [COBG03] the Treasure Island (Fig. 5.32) soil profile was analysed as a one-dimensional non-linear wave propagation problem. A good agreement of measured and predicted free field accelerations was found.


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The shallow foundation consists of an RC mat, which lies on a sandy fill two metres beneath the water level. The monopile and the pile group foundation are embedded in the deeper silty sand layer. Both cohesionless soil layers are modelled with hypoplasticity. The RC mat has a width of 9 m and a thickness of 0.5 metres. The width of the monopile is 1 m; the one of the piles in the group is 0.5 m. The modelling of the RC frames of the 3-storey building using plane concrete (elasto-plastic material behaviour) and rebar elements (elastic-ideal-plastic material behaviour) for the reinforcement is described in detail by [CC04]. A lateral periodic boundary condition of the soil is imposed by constraining opposite nodes (see nodes A-A’ in Figure 5.33) on these boundaries to undergo the same displacement. This boundary condition is reasonable for strong earthquakes since the energy dissipation in the soil due to hysteretic damping supersedes the energy radiation from the foundation. The periodic boundary condition provides exact results in case of level ground with free surface subjected to base shaking without structure [GCLBB04] but it is still a good approximation in case of strong earthquakes if the boundaries are located far from the foundation (Fig. 5.31). The numerical simulations are carried out with the programme ABAQUS version 6.5 [ABA05b]. The FE-models consists of 6172 elements and 6491 nodes, which makes a total number of 13153 variables to follow up. The simulations consist of two steps. In the first step, which is a static one, the gravitational loads including the weight of the structure are applied. In a second step, which is a dynamic one, the earthquake motion is applied. During the earthquake motion, water drainage is not permitted, i.e. undrained soil behaviour is assumed.

5.4.3

Results and their Discussion

During and after strong earthquakes, especially when soil liquefaction occurs, permanent ground deformation as large ground settlements, lateral spreading, and land-sliding can have devastating effects on structures. These phenomena have been observed for many years. In fact, based on the knowledge we have today, we know that many of the structural failures during ancient earthquakes can be associated with soil liquefaction. The scientific investigation of this phenomenon was initiated after the Niigata [Kaw68] and the Alaska earthquake [GPK64], both in 1964. Since then, careful observations on this phenomenon have been carried out by engineers and scientists all over the world. However, due to the complex nature of soil behaviour and liquefaction mechanisms, this phenomenon is not thoroughly understood yet.

194


shallow foundation

monopile

pile foundation depth [m]

ground level water level

freefield

2.0 4.0

node A

sandy fill (hypoplastic)

12.5

silty sand (hypoplastic)

0.0

node A'

8.0 11.5 15.0

young bay mud (visco-hypoplastic)

y 30.0

x Figure 5.32: Three FE-Models used for the comparative study of SFSI of a building on shallow foundation, monopile and pile foundation. Periodic boundary condition (node A-A’), idealised soil profile and assumed material behaviour.

Figure 5.33 shows the calculated free-field ground response at Treasure Island for the Loma Prieta earthquake. In order to reduce the computation time, the bedrock was assumed to be 30 m in depth. As expected, the ground velocity history (depicted as a sequence of horizontal velocities vh ) change along the depth (Fig 5.33a). Fig 5.33b presents the power density spectrum (PDS) of the acceleration history at the surface (A1) and in the middle of the silty sand layer (C2) in comparison with the bedrock (D3). It can be seen that the frequency spectrum at the surface is narrower, and the frequency of maximal spectral amplitude is lower (from 1.8 to 1.4Hz) than at the bedrock. This phenomenon, also called peak frequency shift, was also observed by [Pra02] in real earthquake registers. It can be seen that high frequencies (over 3 Hz) vanish at the surface, i.e. after liquefaction, the upper layer acts as a kind of filter for shear waves. The PDS


195

2 2

PDS [(m/s ) /Hz]

c)

D3

0.3

peak frequency shift

A1

0.2

frequency filtering due to liquefaction

0.1

2 2

PDS [(m/s ) /Hz]

0 D3

0.3

C2

0.2

evolution of high frequencies

0.1 0 0

1

2

3

4

5

f [Hz]

a) A2

water level

A3

2.0 B2 B3

8.0

b)

15.0

B3 A1

0

B2

A2

decoupling

-0.5 0.5

C2 C3

0.5 vh [m/s]

0.0

vh [m/s]

A1

amplification C2

C3

D2

0 high frequencies

D2

D3

vh [m/s]

-0.5 0.5 D3

0

30.0 -0.5 0

10

20

30

time [s]

Figure 5.33: Simulated free-field ground response at Treasure Island during the Loma Prieta 1989 earthquake. (a) Velocity vs. time in different depths (bottom right), (b) power density spectra of the acceleration histories in different depth.

196


120

c)

B3

C3

C2

pw [kPa]

80

B2

C1 B1

40 D1

0

A1

0

10

D2

D3

A2 = 0.0 kPa

20

30

time [s] 0

A1 = 0 kPa B1

p' [kPa]

40

A2

B2

80

total liquefaction

C1

B3

C3

120

D1

160

D2

200 0

a)

2

4 6 time [s]

8

A1 0.0 A2 water level b) 0.0 B1 2.0 total 3.0 liquefaction B2 4.0 B3 C1

8.0 10

C2 15.0

C3 D1

t > 15 s

10

0.0 3.0 4.0 4.5

4.5 5.0

5.0 8.0

8.0 15.0 28.0 residual effective pressure

15.0 28.0

D2

depth [m]

20

D3

30.0

t [s]

200 100 p' [kPa]

t [s]

0

0

40 80 120 pw [kPa]

Figure 5.34: Simulated ground response at Treasure Island during the Loma Prieta 1989 earthquake. (a) Effective mean pressure and (b) pore water pressures versus depth at different times. (c) Development of effective mean pressure and (d) pore water pressure versus time at different times.


197

also indicates that the acceleration amplitudes decrease (smaller peaks at A1 compared to D3) while the velocity amplitudes increase (A1: vh,max = 0.49 m/s, D3: vh,max = 0.20 m/s) during liquefaction. This result also agrees with many observations during strong earthquakes, showing that in liquefiable soil, ground surface displacements increase even when accelerations decrease [Kra96]. The PDS and the velocity histories indicate that the motion of the upper two soil layers decouple from the base motion during the earthquake. For this reason, the young bay mud layer produces motion amplification as well as higher frequencies (up to 2.5 Hz in C2), but these effects disappear in the upper layers. 0 free field

u v [m ]

-0.02

pile group uv

-0.04 single pile

-0.06 shallow foundation

-0.08

0

10

20

30

time [s ]

Figure 5.35: Evolution of calculated vertical displacements at the base of the structure for the three foundation types. Post-earthquake settlements due to drainage and creep are not considered.

0.002

pile group

θ [rad]

0.000

level position

uv

-0.002

θ

shallow foundation single pile

-0.004

0

10

20

30

time [s ]

Figure 5.36: Evolution of the structure tilting for the different foundation types.

Fig. 5.34a depicts the evolution of the excess pore water pressure pw and the mean effective pressure p versus time in different depths. The distribution of p and pw over the depth at different times is presented in Fig. 5.34b. In the sandy layer below the ground water table (B1, B2, and B3), pw increases and simultaneously p decays rapidly: 70% and 95%

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of the maximum pw are reached after 5s and 10s, respectively. After about 8 seconds, the effective pressures almost vanish, i.e. the layer liquefies. On the contrary, in the layer underneath (C1, C2, and C3) there is still a residual effective pressure of around 50 kPa at the end of the earthquake. In the soft young bay mud layer (D1, D2, and D3), as well as in the sand layers above the water table (A1 and A2), both pw and p remain practically unchanged during the earthquake. It is important to note that soil liquefaction accompanied by post-earthquake settlement, permanent horizontal displacement, and sand boils were also observed in the Treasure Island during the 1989 Loma Prieta earthquake.

8 cm 6 cm 4 cm 2 cm

Figure 5.37: Displacement vectors at the end of the earthquake for free-field conditions. The colours indicate the displacement magnitude from zero (blue) to maximal displacement (red)

The calculated evolution of the mean vertical displacements at the base of the structure for the three investigated foundation types and the free-field conditions are shown in Figure 5.35. Post-earthquake settlements are not included since drainage is not allowed in the calculation, although it could be done by adding a coupled calculation step enabling filtration. Under undrained conditions, a maximum mean settlement of about 65 mm is obtained for the shallow foundation. A reduction of settlements, which may be necessary to ensure the serviceability of the structure after the earthquake, can be achieved with a


199

24 cm 18 cm 12 cm 6 cm

Figure 5.38: Displacement vectors at the end of the earthquake for shallow foundation. The colours indicate the displacement magnitude from zero (blue) to maximal displacement (red)

deep foundation: The reduction of maximum settlement amounts to 30% in case of the monopile (45 mm) and 70% (20 mm) in case of the pile group. The curves show that most settlements occur between the 5th and 10th second, i.e. during the strong phase of the earthquake. The further increase of the settlements is small. Figure 5.36 compares the tilting of the structure versus time for the different foundation types. The overturning moment, caused by the dynamic forces acting on the pile, is responsible for the larger tilting of the monopile during the earthquake. This moment induces additional soil reactions and displacements on the already weakened soil beneath the base of the structure. The use of a pile group improves the performance noticeably since the reaction moment is translated to the base of the piles where the bearing capacity of the soil is practically not affected by the earthquake. In the first 10 s, the structure reaches a maximum tilting angle 0.1% radian, but it comes almost back to the vertical position in the last 10 s of the earthquake. On the other hand, in case of the shallow foundation, tilting increases continuously during the earthquake. The maximum inclination of 0.3% radian is almost three times the value obtained with the pile group. Although the pile group provides the best protection against permanent displacement, it also allows a

200


12 cm 9 cm 6 cm 3 cm

Figure 5.39: Displacement vectors at the end of the earthquake for monopile foundation. The colours indicate the displacement magnitude from zero (blue) to maximal displacement (red)

better transition of shear forces from the ground, which could damage the structure. Figures 5.38, 5.39, and 5.40 exhibit the displacement magnitude for the three considered foundation types and free-field conditions (Fig. 5.38) at the end of the earthquake. The maximal displacement in the free-field case (Fig. 5.37) amounts about 62 mm (red) and occurs in the liquefied sandy fill layer. As mentioned before, when the shear stiffness in the liquefied layer decays, the motion of the soil layer above the liquefied zone decouples from the rest, and the upper layer moves almost as a rigid body. For this reason, the soil layer above the ground water table shows a permanent but almost uniform displacement at the end of the earthquake. The permanent displacements of the deeper layers are smaller than the ones of the liquefied layer. In case of the shallow foundation (Fig. 5.38), the reduction of the shear resistance due to the decay of the effective stresses leads to a reduction of the bearing capacity of the soil. The development of typical zones indicates clearly a punching of the foundation: large displacements of the soil and the structure take place. The maximal movements of the surrounding soil of approx. 240 mm is the largest one compared with the values for the other foundation types. The maximal soil movements in case of the monopile foundation amounts to 120 mm. In this case, the


201

8 cm 6 cm 4 cm 2 cm

Figure 5.40: Displacement vectors at the end of the earthquake for pile foundation. The colours indicate the displacement magnitude from zero (blue) to maximal displacement (red)

bearing capacity is severely affected by the earthquake, which is indicated by the shear zones around the pile toe. The performance of the pile group (Fig. 5.40) is better than that of the monopile. From the fact that only a small shear zone develops at the left side of the base of the piles, it can be deduced that the bearing capacity of the pile group is not strongly affected by the earthquake. The maximal soil displacements are limited to 78 mm. For the deep foundations, the largest total displacements occur in the upper layer. Figure 5.41 shows the PDS of the horizontal acceleration histories in the middle of the base of the structure (Fig. 5.41a), at the ground surface in the vicinity of the structure (Fig. 5.41b), and at the top of the structure (Fig. 5.41c), for the different types of foundations. The PDS of the free-field and bedrock accelerations is also plotted for comparison. It can be seen, that the peak amplitudes and frequencies content of the bedrock motion are modified not only by the soil profile and the structure, but also by the foundation type. This means that the motion, the deformation, and the shear forces induced in the structure by the earthquake also depend on soil-foundation-structure-interaction. For example, the PDS for the pile group at the base of the structure shows strong amplifications

202


a) PDS [(m/s2)2/Hz]

0.4 single pile

0.3

pile group

0.2

shallow foundation

0.1 0

PDS [(m/s2)2/Hz]

b) free field

0.3

single pile

0.2 shallow foundation

0.1 0

PDS [(m/s2)2/Hz]

c) bedrock

pile group

0.3 0.2 0.1 0 0

1

2

3

f [Hz]

Figure 5.41: PDS of the horizontal acceleration at the surface (free-field conditions) and bedrock in comparison with the PDS at the top of the structure (a), on the soil surface in vicinity of the structure (b) and at the base of the structure (c) for three foundation types.

with respect to the bedrock at 1.3 and 1.6 Hz, which do not coincide with the peak frequencies for free-field conditions or the bedrock (Fig. 5.41a). In the ground surface, both the pile group and the single pile cause an amplification of the motion for higher frequencies, which is not observed in case of the shallow foundation (Fig. 5.41b). The PDS at the top of the structure shows a peak between 1.4 and 1.5 Hz for all types of foundations (Fig. 5.41c). The smallest amplitude of this peak corresponds to the shallow foundation, the largest one to the monopile. In case of the pile group, a second peak with almost the same amplitude is observed for a frequency of about 1.6 Hz. The amplitudes for low (below 1 Hz) and high (above 2 Hz) frequencies contained in the bedrock acceleration


203

16 single pile

free-field

2

Sa [m/s ]

12 8 4 0 0. 1

shallow foundation

pile group

bedrock

1 f [Hz]

10

Figure 5.42: Acceleration Response Spectrum Analysis (RSA) of a single degree of freedom system with 5% viscous damping due to the acceleration histories at the bedrock, freefield, pile group head, shallow foundation, and single pile head.

decay noticeably at the top of the structure, and all peak frequencies are shifted towards lower frequencies (up to 0.5 Hz). The acceleration histories of the bedrock, the free-field, the pile group head, the shallow foundation, and the single pile head (cf. Fig. 5.41 bottom) are applied to a single degree of freedom (SDoF) system with viscous damping of 5% to analyse systematically the dynamic response of structures as a function of the frequency. Figure 5.42 shows the pseudo Acceleration Response Spectra (pseudo-acceleration Sa ) of all mentioned cases. As it can be seen, the response spectra for the different foundations lie approximately between the bedrock and the free-field response. This sort of analysis gives the impression that the use of the free-field acceleration assures a safe structural design. However, this analysis is misleading since the dynamic response at the base of the structure is tacitly assumed to remain unchanged independently on the structure, i.e. soil-foundation-structure interaction is completely disregarded. Figs. 5.43 to 5.46 show zones with vanishing effective pressures at different times from the beginning of the earthquake. In the free-field case, a liquefied zone develops firstly close to the water table and, subsequently, propagates downwards. After some time, the zone with vanishing effective pressure extends to the complete layer being susceptible to liquefaction (Fig. 5.43, compare also with Fig. 5.34). Fig. 5.44 shows the results for the shallow foundation. Liquefaction starts at both sides of the mat. The liquefied zone develops more irregularly than in the free-field situation. Beneath the mat the effective

204


Figure 5.43: Visualisation of zones with calculated vanishing effective pressures (black colour) for the free-field case at (a) t=4.75, 5.0s, (c) 7.5s, (d) 10s. Liquefaction initiated at t=4.75s.

stresses decrease slowly. After 10 s, a thin liquefied zone appears under the mat but the soil at both sides of the shallow foundation does not liquefy and helps to stabilise the foundation. Liquefaction takes a bit longer to occur near the monopile, but its presence does not help to prevent it. At the end of the earthquake, even the layer beneath the base of the building is liquefied. In case of the pile group, liquefaction does not occur between the piles because the shear deformations are considerably smaller there than around the pile group. Figs. 5.47 and 5.48 show the effective stress ratio rp = p /p0 and the pore pressure ratio ru = ∆pw /p0 over the depth at different times for a vertical section beside the foundation. The diagrams confirm that the development and extension of the liquefied zone strongly depend on the foundation type. It should be noted that although the thickness of the liquefied layer for the shallow foundation is even smaller than under free-field conditions, the displacement of the soil and the structure are the largest in


205

Figure 5.44: Visualisation of zones with calculated vanishing effective pressures (black zones mean liquefaction) for the shallow foundation at (a) t=3.75, (b) 5.0, (c) 7.5, (d) 10s. Liquefaction initiates at t=3.75s.

comparison with those resulting for the other foundation types, i.e. less liquefaction does not necessarily mean more safety, nor an improvement of the serviceability. These results emphasise the importance of taking into account soil-foundation-structure interaction for assessing the serviceability of structures founded on soft and liquefiable soils after strong earthquakes.

5.4.4

General Remarks on the Seismic SFSI Analysis

A direct approach that combines the FEM with hypoplastic and visco-hypoplastic constitutive models was applied to the investigation of the non-linear SFSI of an RC-structure

206


Figure 5.45: Visualisation of zones with calculated vanishing effective pressures (black zones mean liquefaction) for the monopile at (a) t=3.5, (b) 5.0, (c) 7.5, 10s. Liquefaction initiates at t=4.35s.

for three foundation types, a shallow foundation, a monopile, and a pile group, during strong earthquakes. The presented model is able to take into account the influence of the soil, the structure, the foundation, as well as the interaction among them on the dynamic response of structures. In contrast to other existing approaches of SFSI, in the presented model the non-linear soil behaviour can be modelled realistically. By means of our model, the influence of local site conditions can be assessed, including soil liquefaction. Soil liquefaction induces changes of the amplitude and frequency content of the ground, structure, and foundation motions. Compared to the bedrock, the peak spectral amplitudes for the surface, the structure, and the foundation reduce and shift towards lower frequencies; spectral amplitudes vanish for very low as well as high frequencies. Shear softening of the liquefiable layer causes an increase of displacements and velocities, but


207

Figure 5.46: Visualisation of zones with calculated vanishing effective pressures (black zones mean liquefaction) for the pile group at (a) t=4.25s, (b) 5.0s, (c) 7.5s, (d) 10s. Liquefaction initiates at t=4.35s.

a decrease of the acceleration at the ground surface. The foundation type influences the evolution and extension of the liquefied zone. In comparison with the shallow foundation, the pile group leads to smaller settlements and tilting after the earthquake. The accelerations at the base and at the top of the structure are larger for the deep foundation than for the shallow foundation. These results show clearly that a design only based on an expected maximal acceleration neither assure the stability nor the serviceability of the structure after a strong earthquake. The proposed numerical approach presents a powerful tool not only to optimise the design of earthquake-resistant structures, but also to evaluate the vulnerability of existing constructions and to judge the effectiveness of structural retrofitting and soil improvement

208


depth [m] 0 3.0 4.0 4.5 5.0 8.0 15.0 28.0

10

20 shallow

b) foundation

a) free-field

pile

single

d) group

c) pile

t [s]

30 0

1 0 rp' [kPa/kPa]

1 0 rp' [kPa/kPa]

1 0 rp' [kPa/kPa]

1 rp' [kPa/kPa]

Figure 5.47: Effective stress ratio versus depth for different times from the beginning of the earthquake. (a) free-field, (b) shallow foundation, (c) monopile and (d) pile group.

measures.

5.5

Summary and Conclusions

Small-scale model tests in a 60-litres-barrel were investigated numerically. The results of the numerical calculations show that the applied models are capable of simulating the experiments satisfactorily. Some details of the numerical model, especially due to discrepancies in the formulation of the boundary conditions, leave room for improvement. The pile-soil contact formulation works well in terms of the accuracy of the results by using a so-called exponential soft contact definition. Nevertheless, in terms of cost and stability it is very time-consuming, and numerically not always too stable. Finer discretisation of the contact surfaces between pile and soils in most cases does not yield any relief. Sometimes it even has the opposite effect. An upscaling towards geotechnically relevant dimensions is possible. It is also justified by using constitutive relations, e.g. hypoplasticity and viscohypoplasticity, which are valid in a broad range of deformations and effective pressures. As a result, the application of the presented models works well for the geotechnical design

5.5. Summary and Conclusions

209

depth [m] 0 3.0 4.0 4.5 5.0 8.0 15.0 28.0

10

20 shallow

b) foundation

a) free-field

pile

single

d) group

c) pile

t [s]

30 0

1 0 ru [kPa/kPa]

1 0 ru [kPa/kPa]

1 0 ru [kPa/kPa]

1 ru [kPa/kPa]

Figure 5.48: Pore pressure ratio for different times from the beginning of the earthquake. (a) free-field, (b) shallow foundation, (c) monopile and (d) pile group.

of horizontally loaded piles and pile foundations, and the assessment of existing damaged pile foundations in order to justify a retrofit. The results of the numerical calculations of in-situ pile load tests show that the applied models also work well with large-scale dimensions. The interpretation of the 3D analysis provides not only the evolution of the state of the soil in the near-field of the test pile, but also a realistic development of the gap between soil and pile. Even the large-scale test itself in-situ is not able to give such an insight into the problem. In this way, bending moments can be evaluated at positions and in periods not recorded by the measuring programme. Matlock [Ert83] actually used the test results in order to adapt empirically the so-called p-y method under consideration of different pile head restrained conditions. For every change in the boundary conditions in this manner, the response of the system and, thus his empirical factors are changed. His over-simplified methods are still used to date for design. The results of the presented numerical models demonstrate a far more universal approach. A direct transition to different and more complex examples can be implemented easily, i.e. pile groups, pile foundations, also including superstructures, excitation from below like earthquakes. Furthermore, the causes and mechanism of damages could be investigated and examined more closely. Possible hidden damages could also be revealed

210


numerically. Finally, a seismic soil-foundation-structure interaction analysis using FEM has been carried out, investigating three different types of foundations. By means of the presented direct SFSI approach, it is possible to investigate the influence of local site effects on the ground response considering the soil type, soil state (i.e. density, pressure, and loading history) and earthquake characteristics as well as geological and hydrogeological particularities. The method is capable to investigate the vulnerability of foundations and their superstructures, in particular the susceptibility against liquefaction of the soil in vicinity of the foundation and its consequence on the behaviour of the foundation as well as the dynamic response of the structure. Thus, stability and serviceability (i.e. permanent displacements and tilting, large soil movements in vicinity) of different types of structures and foundations, as well as the success of soil improvement measures, can be systematically investigated. From the outcomes, the engineer will be able to decide, which type of foundation and structure adjusts better to the local site conditions and, subsequently, an adapted design can lead to optimised foundations.

Chapter 6 Recommendations 6.1

Mitigation of Liquefaction Susceptibility

It is the responsibility of geotechnical engineers to assess and reduce the liquefaction susceptibility of soils in order to avoid the failure of structures built on liquefiable ground. Although there is still a lot to learn about soil liquefaction, some general rules achieved by the findings of the presented investigation should be followed in order to reduce the potential of soil-liquefaction-induced structure failures. The simplest policy is to avoid building structures in areas that are susceptible to soil liquefaction, namely areas known to have experienced soil liquefaction during past earthquakes, viz. loose granular fills, geologically young sediments, or relatively steep slopes. In order to build on liquefaction-susceptible areas, the soil has to be improved by soil replacement, dynamic soil compaction, concrete grouting, by installing stone columns, concrete columns, or at least vertical drains for increasing the drainage of the ground in vicinity of the foundation. A combination of two or more of these methods could be even more effective in reducing the liquefaction potential, but this possibility has not been explored so far. In order to limit settlements and tilting, and to assure the serviceability of structures after an earthquake, special care should be taken for choosing and designing an adequate foundation system. It should be noted that in particular cases liquefaction in deep layers can be beneficial for the structure due to mentioned decoupling and filtering mechanisms. The systematic investigation and practical application of these mechanisms in the design should be intensified. In the quest to deepen our understanding of soil-foundation-structure interaction (SFSI), it is imperative that geotechnical and structural engineers work cooperatively. SFSI cannot be understood by studying only the behaviour of the structure or only the behaviour of the soil.

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214

6.2

Chapter 6. Recommendations

Failure Modes and their Prevention

From observed pile performance in terms of damage during earthquakes, different potential failure modes can be discerned. Failure can be defined as the loss of structural capacity of the pile foundations including the degradation of the load carrying capacity of the pile-soil system.

• Due to liquefaction in case of hard-grained soils, or due to strain softening in case of soft fine-grained soils, the lateral soil support can be lost, especially close to the ground surface. Subsequently, the bending strains in the pile increase due to excessive displacements near the pile head in particular when large structural inertial loads are present. This failure mode results in pile damage at the pile to cap connection, i.e. shear cracks, as well as in heavy distortions of the structure above. • Laterally spreading soil deposits due to liquefaction, which can also include a nonliquefied crust, exert large loads and displacements on piles. This mode of failure can result in pile damage due to shearing and exceeding bending moments. • A loss of bearing capacity can be observed when the soil along the pile shaft softens due to strain softening and liquefaction. In case of pile groups subjected to a loss of bearing capacity, the inertial forces of the superstructure induce rocking modes, causing large and irregular settlements, punching failures, and tensile pullout failures. • A variation of stiffness with depth of the soil or soil layers with different stiffness can cause the piles to be subjected to damaging bending strains, particularly at the interfaces of strong impedance contrast. An interface of strong impedance contrast can also be provided by soil layers undergoing liquefaction or strain softening during earthquakes. • Pile head shear failures often occur due to an inadequate structural design of the connections between pile and cap. To accommodate large lateral loads, inclined piles, so-called battered piles, are often used in foundation design. In case of a strong earthquake, battered piles attract large horizontal forces due to the high system stiffness that can hardly be sustained by the pile heads and pile caps. In such cases, this failure mechanism can be prevented by more ductile types of foundation and by avoiding battered piles, allowing large strains while dissipating energy.

6.2. Failure Modes and their Prevention

215

Lessons were learned by the numerical as well as the experimental investigation. Limitations of the current building codes and recommendations in order to improve the existing codes, i.e. SFSI, have to be taken into account.

Chapter 7 Summary and Perspectives Predicting the behaviour of structures during strong earthquakes remains an ambitious task for the engineer, especially when the soil supporting the structure and its foundation experiences liquefaction or softening. The state-of-the-art methodologies are inadequate in order to include soil-foundation-structure interaction (SFSI ) effects in assessing seismic performance of such structures, although they are improving. The state-of-practice still over-simplifies the behaviour of the soil or even neglects it. SFSI can have a major influence on the seismic performance of important structures such as critical infrastructure (i.e. power plants, harbours, dams, industrial facilities, etc.), lifelines (i.e. pipelines, bridges, etc.) as well as private and public property, and, can thus affect public safety. A better understanding of the interaction of structures and their foundations with the soil is an important prerequisite for determining the dynamic behaviour of structures founded on liquefiable or soft soils. This thesis proposes experimental as well as numerical procedures to better understand and simulate the behaviour of piles and pile groups interacting with the soil during monotonic, alternating as well as dynamic horizontal loading. The applied numerical methods are represented by a hypoplastic and a visco-hypoplastic constitutive model for hard- and soft fine-grained soils, respectively. Material parameters and state variables are strictly separated in these constitutive models. Hypoplastic as well as visco-hypoplastic parameters can either be determined easily from simple laboratory tests, or can be empirically estimated from the granulometric properties of the soil. The parameter determination is presented in detail within this dissertation. The constitutive laws consider the dependency of the incremental stiffness of the soil on its state, viz. density, pressure, and remnants of deformation history. Visco-hypoplasticity additionally considers the rate of deformation. The main objective of this research was to develop a methodology to predict the SFSI

217

218

Chapter 7. Summary and Perspectives

under monotonic, alternating, and dynamic loading by a unified numerical approach, in the literature known as direct approach under application of the finite element method (FEM ), also referred to as the complete finite element approach. For this purpose, several laboratory model tests have been performed under well-defined boundary conditions. Subsequently, their results have been compared with computational simulations. In most cases, a close resemblance of the computed and the measured results has been obtained. In order to investigate systematically the soil-foundation interaction behaviour, firstly single piles were loaded horizontally under quasi-static conditions. For this purpose, smallscale experiments in a 60-litres-barrel were carried out and, subsequently, calculated by means of 3D FE models. An upscaling of these numerical small-scale models towards full-scale completed the validation of the proposed models under full-scale conditions and made it possible to successfully calculate an in-situ horizontal pile test programme under quasi-static alternating loading carried out by Matlock et al. [Ert83]. In a second part, single piles and pile groups are loaded dynamically. For this purpose, model piles in sand and clay were investigated with the shake table and, subsequently, calculated by means of FEM. Finally, a numerical study is presented in order to investigate the SFSI considering different types of foundations. In detail: In the small-scale model tests in the 60-litres-barrel, single piles are installed in dry, loose to dense sand, and saturated silty clay. The model piles are deflected at their pile heads, under load-control as well as under deflection-control. The results of the numerical calculations show that the applied models are capable to successfully simulate the experiments. The instrumentation of the model piles allows an insight beneath the ground surface: the distribution of the time-dependent pile bending moments, inclinations, as well as deflections was determined by integrating the strain along the pile. These results are validated by comparison with the recorded deflections of the pile tip, which coincides for deflections of ±50 mm. Some details of the numerical models, especially due to discrepancies in the formulation of the boundary conditions in order to simplify the problem, leave room for improvement. The pile-soil contact formulation works well in terms of the accuracy of the results, using a so-called exponential soft contact definition. However, in terms of cost and stability, it is very time-consuming and not always numerically stable. A finer discretisation of the contact surfaces between pile and soils in most cases does not bring any relief; sometimes it has even the opposite effect. However, a very fine time discretisation by reason of convergence is mandatory. An upscaling towards geotechnically relevant dimensions is instantly possible. This is adequately justified by using constitutive relations, i.e. hypoplasticity and visco-hypoplasticity, being valid within a wide range of effective pressures. As a result, the application of the presented models works well for the geotechnical design of horizontally loaded piles and pile foun-

219

dations and the assessment of existing eventually damaged pile foundations in order to justify rehabilitation or a retrofit. The results of the numerical calculations of the in-situ pile load tests show that the applied models also work well under large-scale dimensions. The interpretation of the 3D analysis provides not only the evolution of the state of the soil in the near-field of the test pile, but also a realistic development of the gap between soil and pile. Even the large-scale test itself in-situ is not able to give such an insight into the problem. In this way, bending moments at positions and in periods not recorded can be evaluated. Matlock [Ert83] actually used the test results in order to adapt empirically the so-called p-y method under consideration of different pile head restrained conditions. For every change in the boundary conditions in this manner, the response of the system and, thus his empirical factors for p-y relations, are changed. Such over-simplified methods are still used to date for design purpose. The results of the presented numerical models demonstrate a much more realistic and comprehensive approach. A direct transfer to different and more complex examples, viz. pile groups and foundations with superstructures, excitation from below like earthquakes will be legitimate. Furthermore, the causes and mechanism of damages can be investigated and examined more closely. Possible hidden damages can be revealed numerically. In a hinged laminar box mounted on a shake table, piles and pile groups were investigated, installed in dry or saturated loose to dense sand, with or without a covering clay layer, as well as in saturated clay, unconsolidated and fully consolidated. The piles and the soils were loaded horizontally and dynamically from the base with sinusoidal as well as earthquake loading records. The extensive instrumentation of the experimental setup rendered it possible to record time-dependent soil displacements, vertical displacements at the soil surface, pile bending strains, the lateral force, and the lateral deflection at the pile tip, and pore water pressures in the soil specimen during the experiment. Thus, the state of the soil and the piles can be evaluated at any time. The shake table experiments constitute an excellent database in order to validate numerical models. Shortcomings in numerical models can be uncovered by means of the experiments, and vice-versa in case of validation. Accordingly, improvements can be realised. Some results show that the increase of pore water pressure is too fast, which could be improved by means of coupled instead of undrained conditions. For the very fast drainage in the experiments, either the opening of erosion channels has to be taken into consideration or the lateral filtration between soil and laminar box has to be reduced. In other experiments and their numerical calculations, the results show the total loss of effective pressures, i.e. liquefaction. The grain skeleton transforms into a suspension, which cannot be described by the used constitutive relations, i.e. a crossover is needed from soil mechanics towards fluid mechanics. In

220

Chapter 7. Summary and Perspectives

the numerical models, the contact formulation between soil and pile had to be improved in order to stabilise and accelerate the analysis. In addition, the laminar box boundary conditions are rather complex and not easy to implement, thus for the time being a periodic boundary condition is used. The numerical calculations demonstrate that, by means of the applied constitutive relations and known properties, state of the soil and boundary conditions, single piles and pile groups can be simulated under dynamic and horizontal loading. Simultaneously, important information is determined about the change of state of the soil, liquefaction potential, and plastic deformation. Correspondingly, the application of the presented models is examined in order to design or assess pile foundations under dynamic load conditions. Finally, a seismic soil-foundation-structure interaction analysis using FEM has been carried out to investigate different types of foundations. By means of the presented direct SFSI approach, it is possible to determine the influence of local site effects on the ground response, considering the soil type, state (i.e. density, pressure, and remnant of loading history), and earthquake characteristics as well as geological and hydrogeological peculiarities. The method is capable to investigate the vulnerability of foundations and their superstructures, in particular the susceptibility against liquefaction of the soil in the vicinity of the foundation, and its consequence for the behaviour of the foundation as well as the dynamic response of the structure. Thus, stability and serviceability (i.e. permanent displacements and tilting, and excessive soil movements in the vicinity) of different types of structures and foundations, as well as the success of soil improvement measures, can be systematically investigated. Based on the outcomes the engineer is able to decide, which type of foundation and structure adjusts better to the local site conditions and, subsequently, an adaptive design can lead to optimised foundations.

Chapter 8 Zusammenfassung und Ausblick Das Verhalten von Bauwerken während starker Erdbeben vorherzusagen, stellt nach wie vor eine anspruchsvolle Aufgabe f¨ ur den Erdbebeningenieur dar. Vor allem dann, wenn der Boden dem Bauwerk und seiner Gr¨ undung keinen Halt mehr bietet, weil er sich aufgrund der seismischen Einwirkung verfl¨ ussigt oder erweicht. Der Stand der Wissenschaft zur Bestimmung der Erdbebensicherheit von Bauwerken unter Ber¨ ucksichtigung der BodenBauwerk-Gr¨ undungs-Interaktion (engl. soil-foundation-structure interaction, kurz SFSI ) ist, obwohl er sich in den letzten Jahren verbessert hat, noch immer unzulänglich. In der Praxis wird das Verhalten des Bodens noch immer stark vereinfacht - wenn nicht gar ignoriert. Die SFSI kann einen maßgeblichen Einfluss auf das seismische Verhalten von bedeutenden Konstruktionen, wie verletzlicher Infrastruktur (d. h. Kraftwerken, Häfen, Staudämmen, Industrie, etc.), Lebensadern (d.h. Pipelines, Br¨ ucken, etc.) sowie privatem und öffentlichem Eigentum haben, und somit in starkem Maße die öffentliche Sicherheit betreffen. Ein genaues Verständnis der Interaktion zwischen der Struktur, ihrer Gr¨ undung und dem Boden ist eine unerlässliche Voraussetzung, um die dynamische Antwort von Konstruktionen, die auf verfl¨ ussigungsempfindlichen oder weichen Böden gegr¨ undet sind, zu bestimmen. Diese Arbeit schlägt experimentelle und auch numerische Verfahren vor, um das Verhalten von Pfählen und Pfahlgruppen im Boden während monotoner, alternierender und dynamischer Horizontalbeanspruchung besser nachzubilden. Die verwendeten numerischen Methoden wurden mit Hilfe eines hypoplastischen Stoffgesetzes f¨ ur hartkörnige und eines viskohypoplastischen Stoffgesetzes f¨ ur weichkörnige Böden umgesetzt. Materialparameter und Zustandsgrößen werden in diesen Stoffgesetzen streng voneinander getrennt. Hypoplastische und viskohypoplastische Parameter können entweder mit Hilfe von einfachen Laborversuchen bestimmt oder aufgrund granulometrischer Eigenschaften des Bodens empirisch abgeschätzt werden. Die Bestimmung der Parameter wird in Kapitel 3 detailliert vorgestellt. Die Stoffgesetze ber¨ ucksichtigen die

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224

Chapter 8. Zusammenfassung

Abhängigkeit der inkrementellen Steifigkeit des Bodens von seinem Zustand, d. h. Dichte, Druck und Deformationsgeschichte. Die Viskohypoplastizität ber¨ ucksichtigt dar¨ uber hinaus noch die Deformationsrate. Das wissenschaftliche Hauptziel dieser Arbeit war es, eine Methode zu entwickeln, die die Boden-Gr¨ undung-Bauwerk Interaktion unter monotoner, alternierender und dynamischer Einwirkung mit Hilfe eines umfassenden numerischen Ansatzes, in der angloamerikanischen Literatur als direct approach bekannt, unter Anwendung der Finiten Elemente Methode (FEM ) analysiert. Parallel dazu wurden verschiedene Experimente mit Pfählen und Pfahlgruppen im Labor unter eindeutig definierten Randbedingungen durchgef¨ uhrt. Anschließend wurden ihre Ergebnisse mit Computersimulationen verglichen. In den meisten ¨ Fällen wurde eine gute Ubereinstimmung der berechneten mit den gemessenen Ergebnissen erreicht. Zunächst wurden Einzelpfähle unter quasi-statischen Randbedingungen horizontal beansprucht, um systematisch die Boden-Gr¨ undungs-Interaktion zu untersuchen. Zu diesem Zwecke wurden kleinmaßstäbliche Modellversuche in einem 60-Liter-Fass durchgef¨ uhrt, die anschließend mit Hilfe dreidimensionaler FE Modelle nachgerechnet wurden. Ein Hochskalieren der kleinmaßstäblichen numerischen Modelle hin zum Originalmaßstab in-situ erfordert die Validierung der vorgeschlagenen Modellierung auch unter originalmaßstäblichen Verhältnissen. Es ermöglicht so eine erfolgreiche Nachrechnung eines in-situ Versuchsprogramms (durchgef¨ uhrt von Matlock et al. [Ert83]) an horizontal beanspruchten Stahlrohrpfählen unter quasi-statischer alternierender Einwirkung und variierender PfahlkopfRandbedingung. In einem weiteren Teil der Arbeit wurden Einzelpfähle sowie dar¨ uber hinaus auch Pfahlgruppen dynamisch beansprucht. Hierf¨ ur wurden Modellpfähle in Sand und Ton auf dem Sch¨ utteltisch untersucht. Nachfolgend wurden auch diese Versuche mit Hilfe der FEM nachgerechnet. Abschließend wird eine numerische Studie präsentiert, die die SFSI unter Ber¨ ucksichtigung verschiedener Gr¨ undungsarten ermöglicht. Genauer gesagt, wurden in einem kleinmaßstäblichen Modellversuch in einem 60-LiterFass Einzelpfähle in trockenem lockerem Sand, trocknem dichten Sand und gesättigtem schluffigen Ton untersucht. Die Pfähle wurden an ihren Pfahlköpfen ausgelenkt, und zwar einerseits kraftgesteuert, andererseits weggesteuert. Die Ergebnisse der numerischen Nachrechnungen zeigen, dass die angewandten Modelle geeignet sind, Experimente auf zufriedenstellende Weise zu simulieren. Die Instrumentierung der Modellpfähle erlaubt auch einen Einblick unter die Bodenoberfläche in die Verteilung des zeitabhängigen Biegemoments entlang des Pfahls, die Verdrehungen des Pfahls u ¨ber seine Länge durch einfache Integration und auch die zeitabhängigen Biegelinien durch zweifache Integration der entlang des Pfahls gemessenen Dehnungen. Diese Ergebnisse wurden durch den Vergleich mit den aufgenommenen zeitabhängigen Verschiebungen des Pfahlkopfes, der perfekt f¨ ur

225

Verschiebungen im Bereich von ±50 mm u ¨bereinstimmt, verglichen und validiert. Einige Details der numerischen Modelle lassen noch Raum f¨ ur Verbesserungsmöglichkeiten, vor allem bedingt durch die Unterschiede in der Formulierung der Randbedingungen. Die Boden-Pfahl Kontaktformulierung unter Verwendung einer so genannten exponentiellen soft-contact-Formulierung funktioniert hinsichtlich ihrer Genauigkeit gut. In Hinblick auf die erforderlichen Rechenzeiten und die numerische Stabilität ist die verwendete Kontaktformulierung jedoch relativ zeitraubend und nicht immer stabil. Eine feinere Diskretisierung der Kontaktflächen zwischen Pfahl und Boden bringt in den meisten Fällen keine Linderung, oft hat diese gar den gegenteiligen Effekt. Eine sehr feine Zeitdiskretisierung ist hingegen notwendig und zielf¨ uhrend. Eine Hochskalierung in Richtung geotechnisch relevanter Dimensionen ist ohne weiteres möglich. Eine Anwendung und das Einhalten von Modellgesetzen sind nicht erforderlich. Dies ist auch hinreichend gerechtfertigt, da Stoffgesetze, und zwar im Rahmen von Hypoplastizität und Visko-hypoplastizität, Anwendung fanden, welche in einem breiten Bereich von Spannungen und Verformungen g¨ ultig sind. Daher eignen sich die vorgestellten Modelle zur geotechnischen Dimensionierung horizontal beanspruchter Pfähle und Pfahlgr¨ undungen. Dar¨ uber hinaus können auch bestehende Pfahlgr¨ undungen mit Hilfe dieser Modelle beurteilt werden, um beispielsweise eine Sanierung oder Nachr¨ ustung bestehender Gr¨ undungen zu rechtfertigen. Die Ergebnisse der numerischen Berechnungen der horizontalen in-situ Pfahlprobebelastungen zeigen, dass die angewandten Modelle ebenfalls gut unter großmaßstäblichen Bedingungen funktionieren. Die Interpretation der dreidimensionalen Analyse liefert nicht nur die Entwicklung der Bodenzustandsgrößen im Nahfeld des Probepfahls sondern auch die realitätsnahe Entwicklung eines Spalts zwischen Boden und Pfahl. Die horizontale Probebelastung selbst ist nicht in der Lage, solch einen Einblick in das Problem zu liefern. In diesem Sinne könnten auch Biegemomente an Stellen und zu Zeitpunkten ermittelt werden, die nicht durch das Messprogramm erfasst waren. Matlock [Ert83] hingegen verwendete seine Untersuchungen, um die so genannte p-y Methode (Bettungskurvenmethode) unter Ber¨ ucksichtigung unterschiedlicher Pfahlkopf-Randbedingungen empirisch anzu¨ passen. Durch jede Anderung der Randbedingungen wurden so die Antwort des Systems und damit auch die entsprechenden empirischen Faktoren verändert. Matlocks stark vereinfachte Methoden werden noch immer zur Dimensionierung von Pfahlgr¨ undungen herangezogen. Die Ergebnisse der gezeigten numerischen Modelle stellen einen umfassen¨ den und zugleich realitätsnahen Ansatz dar. Eine unmittelbare Uberf¨ uhrung in Richtung anderer und komplexerer Beispiele, beispielsweise Pfahlgruppen, Pfahlplattengr¨ undungen, komplette Bauwerke, oder eine Anregung von unten, wie sie bei Erdbeben der Fall ist, erscheint gerechtfertigt. Dar¨ uber hinaus können mit dieser Methode Ursachen und Mechanismen von Schäden genauer untersucht werden. Mögliche versteckte Schäden an Pfählen

226


können mit den vorgestellten Methoden aufgedeckt werden. In einer neuartigen Laminarbox auf einem Sch¨ utteltisch wurden Pfähle und Pfahlgruppen in trockenem lockerem Sand, trockenem dichten Sand, gesättigtem lockeren Sand, gesättigtem dichten Sand, mit und ohne Tonabdeckung und gesättigtem Ton, jeweils unkonsolidiert und auskonsolidiert, untersucht. Die Pfähle und die Böden wurden horizontal und dynamisch von der Basis mit einer Sinusschwingung und auch mit einem Erdbebensignal beansprucht. Die umfassende Instrumentierung des Versuchsaufbaus machte es möglich, zeitabhängige Bodenbewegungen in acht Höhen u ¨ber dem Probenkörper, vertikale Verschiebungen an zwei Stellen der Bodenoberfläche, Biegedehnungen des Testpfahls, Horizontalverschiebungen des Pfahlkopfes sowie den Porenwasserdruck an drei Stellen der Bodenprobe während des Experiments zu untersuchen. Dadurch konnten der Zustand des Bodens, die Biegemomente, die Verdrehungen und die Verschiebungen entlang des Pfahls zu jedem Zeitpunkt bestimmt werden. Die Sch¨ utteltischversuche stellen eine exzellente Datenbasis dar, um numerische Modelle zu validieren. Unzulänglichkeiten numerischer Modelle können mit Hilfe der Experimente aufgedeckt werden - und sogar umgekehrt, soweit die Modelle bestätigt sind. Dementsprechend können Verbesserungen umgesetzt werden. Einige Ergebnisse zeigen, dass der Porenwasserdruck im numerischen Modell zu schnell ansteigt. Dieses Verhalten könnte mit Hilfe einer gekoppelten anstatt der verwendeten undrainierten dynamischen Berechnung verbessert werden. Um die sehr schnelle Drainage im Experiment zu ber¨ ucksichtigen, kann entweder die Entwicklung von Erosionskanälen in der Simulation ber¨ ucksichtigt werden, oder seitliche Umläufigkeiten zwischen Boden und Laminarboxwand im Versuch m¨ ussen vermindert werden. Andere Experimente und ihre numerische Simulation zeigen den totalen Verlust der effektiven Dr¨ ucke, d.h. eine so genannte Verfl¨ ussigung des Bodens tritt ein. Dabei verwandelt sich das Kornger¨ ust in eine Suspension, deren Verhalten nicht mit Hilfe der verwendeten Stoff¨ gesetze beschrieben werden kann. Folglich ist ein Ubergang von der Bodenmechanik zu Fluidmechanik erforderlich. Bei den numerischen Modellen m¨ usste die Formulierung des Kontakts zwischen Boden und Pfahl verbessert werden, um die Berechnungen zu stabilisieren und zu beschleunigen. Auch sind die Randbedingungen bei der Laminarbox ziemlich komplex und nicht einfach zu implementieren. Daher wurde zunächst eine periodische Randbedingung verwendet. Die numerischen Berechnungen zeigen, dass mit Hilfe der verwendeten Stoffgesetze mit bekannten Bodenparametern, Bodenzustandsgrößen und bekannten Randbedingungen sowohl Einzelpfähle als auch Pfahlgruppen unter dynamischer Horizontalbeanspruchung im Wesentlichen zutreffend simuliert werden können. Gleichzeitig können wichtige Angaben u ussigungsneigung ¨ber Zustandsänderungen, Verfl¨ und bleibende Verformungen gemacht werden. Somit hat sich das numerische Modell f¨ ur den Einsatz zur Dimensionierung und Ert¨ uchtigung von Pfahlgr¨ undungen unter dynami-

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scher Beanspruchung bewährt. Abschließend wurde eine seismische SFSI Analyse unter Verwendung der FEM zur Untersuchung verschiedener Gr¨ undungsvarianten durchgef¨ uhrt. Mit dem vorgestellten direkten SFSI Ansatz ist es möglich, den Einfluss von Ortseffekten auf die Bodenantwort unter Ber¨ ucksichtigung des Bodentyps, des Bodenzustands (d. h. Dichte, Druck und Spuren der Belastgeschichte), der Erdbebencharakteristik wie auch geologischer und hydrogeologischer Besonderheiten zu untersuchen. Mit dieser Methode ist man in der Lage, die Verletzlichkeit von Gr¨ undungen und ihrer dar¨ uberliegenden Bauwerke zu untersuchen, d. h. die Verfl¨ ussigungsneigung des Bodens in der Nähe einer Gr¨ undung und die Auswirkungen auf das Verhalten der Gr¨ undung wie auch die dynamische Antwort der Struktur. Folglich können auch die Stabilität und die Gebrauchstauglichkeit (d. h. bleibende Verschiebungen und Verdrehungen, u ¨bergroße Bodenbewegungen in der Nähe der Gr¨ undung) von verschiedenen Gr¨ undungsvarianten und Bauwerken wie auch der Erfolg von Bodenverbesserungsmaßnahmen systematisch untersucht werden. Aufgrund der Ergebnisse der Untersuchungen ist der Erdbebeningenieur in der Lage zu entscheiden, welche Gr¨ undungsvariante und welches Bauwerk besser zu den örtlichen Gegebenheiten passen. Folglich kann eine geeignete Bemessung zu einer optimierten Gr¨ undungsvariante f¨ uhren.

Nomenclature A

constant, see equation (3.14), page 46

a

constant depending on ϕc , see equation (3.19), page 48

α

exponent, see equation (3.10), page 45

αh

empirical factor to determine the modulus of horizontal subgrade reaction, see equation (2.2), page 18

β

exponent, see equation (3.15), page 47

β0

factor to calculate the exponent, see equation (3.16), page 48

Cc

compression index, see equation (3.6), page 42

D

pile diameter or pile width, see equation (2.2), page 18

δ

intergranular strain tensor, see equation (3.1), page 40

∆h

maximum grid spacing, see equation (2.9), page 29

∆t

maximum time step, see equation (2.10), page 30

e

void ratio, see equation (3.4), page 42

ee0

reference void ratio on the reference isotach, see equation (3.39), page 57

Ep

modulus of elasticity of the pile, see equation (2.3), page 18

ec0

void ratio in the critical state at zero pressure, see equation (3.9), page 44

ed0

minimum void ratio at zero pressure, see equation (3.8), page 44

ei0

maximum void ratio at zero pressure, see equation (3.8), page 44

ε˙

rate of strain, see equation (3.1), page 40

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230


ε˙ v

viscous strain rate tensor, see equation (3.2), page 40

ε50

strain at 50% of the maximum principal stress difference, see equation (2.7), page 20

η

factor to determine pe , see equation (3.37), page 57

fd

scalar factors of the hypoplastic constitutive relation, see equation (3.18), page 48

fmax highest relevant frequency, see equation (2.9), page 29 Γi [ee0 , pe0 , ε˙e0 ] triple defining the reference isotach, see equation (3.33), page 56 hs

granulate hardness, see equation (3.5), page 42

Ip

moment of inertia of the pile section, see equation (2.3), page 18

[Is ]

n + 1 by n + 1 matrix of soil-displacement influence factors determined by the integration of Mindlin’s equation in elasticity theory, see equation (2.8), page 22

Iv

viscosity index introduced by Leinenkugel [Lei76], see equation (3.28), page 53

K0

oedometric stress ratio, see equation (3.25), page 51

kh

modulus of horizontal subgrade reaction, see equation (2.2), page 18

ks

modulus of horizontal soil reaction, see equation (2.1), page 18

κ

swelling coefficient, see equation (3.23), page 50

λ

coefficient of virgin compression, see equation (3.22), page 50

λmin minimum wavelength, see equation (2.9), page 29 M

slope of the critical state line, see equation (3.35), page 57

mi

factor to calculate β0 , see equation (3.20), page 48

n

exponent for pressure dependence, see equation (3.7), page 43

ni

factor to calculate β0 , see equation (3.21), page 48

νp

peak dilatancy angle, see equation (3.13), page 46

{p}

column vector of the horizontal loading between the soil and the pile in elasticity theory, see equation (2.8), page 22

pe

equivalent pressure, see equation (3.36), page 57

pult

ultimate soil resistance per unit length of the pile, see equation (2.6), page 20

ϕc

angle of internal friction in the critical state of the soil, see equation (3.3), page 41

re

relative void ratio, see equation (3.11), page 45

σ

effective stress tensor, see equation (3.0), page 40

σ˙

rate of effective stress tensor, see equation (3.1), page 40

v

wave velocity, see equation (2.9), page 29

εe0

reference strain rate, see equation (3.31), page 56

y

lateral deflection of the pile, see equation (2.3), page 18

{ys }

column vector of the soil displacements in elasticity theory, see equation (2.8), page 22

y50

deflection at one-half the ultimate soil resistance, see equation (2.6), page 20

z

vertical depth, see equation (2.3), page 18

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Appendix A Diagrams - Shake Table Experiments Laminar Box Setup SP-S1L

SP-S2D

single pile with sand

single pile with sand

8

single pile

cm

Karlsruhe sand


PWD1 h=52cm

75 cm ∆s=2.1 cm

Karlsruhe sand

60 cm

54 cm

80

PWD2 h=30cm m

m 1c

60 cm


PWD1 h=52cm PW PWD2 h=8cm m

m 2

c 11

75 cm

single pile

m 0c

51.9 cm

A.1

11

cm 21

cm

20 cm 30 cm 40 cm

20 cm 30 cm 40 cm

Figure A.1: Experimental setup of the single pile installed in saturated sand before (first experiment SP-S1L) and after (last experiment SP-S2D) the experimental programme

251

Appendix A. Diagrams - Shake Table Experiments

SP-SC1L single pile sand & clay


single pile sand & clay

single pile

m 0c


11

cm

m

c 21

75 cm

10.5 cm

PWD1 h=55cm PWD2 h=53cm PWD3 h=6cm

Karlsruhe sand

47 cm

51.5 cm

10.5 cm

8

∆s=4.5 cm

80

60 cm Konstanz lacustral clay cu = 2.49 kPa w = 0.290


SP-SC2D

single pile

cm

sand sand boils

water 60 cm Konstanz sand lacustrine clay cu = 4.23 kPa w = 0.238

Karlsruhe sand

PWD1 h=55cm PWD2 h=47cm m

20 cm 30 cm 40 cm

75 cm

252


20 cm 30 cm 40 cm

Figure A.2: Experimental setup of the single pile installed in saturated sand covered by a clay layer before (first experiment SP-SC1L) and after (last experiment SP-SC2D) the experimental programme




single pile m 0c

80

PWD2 h= 45cm


11

20 cm 30 cm 40 cm

single pile

cm

60 cm

PWD1 h=52cm 58.9cm

64.5 cm

PWD1 h=52cm

75 cm ∆s=5.6cm

8

60 cm


SP-C2D

75 cm

SP-C1L

PWD2 h=45cm


PWD3 h=6cm

m 1c

cm 2

11

cm 21

cm

20 cm 30 cm 40 cm

Figure A.3: Experimental setup of the single pile installed in saturated clay before (first experiment SP-S1L) and after (last experiment SP-S2D) the experimental programme

A.1. Laminar Box Setup

253




pile group

m

c 80

PWD1 h= 52cm PWD2 h=45cm


6c cm 20 cm 30 cm 40 cm

11

cm

21

cm

75 cm

Karlsruhe sand

49.8 cm 10.5 cm

52.5 cm

10.5 cm

8

∆s=2.7 cm

m 0c

60 cm Konstanz lacustrine clay cu = 2.5 kPa w = 0.29


PG-SC2D

water 60 0 cm c Konstanz lacustrine clay cu = 4.4 kPa w = 0.24 PWD1 h=52cm PWD2 h=48,8cm

pile group sand sand boils sand

75 cm

PG-SC1L

Karlsruher sand e = 0.74 γs = 26.5 KN/m³ γ' = 9.45 KN/m³ γd = 15.2 KN/m³ PWD3 h=6cm V = 0.239 m³ m cm 21 c 11 20 cm 30 cm 40 cm

Figure A.4: Experimental setup of the pile group installed in saturated sand covered by a clay layer before (first experiment PG-SC1L) and after (last experiment PG-SC2D) the experimental programme



pile group in clay unconsolidated

pile group in clay fully consolidated

cm 80 pile group

75 cm

80

PWD1 h=48cm PWD2 h= 47cm PWD3 h=6cm

Konstanz lacustrine clay cu = 2.6 kPa w = 0.29 11

20 cm 30 cm 40 cm

cm

21

48.6 cm

52.2 cm

60 cm


PG-C3D

∆s = 3.6 cm

PG-C1L

cm

pile group 75 cm

254

60 0 cm m

PWD1 h=48cm PWD2 h= 47cm


cm 11

cm

21

cm

20 cm 30 cm 40 cm

Figure A.5: Experimental setup of the pile group installed in saturated clay before (first experiment PG-C1L) and after (last experiment PG-C2D) the experimental programme

A.2. Protocols of Shake Table Experiments

A.2

Protocols of Shake Table Experiments Table A.1: Test: SP-SC1L Date:25.05.’05 events time A4 13:51 B3 B4

13:55 13:57

C1

14:11

C2

14:16

description drainage of small amount of water between soil and laminar box boundary Evolution of sand boil at the surface Liquefaction of the soil specimen rapid flooding of the complete soil surface rinse of sand-water suspension along the laminar box boundary fast drainage of water together with air bubbles

Table A.2: Test: SP-SC2D Date:25.05.’05 events time B3 16:00 B4 T1

description fast drainage of water with rapid flooding of the complete soil surface 16:04 development of gap between pile and soil with fast drainage of water 16:18 pile oscillate with characteristic own-value amplitude and frequency

255

256


Table A.3: Test: SP-C1L Date:10.06.’05 events time B3 11:48 B4

11:49

C2

11:51

C3

11:51

S4

12:10

description pile oscillate with characteristic own-value amplitude and frequency development of gap between pile and soil with fast drainage of water from left side increase of gap between pile and soil dilatation of the ground surface and separating the pile from the soil increase of the pile oscillation with pile gap amplification

Table A.4: Test: SP-C2D Date:13.06.’05 events time A2 12:12 B2 B3

12:18 12:19

B4 C2

12:20 12:25

C3 S4 S5

12:27 12:37 12:38

description small drainage of water on one pace-doubtful separating the pile from the soil own-value oscillation of the pile with small drainage of water gap between pile and soil drainage of water with further amplification of the pile gap increase of the pile oscillation separating the pile from the soil dilatation of the ground surface in vicinity of the pile

A.2. Protocols of Shake Table Experiments

Table A.5: Experiment: PG-SC1L Date:16.06.’05 events time B3 14:24 B4

14:25

C1 C2 C3 S5

14:38 14:45 14:54 15:15

description drainage of water from the left side of the ground surface Liquefaction of the soil specimen with rapid drainage of water Evolution of sand boil at the surface rapid flooding of the whole soil surface rapid flooding of the whole soil surface development of gap in vicinity of the pile-group

Table A.6: Experiment: PG-SC2D Date:17.06.’05 events time description A4 16:40 pile-group oscillate with characteristic own-value amplitude and frequency B3 16:43 separating the pile from the soil begin from the gap-formation B4 16:43 amplification of the gap with further increase of the pile oscillation C2 16:46 pile-group oscillate with characteristic own-value amplitude and frequency C3 16:47 rapid drainage of water from the gap S2 17:02 amplification of the gap with dilatation of the ground surface S3 17:02 amplitude is lower S4 17:02 same event like S2

257

258


Table A.7: Experiment: PG-C1L Date:21.06.’05 events time A4 10:43 B2

10:47

B3

10:48

B4

10:51

C2

10:54

description pile-group oscillate with characteristic own-value amplitude and frequency development of gap at little amplitude and high frequency amplification of the gap with dilatation of the ground surface loosening of the whole soil material with soil-degradation in vicinity of pile-group increase of the gap between pile-group and soil

Table A.8: Experiment: PG-C2D Date:24.06.’05 events time A3 11:06 A4

11:07

B2

11:09

B3

11:10

B4

11:11

C2

11:14

C3 S4 S6

11:15 11:53 11:56

description drainage of water from one drain in vicinity of pile-group pile-group oscillate in short sequences with little amplitude development of own-value oscillations of the pile group development of gap between pile-group and soil liquefaction with amplification of the gap and dilatation of the ground surface rapid drainage of water from the gap between pile-group and soil increase of the gap further increase of the gap dilation of the soil material with soil-degradation in vicinity of pile-group

A.3. Shake Table Displacements during the Experiments

A.3

259

Shake Table Displacements during the Experiments SB050525.mea.asc

frequency = 28 mHz C2 C1

B4


B1 B2

A2

A1

20

SP-SC1L

B3

A3

40

0

0

500

amplitude

1000 time [s]

1500

3.0 V

1.5 V

1.5 V

0.75 V

0.375 V

1.5 V

3.0 V

-60

0.75 V

-40

3.0 V

-20

0.375 V



A4

14 mHz*

60

2000

Figure A.6: Table displacements vs. time of the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer

260


S0505252.mea.asc

S2

S1

T3

S4

S3

B4


B3

200 mHz ... 1.2 Hz

T1

SP-SC2D

40 20

200 mHz

S5 S6 S7 S8 S9

Loma Prieta

0 -20 sinus wave

-40 -60

3.0 V

1.5 V


60

10mHz ...

T2

frequency = 28 mHz

amplitude 3.0 V

0.375 V..3.0 V

0

200

400

600

800 time [s]

1000

1200

1400

Figure A.7: Table displacements vs. time of a shake table experiment investigating a single pile installed in dense saturated sand with a covering clay layer

S050609B.mea.asc

S4

800 mHz

sinus wave

S1

single pile in clay

S3

SP-C1L

C1

B3 B2

200 400

B1

A1 A2

20

100

S2

C3

B4

A4 A3

40

0 -20

0

500

1000

1500

3.0 V

3.0 V 1.5 V 3.0 V 1.5 V 3.0 0V

1.5 V

3.0 V

3.0 V

0.375 V 0.75 V 1.5 V

1.5 V

0.75 V

-60

3.0 V

amplitude

-40 0.375 V


frequency = 28 mHz


C2

14 mHz*

60

2000

2500

time [s]

Figure A.8: Table displacements vs. time of a shake table experiment using a single pile installed in unconsolidated clay


261

S050613A.mea.asc

S5

S4

S3

S2

sinus wave

C1

B3

800 1200 mHz

B1 B2

A2

A1

20

B4

single pile in clay

200 400

S1

A4

SP-C2D

A3

40

0 -20

500

1000 time [s]

1.5 V

1.5 V 3.0 V

3.0 V

1.5 V

3.0 V

1.5 V

3.0 V

1.5 V

0.375 V 0.75 V

1.5 V

0

3.0 V

0.75 V

-60

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

amplitude

-40 0.375 V



frequency = 28 mHz C2 C3

14 mHz*

60

100

1500

2000

Figure A.9: Table displacements vs. time of a shake table experiment using a single pile installed in fully consolidated clay

S050616A.mea.asc

S5

S4

S3

S2

S1

C2

C1

B3 B2

A1

20

sinus wave

B1

A2

A3

40

C3


A4

B4


0

0

1000

3000

1.5 V 3.0 V

3.0 V

3.0 V

2000 time [s]

1.5 V 3.0 V

amplitude

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

- 60

1.5 V

-40

0.375 V 0.75 0.7 7 V 1.5 V 3.0 V

-20 0.375 V 0.75 V 1.5 V 3.0 V


60

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

4000

Figure A.10: Table displacements vs. time of a shake table experiment applying a pile group installed in loose saturated sand with a covering clay layer

262


S050617A.mea.asc

10mHz ...

S2

S3

S1

S4

C1

B3


B2

20

frequency = ca. 1.68Hz

PG-SC2D

B1

A1 A2

A3 A4

40

B4


sinus wave

0

1.5 V

-60

3.0 V 0.375 V 0.75 V 1.5 V

-40

0

amplitude

1.5 V

3.0 V

3.0 V 3.0 V

-20

0.375 V 0.75 V


60

C2 C2

14 mHz* frequency = 28 mHz

0.375 V

500

1000

0.75 V

0.75 V

0.375 V

1500

2000

2500

time [s]

Figure A.11: Table displacements vs. time of a shake table experiment using a pile group installed in dense saturated sand with a covering clay layer

S050621A.mea.asc

C3

PG-C1L

B4

A4


B1

B2

B3

A3 A2

A1

20

C1

pile group in clay

40

0 -20 -40

800

1000

3.0 V

3.0 V

1.5 V

600 time [s]

3.0 V

400

1.5 V

0.75 V

0.375 V

200

3.0 V

0

1.5 V

-60

0.75 V

amplitude 0.375 V


60

frequency = 28 mHz C2

frequency = 14 mHz*

1200

Figure A.12: Table displacements vs. time of a shake table experiment using a pile group installed in unconsolidated clay


263

S050621A.mea.asc

S5

S3

C1

B3

pile group in clay

S4

S2

PG-C2D

B4 C2 C3

A1

20

B1 B2

A2

A3

40

100 200 400 800 1200 mHz

S1


sinus wave

0

-40 -60 0

500

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

1.5 V 3.0 V

A4

-20

0.375 V 0.75 V 1.5 V 3.0 V 0.375 V 0.75 V 1.5 V 3.0 V 1.5 5V 3.0 V 3.0 V


60

frequency

28 mHz

14 mHz*

amplitude

1000

1500

2000 time [s]

2500

3000

3500

4000

Figure A.13: Table displacements vs. time of a shake table experiment applying a pile group installed in fully consolidated clay

S050715A.mea.asc

S5

S4

400 800 1200 mHz

S3

200

S2

C3

C2

100

C1

B1 B2 B3 B4

20

A4

40

pile group in clay

A2

60

PG-C3D

S1

28 mHz

Loma Prieta *real time A3

14 mHz*

A1

sinus wave

0 20

80 0

500

1000

1500

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

3.0 V 3.0 V

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V

0.375 V

60

1.5 V

40

3.0 V

amplitude

0.75 V


80

frequency

2000

2500

time [s]

Figure A.14: Table displacements vs. time of a shake table experiment investigating a pile group installed in fully consolidated clay

264

A.4


Evolution of Pore Pressures during the Experiments SB050525.mea.asc

14

frequency = 28 mHz

Loma Prieta real time

SP-SC1L

12

3.0 V initial pore pressure 1.5 V

3.0 V

1.5 V

6

pwd01 pwd02 pwd03

B1 B2

A4

7

A3

A2

0.75 V

8

A1

9

pore pressure increase

3.0 V 0.375 V 0.75 V

10

B3

11

C1


0.375 V

pore pressure [kPa]

C2

B4

14 mHz*

13

amplitude

5 0

500

1000 time [s]

1500

2000

Figure A.15: Evolution of pore water pressure vs. time of the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer

A.4. Evolution of Pore Pressures during the Experiments

S0505252.mea.asc

12

10mHz

frequency = 28 mHz B4

Loma Prieta

11

200 mHz ...1.2 Hz

200 mHz

SP-SC2D

3.0 V

7 6 5

T2

T1

S7 S8 S9

S5

S2 S3 S4

embedded in clay layer

S1

8

S6

B3

pwd01 pwd02 pwd03

9

T3


10

1.5 V

pore pressure [kPa]

265

sinus wave

amplitude

0.375V ... 3.0V

3.0V

4 0

200

400

600

800 time [s]

1000

1200

1400

Figure A.16: Evolution of pore water pressure vs. time of a shake table experiment investigating a single pile installed in dense saturated sand with a covering consolidated clay layer

S050609B.mea.asc

18

A1 A2

S2

S1

S4

S3

C2 C3

single pile in clay

C1

B4

sinus wave

SP-C1L

12

1.5 V

3.0 V

amplitude

1.5 V

3.0 V

1.5 V

6

0.375 V 0 0.75 V 0.7 1.5 V

8

1.5 V

10

1.5 V 3.0 V

pwd01 pwd02 pwd03

0.375 V 0.75 V 1.5 V

pore pressure [kPa]

14

A3 A4 B1 B2 B3


16

100 200 400 800

frequency = 28 mHz

14 mHz*

4 0

500

1000

1500

2000

2500

time [s]

Figure A.17: Evolution of pore water pressure vs. time of a shake table experiment investigating a single pile installed in unconsolidated clay

266


S050613A.mea.asc

16 frequency = 28 mHz

S4

S5


sin

B1 B2 B3 B4 sin

A4

A2 A3

A1

10

C1 C2 C3

single pile in clay

12

8

1.5 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

1.5 V 3.0 V 3.0 V

3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V

1.5 V

4

3.0 V

amplitude

6 0.375 V 0.75 V

pore pressure [kPa]

SP-C2D

S2


S1

14 mHz*

14

100 200 400 800 1200 mHz

2 500

0

1000 time [s]

1500

2000

Figure A.18: Evolution of pore water pressure vs. time of a shake table experiment investigating a single pile installed in fully consolidated clay

S050616A.mea.asc

C3

PG-SC1L

sinus wave

3.0 V

3.0 V

3.0 V

3.0 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

amplitude

1.5 V

3.0 V

S1 S2 S3

B1

S4

B2

6

0.375 V 0.75 V 1.5 V

A1 A2 A3

8


C2

C1

B3


A4

10

0.375 V 0.75 V 1.5 V 3.0 V

pore pressure [kPa]

B4


12

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

4 0

1000

2000 time [s]

3000

4000

Figure A.19: Evolution of pore water pressure vs. time of a shake table experiment investigating a pile group installed in loose saturated sand with a covering clay layer

A.4. Evolution of Pore Pressures during the Experiments

S050617A.mea.asc

frequency = 28 mHz


A4 B1 B2 B3 B4 C1 C2 C3

PG-SC2D S2


sinus wave

S1

A1 A2 A3

10

frequency = 1.68Hz

10mHz ...

S4

14 mHz*

S3

15

5 pwd01 pwd02 pwd03

0.75 V 1.5 V 3.0 V 0.375 V 0.75 V 1.5 V 3.0 V 1.5 V 3.0 V 3.0 V

0 0.375 V

pore pressure [kPa]

267

amplitude 0.375 V

0.75 V 0.375 V

0.75 V

5 500

0

1000

1500 time [s]

2000

2500

3000

Figure A.20: Evolution of pore water pressure vs. time of a shake table experiment investigating a pile group installed in dense saturated sand with a covering consolidated clay layer

S050621A.mea.asc

20

frequency = 28 mHz

frequency = 14 mHz*

C3

C2

B3

1.5 V

B4

B2

0.75 V

B1

A4

A3

A2

A1

C1

pwd01 pwd02 pwd03


15

0

200

400

600 time [s]

800

1000

3.0 V

3.0 V

1.5 V

3.0 V

1.5 V

amplitude 0.375 V

0

0.75 V

5

3.0 V

10

0.375 V

pore pressure [kPa]


1200

Figure A.21: Evolution of pore water pressure vs. time of a shake table experiment investigating a pile group installed in unconsolidated clay

268


S050621A.mea.asc

frequency

S1

C2

B3

0

pile group in clay

S4

B1 C1

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

S5

pwd01 pwd02 pwd03

C3

B4

A2

5

A4 B2

A1 A3

10

sinus wave

PG-C2D

0 0.375 V 0.75 V 1.5 V 3.0 V 0.375 0 3 5V 0.75 0.7 75 V 1.5 V 3.0 V 1.5 V 3.0 V

pore pressure [kPa]


S3

14 mHz* 28 mHz

4 800 1200 mHz 100 0 200 400

S2

15

amplitude

5 500

0

1000

1500

2000 time [s]

2500

3000

3500

4000

Figure A.22: Evolution of pore water pressure vs. time of a shake table experiment investigating a pile group installed in consolidated clay

S050715A.mea.asc

28 mHz

100

200

400 800 1200 mHz

PG-C3D


pile group in clay

0

500

S4 1.5 V 3.0 V

S3

sinus wave

1.5 V 3.0 V

S2 1.5 V 3.0 V

S1

pwd01 pwd02 pwd03

1.5 V 3.0 V

C2 C3 3.0 V 3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V

0

0.75 V

5

3.0 V

A3 A4

A1 A2

10

B1 B2 B3 B4 C1

15

0.375 V

pore pressure [kPa]

frequency

S5

14 mHz*

1.5 V

20

amplitude

1000

1500

2000

2500

time [s]

Figure A.23: Evolution of pore water pressure vs. time of the last shake table experiment investigating a pile group installed in fully consolidated clay

A.5. Evolution of Vertical Displacements during the Experiments

A.5

269

Evolution of Vertical Displacements during the Experiments SB050525.mea.asc

10

B4 B3

B1 B2

A4

A2

A1

A3

Loma Prieta real time e = 0.84

0

SP-SC1L single pile in clay

e = 0.83

-40 0

500

1.5 V

3.0 V

3.0 V

0.375 V 0.75 V 1.5 V

0.375 V

-30

1.5 V

e = 0.76 e = 0.72

C2

-20

3.0 V

e = 0.79

C1

laser01 laser02

-10

0.75 V

settlement [mm]

frequency = 28 mHz

14 mHz*

amplitude

1000 time [s]

1500

2000

Figure A.24: Evolution of vertical displacements vs. time of the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer

270


S0505252.mea.asc

SP-SC2D

S6

-10

S5 S7 S8 S9

B4

sinus wave

S1 S2 S3

B3

e = 0.70

e = 0.72

200 mHz ...1.2 Hz

200 mHz

T1 T2

frequency = 28 mHz Loma Prieta

0

-20

T3


laser01 laser02

-30 3.0 V

e = 0.61

-40 1.5 V

settlement [mm]

10mHz

S4

10

-50

amplitude

0.375V ... 3.0V

3.0V

-60 0

200

400

600

800 time [s]

1000

1200

1400

Figure A.25: Evolution of vertical displacements vs. time of a shake table experiment investigating a single pile installed in dense saturated sand with a covering consolidated clay layer

S050609B.mea.asc

C3

S4

B4


800

sinus wave

S3

S1

laser01 laser02

S2

C1

A4 B1 B2 B3

A2

0.75 V

A3

A1

2

0.375 V

0

500

3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

3.0 V

1.5 V

-4

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V 3.0 V

-2

3.0 V

0

1.5 V

settlement [mm]


C2

frequency = 28 mHz

14 mHz*

4

200 400

100

amplitude

1000 time [s]

1500

2000

Figure A.26: Evolution of vertical displacements vs. time of a shake table experiment investigating a single pile installed in unconsolidated clay


271

S050613A.mea.asc

SP-C2D

S5

S3

S2

C1 C2 C3

sin

B1 B2 B3 B4 sin

A4

A2 A3

A1

4

S4

laser01 laser02

single pile in clay

S1


0 amplitude 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

1.5 V 3.0 V 3.0 V

3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V

1.5 V

-8

3.0 V

-4 0.375 V 0.75 V

settlement [mm]

frequency = 28 mHz

14 mHz*

8

100 200 400 800 1200 mHz

-12 0

500

1000 time [s]

1500

2000

Figure A.27: Evolution of vertical displacements vs. time of a shake table experiment investigating a single pile installed in fully consolidated clay

S050616A.mea.asc

10 B4

∆e = 0.12

B3 B2

C2

1.5 V 3.0 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

3.0 V

S5

S4

S3

S2

S1

sinus wave

e = 0.57 3.0 V

e = 0.60 1.5 V

-40

0.375 V 0.75 V 0.7 1.5 V 3.0 V

-30

C3

e = 0.63

1.5 V 3.0 V

A4

B1

e = 0.65

A1

-20

laser01 laser02


A2

A3

-10

0.375 V 0.75 V 1.5 V 3.0 V

settlement [mm]

e = 0.71


C1

0

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

e = 0.54

amplitude

-50 0

1000

2000 time [s]

3000

4000

Figure A.28: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in loose saturated sand with a covering clay layer

272


S050617A.mea.asc

10mHz ...



PG-SC2D

laser01 laser02

A4 B1 B2 B3 B4 C1 C2 C3

pile group in san & clay

S2

sinus wave

0

S4

S3

e = 0.54

S1

A1 A2 A3

2

-2

-4

0.75 V 1.5 V 3.0 V 0.375 V 0.75 V 1.5 V 3.0 V 1.5 V 3.0 V 3.0 V

e = 0.54

0.375 V

settlement [mm]

4

frequency = 1.68Hz

amplitude

e = 0.53

1000

0

0.75 V

0.75 V 0.375 V

0.375 V

2000

3000

time [s]

Figure A.29: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in dense saturated sand with a covering clay layer

S050621A.mea.asc

B4 C1 B3

B2

B1

A4

A3

A2

A1

2


C3


0

200

400

600 time [s]

800

1000

3.0 V

3.0 V

3.0 V

1.5 V

0.75 V

amplitude 0.375 V

1.5 V

-4

0.75 V

-2

3.0 V

laser01 laser02

1.5 V

0

0.375 V

settlement [mm]

4

C2

frequency = 28 mHz

frequency = 14 mHz*

1200

Figure A.30: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in unconsolidated saturated clay


S050621A.mea.asc

30 14 mHz*

frequency

28 mHz


20

100 200 400 800 1200 mHz

PG-C2D pile group in clay

S5

S3

S4

S1

B1 B3 C1 C3

A1

A3

laser01 laser02

S2

sinus wave

10

A4 B2 B4 C2

A2

0

-20

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

-10 0.375 V 0.75 V 1.5 V 3.0 V 0.375 V 0.75 V 1.5 V 3.0 V 1.5 V 3.0 V 3.0 V

settlement [mm]

273

amplitude

-30 0

1000

2000 time [s]

3000

4000

Figure A.31: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in consolidated clay

S050715A.mea.asc

28 mHz

400 800 1200 mHz

laser01 laser02 S5 S4

S3

C2

sinus wave

C3

C1

B2 B4 B3

B1

A3 A4

A2

A1

200

pile group in clay

5

0

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

3.0 V 3.0 V

1.5 V

0.75 V

0.375 V

-5

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V

amplitude 3.0 V

settlement [mm]

100

PG-C2D


S2

14 mHz*

frequency

S1

10

-10 0

500

1000

1500

2000

2500

time [s]

Figure A.32: Evolution of vertical displacements vs. time of a shake table experiment investigating a pile group installed in fully consolidated clay

274

A.6


Maximal Strains in Model Pile during the Experiments SB050525.mea.asc

400

SP-SC1L

C2

B4

14 mHz* Loma Prieta real time

C1

frequency = 28 mHz

A3

1.5 V

B2

A2

0.75 V

B1

A1

0.375 V

0

500

amplitude

1000 time [s]

1500

3.0 V

1.5 V

3.0 V

-400

0.375 V 0.75 V 1.5 V

0

3.0 V

µε [-]

A4

B3


2000

Figure A.33: Maximal strains measured in the model pile during the first shake table experiment investigating a single pile installed in loose saturated sand with a covering clay layer

A.6. Maximal Strains in Model Pile during the Experiments

S0505252.mea.asc

10mHz

frequency = 28 mHz B4

Loma Prieta

200 mHz ...1.2 Hz

200 mHz

SP-SC2D

T3

800

T2

S5 S7 S8 S9

S6

S4

S1 S2 S3

B3

T1


400

0

3.0 V

µε [-]

275

1.5 V

-400

sinus wave

amplitude

0.375V ... 3.0V

3.0V

-800 0

400

800 time [s]

1200

Figure A.34: Maximal strains measured in the model pile during a shake table experiment investigating a single pile installed in dense saturated sand with a covering clay layer

S050609B.mea.asc

S4

C3

B4

800 mHz

S3

S2

S1

C1

single pile in clay

B2

B3

200 400

SP-C1L

B1

A1 A2 A3

A4

200

µε [-]

frequency = 28 mHz


C2

14 mHz*

400

100

sinus wave

0

0

1000

3.0 V

3.0 V 1.5 V 3.0 V 1.5 V 3.0 0V

amplitude

1.5 V

3.0 V

3.0 V

0.375 V 0.75 V 1.5 V

1.5 V

3.0 V

-400

0.75 V

0.375 V

-200

2000 time [s]

Figure A.35: Maximal strains measured in the model pile during a shake table experiment investigating a single pile installed in unconsolidated clay

276


S050613A.mea.asc

1500

SP-C2D

0

S4

S3

S2

S1

sin

sin

B1 B2 B3

A4

A1

A2 A3

B4

C1 C2 C3

single pile in clay

500 µε [-]

S5


1000

100 200 400 800 1200 mHz

frequency = 28 mHz

14 mHz*

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V 1.5 V

1.5 V 3.0 V 3.0 V

3.0 V

1.5 V

0.375 V 0.75 V 1.5 V 3.0 V

3.0 V

0.375 V 0.75 V

-500

1.5 V

amplitude

-1000 500

0

1000 time [s]

1500

2000

Figure A.36: Maximal strains measured in the model pile during a shake table experiment investigating a single pile installed in fully consolidated clay

S050616A.mea.asc

frequency = 28 mHz

14 mHz*

S4

S3

S1 S2

C1

S5

C3

B4

B2 B3

A3 A1 A2

sinus wave

1.5 V 3.0 V

1.5 V 3.0 V

3.0 V

3.0 V

1.5 V 3.0 V 1.5 V 3.0 V 1.5 V 3.0 V

amplitude

1.5 V

-200

0.375 V 0.75 V 0.7 1.5 V 3.0 V

0

0.375 V 0.75 V 1.5 V 3.0 V

µε [-]

200


B1

A4


C2

400

100 200 400 800 1200 mHz

-400 0

1000

2000 time [s]

3000

4000

Figure A.37: Maximal strains measured in a model pile of a pile group during a shake table experiment investigating a pile group installed in loose saturated sand with a covering clay layer

A.6. Maximal Strains in Model Pile during the Experiments

277

S050617A.mea.asc

2000 10mHz ...


frequency = ca. 1.68Hz


B3 B4 C1 C2 C3

PG-SC2D S3

S2

S1

S4


A3 A4 B1 B2

A1 A2

1000

µε [-]

sinus wave

0.375 V 0.75 V 1.5 V 3.0 V 0.375 V 0.75 V 1.5 V

-1000

1.5 V

3.0 V

3.0 V 3.0 V

0

0.375 V

amplitude

0.75 V

0.375 V

0.75 V

-2000 0

1000

2000

3000

time [s]

Figure A.38: Maximal strains measured in a model pile of a pile group during a shake table experiment investigating a pile group installed in dense saturated sand with a covering clay layer

S050621A.mea.asc

2000

frequency = 28 mHz

B4 C1

B3

B2

B1

A4

A3

A2

A1

1000

3.0 V

3.0 V

3.0 V

1.5 V

0.75 V

0.375 V

1.5 V

0.75 V

0.375 V

-1000

amplitude

1.5 V

0

3.0 V

µε [-]

C2


C3

frequency = 14 mHz* Loma Prieta *real time

-2000 0

400

800

1200

time [s]

Figure A.39: Maximal strains measured in a model pile of a pile group during a shake table experiment investigating a pile group installed in unconsolidated clay

278


S050715A.mea.asc

400 800 1200 mHz

S5

PG-C3D

S3 1.5 V 3.0 V

S4

S2 1.5 V 3.0 V

S1

B4 C1

pile group in clay

B1 B2 B3

A2

200

sinus wave

0

1000

1.5 V 3.0 V

1.5 V 3.0 V

1.5 V 3.0 V

3.0 V 3.0 V

0.375 V 0.75 V 1.5 V 3.0 V 1.5 V

0.75 V

0.375 V

-2000

3.0 V

0

1.5 V

µε [-]

A1

A3

2000

100

C2 C3

28 mHz


A4

14 mHz*

frequency

amplitude

2000 time [s]

Figure A.40: Maximal strains measured in a model pile of a pile group during a shake table experiment investigating a pile group installed in fully consolidated clay

A.7. Pore Water Pressure during Event B4

A.7

279

Pore Water Pressure during Event B4 20 pwd01 pwd02 pwd03

15

pwd01 pwd02 pwd03

SP-SC1L 10

SP-SC2D single pile in sand & clay

7.0 KPa


5.1 KPa

pore pressure [kPa]

B4

5

0 250

260

250

260

time [s]

Figure A.41: Evolution of pore water pressure during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

280


20 pwd01 pwd02 pwd03

pore pressure [kPa]

B4

pwd01 pwd02 pwd03

15 A

10 A'

5

SP-C1L

SP-C2D

single pile in clay

0 680

single pile in clay

690

680 time [s]

690

Figure A.42: Evolution of pore water pressure during event B4 for the shake table experiments investigating a single pile installed in saturated clay

14

B4


pore pressure [kPa]

12

pwd01 pwd02 pwd03

dissipation A Inc

10

dissipation B dissipation C

8

6

PG-SC2D pile group in sand & clay

790

Dec

800

810 time [s]

Figure A.43: Evolution of pore water pressure during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

A.7. Pore Water Pressure during Event B4

281

20

pore pressure [kPa]

B4

pwd01 pwd02 pwd03

pwd01 pwd02 pwd03

pwd01 pwd02 pwd03

15 A1

PG-C2D pile group in sand & clay

10

∆u2

∆u1

∆u3

A2

A3

5

PG-C1L

p*

PG-C3D



0 850

860

870

time [s]

Figure A.44: Evolution of pore water pressure during event B4 for the shake table experiments investigating a pile group installed in saturated clay

282

A.8


Pile Head Deflection during Event B4 100

B4 ∆s

head table

amp


∆satt

0


-100 100

∆samp

SP-SC2D

∆satt


0 head table

-100 250

260

270

280

time [s]

Figure A.45: Pile head deflection vs. time during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

A.8. Pile Head Deflection during Event B4


100

B4

283

∆samp

head table

0


-100 100

∆samp

head table

0


-100 580

590

600

610

time [s]

Figure A.46: Pile head deflection vs. time during event B4 for the shake table experiments investigating a single pile installed in saturated clay


100

B4

head table

∆samp

0


-100 100

∆samp

0

PG-SC2D

head table

-100 790


800

810

820

time [s]

Figure A.47: Pile head deflection vs. time during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

284



100

B4

head table

0


-100 100

0

PG-C2D

head table

-100 840

pile group in clay

850

860

870

time [s]

Figure A.48: Pile head deflection vs. time during event B4 for the shake table experiments investigating a pile group installed in saturated clay

A.9. 3D Pile Bending Moments vs. time during Event B4

A.9

285

3D Pile Bending Moments vs. time during Event B4 t [s] 10.0

t [s] 10.0

8.0 8.0

6.0 6.0

zero-moments 4.0

[N m]

4.0

m]

M

2.0

2.0

ze ro

-m

om

-2.

en

0

ts

0

sta

bil

iza

tio n

-1.

-2.

0.0

1.0

2.0

∆MFd

0

0 -1.

0.0

1.0

2.0

M

[N

∆MFl

∆ME



Figure A.49: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

286


t [s]

t [s] 10.0

10.0

8.0

8.0 6.0

6.0 4.0

m] M

[N

2.0

ts

0 ze ro

-m

om

en

-2.

-2.

0

-1.

0.0

1.0

2.0

∆MFd

0 -1.

0.0

∆MFl

1.0

2.0

M

[N

2.0

0

m]

4.0

∆ME

B4


B4


Figure A.50: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

A.9. 3D Pile Bending Moments vs. time during Event B4

287

t [s

]

10

.0 8.0

6.0

6.0

4.0

m

M

[N

2.0

M

.0

2

4.0

] m [N

2.0

0 2.

0

1.

0 1.

.0

0

0

. -1

]

.0

8.0

]

t [s

10

.0

∆ME ∆MFd

0 0.

.0

-1

-2

.0

-2

ts

en

om

m

ro

ze i

at

a

liz bi

st ∆ME

on



Figure A.51: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

288


t [s

]

10

[N

m

8.0 6.0

4.0

]

M

0

2.

∆ME

0 1.

0

0.

m

[N

2.0

0

-

ts

en

0 2.

-

om

B4


∆ME

0

1.

0

0.

0 1.

-

0 2.

s nt

-


.0

-2

om

m

o-

r ze

B4

.0

-1

e

-m

o

r ze

2.0

0

∆MFm

0

[N

2.

∆ME

0 1. 0.

0 1.

M

2.

∆MFl

4.0

]

m

2.0

]

.0

6.0

4.0

t [s

10

8.0

6.0

M

]

.0

8.0

]

t [s

10

.0

∆ME

B4


Figure A.52: Pile bending moments vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated clay

A.10. 3D Lateral Soil Displacements vs. time during Event B4

A.10

289

3D Lateral Soil Displacements vs. time during Event B4 t [s

]

10

8.0

6.0

s[ 20

m

s[

2.0

.0

20

0

. 10

6.0

4.0

]

0

0.

-

. 10

0

]

.0

8.0

m

t [s

10

.0

m

m

4.0

]

2.0

.0 10

.0 0.

0

0 -1

. 20

-

0.

0


0

0.

-2


Figure A.53: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

290


t [s

]

10

.0 8.0

6.0

s

[m

s[

2.0

.0

20

. 10

6.0

4.0

]

20

0 0.

0 -

. 10

m

m

-

4.0

]

2.0

.0 10

.0

0 . 20

0

0.

0 -1

0.

0


0

0.

-2

B4

]

.0

8.0

m

t [s

10

B4


Figure A.54: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

A.10. 3D Lateral Soil Displacements vs. time during Event B4

291

t [s]

t [s]

10.0

10.0

8.0

8.0

6.0

6.0

4.0

]

m

s

]

m

2.0

[m

s

.0

10

4.0 2.0

[m .0

10

0

0.

.0

0

0.

0

-1

0

0.

-1



Figure A.55: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

292


t [s] 10.0

t [s] 10.0

8.0

8.0

6.0

]

m

s

]

s

.0

]

s

0

2.0

[m .0

10

.0

4.0

m

2.0

[m .0

10

6.0

4.0

m

2.0

8.0

6.0

4.0

[m

t [s] 10.0

10

.0

0 0

0

0.

0

0

0.

0.

0.

-1

-1

-1

B4


B4


B4


Figure A.56: Lateral soil displacements vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated clay

A.11. 3D Lateral Pile Deflections vs. time during Event B4

A.11

293

3D Lateral Pile Deflections vs.

time during

Event B4 t [s ] 10. 0

t [s ] 10. 0

8.0

8.0 6.0

6.0

mm

mm

]

4.0

]

4.0

0

s[

2.0

0


-1

00

.0

-5

0.

0

0.

50

.0

0. 10 -1

00

.0

-5

0.

0

0. 0

.0 50

10

0.

0

s[

2.0


Figure A.57: Lateral pile deflections vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated sand covered by a clay layer

294


t [s ] 10. 0

t [s

]

10.

0 8.0

8.0 6.0

6.0 4.0

2.0

.0

.0 00

-1

00

-1

.0

-5

0.

-5

0

0.

0.

0

50

0. 0

0

.0 50

10

0.

10

0

0.

0

s[

2.0

s[

mm

]

mm

]

4.0

B4


B4


Figure A.58: Lateral pile deflections vs. time and vs. depth during event B4 for the shake table experiments investigating a single pile installed in saturated clay

A.11. 3D Lateral Pile Deflections vs. time during Event B4

295

t [s ] 10. 0

t [s ] 10. 0 8.0

8.0 6.0

6.0 4.0

]

]

4.0

mm

0 -1

-1

0.

0.

0

0

0.

0.

0

10

.0

.0 10

2.0

s[

s[

mm

2.0

loose B4 PG-SC1L single pile in clay

dense B4 PG-SC2D single pile in clay

Figure A.59: Lateral pile deflections vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated sand covered by a clay layer

296


t [s ] 10. 0 8.0

8.0 6.0

]

4.0

s[

mm

2.0


B4


0

0 0. -2

-2

0.

-1

0

0.

0.

0

.0 10

0

0 -1

0

0.

0.

10

.0

20

.0

s[

mm

2.0

.0 20 0 0. -2

-1

0.

0.

0

.0

6.0

4.0

]

] mm s[

.0 10

20

B4

8.0

6.0

4.0 2.0

t [s ] 10. 0

t [s ] 10. 0

B4


Figure A.60: Lateral pile deflections vs. time and vs. depth during event B4 for the shake table experiments investigating a pile group installed in saturated clay