PhD Thesis : Strain Localization in sensitive SOFT CLAYS PDF

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STRAIN LOCALIZATION IN SENSITIVE SOFT CLAYS Vikas Thakur Geotechnical Division Department of Civil and Transport Engineering Norwegian University of Science and Technology, Trondheim and Norwegian Centre of Excellence: International Centre for Geohazards Strain Localization in Sensitive Soft Clays 2...

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STRAIN LOCALIZATION IN SENSITIVE SOFT CLAYS

Vikas Thakur

Geotechnical Division Department of Civil and Transport Engineering Norwegian University of Science and Technology, Trondheim and Norwegian Centre of Excellence: International Centre for Geohazards

Strain Localization in Sensitive Soft Clays

2007

The evaluation committee of this thesis comprised of the following members: Professor Stein Sture, University of Colorado at Boulder, U.S.A.

(First opponent)

Professor Kennet Axelsson, Uppsala University, Sweden

(Second opponent)

Professor emeritus Kåre Senneset, Norwegian University of Science and Technology, NTNU, Norway

(Administrator)

Advisors during this study: Professor Steinar Nordal, Department of Civil and Transport Engineering, NTNU, Norway Dr. Hans Petter Jostad, Geomechanics Division, Norwegian Geotechnical Institute, Norway Dr. Lars Andresen, Geomechanics Division, Norwegian Geotechnical Institute, Norway Dr. Geir Svanø, Rock and Soil Mechanics group, The Foundation for Scientific and Industrial Research at the Norwegian Institute of Technology, SINTEF, Norway

Key contacts during this study: Professor Gioacchino (Cino) Viggiani, Laboratoire 3S and University Joseph Fourier, Grenoble, France Assistant Professor Ronald B J Brinkgreve, Delft University of Technology, and Manager Research and Development, PLAXIS BV, Delft, the Netherlands Dr. Erick Septanika, PLAXIS BV, Delft, the Netherlands Mr. Pascal Charrier, Laboratoire 3S, Grenoble, France

Institutes participated during this study: Norwegian University of Science and Technology, NTNU, Norway International Centre for Geohazards, ICG, Norway Norwegian Geotechnical Institute, NGI, Norway Laboratoire 3S, Grenoble, France PLAXIS BV, Delft, the Netherlands

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TABLE OF CONTENTS 1.

INTRODUCTION..................................................................................................................................... 8

2.

LOCALIZED FAILURE IN SENSITIVE SOFT CLAYS .................................................................... 9 2.1 2.2 2.3

BASICS ................................................................................................................................................ 11 SHEAR BAND THICKNESS DEPENDENT POST PEAK BEHAVIOUR ............................................................ 14 THE INCLINATION ANGLE OF THE SHEAR BAND ................................................................................... 15 BACKGROUND: NUMERICAL MODELLING ................................................................................ 16

3.1 3.2

BASICS ................................................................................................................................................ 16 LITERATURE REVIEW: LOCALIZATION AND REGULARIZATION ............................................................ 18 DISCONTINUITY MODELLING........................................................................................................ 28

4.1 4.2

MECHANICS OF GENERATION–DISSIPATION OF PORE WATER PRESSURE FROM THE SHEAR BAND ........ 29 A SIMPLE ANALYTICAL MODEL FOR TOTALLY UNDRAINED SOFTENING............................................... 31 WEAK DISCONTINUITY MODELLING .......................................................................................... 38

5.1 5.2 6.

RATE INDEPENDENT MODELLING ........................................................................................................ 38 RATE DEPENDENT MODELLING ........................................................................................................... 60 DISCUSSIONS ON SHEAR BAND ...................................................................................................... 64

7.

ORIENTATION OF PARTLY DRAINED SHEAR BANDS ............................................................. 70

3.

4.

5.

7.1 7.2

INITIAL STUDY .................................................................................................................................... 70 DETAILED STUDY ................................................................................................................................ 72 STRONG DISCONTINUITY MODELLING: X-FEM....................................................................... 80

8.1 8.2 8.3

ONSET AND PROPAGATION OF DISCONTINUITY ................................................................................... 80 SLIP LINE MODELLING ......................................................................................................................... 81 A NEW PORE PRESSURE JUMP BASED ONSET CRITERIA FOR MODELLING STRONG DISCONTINUITIES .... 89 EXPERIMENTAL STUDY.................................................................................................................... 92

8.

9.

9.1 INTRODUCTION ................................................................................................................................... 92 9.2 THE PLANE STRAIN APPARATUS .......................................................................................................... 94 9.3 SPECIMEN PREPARATION..................................................................................................................... 95 9.4 RESULTS AND DISCUSSIONS................................................................................................................ 98 9.5 SHEAR BANDING IN SENSITIVE SOFT CLAYS ...................................................................................... 101 9.6 LOCAL PORE PRESSURE PUMP AND STRAIN LOCALIZATION ............................................................... 108 CONCLUSIONS ............................................................................................................................................... 112 FUTURE SCOPE OF THE WORK ................................................................................................................ 114 ACKNOWLEDGEMENTS.............................................................................................................................. 115 REFERENCES.................................................................................................................................................. 116

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APPENDIX A: PUBLICATIONS 1. Thakur V, Nordal S, Jostad H P, Andresen L, (2005) Study on pore water pressure dissipation during shear banding in sensitive clays. 11th International conference on computer methods and advances in geomechanics, G Barla and M Barla Eds, Vol. 4, Italy, pp: 289-296 ………………………………………………………………………………………………..C1 2. Thakur V, Grimstad G, Nordal S (2006) Instability in sensitive soft clays. ECI: Geohazards and Risk Evaluation conference, Farrokh Nadim, Rudolf Pöttler, Herbert Einstein, Herbert Klapperich, and Steven Kramer Eds, ECI Symposium Series, Norway, Vol. P7, http://services.bepress.com/eci/geohazards/43.........................................................................C2 3. Jostad H P, Andresen L, Thakur V (2006) Calculation of shear band thickness in sensitive clays. 6th Numerical methods in geotechnical engineering NUMGE, H Schweiger Eds, Austria, pp: 27-32……...…………………………………………………...……………..…C3 4. Thakur V (2006) “Shear band analyses in sensitive soft clays using inherent regularization technique. The 17th European Young geotechnical engineers conference, Zagreb, Croatia, pp: 247-260……………………………………………………………………………………….C4 5. Septanika E, Thakur V, Brinkgreve RBJ, Nordal S (2007) Modelling undrained instability in geomaterial using extended finite element method (PUM/XFEM). International Geomechanics conference, Nessebar, Bulgaria…………………………………………...………………….C5 6. Grimstad G, Thakur V, Nordal S (2005) Experimental Observation on Formation and propagation of shear zone in Norwegian Quick clay. Landslides and avalanches: 11th ICFL, Norway, pp: 137-141 ……………………………………………………………….............C6

APPENDIX B: MATERIAL MODELS 1. Mohr- Coulomb Elastic Perfectly Plastic Model in Plaxis 2. Hardening Soil Model in Plaxis 3. Mobilized Friction Model (MFM) in Geonac

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STRAIN LOCALIZATION IN SENSITIVE SOFT CLAYS Preface: This thesis mainly deals with discontinuity modelling and an experimental investigation related to the localized failure in sensitive soft clays during rapid load changes. This study manifests some novel numerical procedures to control strain softening and regularize strain localization in sensitive soft clays. The thesis has been divided into two parts, the first part is a summary of the research done and the second part is a collection of published research papers. In the first part of the thesis, two different approaches for discontinuity modelling and experimental work are presented. Weak discontinuity modelling describes development of shear bands while strong discontinuity modelling introduces distinct cracks or slip lines in the material. The second part of the thesis is a compilation of six research papers (C1 to C6) written together with co-authors. The author of this thesis is the first author of three papers, and for these papers (C1, C2, C4), the first author did most of the work while co-authors contributed with discussion and feedback. For the paper C3, the author of this thesis worked on the development of the model and its validation at Norwegian Geotechnical Institute (NGI) in close contact with the other authors. For the paper C5, the author of this thesis worked on improvement and validation of model at the Plaxis group in close contact with the other authors. For the paper C6, the author of this thesis has been key supervisor for the first author. In general, it is difficult to quantify the exact contribution from the individual authors in all papers, but the author of this thesis, who gratefully acknowledges all co-authors for their contributions, has made major part of the work. Finally, note that this thesis has been written in such a way that the “summary” and the “research papers” are complimentary to each other. Hence, it may be necessary to refer to the enclosed papers while reading the summary to obtain a complete description of the work done. Internal references are made to help reader in this respect. Abstract: Progressive failures in sensitive soft clays such as quick clays are well know in Scandinavia. Instability in such clays is often associated with material softening due to generation of shear induced pore pressure within shear bands. Shear bands defined as narrow zones of localized strain. The formation and progression of shear bands is governed by basic properties of the softening material. These mechanisms have been studied in this thesis. Numerical modelling of the formation and progression of shear bands becomes difficult due to non-unique solutions and ill-posedness of the governing equations. In particular, since the solutions relate to the thickness of shear bands becomes dependent on element size. Various techniques for regularization have been proposed to make the problem well posed and to obtain mesh independent solutions. Most regularization techniques have been developed for granular materials where the thickness of a shear band is a function of the average grain size. In contrast, no specific regularization technique has been developed for soft clays since a proper micro-structural length-parameter is not identified. In this study, the hypothesis is that generation and dissipation of shear induced pore pressure could regularize the strain softening and result in a mesh independent shear band thickness. A coupled consolidation formulation models the generation and dissipation of excess pressure. The simulation aims at modelling two counteracting mechanism in the sensitive clay. First, the shear band will be narrowing due to strain softening while; second, the internal pore water drainage will enlarge the zone with plastic deformation. A finite shear band thickness could result. This 5

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study presents some analytical and numerical results involving the two counteracting mechanisms. This study reveals that coupled pore water flow type regularization technique is sensitive to choice of the shear band factor, a ratio of clay permeability to the applied rate of loading. Moreover, the posedness of a problem is controlled by the selection of the shear band factor. It is found that the shear band thickness seems to be a continuous function of the shear band factors. The thickness of shear band monotonically increases with the shear band factor. From this study it is learnt that the thickness of shear band may vary from a few microns to several meters depending on shear band factor. However, this study has been limited to the modelling and the measurement of the shear band in meso-scale only: scale in-between millimetres to a few centimetres. The meso-scale usually covers the size of specimens usually tested in geotechnical laboratories. Therefore based on this scale, the shear band factor may separate a problem in three categories; locally drained, partly drained and locally undrained. Locally drained condition is met by the combinations of permeability and rates of loading in such a way that shear induced pore pressure gradient across the shear band becomes particularly zero. In this situation, size of model/specimen itself is a representative of the shear band. Therefore, strain softening also becomes mesh independent and well posed from a numerical point of view. In addition to that, all material points within the model/specimen are localized and are not subjected to elastically unloading. Hence, the numerical instability is avoided too. In short, locally drained situation also represents uniqueness in boundary value problems. In the locally undrained case, selected permeability and applied rates of loading causes a situation where the total volumetric strain at every material point may be zero. No dissipation of pore water pressure may occur across the shear band, which ultimately causes in severe strain softening. Therefore, the shear bands thickness tends to go to zero and reduces with size of elements. This ultimately results in non-uniqueness in the solution. Finally, in partial drained condition, it is possible to have internal volumetric exchange; volumetric compression in shear bands may be balanced by equal volumetric expansion in elastically unloading parts. In this condition, a pore pressure gradient establishes across the shear band. Partial drainage condition is the only situation where mesh independent shear band thickness associated with pore pressure induced softening can be achieved. In general, partial drainage condition may be more realistic in the field as well where the boundaries are far away from the shear band unlike laboratory testing with limited size. Hence, major part of this study deals with modelling of shear bands under partly drained conditions. Classification of discontinuity as strong or weak depends on the physical scale adopted during the analyses. However, shear bands in sensitive clays will be so thin that in practice they can be modelled as strong discontinuities or slip lines. Experimental work has been carried out in a plane strain device at laboratory 3S Grenoble France, by the author to observe the formation and propagation of shear bands in Norwegian quick clay. Particle Image Velocimetry (PIV) analysis is done to detect shear band thickness and modes of failure. The experimental work shows the development of multiple shear bands and fluctuating modes of deformation until a distinct failure mechanism is seen. Local variation in excess pore pressure is measured. Shear band thickness is measured at the onset of localization to be 3 to 4 mm. Modelling shear band of 3 to 4 mm with classical finite elements is impractical for simulating real slope stability problems. A novel technique called the extended finite element method (X-FEM) has been studied in cooperation with Delft University and Plaxis BV, Netherlands. X-FEM is capable of modelling progressive failure with a strong discontinuity

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(an extremely thin shear band). The procedure involves an elasto-plastic linear-cohesionsoftening damage model. A pore pressure jump based onset criteria has been developed and implemented in X-FEM. Further, the propagation of the strong discontinuity has been controlled using a gradient of incremental displacement and a non-local method. Progressive failure mechanisms have been modelled using X-FEM for various geotechnical problems. The primary aim of this PhD work has been to study the shear band formation and propagation in sensitive soft clays experimentally as well as numerically. This study suggests that one should focus less on finding a shear band thickness and more on practical modelling of progressive failure in soft sensitive clay; using strong discontinuities i.e. slip lines. One possible method is the X-FEM. It is worth mentioning that X-FEM tool used in this study is under developing which means that analyses shown are pilot study. Finally, the motivation behind this study can be described in brief as follows; Modelling progressive failure in sensitive soft clays has always been challenging for geoscientists. So far, only one physical parameter has been identified that governs the failure mechanism in sensitive soft clays. This parameter is the shear band thickness. Therefore, detection and realistic modelling of the real thickness of the bands or the slip lines becomes crucial for developing practical methods. These methods will then help in modelling progressive failure. Keeping this in view, this PhD work is mainly focusing on modelling and the measurement of shear band thickness in sensitive soft clays. Less focus is made on modelling progressive failure. Key words: shear band, coupled pore water flow, finite element modelling, strong discontinuity, cohesion softening, extended finite element modelling (X-FEM), plane strain testing, quick clays, shear band thickness and orientation

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INTRODUCTION

All evidence from Verdal (1893) and Rissa (1978) in Norway indicates that slides in slopes of quick clays are preceded by development of a continuous sliding surface by progressive failure. The sliding surface has been often referred to as a discontinuity, shear band, rupture zone or simply a slip line. These slip surfaces are localized with tremendous plastic strain, and the phenomenon is known as strain localization. Localization in a form of progressive failure may occur in any geomaterial such as flaky material like stiff clays, granular materials like sands or in rocks etc. In stiff clays, sliding surface is interpreted through an approach based on the principles of fracture mechanics, whereas in granular soils, a bifurcation problem is interpreted. In the past three decades, considerable attention has been given to a more fundamental description of the localization phenomenon, where the problem is treated as a bifurcation problem within the framework of continuum mechanics. Bifurcation here means that the continuing solution (load –displacement paths) is not unique and thus there is more than one solution. The buckling of an axially loaded beam column is a classical example of a bifurcation problem. However, whereas the buckling of a beam column is a result of geometrical effects, localization in geomaterial is caused by instability in the behaviour of the material. The material instability may arise when soft...