Recent experiences from the Darfield and Canterbury, New Zealand earthquakes have shown that the soft soil condition of saturated liquefiable sand has a profound effect on seismic response of buildings, bridges and other lifeline infrastructure. For detailed evaluation of seismic response three dimensional integrated analysis comprising structure, foundation and soil is required; such an integrated analysis is referred to as Soil Foundation Structure Interaction (SFSI) in literatures. SFSI is a three-dimensional problem because of three primary reasons: first, foundation systems are three-dimensional in form and geometry; second, ground motions are three-dimensional, producing complex multiaxial stresses in soils, foundations and structure; and third, soils in particular are sensitive to complex stress because of heterogeneity of soils leading to a highly anisotropic constitutive behaviour. In literatures the majority of seismic response analyses are limited to plane strain configuration because of lack of adequate constitutive models both for soils and structures, and computational limitation. Such two-dimensional analyses do not represent a complete view of the problem for the three reasons noted above. In this context, the present research aims to develop a three-dimensional mathematical formulation of an existing plane-strain elasto-plastic constitutive model of sand developed by Cubrinovski and Ishihara (1998b). This model has been specially formulated to simulate liquefaction behaviour of sand under ground motion induced earthquake loading, and has been well-validated and widely implemented in verifcation of shake table and centrifuge tests, as well as conventional ground response analysis and evaluation of case histories. The approach adopted herein is based entirely on the mathematical theory of plasticity and utilises some unique features of the bounding surface plasticity formalised by Dafalias (1986). The principal constitutive parameters, equations, assumptions and empiricism of the existing plane-strain model are adopted in their exact form in the three-dimensional version. Therefore, the original two-dimensional model can be considered as a true subset of the three-dimensional form; the original model can be retrieved when the tensorial quantities of the three dimensional version are reduced to that of the plane-strain configuration. Anisotropic Drucker-Prager type failure surface has been adopted for the three-dimensional version to accommodate triaxial stress path. Accordingly, a new mixed hardening rule based on Mroz’s approach of homogeneous surfaces (Mroz, 1967) has been introduced for the virgin loading surface. The three-dimensional version is validated against experimental data for cyclic torsional and triaxial stress paths.

La terre compactée est considérée comme un mélange granulaire dans lequel l'argile joue un rôle de liant mais cette dernière exhibe une forte interaction avec l'eau. Pendant la durée de vie en service, la terre compactée est soumise aux changements de l’humidité relative. En raison de ces changements des conditions ambiantes perpétuels, la teneur en eau dans la terre varie, impactant leur performance mécanique. Le présent travail a ainsi pour but d’étudier l’impact de l’humidité relative et de la teneur d'argile sur le comportement mécanique de la terre compactée. Il se réalisera au travers d’études expérimentales et d'une modélisation constitutive. Dans la première partie de cette thèse, quatre terres régionales de provenances et de teneurs d'argile différentes sont identifiées. Une étude comparative a été réalisée entre le double compactage statique et le compactage dynamique. En parallèle, trois types d'essais spécifiques : essais de succion par la méthode de papier-filtre, essais de retrait et essais d'absorption d'eau, ont été menés pour donner des indications préliminaires quant aux effets d'interaction entre l'eau et l'argile. Dans la deuxième partie, l’impact de l’humidité relative et de la teneur d'argile sur le comportement de cisaillement a été étudié, prenant en compte des cycles de chargement-déchargement. En adoptant une définition particulière de la contrainte effective de Bishop, il a également été observé que les états de rupture dans le plan (p'-q) pour tous les échantillons sont alignés approximativement à une ligne droite unique passant par l'origine, quelque soit la succion et la pression de confinement. Sur la base des résultats expérimentaux, un nouveau modèle constitutif a été développé pour la simulation du comportement mécanique de la terre compactée. Ce nouveau modèle a ainsi été formulé dans la cadre de la mécanique de l'endommagement des milieux continus et de la théorie de Bounding Surface Plasticity. / Compacted earth is regarded as a granular mixture in which clay plays a role of binder but it also exhibits an important interaction with water. During their service life, compacted earth can be subject to large changes in relative humidity. Those perpetual changes of environmental conditions induce continuous changes of water content of the earth that impact significantly its mechanical performances. The present work aimes at studying the mechanical behavior of compacted earth with respect to relative humidity and clay content. It involves an extensive experimental study and a constitutive modelling. In the first part of this thesis, four kinds of local earth are identified with different clay contents. A comparison of compaction method was then conducted between a double static compaction and dynamic compaction. Three types of specific tests: suction test by filter paper method, shrinkage test and sorption-desorption test were carried out, thereby providing a preliminary insight on the interaction effects between clay and water. In the second part, the impact of clay and moisture contents on the shear behavior of compacted earth was investigated taking into account loading-unloading cycles. Adopting a particular definition of Bishop's effective stress, failure states of all samples were observed to lie approximately on a unique failure line crossing the origin in the (p'-q) plane regardless of matric suction and confining pressure. Finally, based on the above experimental results, a new constitutive model was proposed, based on the theories of Bounding Surface Plasticity and continuum damage mechanics, aiming to simulate mechanical behaviour of compacted earth.

The prediction of settlements in infrastructural design puts high demands on the numerical analysis of the subsoil and the associated constitutive model: complex installation processes and the repetitive character of live loads pose considerable challenges. Although in this context the main focus is on the analytical requirements of a geotechnical problem in order to realistically capture soil behaviour, the needs of engineering practice should not be neglected in constitutive modelling. Along these lines, a new soil model for non-cohesive soils has been developed in the theoretical framework of elastoplasticity. Based on the concept of bounding surface plasticity according to Manzari and Dafalias (1997), soil properties such as strength, stiffness and dilatancy depend on the distance between the current stress state and a corresponding model surface in stress space. This way the multi surface model correctly reproduces elementary behavioural patterns of soil, including for example shear related phenomena such as hardening/softening, contraction/dilation and attainment of critical state (constant volume shear strength). Moreover, the model captures the state dependence of soil behaviour (barotropy and pycnotropy). Thus, with only one set of material parameters, the mechanical behaviour of a wide range of initial soil states with respect to stress and void ratio can be simulated (unified modelling). The kinematic hardening mechanism of the conical yield surface contributes to a realistic stiffness evolution in un- and reloading and is hence essential for stress or strain accumulation due to load reversals. Since the chosen modelling framework is suitable for further development, the original formulation has been extended to adapt the model to the defined needs. In order to adequately simulate geotechnically relevant stress paths of low and higher complexity, first of all, a cap shaped yield surface was added to allow for plastic straining not only in shear, but also in constant stress ratio loading (e. g. isotropic or oedometric compression). When it comes to stress paths of unconventional orientation, to load reversals or composed stress paths with changes in loading direction, a supplementary stiffness increase at small strains and its subsequent strain dependent degradation have proven valuable. Furthermore, an additional mechanism accounts for a regressive accumulation of stresses or strains with increasing number of load cycles (in terms of dissipated energy). In view of its suitability for practical use, all model extensions are structured in a modular fashion, so that the complexity of the model (and hence the amount of parameters) can be adapted to the complexity of the geotechnical problem by activating or deactivating certain features. Most model parameters can be determined by conventional laboratory testing. An internal routine optionally facilitates the parameter choice by calibrating certain bounding surface related parameters from an alternative user input, which is more oriented towards experimental outcome. Since a good understanding of a material model is crucial for its reasonable and responsible use, the present thesis aims at offering a sound documentation. Thus, the first part gives an outline of the underlying bounding surface concept and describes the innovations on the constitutive level with reference to theoretical considerations. It is followed by a detailed analysis of capabilities and limitations of the extended model. The next part is dedicated to the numerical implementation of the soil model and its calibration procedure on the basis of laboratory test results. Moreover, the embedded calibration routine including the applied optimisation algorithm is presented. The subsequent section serves model validation: by means of element test simulations, generation of response envelopes as well as the reproduction of more general (e. g. composed) stress paths the performance of the extended bounding surface model is demonstrated. Finally, the last chapter draws conclusions and discloses potential future perspectives.:1 Introduction 1.1 General aspects on constitutive modelling 1.2 Motivation and outline of the thesis 1.3 Basic assumptions and terminology 2 Literature review 2.1 From elastoplasticity to bounding surface plasticity 2.1.1 Bounding surface model according to Manzari and Dafalias (1997) 2.2 Further development of the original model 2.2.1 Papadimitriou and Bouckovalas (2002) 2.2.2 Taiebat and Dafalias (2008) 2.3 Small strain stiffness 2.3.1 Observations 2.3.2 Micromechanical considerations 2.3.3 Very small strain shear modulus G0 2.3.4 Constitutive modelling approaches 2.4 Dilatancy 3 The extended bounding surface model 3.1 Fundamental capabilities of the bounding surface concept 3.1.1 Elastic region 3.1.2 Critical state 3.1.3 Shear strength 3.1.4 Shear stiffness (monotonic) 3.1.5 Contractancy and dilatancy 3.1.6 Barotropy and pycnotropy 3.1.7 Compressive stiffness 3.1.8 Shear stiffness in reversed loading 3.1.9 Additional features 3.2 New features of the extended bounding surface model 3.2.1 Minor modifications 3.2.2 Dilatancy formulation 3.2.3 Cap yield surface 3.2.4 Small strain stiffness mechanism 3.2.5 Cyclic loading mechanism 3.2.6 Summary 3.3 Limitations of the bounding surface model 3.3.1 Intrinsic insuffciencies of the bounding surface concept 3.3.2 Remaining shortcomings of the advanced model version 3.3.3 Newly introduced deficiencies 4 The numerical model and its calibration procedure 4.1 Octave implementation of an element test programme 4.2 Calibration procedure 4.2.1 Sands for calibration 4.2.2 Calibration of basic parameters 4.2.3 Calibration of extended model parameters 4.3 User friendly calibration routine 4.3.1 Conceptual background 4.3.2 Optimisation algorithm 5 Performance of the extended bounding surface model 5.1 Model performance in element tests 5.1.1 Monotonic drained triaxial compression test 5.1.2 Monotonic undrained triaxial compression test 5.1.3 Monotonic eta-constant tests 5.2 Model performance in non-standard triaxial testing 5.2.1 Concept of response envelopes 5.2.2 Simulation of response envelopes 5.3 Model performance on general stress paths 5.3.1 Triaxial compression at small strains 5.3.2 Cyclic triaxial loading 6 Conclusions and perspectives 6.1 Conclusions 6.2 Future perspectives Bibliography Appendices A Mathematical background A.1 Fundamental equations of elastoplasticity A.2 Compilation of major constitutive equations (multiaxial formulation) A.3 Elastoplastic stiffness matrix for singular yield surfaces A.4 Coefficient matrices S and E for loading constraints A.5 Derivation of Mcap and Hcap A.6 Intergranular strain adjustment A.7 Intergranular strain correlation B Details on particle swarm optimisation C Compilation of simulation results C.1 Monotonic triaxial loading C.1.1 Toyoura sand C.1.2 Sacramento River sand C.1.3 Hostun sand C.2 Monotonic eta-constant loading C.2.1 Sacramento River sand C.2.2 Hostun sand C.3 Cyclic triaxial loading / Die Prognose von Setzungen für die Bemessung von Infrastrukturbauwerken stellt hohe Anforderungen an die numerische Untersuchung des Baugrunds und das damit verbundene Stoffgesetz: komplexe Herstellungsprozesse und zyklisch wiederkehrende Verkehrslasten stellen beachtliche Herausforderungen dar. Während das Hauptaugenmerk zumeist auf der realitätsnahen Abbildung des Bodenverhaltens liegt und damit die analytischen Anforderungen des geotechnischen Problems im Fokus stehen, sollten die Bedürfnisse der Ingenieurspraxis in der Stoffgesetzmodellierung nicht außer Acht gelassen werden. In diesem Sinne wurde im Rahmen der Elastoplastizität ein neues Materialmodell für nichtbindige Böden entwickelt. Auf dem Konzept der Bounding Surface Plastizität nach Manzari und Dafalias (1997) beruhend, sind Eigenschaften wie Festigkeit, Steifigkeit und Dilatanz Funktion des Abstands zwischen aktuellem Spannungszustand und einer zugeordneten Modellfläche im Spannungsraum. Auf diese Weise bildet das Mehrflächenmodell fundamentale Verhaltensmuster von Boden korrekt ab, einschließlich beispielsweise scherbezogener Phänomene wie Ver- und Entfestigung, Kontraktanz und Dilatanz oder das Erreichen des kritischen Zustands (Scherfestigkeit bei konstantem Volumen). Des Weiteren erfasst das Modell die Zustandsabhängigkeit des Bodenverhaltens (Barotropie und Pyknotropie). So kann mit nur einem Parametersatz das mechanische Verhalten einer großen Spannweite unterschiedlicher Anfangszustände hinsichtlich Spannung und Lagerungsdichte simuliert werden. Der kinematische Verfestigungsmechanismus der konusförmigen Fließfläche trägt bei Ent- und Wiederbelastungen zu einer realistischeren Steifigkeitsentwicklung bei und ist damit von essenzieller Bedeutung für die Akkumulation von Spannungen oder Verformungen infolge von Lastwechseln. Da sich der gewählte konstitutive Rahmen für Weiterentwicklungen eignet, wurde die ursprüngliche Formulierung des Stoffgesetzes erweitert, um das Modell an die definierten Anforderungen anzupassen. Um geotechnisch relevante Spannungspfade niedriger und höherer Komplexität adäquat reproduzieren zu können, wurde zunächst eine kappenförmige Fließfläche ergänzt. So können irreversible Verformungen nicht nur bei Scherung, sondern auch bei Belastungen ohne Änderung des Spannungsverhältnisses, wie z. B. bei isotroper oder ödometrischer Kompression, auftreten. Bei Spannungspfaden ungewöhnlicher Orientierung, bei Lastwechseln oder zusammengesetzten Spannungspfaden mit Änderung der Belastungsrichtung hat sich eine erhöhte Steifigkeit bei kleinen Dehnungen mit anschließendem dehnungsabhängigen Abfall als nützlich erwiesen. Darüber hinaus berücksichtigt ein zusätzlicher Mechanismus die rückläufige Akkumulation von Spannung oder Verformung mit zunehmender Zyklenanzahl (mittels dissipierter Energie). Im Hinblick auf die Eignung des Stoffgesetzes für die Praxis ist das Modell modular aufgebaut. So kann die Komplexität des Modells (und damit die Anzahl der Parameter) durch Ein- und Ausschalten bestimmter Erweiterungen an die Komplexität des geotechnischen Problems angepasst werden. Die Mehrzahl der Modellparameter wird mit Hilfe konventioneller Laborversuche bestimmt. Eine interne Routine erleichtert durch die Kalibrierung bestimmter Bounding Surface bezogener Größen anhand eines alternativen, stärker an Versuchsergebnissen orientierten User-Inputs bei Bedarf die Parameterwahl. Da die Kenntnis eines Stoffgesetzes entscheidend ist für dessen vernünftigen und verantwortungsvollen Einsatz, soll die vorliegende Arbeit eine fundierte und umfassende Dokumentation bieten. Der erste Teil vermittelt daher zunächst einen Überblick über das zugrunde liegende Bounding Surface Konzept und beschreibt die Neuerungen auf konstitutiver Ebene mit Bezug auf theoretische Hintergründe. Er wird gefolgt von einer detaillierten Darlegung von Potenzialen und Einschränkungen für die Nutzung des erweiterten Modells. Der nächste Abschnitt widmet sich der numerischen Implementierung des Stoffgesetzes und seiner Kalibrierung auf Basis von Versuchsergebnissen. Des Weiteren wird die Kalibrierungsroutine einschließlich des verwendeten Optimierungsalgorithmus präsentiert. Der nachfolgende Teil dient der Modellvalidierung: durch die Simulation von Elementversuchen, die Erzeugung von Antwortellipsen sowie die Abbildung allgemeinerer (beispielsweise zusammengesetzter) Spannungspfade wird die Leistungsfähigkeit des erweiterten Bounding Surface Modells demonstriert. Abschließend werden Schlussfolgerungen gezogen und potenzielle Perspektiven aufgezeigt.:1 Introduction 1.1 General aspects on constitutive modelling 1.2 Motivation and outline of the thesis 1.3 Basic assumptions and terminology 2 Literature review 2.1 From elastoplasticity to bounding surface plasticity 2.1.1 Bounding surface model according to Manzari and Dafalias (1997) 2.2 Further development of the original model 2.2.1 Papadimitriou and Bouckovalas (2002) 2.2.2 Taiebat and Dafalias (2008) 2.3 Small strain stiffness 2.3.1 Observations 2.3.2 Micromechanical considerations 2.3.3 Very small strain shear modulus G0 2.3.4 Constitutive modelling approaches 2.4 Dilatancy 3 The extended bounding surface model 3.1 Fundamental capabilities of the bounding surface concept 3.1.1 Elastic region 3.1.2 Critical state 3.1.3 Shear strength 3.1.4 Shear stiffness (monotonic) 3.1.5 Contractancy and dilatancy 3.1.6 Barotropy and pycnotropy 3.1.7 Compressive stiffness 3.1.8 Shear stiffness in reversed loading 3.1.9 Additional features 3.2 New features of the extended bounding surface model 3.2.1 Minor modifications 3.2.2 Dilatancy formulation 3.2.3 Cap yield surface 3.2.4 Small strain stiffness mechanism 3.2.5 Cyclic loading mechanism 3.2.6 Summary 3.3 Limitations of the bounding surface model 3.3.1 Intrinsic insuffciencies of the bounding surface concept 3.3.2 Remaining shortcomings of the advanced model version 3.3.3 Newly introduced deficiencies 4 The numerical model and its calibration procedure 4.1 Octave implementation of an element test programme 4.2 Calibration procedure 4.2.1 Sands for calibration 4.2.2 Calibration of basic parameters 4.2.3 Calibration of extended model parameters 4.3 User friendly calibration routine 4.3.1 Conceptual background 4.3.2 Optimisation algorithm 5 Performance of the extended bounding surface model 5.1 Model performance in element tests 5.1.1 Monotonic drained triaxial compression test 5.1.2 Monotonic undrained triaxial compression test 5.1.3 Monotonic eta-constant tests 5.2 Model performance in non-standard triaxial testing 5.2.1 Concept of response envelopes 5.2.2 Simulation of response envelopes 5.3 Model performance on general stress paths 5.3.1 Triaxial compression at small strains 5.3.2 Cyclic triaxial loading 6 Conclusions and perspectives 6.1 Conclusions 6.2 Future perspectives Bibliography Appendices A Mathematical background A.1 Fundamental equations of elastoplasticity A.2 Compilation of major constitutive equations (multiaxial formulation) A.3 Elastoplastic stiffness matrix for singular yield surfaces A.4 Coefficient matrices S and E for loading constraints A.5 Derivation of Mcap and Hcap A.6 Intergranular strain adjustment A.7 Intergranular strain correlation B Details on particle swarm optimisation C Compilation of simulation results C.1 Monotonic triaxial loading C.1.1 Toyoura sand C.1.2 Sacramento River sand C.1.3 Hostun sand C.2 Monotonic eta-constant loading C.2.1 Sacramento River sand C.2.2 Hostun sand C.3 Cyclic triaxial loading