In dense cities, the interactions between all structures, from tall skyscrapers to complex underground tunnel systems, need to be carefully analysed as soon as a new project is considered. This is necessary because of the stress changes in the soil induced by each new construction. Demolishing a building could cause heave at the base of the excavation, deflections in supporting structures and settlements of the surroundings. The behaviour can be modelled in order to predict how large the deformations will be. This thesis investigates the effectiveness of such models. This is done through the application of a parameter sensitivity analysis on models created in Plaxis. The purpose of the analysis is to identify which factors cause discrepancies between the models and the actual displacements monitored on site. The project being examined is located in central London. The analysis focuses on the displacements of existing tunnels below the site caused by the demolition of two buildings. An analysis was carried out to investigate the significance of different parameters, of different material models and methods of analysis, of 3D effects and of inaccurate groundwater data. Ground investigations, laboratory tests and published data were the main sources used to collect reliable initial input parameters for the material models. A model was created in Plaxis 2D using the Mohr-Coulomb and the Hardening Soil with small-strain stiffness material models, using two types of undrained analysis. A model using the Mohr-Coulomb material model was created in Plaxis 3D as well. A sensitivity analysis was then carried out on the 2D models to identify which input parameters were most significant to the tunnel displacements. The results were compared to monitoring data and a back-analysis was carried out to produce more accurate results. The initial and adjusted input parameters were also tested on the 3D model. Finally, the groundwater level was altered. The results indicate that soil stiffness and effective cohesion are the most significant. Small-strain stiffness is shown to be especially important when analysing small tunnel deformation. The 3D model generally yielded more accurate results than the 2D model, while the groundwater level did not appear to affect the deformations. / I tätbebyggda städer bör samspelet mellan olika konstruktioner, från skyskrapor till tunnelsystem, analyseras noga så fort ett nytt projekt ska påbörjas. Detta är kritiskt på grund av den förändrade spänningsfördelning som uppstår i marken vid varje ny byggnation. Marken häver sig, stödmurar deformeras och den omkringliggande marken sätter sig när en byggnad rivs. Denna process kan modelleras för att uppskatta hur stora deformationerna kommer att bli. Det här examensarbetet utvärderar hur effektiv en sådan modell är. En känslighetsanalys utfördes på modeller skapade i Plaxis. Syftet med denna analys är att undersöka vilka faktorer som orsakar skillnader mellan modellerna och mätdata. Projektet ligger i centrala London och analysen fokuserar på tunneldeformationer orsakade av att två byggnader rivs. Tunnlarna befinner sig i ett lager av Londonlera under byggarbetsplatsen. En analys utfördes för att undersöka huruvida olika parameterar, olika materialmodeller och analysmetoder, 3D effekter och grundvattennivån påverkar tunnelförflyttningarna. Markundersökningar, labbtester och publicerad data användes som grund för att bestämma indatavärden. En 2D modell skapades i Plaxis genom att använda materialmodellerna Mohr-Coulomb och ”Hardening Soil with small-strain stiffness”. En Mohr-Coulomb modell skapades dessutom i Plaxis 3D. En känslighetsanalys utfördes sedan på 2D modellen för att identifiera vilka parametrar som påverkade tunnelförflyttningarna mest. Resultaten jämfördes med mätdata och viktiga parameterar ändrades för att ge bättre resultat. Inverkan av att ändra dessa värden undersöktes även i 3D modellen. Slutligen undersöktes påverkan av en förhöjd grundvattennivå. Resultaten antyder att jordens styvhet och den effektiva kohesionen har störst inverkan på resultaten. Styvheten vid små töjningar visar sig vara särskilt viktigt eftersom deformationerna år små. 3D modellen gav generellt sätt mer korrekta resultat än modellen i 2D. En högre grundvattennivå påverkade inte resultaten nämnvärt.

During the casting of a concrete bridge deck, the temporary formwork is causing the underlying ground to deform if a shallow foundation solution is used. There are often demands on the maximum deformation of the superstructure when designing the foundation for the formwork.  To keep the deformations within the desired limits, several ground improvement methods like deep mixing columns or deep foundation methods like piling can be used. Permanent ground improvement methods are however expensive, and far from always needed. To reduce the need for unnecessary ground improvements, it is crucial to calculate the predicted deformations accurately during the design phase. The purpose of this thesis was to investigate how short-term deformations in clay under a formwork during bridge construction should be calculated more generally in future projects. Three different calculation models have here been used to calculate the ground deformations caused by the temporary formwork. A simple analytical calculation and two numerical calculations based on the Mohr Coulomb and Hardening Soil-Small constitutive models. The three calculation models were chosen based on their complexity. The analytical calculation model was the most idealised and the Hardening Soil-Small to be the most complex and most realistic model. Results show that the numerical calculation model Mohr Coulomb and the analytical calculation model gives the best results compared to the measured deformation. One of the most probable reasons for the result is that both of the models require a few input parameters that can easily be determined by well-known methods, such as triaxial-, routine- and CRS-tests. The more advanced Hardening soil small model requires many parameters to fully describe the behaviour of soil. Many of the parameters are hard to determine or seldom measured. Due to the larger uncertainties in the parameter selection compared with the other two models, the calculated deformation also contains larger uncertainties. / Vid gjutning av betongbrodäck kommer den underliggande marken att deformeras av den temporära formställningen, som tar upp lasterna medan betongen härdar. Det finns oftast krav på hur stora markdeformationerna maximalt får vara. För att hålla deformationerna inom gränserna kan diverse markförstärkningsmetoder, så som kalkcementpelare eller pålar, användas. Permanenta markförstärkningar är oftast väldigt dyra och inte alltid nödvändiga. Ett alternativ till att använda dyra markförstärkningar skulle kunna vara att beräkna den förutspådda deformationen med stor exakthet i projekteringsstadiet. Syftet med det här arbetet var att undersöka hur korttidsstätningar i lera vid en bronybyggnation ska beräknas mer generellt i framtida projekt.  I detta arbete har tre beräkningsmodeller använts för att beräkna markdeformationerna från den temporära formställningen. En enklare analytisk modell samt två numeriska beräkningsmodeller som baseras på Mohr Coulomb och Hardening Soil Small teorierna. De tre beräkningsmodellerna valdes utifrån deras komplexitet. Den analytiska beräkningen ansågs vara den mest förenklade modellen medan Hardening Soil-Small var den mest komplexa och realistiska modellen.   Resultatet visar att trots sin enkelhet så ger den numeriska beräkningsmodellen Mohr Coulomb och den analytiska beräkningen bäst resultat jämfört med de uppmätta deformationerna. En möjlig anledning till det goda resultatet är att modellerna endast kräver ett fåtal ingångsparametrar som kan bestämmas med hjälp av välkända fält- och laboratoriemetoder så som triaxialförsök, rutinlaboratorieförsök och CRS-försök. Den mer komplexa modellen Hardening Soil Small kräver flera ingångsparametrar för att kunna modellera jordens beteende. Många av parametrarna är svåra att bestämma då mätdata oftast saknas. Osäkerheterna i valet av ingångsparametrar för den mer komplexa hardening soil small modellen är större än de två andra studerade modellerna, vilekt även ger upphov till större osäkerheter i dem beräknade deformationerna.

I samband med Förbifart Stockholm och Tvärförbindelse Södertörn förväntas en flaskhals skapas vid Vårbybron i södra Stockholm. För att förhindra överbelastning planeras en nybyggnation där pålgrundläggning med grävpålar föreslås. Markförhållanden är ovanliga i Stockholm, med över 100 meter ned till berg. Komplexa omständigheter i området gör det nödvändigt att analysera markrörelser som verkar på grundläggningen. Syftet med studien är att undersöka horisontella- och vertikala sättningar vid ett brolandfäste. Syftet är vidare att analysera vilken typ av numerisk konstitutiv modell som är lämplig med hänsyn till studiens specifika fall och område; Mohr-Coulomb (MC), Hardening Soil (HS) och Hardening Soil med small-strain stiffness (HSS). Slutligen ska jordparametrarnas väsentlighet avgöras i en parameterstudie. Sonderingsdata tillämpas i studien för att skapa en jordlagermodell i AutoCAD Civil 3D 2019 Metric och vidare simulering av sättningar i Plaxis 2D. Vid modellering av sättningar i förekommande geologi rekommenderas att en avancerad modell används, med fördel HSS. Däremot kräver mer avancerade modeller noggranna indata för tillförlitligt resultat och ytterligare tester för styvhetsparametrar bör utföras. I detta projekt kan dyrare tester tänkas sänka slutgiltig budget, eftersom underskattning av moduler i djupa och fast lagrade jordar baserade på konservativt valda moduler ger upphov till en dyrare konstruktion. / In conjunction with the opening of the Stockholm Bypass and Tvärförbindelse Södertörn, a bottleneck is expected at the bridge Vårbybron in southern Stockholm. To prevent traffic congestion, a new construction is planned where pile foundation consisting of bored piles is proposed. The ground conditions are unusual and not typical for Stockholm involving over 100 meters distance to rock. Complex circumstances in the area makes it complicated as well as necessary to analyze ground movements. The aim of the study is to investigate horizontal- and vertical settlements at a bridge abutment. The aim is further to analyze which type of numerical constitutive model that is appropriate with respect to the specific case and area; Mohr-Coulomb (MC), Hardening Soil (HS) and Hardening Soil with small-strain stiffness (HSS). Finally, the significance of the soil parameters is to be determined in a parameter analysis. Results from soundings are used to create a geological model in AutoCAD Civil 3D 2019 Metric. Furthermore, simulation of settlements in Plaxis 2D is performed. It is recommended to apply advanced models for this type of geology, advantageously HSS. However, more advanced models require accurate input data to obtain reliable results, and additional tests for stiffness parameters must be performed for accuracy in the results. In this project, more expensive tests can be thought of as lowering the final budget, as underestimation of modules in deep and stiff soils based on conservatively selected modules leads to an unnecessarily expensive construction.

Doctor of Philosophy(PhD) / Soil Stiffness is an important parameter for any geotechnical engineering design. In laboratory tests it can be derived from stress-strain curves or from dynamic measurement based on wave propagation theory. The second method is a more accurate and direct method for measuring stiffness at very small strains. Until now dynamic measurements have usually been obtained manually from the triaxial test. Attempts have been made to automate the procedure but have apparently failed due to the high level of variability in dynamic measurements. Moreover, triaxial tests of soil can be very lengthy and manual dynamic measurements can be very tedious and impractical for long stress-path tests. In this research a computer program has been developed to automate the stiffness measurement (using bender elements) based on the cross- correlation technique. In this method the program records all the peaks and corresponding arrival times in the cross-correlation signal during the test. The stiffness is calculated and displayed on the screen continuously. The Bender Element enabled to get the small strain shear modulus. An arbitrary “Chirp” waveform of 4 kHz frequency was used for this purpose. Subsequently Bender Element test results were checked by ‘Sine’ waveforms of frequencies 5kHz to 20kHz, as well as by manual inspection of the arrival time. This thesis discusses the method and some of the difficulties in truly automating the process. Finally some results from a number of stress path tests on uncemented and cemented calcareous sediments are presented. Bender elements have been used by many researchers to determine the shear modulus at small strain. Most previous studies have used visual observation of arrival time, which is time consuming and often requires some judgement from the operator. This thesis will describe the use of cross-correlation as a method for automation of Gmax measurement. Cross-correlation has been claimed to be unreliable in the past. However, it will be shown that provided several peaks in the cross-correlation signal are monitored it is possible to follow the variation of Gmax throughout consolidation and shearing. The measurement can be made at regular intervals within the software controlling a stress-path apparatus. Details of the apparatus used and practical considerations including selection of waveform and frequency are discussed. A series of drained cyclic triaxial tests was carried out on artificially cemented and uncemented calcareous soil of dry unit weights 13, 15, and 17 kN/m3 and sheared with constant effective confining stress 300 kPa. Gypsum cement contents of 10%, 20% and 30% of the dry soil weight were used. In addition a series of stress path tests were performed on Toyuora sand samples. Results will be presented for two uncemented and one cemented sand. In addition to the bender elements, all tests had internal instrumentation to monitor axial and lateral strains. Results will be presented for Toyura sand to show that the measurements are consistent with those obtained by other methods. Results will also be presented for carbonate sand subjected to a wide range of stress paths. Finally, results will be presented for the carbonate sand cemented with gypsum. The degradation of Gmax of the cemented soil subjected to variety of monotonic and cyclic stress-paths is presented. Analysis of the results includes assessment of the factors influencing Gmax for uncemented sand. Preliminary analysis indicates that in order of importance these are the mean effective stress, the stress history, void ratio and stress ratio. For cemented sand, Gmax is initially constant and independent of stress path. After yielding the modulus degrades, becoming increasingly stress level dependent and eventually approaches the value for uncemented sand. Factors influencing the rate of degradation are discussed. For the Toyuora sand samples the effects of end restraint on the stress-strain response at small strains were investigated. The conventional method of mounting triaxial specimen has the effect of introducing friction between sample and end platen during a compression test. This inevitably restricts free lateral movement of the specimen ends. Frictional restraint at the sample ends causes the formation of 'dead zones' adjacent to the platens, resulting in non-uniform distribution of stress and strain (and of pore pressure if undrained). On the other hand the specimen with 'free' ends maintain an approximate cylindrical shape instead of barrelling when subjected to compression, resulting in a more uniform stress distribution.

Doctor of Philosophy(PhD) / Soil Stiffness is an important parameter for any geotechnical engineering design. In laboratory tests it can be derived from stress-strain curves or from dynamic measurement based on wave propagation theory. The second method is a more accurate and direct method for measuring stiffness at very small strains. Until now dynamic measurements have usually been obtained manually from the triaxial test. Attempts have been made to automate the procedure but have apparently failed due to the high level of variability in dynamic measurements. Moreover, triaxial tests of soil can be very lengthy and manual dynamic measurements can be very tedious and impractical for long stress-path tests. In this research a computer program has been developed to automate the stiffness measurement (using bender elements) based on the cross- correlation technique. In this method the program records all the peaks and corresponding arrival times in the cross-correlation signal during the test. The stiffness is calculated and displayed on the screen continuously. The Bender Element enabled to get the small strain shear modulus. An arbitrary “Chirp” waveform of 4 kHz frequency was used for this purpose. Subsequently Bender Element test results were checked by ‘Sine’ waveforms of frequencies 5kHz to 20kHz, as well as by manual inspection of the arrival time. This thesis discusses the method and some of the difficulties in truly automating the process. Finally some results from a number of stress path tests on uncemented and cemented calcareous sediments are presented. Bender elements have been used by many researchers to determine the shear modulus at small strain. Most previous studies have used visual observation of arrival time, which is time consuming and often requires some judgement from the operator. This thesis will describe the use of cross-correlation as a method for automation of Gmax measurement. Cross-correlation has been claimed to be unreliable in the past. However, it will be shown that provided several peaks in the cross-correlation signal are monitored it is possible to follow the variation of Gmax throughout consolidation and shearing. The measurement can be made at regular intervals within the software controlling a stress-path apparatus. Details of the apparatus used and practical considerations including selection of waveform and frequency are discussed. A series of drained cyclic triaxial tests was carried out on artificially cemented and uncemented calcareous soil of dry unit weights 13, 15, and 17 kN/m3 and sheared with constant effective confining stress 300 kPa. Gypsum cement contents of 10%, 20% and 30% of the dry soil weight were used. In addition a series of stress path tests were performed on Toyuora sand samples. Results will be presented for two uncemented and one cemented sand. In addition to the bender elements, all tests had internal instrumentation to monitor axial and lateral strains. Results will be presented for Toyura sand to show that the measurements are consistent with those obtained by other methods. Results will also be presented for carbonate sand subjected to a wide range of stress paths. Finally, results will be presented for the carbonate sand cemented with gypsum. The degradation of Gmax of the cemented soil subjected to variety of monotonic and cyclic stress-paths is presented. Analysis of the results includes assessment of the factors influencing Gmax for uncemented sand. Preliminary analysis indicates that in order of importance these are the mean effective stress, the stress history, void ratio and stress ratio. For cemented sand, Gmax is initially constant and independent of stress path. After yielding the modulus degrades, becoming increasingly stress level dependent and eventually approaches the value for uncemented sand. Factors influencing the rate of degradation are discussed. For the Toyuora sand samples the effects of end restraint on the stress-strain response at small strains were investigated. The conventional method of mounting triaxial specimen has the effect of introducing friction between sample and end platen during a compression test. This inevitably restricts free lateral movement of the specimen ends. Frictional restraint at the sample ends causes the formation of 'dead zones' adjacent to the platens, resulting in non-uniform distribution of stress and strain (and of pore pressure if undrained). On the other hand the specimen with 'free' ends maintain an approximate cylindrical shape instead of barrelling when subjected to compression, resulting in a more uniform stress distribution.

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

This thesis has a theoretical and a practical part. The first part contains theoretical introduction to the phenomenon of increased stiffness at very small strains and possibilities of its practical applications. The available methods for evaluating initial shear modulus tests are described below. Increased attention is paid to the method of evaluation of test data in the frequency domain using the Fourier transform. The last chapter in this part describes an algorithm designed for automatic evaluation of measurements in the frequency domain. The practical part deals with measurement and evaluation of initial shear modulus for Brno clay as a function of vertical stress in oedometric test. Firstly, a device is presented that allows the extension of the oedometric test with sensors for measuring initial shear modulus of soil. This device was designed for the test in this thesis. Subsequently, the test plan is described including description of all soil samples. In this thesis, several types of soil samples from a single site were tested. Next, the results of the individual tests are evaluated by the selected methods. Examples are used for showing the differences in evaluation of the same data by other methods. At the end, the results of the individual tests for all sample types are compared with each other and with data from literature.