Elasto-viscoplastic modelling of unsaturated soils under static and dynamic loading in 3D stress space

Consolidation, dynamic analysis, and wave propagation are some of the topics in geomechanics in which a complete characterization of coupling of the solid skeleton deformation and fluid flows is necessary for an accurate evaluation of material response. Dynamic behavior of soils is widely investigated in the past decades; however, they have mainly concerned the behaviour of dry or fully saturated porous media. Considering a three-phase continuum system which accounts for the interactions between the phases is crucial for investigating dynamic behavior of real soils which are invariably in an unsaturated state. Deposits located near the surface of the earth with relatively low water content, highly plastic clays which undergo changing environment or loose silty sands which collapse under wetting process are examples of unsaturated soils and experience severe situations especially under dynamic conditions. This thesis presents an elasto-visco-plastic flow-deformation model for dynamic analysis of unsaturated soils including mechanical and hydraulic hysteresis. Governing equations of fluid and solid phases are derived based on theory of continuum mechanics considering phase interaction, and nonlinear deformation of solid skeleton subject to dynamic loading. A numerical scheme is developed using a robust Finite Element method as the global solution to solve various boundary value problems. For the local solution, a comprehensive bounding surface viscoplastic model is presented for unsaturated soils which accounts for suction hardening and rate effects and can simulate monotonic and cyclic loading paths. Consistency condition theory is used to describe the viscosity behaviour of the material. A unique relationship between stress, strain, and strain rate of the material is also defined to perfectly describe the effect of the strain rate hardening. Several examples are solved to validate the model and demonstrate the capability of the proposed framework for investigating behaviour of soils in complex hydro-mechanical conditions

A COUPLED HYDRAULIC-MECHANICAL ELASTOPLASTIC CONSTITUTIVE MODEL FOR UNSATURATED SANDS AND SILTS

Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore water, and pore air. It is well known that the behavior of unsaturated soils is influenced heavily by the matric suction (pore air pressure minus pore water pressure). Soil water characteristic curves (SWCCs) describe the relationship between matric suction and water content in unsaturated soils. In terms of constitutive modeling of soils, the relationship between matric suction and water content can be termed the hydraulic behavior of soils. SWCCs show hysteretic behavior depending on wetting/drying history of the soil. Recently geotechnical engineers have begun to notice that SWCCs also depend on the stress-strain history (mechanical behavior) of a soil. The hydraulic behavior of unsaturated soils, on the other hand, influences the mechanical behavior through matric suction. All of these facts, especially the coupling effects between hydraulic and mechanical behavior, demonstrate a very complex behavior of unsaturated soils.Unsaturated soils are prevalent in many parts of the world and geotechnical engineers are often called to predict the behavior of these structures such as the rainfall induced failure of a compacted soil slope. In order to predict the behavior of unsaturated soil geotechnical engineering structures, a hysteretic SWCCs model is first proposed based on the bounding surface plasticity concept. The hysteresis in SWCCs is modeled using concepts that parallel the elastoplastic theory used to model stress-strain behavior of soils. Matric suction is used as the stress variable and volume fraction of water or volumetric water content is used as the strain variable in modeling the SWCCs. This hysteretic SWCCs model is incorporated into a simple isotropic constitutive model to verify the proposed concepts that account for the coupling effects between hydraulic and mechanical behavior of unsaturated soils. Then a comprehensive constitutive model for unsaturated soils is developed in the general stress space. The rate equations of the proposed unsaturated soil model are integrated using a fully implicit integration scheme. Two sets of laboratory tests, one for Minco silt and another for Toyoura sand are used to calibrate and validate the model performance. The model is shown to capture the influence of stress-strain history on the SWCCs and the influence of SWCCs on the stress-strain behavior of silts and sands and predict the laboratory tests reasonably well

Geomechanical Stability Analysis for Co2 Sequestration in Carbonate Formation

Geomechanical analysis is one of the fundamental pillars to build up the confidence of geological sequestration of CO2. Large scale CO2 sequestration in deep carbonate formation is a complicated geological process, which will non-reversibly transform the presumed equivalent and stable status of a sedimentary basin that formed over millions of years: chemically, hydraulically, geothermally, and geomechanically. In this dissertation, thermoporoelasticity guides the theoretical establishment of a conservative baseline for the geomechanical stability analysis of CO2 sequestration. Extensive laboratory tests, including CO2 flooding tests, permeability tests, uniaxial and triaxial tests, Brazilian tensile strength tests, poroelasticity tests, point load tests, and fracture toughness tests, etc, were conducted on Indiana limestone and Pierre shale to investigate the effects of CO2 sequestration on storage rock and caprock. Numerical simulations using finite difference method of FLAC3D were also conducted to understand the mechanism of strain localization due to pore pressure fluctuation. Based on these laboratory and numerical tests, it is concluded that two mechanisms are competing for rock failures in deep carbonate formations during CO2 sequestration. One is the faulting induced by pore-pressure buildup, and another is the compaction failure because of rock quality deterioration due to exposure to CO2 enriched solution. Fracture toughness measurements on limestone and shale suggest that the fracture toughness of target formation may not be necessarily lower than that of cap rock formation; then the fractures developed in target formation may be easily extended to the cap rock formation, ruining the sealing mechanism. As such, preventing extensive fracturing, and monitoring the seismicity in target formation are essential. Finally, the potential problems of CO2 sequestration in the Williston Basin were investigated. The in-situ stress regime of the Williston Basin was estimated as a mixture of normal and strike-slip faulting regimes, in favor of a vertical or sub-vertical fracture development pattern, which is negative to the CO2 sequestration. However, as the basin is not very close to an incipient failure, compaction failures are expected to be more pronounced, and naturally occurred geological phenomena, stylolites, will help to understand the CO2 sequestration in deep carbonate formation in the long run

Physical-Mathematical modeling and numerical simulations of stress-strain state in seismic and volcanic regions

The strain-stress state generated by faulting or cracking and influenced by the strong heterogeneity of the internal earth structure precedes and accompanies volcanic and seismic activity. Particularly, volcanic eruptions are the culmination of long and complex geophysical processes and physical processes which involve the generation of magmas in the mantle or in the lower crust, its ascent to shallower levels, its storage and differentiation in shallow crustal chambers, and, finally, its eruption at the Earth’s surface. Instead, earthquakes are a frictional stick-slip instability arising along pre-existing faults within the brittle crust of the Earth. Long-term tectonic plate motion causes stress to accumulate around faults until the frictional strength of the fault is exceeded. The study of these processes has been traditionally carried out through different geological disciplines, such as petrology, structural geology, geochemistry or sedimentology. Nevertheless, during the last two decades, the development of physical of earth as well as the introduction of new powerful numerical techniques has progressively converted geophysics into a multidisciplinary science. Nowadays, scientists with very different background and expertises such as geologist, physicists, chemists, mathematicians and engineers work on geophysics. As any multidisciplinary field, it has been largely benefited from these collaborations. The different ways and procedures to face the study of volcanic and seismic phenomena do not exclude each other and should be regarded as complementary. Nowadays, numerical modeling in volcanology covers different pre-eruptive, eruptive and post-eruptive aspects of the general volcanic phenomena. Among these aspects, the pre-eruptive process, linked to the continuous monitoring, is of special interest because it contributes to evaluate the volcanic risk and it is crucial for hazard assessment, eruption prediction and risk mitigation at volcanic unrest. large faults. The knowledge of the actual activity state of these sites is not only an academic topic but it has crucial importance in terms of public security and eruption and earthquake forecast. However, numerical simulation of volcanic and seismic processes have been traditionally developed introducing several simplifications: homogeneous half-space, flat topography and elastic rheology. These simplified assumptions disregards effects caused by topography, presence of medium heterogeneity and anelastic rheology, while they could play an important role in Moreover, frictional sliding of a earthquake generates seismic waves that travel through the earth, causing major damage in places nearby to the modeling procedure This thesis presents mathematical modeling and numerical simulations of volcanic and seismic processes. The subject of major interest has been concerned on the developing of mathematical formulations to describe seismic and volcanic process. The interpretation of geophysical parameters requires numerical models and algorithms to define the optimal source parameters which justify observed variations. In this work we use the finite element method that allows the definition of real topography into the computational domain, medium heterogeneity inferred from seismic tomography study and the use of complex rheologies. Numerical forward method have been applied to obtain solutions of ground deformation expected during volcanic unrest and post-seismic phases, and an automated procedure for geodetic data inversion was proposed for evaluating slip distribution along surface rupture

Modellierung und Analyse von Wellen-Bauwerk-Boden Interaktion für monolithische Wellenbrecher

Monolithic breakwaters are preferred to other types of structures in terms of economical and environmental aspects. Nevertheless, they are more vulnerable to foundation failures, especially to stepwise failures. Due to the highly complex processes involved in wave-structure-foundation interaction, no reliable model yet exists for this failure mechanism. Therefore, a semi-coupled CFD-CSD model system and a simplified model are developed in OpenFOAM to describe wave-structure-foundation interaction for monolithic breakwaters, and particularly stepwise failures. The CFD model is an extension of the incompressible multiphase Eulerian solver of OpenFOAM by introducing different seepage laws and a simplified fluid compressibility model. The CFD model is successful in reproducing breaking wave impact including effect of entrapped air. A new CSD model is developed to solve the fully dynamic, coupled Biot equations with a new approach taking advantage of the PISO algorithm to resolve pore fluid velocity-pressure coupling. Soil-structure interaction is introduced via a frictional contact model and for soil behaviour, a multi-surface plasticity model is implemented. The model is validated against analytical models and physical tests. The model succeeds to reproduce wave-induced residual pore pressure buildup and soil densification followed by pore pressure dissipation. A one-way coupling of both models is achieved by transforming the CFD model output into input for the CSD model. The semi-coupled model system is applied successfully to reproduce selected results of a caisson breakwater subject to breaking wave impact in the Large Wave Flume (GWK). The model system is applied to expand the range of conditions tested in GWK for response of the soil foundation. A new load eccentricity concept, is proposed to classify response of the foundation in four load eccentricity regimes. Load eccentricity carries all significant information related to wave loads (horizontal and uplift) and to properties of the structure (mass and geometry). Using this concept, recommendations are drawn for design of monolithic breakwaters, and a new simplified nonlinear 3-DOF model is developed with elastoplastic springs. Model parameters are calibrated using results from the CFD-CSD model for different sand relative densities and different load eccentricities. The simplified model can simulate the stepwise failure (sliding, settlement and tilt) as well as the overall failure (overturning).Caisson-Wellenbrecher werden aufgrund ökonomischer und Umweltaspekte bevorzugt. Jedoch sind sie empfindlicher gegen das Versagen des Baugrundes insbesondere gegen schrittweises Versagen. Aufgrund der Komplexität der Wellen-Bauwerk-Boden Interaktion liegt noch kein verlässliches Modell für diesen Versagensmechanismus vor. Deswegen werden ein semi-gekoppeltes CFD-CSD Modellsystem und ein vereinfachtes Modell in OpenFOAM entwickelt. Das CFD-Modell stellt eine durch Sickerströmungsgesetze und ein vereinfachtes Modell der Fluidkompressibilität erweiterte Version des mehrphasigen Strömingslösers von OpenFOAM dar. Das CFD-Modell wurde erfolgreich eingesetzt, um Druckschlagbelastungen durch brechende Wellen mit Lufteinschlüssen zu reproduzieren. Ein neues CSD-Modell wurde für die Lösung der voll dynamischen, gekoppelten Biot-Gleichungen mit einem neuen Ansatz entwickelt. Dabei wird der PISO-Algorithmus genutzt, um die Kopplung von Geschwindigkeit und Druck des Porenfluids zu lösen. Die Bauwerk-Boden Interaktion wird über ein Reibungs-Kontaktmodell eingeführt und für die Plastizität des Bodens ein Mehrflächenmodell implementiert. Die Validierung des CSD-Modells erfolgte durch analytische Modelle und Laborversuche. Mit dem Modell ist es gelungen, den Porenwasserdruckaufbau, die Bodenverdichtung und die Dissipation des Porenwasserdruckes zu reproduzieren. Es wurde eine Einweg-Kopplung der Modelle implementiert, in dem der Output des CFD-Modells als Input für das CSD-Modell aufbereitet wird. Mit dem validierten semi-gekoppelten Modellsystem ist es gelungen die Experimente im Großen Wellenkanal (GWK) zu reproduzieren. Darüber hinaus wurde das Modellsystem eingesetzt, um die getesteten Bedingungen zu erweitern. Ein neues Lastexzentrizitätskonzept wurde eingeführt, um die Gründungsverhaltens in vier Regime zu klassifizieren. Die Lastexzentrizität fasst alle relevanten Informationen der Wellenbelastung (Horizontal und Auftrieb) und der Bauwerkseigenschaften (Masse und Geometrie) zusammen. Unter Anwendung dieses Konzepts werden Empfehlungen für die Bemessung monolithisches Wellenbrechers ausgesprochen. Darüber hinaus wurde ein vereinfachtes nichtlineares 3-DOF Modell mit elasto-plastischen Federn entwickelt. Die Modellparameter wurden für unterschiedliche relative Dichte des Bodens und Lastexzentrizität kalibriert. Das vereinfachte Modell kann das schrittweise Versagen (Gleiten, Setzung und Kippen) sowie das Gesamtversagen (Umkippen) simulieren

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells