Éditeur(s) : HAL CCSD Elsevier
Résumé : This paper presents a numerical investigation on the mechanical behavior of cemented granular materials by means of discrete element simulations. In particular, two conceptual elements of this behavior were explored: the yield surfaces and the plastic potentials, as defined in the framework of elastoplastic constitutive models. For this purpose, we implemented a contact model that mimics the mechanical behavior of cemented bonds, we constructed a set of polydisperse samples with different solid fractions, and we tested these samples by means of a biaxial device with four rigid walls. The yield surfaces and plastic potentials were thus obtained and analyzed as functions of the solid fraction of the material, drawing interesting conclusions, confirming previous experimental findings, and, consequently, evidencing the great potential of discrete element simulations in exploring the behavior of real cemented geomaterials.
ISSN: 0266-352X

hal-00853748
https://hal.archives-ouvertes.fr/hal-00853748
DOI : 10.1016/j.compgeo.2012.11.001

Éditeur(s) : HAL CCSD
Résumé : The present PhD thesis is devoted to the numerical simulation and analysis of shear on cohesive granular materials. In the framework of the Contact Dynamics method, we developed a model of cohesive bonding, which mimics cohesion by cementation. This model involves three contact strength parameters (a tensile strength, a coefficient of sliding friction, and a coefficient of rolling friction) as well as a local criterion, which controls the creation and the breaking of cohesive bonds. All contacts are cohesive at the beginning of the numerical simulations, and contact rupture leads to an irreversible loss of tensile strength (debonding). We varied systematically the three contact strength parameters and studied their influence on the shear strength, the dilatancy, and the microstructure of the granular media. Our results show that internal friction and macroscopic tensile strength have different origins at the contact scale. We also find that the microstructure of the granular media, when sheared at the steady state (also known as the `critical state"), is strongly affected by the local coefficients of sliding and rolling friction. In particular, the mechanical role of the weak network changes with these two contact parameters, which results from the formation of a new structure of force transmission. On the other hand, we also applied the same numerical simulation method to the simulation of landslides. We developed a methodology, which takes into account the initial morphology of the hillslope, the strength of geomaterials, and a triggering factor, integrating in the same model the initiation and propagation phases of the landslide. To illustrate this methodology, we applied it to the simulation of a hypothetical example of avalanche triggered by the progressive rise of a water table.
Ce travail de thèse porte sur la modélisation numérique et l'analyse du cisaillement dans les milieux granulaires cohésifs. Dans le cadre de la méthode de la Dynamique des Contacts, nous avons développé un modèle de cohésion qui cherche à imiter la cohésion par cimentation. Ce modèle fait intervenir trois paramètres de résistance au niveau des contacts (une résistance à la traction, un coefficient de frottement de glissement, et un coefficient de frottement de roulement) ainsi qu'un critère de création et de rupture des liens cohésifs. Les contacts sont cohésifs au début des simulations et leur rupture entraîne la perte irréversible de la résistance à la traction. Nous avons fait varier les trois paramètres microscopiques et nous avons étudié leur influence dans la résistance au cisaillement, la dilatance, et la microstructure du milieu. Nos résultats montrent que le frottement interne et l'adhésion macroscopiques ont des origines microscopiques différentes. Nous observons aussi que la microstructure du milieu cisaillé à l'état stationnaire (aussi connu comme ``l'état critique") est fortement affectée par l'angle de frottement et la résistance au roulement au niveau des contacts. En particulier, le rôle mécanique du réseau faible change avec ces deux paramètres microscopiques, ce qui résulte de la formation d'une nouvelle structure de transmission de forces. D'autre part, nous avons appliqué cette méthode de simulation numérique à l'étude d'un processus naturel : les glissements de terrain. Nous avons développé une méthodologie qui tient compte de la morphologie initiale du système, de la résistance des géomatériaux, et d'un mécanisme de déclanchement, ce qui permet d'intégrer dans le même modèle les phases d'initiation et de propagation du glissement. Pour illustrer cette méthodologie, nous l'avons appliquée à la modélisation d'un exemple hypothétique d'avalanche déclenchée par la montée progressive du niveau d'une nappe d'eau.
https://tel.archives-ouvertes.fr/tel-00311303

tel-00311303
https://tel.archives-ouvertes.fr/tel-00311303
https://tel.archives-ouvertes.fr/tel-00311303/document
https://tel.archives-ouvertes.fr/tel-00311303/file/these_estrada.pdf

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements
ISSN: 0885-7474

hal-00383423
https://hal.archives-ouvertes.fr/hal-00383423
DOI : 10.1007/s10915-004-4806-4

Éditeur(s) : HAL CCSD Oxford University Press (OUP)
Résumé : This paper presents an inversion method using the interseismic velocity field to determine effective rigidity of the lithosphere. The method is based on the minimization of a cost function defined as the quadratic measure of the difference between measured and modelled velocity fields on a discrete set of points. The continuous mapping of the rigidity is fulfilled with a limited set of parameters and the forward solution is achieved using a plane stress finite element code. The computation of the cost function gradient in the parameters' space allows one to iteratively find the best parameters set through a suitable optimization algorithm.;We first design a benchmark including an abrupt rigidity variation that cannot be described by a continuous function. For such a case, we show that increasing the number of parameters is a way to accurately describe sharp variations of the rigidity map. Then, we use a dense GPS velocity field over the southwestern United States to estimate the corresponding rigidity variations for different spatial resolutions of the parameters' grid. We analyse the conceptual and practical difficulties associated with our methodology. Finally, rigidity maps obtained by our inversion method in southwestern United States and particularly across the San Andreas Fault System are reviewed and compared to current plate rigidity estimates and geophysical data over this area.
ISSN: 0956-540X

hal-00669897
https://hal.archives-ouvertes.fr/hal-00669897
DOI : 10.1111/j.1365-246X.2011.05192.x

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
In this paper, the generalized Stokes problem αu−νΔu+∇p=f, ∇u=0, is considered, where ν denotes the kinematic viscosity, α is a positive parameter proportional to the inverse of the time-step, and the source term f gathers the external forcing, the nonlinear term, and the explicit part of the linear term. The system is derived from a time discretization for the Navier-Stokes equation governing the motion of a two-dimensional incompressible fluid. A domain decomposition numerical method is developed for solving the system. The original domain is divided into several nonoverlapping subdomains, and in each subdomain the concerned equations are discretized by certain finite element methods. A new feature of the method is that the pressure p is required to be piecewise linear rather than piecewise constant, so that the nonphysical oscillations in the solution using piecewise linear pressure are eliminated. However, a difficulty in using piecewise linear pressure is that the Stokes problem in each subdomain involves Dirichlet boundary conditions on pressure at the interface, which is not a real Stokes problem. To avoid the difficulty, a modification is proposed which removes the continuity conditions on the pressure across the interface. In this way, the Stokes problem in each subdomain has only Dirichlet boundary conditions on the velocity. Formulations and discussions for both the methods are presented, which shows that the modified method is simpler than the original one. Numerical experiments are displayed to show the efficiency of the methods, especially that the modified method has the same accuracy as the original one.
ISSN: 0749-159X

hal-00730200
https://hal.archives-ouvertes.fr/hal-00730200

Éditeur(s) : HAL CCSD Institute for Scientific Computing and Information
Résumé : International audience
The production of oil in soft highly compacted reservoirs produces a significant reduction in the pore space which in turn causes the surface to subside. The authors couple two simulators to model the mechanical deformations in the presence of a Darcy flow, both one- and two-phase. The simulators solve for flow in a porous medium using a finite volume method, and solve for the mechanical deformation of the porous media using a finite element method. The flow equations and the deformation equations are coupled using Biot's law. The authors use two different methods for the coupling: the first uses a staggered algorithm; the second is based on a preconditioned conjugate method. The authors use a multiscale method in both approaches. The authors show that the inf-sup condition is not satisfied, because of the mixed discretization which is done by using two separate simulators. The authors give convergence comparisons for the two methods for several examples. Two of the examples are for the linear problem (one-phase) where they know the exact solution and one is for the nonlinear problem (two-phase). In all cases, the preconditioned conjugate algorithm is faster and more robust, in particular when the inf-sup condition is not satisfied. In the nonlinear problem the authors state that the results agree with physical predictions but do not give actual empirical data. Finally, they show the effects of grid orientation on the nonlinear problem.
ISSN: 1705-5105

hal-00730673
https://hal.archives-ouvertes.fr/hal-00730673