Éditeur(s) : HAL CCSD Elsevier
Résumé : We present the hierarchical matrix (H-matrix) technique combined with the adaptive cross-approximation (ACA) applied to a three-dimensional (3D) elastostatic problem using the boundary element method (BEM). This is used in structural geology and geomechanics for the evaluation of the deformation and perturbed stress field associated with surfaces of displacement discontinuity. Such optimization significantly reduces (i) the time and memory needed for the resolution of the system of equations, but more importantly (ii) the time needed for the post-processing at observation points where the deformation and the perturbed stress field are evaluated. Specifically, it is shown that the H-matrix structure used with the ACA, clearly captures the kernel smoothness during the post-processing stage according to the field point positions, and optimizes the computation accordingly. Combined with the parallelization on multi-core processors, this technique allows intensive computations to be done on personal desktop and laptop computers. Numerical simulations are presented, showing the advantages of such optimizations compared to the standard method.
ISSN: 0955-7997

hal-00561032
https://hal.archives-ouvertes.fr/hal-00561032
DOI : 10.1016/j.enganabound.2009.10.016

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Wallace (1951) and Bott (1959) were the first to introduce the idea that the slip on each fault surface has the same direction and sense as the maximum shear stress resolved on that surface. However, this simplified hypothesis is questionable since fault mechanical interactions may induce slip reorientations. Earlier numerical geomechanical models confirmed that the slickenlines (slip vectors) are not necessarily parallel to the maximum resolved shear stress but are consistent with local stress perturbations. This leads us to ask as to what extent the Wallace and Bott simplifications are reliable as a basis hypothesis for stress inversion from fault slip data. Here, a geomechanical multi-parametric study using a 3D boundary element method, covering (i) fault geometries such as intersected faults or corrugated fault surfaces, (ii) the full range of Andersonian state of stress, (iii) fault friction, (iv) fault fluid pressure, (v) half space effect and (vi), rock properties, is performed in order to understand the effect of each parameter on the misfit angle between geomechanical slip vectors and the resolved shear stresses. It is shown that significant misfit angles can be found under specific configurations invalidating the Wallace and Bott assumptions, even though fault friction tends to minimize the misfit. We therefore conclude that in such cases, stress inversions based on fault slip data should be interpreted with care.
ISSN: 0040-1951

hal-01218418
https://hal.archives-ouvertes.fr/hal-01218418
DOI : 10.1016/j.tecto.2015.06.030

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : Some major challenges for geophysicists and structural geologists using three-dimensional boundary element method codes (3D-BEM) are: (1) reducing the amount of memory required to solve large and dense systems and (2) incorporation of inequality constraints such as traction inequality constraints (TIC) and displacement inequality constraints (DIC). The latter serves two purposes. First, for example, inequality constraints can be used to simulate frictional slip (using TIC). Second, these constraints can prevent element interpenetration while allowing opening mode (using DIC). We have developed a method that simultaneously incorporates both types of functionality of the inequality constraints. We show that the use of an appropriate iterative solver not only avoids the allocation of significant memory for solving the system (allowing very large model computation and simplifying parallelization on multi-core processors), but also admits interesting features such as natural incorporation of TICs and DICs. Compared to other techniques of contact management (e.g., Lagrange multipliers, penalty method, or complementarity problem), this new simple methodology, which does not use any incremental trial-and-error procedures, brings more flexibility, while making the system more stable and less subject to round-off errors without any computational overhead. We provide validations and comparisons of the inequality constraints implementation using 2D analytical and numerical solutions.
ISSN: 1420-0597

hal-00561035
https://hal.archives-ouvertes.fr/hal-00561035
DOI : 10.1007/s10596-009-9170-x