P. Souloumiac1, 2, A. Modaressi-Farahmand-Razavi1
1 Laboratoire MSS-Mat, CNRS UMR 8579, Ecole Centrale Paris, Châtenay Malabry, France
2 Laboratoire de Géologie, CNRS, Ecole Normale Supérieure, Paris, France
Keywords: limit analysis, FEM, geomorphology, stress distributions
ABSTRACT:
The objective is to compare the merits of the Equilibrium Element Method (EEM), based on the
internal approach of limit analysis, and the Finite-Element Method (FEM) for elastic perfectly plastic materials, inpredicting the stress field in geological structures such as fault-bend folds. The two methods predict the samefailure mode although the discontinuities in the stress fields constructed with the EEM lead to a sharper spatial resolution due to the density of the discretization used for the mesh. The FEM has the advantage to give an insight on the whole stress history and the development of the failure mechanics but at a computational cost
which remains orders of magnitude larger than the one required for the EEM.
Introduction
This research is part of an effort to account for mechanical equilibrium and material strength in geometrical models of folds. Cubas et al. (2008) have shown that the external approach of limit analysis (Salençon, 2002) could be applied to thrusting providing the means to assess the life time of a thrust fold and to construct sequences of folds while keeping the geometrical simplicity of the constructions proposed in the seminal work of Suppe (1983). The next objective was to construct statically admissible stress fields on these structures. The EEM, which is a direct application of the internal approach of limit analysis, has been shown by Souloumiac et al.
(2008), to applicable to these geological structures. The stress field obtained by numerical means, following the implementation of Krabbenhøft et al. (2005), is statically admissible and respect the maximum strength (yield limit) point wise. The objective is now to compare the application of the EEM with results obtained with the FEM for elastic-perfectly plastic materials. The latter requires the introduction of a non-associated flow rule which is incompatible with bounding theorems. Putting aside this endless debate (Sloan, 2005), this paper concentrates on the comparison of the predicted stress and the potential of the two approaches.
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