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Predicting stress distributions in fold-and-thrust belts and accretionary wedges by optimization

Abstract : The objective is to demonstrate that the equilibrium element method (EEM) provides the stress distribution in geometrical models of folds, relevant to fold-and-thrust belts as well as accretionary wedges. The core of the method, inherited from limit analysis, is the search for an optimum stress field that (1) is in equilibrium, (2) remains everywhere below or equal to the maximum strength of the rock, and (3) balances the largest possible applied tectonic force. This force and the associated stress field are interpreted as those at the onset of rupture. The method makes no appeal to the rock rheology nor to its elasticity, except for its maximum strength described here with the Coulomb criterion. The stress fields are discretized by elements covering the whole domain and allowing for discontinuities. The example chosen to illustrate the potential of the EEM and to validate our implementation is the thrusting of a rectangular sheet over a flat and weak decollement. The EEM reproduces the solution proposed by Hafner (1951) on the basis of ́ linear elasticity, as long as the strength limit is not reached in the bulk of the domain. The EEM shows in addition that failure in the bulk prevents the activation of the decollement. The EEM is then applied to two fault-bend folds, with known ramp and flat ́ decollement, with and without relief buildup. It is shown that the transition from the flat to ́ the ramp hanging walls occurs through a narrow fan defining the back thrust. The predicted dip of this back thrust decreases with increase in the ramp friction angle, the relief buildup, as well as the ramp curvature. A sharp increase and then a sharp decrease in the magnitudes of the equivalent shear stress and of the mean stress are observed as one moves from the lower flat, through the back thrust up the ramp. If the ramp friction angle is too large, or the relief too important, the EEM predicts the initiation of a new thrust rooting at the back wall, instead of activating the proposed ramp. The application to detect the incipient thrust system within the toe of Nankai's accretionary wedge, southeast coast of Japan, is proposed in the auxiliary material.
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P. Souloumiac, Y. M. Leroy, B. Maillot, K. Krabbenhøft. Predicting stress distributions in fold-and-thrust belts and accretionary wedges by optimization. 2009, pp.B09404. ⟨10.1029/2008JB005986⟩. ⟨hal-00584130⟩

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