Failure in accretionary wedges with the maximum strength theorem: numerical algorithm and 2D validation

The objective is to capture the 3D spatial variation in the failure mode occurring in accretionary wedges and their analog experiments in the laboratory from the sole knowledge of the material strength and the structure geometry. The proposed methodology relies on the maximum strength theorem which is inherited from the kinematic approach of the classical limit analysis. It selects the optimum virtual velocity field which minimizes the tectonic force. These velocity fields are constructed by interpolation thanks to the spatial discretization conducted with ten-noded tetrahedra in 3D and six-noded triangles in 2D. The resulting, discrete optimization problem is first presented emphasizing the dual formalism found most appropriate in the presence of nonlinear strength criteria, such as the Drucker-Prager criterion used in all reported examples. The numerical scheme is first applied to a perfectly triangular 2D wedge. It is known that failure occurs to the back for topographic slope smaller than and to the front for slope larger than a critical slope, defining subcritical and supercritical slope stability conditions, respectively. The failure mode is characterized by the activation of a ramp, its conjugate back thrust, and the partial or complete activation of the d,collement. It is shown that the critical slope is captured precisely by the proposed numerical scheme, the ramp, and the back thrust corresponding to regions of localized virtual strain. The influence of the back-wall friction on this critical slope is explored. It is found that the failure mechanism reduces to a thrust rooting at the base of the back wall and the absence of back thrust, for small enough values of the friction angle. This influence is well explained by the Mohr construction and further validated with experimental results with sand, considered as an analog material. 3D applications of the same methodology are presented in a companion paper.