Stability of accretionary wedges based on the maximum strength theorem for fluid-saturated porous media

Accretionary wedges are idealized as triangular-shaped regions, the top surface corresponding to the topography, the bottom surface to the weak, frictional contact (décollement) with the subducting plate and the last side, the back-wall, to the contact with the continent. New critical stability conditions are obtained and defined by the sets of geometrical and material parameters for which the deformation occurs concurrently in two regions of the wedge e.g., the front and the rear. They extend the classical critical stability conditions, restricted to triangular regions of infinite extent and composed of frictional materials, by accounting for arbitrary topography, finite geometry and cohesive materials. They are obtained by the application of the kinematic approach of limit analysis, referred to as the maximum strength theorem, which is first extended to fluid-saturated porous media. The basic failure mode used to defined these stability conditions consists of two reverse faults intersecting the décollement at a common point, the root. The décollement is activated from the back wall to the root. The root position is indeterminate for our extended critical stability conditions. The proposed theory predicts the classical stability conditions as a special case. A first application to the Barbados prism is proposed accounting for a non-linear gradient in fluid pressure within the décollement. The details of the topography is responsible for several sets of critical stability conditions. Our pressure predictions necessary to explain the activation of the frontal thrust are significantly less than the estimates done during the drilling on site. Finally, the theory is applied to a wedge with the décollement partitioned into two regions, the deepest corresponding to the seismogenic zone. The associated failure modes include one composed of two blocks sliding at different velocities over the décollement and separated by a single discontinuity, dipping either towards the front or towards the rear of the wedge. This special mode dominance is facilitated by large pressures and small friction coefficients in the shallowest region of the décollement.