Structural consequences of cohesion in gravitational instabilities triggered by fluid overpressure: Analytical derivation and experimental testing

The critical taper theory of Coulomb wedges has been classically applied to compressive regimes (accretionary prisms/fold-and-thrust belts), and more recently to gravitational instabilities. Following the initial hypothesis of the theory, we provide an alternative expression of the exact solution for a non-cohesive wedge by considering the balance of forces applied to the external surfaces. Then, we use this approach to derive a solution for the case of cohesive wedges. We show that cohesion has conspicuous structural effects, including a minimum length required for sliding and the formation of listric faults. The stabilizing effect of cohesion is accentuated in the foremost thin domain of the wedge, defining a required Minimum Failure Length (MFL), and producing sliding of a rigid mass above the detachment. This MFL decreases with less cohesion, a smaller coefficient of internal friction, larger fluid overpressure ratio, and steeper upper and basal surfaces for the wedge. Listricity of the normal faults depends on the fluid overpressure magnitude within the wedge. For moderate fluid overpressure, normal faults are curved close to the surface, and become straight at depth. In contrast, where fluid overpressure exceeds a critical value corresponding to the fluid pressure required to destabilize the surface of a noncohesive wedge, the state of stress changes and rotates at depth. The faults are straight close to the surface and listric at depth, becoming parallel to the upper surface if the wedge is thick enough. We tested some of these structural effects of a cohesive wedge on gravitational instabilities using analogue models where cohesive material was subjected to pore-fluid pressure. The shape of the faults obtained in the models is consistent with the predictions of the theory.