Mathematical model of flexure in a saturated geological layer: application to faulting

International audienceWe model the flexure of an isotropic, poroelastic layer. We study two sets of boundary conditions: prescribed displacement and prescribed bending moment. These two kinds of boundary conditions are equivalent for an elastic, not for a poroelastic medium. The model is simple enough to yield analytic solutions. Late deformation takes place under constant bending moment, but stress relaxation is obtained under constant curvature. The magnitude of these phenomena depends on Poisson's ratio. Faulting proves to be sensitive to the loading conditions (prescribed curvature or bending moment). For the Tresca strength criterion, faulting is most critical in the state reached immediately after loading at prescribed curvature, but is time-independent if the bending moment is prescribed. For the Mohr–Coulomb criterion at prescribed bending moment, the asymptotic state is most critical. At prescribed curvature, the conclusion depends on Poisson's ratio