In order to better understand the interaction between pore-fluid
overpressure and failure patterns in rocks we consider a porous
elasto-plastic medium in which a laterally localized overpressure line
source is imposed at depth below the free surface. We solve numerically
the fluid filtration equation coupled to the gravitational force balance
and poro-elasto-plastic rheology equations. Systematic numerical
simulations, varying initial stress, intrinsic material properties and
geometry, show the existence of five distinct failure patterns caused by
either shear banding or tensile fracturing. The value of the critical
pore-fluid overpressure p(c) at the onset of failure is derived from an
analytical solution that is in excellent agreement with numerical
simulations. Finally, we construct a phasediagram that predicts the
domains of the different failure patterns and p(c) at the onset of
failure.