Pore pressure and poroelasticity effects in Coulomb stress analysis of earthquake interactions

Pore pressure changes are rigorously included in Coulomb stress calculations for fault interaction studies. These are considered changes under undrained conditions for analyzing very short term postseismic response. The assumption that pore pressure is proportional to fault‐normal stress leads to the widely used concept of an effective friction coefficient. We provide an exact expression for undrained fault zone pore pressure changes to evaluate the validity of that concept. A narrow fault zone is considered whose poroelastic parameters are different from those in the surrounding medium, which is assumed to be elastically isotropic. We use conditions for mechanical equilibrium of stress and geometric compatibility of strain to express the effective normal stress change within the fault as a weighted linear combination of mean stress and fault‐normal stress changes in the surroundings. Pore pressure changes are determined by fault‐normal stress changes when the shear modulus within the fault zone is significantly smaller than in the surroundings but by mean stress changes when the elastic mismatch is small. We also consider an anisotropic fault zone, introducing a Skempton tensor for pore pressure changes. If the anisotropy is extreme, such that fluid pressurization under constant stress would cause expansion only in the fault‐normal direction, then the effective friction coefficient concept applies exactly. We finally consider moderately longer timescales than those for undrained response. A sufficiently permeable fault may come to local pressure equilibrium with its surroundings even while that surrounding region may still be undrained, leading to pore pressure change determined by mean stress changes in those surroundings.