Time dependent strain following faulting of a porous medium

A fracture that redistributes shear stress in a porous medium produces local fluid pore pressure changes. Decay of this pore pressure due to flow causes strain. Using the theory of Biot, I calculate the time dependent stress, strain, and pore pressure fields after a plane fracture whose offset varies sinusoidally in the direction of slip. The results permit construction of arbitrary one-dimensional slip functions by Fourier synthesis. In particular, I investigate the simple crack made from two edge dislocations. The fracture surface is slowly reloaded after an initial shear stress drop, and the shear strength of the material adjacent to the fracture varies with time. This behavior is useful in explaining earthquake foreshocks, aftershocks, and delayed creep. For the simple crack the frequency of aftershocks associated with the reloading decays like t−1.