Steady propagation of plane strain shear cracks on an impermeable plane in an elastic diffusive solid

Abstract

Quasi-static shear crack propagation in a linear elastic fluid-saturated porous solid causes a change of pore pressure on the crack plane if it is impermeable but not if it is permeable. Assuming that the pore pressure induced on the crack plane reduces the effective compressive stress (total stress minus pore fluid pressure) and as a result, the frictional resistance, we find that the energy required to drive the crack is decreased by up to about 60% of the value required in a purely elastic solid. The required energy decreases with velocity at low and high velocities, but increases with velocity for Vl/c in the range of 100.5–102, where V is th speed of propagation. l is the loaded length of the semi-infinite crack and c is the diffusivity. When the effect of the pore pressure induced on the crack plane is neglected, the results are qualitatively similar to those of Rice and Simons (1976. J. Geophys. Res.81, 5322–5344) for the permeable crack: coupling between deformation and diffusion stabilizes propagation in the sense that the energy that must be supplied to drive the crack increases with velocity within a finite range of the ratio Vl/c is about an order of magnitude lower than that for the permeable crack, but includes the range cited above and is within the range of observed creep events on the San Andreas fault.