Plane-Strain Shear Dislocations Moving Steadily in Linear Elastic Diffusive Solids

Abstract

This paper derives the stress and pore pressure fields induced by a plane-strain shear (gliding edge) dislocation moving steadily at a constant speed V in a linear elastic, fluid-infiltrated (Biot) solid. Solutions are obtained for the limiting cases in which the plane containing the moving dislocation (y = 0) is permeable and impermeable to the diffusing species. Although the solutions for the permeable and impermeable planes are required to agree with each other and with the ordinary elastic solution in the limits of V = 0 (corresponding to drained response) and V = ∞ (corresponding to undrained response), the stress and pore pressure fields differ considerably for finite nonzero velocities. For the dislocation on the impermeable plane, the pore pressure is discontinuous on y = 0 and attains values which are equal in magnitude and opposite in sign as y = 0 is approached from above and below. The solution reveals the surprising result that the pore pressure on the impermeable plane is zero everywhere behind the moving dislocation (x < 0). For the dislocation on the permeable plane, the pore pressure is zero on y = 0 and attains its maximum at about (2c /V , 2c /V ) where c is the diffusivity, and the origin of the coordinate system coincides with the dislocation. For the impermeable plane, the largest pore pressure change occurs at the origin.