Plane Strain Dislocations in Linear Elastic Diffusive Solids

Abstract

Solutions are obtained for the stress and pore pressure due to sudden introduction of plane strain dislocations in a linear elastic, fluid-infiltrated, Biot, solid. Previous solutions have required that the pore fluid pressure and its gradient be continuous. Consequently, the antisymmetry (symmetry) of the pore pressure p about y = 0 requires that this plane be permeable (p = 0) for a shear dislocation and impermeable (∂p /∂y = 0) for an opening dislocation. Here Fourier and Laplace transforms are used to obtain the stress and pore pressure due to sudden introduction of a shear dislocation on an impermeable plane and an opening dislocation on a permeable plane. The pore pressure is discontinuous on y = 0 for the shear dislocation and its gradient is discontinuous on y = 0 for the opening dislocation. The time-dependence of the traction induced on y = 0 is identical for shear and opening dislocations on an impermeable plane, but differs significantly from that for dislocations on a permeable plane. More specifically, the traction on an impermeable plane does not decay monotonically from its short-time (undrained) value as it does on a permeable plane; instead, it first increases to a peak in excess of the short-time value by about 20 percent of the difference between the short and long time values. Differences also occur in the distribution of stresses and pore pressure depending on whether the dislocations are emplaced on permeable or impermeable planes.