Plane-Strain Shear Dislocation on a Leaky Plane in a Poroelastic Solid

Solutions for the stress and pore pressure p are derived due to sudden introduction of a plane strain shear dislocation on a leaky plane in a linear poroelastic, fluid-infiltrated solid. For a leaky plane, y = 0, the fluid mass flux is proportional to the difference in pore pressure across the plane requiring that Δp = R∂p=∂y, where R is a constant resistance. For R = 0 and R→1, the expressions for the stress and pore pressure reduce to previous solutions for the limiting cases of a permeable or impermeable plane, respectively. Solutions for the pore pressure and shear stress on and near y = 0 depend significantly on the ratio of x and R. For the leaky plane, the shear stress at y = 0 initially increases from the undrained value, as it does from the impermeable plane, but the peak becomes less prominent as the distance x from the dislocation increases. The slope (∂r_xy=∂t) at t = 0 for the leaky plane is always equal to that of the impermeable plane for any large but finite x. In contrast, the slope ∂r_xy=∂t for the permeable fault is negative at t = 0. The pore pressure on y = 0 initially increases as it does for the impermeable plane and then decays to zero, but as for the shear stress, the increase becomes less with increasing distance x from the dislocation. The rate of increase at t = 0 is equal to that for the impermeable fault.