Transient Green's functions of dislocations in transversely isotropic and layered poroelastic half-spaces

Abstract

We derive, for the first time, the transient response (or Green's function, GF) induced by a general point dislocation in a transversely isotropic and layered poroelastic half-space where the contributions from the fluid dislocation and fluid-phase coupling effect are considered. The GF is expressed in terms of the powerful Fourier-Bessel series system of vector functions recently introduced (with the expansion coefficients being the novel dislocation Love numbers). The corresponding source functions, i.e. discontinuities across the source level, are derived, which show that 1) the fluid-phase creates a new type of source functions called fluid dislocation, and 2) it further contributes directly to the traditional solid horizontal tensile dislocation (or tensile-fracture) via the Biot effective stress coefficient. While the dual-variable and position (DVP) method is applied to take care of multilayers, the Talbot's method is employed to carry out the inverse Laplace transform, both showing excellent numerical stability, efficiency, and accuracy. Key features of these GFs are analyzed numerically. It is shown that 1) the poroelastic process is featured by some transient statuses, including drained and undrained limits; 2) while these two limits are sharply different when the dislocation source is a vertical strike-slip or horizontal tensile-fracture, they are the same when a vertical dip-slip or vertical tensile-fracture is in a homogeneous half-space; 3) in all the cases, there are temporal poroelastic deformations which are significantly different from these two limits; and 4) the fluid dislocation alone could significantly contribute to the poroelastic deformation at the earlier time history. These GFs provide the kernel functions in the corresponding boundary element formulation and the method of fundamental solutions, with potential applications in geomechanics and biomedical engineering.