Deformation Due To a Dip–Slip Fault At 45° In Dislocation–Like Imperfectly Bonded Elastic Half–Spaces

Abstract

Closed-form analytical expressions for the displacements and stresses caused by a two-dimensional line source in two homogeneous, isotropic elastic half-spaces with imperfect bonding are derived using a dislocation-like interface model. In this model, the tractions are transmitted continuously across the interface, while the displacements may exhibit a discontinuity. As a special case, the deformation field associated with a dip-slip fault dipping at 45° is obtained in closed form. The effects of perfect and several imperfect bonding conditions on the dimensionless displacements and stresses are illustrated using line graphs, discontinuity plots, and three-dimensional mesh-grid maps with contour lines. The results show that imperfect bonding introduces a jump in displacement across the interface and substantially alters the surrounding deformation field. For the considered source, the vertical displacement is symmetric about the fault, whereas the horizontal displacement is antisymmetric. This behaviour is opposite to that observed for the vertical dip-slip case.