Deformation of two welded half-spaces caused by a centre of rotation source

Abstract

Closed-form analytic expressions for Papkovich-Neuber displacement potentials, displacements, and stresses due to the centre of rotation source in an elastic half-space overlying an elastic half-space are obtained. The elastic results are valid for different values of Poisson's ratio and a change in the rigidity of the two half-spaces. Further, the correspondence principle of linear viscoelasticity is used to obtain the corresponding solutions in an elastic half-space overlying a viscoelastic half-space. The viscoelastic results are valid for different values of relaxation time and a change in the rigidity of the two half-spaces. The variation of the displacements and stresses with the epicentral distance as well as with the relaxation time are studied. The magnitude of displacement and normal stress components assume a maximum value for the Maxwell model and minimum value for the Kelvin model whereas the shear stresses assume a minimum value for the Maxwell model and maximum value for the Kelvin model.