The Transient Ground Surface Displacements due to a Point Sink/Heat Source in an Elastic Half-Space

Abstract

Thermoelastic deformation due to a point heat source is the analog of poroelastic response caused by a point sink. In this paper, Biot’s three-dimensional consolidation theory is introduced to derive the analytical solutions of the transient consolidation deformation with a point sink in saturated isotropic porous elastic half-space. The transient ground surface displacement produced by a point heat source is described through analog quantities between poroelasticity and thermoelasticity. Closed-form solutions of the horizontal and vertical displacements are obtained by using Laplace and Hankel integral transforms. Attention is focused on the maximum surface horizontal displacement compared to the maximum surface settlement. Results show that the horizontal displacement is about 30% of the maximum ground surface settlement. The study concludes that horizontal displacement is significant and should be considered in prediction of the transient settlement induced by groundwater withdrawal.