Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

Abstract

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.