Transient Solutions of an Isotropic Thermostatic Pervious Half Space Subjected to a Point Hot Fluid Injection

Abstract

Elastic transient deformation of a half space due to a point of hot fluid injection at constant rate is studied in this paper. The half space ground surface is modelled as a thermostatic pervious boundary. Biot’s three-dimensional consolidation theory with thermal effect is introduced to derive the analytical solutions of the transient consolidation deformation due to a point of hot fluid injection. The stratum is modelled as a saturated isotropic poroelastic half space. Using Laplace and Hankel integral transforms, closed-form solutions of the horizontal and vertical displacements are obtained. The maximum ground surface horizontal displacement can be exactly derived, and it is around 30% of the maximum ground surface vertical displacement. Moreover, the golden ratio appears in the maximum ground surface horizontal displacement and corresponding vertical displacement of a half space. The study concludes that golden ratio emerges in this phenomenon, and the horizontal displacement should be properly considered in the prediction of vertical displacement induced by a hot fluid injection. The study can provide better understanding of the hot fluid injection induced responses of an isotropic porous elastic half space.