Three-dimensional Green's functions of thermoporoelastic axisymmetric cones

Abstract

On the base of Biot's consolidation theory, we introduce the steady-state general solutions of thermoporoelastic axisymmetric media initially. Several three-dimensional problems of porous media, such as the apex of a solid cone and a hollow cone under the action of a point fluid source and a point heat source in a steady state, are analyzed afterwards, respectively. By introducing the potential functions with the coefficients determined in line with the corresponding liquid-heat-force equilibrium relations and boundary conditions, we obtain the coupled fields of thermoporoelastic cones suffered from the point sources. Furthermore, the numerical examples as well as the contour plots of the coupled fields of thermoporoelastic cones are presented. The numerical results show that the phenomenon of stress concentration can occur near the point of action. The results associated with the apex angle π/2 are of importance to be used for constructing the analytical solutions of the boundary value problems as well as the defect problems.