Thermal Response of Saturated Porous Spherical Body Containing a Cavity under Several Boundary Conditions

A semi-analytical solution for the saturated porous spherical body containing a hollow space is discussed under several boundary conditions, including pervious surface versus impervious surface, boundary surface subjected to a variable temperature loading versus adiabatic surface, boundary surface subjected to a variable mechanical loading versus fixed displacement surface, and combined boundary conditions. Methods for determining the integration constants of the analytical expressions are derived. Numerical analyses are compared to demonstrate the thermal effects on the evolution of temperature, pore pressure, radial displacement, radial and tangential stresses in and around the geometry of the hollow spherical body subjected to thermal or mechanical perturbations.