Analytical Solutions Under Spherical Condition

Due to the complex geometry and boundary conditions of porous materials in various engineering applications, it is essential to derive analytical solutions for typical problems. This chapter presents a semi-analytical solution for a saturated porous spherical body that includes a hollow region, considering different boundary conditions such as pervious or impervious surfaces, and a range of temperature, displacement, and mechanical boundary conditions, along with their combinations. Furthermore, analytical solutions for a spherical space containing a spherical cavity are proposed, based on the irreversible coupled governing equations for saturated porous thermo-elastic materials. These solutions take into account the effects of coupled mechanical and thermal loadings on both the inner and outer boundary surfaces. A concept known as “semi-permeability” is introduced to model the impact of boundary conditions, varying from a fully pervious to a fully impervious surface.