Spherically Symmetric Thermo-Poroelasticity Problems for a Solid Sphere

In this chapter, we continue to discuss the solutions to thermo-poroelasticity problems and to study effects that cannot be captured by one-dimensional poroelasticity analysis. Such an example is the Mandel–Cryer effect of amplification of the pore fluid pressure in a three-dimensional poroelastic analysis, which was identified by Mandel (1950) and Cryer (1963) and observed by Gibson et al. (1963) during radial loading of a saturated clay sphere. Of related interest are the studies by de Josselin de Jong (1953), where similar manifestations in the pore pressure response of piezometers installed in low-permeability soils such as clay were observed. References to further studies are also given by Selvadurai and Shirazi (2004a, b). The thermo-poroelastic problem for a hollow sphere subjected to a sudden rise in temperature and pressure on its inner wall was studied by Kodashima and Kurashige (1996). In their work, the heat transport equation included a nonlinear convective term; the analytical solution of the problem was obtained for the steady-state case, and the transient solution was obtained numerically. Rehbinder (1995) considered problems with cylindrical and spherical symmetries, and the stationary solutions for the nonlinear thermo-poroelastic problem were obtained using a perturbation technique. Belotserkovets and Prevost (2011) studied the transient response of a thermo-poroelastic sphere subjected to an applied radial stress; their goal was to characterize the influence of the applied stress on the change in temperature within the sphere. The poroelastic framework can also be extended to accommodate poroelastic solids that experience brittle damage, which could lead to micromechanical damage as opposed to failure; here the poroelastic behavior is maintained, albeit with altered mechanical and fluid transport properties (Mahyari and Selvadurai, 1998; Selvadurai and Mahyari, 1998; Selvadurai, 2004; Selvadurai and Shirazi, 2004a, b, 2005; Shirazi and Selvadurai, 2005; Massart and Selvadurai, 2012, 2014). This chapter examines thermo-hydro-mechanical (THM) problems related to the three-dimensional deformation of a poroelastic sphere subjected to uniform heating at the boundary. Zero fluid pressure and zero radial stress are maintained at the boundary of the sphere at all times. The fluid flow and heat transfer in such a sphere occur only in the radial direction.