Deformation of spherical cavities and inclusions in fluid-infiltrated elastic materials

The problem of a spherical cavity which is embedded in a linear, fluid-infiltrated, elastic porous medium and which is subjected to the sudden quasi-static application of a stress at the cavity boundary is solved. It is demonstrated that the deformation of the cavity is homogeneous regardless of the boundary condition imposed on the pore fluid at the cavity wall. For the case in which the pore pressure vanishes at the cavity wall, the time dependence of the cavity strain is evaluated explicitly and is shown to vary between the limits of the ordinary linear elastic response based on the short-time (undrained) and on the long-time (drained) properties of the fluid-saturated solid. The results are then used to obtain a relation between the uniform stress or strain applied at infinity and the stress and strain in a highly permeable, possibly non-linear spherical inclusion. The application of this relationship to a study of earthquake premonitory processes based on the deformation of a rock mass with a spherical weakened zone is outlined. It is argued that the fluid coupling effects serve to stabilize the weakened rock against rapid fracture, and give rise instead to a precursory period of accelerating but initially quasi-static straining which ultimately leads to dynamic instability.