4. Basic Equations for Linear Thermoporoelasticity

In this chapter, we present mathematical theory of linear poroelasticity, following earlier works. Since high-pressure fluids seem to be deeply involved in the generation of earthquakes as exemplified in the preceding chapters, it will be appropriate to apply the poroelasticity theory to understanding of crustal deformation and generation mechanism of earthquake rupture. Here we consider only a simple case in which the porous medium is homogeneous and isotropic; the pore space is also assumed to be connected and saturated with a single kind of pore fluid. We present basic equations of linear poroelasticity in Sects. 4.3–4.9 and 4.12, after shortly reviewing the historical development of poroelasticity theory in Sect. 4.1 and introducing key concepts in Sect. 4.2. While we focus on the deformation under isothermal condition in earlier sections, nonisothermal condition is assumed in the analysis in later sections. Since high temperature elevation is expected to occur during dynamic slip because of high confining pressure, temperature change will actually affect the fluid pressure change. Some specific effects are incorporated in Sects. 4.10 and 4.14 so that the equations may be applicable to the modeling of earthquake rupture. We lastly address a simple problem of quasi-static poroelastic deformation applying the linear poroelasticity theory in Sect. 4.15.