Thermo-poro-mechanical analysis of rapid fault deformation

In this paper the basic mathematical structure of a thermo-poro-mechanical model for faults under rapid shear is discussed. The analysis is 1D in space and concerns the infinitely extended fault. The gauge material is considered as a two-phase material consisting of a thermo-elastic fluid and of a thermoporo-elasto-viscoplastic skeleton. The governing equations are derived from first principles, expressing mass, energy and momentum balance inside the fault. They are a set of coupled diffusion-generation equations that contain three unknown functions, the pore-pressure, the temperature and the velocity field inside the fault. The original mathemetically ill-posed problem is regularized using a viscous-type and a 2 gradient regularization. Numerical results are presented and discussed. ) t , z ( p , the temperature ) t , z ( θ and the velocity ) t , z ( v are assumed to be functions only of the time t and of the position z in normal to the band direction (Figure 1). Figure 1. The deforming shear-band with heat and fluid fluxes As is shown in Vardoulakis (2000) mass and energy balance equations together with Darcy's and Fourier's laws lead to a set of coupled diffusiongeneration equations for the pore-water pressure ) t , z ( p and the temperature field ) t , z ( θ inside the shear band. For easy reference we summarize here these equations and define the pertinent material parameters.