A thermal pressurization model for the spontaneous dynamic rupture propagation on a 3–D fault: Part I – Methodological approach

Abstract

We investigate the role of frictional heating and thermal pressurization on earthquake ruptures by modeling the spontaneous propagation of a 3–D crack on a planar fault governed by assigned constitutive laws and allowing the evolution of effective normal stress. We use either slip–weakening or rate– and state–dependent constitutive laws; in this latter case we employ the Linker and Dieterich (1992) evolution law for the state variable and we couple the temporal variations of friction coefficient with those of effective normal stress. In a companion paper we investigate the effects of thermal pressurization on the dynamic traction evolution within the breakdown zone. We solve the 1–D heat conduction equation combined with the Darcy’s law for fluid flow in porous media. We obtain a relation that couples pore fluid pressure to the temperature evolution on the fault plane. We analytically solve the thermal pressurization problem by considering an appropriate heat source for a fault of finite thickness. Our modeling results show that thermal pressurization reduces the temperature increase caused by frictional heating. However, the effect of the slipping zone thickness on temperature changes is stronger than that of thermal pressurization, at least for a constant porosity model. Pore pressure and effective normal stress evolution affects the dynamic propagation of the earthquake rupture producing a shorter breakdown time, larger breakdown stress drop and rupture velocity. The evolution of the state variable in the framework of rate– and state– dependent friction laws is very different when thermal pressurization is of relevance. In this case the evolution of the friction coefficient differs substantially from that inferred from a slip– weakening law. This implies that the traction evolution and the dynamic parameters can be strongly affected by thermal pressurization.