Modelling contact problems with friction in fault mechanics

The aim of this contribution is two-fold. First, we review the friction models applied in geophysics. These models cover: state- and rate-dependent friction, rate-dependent friction and slip-dependent friction.

Second, we propose a new description of friction in the spirit of modern contact mechanics, introducing sliding rules which interrelate the contact stresses with the slip velocity. Sliding rules are formulated in a subdifferential form. Initial-boundary value problems are formulated in the strong and variational forms. By applying Green's function, the variational formulation for finding normal and tangential contact stresses is proposed.