The Dynamics of a one-dimensional Fault in the Presence of Friction?

The tearing and healing of a one-dimensional crack in a solid, in the presence of external tectonic forces, pre-stress, static friction, cohesion and dynamic friction is investigated. It is found that cohesive forces have a strong influence on the velocity of rupture; the velocity of rupture is always less than or equal to the velocity of sound. The extension of the crack ceases either when the crack enters a region with too high a cohesive force or when the difference between the tectonic stress and the dynamical shear stress becomes negative over a substantial region of space. For one simple model, a high displacement, high energy release event has been found, while in another model of the same fault length, a low displacement, low energy release event with the same stress drop takes place; the difference between the two models is in the mode of healing, and, in particular, whether the fault breaks out at the free surface of the Earth.