Mathematical modeling of slip in a rock along the uneven fracture

A mathematical model is presented for the unstable deformation of rock alon g an existing fracture in it. It is shown that this process is essentially nonlinear and can be described by the Gordon equation. An analysis is made for the influence of geometric irregularities and friction of the contact s urfaces on the evolution of the velocity of solitary slip waves which are c aused by local deformation effects and propagate along the fracture.