Solitary shear waves in a granular medium

A mathematical model describing the deformation of a granular medium with v iscous interlayers in the grain contacts is presented. The model leads to a perturbed sin-Gordone equation. The assumption that the resistance force o f the rough surfaces of grain contacts is proportional to the squared veloc ity of the interlayer flow allows one to obtain an exact analytical solutio n in the form of a solitary sheer wave. The dependences of the solitary wav e velocity on the friction parameter, viscosity of interlayer material,and ratio of the layer thickness to its length are calculated. It is demonstrat ed that the velocity of a solitary wave is always less than the velocity of a transverse seismic wave.