Nonlinear viscoelastic medium equivalence for stress wave propagation in a jointed rock mass

A nonlinear viscoelastic equivalent medium model is proposed for longitudinal stress wave propagation in a rock mass that contains equally spaced parallel joints. The joint deformation is assumed to satisfy the nonlinear Bandis–Barton (B–B) deformational model. By the simplification of the nonlinear B–B model into piecewise linear segments, the material parameters in the equivalent medium model are analytically derived. The nonlinear viscoelastic equivalent medium model is verified by comparison with the results based on the displacement discontinuity method. It is shown that for smaller amplitude stress waves, when the rock joints deform in the linear elastic region, the nonlinear viscoelastic equivalent medium model is reduced to its linear form, whereas for larger amplitude stress waves, the present nonlinear model describes the wave amplitude-dependence of wave velocity. Two important properties, i.e., the wave transmission coefficient and the effective wave propagation velocity, are discussed in detail