Inelastic plane-wave propagation in anisotropic rocks

Abstract

The equations for combined elastic and inelastic plane‐wave propagation in anisotropic rocks are developed in terms of familiar laws of plasticity. The total strain is the sum of the elastic and plastic contributions. The elastic component of strain is related to the stress according to Hooke's law, and the plastic strain is obtained from the yield function and an associated flow rule. The general equations apply to materials of any symmetry, but specific calculations are performed for materials of transverse isotropy related to parallel planes of weakness, i.e., bedding planes. Wave speeds, stress amplitudes, etc., depend on the direction of wave propagation with respect to the bedding planes. Velocities of the inelastic waves differ in loading and unloading. Analytical and numerical solutions to the problem of a finite‐duration step load applied over a planar surface are presented. It is shown that wave attenuation is also dependent on wave propagation direction.