Effects of joints of Maxwell viscoelastic behavior on wave propagation

Wave propagation across a single filled joint and a filled joint set of Maxwell viscoelastic behavior is analytically studied in this paper. Rock joints are often filled with materials, e.g., saturated clay or sand, of viscoelastic nature. Their effects on wave propagation are reflected as displacement and stress discontinuity conditions across the joints. The viscoelastic behavior is described by the Maxwell model. The analytical solutions for wave propagation across a single joint are derived in this paper by accounting for the nondimensional joint stiffness, the nondimensional joint viscosity and the acoustic impedance ratio of the filled joint. It is shown that the viscoelastic behavior results in dissipation of wave energy and frequency-dependence of the reflection and transmission coefficients. In order to take into account multiple wave reflections among different joints, the modified recursive method is introduced, which is superior to previous recursive method by the higher computational efficiency. Then, wave transmission across a filled joint set is studied with the modified recursive method. It is shown that the nondimensional joint spacing and the number of joints have significant effects on the transmission coefficients.