A time-domain recursive method to analyse transient wave propagation across rock joints

The present investigation is concerned with transient wave propagation in a rock mass with a set of parallel joints by using a recursive method. According to the displacement field of a rock mass with a set of parallel joints, the interaction between four plane waves (two longitudinal-waves and two transverse-waves) and a joint is analysed first. With the displacement discontinuity model and the time shifting function, the wave propagation equation based on the recursive method in time domain for obliquely longitudinal-(P) or transverse-(S) waves across a set of parallel joints is established. The joints are assumed linearly elastic. The analytical solution obtained by the proposed method is compared with the existing results for some special cases, including oblique incidence across a single joint and normal incidence across a set of parallel joints. By verification, it is found that the solutions by the proposed method match very well with the existing methods. The applicability and limitations of the new method are then discussed for incident waves with different properties.