Wave propagation across non-linear rock joints based on time-domain recursive method

Studying wave propagation across joints is crucial in geophysics, mining and underground construction. Limited analyses are available for oblique incidence across non-linear joints. In this paper, the time-domain recursive method (TDRM) proposed by Li et al. is extended to analyse wave propagation across a set of non-linear joints. The Barton-Bandis model (B-B model) and the Coulomb-slip model are adopted to describe the non-linear normal and shear properties of the joints, respectively. With the displacement discontinuity model and the time shifting function, the wave propagation equation is established for incident longitudinal-(P-) or transverse-(S-)wave across the joints with arbitrary impinging angles. Comparison between the results from the TDRM and the existing methods is carried out for two specific cases to verify the derived wave propagation equation. The effects of some parameters, such as the incident angle, the joint spacing, the amplitude of incidence and the joint maximum allowable normal closure, on wave propagation are discussed.