Transmission of Normal P‐Waves across a Single Joint Based on g‐λ Model

Abstract

This paper investigates the wave transmission and reflection of an elastic P‐wave at a single joint for normal incidence. First, considering a coupled joint (correction parameter λ, 0 < λ < 1), a normal deformation constitutive model of the joint (g‐λ model) under static or quasi‐static loading is introduced and then extended to dynamic loading. The nonlinearity of the joint stress‐deformation curve increases with increasing λ. Second, the interaction between the P‐wave and the joint is investigated by using the method of characteristics and the displacement discontinuity method to deduce the differential expression of the transmitted wave’s particle velocity. The approximate analytical expressions of the transmission and reflection coefficients are obtained according to the Lemaitre equivalent strain assumption. Third, parametric studies are conducted to evaluate the effects of λ on transmission characteristics for a normally incident P‐wave at a single joint. The results show that the particle velocity of the transmitted wave depends on λ. When λ takes the limit values 0 and 1, the transmitted wave’s particle velocities are then consistent with the conclusions of the classical exponential model and the Barton–Bandis model. In addition, the transmission and reflection coefficients are discussed with respect to λ and also to the ratio of the joint closure to the maximum allowable joint closure.