A Study on the Normal Transmission of a One-Dimensional P-Wave across a Single Nonlinear Joint in a Rockmass

Abstract

The presence of nonlinear discontinuities in a rockmass makes the stress wave propagation rules in a continuous medium not applicable. In an attempt to reveal the transmission laws of a one-dimensional P-wave across a single nonlinear joint in a rockmass, a recurrence equation is deduced using a semianalytical and seminumerical method from the nonlinear wave equation by introducing the static Bandis−Barton (BB) model for a single rock joint. Parametric studies are conducted to analyze the effects of the joint position and incident wave frequency. Results demonstrated that incident one-cycle sinusoidal pulse shifted into a wave that had two lobes after propagation in nonlinear rock within a certain distance. *ewave then became a wave with two lobes in a different shape after normal transmission across a nonlinear single joint. *e amplitude of the recorded waveform before the joint had an obvious inverse correlation with the frequency of the incident pulse. In addition, the amplitude of the transmitted waveform had a positive correlation with the incident pulse within a fixed distance from the joint. *e magnitude of the transmission coefficient increased with the incident wave frequency. *e conclusions drawn from this study provide a reference for the assessment of the stability of rock structures when they are subjected to dynamic disturbance."