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. The wave then became a wave with two lobes in a different shape after normal transmission across a nonlinear single joint. The 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. The magnitude of the transmission coefficient increased with the incident wave frequency. The conclusions drawn from this study provide a reference for the assessment of the stability of rock structures when they are subjected to dynamic disturbance.