Analysis of Wave Propagation Across Layered Rock Masses Considering Multiple Reflection Effects

The impacts of multiple reflection within the interlayer on wave propagation across layered rock masses have remained unclear. To address this, we first derive the governing equations for the wave propagation in time domain based on an equivalent layer model. These equations are validated by comparing them with a previously used method in an idealized case. Subsequently, a systematic investigation is carried out, progressing from idealized to generalized cases, to explore the frequency-dependent characteristics of the transmission and reflection coefficients, as well as energy dissipation rate. The mechanisms behind these frequency-dependent features are thoroughly analyzed, in conjunction with the evolution of waveforms and the effects of multiple reflections. The results indicate that the proposed model and derived equations effectively simulate the multiple reflection effects in the wave propagation behavior of layered rock masses. Multiple reflections within the interlayer result in an oscillatory decay of the transmission coefficient in layered rock masses as wave frequency increases. Interestingly, stress waves with frequencies that are even multiples of the ratio of wave speed to interlayer thickness demonstrate a robust capability to propagate across the interlayer. This phenomenon arises from the superposition of multiple reflected waves in phase within the interlayer, and gradually disappears with a decrease in quality factor of interlayer or an increase in wave frequency. The underlying mechanisms of these features are convincingly explained by combining the effects of multiple wave reflections.