A modified displacement discontinuity method for seismic wave propagation across rock masses with thin-layer joints

Seismic wave propagation across rock masses with thin-layer joints by the modified displacement discontinuity method (M-DDM) is of great importance for geophysical surveys. The M-DDM introduces a frequency-dependent effective stiffness to describe the dynamic stress-closure relationship of a thin-layer joint. We verify the accuracy of M-DDM in studying seismic wave propagation across rock masses with thin-layer joints. Subsequently, we evaluate the influence of the joint thickness and the incident wave frequency on M-DDM accuracy. We analyze the prediction error of the transmission coefficient obtained with M-DDM. The results demonstrate that the frequency-dependent effective joint stiffness increases with increasing incident wave frequency and decreases with increasing joint thickness. Compared with the traditional displacement discontinuity method (DDM), M-DDM more accurately predicts the transmission coefficients of seismic waves propagating across thin-layer joints. The transmission coefficient prediction error obtained based on M-DDM increases with increasing joint thickness and incident wave frequency and is always smaller than that obtained based on DDM. Therefore, the M-DDM can be used to effectively investigate seismic wave propagation across rock masses with thin-layer joints.