New peak shear strength criterion of rock joints based on two-order roughness

The primary objective of this work is to improve our understanding of the mechanical involvements of two-order roughness in shear. First, wavelet analysis is used to separate the waviness (first-order) and unevenness (second-order) from four granite joint surfaces, with roughness characterized using Grasselli's 3D morphology parameters. The results reveal that first-order roughness is more pronounced than second-order roughness, highlighting the dominant role of waviness in joint surface roughness. Additionally, the variation in first-order roughness with strike direction corresponds to the total roughness, while second-order roughness remains largely constant, indicating that roughness anisotropy is primarily driven by waviness. Then, direct shear tests on joint replicas are performed to investigate the contributions of both roughness orders to peak shear strength. The results show that the peak dilation angle is closely related to first-order roughness, while the shear component angle is closely associated with second-order roughness, both exhibiting a linear correlation. Based on these findings, relationships are established between the angles and their respective roughness orders. Finally, a joint shear strength criterion based on two-order roughness is proposed. A comparative analysis of prediction accuracy reveals that the average relative error for the proposed criterion is 13.79%, while the errors for Xia's, Yang's, and Ban's criteria are 15.19%, 16.29%, and 13.87%, respectively. It demonstrates the proposed criterion can predict the peak shear strength of rock joints.