Study on three-dimensional roughness index of rock joints based on improved apparent dip distribution function

The three-dimensional morphology characteristics of rock joints significantly influence their shear mechanical behavior. To accurately characterize the joint surface morphology, this study conducted 3D laser scanning on five groups of red sandstone joint specimens. The apparent dip angles of the joint surface morphology were then fitted using an existing distribution function. However, the results revealed limitations in the function’s ability to accurately fit the density distribution. To address this issue, this study proposes an improved apparent dip angle distribution function combining Weibull and exponential terms, which achieves superior fitting performance for both cumulative and density distributions. Based on the improved function, a novel three-dimensional roughness index is developed. This new index possesses clear physical significance and can effectively characterize the anisotropy of joint roughness. Its effectiveness is validated through comparison with conventional roughness indices. Furthermore, the new index shows strong correlations with shear strength-related parameters, indicating its potential applicability in the development of joint shear strength models.