Modeling of peak shear strength of rock joints based on a three-dimensional roughness index

Rock joints are widely present in engineering rock masses, and their peak shear strength directly governs the stability of jointed rock masses. To investigate the influence mechanism of joint surface morphology on the peak shear strength, this study fabricated 35 sets of joint specimens with five distinct morphological types using a combination of three-dimensional laser scanning and CNC engraving technologies. Based on the scanning results, an improved 3D apparent dip angle distribution function was proposed, which more accurately captures the spatial distribution characteristics of joint surface morphology. By integrating this function, a new 3D roughness index was developed. This index exhibits a clear linear relationship with the sampling interval and decreases as the interval increases. Subsequently, a series of constant-normal-load direct shear tests on rock joints was conducted. Test results revealed a strong linear correlation between this roughness index and the initial (zero-normal-stress) peak dilation angle. Moreover, the degradation trend of the peak dilation angle with increasing normal stress can be effectively described by an exponential function. On this basis, a peak dilation angle degradation model was defined, which enables accurate prediction of peak dilation angles under varying normal stress conditions. By incorporating this model into the Mohr-Coulomb criterion, a peak shear strength model was established. Comparative analysis with existing models, including validation against published data on granite joints, demonstrates that the proposed model offers the highest prediction accuracy ( R 2 = 0.978; mean relative error = 4.25%), making it suitable for reliably estimating the peak shear strength of rock joints.