A modified roughness index based on the root mean square of the first derivative and its relationship with peak shear strength of rock joints

Based on the index, the root mean square of the first derivative of the profile (Z2), the contribution of the asperities with different geometric characteristics to the peak shear strength (PSS) is considered, and an improved roughness index (Z2)ds is proposed. (Z2)ds is reasonably related to the PSS and can reflect the directionality of the PSS. The direct shear tests of 60 joints under different normal stress are carried out. Test results show...