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 (Z(2)), the contribution of the asperities with different geometric characteristics to the peak shear strength (PSS) is considered, and an improved roughness index (Z(2))(ds) is proposed. (Z(2))(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 that the PSS is related to normal stress, surface morphology and shear direction. The joint equivalent dip angles and the abrasion zone of joints after shearing share a similar distribution. There is a clear linear relationship between (Z(2))(ds) and the joint PSS. Accordingly, a new relationship between the roughness index (Z(2))(ds) and PSS is proposed. The new relationship can eliminate the influence of sampling intervals. The proposed index (Z(2))(ds) establishes a reasonable relationship between the surface roughness and shear mechanical properties of rock joints. This is helpful to study the shear behavior of rock masses in a specific direction in engineering geology.