A new three-dimensional roughness metric based on Grasselli's model

The roughness of joint surface has a significant influence on the shear behavior and hydraulic behavior of rock mass. In order to acquire a three-dimensional roughness metric which can capture the anisotropic characteristics of rough surface and reflect the shear mechanism of rock joint, morphological scanning tests were performed on four groups of sandstone joints by using a three-dimensional laser scanner. Based on Grasselli's roughness model, a new three-dimensional roughness metric was proposed. Comparisons between another three models (Grasselli's model, Liu's model and Tian's model) and the new model show that the new model is more consistent with the test results. In addition, a new concept that characterizes the density of the apparent dip angle facing the shear direction is established in this study, and it is found that Liu's model conforms to the Weibull distribution. Compared to the theoretical density function of Grasselli's model, Liu's model, and Tian's model, the new model has a better agreement with the experimental data, which verifies the rationality of the new model. The new roughness metric is simple and clear physically since it only takes the apparent dip angle facing the shear direction into account. The new roughness metric is positively correlated with the roughness of joints. Furthermore, the anisotropy of surface roughness can also be well characterized by the new roughness metric.