Novel Evaluation Method of 3D Joint Roughness Based on Random Field Theory

The roughness of a joint has a significant influence on the physical and mechanical properties of rock mass, and it is a hot and challenging research topic to determine the joint roughness quickly and accurately. In this paper, based on the random field theory and the traditional roughness evaluation index Z2s, a novel three-dimensional (3D) joint roughness evaluation index named Zσ,θd is proposed. The novel index involves three parameters: the standard deviation (SD) and the scales of fluctuation (SOF) of elevation distribution, which are related to the joint shape, and the sampling interval (SI), which is determined by the sampling method. The 3D joint is generated by the random field method, and the variation of Zσ,θd with SD, SOF, and SI is investigated. The results show that the roughness of the 3D joint generated by the random field method has good robustness, with a maximum fluctuation error of 3.87%. The roughness increases linearly with the increase of SD and decreases exponentially with the increase of SOF and SI, and the fitting formula is obtained. On this basis, the normalization method of Zσ,θd is put forward to eliminate the influence of SI on roughness, and the validity of Zσ,θd is verified by the actual joint in the public database. Finally, the application prospect of this method in the preparation of joint specimens is discussed, and the corresponding 3D surfaces are given according to the 10 typical joint profiles provided by Barton. This paper contributes a quantitative roughness evaluation index and a method for generating the 3D joint, which can serve as a basis for model experiments and numerical calculations.