Heterogeneity Measures for Analyzing the Scale Effect and Anisotropy of Joint Roughness

Joint roughness of rock joints is one of the key factors influencing the mechanical properties of rock joints. The influence of joint roughness on the mechanical properties of rock mass is usually quantitatively characterized by joint roughness coefficient (JRC). The scale effect and the anisotropy of joint roughness are its important characteristics. The lack of a suitable heterogeneity measure for the scale effect and anisotropy of joint roughness makes it difficult to analyze its heterogeneity quantitatively. To solve this issue, this paper proposes the uniformity measure (normalized information entropy measure) and the nonuniformity measure (normalized information enthalpy measure) of a multivalued sequence based on the Shannon/probability entropy notion. Then, a heterogeneity measure of joint roughness is proposed, which realizes the quantitative characterization of the heterogeneity of the scale effect and anisotropy of joint roughness. Actual rock joint cases were used to collect JRC data with 10 sample sizes from 10 to 100 cm and 24 measurement directions from 0° to 345° and to calculate the heterogeneity measures of the joint roughness scale effect in 24 directions and joint roughness anisotropy in 10 sizes. The analysis results show the rationality and efficiency of the proposed measure. The proposed measure provides researchers and engineers with a reliable heterogeneity analysis tool for joint roughness scale effect and anisotropy.