A new quantitative assessment model for the joint roughness of rock masses

Objective The joint roughness of rock masses significantly affects their mechanical properties such as shear strength and permeability. Therefore, its quantitative characterization is significant for the engineering practices of jointed rock masses. Current research achievements indicate that among statistical parameters, the root mean square (RMS) of first derivatives (Z₂) exhibits the strongest correlation with the joint roughness of rock masses, serving as a vital method for characterizing joint roughness. However, the characterization using this parameter is severely affected by the sampling interval (SI).

Methods Based on a systematic analysis of the drawbacks of Z₂ in characterizing the joint roughness, this study proposed the concept of effective spacing between two adjacent calculation points on a joint profile. Accordingly, it improved the RMS algorithm of first derivatives that considers the inclination angle and its direction (Z_2^+ ) in the case where SI approached the minimum sampling resolution. Then, a unified evaluation model incorporating SI was established. Finally, this study verified the reliability of the model using direct shear tests.

Results and Conclusions The results indicate that the improved RMS of first derivatives (Z_2ma^+ ) is more effective in characterizing joint roughness when SI approaches the minimum sampling resolution. Under sampling intervals of 2.13 mm,10.1 mm, 38 groups of artificial joint planes exhibited average deviations between estimated and measured roughness values in four directions of 3.0 or less, with those in the direction of 180° of as low as 1.249. The proposed model addresses the limitation of using the RMS of first derivatives for joint roughness characterization, which is highly sensitive to SI and thus has limited applicability, thus providing a novel approach for the precise quantification of joint roughness. The research scheme of this study can also serves as a referential for the widespread application of other statistical parameters to the accurate assessment of joint roughness.