Estimating the Joint Roughness Coefficient of Rock Joints from Translational Overlapping Statistical Parameters

When translating digital roughness profiles of a closed rock joint along the shear direction, the overlapping translational areas can reasonably represent the main potential contact areas in shear tests. By translating Barton’s ten typical roughness profiles, a series of statistical parameters, including the overlapping areas (S*), overlapping number (N*), cumulative overlapping projection length (\(L_{{{\text{sum}}}}^{*}\)), and the weighted cumulative overlapping projection length (\(S_{{{\text{sum}}}}^{*}\)), were utilized to quantify the 2D joint roughness. Based on the dimensional analysis, these parameters were combined to estimate the joint roughness coefficient. The correlation coefficient results show that the parameter combinations of \(\sqrt {{S^*}} /L\) and \({N^{* - 1}}\) or \(S_{{{\text{sum}}}}^{*}/{S_{{\text{Total}}}}\) allow good estimation of the joint roughness coefficient of Barton’s 2D roughness profiles. A conceptual joint model was used to extend the 2D translational overlapping statistical parameters to a 3D condition, revealing the suitability of the 3D translational overlapping volume parameter \(\sqrt {{V^*}/SL}\) and the hourglass parameter to estimate the joint roughness coefficient of common rock joints. However, the overlapping number parameter N^*−1 becomes unreliable and lacks practical significance for common rock joints because there are so many meaningless weak links among the overlapping volumes. Shear tests were conducted on 25 sandstone joints to verify the applicability of \(\sqrt {{V^*}/SL}\) and \(V_{{{\text{sum}}}}^{*}/{V_{{\text{Total}}}}\) to estimate the joint roughness coefficient. The results indicated that these two parameters show good agreement with the experimentally back-calculated values, allowing the establishment of a new joint roughness coefficient fitting formula.