Estimating the three-dimensional joint roughness coefficient value of rock fractures

Measurement and estimation of the joint roughness coefficient (JRC) is a critical but also difficult challenge in the field of rock mechanics. Parameters for estimating JRC based on a profile derived from a fracture surface are generally two-dimensional (2D), where a single or multiple straight profiles derived from a surface cannot reflect the roughness of the entire surface. It is therefore necessary to derive the three-dimensional (3D) roughness parameters from the entire surface. In this article, a detailed review is made on 3D roughness parameters along with classification and discussion of their usability and limitations. Methods using Triangulated Irregular Network (TIN) and 3D wireframe to derive 3D roughness parameters are described. Thirty-eight sets of fresh rock blocks with fractures in the middle were prepared and tested in direct shear. Based on these, empirical equations for JRC estimation using 3D roughness parameters have been derived. Nine parameters ((s), (g), (2s), S-sT, S-sF, V-an, Z(sa), Z(rms), and Z(range)) are found to have close correlations with JRC and are capable of estimating JRC of rock fracture surfaces. Other parameters (Z(ss), Z(sk), V-svi, V-sci, S-dr and S-ts) show no good correlations with JRC. The sampling interval has little influence when using volume and amplitude parameters (V-an, Z(sa), Z(rms), and Z(range)) for JRC estimation, while it influences to some extent when other parameters ((s), (g), (2s), S-sT and S-sF) are used. For their easy calculation, the equations with amplitude parameters are recommended to facilitate rapid estimation of JRC in engineering practice.