Isomerism of using the classic discretization algorithm Z2 for characterizing joint profile morphology roughness and its improvement

Abstract

The discretization algorithm for the root mean square of the first derivative (RMSFD) significantly affects the effective characterization of rock joint profile roughness and the accurate evaluation of the joint roughness coefficient (JRC). The classic discretization algorithm Z₂ fails to distinguish morphology roughness differences in isomeric profiles, limiting its characterization capability. To address this, we revisit the original definition of RMSFD and propose an improved algorithm. The discretization scheme for curve profiles in the algorithm is modified. By fully considering the spatial configuration and mutual relationship of the position between adjacent-point microsegments, the forward difference form in Z₂ is changed to a central difference form, and another RMSFD discretization algorithm, Z_n, is developed. Comparative analysis of RMSFDs for reconstructed profiles using Z_n and Z₂ demonstrates that the proposed algorithm avoids isomerism and exhibits superior ability in characterizing profile morphology roughness. Furthermore, we establish a functional relationship between Z_n and JRC based on retrieved data and validate the superiority of the improved algorithm in characterizing profile morphology roughness. In addition, the capability of Z_n on the distinguishing differences of profiles is further confirmed, and the isomerism induced by other indicators is also examined. An anisotropic algorithm and three-dimensional (3D) improved discretization algorithms for the RMSFD are derived. The proposed algorithm Z_n is expected to enhance the understanding of morphology characteristics and improve the modeling of roughness for rock joints.