Class Ratio Transform with an Application to Describing the Roughness Anisotropy of Natural Rock Joints

In this study, we explore the potential of class ratio transform with an application to describing the roughness anisotropy of natural rock joints. Roughness smooth coefficient, used for suitably smoothing the roughness parameter values to realize an anisotropic model, is proposed to represent the apparent anisotropy of surface roughness. The geometric irregularities of roughness parameters in polar plots allow transforming to a regular roughness asperity pattern, which can be readily approximated by the ellipse function. The joint roughness coefficients in different orientations of natural rock joints were measured and revealed to be identical after applying the smoothing process using the class ratio transform method. The results show that the roughness smooth coefficient increases with sample size but decreases as azimuthal interval narrows. This method demonstrates the ability in describing the roughness anisotropy and inferring the roughness parameters Z₂, R_p, and θ*_max/(C+1)2D.

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