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Anisotropy in rock joint is strongly dependent on undulating surface morphology. Recent research of the morphology showed the parameter can express the different types of anisotropic characteristics of the joint surface separately. This report aims to analyze the common characteristic of the anisotropic distribution and exhibit the anisotropic variation trend. The joint morphology function consists of two morphology functions of regular plane in orthogonal directions, and the anisotropic variation determined by the contribution ratios of the two morphology. The roughness weight ratio in orthogonal direction of joint surface is used as an index to describe the anisotropic variation behavior, which proposes the anisotropic variation coefficient (AVC). On this basis, it is divided into 5 levels from strong anisotropic to isotropic. According to the assumption of anisotropic arc distribution, the anisotropic analytic function is derived and the agreement between the deduced curves and measured data therefore suggests the possibility of defining the morphology anisotropy through the index AVC. Finally, we verify the characteristic of three natural rock joints, and prove the proposed function can reflect the anisotropic distribution trend. The new index can be used to describe the anisotropic variation behaviour of rock joint surfaces.

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The greatest variability in both shear strength and roughness exists for joint samples with smaller size, which underscores the necessity of performing representative sampling. This study aims to provide a representative sampling method for series size joint surfaces. The progressive coverage statistical method is introduced to provide the sufficient sample capacity for series sampling sizes by setting different propulsion spaces. The statistical law of the joint surface morphology at different sampling sizes is measured by the 3D roughness parameter with $${{\theta }}_{\max }^{\ast }/({C}+1)$$θmax⁎/(C+1). Through an application in nine natural large-scale rock joints, nine consecutive sampling sizes from 100 mm × 100 mm to 900 mm × 900 mm are selected and 121 samples are successfully acquired from each sampling size. According to the frequency distribution of roughness statistics, a new sampling method combining the layering principle and K-medoids clustering algorithm is proposed to screen representative joint samples for each sampling size. The sampling results that meet the test accuracy requirements suggest the possibility of realizing an intelligent sampling method. In addition, the representative of the interlayer cluster center is validated. Finally, the comparison results with the traditional stratified sampling method prove that the proposed method has better stability.