Fractal Characterization on Anisotropy and Fractal Reconstruction of Rough Surface of Granite Under Orthogonal Shear

Abstract

The anisotropy of three orthogonal surfaces is studied based on the fractal description of profiles and its statistical evaluation. Under shear tests, three granite cubes are prepared for the generation of orthogonal rough surfaces and the morphology reconstruction is based on laser scanning. Four roughness descriptors of asperity height, inclination angle, line length and surface area are proposed for investigating the anisotropy, which is dependent on the skewed normal distribution. The compared distribution of four descriptors for parallel and perpendicular profiles is deeply analysed for the coupled effect of orthogonal roughness. The surface roughness is described by fractal dimension based on the set product of orthogonal fractal profiles. The result shows that the fractal reconstruction describes the anisotropy effectively and the four descriptors show high precision for fractal dimension calculation. Moreover, on the asperity scale, three behaviours of compression–shear, pure shear and tension–shear show different distribution and contribution for roughness determination. With the increasing covering length, the proportion distribution shows the compression–shear dominates the macrobehaviour, which is just dependent on the two other behaviours on the asperity scale. Finally, the separation distribution of proportion line for compression–shear and tension–shear is obtained. The linear relationship with shear strength shows good adaptability for four roughness descriptors to analyse the anisotropy.