Characterization of discontinuity surface morphology based on 3D fractal dimension by integrating laser scanning with ArcGIS

The fractal geometry method has been employed to quantitatively characterize the roughness of a rock discontinuity, which is one of the key factors affecting its shear strength and the seepage characteristics of a rock mass. However, the current fractal methods involving the three-dimensional discontinuity morphology suffer from one or more problems, such as a complicated calculation procedure, an inaccurate calculation result and an inability to characterize the undulation and anisotropy of a discontinuity. To cope with these problems, the discontinuities in artificial granite samples with irregular and undulating surfaces were taken as examples, and a quantitative study on the discontinuity morphology was conducted based on the method of three-dimensional laser scanning in combination with ArcGIS data processing, geographical research, theoretical calculations and regression analysis. After performing systematic research, we proposed an extensive 3D fractal dimension including three discontinuity morphological parameters, i.e. the fractal dimension of discontinuity morphology, the ratio between the maximal undulating amplitude and the discontinuity length, and the average value of all the apparent dip angles of the discontinuity surfaces dipping opposite the shear direction. The extensive 3D fractal dimension can comprehensively characterize the roughness, undulation and anisotropy of the discontinuity morphology. A set of theoretical calculation methods were then developed to determine the three discontinuity morphological parameters of the extensive 3D fractal dimension based on ArcGIS. We finally established a mathematical expression of the extensive 3D fractal dimension. Compared with the current fractal methods, the extensive 3D fractal dimension can effectively compensate for the inability to characterize the undulation and anisotropy of the discontinuity morphology. Its calculation methods have the advantages of simplification, low-time consumption and high precision.