ON FRACTAL DIMENSION OF A FRACTURE SURFACE BY VOLUME COVERING METHOD

An accurate calculation of the fractal dimension of a fracture surface is of prime significance for the quantitative evaluation of mechanical behavior. A laser profilometer is employed to measure a surface roughness of a large sandstone sample. Based on the definition of Minkowski dimension, a new method, referred to as the volume covering method, is proposed to estimate fractal dimension by accurately calculating the number of virtual cell needed to cover prism-like volume. It is indicated that the method can fully use laser scanning-based elevation data of the surface and make an accurate estimation of fractal dimension of a fracture surface. Furthermore, another method related to the opposite corner is adopted to estimate the same rough surface with little error of the fractal dimension. A comparison analysis indicates that the volume covering method has the advantage of high accuracy and good applicability for a real fracture surface.