Algorithm of fractal dimension of rock fracture surface based on volume estimation

For calculating the fractal dimension of rock fracture rough surface, the prism-like or 3-side parallel bodies may be generated by connecting the data points on the fracture surface in order to take full account of laser scanning-based elevation data of the surface. A volume covering method is proposed for estimation of the fractal dimension of rough surface according to the definition of Minkowski dimension. Compared with the traditional cubic covering method, the volume covering method can be employed to directly calculate the volume of covering body and to estimate the fractal dimension without correction point of laser scanning data so as to avoid the differences caused by different coordinate systems. Furthermore, by comparing the two different types of parallel body covering methods for the same rough surface, all the volume covering methods have high accuracy in calculating the fractal dimension and have strong applicability overcoming the uniform shape requirements of the covering cells (all cubes or all cylinders).