Study on generation of rock fracture surfaces by using fractal interpolation

Abstract

The mathematical model of a fractal interpolation surface on a rectangular field is proposed in this paper. The theory of a fractal interpolation surface is applied to the generation of rock fracture surfaces. The methods of the improved self-affine fractal interpolation surface are proposed. Based on the statistical fractal character of fracture surfaces, the new ideas and methods of the partition of the local field and the determination of a vertical scaling factor are given by using the principles of geostatistics and trend surface analyses, so that the local stochastic irregular roughness on the fracture surface can be simulated. Fractal interpolated surfaces based on 5.5–25.62% of information data on 12 measured rock fracture surfaces are in good agreement with the measured rock fracture surfaces, and the relationship of the information point number used in the interpolation and the interpolation precision is obtained.