Simulation Method and Application of Three-Dimensional DFN for Rock Mass Based on Monte-Carlo Technique

Abstract

In this study, the authors simulate a polygonal discrete fracture network (DFN) in rock masses. The probability models of the relevant geological parameters, including the orientation, trace length, volume density, and coordinates of the centroid, are firstly developed as fractures are in the shape of rectangles. In the process, the probability distribution of rectangular fractures with side lengths as random variables is introduced and described in terms of mean trace lengths on the basis of the probability model of disk-shaped fracture with the diameter as the random variable. The relationship between the volume density and the linear density of rectangular fractures is given for a negative exponential distribution. Following this, the coordinates of the vertices of fractures are derived based on spatial algebraic geometry, and the data for the three-dimensional DFN model are generated using the Monte-Carlo technique. The resulting three-dimensional DFN is visualized by calling the Open GL graphics database in the environment of Visual C, and the process of implementation of the DFN simulation is given. Finally, the validity of the simulation is verified by applying it to engineering practice.