The influence of normal distribution dispersion of fracture size on blockiness and REV of fractured rock masses

Abstract

The fractures of different sizes in rock masses are important for describing rock fragmentation. The distribution dispersion of fracture size influences the blockiness level of the rock masses. Based on a normal statistical distribution, the volume ratio of blocks to rock (B) was obtained to describe the blockiness level. For exploring the effect of the dispersion of fracture size on blockiness level and the representative elementary volume (REV) of rock masses, the laboratory model and numerical simulation were established, and the theory of statistics and the method of analytical solution were applied. In addition, 4,525 practical rock models were established to qualitatively reproduce the behavior of B with changing domain size. The results show that by comparing the degree of convergence, the REV of a rock mass is determined by the fracture size rather than the degree of fracture dispersion. The value of B increases with the distribution dispersion of fracture size, indicating a higher blockiness level. From the experimental analysis of coin tossing, when the number of trials exceeds 69, the random results are nearly stable. In this study, 100 calculations were performed. A formula to calculate the blockiness by considering the dispersion degrees of fracture size was obtained. Moreover, a positive linear correlation between B and the coefficient of variation of fracture size was obtained. The rate of increase in B has a parabolic relationship with the ratio of fracture size to fracture spacing (L).