Statistical analysis of stochastic blocks and its application to rock support

• The statistical distributions of the block size and overlaying ratio are explored.
• The block size has a negative exponential distribution and the overlaying ratio follows a Γ distribution.
• The lengths and anchor forces and spacings of the rock bolts are quantitatively determined.

The orientation, trace length, spacing, and location of probabilistic discontinuities in rock masses are randomly developed. Thus, the shape, size, and location of blocks cut off by these probabilistic discontinuities are accordingly stochastic. It is difficult, or even impossible, to determine the volume and location of the blocks using the block theory proposed by Goodman and Shi (1985). Stochastic block analysis (SBA) is capable of identifying three-dimensional (3-D) stochastic blocks from a randomly developed discontinuity network (discrete fracture network). However, in practice, 3-D blocks are not identified well in simulated fracture networks and so the use of SBA is seldom encountered. In this paper, the procedures involved in stochastic block identification are first outlined. The concept and calculation of overlaying area and ratio are then introduced. Then, the stochastic block identification results are used to explore the statistical distribution of the block size and overlaying ratio. Subsequently, the laws governing development of the stochastic blocks were elucidated. The results show that the block size has a negative exponential distribution and the overlaying ratio follows a Γ distribution. The overlaying ratio increases as the trace length to spacing ratio increases. We further outline, for the first time, approaches to determine block support measures by analyzing the characteristics of the statistical distributions of the stochastic blocks. Block support issues relating to a practical underground plant were also studied. The lengths and anchor forces and spacings of the rock bolts were quantitatively determined according to the results of a statistical analysis of the stochastic blocks. Statistical analysis of stochastic blocks is of great significance in understanding the development characteristics of the stochastic blocks and in quantitatively determining block support measures.