Study on a General Cutting Algorithm of Complex Blocks

Abstract

Rock block is the key research object of underground cavern and slope as well as foundation engineering. Block theory is one of the critical methods of stability analysis in rock mechanics. Based on the classical block theory, in this study the essential concepts of block is extended firstly to include both intersections and unions of half-spaces. After that, a unified and generalized symbolic representation method was proposed based on three classical methods of representation for convex blocks. A symbol i in the middle of two notations of face half-spaces suggests intersection of the two half-spaces while a symbol u suggests union of the two half-spaces. After that, the algorithm of successive cutting of remaining block is proposed. A non-convex block can be cut into a number of convex blocks connected only by the cutting planes. The shape and size of the non-convex block can therefore be obtained. Comparative study was carried out on a practical example. Compared to the conventional method, the efficiency of the proposed method is improved significantly.

Seismic stability analysis of a rock block using the block theory and Newmark method

“…Although the basic assumption of the block theory is that the structural plane is infinite, the free plane may be a finite plane, which means that, the rock block may be concave. For the geometric description of such a complex rock block, the combination method is employed . In the combination method, the complex rock block is divided into several convex subblocks, and these convex subblocks are connected with several common planes.…”

“…For the geometric description of such a complex rock block, the combination method is employed. [41][42][43] In the combination method, the complex rock block is divided into several convex subblocks, and these convex subblocks are connected with several common planes. In Figure 1, the complex rock block is formed by cutting the rock with 16 planes marked with A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, and P, where E, I, N, and P are the structural planes and the others are free planes.…”