To overcome some limitations of the mode and stability analyses of Block Theory, Block Theory?s removabilityanalysis is coupled with three-dimensional Discontinuous Deformation Analysis (3D DDA) single block analysis. This results in adesign method for discontinuous rock masses: Block Theory?s removability analysis is used to identify all removable block types,and the 3D DDA single block analysis is used to determine the mode and stability of each removable block type. In this paper, acomputer program that implements the coupled method is introduced. Selecting a block size for design is also discussed. Thestability analyses will give the factors of safety and if necessary allow the design of stabilization using rock anchors. A case historyis used to test the method. The results show that the coupled method can be applied as a design method for rock slope engineering,with potential applications in the design of tunnels and underground chambers.


Block Theory, developed by Goodman and Shi(1985), is a three-dimensional geometrical methodthat allows a rigorous inventory and analysis of rockblocks that can be formed by intersecting rock massdiscontinuities and free surfaces. A complete BlockTheory analysis consists of the removabilityanalysis, mode analysis and the stability analysis.The removability analysis gives a list of removableblocks that can be formed by intersecting rock massdiscontinuities and free surfaces. A removableblock is one that can move in some way into thefree space without pushing into neighbouring blocks.Whether it will move or not, however, also dependson whether it has a mode of failure, determined bythe mode analysis. Finally, a stability analysis isperformed on each removable block that has a modeof failure to arrive at the keyblocks, blocks thatwould fail without support. By the fundamentalaxiom of block theory, if all the keyblocks arestabilised, the entire rock mass will be stable.Therefore, one only needs to stabilise all keyblocksto assure stability of the entire rock mass. Thisrigorous narrowing down of the types of blocks thatneed to be considered, from the many possibilitiesthat exist in a discontinuous rock mass to just ahandful of keyblocks, is the beauty of Block Theory.

At present, there are limitations to the mode andstability analyses of Block Theory. The mode andstability analyses consider only sliding modes andsome special rotational modes and cannot handlegeneral modes of simultaneous sliding and rotation.Furthermore, they do not consider dynamicequilibrium, which has been shown to give correctfailure modes of blocky systems. To overcomethese limitations, three-dimensional DiscontinuousDeformation Analysis (3D DDA) single blockanalysis, which has been developed from theoriginal two-dimensional DDA (2D DDA) (Shi andGoodman, 1988), is proposed to perform the modeand stability analyses because DDA considersdynamic equilibrium and can handle general modesof failure including simultaneous sliding androtation. In this way, the advantages of both BlockTheory and DDA can be realized.

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