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Keyblock size distributions are of fundamental importance in many branches of applied rock mechanics, including tunnelling, mining and rock slope engineering. While strongly dependent on discontinuity parameters such as spacing, persistence (or size) and orientation, keyblock size distributions and occurrence probabilities depend additionally on the size, shape and orientation of the free surface. Previous analytical models for keyblock size have been based on the assumption of infinite (persistent) discontinuities. In this paper a general model for the size distribution and probability of occurrence of simple 2-D keyblocks for arbitrary distributions of discontinuity size is developed. The method is appropriate for blocks formed by sparse fractures in tunnels or slopes. Closed form solutions are obtained for discontinuities of constant size. Application to the 3-D case is discussed and extension of the method to 3-D outlined. The results, which may depart significantly from predictions based on the assumptions of infinite fractures, are directly applicable to rock support and excavation design. |
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