This paper discusses the problem of rock slidings. Since there always exists a stochastic distribution of geological discontinuities within a rock mass, it is not easy to determine the sliding zone. In order to overcome the difficulty, we firstly regard the geological discontinuities as divided into families according to parallelism. In the basis of these families we introduce the concept of "cutting pyramid" of a sliding rock volume. Cutting pyramids give the basic information of a sliding rock volume: the sliding types, the sliding direction, the sliding forces, the relative positions of a sliding rock volume to the geological discontinuities. Then we give the method of the vector operation and the method of the stereographic projec-tion, which, for given free surfaces, determine all cutting pyramids contain-ing sliding rock volumes, for preliminaryly evaluating the stability of a rock slope, and the underground structure in the stage of site investigation [4]. As for the analysis of rock stability of dam foundations, the theory of "cutting pyramid" seems to have a wider scope of application than the method described in [2]. For example using the method suggested in this paper can be analyzed the stability of a rock volume of a type more complicated than the rock wedge.

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