Analysis Of Slopes In A Discontinuous Rock Mass

An open pit rock structure usually contains geological planes of weakness. They are formed by joints, faults, bedding planes, fractures, and cleavages. Rock slope failures often occur in the form of sliding of rock blocks along a plane or several planes. Such a rock block has three- dimensional geometry, and consequently a vector method of analysis has been found useful in evaluating its stabi1ity.l-3 Rock blocks of a tetrahedral shape with one free surface have been analyzed by Londe.3 Rock blocks formed by sets of parallel joints have been analyzed by Wittke.1,2 The present chapter presents the analysis of rock blocks formed by planes of weakness of arbitrary orientation, and of three-dimensional geometry. A plane of weakness is represented by its dip and strike in vector form and is reduced to the form of a linear equation. The geometry of the rock block is defined by solving the linear equations. The geometric characteristics of a rock block are based on triangles and tetrahedrons. By this treatment, the three-dimensional geometry is simplified and the number of calculations of forces and moments is reduced. Methods of finding the geometric characteristics are presented, along with equations for calculating the resultant forces and moments and the factor of safety. BASIC ASSUMPTIONS The following assumptions are used : The solid part of the rock mass is much stronger than the rock mass at the plane of weakness and the rock mass will only fail along planes of weakness.