ROCK MECHANICS 447 techniques can conveniently be classified in terms of those applicable to rock that is obviously discontinuous, and those that are strictly valid only for continuous rock This effectively separates the applications into those for near-surface structures (such as slopes, foundations, and tunnels) and those for structures at depth (such as mine excavations and petroleum wellbores) Engineering in Fractured Rock Figure 13 Illustration and analysis of wedge instability in a rock face (A) Basic equation for factor of safety against sliding, where b and x are shown in the sketch, ci is the plunge of intersection and f is the friction angle of the fractures (B) The factor of safety against wedge sliding, FW, is 1.48 for the case of Near-surface engineering is often controlled entirely by the strength and geometry of fractures It is common, and conservative, to assume that the strength of fractures is purely frictional, i.e., the fractures have zero cohesion This has an added advantage in that, in the absence of any external forces such as those generated by water pressure, an analysis of static equilibrium reduces to one that is governed by the orientation of the fractures These orientations may conveniently be determined using standard hemispherical projection techniques Of course, the blocks of rock that exist in a rock mass may possess a great many shapes and sizes In order to develop a tractable problem, only tetrahedral blocks of the maximum size that can fall or slide into an excavation are analysed Such tetrahedral blocks are generally formed from either two fracture surfaces and two excavation surfaces or from three fracture surfaces and one excavation surface Polyhedral blocks (i.e., those possessing five or more surfaces) are usually ignored, both for analytical convenience and because such a block can be cut from, and hence will be smaller and less critical than, a tetrahedral block An example of how the hemispherical projection is used in rock block stability analysis is given by the case of a rock slope containing a wedge of rock that is delineated by two fracture surfaces, as shown in Figure 13 This figure also shows how the stability of this wedge is a function of the friction angle of the fractures and three angles that relate to the geometry of the fractures These latter three angles can be measured directly and quickly from the hemispherical projection Further simplification of this analysis is possible by ignoring the stabilizing effect of the wedge factor, i.e., the quotient sin b/sin 1=2x This leads to kinematic analyses, in which only the feasibility of instability, given the interaction between the fracture and excavation geometry, is considered Kinematic analyses test for whether the geometry of the fractures and the excavation surface are capable of defining blocks that can be released into two fractures of orientation 046/69 and 182/52 and a friction angle of 29 Dashed line plane whose normal is the intersection of planes and