Rapid graphical analysis of rock slopes

"When two discontinuities form a tetrahedral wedge in a rock slope, a factor of safety for the wedge can be simply calculated (if motion is driven only by gravity and resisted only by friction) from plots of the normals to discontinuities on an overlay of a polar, equal-area spherical projection to which the great circles of a similar equatorial projection have been added.IntroductionThe stability of slopes in rock masses is often controlled by the discontinuities that exist in the masses. In particular, the geometry of the discontinuities constrains the ways in which the mass may fail. Displaying the orientation of the discontinuities on a spherical projection has been found to be a useful way of identifying possible failure modes. The most concise display shows the orientation of the normals (or poles) to the discontinuities that compose the fabric of the rock mass. Computer processing of large samples of discontinuity orientations is necessary if the sampling biases identified by Terzaghi (1965) are to be routinely corrected. Fortunately, displays of the poles to discontinuities (or pi diagrams) are relatively easily produced on the line printer of a computer or by a computer plotter (Cruden , 1978; Ramsden and Cruden, 1979). Unfortunately, further analysis of the stability of a rock mass has tended to use traces of typical discontinuities on a spherical projection rather than pi diagrams; examples may be seen in Hoek and Bray's book (1981)."