integrated by means of the central difference expressions so on diagonal mass and damping matrices the velocity amplitude of some sub-body or block is completely determined by the unbalanced forces and the velocity amplitudes of the previous time step of the same sub-body. Then each problem can be solved block-wise which makes the method particularly suitable for use on personal computers. Applications of the discrete element method to slope stability (steeply dipping foliation planes) and mining problems are found in Cundall (1987) and Lorig et al. (1989); applications of the discrete element method to the collapse of a soil embankment, and penetration of a projectile into a soil can be found in Williams (1987).

The most widely used distinct and discrete element code appears to be UDEC (Cundall and Hart, 1983). The computational effort in the application of the distinct/discrete element methods to practical problems is considerable. Alternative methods that are between the conventional continuum theory and the detailed discrete methods are therefore desirable.

This approach describes a series of theorems and application methods governing the 3D geometry of intersecting fractures (joints) and excavated surfaces (Warburton, 1981; Goodman and Shi, 1983; Lin and Fairhurst, 1988). By means of topological programs manipulating these relationships, all possible rock blocks are divided into a small number of types, each of which is analyzed for its support needs in a specific excavation. The underlying principle of block theory is that prevention of the movement of “keyblocks”⁶ assures the complete safety of the entire excavation. The input for the analysis has, as a minimum, the orientations of each of the joint sets and the shape and orientation of the excavation. The friction angles of each joint set are needed to quantify support requirements but optimum directions and shapes of excavations can be determined even without this knowledge. With these data, one program determines the supporting force needed per unit length of tunnel as a function of tunnel orientation. A recent development of block theory is the statistical simulation of the traces of intersection of the tunnel wall and the system of discontinuities, and