Comparison of an analytical and a numerical approach to probabilistic keyblock analysis

The issue of keyblock analysis in underground excavations in jointed rock masses has been considered in a number of design situations. Deterministic methods of block theory in rock engineering were advanced by Warburton (1981) and Goodman and Shi (1985). Subsequent work by Chan (1986), Hoerger and Young (1990), Tyler, et. al. (1991), Kuszmaul (1993), and Stone (1994) has been oriented towards probabilistic risk assessment of keyblock failure. These methods are suited for analysis of densely jointed and faulted rock masses where planar joint surfaces can be assumed. In the case of deterministic analysis, theoretical approaches to the solution of keyblock problems are straightforward. However, due to the complexity of probabilistic analysis, most probabilistic methods employ a numerical solution based upon Monte-Carlo simulation. The closed form probabilistic solution developed by Kuszmaul can be easily applied to simple jointing patterns. However, the method is restricted by limiting assumptions which preclude its use in rock masses with complex joint patterns. The numerical approaches can handle more complicated problems but typically require a large amount of computation time. An example problem has been solved using the analytical approach by Kuszmaul and the numerical approach by Stone. Analysis of the results with a Kolmogorov-Smirnov test shows that the solutions produced by the two methods compare favorably