Fractures, joints, and other discontinuities significantly influence the stability of excavations in rock. Unstable blocks of rock in the roofs of tunnels can have a significant effect on the safety and economic feasibility of highways and railroads. The stability of tunnel roof keyblocks subject to self-weight and surface forces is examined using linear programming methods. An instability measure based on the concept of fuzzy sets is used to characterize the level of instability. On the basis of analysis of the instability measure, the support pressure required to stabilize the tunnel roof can be estimated. A probabilistic analysis based on the expectation of the instability measure is used to examine the effect of the uncertainties caused by the variability of rock material properties.
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