In this study, the probabilistic analysis is applied to evaluate the removability of a rock block. The approach to directly apply probability integration involves complex mathematics and is often formidable for the solution. In order to overcome this limitation, the first-order second-moment (FOSM) approximations of the probabilities are utilized. The technique simplifies the computation significantly and allows for the analysis of relatively complex stability problems. Two different random variable distributions are applied in the study, namely the Beta distribution and the Fisher distribution. Monte Carlo simulations are also conducted in the study for comparison. A case study is presented for the occurrence probability of a removable block. The study indicates that the two distributions give the same general trend in the occurrence probability of a removable block but slightly different probability values. The study also reveals that with the same mean values of random variables, the block removable probabilities differ significantly if the dispersions of the random variables are different. The conventional methods considering only the mean values may not provide accurate determination of rock block removability.
The stability of rock excavations depends on many factors, such as mechanical properties of rock masses, orientations and properties of rock discontinuities, hydrological conditions, excavation geometries, and others. In an excavation stability analysis, these parameters are acquired by either in-situ investigations and/or laboratory tests. Because of the complex nature of rock masses, these parameters do not usually appear to be uniquely valued, but vary over a certain range. With the conventional limit equilibrium analysis, the average values of these parameters are used and a factor of safety, a deterministic number, is computed to indicate the stability of an excavation. This deterministic description of excavation stability, however, does not take into account of the uncertainties involved.