Estimating keyblock sizes in underground excavations: accounting for joint set spacing

Abstract

Abstract A new method is introduced for use in the design of underground excavations in jointed rock. A model of discontinuities in a rock mass provides the basis for a closed-form solution to the expected keyblock occurrences within the excavation. The limitations of the assumptions made about the discontinuities are significant but are also, for the most part, conservative assumptions. Initially a two-dimensional formulation of the expected probability of keyblock formulation is introduced. This is valuable because it provides a simple basis for introducing the method. The two-dimensional method is demonstrated for two different excavation cross sections. The case involving excavations of rectangular cross section is validated using simulation models of tetrahedral keyblock formation. The three-dimensional case is also introduced allowing two different probabilistic formulations. One technique predicts the expected probability of a keyblock forming within a randomly selected excavation cross section. The other technique predicts the number of keyblocks (within a nominated size category) expected to form along a nominated excavation length. Both three-dimensional techniques are validated using numerical simulation. Finally, procedures for application of the unit–cell method in excavation design are provided.