Stochastic fracture network models are commonly employed to deal with uncertainties in the characterization of discontinuities in rock masses. We explore the engineering significance of parameters of the network model in the context of problem of formation of removable wedges in rock excavations. Discontinuities are simulated using the Poisson disk model, and removable wedges in the excavation are identified using block theory. The formation of removable wedges of different sizes is assumed to follow a Poisson process. Poisson regression and Monte Carlo simulations are used to identify statistically relevant parameters of the model and to study the effects that variations in their values have in formation of removable blocks. Results indicate that the volumetric intensity significantly affects the computed estimates of removable blocks. Estimates are sensitive to changes in discontinuity size in cases in which discontinuities are "small" compared to the height of the slope, and the interaction between the mean size and the coefficient of variation of discontinuity sizes is also found to be significant. The rates of formation of removable wedges are higher when joint sets with small orientation variability are considered.
Stochastic fracture network models (Dershowitz & Einstein 1988) are commonly employed to deal with uncertainties in the mechanical and geometrical characterization of discontinuities in rock masses. The estimation of joint network model parameters, is, however, a challenging problem that needs to be solved for the use of such models in rock engineering applications. In that sense, being able to asses the influence that different parameters of the stochastic network model have in the engineering performance of the project of interest becomes a relevant aspect of rock engineering, as it allows rock site characterization and design procedures to be optimized, or at least more efficiently accomplished (Starzec & Andersson 2002).
In this work we study the problem of formation of removable blocks in rock excavations. Monte Carlo simulation methods are used - in conjunction with the Poisson Disk model - to generate successive realizations of the discontinuity network in the rock mass, and block theory (Goodman & Shi 1985, Goodman 1995) is employed to identify removable blocks - i.e., blocks with kinematical admissibility for displacement toward the excavated free face. Poisson regression is then used to develop a predictive model of the rate of formation of removable blocks of different sizes. In addition, we explore the engineering significance of parameters - or interactions between parameters - of the network model, identifying those that are not statistically relevant in the context of removable blocks formation, and studying the effects that variations in their values have in the rate of formation of removable blocks.
Removability is a necessary condition for a block to fail. Accordingly, the methodology presented herein might be further extended to compute the prediction of rates of formation of unstable blocks. To that end, once that removable blocks are identified, their stability may assessed - using, for instance, limitequilibrium or vector methods (Warburton 1993) - in order to identify removable, unstable blocks.