Effect of uncertainties on block volume estimation

The combination of the aleatory nature of the rock mass structure and the epistemic errors related to the survey methods make rock mass characterization a challenge despite the remarkable evolution of the survey tools and the research on the subject. In particular, significant uncertainties affect block volume estimation: the need for simplification connected to the engineering approach to rockfall problems, for instance, risks to mask the ripple effect of uncertainties on the reliability of the results. Even considering a simplified shape of the block created by three sets of discontinuities (i.e., a prism), the uncertainties on the geometrical characteristics of the discontinuities (orientation, spacing, and persistence) greatly influence the resulting volume distribution. It is a fact that a single value of the volume cannot be representative of the rock mass: the In Situ Block Size Distribution (IBSD) should be built to describe the variability of block volumes. Many statistical distribution functions can be used for fitting spacing data (i.e., gamma, negative exponential, log-normal, Weibull). The choice of the function must follow a rigorous evaluation of the goodness of fit. This research aims to assess the influence of the uncertainties related to the discontinuities sets, with particular reference to spacing samples, on block volume estimation. Through numerical examples and a case study, this research shows that a reduction of uncertainty can be reached by rigorous statistical processing of the data.