A New Analytical Solution for Calculating Rock Block Volume

The study of rock slope stability and evolution suffers from many uncertainty factors related to block size and shape, and slope morphology. While nothing can be done to remove the aleatory component of these uncertainties, efforts in reducing the epistemic ones are desirable. This research aims to propose a new analytical solution for calculating rock block volume in the case of three discontinuity sets whose orientation and true spacing are known. Researchers and practitioners can take advantage of such a correct analytical formula thanks to its easiness of use: guidelines based on stereogram are provided in order to explain how to obtain the required input data. The correctness of the equation is demonstrated by comparing the results of the new solution applied to 12 theoretical blocks with those obtained with 3DEC (Itasca Consulting Group). Also, the differences with respect to results obtained with the well-known Palmstrom's formula are reported. The new methodology is applied to the case study of Elva valley road (Northern Italy), which is overhung by steep rocky cliffs and is subject to the consequences of frequent rockfall phenomena. The results are used to discuss the proposed method's applicability: while it is evident that such a formula is not able to compete with the great potentiality of DFNs, this user-friendly tool can quickly and at no cost assess rock block volume in rockfall or rock slope stability studies.The correct analytical solution for calculating rock block volume is demonstrated.The formula is valid in the case of three discontinuity sets.Orientation and true spacing of the three sets are the input of the formula.Validation is performed through a Discrete Fracture Network generator.