Block Volume and Shape: Comparison of Calculation Methods and Investigation of Possible Relationships

Abstract In dealing with rockfall risk mitigation, a proper assessment of the phenomenon is the key to correctly and precisely managing its possible consequences. In doing so, numerical simulations are an unavoidable step of the assessment process. The proper description of the slope and the falling rock is paramount. Thus, it is highly relevant to accurately assess block size and shape. Block size directly defines the kinetic energy involved in the phenomenon, whilst shape directly influences its trajectory. Tools to properly assess both block size and shape are available, either in analytical form or relying upon Discrete Fracture Network (DFN) models. However, at present, no concrete demonstration of the equivalence of these two methods is provided in the literature. Moreover, block size and shape are always treated separately, while it is likely that a relationship of some sort exists between the two as they derive from the same features of the rock mass (i.e., the 3D geometry of its discontinuities). This paper presents a comprehensive study concerning (1) the comparison between DFN and analytical approaches and (2) the existence and quantification of a shape–size correlation. A modeling campaign consisting of 20 different geometrical structures is performed with both methods, with the aim of obtaining In Situ Block Size Distributions and Shape Distributions. Although the DFN and the analytical approach have different advantages and disadvantages, they have proved to be comparable in terms of results. Both methods identify the existence of a correlation between shape and size of the blocks: the shape distribution changes with reference to block size. This result points out the importance of implementing shape distribution in rockfall numerical simulations. Finally, a suitable case study from the literature has been selected to test the applicability and usefulness of the new findings for the design of rockfall barriers.