Determination of Meaningful Block Sizes for Rock Fall Modelling

Abstract The determination of the so-called design block is one of the central elements of the Austrian Guideline for rock fall protection ONR 24810. It is specified as a certain percentile (P95-P98, depending on event frequency) of a recorded block size distribution (BSD). BSDs may be determined from the detachment area (IBSD) and/or from the deposition area (RBSD). Deposition areas, if available, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. Also, rock fall blocks are often fragmented due to the preceding fall process. The IBSD is (also) required for meaningful rock fall modelling. The statistical method seems the most efficient and cost-effective method to determine IBSDs with many blocks within the full range of block sizes. In current literature, joint properties are often described by the lognormal and exponential distribution functions. Today, we can model Synthetic Rock Masses (SRM) based on Discrete Fracture Networks (DFN). DFNs statistically describe the geometric properties of the joint sets. This way, we can carry out exact rock mass block surveys and determine IBSDs. We asked whether IBSDs derived from SRM models can be described by probability distribution functions and if yes, how well. We fitted various distribution functions to three determined IBSDs of different lithologies. We compared their correlations using the KS test and the MSE method. We show that the generalized exponential distribution function best describes IBSDs across various lithologies, when compared to 78 other distribution functions. This could allow for more certain, accurate, verifiable, holistic, and objective results. Further investigations are required.