Deriving reliable block size distributions using synthetic rock mass models

The determination of the so-called design block is one of the central elements of the Austrian guideline for rockfall protection ONR 24810. It is specified as a certain percentile (P95–P98, depending on the event frequency) of a recorded block size distribution. Block size distributions may be determined from the detachment area (in-situ block size distribution) and/or from the deposition area (rockfall block size distribution). Deposition areas, if present, are generally accessible and measurable without technical aids. However, most measuring methods are subjective, uncertain, not verifiable, or inaccurate. There is no specification of minimum measurements, which influences the reliability of the block size distributions (the more measurements the more reliable). Also, rockfall blocks are often fragmented due to the preceding fall process. The in-situ block size distribution is (also) required for meaningful rockfall modelling. The statistical method seems to be the most efficient and cost-effective method to determine in-situ block size distributions with many blocks within the whole range of block sizes. Illeditsch & Preh (2023) have introduced a new approach to evaluate rockfall hazard using synthetic rock mass models based on Discrete Fracture Networks (DFNs). A general stochastic DFN approach assumes that fractures are planar discs and treats the other geometrical properties (e.g. position, frequency, size, orientation) as independent variables obeying certain probability distributions derived from field measurements of outcrops. Using DFNs it is possible to carry out exact rock mass block surveys and to determine in-situ block size distributions. Various distribution functions were fitted to several determined in-situ block size distributions of different lithologies. Their correlations were compared using the Kolmogorov–Smirnov test and the mean-squared error method. It is shown that the generalized exponential distribution function best describes the in-situ block size distributions across various lithologies compared to 78 other distribution functions. This approach could lead to more certain, accurate, verifiable, holistic, and objective results.