Evaluation of Maximum Rockfall Dimensions Based on Probabilistic Assessment of the Penetration of the Sliding Planes into the Slope

Abstract

There is intrinsic difficulty in the investigation of the largest volume of rockfalls that is expected in an area, which lies in the small number of large events, in registrable times. The maximum credible rockfall size has been associated with the properties of the rock mass discontinuities, as they delimit detachable rock blocks, and in particular with the penetration of those discontinuities that comprise rockfall sliding planes. In highly fractured rock masses, the evaluation of the penetration remains an issue. A probabilistic methodology is proposed, to measure the penetration of potential sliding planes into the interior of a rocky slope. The main hypothesis of the method is that the sliding plane persistence is interrupted along its two directions, at the intersection with two lateral discontinuity sets, as the latter displaces the former. Due to the displacement, the sliding planes are formed by quasi-planes that contain a maximum number of spacings of the intersecting joints, hence their size is restricted. The methodology requires as an input the spacing of the intersecting joint sets. Its application to a granodiorite slope confirms that for the study site, there is a maximum volume of rockfalls, excluding the possibility of large stepped failures and rupture of rock bridges. The maximum calculated persistence for the two existing sliding planes in the study site is, respectively, 28.0 m and 48.5 m. The maximum calculated sliding plane surfaces are, accordingly, 282.5 m 2 and 289.3 m 2 . These results are compared against the observed scar dimensions at the study site, which have been retrieved alternatively, by processing a LiDAR point cloud. The results from the two alternative sources are similar, indicating that the methodology can be efficiently used to assess the sliding plane persistence and the expected maximum rockfall magnitude at the study site.

Definitions and Concepts for Quantitative Rockfall Hazard and Risk Analysis

“…The question arises of the maximal possible volume of a rockfall event (or a rock fragment) to be considered in the hazard assessment, which is usually higher than the maximal observed volume. This was discussed by [59]. The spatial-temporal frequency of rockfalls bigger than 1 m 3 is at about 10 times smaller in massive limestone than in bedded limestone.…”

“…The question arises of the maximal possible volume of a rockfall event (or a rock fragment) to be considered in the hazard assessment, which is usually higher than the maximal observed volume. This was discussed by [59].…”

“…where W a is the width of the area of interest. As the passage frequency refers to an area of interest that is much wider than the element at risk, the probability that a rockfall reaching this area impacts the element at risk must be introduced [59]. Refs.…”

“…Refs. [57,59] named this probability the spatial probability (of an event reaching the element at risk given that it occurs in the area of interest). It can be expressed as…”

Definitions and Concepts for Quantitative Rockfall Hazard and Risk Analysis

“…The question arises of the maximal possible volume of a rockfall event (or a rock fragment) to be considered in the hazard assessment, which is usually higher than the maximal observed volume. It has been discussed [55].…”