Evaluation of maximum rockfall dimensions based on probabilistic assessment of the penetration of the sliding planes into the slope

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 m2 and 289.3 m2. 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.Peer ReviewedPostprint (published version

Comparing rockfall scar volumes and kinematically detachable rock masses

Scenario-based risk assessment for rockfalls, requires assumptions for different scenarios of magnitude (volume). The magnitude of such instabilities is related to the properties of the jointed rock mass, with the characteristics of the existing unfavourably dipping joint sets playing a major role. The critical factors for the determination of the maximum credible rockfall volume in a study site, the Forat Negre in Andorra, are investigated. The results from two previous analyses for the rockfall size distribution at this site are discussed. The first analysis provides the observed size distribution of the rockfall scars, and it is an empirical evidence of past rockfalls. The second one, calculates the kinematically detachable rock masses, indicating hypothetical rockfalls that might occur in the future. The later gives a maximum rockfall volume, which is one order of magnitude higher, because the persistence of the basal planes is overestimated. The tension cracks and lateral planes interrupt systematically the basal planes, exerting a control over their persistence, and restricting the formation of extensive planes and large rockfall failures. Nonetheless, the formation of basal planes across more than one spacings of tension cracks is possible and small step-path failures have been observed too. Concluding, the key factor for the determination of the maximum credible volume at the study-site is the maximum realistic length of the basal planes, penetrating into the rock mass, their spacing, and, if applied, the contribution of the rock bridges to the overall rock mass resistance.Peer ReviewedPostprint (author's final draft

Magnitude and frequency relations: are there geological constraints to the rockfall size?

The final publication is available at Springer via http://dx.doi.org/10.1007%2Fs10346-017-0910-zThere exists a transition between rockfalls, large rock mass failures, and rock avalanches. The magnitude and frequency relations (M/F) of the slope failure are increasingly used to assess the hazard level. The management of the rockfall risk requires the knowledge of the frequency of the events but also defining the worst case scenario, which is the one associated to the maximum expected (credible) rockfall event. The analysis of the volume distribution of the historical rockfall events in the slopes of the Solà d’Andorra during the last 50 years shows that they can be fitted to a power law. We argue that the extrapolation of the F-M relations far beyond the historical data is not appropriate in this case. Neither geomorphological evidences of past events nor the size of the potentially unstable rock masses identified in the slope support the occurrence of the large rockfall/rock avalanche volumes predicted by the power law. We have observed that the stability of the slope at the Solà is controlled by the presence of two sets of unfavorably dipping joints (F3, F5) that act as basal sliding planes of the detachable rock masses. The area of the basal sliding planes outcropping at the rockfall scars was measured with a terrestrial laser scanner. The distribution of the areas of the basal planes may be also fitted to a power law that shows a truncation for values bigger than 50 m2 and a maximum exposed surface of 200 m2. The analysis of the geological structure of the rock mass at the Solà d’Andorra makes us conclude that the size of the failures is controlled by the fracture pattern and that the maximum size of the failure is constrained. Two sets of steeply dipping faults (F1 and F7) interrupt the other joint sets and prevent the formation of continuous failure surfaces (F3 and F5). We conclude that due to the structural control, large slope failures in Andorra are not randomly distributed thus confirming the findings in other mountain ranges.Peer ReviewedPostprint (author's final draft

Size distribution for potentially unstable rock masses and in situ rock blocks using LIDAR-generated digital elevation models

In this paper, two analytical procedures which are independent from the existence of empirical data are presented for the calculation of (1) the size distribution of potentially unstable rock masses that expresses the potential rockfall size distribution, including big volumes corresponding to potential rare events with low susceptibility of failure and (2) the in situ block distribution on the slope face. Two approaches are, respectively, used. The first one involves the detection of kinematically unstable surfaces on a digital elevation model (DEM) and on orthophotos and the calculation of the volumes resting on them. For the second one the in situ block volumes formed by the intersection of the existing discontinuity sets are calculated using a high-resolution DEM. The procedures are presented through an application example at the country of Andorra and in particular at the chute of Forat Negre. The results from the first procedure indicate that it is kinematically possible to have mobilized volumes of some thousands of cubic meters; however, these are considered rare events with low susceptibility of failure. The size distribution of potentially unstable rock masses for big volume events was well fitted by a power law with an exponent of -0.5. The in situ block distribution on the slope face from the second procedure, assuming three types of intersection between the joints of the existing discontinuity sets and two extreme cases of discontinuity persistence, was also found to follow a power law, but with an exponent of -1.3. The comparison with the observed in the field block volume distribution on the slope face indicates that in reality discontinuities have a very high persistence and that considering only their visible trace length overestimates volumes, which is conservative.Peer ReviewedPostprint (author’s final draft

Aproximación probabilística al número y tamaño de bloques en desprendimientos con fragmentación

La mayoría de las masas rocosas que se desprenden se fragmentan en los primeros impactos contra el terreno. El riesgo asociado a los desprendimientos debe calcularse, por lo tanto, teniendo en cuenta este proceso de fragmentación. Para incorporar la fragmentación en la simulación de trayectorias es necesario prever el número y el volumen de los fragmentos rocosos resultantes en cada desprendimiento. Se presenta aquí un método para estimar estas dos variables. Se parte de la hipótesis que la distribución del volumen de los bloques acumulados en el canchal puede ser utilizada para generar aleatoriamente conjuntos de bloques, cada uno de ellos simulando el conjunto de bloques resultantes de un desprendimiento. Esta aproximación se ha aplicado a un canchal del Solà d’Andorra, Andorra la Vella (Principado de Andorra). La validez del método se ha contrastado comparado los resultados obtenidos con lo observado en desprendimientos recientes, inventariados por un plan de vigilancia de la zona.Postprint (published version

Recommendations for the quantitative analysis of landslide risk

This paper presents recommended methodologies for the quantitative analysis of landslide hazard, vulnerability and risk at different spatial scales (site-specific, local, regional and national), as well as for the verification and validation of the results. The methodologies described focus on the evaluation of the probabilities of occurrence of different landslide types with certain characteristics. Methods used to determine the spatial distribution of landslide intensity, the characterisation of the elements at risk, the assessment of the potential degree of damage and the quantification of the vulnerability of the elements at risk, and those used to perform the quantitative risk analysis are also described. The paper is intended for use by scientists and practising engineers, geologists and other landslide experts.Peer ReviewedPostprint (published version

The RockRisk project: rockfall risk quantification and prevention

Rockfalls are frequent instability processes in road cuts, open pit mines and quarries, steep slopes and cliffs. The orientation and persistence of joints within the rock mass define the size of the kinematically unstable rock volumes and determine the way how the detached mass be-comes fragmented upon the impact on the ground surface. Knowledge of the size and trajectory of the blocks resulting from fragmentation is critical for calculating the impact probability and intensity, the vulnerability the exposed elements and the performance of protection structures. In this contribution we summarize the main goals and achievements of the RockRisk project. We focused on the characterization of the rockfall fragmentation by means of the analysis of the fracture pattern of intact rock masses, the development of a fragmentation model and its integration into rockfall propagation analysis. The ultimate goal of the project is to quantify risk due to rockfalls and develop tools for the improvement of prevention and for protection from its occurrence.Postprint (published version

Evaluation of the susceptibility to failure of rocky slopes based on the SMR index

Postprint (published version