RockGIS: a GIS-based model for the analysis of fragmentation in rockfalls

A rockfall is a mass instability event frequently observed in road cuts, open pit mines and quarries, steep slopes and cliffs. After its detachment, the rock mass may disaggregate and break due to the impact with the ground surface, thus producing new rock fragments. The consideration of the fragmentation of the rockfall mass is critical for the calculation of the trajectories of the blocks and the impact energies and for the assessment of the potential damage and the design of protective structures. In this paper, we present RockGIS, a GIS-based tool that simulates stochastically the fragmentation of the rockfall, based on a lumped mass approach. In RockGIS, the fragmentation is triggered by the disaggregation of the detached rock mass through the pre-existing discontinuities just before the impact with the ground. An energy threshold is defined in order to determine whether the impacting blocks break or not. The distribution of the initial mass between a set of newly generated rock fragments is carried out stochastically following a power law. The trajectories of the new rock fragments are distributed within a cone. The fragmentation model has been calibrated and tested with a 10,000 m³ rockfall that took place in 2011 near Vilanova de Banat, Eastern Pyrenees, Spain.     

A fractal fragmentation model for rockfalls

The impact-induced rock mass fragmentation in a rockfall is analyzed by comparing the in situ block size distribution (IBSD) of the rock mass detached from the cliff face and the resultant rockfall block size distribution (RBSD) of the rockfall fragments on the slope. The analysis of several inventoried rockfall events suggests that the volumes of the rockfall fragments can be characterized by a power law distribution. We propose the application of a three-parameter rockfall fractal fragmentation model (RFFM) for the transformation of the IBSD into the RBSD. A discrete fracture network model is used to simulate the discontinuity pattern of the detached rock mass and to generate the IBSD. Each block of the IBSD of the detached rock mass is an initiator. A survival rate is included to express the proportion of the unbroken blocks after the impact on the ground surface. The model was calibrated using the volume distribution of a rockfall event in Vilanova de Banat in the Cadí Sierra, Eastern Pyrenees, Spain. The RBSD was obtained directly in the field, by measuring the rock block fragments deposited on the slope. The IBSD and the RBSD were fitted by exponential and power law functions, respectively. The results show that the proposed fractal model can successfully generate the RBSD from the IBSD and indicate the model parameter values for the case study.     

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

There 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.     

Rockfalls: analysis of the block fragmentation through field experiments

Landslides - Fragmentation is a common feature of rockfall that exerts a strong control on the trajectories of the generated blocks, the impact energies, and the runout. In this paper, we present a...