(150-250 words)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 blocks 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.
Rock masses detached as rockfalls usually disintegrate upon impact on the ground surface. The knowledge of the Rockfall Block Size Distribution (RBSD) generated in the rockfall deposit is useful for the analysis of the trajectories of the rock blocks, run-out distances, impact energies and for the quantitative assessment of the rockfall hazard. Obtaining the RBSD of a large rockfall deposit may become a challenge due to the high number of blocks to be measured. In this paper, we present a methodology developed for mid-size fragmental rockfalls (10 3 up to 10 5 m 3 ) and its application to the Cadí massif, Eastern Pyrenees. The methodology consists of counting and measuring block fragments in selected sampling plots within homogeneous zones in the young debris cover generated by the rockfall along with all the large scattered rock blocks. The size distribution of blocks obtained in the sampling plots is extrapolated to the whole young debris cover and summed to the inventoried large scattered blocks to derive the RBSD of the whole rockfall event. The obtained distributions from the fragments can be well fitted by a power law distribution, indicating the scale invariant character of the fragmentation process (Hartmann 1969 ;Turcotte, 1986). The total volume of the rockfall fragments has been checked against the volume at the rockfall source. The latter has been calculated comparing 3D digital surface models before and after the rockfall event.
The analysis of seismic signals obtained from near‐source triaxial accelerometer recordings of two sets of single‐block rockfall experiments is presented. The tests were carried out under controlled conditions in two quarries in northeastern Spain; in the first test (Foj limestone quarry, Barcelona), 30 blocks were released with masses ranging between 475 and 11,480 kg. The second test (Ponderosa andesite quarry, Tarragona) consisted of the release of 44 blocks with masses from 466 to 13,581 kg. An accelerometer and three high‐speed video cameras were deployed, so that the trajectories, velocities, and block fragmentation could be tracked precisely. These data were used to explore the relationship between seismic energy and rockfall kinetics (the latter obtained from video analysis). We determined absolute and relative values of seismic energy and used them to estimate rockfall volumes. Finally, the seismic signature of block fragmentation was assessed in both the frequency and time domains. The ratios of seismic energy after impact to kinetic energy before impact ranged between 10−7 and 10−4. These variables were weakly correlated. The use of seismic energy relative to impacting kinetic energy was preferred for the estimation of volumes. Block fragmentation impacts were dominated by higher acceleration spectrum centroid frequencies than those of nonfragmentation impacts: 56.62 ± 2.88 and 48.46 ± 4.39 Hz at Foj and 52.84 ± 12.73 and 38.14 ± 4.73 Hz at Ponderosa.
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 were 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 m 2 and a maximum exposed surface of 200 m 2. The analysis of the geological structure of the rock mass at the Solà d'Andorra make 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.
We present the performance of the rockfall fractal fragmentation model (RFFM) developed by Ruiz-Carulla et al. (2017) and based on Perfect (1997). The RFFM combines disaggregation of the initial rock mass and breakage of the blocks. The model has been upgraded as to meet the mass balance, and to generate both a continuous decreasing and scale variant distribution of fragments volumes. The input of the model may be either a single block or a rock mass characterized by its In situ Block Size Distribution (IBSD). The measured fragment size distributions of seven inventoried rockfall events, are used to calibrate the model. The results of the simulations fit well to the measured volume distributions. Our findings indicate that fragmentation is better characterized by the whole volume distribution of fragments generated and the increase of new surface area of the rock fragments. A relation has been observed between the potential energy of the first impact, the new surface area of fragments generated, and the model parameters. Although a greater number of parametric analyses and calibration exercises are required, this relation is proposed as a first approach to model rockfall scenarios.
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