A fractal fragmentation model for rockfalls

Abstract

(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.

Sidewall erosion: Insights from in situ‐produced 10Be concentrations measured on supraglacial clasts (Mont Blanc massif, France)

“…2 As the cliffs of the Mont Blanc massif exceed several hundred metres in height, there are numerous impacts, during falls, both in-between blocks and against the rockwall. The estimation of parameters for such a fractal model (Ruiz-Carulla et al, 2016) is beyond the scope of this paper, but we suggest that this type of model explains why the supraglacial 10 Be concentration is not dependent on clast size. Therefore, the block size distribution on top of the glacier extends over several orders of magnitude (Godon et al, 2013), and the debris mass has fractal properties (Turcotte, 1986).…”

“…This transformation leads to a fractal distribution of the debris deposited in a supraglacial location from sand to boulders (adapted fromRuiz-Carulla et al, 2016). The rockfall event can be considered as a transformation from the block size distribution in the rockwall to the resulting block size distribution in the rockfall.…”

The Importance of Monitoring Interval for Rockfall Magnitude‐Frequency Estimation

“…This behavior is observed here, with a threefold reduction in for T int = 1 hr, as compared to T int = 30 days. Conversely, while our monitoring should not alter the assessment of the largest or worst‐case event (Corominas et al, ), an increase in f (V R ) and a reduction in at the point of release is significant for rockfall remediation (Corominas et al, ), for models that predict the ease with which rockfall debris can be remobilized or weathered based on clast volume or surface area (Messenzehl et al, ), and for interpretations of rockfall magnitude‐frequency from deposit granulometry (Crosta et al, ; Ruiz‐Carulla et al, ).…”

Seismic Energy Analysis as Generated by Impact and Fragmentation of Single‐Block Experimental Rockfalls

“…The first experiment was conducted at Foj quarry (41.361°N, 1.923°E), and the second at Ponderosa quarry (41.163°N, 0.943°E). Both tests were carried out in the framework of the project RockRisk (Corominas et al, ), an important part of which has been dedicated to determining fragmentation of rock masses and its application in fragmentation and propagation models (Matas et al, , ; Ruiz‐Carulla et al, , ). In this study, we concentrated on the emitted seismic energy values and time ( t )‐frequency ( f ) features of recorded signals and compared them to free‐fall kinetics and fragmentation, respectively.…”