Block Size Distribution Research Articles

Gravitational slope processes triggered by past earthquakes on the Western Cantabrian Mountains (Sierra de la Sobia, Northern Spain)

Sierra de la Sobia is a linear mountain range of arcuate shape, located west of the Cantabrian Mountains. The long-lived crustal León Fault runs along its western hillslope, and its trace is partially covered by multiple rock-avalanches. Here we discuss if recurrent paleo-earthquakes in the M6+ range could have acted as the triggering factor for rock-avalanches in a region where the historical and instrumental seismic records only include seismic events up to Ms 4.6. Evidence concurring with a coseismic origin includes: (i) kinematic of current minor transverse and parallel faults to Sierra de la Sobia being consistent with a horizontal North-South compression of the Cantabrian Arc; (ii) slopes of the depletion zones that would become unstable if horizontal seismic ground rose 0.10–0.15 g; and (iii) block size-reduction by dynamic fragmentation creating block size distribution with fractal dimension, ranging between 2.24 and 2.70. U/Th dating of seven calcite precipitates coating the blocks of cemented rock-avalanche deposits suggesting that cementation has taken place in multiple episodes since MIS-9a. Neotectonics of Sierra de la Sobia are expressed in subtle changes in relief after extremely rapid co-seismic events, with average recurrence intervals much longer than the time covered by the regional historical and instrumental period.

In-Situ Block Characterization of Jointed Rock Exposures Based on a 3D Point Cloud Model

The importance of in-situ rock block characterization has been realized for decades in rock mechanics and engineering, yet how to reliably measure and characterize the geometrical properties of blocks in varied forms of exposures and patterns of jointing is still a challenging task. Using a point cloud model (PCM) of rock exposures generated from remote sensing techniques, we developed a consistent and comprehensive method for rock block characterization that is composed of two different procedures and a block indicator system. A semi-automatic procedure towards the robust extraction of in-situ rock blocks created by the deterministic discontinuity network on rock exposures (PCM-DDN) was developed. A 3D stochastic discrete fracture network (DFN) simulation (PCM-SDS) procedure was built based on the statistically valid representation of the discontinuity network geometry. A multi-dimensional block indicator system, i.e., the block size, shape, orientation, and spatial distribution pattern for systematic and objective block characterization, was then established. The developed method was applied to a synthetic model of cardboard boxes and three different rock engineering scenarios, including a road cut slope from Spain and two open-pit mining slopes from China. Compared with existing empirical methods, the proposed procedures and the block indicator system are dependable and practically feasible, which can help enhance our understanding of block geometry characteristics in related applications.

A new approach to improve the assessment of rock mass discontinuity spacing using image analysis technique

The mean discontinuity spacing can significantly varies with varying the scanline direction. To clarify the assessment of mean discontinuity spacing using measurement and relevant conventional equations, several artificial cubic models having three different discontinuity sets with various spacings and orientations were made by foam. The grand mean measured discontinuity spacing (XGMM) of various scanline directions on different profile planes had a linear correlation with the block size (XBS) of the typical artificial models (XGMM = 0.725XBS). Then, a new method using image analysis of in-situ rock mass was applied to assess mean rock mass block size as an alternative solution to represent the mean discontinuity spacing. The scaled images were prepared from ninety-four cases of twenty zones of in-situ rock masses in several mines, and the discontinuity spacing was also measured in six scanline directions for each case, as measurement was carried out in 564 scanlines. The images of in-situ rock masses were analyzed by Split-Desktop software and rock block size distribution, X20, X50 (mean size) and X80 were determined. The rock block size obtained by the images analysis (X50-image analysis) had a good linear correlation with the grand mean measured discontinuity spacing of six scanline directions of each case (XGM-measured) for various rock mass conditions (XGM-measured = 0.70X50-image analysis). The obtained relation can be a reliable solution to specify the mean value of discontinuity spacing using image analysis of rock mass.

The Impact of Fracture Persistence and Intact Rock Bridge Failure on the In Situ Block Area Distribution

The in situ block size distribution is an essential characteristic of fractured rock masses and impacts the assessment of rockfall hazards and other fields of rock mechanics. The block size distribution can be estimated rather easily for fully persistent fractures, but it is a challenge to determine this parameter when non-persistent fractures in a rock mass should be considered. In many approaches, the block size distribution is estimated by assuming that the fractures are fully persistent, resulting in an underestimation of the block sizes for many fracture geometries. In addition, the block size distribution is influenced by intact rock bridge failure, especially in rock masses with non-persistent fractures, either in a short-term perspective during a slope failure event when the rock mass increasingly disintegrates or in a long-term view when the rock mass progressively weakens. The quantification of intact rock bridge failure in a rock mass is highly complex, comprising fracture coalescence and crack growth driven by time-dependent changes of the in situ stresses due to thermal, freezing-thawing, and pore water pressure fluctuations. This contribution presents stochastic analyses of the two-dimensional in situ block area distribution and the mean block area of non-persistent fracture networks. The applied 2D discrete fracture network approach takes into account the potential failure of intact rock bridges based on a pre-defined threshold length and relies on input parameters that can be easily measured in the field by classical discontinuity mapping methods (e.g., scanline mapping). In addition, on the basis of these discrete fracture network analyses, an empirical relationship was determined between (i) the mean block area for persistent fractures, (ii) the mean block area for non-persistent fractures, and (iii) the mean interconnectivity factor. The further adaptation of this 2D approach to 3D block geometries is discussed on the basis of general considerations. The calculations carried out in this contribution highlight the large impact of non-persistent fractures and intact rock bridge failure for rock mass characterization, e.g., rockfall assessment.

Digital Image Processing Method for Characterization of Fractures, Fragments, and Particles of Soil/Rock-Like Materials

Natural soil and rock materials and the associated artificial materials have cracks, fractures, or contacts and possibly produce rock fragments or particles during geological, environmental, and stress conditions. Based on color gradient distribution, a digital image processing method was proposed to automatically recognize the outlines of fractures, fragments, and particles. Then, the fracture network, block size distribution, and particle size distribution were quantitatively characterized by calculating the fractal dimension and equivalent diameter distribution curve. The proposed approach includes the following steps: production of an image matrix; calculation of the gradient magnitude matrix; recognition of the outlines of fractures, fragments, or particles; and characterization of the distribution of fractures, fragments, or particles. Case studies show that the fractal dimensions of cracks in the dry mud layer, ceramic panel, and natural rock mass are 1.4332, 1.3642, and 1.5991, respectively. The equivalent diameters of fragments of red sandstone, granite, and marble produced in quasi-static compression failures are mainly distributed in the ranges of 20–40 mm, 25–65 mm, and 10–35 mm, respectively. The fractal dimension of contacts between mineral particles and the distribution of the equivalent diameters of particles in rock are 1.6381 and 0.8–3.6 mm, respectively. The proposed approach provides a computerized method to characterize quantitatively and automatically the structure characteristics of soil/rock or soil/rock-like materials. By this approach, the remote sensing for characterization can be achieved.

Assessing the effect of lithological setting, block characteristics and slope topography on the runout length of rockfalls in the Alps and on the island of La Réunion

Abstract. In four study areas within different lithological settings and rockfall activity, lidar data were applied for a morphometric analysis of block sizes, block shapes and talus cone characteristics. This information was used to investigate the dependencies between block size, block shape and lithology on the one hand and runout distances on the other hand. In our study, we were able to show that lithology seems to have an influence on block size and shape and that gravitational sorting did not occur on all of the studied debris cones but that other parameters apparently control the runout length of boulders. Such a parameter seems to be the block shape, as it plays the role of a moderating parameter in two of the four study sites, while we could not confirm this for our other study sites. We also investigated the influence of terrain parameters such as slope inclination, profile curvature and roughness. The derived roughness values show a clear difference between the four study sites and seem to be a good proxy for block size distribution on the talus cones and thus could be used in further studies to analyse a larger sample of block size distribution on talus cones with different lithologies.

Investigation of rock properties distribution effect on pressure transient analysis of naturally fractured reservoirs

Naturally fractured reservoirs (NFRs) are considered as one of the main resources of oil and gas around the world. The nature of fractures in this kind of reservoirs splits these reservoir rocks into two parts; matrix and fracture. In these two media, geometrical properties like matrix block size and also petrophysical properties such as porosity and permeability cannot considered to be constant and they usually contain heterogeneity in extent of the reservoir. In this study, a statistical distribution concept is used to be able to model variance of properties including matrix block size, matrix and fracture permeability, and matrix and fracture porosity as independent statistical variables. For the purpose of investigating effect of the five aforementioned properties distribution on pressure transient analysis (PTA) plots, five distinct cases of property distributions are considered with their corresponding precise statistical modeling applied on governing flow equation of a dual-porosity base case reservoir model. Abovementioned distributed parameters are included in semi-analytically derived dual porosity reservoir models and results are compared to their corresponding constant-value response. In each case the constant parameter is the median of corresponding statistical distribution. The statistical approach is validated using numerical modeling and field data applications are also presented. Different unimodal and bimodal matrix properties (block size, permeability, and porosity) distribution have slight to intense effects on PTA plots of an NFR. In matrix block size and porosity distribution cases, lower values, and in matrix permeability distribution case, higher values of the range dominate the pressure behavior of the fractured system. On the other hand, although fracture permeability and porosity distribution can shift PTA plots of the model but the effect is not significant and both fracture permeability and porosity distribution can be represented by constant representative values instead of a statistical model. It is worth mentioning that all matrix properties bimodal distribution has a common signature on PTA plots which is similar to the triple porosity reservoir response (i.e. the presence of double-bump descent on pressure derivative plot).

A New Approach to Represent Impact of Discontinuity Spacing and Rock Mass Description on the Median Fragment Size of Blasted Rocks Using Image Analysis of Rock Mass

Several in-situ rock mass properties and blasthole parameters can affect the rock fragmentation. Because of the complexity of the variables affecting the fragmentation results of blasted rocks, to predict a proper value of the median fragment size has long been a difficult task. The blastability index (BI) represents the effect of five parameters of rock mass description (RMD), joint plane spacing (JPS), joint plane orientation, specific gravity and uniaxial compressive strength on the rock fragmentation. The median discontinuity spacing significantly varies with varying the scanline direction and an acceptable value of the median discontinuity spacing will not be expected in practice. The JPS rating also has a constant value of 20 for a wide range of joint spacing values between 0.1 and 1 m, whereas joint spacing can be in this range for most cases. A new method using image analysis of the in-situ rock mass was applied to represent JPS and RMD (belonging to one of the cases: friable, blocky and massive) as an alternative solution. The images contain the details of all individual discontinuities and interlocked in-situ small and large rock blocks. BI, rock strength factor, blasthole parameters, powder factor, fragment size distribution of blasted rock and in-situ block size distribution using image analysis technique were assessed in 15 zones of Sungun open pit copper mine, Angouran lead and zinc open pit mine, Bonab silica mine, Soufian limestone mine and Rashakan limestone mine. The results for rock mass properties and blasthole patterns cover a wide range using different mines. The fragment size distribution was assessed by Split Desktop program with proper delineating images using the Pixler software and blasting was carried out with electric delay detonators. The relations between fragment size and parameters such as in-situ block size (F50), σc, rating of joint plane orientation, powder factor (q), ϕh, Q and Lc were analyzed. The relations with high correlations were achieved by applying the new approach for the defined conditions. Not only the problem of assessing discontinuity spacing has been improved using this method but also the lower number of parameters that properly represent the factors affecting the rock fragmentation have been used. The results were also analyzed by the Sanchidrian and Ouchterlony model and modified Kuz–Ram models. The fragment size obtained by the new method in this study, Sanchidrian and Ouchterlony model and extended modified Kuz–Ram model by Cunningham (in: Proceedings of 3rd world conference on explosives and blasting, Brighton, 2005) after using correction factor [c(A)] significantly better fitted to the results than the modified Kuz–Ram models by Cunningham (in: Fourney, Dick (eds) Proceedings of 2nd international symposium on rock fragmentation by blasting, Keystone, 1987) and Gheibie et al. (Int J Rock Mech Min 46(6):967–973, 2009).

A new method for constructing finite difference model of soil-rock mixture slope and its stability analysis

A new method for constructing a digital model of soil-rock mixture is proposed in this paper. Using this method, rock blocks of arbitrary shapes can be considered and the construction of soil-rock mixtures with different block size distribution and rock content can be realized. First, through digital image processing, a large number of rock block contours that are analogous with reality are obtained. Then, a corresponding rock block library is established. Next, an improved intersection detection algorithm based on axis-aligned bounding box is developed to construct the digital model of the soil-rock mixture slope. Furthermore, the stabilities of soil-rock mixture slopes with different block size distribution and rock content are investigated. The results show that the soil-rock mixture slope exhibits multiple sliding zone under the combined action of various plastic zone expansion. And the influence of block size distribution and rock content on the stability of soil-rock mixture slope has a coupling effect.

Phase Behavior of Gradient Copolymer Melts with Different Gradient Strengths Revealed by Mesoscale Simulations.

Design and preparation of functional nanomaterials with specific properties requires precise control over their microscopic structure. A prototypical example is the self-assembly of diblock copolymers, which generate highly ordered structures controlled by three parameters: the chemical incompatibility between blocks, block size ratio and chain length. Recent advances in polymer synthesis have allowed for the preparation of gradient copolymers with controlled sequence chemistry, thus providing additional parameters to tailor their assembly. These are polydisperse monomer sequence, block size distribution and gradient strength. Here, we employ dissipative particle dynamics to describe the self-assembly of gradient copolymer melts with strong, intermediate, and weak gradient strength and compare their phase behavior to that of corresponding diblock copolymers. Gradient melts behave similarly when copolymers with a strong gradient are considered. Decreasing the gradient strength leads to the widening of the gyroid phase window, at the expense of cylindrical domains, and a remarkable extension of the lamellar phase. Finally, we show that weak gradient strength enhances chain packing in gyroid structures much more than in lamellar and cylindrical morphologies. Importantly, this work also provides a link between gradient copolymers morphology and parameters such as chemical incompatibility, chain length and monomer sequence as support for the rational design of these nanomaterials.

Continuous Monitoring and Improvement of the Blasting Process in Open Pit Mines Using Unmanned Aerial Vehicle Techniques

The current techniques used for monitoring the blasting process in open pit mines are manual, intermittent and inefficient and can expose technical manpower to hazardous conditions. This study presents the application of unmanned aerial vehicle (UAV) systems for monitoring and improving the blasting process in open pit mines. Field experiments were conducted in different open pit mines to assess rock fragmentation, blast-induced damage on final pit walls, blast dynamics and the accuracy of blastholes including production and pre-split holes. The UAV-based monitoring was done in three different stages, including pre-blasting, blasting and post-blasting. In the pre-blasting stage, pit walls were mapped to collect structural data to predict in situ block size distribution and to develop as-built pit wall digital elevation models (DEM) to assess blast-induced damage. This was followed by mapping the production blasthole patterns implemented in the mine to investigate drillhole alignment. To monitor the blasting process, a high-speed camera was mounted on the UAV to investigate blast initiation, sequencing, misfired holes and stemming ejection. In the post-blast stage, the blasted rock pile (muck pile) was monitored to estimate fragmentation and assess muck pile configuration, heave and throw. The collected aerial data provide detailed information and high spatial and temporal resolution on the quality of the blasting process and significant opportunities for process improvement. The current challenges with regards to the application of UAVs for blasting process monitoring are discussed, and recommendations for obtaining the most value out of an UAV application are provided.

Reliability-Based Design of Protection Net Fences: Influence of Rockfall Uncertainties through a Statistical Analysis

Net fences are among the most widespread passive protective measures to mitigate the risk from rockfall events. Despite the current design approach being based on partial safety factors, a more efficient time-dependent reliability approach has been recently introduced by the authors. This method is influenced by various parameters related to the geometry and the kinematics of the block, i.e., the uncertainty related to the distribution of the size of the impacting block, its occurrence probability, and the shape of the right-tail of the distributions of its velocity and trajectory height at the location of the net fence. Furthermore, the block size distribution of the deposit greatly affects the results. The present work focuses on the possible range of such parameters to encompass the great majority of real events. The obtained results are compared with the current design approaches based on fixed partial safety factors. It emerges that the choice of the characteristic mass of the block and the failure probability greatly influence the results. Moreover, if a set of partial safety factors is assigned to different sites, an intrinsic variability in the failure probability has to be accepted. Suggestions for an accurate procedure and future developments are provided.

Fracture Frequency and Block Volume Distribution in Rock Masses

There are important potential engineering applications of a prediction model for rock mass block size distribution from linear fracture frequency measurements along scanlines on exposed rock walls along diamond drill cores, or along digitized borehole walls. These pertain to the characterization of rock masses in mining and geotechnical engineering projects either using rock mass classification systems or empirical equations for the reduction of rock mass parameters or numerical simulation codes. Another application is the resource estimation of decorative stone deposits using diamond drill coring or image analysis of borehole walls. In these cases, the resources are derived from the distribution of rock block volumes greater than a certain cut-off volume. It could be realized that such a prediction could lead apart from the evaluation of the measured decorative stone resources, also to the optimization of pit limits and the final estimation of proven reserves. Further, it could lead to optimization of block volume diamond wire cuts at the later stage of squaring of block volumes by comparing the final distribution after squaring with the original in situ block size distribution. Towards this aim and based on the results of a previous paper, we further elaborate: (a) on the composition of the method to characterize the fracture frequencies observed along diamond drill cores and (b) on the analytical prediction of the block volume distribution. Analytical model predictions are finally validated against actual production data from a white dolomitic marble quarry and they are compared with predictions of a more rigorous numerical simulation model based on a non-homogeneous Poisson process.

In Situ Block Size Distribution Aimed at the Choice of the Design Block for Rockfall Barriers Design: A Case Study along Gardesana Road

When studying rockfall phenomena, a single value of the block volume is not sufficient to take into account the natural variability of the geometrical features (orientation, spacing, persistence) of the discontinuity sets. Different approaches for obtaining cumulative distributions of potentially detachable block volumes are compared. A highly fractured rock mass outcropping along the western Lake Garda (Italy), consisting of prevailing limestone and interbedded marls, is studied in detail from geological and geostructural points of view. Then, a representative rock face has been selected and analyzed with traditional and non-contact survey methods to identify the main discontinuity sets and to collect spacing samples. Based on these data, in situ block size distributions for different combinations of sets are built following statistically-based approaches, without the use of a Discrete Fracture Network (DFN) generator. The validation of the obtained distributions is attempted based on the detached block surveyed at the foot of the slope. However, in this particular case study, the detached blocks cover only a minimal volume range compared to both theoretical values and visible rockfall scars. The fallen rock blocks have a marginal role in design block determination, since their volume depends on geological discontinuities (bedding and fractures) and could be affected by other processes after the detachment (e.g., fragmentation). The procedure here described should be standard practice in the study of rockfall events, and it should be uniform in European standards such as Eurocodes. Future developments should involve the scientific community for setting the percentiles of the probability distribution to be considered for block design definition.

Methodology for the Estimation and Classification of White Marble Reserves

In the marbel industry, ore reserves refer to the produced tonnage of orthogonal prismatic, defect-free blocks of commercial sizes and of marketable aesthetical quality. On the contrary, in the mining sector, ore reserves refer to the tonnage of ore with grade above some cut-off value. While in the mining sector ore reserves are reported according to existing standard guidelines, the marble industry has no standard method. The purpose of this paper is to present a method to estimate white marble reserves using drill coring or borehole wall logging and limited joint mapping on exposed marble surfaces. Data pertaining to fracture orientation, fracture frequency, size, and whiteness were collected. The primary phase of marble characterization is followed by the discretization of the orebody into a three-dimensional array of orthogonal prismatic blocks, where the marble whiteness and fracture intensity are attribute values. Both these variables are considered to obey continuous and not discrete probability distributions. The discretization is performed using computer aided design and the Block Kriging techniques. An outline to improve the description of a given marble ore deposit at the exploration stage is presented for the prediction of marble block size distribution from joint count measurements along diamond drill cores. An example case of a white dolomitic marble quarry is used to demonstrate these methods.

Characteristics and dynamics of the Ganqiuchi rock avalanche triggered by a paleo-earthquake in the Northern Qinling Mountains

Analyzing large prehistoric rock avalanches provides significant data for evaluating the disaster posed by these relatively infrequent but destructive geological events. This paper attempts to study the characteristics and dynamics of the Ganqiuchi granitic rock avalanche, in the middle of the northern margin of Qinling Mountains, 30 km to the south of Xi’an, Shaanxi Province, China. In plane view, this rock avalanche is characterized by source area, accumulation area and dammed lake area. Based on previous studies, historical records and regional geological data, the major trigger of the Ganqiuchi rock avalanche is considered to be a strong paleo-earthquake with tremendous energy. The in situ deposit block size distributions of the intact rock mass and the debris deposits are presented and analyzed by using a simple model for estimating the number of fragmentation cycles that the blocks underwent. The results show that the primary controlling factor of the fragmentation process is the pre-existing fractures, and there is a relationship between the potential energy and the fragmentation energy: the latter is approximately 20% of the former. Based on the dynamic discrete element technique, the study proposes a four-stage model for the dynamic course of the Ganqiuchi rock avalanche: (1) failing; (2) highspeed sliding; (3) collision with obstacles; (4) decelerated sliding, which has implication for hazard assessment of the potential rock avalanches in China and other countries with similar geological setting.

Assessment of block size distribution in fractured rock mass and its influence on rock mass mechanical behavior

The response of rock mass to engineering activities related to environment greatly depends on the scale of rock mass. Therefore, the scale dependency of rock mechanical behavior under different rock mass conditions is investigated in this research. As a crucial parameter, the volume of the block provides a fundamental understanding to define the rock mass condition and possible mechanical response. In this paper, at first, a systematic approach to calculate the block size distribution (BSD) based on the natural fracture parameters using most suitable distribution functions was established with the R language. Then, the rock mass parameters were extracted from core mapping in the depth of 1500 m–2000 m and the BSD was presented in a similar manner to soil particle size distribution. Finally, the rock mass behavior under different block sizes was investigated. The results showed that Vb25 = 3.4 dm3, Vb50 = 6.4 dm3, and Vb75 = 11.2 dm3, which were the average percentages to represent the BSD. In the research area, therefore, the fractured rock mass was dominated by minor blocks. Besides, the variation of rock mass deformation vs BSD showed that the fractured rock mass was aggravated with the decrease in the block size. The results will enhance the effect of BSD on rock mass mechanical properties.

Fluid flow in fractured reservoirs: Estimation of fracture intensity distribution, capillary diffusion coefficient and shape factor from saturation data

Naturally fractured carbonate reservoirs which possess most of the remaining oil in the world, can fulfill the needs of widely nowadays energy demand. Most of the oil remains in the matrix block during production from naturally fractured reservoirs. Water flooding is a technique implemented in naturally fractured reservoirs to recover additional amounts of oil from the matrix blocks. In this paper, for the first time, an analytical model for water flooding in the naturally fractured carbonate reservoirs is developed that describes the transient behavior of the imbibition mechanism in the dual porosity models. Using the fracture-matrix fluid transfer of the dual porosity model, the presented analytical model takes the account of viscous-capillary and capillary imbibition mechanisms in fracture and matrix system, respectively. The analytical solution is validated using both laboratory data and a numerical solution. In order to consider the effect of the heterogeneity in fractured reservoirs, the proposed analytical model is developed for various distributions of block sizes. In addition, a graphical method is developed to estimate capillary diffusion coefficient and matrix block size distribution based on the water saturation data in the monitoring well during water injection. The monitoring well is used to monitor and evaluate reservoir during water flooding. The proposed methodology which is based on water saturation data in the monitoring well, does not call for a specific test in the reservoir.Moreover, the relating shape factor is calculated with the aid of dual porosity model equipped with variable fracture intensity distribution. The findings imply that the fluid transfer is highly dependent on the distribution of matrix block size.

Determination of rockfall design blocks in Upper Triassic limestones and dolomites (Dachstein Formation, Northern Calcareous Alps)

Design block size is of vital importance for rockfall countermeasure design. According to the Austrian normative document ONR 24810, the design block is specified as fractile (V95-V98) of the block size distribution depending on rockfall frequency. For rock formations, which form very large rockfall blocks (> 10 m3), the use of fractiles V95–V98 appears too high with regard to economically justifiable protective measures. The paper deals with the determination of design blocks for the Dachstein Formation on the basis of data from three Austrian test regions. The formation’s bedded limestone represents a key rock of the eastern part of the Northern Calcareous Alps and is very common along some major transport routes. A range of design blocks is derived from a synopsis of block size distributions, magnitude-frequency relations, and considerations about the rockfall barriers’ service life. In the process, the knowledge of the return period of the determinated design block is considered more important than the overall rockfall frequency. Analyzing available rockfall event data and block size distributions, it is possible to identify a return period of 21–26 years for a rockfall event ≥ 1 m3/1000 m route section. Thus, such events are rare. Events that affect the V97–V100 fractiles of the block size distribution are even rarer; they yield very large design block volumes, which show return periods > 100 years. For the bedded Dachstein limestone of the test areas, the application of the fractiles V95–V96 (0.15–2.25 m3) is useful for adapting the return period of the design block to the working life of the rock fall barrier (25–50 years).

Analysis of Rockfalls by Means of a Fractal Fragmentation Model

We present the performance of the rockfall fractal fragmentation model (RFFM) developed by Ruiz-Carulla et al. (Landslides 14(3):875–889. doi.org/10.1007/s10346-016-0773-8, 2017) and based on Perfect (Eng Geol 48:185–198, 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.