Multi-scenario Rockfall Hazard Assessment Using LiDAR Data and GIS

Transportation corridors that pass through mountainous or hilly areas are prone to rockfall hazard. Rockfall incidents in such areas can cause human fatalities and damage to properties in addition to transportation interruptions. In Malaysia, the North–South Expressway is the most significant expressway that operates as the backbone of the peninsula. A portion of this expressway in Jelapang was chosen as the site of rockfall hazard assessment in multiple scenarios. Light detection and ranging techniques are indispensable in capturing high-resolution digital elevation models related to geohazard studies. An airborne laser scanner was used to create a high-density point cloud of the study area. The use of 3D rockfall process modeling in combination with geographic information system (GIS) is a beneficial tool in rockfall hazard studies. In this study, a 3D rockfall model integrated into GIS was used to derive rockfall trajectories and velocity associated with them in multiple scenarios based on a range of mechanical parameter values (coefficients of restitution and friction angle). Rockfall characteristics in terms of frequency, height, and energy were determined through raster modeling. Analytic hierarchy process (AHP) was used to compute the weight of each rockfall characteristic raster that affects rockfall hazard. A spatial model that considers rockfall characteristics was conducted to produce a rockfall hazard map. Moreover, a barrier location was proposed to eliminate rockfall hazard. As a result, rockfall trajectories and their characteristics were derived. The result of AHP shows that rockfall hazard was significantly influenced by rockfall energy and then by frequency and height. The areas at risk were delineated and the hazard percentage along the expressway was observed and demonstrated. The result also shows that with increasing mechanical parameter values, the rockfall trajectories and their characteristics, and consequently rockfall hazard, were increased. In addition, the suggested barrier effectively restrained most of the rockfall trajectories and eliminated the hazard along the expressway. This study can serve not only as a guide for a comprehensive investigation of rockfall hazard but also as a reference that decision makers can use in designing a risk mitigation method. Furthermore, this study is applicable in any rockfall study, especially in situations where mechanical parameters have no specific values.     

The Son Poc rockfall (Mallorca,Spain) on the 6th of March 2013: 3D simulation

The Son Poc rockfall took place on the 6th of March 2013 in the municipality of Bunyola, on the southern side of the Tramuntana Range (Mallorca) and after a rainy and cold period on the region. A volume of rock of 4.000 m³ was detached from the cliff crowning the peak falling down by toppling. The impact of the boulder caused its fragmentation, and numerous boulders bounced and rolled downslope with volumes from 1 to 35 m³, following two trajectories: southwest (SW) and southeast (SE). The SE trajectory, with a larger runout (376 m), reached an urban area, where some of the boulders hit the roofs and walls of nearby houses, stopping others in their gardening areas. Fortunately, no fatalities occurred despite of the presence of some people at that moment, but the event caused great concern in a region which lives from and for tourism. The Son Poc rockfall has been simulated using RocPro3D software which uses GIS technology to produce 3D rockfall trajectories lines, estimated velocity and energy of falling blocks, as well as bounce heights, impacts, and stopping points. The results are in agreement with field observations and with a very good accuracy between real and modeled outcomes.     

Rockfall trajectory modeling combined with heuristic analysis for assessing the rockfall hazard along the Maratea SS18 coastal road (Basilicata,Southern Italy)

In this paper, a study aimed to assess the rockfall hazard along a portion of the SS18 coastal road, located in the coastal area of Maratea (Basilicata Region, Southern Italy), is presented. The relevance of this study derives from the location of the study area, because the SS18 is a strategic roads in a touristic area, and, since the hazard assessment was performed in 2004 within a project financed by the Viability Regional Department of Autonomous National Company of Roads (ANAS), from the possibility to validate the results by using real rockfall events occurred after 2004. The procedure for assessing the rockfall hazard was composed of four sequential analyses: (i) geomechanical and kinematic characterization of rock mass, (ii) implementation of Romana’s (1985) Slope Mass Rating (SMR) method for identifying the potential boulder release areas (rockfall initiation areas), (iii) determination of rockfall trajectories by using a 3D numerical model (ROTOMAP), (iv) calculation and mapping of the hazard index by combining three factors, i.e., (a) lithological features of outcropping materials on rock faces, (b) kinematic compatibility defined by simulating the rockfall trajectories, and (c) spatial distribution of occurred rockfall events. Finally, the proposed methodology was validated by combining the distribution of the hazard levels along the road with the location on the SS18 of the rockfall events occurred from 2004 to 2014.     

Rockfall-induced block propagation on a soil slope,northern Italy

This paper reports the field evidence and the kinematical study of the motion of two blocks (A and B) mobilised by a rockfall in Lavone (Valtrompia, northern Italy) on 14 February 1987. The two sequences of impact marks left by the blocks on the ground surface were measured and the lithostratigraphical features of the debris slope were surveyed. On the basis of the field-collected input data, several computer simulations were carried out to calculate the coefficients of restitution (E) satisfying the trajectory conditions. The computed output values show that rebound trajectories require high coefficients of restitution (0.8 ≤ E ≤ 0.9). Back-calculated impact velocities range from 9.2 to 19.8 m/s. Trajectory heights vary from 0 to 2.4 m above the slope surface. Block trajectories differ considerably according to the circumstances of initial air projection, i.e. to initial rebound angle (α_r). The calculated values of (α_r) denote a considerable range (36°), emphasising the random nature of this parameter. The described case-history shows that rockfall computer analyses can be an effective tool to describe the bouncing propagation of single blocks but care must be taken in choosing the restitution coefficient E and the geometrical parameters of initial air projections.     

Field Evidence and Kinematical Back-Analysis of Block Rebounds: The Lavone Rockfall,Northern Italy

This paper reports the field evidence and the kinematical study of the motion of two blocks (A and B) mobilised by a rockfall in Lavone (Valtrompia, northern Italy) on 14th February 1987. The two sequences of impact marks left by the blocks on the ground surface were measured and the lithostratigraphical features of the debris slope were surveyed. On the basis of the field-collected input data, several computer simulations were carried out to calculate the coefficients of restitution (E) satisfying the trajectory conditions. The computed output values, obtained by running a specific automatic program for rockfall modelling, show that rebound trajectories require high coefficients of restitution (0.8 ≤ E ≤ 0.9). Back-calculated impact velocities range from 9.2 to 19.8 m/s. Trajectory heights vary from 0 to 2.4 m above the slope surface. Block trajectories differ considerably according to the circumstances of initial air projection, i.e. to the initial rebound angle (α _r). The calculated values of α _r denote a considerable range (36°), emphasising the high variability and the random nature of this parameter. The described case history shows that rockfall computer analyses can be an effective tool to describe the bouncing propagation of single blocks, but care must be taken in choosing the restitution coefficient E and the geometrical parameters of initial air projections.     

Application of the Swiss Federal Guidelines on rock fall hazard: a case study in the Cilento region (Southern Italy)

On December 15, 2008, a rock slide of approximately 4,000 m³ occurred near San Severino di Centola (Cilento, Province of Salerno). The landslide occurred along very steep bedding planes intersected by tectonic joints affecting a rocky cliff. The landslide debris, formed by several boulders, came to a halt along the gentler slope below. Many blocks reached the slope base including the national road n° 562 and injuring a motorist on the road. Furthermore, the road suffered heavy damages causing a halt in traffic for many weeks. Several signs of the impacts were detected along the slope and on the road; also, the volumes of some boulders were measured. The area affected by block trajectories stretch down slope about 4,900 m². By means of 2D and 3D trajectory codes using the “lumped-mass” method, it was possible to estimate more suitable impact energy restitution and rolling friction coefficients, to reconstruct rock fall trajectories, and to calculate total kinetic energies. Extending to the surrounding slope (surface about 2 ha) these data, a hazard scenario was carried out, displaying the pattern of iso-energy distribution curves calculated along 11 critical profiles, and zones exposed to 70% and 30% of frequencies of block transits and endpoints. Successively, with reference to the Swiss Federal Guidelines, another scenario was prepared on the basis of rock fall intensity values and the return period of the 2008 landslide event. In this way, it was possible to define areas of high, moderate and low hazard. The degrees of hazard are assigned according to their consequences for construction activity and outline zones where additional protection is required. The construction of a retaining embankment was believed suitable for local risk mitigation.     

Digital mapping of coastal boulders – high-resolution data acquisition to infer past and recent transport dynamics

Coastal boulder fields provide clues to long-term frequency-magnitude patterns of coastal flooding events and have the potential to play an important role in coastal hazard assessment. Mapping boulders in the field is time and labour-intensive, and work on intertidal reef platforms, as in the present study, is physically challenging. By addressing coastal scientists who are not specialists in remote sensing, this contribution reports on the possibilities and limitations of digital applications in boulder mapping in Eastern Samar, Philippines, where recent supertyphoons Haiyan and Hagupit induced high waves, coastal flooding and boulder transport. It is demonstrated how satellite imagery of sub-metre resolution (from Pléiades and WorldView-3 imagery) enables efficient analysis of transport vectors and distances of larger boulders, reflecting variation in latitudes of both typhoon tracks and approaching angles of typhoon-generated waves. During the investigated events, boulders with a-axes of up to 8 m were clearly identified to have been shifted for up to 32 m, mostly along the seaward margin of the boulder field. It is, however, hard to keep track of smaller boulders, and the length of a-axes and b-axes including their orientation is often impossible to map with sufficient accuracy. Orthophotographs and digital surface models created through the application of an unmanned aerial vehicle and the ‘Structure from Motion’ technique provide ultra-high-resolution data, and have the potential to not only improve the results of satellite image analysis, but also those from field mapping and may significantly reduce overall time in the field. Orthophotographs permit unequivocal mapping of a-axes and b-axes including their orientation, while precise values for c-axes can be derived from the respective digital surface models. Volume of boulders is best inferred from boulder-specific Structure from Motion-based three-dimensional models. Battery power, flight speed and altitude determine the limits of the area covered, while patches shielded by the boulders are difficult to resolve. For some tasks, field mapping remains mandatory and cannot be replaced by currently available remote sensing tools: for example, sampling for rock type, density and age dating, recording of lithological separation of boulders from the underlying geological unit and of geomorphic features on a millimetre to decimetre-scale, or documentation of fine-grained sediment transport in between the boulders in supratidal settings. In terms of future events, the digital products presented here will provide a valuable reference to track boulder transport on a centimetre to decimetre-scale and to better understand the hydrodynamics of extreme-wave events on a fringing reef coastline.     

Hazard assessment in rockfall-prone Himalayan slopes along National Highway-58, India: rating and simulation

A massive disaster occurred in June 2013 in Kedarnath, India, due to cloudburst and extremely heavy rain along the Chorabari glacier. The resulting flash floods further aggravated the instability of natural and hill cut slopes at different places on the downstream side. The village Rambara that existed in close proximity of Kedarnath was swept away under flow of debris and water. The immediate surrounding area, which housed over a hundred and fifty shops and hotels, was completely washed away leaving no trace of civilization. This calamity in Uttarakhand is considered as India’s worst natural disasters after the tsunami in December 2004. On the downstream of the affected areas lie other pilgrim destinations that witness innumerable footfalls every year. Investigation of the health of the slopes on the routes to these destinations is therefore very important to ensure minimal damage to humans and machinery. The Himalayan terrain is a tectonically active mountain belt, having a large number of unstable natural and road cut slopes. Such slopes with rugged topography lie in the high seismic vulnerability zone. Further, the instability is aggravated by natural and anthropogenic activities increasing at a rapid and uncontrollable rate. In the light of the Kedarnath tragedy, more advanced research is being conducted along the National Highways to monitor and prevent slope/structure failures. This study was conducted to evaluate the hazard potential along National Highway-58, near Saknidhar village of Devprayag district by analysing rockfall using hazard rating systems and numerical simulation. Rockfall hazard rating systems were applied to evaluate the conditions of the slopes and to identify the associated risks. Based on the field and laboratory analyses, the parameters required for numerical models were determined. The bounce height, roll-out distance, kinetic energy and speed of the detached blocks were determined by using a competent rockfall simulator. The results obtained were used to identify rockfall risk in the region. Optimization strategies were applied during investigation by modifying the slope angle, ditch width and ditch angle to assess the possibility of a hazard to occur in different scenarios. The simulation studies revealed that an increasing slope angle could significantly increase the kinetic energy of the rock blocks. However, an increase in the ditch angle and the ditch width reduces the energy of moving blocks. The maximum bounce height above the slope varied from 0.003 m to 0.8 m for 10-kg blocks, whereas the maximum velocity and the maximum kinetic energy under such circumstances were 7.882 m/s and 379.89 J, respectively. The barrier capacity was found to be 233.18 J for 10-kg falling blocks at a height of 10.02 m. From the optimization studies, it was found that the risk can be reduced by up to 13 % if the slope of 70° has a ditch angle of 15° while on a flat ditch, the maximum risk will be at an angle of 65°. If the ditch angle is increased, the vertical component of the falling blocks is more effective than that in case of a flat ditch. These optimization studies lay foundation for advanced research for mitigation of rockfall hazards in similar potential areas.

     

Facies characteristics of the basal part of the Talchir Formation,Talchir Basin,India — Depositional history revisited

The lowest unit of the Talchir Formation of Talchir Basin, Orissa, was described by pioneer workers as the ‘basal boulder bed’. In an attempt to explain the co-existence of gravel and clay, materials of contrasting hydraulic properties, a probable situation resembling the effects of the action of ground-ice enabled boulders to be carried down by sluggish currents resulting in an intermixture of large boulders and fine mud was conceived. Misinterpretation of this conclusion led to a general tendency to describe the ‘basal boulder bed’ as ‘glacial tillite’. However, the unit described as ‘basal boulder bed’ is actually represented by a matrix rich conglomerate with pockets of normally graded silty clay. The present study reveals that the depositional imprints preserved in this part of the sedimentary succession indicate emplacement of successive debris flows generated through remobilization of pre-existing unconsolidated sediments. Small pockets of fine-grained turbidites presumably deposited from the entrained turbidity currents associated with the debris flows suggest the composite character of the debris flow deposit.     

Monitoring the sedimentary budget and dislocated boulders in western Greece – results since 2008

Dislocated boulders are one sign of high-energy wave impacts on coasts. These high-energy impacts, caused by severe storms or tsunamis, can trigger initial cracking and transport of boulders. Monitoring of these boulders, as well as the associated coastal sites is important in distinguishing between gradual coastal processes and high-energy events. Western Greece is a seismically active area, where tsunamis and high-energetic storms might occur and such past events are documented by historic and geoscientific research, making it an ideal location for monitoring dislocated boulders. Since 2008, monitoring of eight different coastal sites in this region was conducted by terrestrial laser scanning and photogrammetric approaches, with low-cost unmanned aerial vehicles. The re-use of similar surveying points in following years, allowed highly accurate monitoring. Point clouds derived from these methods were evaluated for change detection by point cloud comparisons. The data were also used to establish accurate three-dimensional models of dislocated boulders (n = 70). The determined boulder volumes of these accurate three-dimensional models were incorporated in wave transport equations and wave decay curves, and compared with monitoring results. A comprehensive overview of dislocated boulders in western Greece is presented. Three-dimensional boulder reconstruction is compared to an approach which uses a tape-based measuring of boulder axes, with the tape-based measurement showing a mean overestimation of mass by 32%. Accurate monitoring over time by both methods, is achieved by using fixed networks of reference points. Changes for each site over time, detected by direct point cloud comparisons, are fit to the possible inundation calculated by wave decay curves based on computed minimum wave heights for boulder transport. Both storm and tsunami waves may have initiated movement from the cliff edge and further transport is also possible. However, boulders showed no further movement from their current position in the area for the time period of this study.     

重庆甑子岩崩塌落石动力学特征及危险性分区

针对重庆市南川区甑子岩危岩体面临的崩塌地质灾害问题,分析不同高度、不同规模的危岩体对东侧居民区的落石风险及危害性。以甑子岩处岩质边坡为研究对象,根据其结构面发育情况及崩塌落石特征确定模型尺寸,运用RocFall软件对崩塌落石的能量、速度、运动轨迹、落点位置及冲击力等进行模拟计算。以此对崩塌落石区进行落石风险评估,根据崩塌落石的动量和动能,按最危险原则法将崩塌落石的危险性分区,分为Ⅰ危险性极大、Ⅱ危险性大、Ⅲ危险性一般、Ⅳ危险性较小、Ⅴ无危险五个分区,并将此分区应用于甑子岩危岩体,评价崩子岩危岩体居民区的落石风险及危险性,确保居民安全。通过对崩塌落石区的危险性分区,可以用来指导居民区的安置和防护措施。     

Rockfall susceptibility zoning based on back analysis of rockfall deposit inventory in Gunung Kelir,Java

A rockfall susceptibility based on trajectory-energy/velocity approach needs release area or rockfall source. However, identification of rockfall source is not always possible for some areas in Indonesia. This paper presents a rockfall susceptibility zoning based on back analysis technique of rockfall deposit inventory in Gunung Kelir, Java. There were several steps in the rockfall susceptibility zoning: (1) rockfall deposit inventory, (2) rockfall simulation based on back analysis of rockfall deposit inventory, (3) sensitivity analysis, and (4) rockfall susceptibility zoning. The result suggests that the travel distance is affected by the spatial distribution of rockfall source, lithology or surface material, and topography (angle of slope and angle of aspect). Final trajectories were employed to generate landslide susceptibility map which may allow a policy maker to have an advanced consideration to achieve specified risk measures and evaluation of their cost efficiency to optimize budget and design. Application of rockfall susceptibility zoning based on back analysis of rockfall deposits is efficient where rockfall source information is unavailable.     

Calibration and validation of rockfall modelling at regional scale: application along a roadway in Mallorca (Spain) and organization of its management

The Tramuntana range, in the northwestern sector of the island of Mallorca (Balearic Islands, Spain), is frequently affected by rockfalls which have caused significant damage, mainly along the road network. In this work, we present the procedure we have applied to calibrate and validate rockfall modelling in this region, using 103 cases of the available detailed rockfall inventory (630 rockfall events collected since the eighteenth century). We have exploited STONE (Guzzetti et al. 2002), a GIS-based rockfall simulation software which computes 2D and 3D rockfall trajectories starting from a DTM and maps of the dynamic rolling friction coefficient and of the normal and tangential energy restitution coefficients. The appropriate identification of these parameters determines the accuracy of the simulation. To calibrate them, we have selected 40 rockfalls along the range which include a wide variety of outcropping lithologies. Coefficients values have been changed in numerous attempts in order to select those where the extent and shape of the simulation matched the field mapping. Best results were summarized with the average statistical values for each parameter and for each geotechnical unit, determining that mode values represent more precisely the data. Initially, for the validation stage, 10 well-known rockfalls exploited in the calibration phase have been selected. Confidence tests have been applied to their modelling results taking into account not only the success but also the mistakes. The best accuracy is obtained when the rockfall has a preferential trajectory and worse results when the rockfall follows two or more trajectories. Additionally, the greater the rockfall runout length, the less precise the simulation is. We have further validated the calibrated parameters along the Ma-road (111 km), the main transportation corridor in the range, using 63 rockfall events that occurred during the past 18 years along the road. Of the rockfalls where source areas were properly identified, 81.5 % are well represented by STONE modelling, as the travel paths and the depositional areas are successfully ascertained. Results of the analysis have been used by the Road Maintenance Service of Mallorca to assess hazard and risk posed by rockfall at regional scale to design the road management plan.     

Large-scale physical modeling study on the interaction between rockfall and flexible barrier

Flexible barriers have been widely applied in rockfall mitigation in recent years. However, the behavior of flexible barriers under the impact of boulders is still not fully understood. To investigate the interaction between a flexible barrier and a falling boulder, a large-scale physical modeling device has been constructed at a site in Hong Kong. Using this device, large-scale impact tests using boulders with different diameters were conducted. Test results are presented and analyzed in this paper. The motion of the boulder during impact is traced and analyzed. The impact forces on the flexible ring net and the supporting structures are measured and compared. From the comparison, the impact reduction rates (IRR) of boulders with different diameters are calculated. Moreover, a simple approach for estimating the impact loading of a boulder on a flexible barrier is proposed in this study. This approach is calibrated and verified using measured impact forces in the tests.     

Rockfall hazard assessment along a road in the Sorrento Peninsula,Campania, southern Italy

Rockfalls are common in the steep and vertical slopes of the Campania carbonate massifs and ridges, and frequently represent the main threat to the anthropogenic environment, potentially damaging urban areas, scattered houses, roads, etc. Despite the generally limited volumes involved, the high velocity of movement (from few to tens of metres per second) poses rockfalls among the most dangerous natural hazards to man. Evaluating the rockfall hazard is not an easy task, due to the high number of involved factors, and particularly to the difficulty in determining the properties of the rock mass. In this paper, we illustrate the assessment of the rockfall hazard along a small area of the Sorrento Peninsula (Campania region, southern Italy). Choice of the site was determined by the presence of a road heavily frequented by vehicles. In the area, we have carried out detailed field surveys and software simulations that allow generating simple rockfall hazard maps. Over twenty measurement stations for geo-mechanical characterization of the rock mass have been distributed along a 400-m-long slope of Mount Vico Alvano. Following the internationally established standards for the acquisition of rock mass parameters, the main kinematics have been recognized, and the discontinuity families leading to the different failures identified. After carrying out field experiments by artificially releasing a number of unstable blocks on the rock cliff, the rockfall trajectories along the slope were modelled using 2-D and 3-D programs for rockfall analysis. The results were exploited to evaluate the rockfall hazard along the threatened element at risk.     

Rockfall susceptibility zoning at a large scale: From geomorphological inventory to preliminary land use planning

Rockfall, up to several hundreds of cubic meters, is a frequent and rapid landslide which menaces extensive areas in mountainous territories. Rockfall susceptibility zoning map at a large scale (1:5000–1:25 000) can be the first tool for land use planning in order to manage rockfall risk. A methodology allowing to analyze susceptibility in extensive areas with optimum cost/benefit relationship is needed. This work analyzes rockfall susceptibility in an extensive rocky mountain of the Principality of Andorra (Pyrenees Mountains), first on the rock slope and then on the exposed area located below. The rockfall record, obtained by means of geomorphological analysis, supplies the main data to analyze the susceptibility on the rock slope. An additional historical inventory verifies the accuracy of rockfall sizes recorded by means of the geomorphological analysis. According to the classification recommended by the Guidelines of Joint Technical Committee, the density of rockfall features on the rock slope assesses susceptibility in four levels. Subsequently, susceptibility on exposed areas has been analyzed by means of reach probability of rock blocks analysis using empirical models. Data acquired from thirteen recent events, from 1999 to 2004, have been used to verify the accuracy of the two empirical models mainly used (reach angle and shadow angle). Five reach probability limits (1, 0.5, 0.25, 0.01, and 0) establish boundaries between susceptibility levels. The resulting rockfall susceptibility zoning map allows: (a) to identify land areas and human elements exposed to rockfalls and, (b) to establish several exposition levels. This map can be a useful and cost-effective tool for administrations responsible to manage natural risk in order to guide urban grow in extensive areas or decide upon work programs based on in-depth analysis (hazard and risk).     

Utilizing glacial geology in uranium exploration; Dismal Lakes, Northwest Territories, Canada

A field of uraniferous boulders was discovered in a drift-covered valley west of Dismal Lakes. Glacial geological information was combined with boulder location and trace element till geochemical data to model the dispersal of the boulders; and to predict their likely bedrock source. Uraniferous bedrock was eroded by the last, westward flowing glacial ice to cover the area. The debris was englacially transported and subsequently deposited during subglacial melt-out of ice block(s) stagnating below active ice. The distribution of the boulders forms acrude, westward-opening fan centred on the easternmost boulder and oriented with the last ice-flow direction. The largest uranium values from surface till samples (-2 μm fraction) occur 6.2 km east of the main boulder concentration or 1.5 km east of the first boulder occurrence. The likely bedrock source is 6.0 to 6.6 km east of the main boulder concentration.     

The Rabat and Larache boulder fields; new examples of high-energy deposits related to storms and tsunami waves in north-western Morocco

The coastal areas of south-west Iberia and north-west Morocco host numerous megaclast accumulations thought to have been emplaced by high-energy waves, namely by the major tsunami related to the 1 November 1755 AD earthquake. New observations were carried out along several transects from Rabat and Larache areas, using statistical methods applied to boulder size. The main results are (a) the boulders belong to two or three sources located within the Pleistocene–Holocene formations of both areas, but only from a single source at Harhoura; (b) the boulders in Larache are generally small, thin and show a normal polarity, whereas those of Rabat are much larger and are often overturned; (c) the directions of inclination of imbricate boulders are variable at Rabat (N, NW and W), whereas they are constant in Larache (WNW); (d) the blocks were displaced for distances up to 150 m in Rabat, while the displacement of the Larache boulders was stopped by the MHW cliff; (e) the hydrodynamic equations suggest that tsunami waves, with maximum amplitudes of 5–11 m in Rabat and 4.5 m in Larache, were responsible for the displacement of the largest boulders, whereas storms may have displaced smaller ones.     

边坡落石运动轨迹计算新方法

考虑落石形状对落石运动轨迹的影响,将落石近似成椭圆形。根据落石运动的5种常见形式,即自由落体运动、斜抛运动、碰撞、滑动和滚动,分别得到了各种运动形式的运动速度计算公式。在碰撞阶段考虑了地面的弹塑性变形,得到了与碰撞前速度、落石形状和地面材料有关的恢复系数计算公式,并根据接触力学的有关理论得到了碰撞冲击力的计算公式,给出了落石连续滚动的判别条件。将理论公式应用于重庆万州首立山落石运动轨迹预测,验证了理论公式的可行性和有效性。     

Rockfalls detached from a lateral moraine during spring season. 2010 and 2011 events observed at the Rebaixader debris-flow monitoring site (Central Pyrenees, Spain)

Instability processes at glacial deposits represent an important hazard in mountainous areas. During the spring seasons of 2010 and 2011, two falls of large boulders (18 and 55? m³) initiated in a lateral moraine in the Rebaixader catchment (Central Pyrenees, Spain). Detailed information was gathered due to the debris-flow monitoring system installed along the torrent. Meteorological data showed that the two rockfalls were triggered without important rainfall amounts. Field surveys, ground vibration acquired at geophones and the movie recorded with a video camera provided unique information on the rockfall occurrence and dynamics. In addition, the information gave an excellent opportunity to show the importance of monitored data for the calibration of model parameters for runout simulations. The analysis focussed on the 2011 event and showed that the boulder passed rolling and bouncing through the monitored torrent reach. The velocity estimates in this reach range from 3 to 9 ?m/s. The 2011 rockfall was also back-analysed by a two-dimensional physically based model, which was fitted by the monitored and field data. The results of the simulation coincided well with recorded measurements, although the output could be improved by the application of a three-dimensional model.