The slope modeling method with GIS support for rockfall analysis using 3D DDA

Rockfall is the most frequent major hazard in mountainous areas. For hazard assessment and further countermeasure design, realistic and accurate prediction of rockfall trajectory is an important requirement. Thus, a modeling method to represent both geometrical parameters of slope and falling rock mass is required. This study, suggests taking the advantages of discontinues deformation analysis (DDA) and geographical information system (GIS). In this study, after developing a three dimensional (3D) DDA program, firstly a special element named contact face element (CFE) was introduced into 3D DDA; secondly, effectively modeling tools with GIS support were developed. The implementation of CFE also improves the efficiency of both the contact searching and solution process. Then a simple impact model was devised to compare the 3D DDA implemented directly with a sliding model with theoretical analysis to verify the reliability of the modified 3D DDA program and investigate the parameter settings. Finally, simulations concerning rock shapes and multi-rocks were carried out to show the applicable functions and advantages of the newly developed rockfall analysis code. It has been shown that the newly developed 3D DDA program with GIS support is applicable and effective.     

Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)

This paper presents a new numerical model that can add a finite element mesh into each block of the three-dimensional discontinuous deformation analysis (3-D DDA), originally developed by Gen-hua Shi. The main objectives of this research are to enhance DDA block’s deformability. Formulations of stiffness and force matrices in 3-D DDA with conventional Trilinear (8-node) and Serendipity (20-node) hexahedral isoparametric finite elements meshed block system due to elastic stress, initial stress, point load, body force, displacement constraints, inertia force, normal and shear contact forces are derived in detail for program coding. The program code for the Trilinear and Serendipity hexahedron elements have been developed, and it has been applied to some examples to show the advantages achieved when finite element is associated with 3-D DDA to handle problems under large displacements and deformations. Results calculated for the same models by use of the original 3-D DDA are far from the theoretical solutions while the results of new numerical model are quite good in agreement with theoretical solutions; however, for the Trilinear elements, more number of elements are needed.     

Recent insights into analytical precision and modelling of DDA and NMM for practical problems

This paper discussed the analytical precision on equations of motion in some practical studies that use 2-D DDA, 2D-Coupled analysis of NMM & DDA, and 3D-DDA. We point out the main reason for numerical instability in DDA is loss of the effective digits when superposing the global stiffness matrix under the variable conditions of large and the small blocks. Categories of analyses are distributed in 2D-DDA static masonry structures such as the Great Pyramid and the Pont du Gard, 2D-DDA dynamic rock fall problems and the sensitivity of its analysis on the velocity ratio and the penalty, earthquake response analysis of rock slopes, 2D-NMM, 2D-coupled analysis of DDA and NMM and 3D-DDA rock fall problem. The selected examples on the Great Pyramid, Pont du Gard and Bayon Temple at Angkor Thom are located in Egypt, France and Cambodia respectively as UNESCO world heritages sites. The authors evaluated the applicability of the methods and the reliability of the results by comparing different methods and site observations from the practical problems.     

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.     

New point-to-face contact algorithm for 3-D contact problems using the augmented Lagrangian method in 3-D DDA

This paper presents a new point-to-face contact algorithm for contacts between two polyhedrons with planar boundaries. A new discrete numerical method called three-dimensional discontinuous deformation analysis (3-D DDA) is used and formulations of normal contact submatrices based on the proposed algorithm are derived. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. This approach does not need to use an iterative algorithm in each time step to obtain the contact plane, unlike the ‘Common-Plane’ method applied in the existing 3-D DDA. In the present 3-D DDA method, block contact constraints are enforced using the penalty method. This approach is quite simple, but may lead to inaccuracies that may be large for small values of the penalty number. The penalty method also creates block contact overlap, which violates the physical constraints of the problem. These limitations are overcome by using the augmented Lagrangian method that is used for normal contacts in this research. This point-to-face contact model has been programmed and some illustrative examples are provided to demonstrate the new contact rule between two blocks. A comparison between results obtained by using the augmented Lagrangian method and the penalty method is presented as well.     

郑万高铁宜万段边坡危岩崩落破坏特征

危岩是山区常见的地质灾害之一。以往研究缺少对危岩整体破坏导致危岩解体方面的关注,而危岩在失稳崩落过程中的解体行为却是预测危岩影响范围和防治成效的关键所在。为此,文章以郑万（郑州—万州）高铁宜万段沿线隧道洞口边坡危岩为研究对象,从结构面角度出发,对危岩崩落破坏特征进行研究。通过对15个隧道洞口边坡的调查,首先从边坡坡度、岩性组合、相对高差三个方面总结了研究区危岩发育分布规律;然后根据边坡岩体结构特征,分析了危岩失稳模式,并基于边坡上部危岩和下部落石的体积和形状对应关系,进一步探讨了边坡危岩崩落破坏演化过程;在此基础上,利用Rockfall模拟软件对落石运动特征进行预测分析。结果表明:（1）研究区边坡呈上陡下缓地形,上部基岩裸露,坡度基本上≥70°;危岩主要发育于弱风化的灰岩和白云岩中;边坡高差在150~300 m之间。（2）边坡上部危岩将呈阶梯状方式逐渐沿基底结构面滑移或者沿后缘结构面拉裂坠落。（3）研究区危岩崩落破坏模式主要为边坡上部岩体沿结构面解体破坏。（4）大部分隧道洞口边坡落石危险性较大,严重威胁隧道洞口的安全,需要采取相应的防治措施。研究成果可为在建的郑万高铁宜万段隧道边坡危岩的有效防治提供参考。     

边坡滚石运动轨迹分段循环算法

边坡滚石是在基本建设中常遇到的一种工程灾害。其防护结构的设计依据主要是边坡滚石的运动轨迹,因而要对这种灾害进行防治,首先要确定滚石的运动轨迹。根据落石运动全过程的三个阶段,即滚动(滑动)运动阶段、抛物运动阶段和与坡面碰撞阶段,利用分段循环算法分别得到了三个运动阶段的运动速度计算公式。以某岩质边坡构建相似模型,将该理论公式应用于落石运动轨迹预测,验证了公式的可行性和有效性。与现有方法相比,分段循环算法具有计算原理简单明确、易于使用等优点。该方法可用于斜坡区滚石运动特征的预测,并可作为斜坡区滚石灾害防治的依据。     

地震荷载下危岩运动特征的模拟研究

西南地区地形复杂,位于地震高发区域。为了进一步研究该区域地震作用下落石的运动特征,以我国九寨沟景区内荷叶寨后山危岩带2为例。首先研究危岩带2中单一危岩体在自重荷载下的失稳情况,分别采用RocFall和非连续变形分析方法(DDA)进行模拟,结果表明:DDA和RocFall的模拟结果相近。DDA中落石水平位移模拟结果为210.6 m,RocFall中大部分落石水平位移分布在205 m附近。鉴于RocFall的局限性,采用DDA方法继续研究地震作用下危岩体的密度、高度、体积和地震波峰值加速度等因素对落石运动特征如运动轨迹、水平位移和速度的影响规律,并监测落石在坡脚附近的最大弹跳高度。研究结果表明:(1)危岩带2所处边坡自然坡角范围为65°~75°,落石在坡面上加速,在高程约2292 m(与居民区相对高差约为132 m)处发生抛射,运动方式以滚动、碰撞、弹跳为主;(2)岩体软弱结构面的贯通时间随落石密度、体积以及地震波峰值加速度增大而减小;(3)峰值速度随边坡高度、体积及地震波峰值加速度增大而增大;(4)水平位移随落石密度、边坡高度及地震波峰值加速度增大而增大;(5)坡脚处落石最大弹跳高度随各因素变量增大而增大。继续研究内部存在节理裂隙的岩体(3条平行节理将危岩分为K1~K4部分)在地震荷载下的运动特征:(1)在地震荷载作用下,危岩沿节理面发生倾倒破坏,落石水平位移模拟结果为191.5~243.8 m;(2)落石在坡脚附近的最大弹跳高度范围为0~13.8 m。     

Comparison of rockfall susceptibility assessment at local and regional scale: a case study in the north of Beijing (China)

This study shows a rockfall susceptibility assessment at local scale in north Beijing of China, including the identification of rockfall sources onsite by terrain and rock discontinuities analysis and run-out distance prediction by Rocfall^? simulation. Two types of rockfall were defined including one type on the cliffs with long inclined slopes and another type on the road slopes with low height. Two historical rockfall events were used to back-calibrating the parameters used for run-out distance simulation. Based on the work, rockfall susceptibility map at local scale was created in GIS, which was compared with the map obtained at regional scale (entire Huairou district scale). Due to the difference of approaches applied, procedure of assessment and types of source data acquired, the two resulting rockfall susceptibility maps are proved to be different. Still, both of them are useful and could be used at different level’s decision for rockfall prevention and mitigation. Different types of uncertainties exist in the study of rockfall susceptibility assessment. To reduce the uncertainties, studies on both approaches and techniques are suggested.     

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.     

Sphere-boundary edge and sphere-boundary corner contacts model in DDA for simulating particulate media in 3-D

In modelling particulate media, such as soils, using 3-D DDA, there are four types of contacts: sphere to sphere, sphere to boundary face, sphere to boundary edge, and sphere to boundary corner contacts. The first two were studied by the authors in a previous work (Beyabanaki and Bagtzoglou 2012). In this paper, we present a new contact model for sphere-boundary edge and sphere-boundary corner contacts in sphere-based 3-D DDA. The model includes a new algorithm to search for contacts, detect the contact types and calculate contact points. Moreover, formulas for contact sub-matrices are derived. The proposed contact model has been implemented into a sphere-based 3-D DDA program and three test cases are studied in order to verify the workability of the new contact model. The numerical results obtained demonstrate the capability of the model to deal with sphere-boundary interaction in particulate media.     

基于GIS的泥石流过程模拟三维可视化

泥石流过程模拟的三维可视化不仅能改善泥石流过程信息的视觉效果,更能有助于发现泥石流运动的宏观规律,并为过程模拟数据的深层次分析奠定基础.分析了基于流团模型的泥石流过程模拟系统(DEBRIS)的数据结构和栅格式GIS-ERDAS系统的数据结构,设计了DEBRIS与ERDAS间的数据转换算法,从而实现了两个系统间的可视化集成即基于地理信息系统(GIS)的泥石流过程模拟三维可视化.     

SARETL: an expert system for probabilistic displacement-based dynamic 3-D slope stability analysis and remediation of earthquake triggered landslides

 Different models were developed for evaluating the probabilistic three-dimensional (3-D) stability analysis of earth slopes and embankments under earthquake loading using both the safety factor and the displacement criteria of slope failure. In the 3-D analysis, the critical and total slope widths become two new and important parameters. The probabilistic models evaluate the probability of failure under seismic loading and consider the different sources of uncertainties involved in the problem, i.e. uncertainties stemming from the discrepancies between laboratory-measured and in situ values of shear strength parameters, randomness of earthquake occurrence, and earthquake-induced acceleration. The models also take into consideration the spatial variabilities and correlations of soil properties. The developed models are incorporated in a computer program, PTDDSSA (probabilistic three-dimensional dynamic slope stability analysis). These developed analysis/design procedures are incorporated within a code named SARETL (stability analysis and remediation of earthquake-triggered landslides) that was developed in this study for stability analysis and remediation of earthquake-triggered landslides. In addition to the dynamic inertia forces; the developed system takes into consideration the local site effects. The code is capable of: 1. Prediction of permanent deformations that result from landslides under seismic loading using both probabilistic and deterministic approaches. 2. The assessment of landslide hazard that affects major transportation routes in the event of earthquakes, and the preparation of earthquake-induced landslide hazard maps (i.e. maps that show expected displacements and probability of slope/embankments failure) for different earthquakes magnitudes and environmental conditions. 3. Proposing a mitigation strategy against landslides and suggesting guidelines for remedial measures. The developed expert system is applied to a major highway case study. Design maps are developed for the highway under seismic loading. Received: 18 March 1999 · Accepted: 11 October 1999     

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。     

A Review of Studies Dealing with Tree Rings and Rockfall Activity: The Role of Dendrogeomorphology in Natural Hazard Research

Over the last few years, rockfall research has increasingly focused on hazard assessment and risk analysis. Input data on past rockfall activity were gathered from historical archives and lichenometric studies or were obtained through frequency–volume statistics. However, historical records are generally scarce, and lichenometry may only yield data with relatively low resolutions. On forested slopes, in contrast, tree-ring analyses may help, generally providing annual data on past rockfall activity over long periods. It is the purpose of the present literature review to survey the current state of investigations dealing with tree-ring sequences and rockfall activity, with emphasis on the extent to which dendrogeomorphology may contribute to rockfall research. Firstly, a brief introduction describes how dendrogeomorphological methods can contribute to natural hazard research. Secondly, an account is provided of the output of dendrogeomorphological studies investigating frequencies, volumes or spatial distributions of past rockfall activity. The current and potential strengths of dendrogeomorphology are then presented before, finally, the weaknesses of tree rings as natural archives of past rockfall activity are discussed and promising directions for further studies outlined.     

石经山藏经洞坡体滚石灾害危险性分析

对影响滚石的岩性、地形坡高和地质结构等因素进行现场地质调查和分析,初步确定存在潜在滚石的坡体。借助BJSD-2B型激光断面仪,选取上述坡体的4个典型剖面进行坡形测量。结合数值分析结果,确定块石A~F发生滚石的可能性较大。现场测量确定A~F块石的体积。在此基础上,利用Rocfall模拟软件对6块块石滚落的运动特征（运动距离、弹跳高度、动能和运动速度）进行预测和分析。结果表明：块石D的失稳对游客的生命安全威胁相对较小,但会直接导致7号洞洞室发生严重破坏;其余5块块石的失稳均会对游人的生命安全造成重大威胁,但不会严重影响到相应洞室的稳定。建议对上述6块块石所在坡体的关键部位及时采取工程措施进行加固。     

Three-dimensional discontinuous deformation analysis (3-D DDA) using a new contact resolution algorithm

This paper presents a new contact calculating algorithm for contacts between two polyhedra with planar boundaries in the three-dimensional discontinuous deformation analysis (3-D DDA). In this algorithm, all six type contacts in 3-D (vertex-to-face, vertex-to-edge, vertex-to-vertex, face-to-face, edge-to-edge, and edge-to-face) are simply transformed into the form of point-to-face contacts. The presented algorithm is a simple and efficient method and it can be easily coded into a computer program. In this paper, formulations of normal contact, shear contact and frictional force submatrices based on the new method are derived and the algorithm has been programmed in VC⁺⁺. Examples are provided to demonstrate the new contact rule between two blocks.     

鄂西山区崩塌落石运动特征及危险性分析

以远安县瓦坡崩塌区为例,通过地质调查、野外测绘、无人机航拍,建立了瓦坡崩塌区三维模型,基于Rockfall Analyst（RA）分析软件,实现了瓦坡崩塌区大量崩塌落石三维空间下运动路径、高度、能量等要素模拟,探究了崩塌区落石的三维运动特征,开展了崩塌区落石危险性评估,为崩塌落石的防治提供科学参考。研究结果表明:崩塌区危岩主要破坏形式为倾倒式,目前处于欠稳定状态;模拟落石三维运动轨迹与已有落石点基本重合,说明此次模拟结果与实际情况较为吻合;落石运动过程中以碰撞弹跳、自由飞落为主,落石主要集中在崩塌区下部冲沟及公路内,部分落石达到居民区,在崩塌落石区下部公路、冲沟及崩塌区右侧危险性较高;崩塌落石防治工程建议采用危石孤石清除+被动防护网,在公路内侧、斜坡下方分别设置5 m高和3 m高抗冲击力2 000 kJ的被动防护网,可有效拦截落石。     

Rockfall hazard and risk analysis for Monte da Lua,Sintra, Portugal

The prediction of rockfall trajectories below a rock cliff is essential in susceptibility, hazard and risk maps, particularity close to populated areas. The Monte da Lua hill area in Portugal, a tourist destination close to the historic city of Sintra (UNESCO World Heritage), is a typical granite boulder chaos landscape where from time to time rockfalls occur, the last such event having occurred on 29 January 2002. This area is therefore suitable to develop a rockfall study in order to provide hazard and risk maps a basis for mitigation measures. A preliminary investigation of the area leads to the identification of 188 potentially dangerous boulders. Detailed locations and geotechnical characteristics in terms of geometry, strength and context were sampled for each boulder. Digital elevations at 1 × 1 m resolution, known rockfall trajectory and building locations are provided in a GIS project for the study together with the spatial database of boulder characteristics. The modelling approach was conducted in two steps: (1) discrimination of the boulders in terms of static and dynamic mobility behaviour with multivariate analysis; (2) stochastic simulation of rockfall trajectories. The rockfall trajectory algorithm proposed is straightforward and is only dependent on elevation data, initial location of boulders and a friction angle. Due to the slope of the area, it assumes that rockfall is always of the rolling or sliding type. The friction angle was calibrated on the basis of the rockfall travel distance recorded on 29 January 2002 and generates simulated “realistic” trajectories. A smaller friction angle increases all simulated trajectories, leading to more “pessimistic” scenarios. The combined analysis of trajectories and potential damage to buildings and discrimination in terms of static and dynamic behaviour provides a final table in which all 188 sampled boulders are classified in one of the five risk grades.     

二维粒子图像测速实验中三维涡旋可测性分析

现今二维粒子图像测速（PIV）广泛应用,为进一步提高PIV测量结果对紊流及水流和泥沙相互作用机理的理解,分析了二维PIV中三维涡旋的可测性。结合涡旋识别的旋转强度方法、坐标旋转定理和紊流经典Burgers涡模型,推导得出:二维PIV能否检测出三维涡旋,主要受涡旋环量和旋涡与测量平面之间的倾角两个因素影响,且仅当涡旋环量大于某一特定值（为倾角的函数）时,三维涡旋才可以被测量出。利用广泛使用的直接数值模拟（DNS）槽道紊流数据统计分析,得出了该条件下倾角和环量的相关曲线与拟合方程;结合环量概率密度累积分布可知,在常规二维PIV实验中,涡旋被测量出的概率越大,相应的倾角也越大,其中以90%、50%和10%的概率被测量出的三维涡旋与测量平面间分别呈20°、11°和5°的倾角。