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.     

Numerical Simulation in Rockfall Analysis: A Close Comparison of 2-D and 3-D DDA

Accurate estimation of rockfall trajectory and motion behaviors is essential for rockfall risk assessment and the design and performance evaluation of preventive structures. Numerical simulation using discontinuous deformation analysis (DDA) is effective and helpful in rockfall analysis. Up to now, there have been many reports on application of two-dimensional (2-D) DDA programs. In this paper, the major advantages of rockfall analysis using 2-D and extensions to three-dimensional (3-D) analysis are presented. A practical 3-D DDA code is demonstrated to be capable of simulating free falling, rolling, sliding, and bouncing with high accuracy. Because rockfall trajectories and motion behaviors can be described as combinations of these four types, this demonstration indicates that the implemented code is capable of providing reliable rockfall analysis. Finally, specific tests are conducted to compare 2-D and 3-D DDA rockfall analysis in predicting trajectory and dynamic behavior. The results indicate that 3-D DDA simulations are more appropriate for rough tree-laden inclined slopes in providing detailed spatial distribution, whereas 2-D DDA simulations have better efficiency for slopes dominated by valleys and ravines. These results can help in selecting the appropriate DDA simulation for rockfall analysis.     

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.     

Implementation of the finite element method in the three‐dimensional discontinuous deformation analysis (3D‐DDA)

A modified three‐dimensional discontinuous deformation analysis (3D‐DDA) method is derived using four‐noded tetrahedral elements to improve the accuracy of current 3D‐DDA algorithm in practical applications. The analysis program for the modified 3D‐DDA method is developed in a C++ environment and its accuracy is illustrated through comparisons with several analytical solutions that are available for selected problems. The predicted solutions for these problems using the modified 3D‐DDA approach all show satisfactory agreement with the corresponding analytical results. Results presented in this paper demonstrate that the modified 3D‐DDA method with discontinuous modeling capabilities offers a useful computational tool to determine stresses and deformations in practical problems involving fissured elastic media with reasonable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

Formulation of discontinuous deformation analysis (DDA) — an implicit discrete element model for block systems

Continuum-based numerical methods have played a leading role in the numerical solution of problems in rock mechanics and engineering geology. However, for fractured rocks, a continuum assumption often leads to difficult parameters to define and over-simplified geometry to be realistic. In such case, discrete representations of fractures and individual blocks must be adopted. In this paper, a newly emerged member in the family of discrete element methods (DEM), the discontinuous deformation analysis (DDA), is presented, including its variational principle, governing equations, solution techniques and contact representation and detection algorithms. Its relative advantages and shortcomings are compared with the explicit distinct element method and the finite element method. An example of the analysis of tunnel stability is provided to demonstrate the capability of this new method.     

簧式缓冲器的工作原理及其在滚石柔性防护系统中的应用

滚石是突发于人工边坡或自然边坡上的一类特殊的地质灾害,对坡下的人类活动和基础设施的安全构成极大威胁.柔性防护系统是滚石灾害防治的重要方法之一,而摩擦制动环是应用于钢绳拦石网并起到关键缓冲作用的部件.作者发现,当前使用的摩擦制动环存在着缓冲效率较低、较易损坏、成本较高等诸多不足.针对这些不足,提出了一种可应用于滚石柔性防护系统的簧式缓冲器.理论研究表明,它具有缓冲效率较高、不易损坏、价格较低等优点,可望在滚石柔性防护系统中得到广泛应用.     

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.     

全国地质灾害趋势预测及预测图编制

区域地质灾害预测是地质灾害研究的难题。本文运用基于地理信息系统的风险评价方法对这一问题进行了探讨。将全国剖分为２７００个单元，对地质灾害进行现状评价，并与已数字化的地质灾害图件进行单要素叠加，编制了全国地质现状等值线图，在现状评价基础上，对地质灾害进行趋势预测，将降雨条件、区域地震活动、区域地壳稳定程度、区域岩组条件和人类工程活动等作为区域地质灾害演变的因素，运用模糊综合评判模型进行综合评判，编制了１：６００万中国地质灾害趋势预测图。     

2D and 3D rockfall hazard analysis and protection measures for Saptashrungi Gad Temple,Vani, Nashik,Maharashtra – A case study

The Saptashrungi gad temple (SGT) situated on basaltic hills belongs to Deccan volcanic of Upper Cretaceous to Lower Eocene, is one among the 51 Shakti Peeths and most holy place for pilgrims. Rockfall is a major problem in the past and causing danger to the lives of the villagers settled at the toe of the SGT hill as well as the pilgrims who perform parikrama along the tracks. On the evening of 16 April 2011, an old woman died due to rockfall at SGT hill when she was performing parikrama, moreover, two persons got injured during the deliverance process of this old woman from the continuous rockfall activity. The problem of rockfall could be linked to rainfall, jointing, weathering, man-made or the compounding of all. In this research, the rockfall hazard analysis at SGT hill is assessed using both 2D and 3D rockfall programs along the two parikrama paths: Parikrama Path 1 (or the Badi Parikrama Path ‘BPP’), and Parikrama Path 2 (or the Chhoti Parikrama Path ‘CPP’). Also, the study area of the SGT hill has been divided into eight zones (Zone#01 to Zone#08), based on field observations, orientations of joint sets and hill slope faces and eighteen topographic profiles (AA' to RR') have been taken from these eight zones for rockfall analysis. A detailed topographic survey along with field investigation has been carried out along the temple for ascertaining the nature of rock, discontinuity orientations, and slope geometry. DEM has been generated using topographic profile in ArcGIS to facilitate the 3D rockfall analysis. Maximum rock block sizes are taken into the analysis and run-out distance, bounce height, kinetic energy and velocity of the basaltic blocks are evaluated separately. Based on the analyzed data, the rockfall hazard zone map has been prepared and site having potential rockfall risks have been identified. Finally, wire/net meshing has been proposed after removal of unstable blocks as a stabilization and protection measures.It is worth mentioning here that for the first time rockfall hazard assessment was made in such detail for a site. Suggestions made are implemented by the State Government for the protection of the temple as well as the life of pilgrims performing the parikrama from the rockfall.     

A development of the discontinuous deformation analysis for rock fall analysis

Discontinuous deformation analysis (DDA), a discrete numerical analysis method, is used to simulate the behaviour of falling rock by applying a linear displacement function in the computations. However, when a block rotates, this linear function causes a change in block size called the free expansion phenomenon. In addition, this free expansion results in contact identification problems when the rotating blocks are close to each other. To solve this problem of misjudgment and to obtain a more precise simulation of the falling rock, a new method called Post‐Contact Adjustment Method has been developed and applied to the program. The basic procedure of this new method can be divided into three stages: using the linear displacement function to generate the global matrix, introducing the non‐linear displacement function to the contact identification, and applying it to update the co‐ordinates of block vertices. This new method can be easily applied to the original DDA program, demonstrating better contact identification and size conservation results for falling rock problems than the original program. Copyright © 2005 John Wiley & Sons, Ltd.     

A Model of Point-to-Face Contact for Three-Dimensional Discontinuous Deformation Analysis

Summary The key to three-dimensional discontinuous deformation analysis (3D DDA) is a rigorous contact theory that governs the interaction of many three-dimensional blocks. This theory must provide algorithms to judge contact types and locations and the appropriate state of each contact, which can be open, sliding or locked. This paper presents a point-to-face contact model, which forms a part of the contact theory, to be used in 3D DDA. Normal spring, shear spring and frictional force submatrices are derived by vector analysis and the penalty method. Also given are the open-close iteration criteria and operations performed for different changes in contact state. Sliding at a contact can occur in any direction parallel to the contact face, as opposed to one of two directions in two-dimensional DDA. This point-to-face contact model has been implemented into a 3D DDA computer program, and numerical results from several test cases demonstrate the validity of the model and the capability of the program.     

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.     

Boundary Element based Discontinuous Deformation Analysis

A Boundary Element based Discontinuous Deformation Analysis (BE‐DDA) method is developed by implementing the improved dual reciprocity boundary element method into the open close iterations based DDA. This newly developed BE‐DDA is capable of simulating both the deformation and movement of blocks in a blocky system. Based on geometry updating, it adopts an incremental dynamic formulation taking into consideration initial stresses and dealing with external concentrated and contact forces conveniently. The boundaries of each block in the discrete blocky system are discretized with boundary elements while the domain of each block is divided into internal cells only for the integration of the domain integral of the initial stress term. The contact forces among blocks are treated as concentrated forces and the open–close iterations are applied to ensure the computational accuracy of block interactions. In the current method, an implicit time integration scheme is adopted for numerical stability. Three examples are used to show the effectiveness of the algorithm in simulating block movement, sliding, deformation and interaction of blocks. At last, block toppling and tunnel stability examples are conducted to demonstrate that the BE‐DDA is applicable for simulation of blocky systems. Copyright © 2016 John Wiley & Sons, Ltd.     

On the Implementation of augmented Lagrangian method in the two‐dimensional discontinuous deformation Analysis

The discontinuous deformation analysis (DDA) is a discontinuum‐based method, which employs a penalty method to represent the contact between blocks. The penalty method is easy to be implemented in the program, but the contact constraint is only approximately satisfied. Penetrations between contacting blocks are unavoidable even if the penalty value is very large. To improve the contact precision in the DDA, an augmented Lagrangian method is introduced, which can make use of advantages of both the Lagrangian multiplier method and the penalty method. This paper provides a detailed implementation of the augmented Lagrangian method in the DDA program and compares it with the standard DDA on the computational efficiency and contact precision. Copyright © 2013 John Wiley & Sons, Ltd.     

无人机影像在高陡边坡危岩体调查中的应用

在高陡边坡危岩体的调查中,复杂的地形条件经常限制工作的正常开展,如何快速准确地获取地质灾害信息一直是地质灾害调查研究中的难点之一。以往的研究中对无人机遥感技术在黄土、高原等地区应用有所报道,但对西南地区高陡边坡危岩体灾害调查的研究尚无报道。文章以锦屏二级水电站出线场边坡落石灾害所在区域为例,将无人机摄影测量技术应用于高陡边坡危岩体调查中,通过无人机倾斜摄影获取高分辨率遥感影像,开展遥感影像三维建模,进行地质灾害遥感解译,总结了无人机遥感系统在高陡边坡危岩体调查的技术流程。通过三维实景模型,精确地分析了落石灾害的空间分布、失稳模式及演化过程,查明了区域内危岩隐患点的分布特征;基于三维点云模型,提取出地质灾害体的属性信息,测得落石方量为11.7 m3,采用最小二乘法进行平面拟合,得到落石两组主控结构面产状为275.4°∠31.2°、103.5°∠63.3°。实践表明,无人机遥感技术在高陡边坡地区落石灾害调查中具有明显的可行性和优越性,可以较好地应用于高陡边坡危岩体调查中。     

混合多位移模式的非连续变形分析法研究

传统的非连续变形分析法（DDA）法采用简单的线性位移模式计算效率高,描述大块体的高阶多项式位移模式在一定程度保留了该特点,并提高了计算精度。近年来流行的耦合有限元、自然单元的DDA法实质上是引入相应的插值形函数构成块体位移函数,计算相对低效,但具有计算更精细、更容易施加边界条件等优点。为结合传统DDA法与DDA耦合法各自的优点,建立了一种同时利用传统DDA法线性位移模式与耦合型DDA法非线性位移模式的混合法。该方法非线性模式主要针对大块体,采用了自然单元插值,缘于其具有一定无网格特征,且效率比有限元高。建立了混合模式下的整体矩阵并推导出接触等因素刚度子矩阵和荷载子向量的具体表达式。该方法建模更加方便合理,计算精度、效率介于线性模式的传统DDA法和非线性位移模式的耦合法之间。通过基本算例验证了混合法的有效性,并给出了节理围岩-隧道衬砌整体分析模型的计算结果,体现了新方法的优越性。     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

一种基于似三棱柱体元的地质三维建模方法研究

三堆空间建模方法是三堆地劫工程GIS研究的核心问题之一。提出一种基于似三棱柱体元的三堆数据模型，模型包含顶点、线段(棱边、三角形边)、三角形、侧面四边形、三棱柱体元5个基本元素。和点对象、线对象、面对象、体对象、复杂对象、空间对象等6个对象。设计了5个基本元素和3种地质对象的数据结构和它们之间的拓扑关系。以岩体和巷道为例。给出了似三棱柱体建模思路和算法。利用内蒙古某矿区实际钻孔资料和模拟巷道数据对所开发的系统原型进行验证。研究表明。基于似三棱柱体元的数据模型的优势在于可以表示空间对象的表面和内部结构。便于建模和节省存储空间，同时便于不规劓的自然地质体和规则勘探工程建模。     

Assessing rockfall susceptibility in steep and overhanging slopes using three-dimensional analysis of failure mechanisms

Rockfalls strongly influence the evolution of steep rocky landscapes and represent a significant hazard in mountainous areas. Defining the most probable future rockfall source areas is of primary importance for both geomorphological investigations and hazard assessment. Thus, a need exists to understand which areas of a steep cliff are more likely to be affected by a rockfall. An important analytical gap exists between regional rockfall susceptibility studies and block-specific geomechanical calculations. Here we present methods for quantifying rockfall susceptibility at the cliff scale, which is suitable for sub-regional hazard assessment (hundreds to thousands of square meters). Our methods use three-dimensional point clouds acquired by terrestrial laser scanning to quantify the fracture patterns and compute failure mechanisms for planar, wedge, and toppling failures on vertical and overhanging rock walls. As a part of this work, we developed a rockfall susceptibility index for each type of failure mechanism according to the interaction between the discontinuities and the local cliff orientation. The susceptibility for slope parallel exfoliation-type failures, which are generally hard to identify, is partly captured by planar and toppling susceptibility indexes. We tested the methods for detecting the most susceptible rockfall source areas on two famously steep landscapes, Yosemite Valley (California, USA) and the Drus in the Mont-Blanc massif (France). Our rockfall susceptibility models show good correspondence with active rockfall sources. The methods offer new tools for investigating rockfall hazard and improving our understanding of rockfall processes.     

数值流形方法框架下散体系统与连续介质共同作用模拟

数值流形方法是包含流形元、有限元及DDA在内的数值方法体系,建立流形元与DDA块体的接触方程,则可实现流形方法框架下的连续介质和散体系统共同作用模拟。针对填石路堤工程,编制了大型数值计算程序,采用块体随机生成、块体粒径控制及块体自然堆积的方法建立散体系统的DDA模型,对路堤的分层铺设、碾压及工后沉降变形等进行模拟分析。通过算例表明,在数值流形方法框架下,采用流形元与DDA共同作用的方法,可以很好地对同时存在连续变形和散体大变形的体系进行计算分析,其对该类问题的模拟更接近分析对象的实际情况,有助于从根本上揭示分析对象变形的细观机制和规律,并能考察更多因素对工程问题的影响。