基于线黏弹性接触的落石冲击地面参量理论研究

落石与坡面或者防护结构接触过程中冲击参量随时间变化特征是描述落石碰撞过程的重要指标,对于揭示落石与坡面相互作用机制以及采取合理的防护措施具有重要的意义。在现有的相关设计规范中,并没有给出关于落石冲击力时程关系的计算方法,仅参照有关规范或经验方法确定一个落石最大冲击力值。为此,首先基于线黏弹性接触理论,建立落石冲击地面力学模型,根据位移-速度组合初始条件以及速度-加速度组合初始条件分别推导得到两种落石冲击特征参量理论解析解;然后基于 ANSYS/LS-DYNA 非线性动力学软件,建立落石冲击地面三维数值模型,研究球体落石冲击地面力学特点;最后将理论结果对比室内试验和已有的研究成果,得出以下结论：（1）Hertz 弹性接触理论结果中各参量变化在加载阶段和恢复阶段均呈现对称的趋势,速度、加速度初始条件下的落石冲击特征参量和动力有限元法非常接近,而位移-速度初始条件组合并不适用于研究落石冲击下的动力特征;（2）不同速度和下落高度下,落石最大冲击力值随落石下落高度和冲击速度的增大而增加,而落石冲击作用时间随下落高度和冲击速度的增加而减小;（3）计算结果得到的落石最大冲击力以及落石冲击作用时间与室内试验结果和已有成果相接近,相比室内试验和有限元结果的震荡性,此结果更能体现落石冲击力变化规律; （4）多种冲击速度下,对比不同方法得到的落石最大冲击力,可知计算结果均在各种冲击力计算结果的范围内,具有很好的可靠性。考虑到现有研究理论的不足,难以求解落石冲击力时程关系,求解结果丰富了落石碰撞理论,可以指导工程有关落石灾害的防护设计。     

Perforation of Flexible Rockfall Barriers by Normal Block Impact

Flexible rockfall barriers are a common form of protection against falling blocks of rock and rock fragments (rockfall). These barriers consist of a system of cables, posts, and a mesh, and their capacity is typically quantified in terms of the threshold of impact (kinetic) energy at which the barrier fails. This threshold, referred to here as the “critical energy,” is often regarded as a constant. However, several studies have pointed out that there is no single representative value of critical energy for a given barrier. Instead, the critical energy decreases as the block size decreases, a phenomenon referred to as the “bullet effect.” In this paper, we present a simple analytical model for determining the critical energy of a flexible barrier. The model considers a block that impacts normally and centrally on the wire mesh, and rather than incorporate the structural details of the cables and posts explicitly, the supporting elements are replaced by springs of representative stiffness. The analysis reveals the dependence of the critical energy on the block size, as well as other relevant variables, and it provides physical insight into the impact problem. For example, it is shown that bending of the wire mesh during impact reduces the axial force that can be sustained within the wires, thus reducing the energy that can be absorbed. The formulas derived in the paper are straightforward to use, and the analytical predictions compare favorably with data available in the literature.     

基于崩塌滚石运动特征的防护网动态响应规律

为获取被动柔性防护网在不同崩塌滚石运动特征下的动态响应规律,以鲁甸803地震震后崩塌滚石造成防护网损坏现场为例,通过无人机倾斜摄影技术实现地质调查,采用Rockyfor3D获取研究区落石的运动特征,并通过被动柔性防护网有限元模型,对不同落石冲击形式下防护网的动态响应规律进行研究.研究显示区内落石弹跳高度普遍在1~2 m,优势路径上的落石会形成稍高速低弹跳的范围冲击.在范围落石冲击下,防护网绳索最大拉力增加可达123.7%;在低弹跳落石冲击下,绳索最大拉力增加可达181.2%.范围落石冲击会导致防护网网面耗能的降低,并导致上拉锚绳拉力的增大.防护网下一级支撑绳对不同落石弹跳高度的响应较为敏感,部分高弹跳落石会对上拉锚绳和上一级支撑绳产生影响.      

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.     

落石冲击混凝土棚洞力学特性研究

落石冲击棚洞结构作用过程复杂,缺乏统一的落石冲击力表达式。首先,将落石简化为刚性球体,基于Hertz接触理论,推导得到落石冲击力半正弦算法的理论表达式,考虑落石冲击下棚洞的非弹性特征,根据落石与材料碰撞过程中落石加速度曲线特征,采用函数拟合法推导得到落石法向冲击下其冲击力的理论计算方法;然后,基于ANSYS/LS-DYNA软件建立落石冲击棚洞数值计算模型,研究不同冲击速度下落石冲击棚洞动力特征;最后,与现存常见的多种方法进行对比,得出以下结论：Hertz半正弦法得到的落石冲击力远大于函数拟合法和数值法,而函数拟合法和数值法得到的落石冲击力时程曲线相接近,表明函数拟合法更能反映落石与棚洞接触碰撞动力关系;对比其他计算方法可以得到,Hertz算法适用于分析无能量损失下的弹性碰撞问题,而Logistic算法适用于材料大塑性变形的情况,弹塑性接触理论结果和动力有限元结果存在差异,而采用函数拟合推导的计算方法得到的落石最大冲击力和落石冲击作用时间与动力有限元法更接近,更能反映落石冲击棚洞动力响应特征,推导的落石冲击力计算方法可为工程实践中棚洞防护设计提供理论参考。     

滚石冲击力测试研究

以国内外代表性滚石冲击力计算方法为基础,针对冲击力的影响因素,设计了一套滚石冲击力测试装置。通过试验设计,选取不同的滚石质量、冲击速度、入射角度、缓冲材料性质及厚度等影响因素,获得冲击力变化规律。结果表明：最大冲击力随滚石重量的减小或冲击速度的降低而逐渐减小,2 cm厚度缓冲层比直接冲击时减小了90%左右,缓冲效果明显。同时最大冲击力随着入射角度的变小而降低,但入射角度越小,冲击力值降低的幅度越小。结合冲击试验结果,通过冲击力计算方法对比分析,建立了可用于各影响因素的最大冲击力计算方法,验算表明误差很小。研究结果可为滚石灾害的防治设计提供参考依据。     

Choosing a rockfall barrier with the Precautionary Principle: a quantitative approach

The paper illustrates an approach for implementing the Precautionary Principle in risk management, exemplified by a procedure aimed at choosing the height of a rockfall barrier protecting a railway stretch. Risk is expressed by the frequency f of blocks hitting the railway—i.e. by the ratio between the number of blocks reaching the railway and the number of blocks falling from the slope—assessed through software simulation of the falling of the blocks. The height from which a block may fall is considered to be the main uncertainty factor in risk estimation, which translates into uncertainty as to the level of risk, as every simulation shows that more than one impact frequency is possible. Such uncertainty justifies the precautionary approach to the design of the barrier, and is represented mathematically by means of possibility and probability distribution functions. The distributions make it possible to express the degree of precaution related to a barrier as the level of confidence, in terms of necessity or probability measures—that can be placed on the fact that, because of the barrier, the impact frequency, although uncertain, will not exceed what is acceptable. It will be shown that the degree of precaution takes quite different values if possibility theory is used instead of probability theory. Finally some simple cost/benefit analyses, that explicitly and quantitatively consider the degree of precaution, are exemplified.     

A Factor Strength Approach for the Design of Rock Fall and Debris Flow Barriers

This paper discusses the applicability and the limitations of an approach to the limit states design of flexible barrier in which the soil/rock strength are factored as required in the European construction code. It shows as this approach has different implications if it is applied to the same kind of structure when loaded by different phenomena (rockfall and debris flow in particular). Flexible barriers are common countermeasures to protect from rockfall hazard and to restrain debris flow events. Even if an intense scientific production has demonstrated the difference between the two phenomena, the protection systems are still often designed in the same way. Additionally, the Eurocode 7 (EC7), which is the European Standard concerning geotechnical design, has not been conformed to these kinds of structures and consequently a relationship between the reliability of the system and the partial factors does not exist. Since most of the parameters that rule these systems are not even considered in the code, the Authors propose the study of two cases, in which rockfall and debris flow occur, respectively, to analyse the applicability and the limitations of EC7 principles to design the suitable kind of structure.     

Overturning stability of L-shaped rigid barriers subjected to rockfall impacts

Reinforced concrete barriers are commonly used as defence measures in hilly areas to contain falling boulders and landslide debris. These barriers are conventionally designed to satisfy the conditions of force and momentum equilibrium with a factor of safety. A major limitation of this approach is that the inertial resistance of the barrier is neglected such that the design could be over-conservative. This paper presents a novel displacement-based approach for the assessment of overturning stability of rigid L-shaped barriers subjected to rockfall impacts. Analytical solutions, which are derived based on conservation of momentum and energy, are used to take into account the contributions of the self-weight and, thus, the inertial resistance of the barrier in resisting an impact. The actual amount of energy transferred from the impacting boulder to the barrier is considered by including the coefficient of restitution between the two objects. The accuracy of the analytical solutions has been confirmed by laboratory impact experiments. Numerical assessments conducted using the new solutions indicate that a reasonably sized rigid barrier, due to its own inertial resistance, may adequately withstand the impact action of a heavy boulder rolling down a hillslope without relying on any anchorage to its support. A range of geometric design of the barriers with L-shaped cross sections also has been considered and analysed. The new approach presented in this paper is easy to apply in practice and will be useful for engineers designing concrete barriers as passive rockfall mitigation measures.     

Vulnerability of simple reinforced concrete buildings to damage by rockfalls

A procedure is presented for investigating the response of reinforced concrete buildings to rockfall impact. The method considers a single rock hit on the basement columns, and it includes four steps: (a) calculation of the probability of a rock impact on a member of the load-bearing system, taking into account the block size and the design of the structure; (b) evaluation of the response of one or more structural elements to the hit based on element capacity; (c) in the case of structural element failure, assessment of the robustness of the whole structural system, calculating the potential for progressive collapse; and (d) calculation of a damage index (DI), which is the ratio of structural elements that fail to the total number of structural elements. The proposed method is applied to a reinforced concrete building for a range of rockfall paths and intensities. The analysis has been carried out for a 2-m-diameter block and velocities < 3.5 m/s. The possible damage range is found to be highly variable, with DI values ranging from 0.01 to 1 depending on the impact location and block velocity.     

Dynamic response of flexible rockfall barriers under different loading geometries

Flexible steel barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible barriers is conventionally performed using full-scale field tests by dropping a weight onto the barriers in accordance with the European test standard ETAG 27. The weight typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. A rigid slab may load a barrier over a larger area and its effect has not been investigated. In this study, a calibrated three-dimensional finite-element model was developed to study the performance of vertically and horizontally orientated rockfall barriers under concentrated areal impact loads. A new bilinear force-displacement model was incorporated into the model to simulate the behavior of the energy-dissipating devices on the barriers. The effect of different weight geometries was studied by considering impacts by a rigid single spherical boulder and a rigid slab. Results reveal that areal loading induced by a rigid slab increases the loading on the barrier foundation by up to 40 % in both horizontally and vertically positioned barriers when compared to a concentrated load scenario with a single boulder. This indicates that barriers tested under the current test standard does not give the worst-case scenario in terms of foundation loads, and barrier designers should take into account the possible effect of increased foundation loads by reinforcing the barrier posts and/or increasing their spacing.     

滚石防护加筋土挡墙研究综述

滚石防护加筋土挡墙是工程上常见的落石防护工程结构, 通常用于拦截大体积或高速滚落的山坡落石。滚石防护加筋土挡墙能有效拦截具有高冲击动能的岩块滚落。但由于其结构较大, 受滚石撞击时会发生不可逆的诱发性破坏变形, 加筋土体应力-应变性状非线性, 不同加筋材料与土体界面特性及作用机制相当复杂, 目前防滚石撞击的加筋土防护挡墙的设计方法不够完善。通过总结已有文献的研究成果, 重点阐述了受滚石撞击的加筋土挡墙结构响应性状, 从落石轨迹控制和挡墙稳定性两个方面对挡墙设计方法进行了讨论。同时指出滚石旋转动能不可忽略, 已有成果在滚石冲击力计算、结构撞击响应分析方法等问题的研究仍显不足, 为今后研究提供参考。     

RockGIS: a GIS-based model for the analysis of fragmentation in rockfalls

A rockfall is a mass instability event frequently observed in road cuts, open pit mines and quarries, steep slopes and cliffs. After its detachment, the rock mass may disaggregate and break due to the impact with the ground surface, thus producing new rock fragments. The consideration of the fragmentation of the rockfall mass is critical for the calculation of the trajectories of the blocks and the impact energies and for the assessment of the potential damage and the design of protective structures. In this paper, we present RockGIS, a GIS-based tool that simulates stochastically the fragmentation of the rockfall, based on a lumped mass approach. In RockGIS, the fragmentation is triggered by the disaggregation of the detached rock mass through the pre-existing discontinuities just before the impact with the ground. An energy threshold is defined in order to determine whether the impacting blocks break or not. The distribution of the initial mass between a set of newly generated rock fragments is carried out stochastically following a power law. The trajectories of the new rock fragments are distributed within a cone. The fragmentation model has been calibrated and tested with a 10,000 m³ rockfall that took place in 2011 near Vilanova de Banat, Eastern Pyrenees, Spain.     

Dynamic response of flexible rockfall barriers with different block shapes

Flexible rockfall barriers are commonly constructed on steep hillsides to mitigate rockfall. The evaluation of the dynamic response of proprietary flexible rockfall barriers is conventionally performed using full-scale field tests by dropping a block onto the barriers in accordance with the European test standard ETAG 027. The block typically has a spherical or polyhedral shape and cannot reproduce more complex rockfall scenarios encountered in the field. Little attention has been paid to the effects of the block shape on the impact force and structural response. This paper aims to quantitatively reveal the influence of the block shape on the dynamic response of flexible rockfall barriers. First, an ellipsoidal model is established to approximately simulate the block, and the sphericity is employed as the representative index of the block’s shape. A full-scale test on a typical flexible barrier system is carried out and then used to calibrate an advanced three-dimensional finite element model. Finally, the dynamic responses of flexible rockfall barriers are analyzed and discussed, focusing on the effects of the block’s shape. The numerical results show that the sphericity will obviously influence the maximum elongation of flexible barriers, the peak impact force, the peak force of the upslope anchor cable, the peak force of the lower main support cable, the axial peak force of the post, and the peak shear force at the post foundation. The assumption of spherical or polyhedral blocks in the test standard could lead to the defensive failure of flexible rockfall barriers in some impact scenarios.

     

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.     

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.     

Full-Scale Dynamic Analysis of an Innovative Rockfall Fence Under Impact Using the Discrete Element Method: from the Local Scale to the Structure Scale

In order to protect infrastructures against rockfalls, civil-engineered mitigation measures are widely used. Flexible metallic fences are particularly well suited to stop the propagation of blocks of rock whose kinetic energy can reach 5000?kJ before impact. This paper focuses on the design of highly flexible rockfall fences under the new European guideline ETAG027. The experimental testing and the numerical modeling using the discrete element method (DEM) of a new metallic rockfall fence are presented. Several scales of study were considered; the mesh, the net and the entire structure. The calibration of the DEM models is described and a parametrical study is proposed. The latter aims to underline the type of information that can be obtained from numerical simulations of such a system to enhance its design.     

Experimental Testing of Rockfall Barriers Designed for the Low Range of Impact Energy

Most of the recent research on rockfall and the development of protective systems, such as flexible rockfall barriers, have been focused on medium to high levels of impacting energy. However, in many regions of the world, the rockfall hazard involves low levels of energy. This is particularly the case in New South Wales, Australia, because of the nature of the geological environments. The state Road and Traffic Authority (RTA) has designed various types of rockfall barriers, including some of low capacity, i.e. 35 kJ. The latter were tested indoors using a pendulum equipped with an automatic block release mechanism triggered by an optical beam. Another three systems were also tested, including two products designed by rockfall specialised companies and one modification of the initial design of the RTA. The research focused on the influence of the system’s stiffness on the transmission of load to components of the barrier such as posts and cables. Not surprisingly, the more compliant the system, the less loaded the cables and posts. It was also found that removing the intermediate cables and placing the mesh downslope could reduce the stiffness of the system designed by the RTA. The paper concludes with some multi-scale considerations on the capacity of a barrier to absorb the energy based on experimental evidence.     

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.     

崩塌落石冲击埋地油气管道的动力响应机理研究

高位崩塌落石是造成长输埋地油气管道破坏的主要地质灾害之一.本文通过111处山区管道崩塌案例分析,归纳出崩塌与埋地管道相互作用的3种模式:冲砸管道、牵引管道及埋没管道,其中冲砸管道的危害性最大,并建立了崩塌与管道相互作用的地质力学模型.采用有限元仿真软件系统模拟了落石冲击、土体与管道变形响应过程及影响因素,发现落石冲击管...