Robust algorithms for polyhedral modelling of fractured rock mass structure

This paper presents robust algorithms for application in polyhedral modelling of rock mass structure based on discrete fracture networks. The algorithms improve the robustness of current polyhedral modellers to challenging or degenerate geometries and geometrical errors. These issues are inevitably encountered when the fracture network realisations incorporate large numbers of fractures, or regions of densely packed fractures are modelled, or when the number of fracture network realisations interrogated is large. Several stages in the polyhedral modelling process which are sensitive to geometrical errors are reviewed and algorithms which are robust and capable of handling topological errors in the input fracture network geometry are presented.     

A comparative study of various commercially available programs in slope stability analysis

The objective of this paper is to study the effect of different slip surface search techniques on the factors of safety obtained using the limit equilibrium (LE) slope stability methods. This objective is accomplished by comparing results from the finite element method, the linear grid method, the rectangular grid method, and the Monte-Carlo searching techniques using different commercially available programs. The results showed that the LE methods are very efficient methods when coupled with a robust searching technique namely the Monte-Carlo method. In addition, the selected slip surface search technique highly influenced the location of the critical slip surfaces as well as the value of the calculated factors of safety.     

Improved Bell's method for the stability analysis of slopes

A new procedure based on the approximation to the total normal pressure along the slip surface is developed to compute the factor of safety of slopes for slip surfaces of all shapes. By taking the whole sliding body, instead of an individual slice, as the loaded object, all the equilibrium equations are formulated according to the three‐moment equilibrium conditions rather than the two force equilibrium conditions and one‐moment equilibrium condition. The system of nonlinear equations deduced in this way is well‐scaled and enjoys excellent numerical properties such as the existence of solution with a positive factor of safety, a nearly unlimited scope of convergence and a rapid convergence rate associated with the Newton method. In the case of ?_u =0—the situation where no drainage and no consolidation are involved, furthermore, the system has a unique solution and the factor of safety has an explicit expression. Some typical examples are analyzed to demonstrate the numerical properties of the proposed procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Explicit limit equilibrium solution for slope stability

Conventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non‐linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non‐convergence occasionally occurring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed‐form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern–Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley & Sons, Ltd.     

An analysis of the action of dowels on the stabilization of rock blocks on underground excavation walls

Summary  Underground excavation in fractured rock masses can lead to instability of rock blocks on its perimeter. Among the stabilization measures that are often used, dowels or passive bolts play an important role. These passive reinforcement measures cannot, however, be easily considered in simplified calculation techniques based on the Limit Equilibrium Method (LEM). The analysis of such elements cannot be separated from rock-dowel interaction following the displacement of the block. A new simplified calculation procedure is presented in this paper for the analysis of the interaction between rock and dowels on walls of an underground excavation where potentially sliding rock blocks are present. The assumed interaction scheme is, however, partial in that dowel reinforcement is only activated by a small displacement, while this displacement does not induce a destressing of the rock block. Such a procedure allows a fast dimensioning of the dowels, considering the maximum stabilizing force that they are able to apply to the block without reaching a critical condition with reference to dowel failure or to its connection to the rock. Correspondence: Dr. Pierpaolo Oreste, Politecnico di Torino, DITAG, C. so Duca degli Abruzzi 24, 10129 Torino, Italy     

Seismic stability analysis of a layered rock slope

In general, the determination of the factor of safety and the location of the critical slip surface are two major challenges in seismic slope stability analysis. In this paper, a new approach for determining the factor of safety and the corresponding critical slip surface of a layered rock slope subjected to seismic excitations is presented, through a case study based on the combination of the shear strength reduction technique and distinct element method. According to this proposed method, the seismic factor of safety and the critical slip surface of the slope are estimated and compared with those obtained by the pseudo-static approach, combined with the limit equilibrium method. It is found that the factor of safety obtained from the proposed method is slightly greater than that computed by the pseudo-static analysis, with a difference of 4.2%, and that the critical slip surface obtained from the two methods is identical, which confirms the reasonability and feasibility of the proposed method.     

节理岩体边坡稳定性分析新方法

节理岩体边坡失稳破坏同时受控于节理与岩体抗剪强度。在对具有2组平行节理的岩体坡边失稳破坏机制研究基础上,研究了具有2组平行节理岩体边坡的极限平衡分析方法,并推导了相应的边坡稳定性分析计算公式,编制了基于潜在滑动面自动搜索的边坡稳定性研究程序。通过与文献中算例的对比研究,证明了所提出的节理岩体边坡稳定性分析方法的正确性,为具有2组平行节理岩体边坡的稳定性分析提供一条新的有效途径。     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

Rigid block based lower bound limit analysis method for stability analysis of fractured rock mass considering rock bridge effects

A rigid block based lower bound limit analysis method for analyzing stability of fractured rock mass in 2D and 3D conditions is proposed. The rock bridge effects are considered in the general formation. No assumptions are imposed on the inter-element forces, and the solution obtained is statically admissible. The proposed method is theoretically rigorous and simple. The validation and efficiency of the proposed method have been demonstrated through three typical types of slopes, indicating that apart from the fractures, rock bridge plays a key role in stabilizing rock blocks, which should be greatly concerned in stability analysis of rock mass.     

溪洛渡水电站某危岩体稳定性及加固措施研究

在现场调查分析的基础上,提出了溪洛渡水电站某危岩体的两种可能失稳模式（剪切坠落或拉裂倾倒失稳）,进而建立了相应的稳定性计算极限平衡力学模型,而且对危岩体的变形和破坏特征进行了数值模拟分析,分析结果表明,危岩体抗拉裂倾倒稳定性较差,剪切坠落失稳的稳定性系数较高。在稳定性分析的基础上,计算出危岩体倾倒失稳时,安全系数为1.5时的锚固力,进而提出了危岩体加固方案：充填凹岩腔+填充裂隙+预应力锚索＋锚杆联合加固,数值模拟表明此加固方案效果良好。     

节理岩体关键块体稳定的概率分析

基于地下岩体受节理面的控制,节理面的几何和力学参数随机分布,从而导致岩体系统具有高度不确定性,提出以关键块体理论为基础,考虑节理几何和力学参数随机性的岩体开挖可靠度分析方法,并给出了块体稳定的总失效概率评价模型。以澳大利亚阿德莱德地区一铜矿地质条件为例,以节理面倾角、倾向、摩擦系数和黏聚力为随机变量,通过Monte Carlo模拟和概率图方法,进行了岩体可靠度和失效概率的计算。最后,采用条件概率的分析方法,计算了单面滑动块体的总失效概率。计算结果表明,块体沿单面滑动并且出现的概率为11.0%,总的失效概率为3.85%,超过一般岩体工程可允许的风险水平,认为该方法可以作为评价块体可靠性的依据。     

采矿引起的边坡倾倒滑移变形机理与变形安全性分析研究—以抚顺西露天矿边坡为例

在矿山开发、水电建设过程中倾倒变形问题日渐突出。倾倒变形边坡一般具有反倾边坡结构,变形的过程和机理比较复杂、涉及的变形岩体范围较大、危害严重。论文以抚顺西露天矿边坡为例,通过岩体位移监测资料的跟踪分析、底面摩擦模拟试验,以岩体力学、松散介质力学原理为理论基础,探讨了采矿影响下边坡倾倒滑移体的变形机理,分析认为采矿引起的倾倒滑移变形问题是在特定的地质构造和采矿工程条件下产生的,并提出了岩体变形安全性分析方法。通过工程实例,验证了方法的实用性,并针对实际问题提出了变形整治对策。     

裂隙化硬岩洞室围岩失稳分析方法

根据岩体的力学介质分类和块体理论及赤平投影,结合工程实例,推导了滑动方向的计算公式,研究了裂隙化岩体地下采空区围岩的稳定性分析方法。利用该方法分析了华北某大型地下采空区围岩的稳定性,展示了该模型的实用性。     

主应力对巷道交岔点围岩稳定性影响研究

为研究主应力对交岔点围岩稳定性的影响,以某矿为工程背景,建立5组交岔点数值计算模型,研究了交岔点开挖前的扰动应力场偏转规律,并引入点安全系数法研究了主应力和交岔角度对交岔点围岩位移场、扰动破碎区的影响规律。研究结果表明：在交岔点开挖之前,交岔点附近围岩的主应力方向发生偏转,偏转后的应力场类型由σh型变为σv型,交岔点开挖过程中围岩受σv型应力场影响;交岔角（α≤90°）越大,交岔点越稳定;交岔角度相同时,新掘巷道轴向较靠近最大水平主应力方向的交岔点更稳定。交岔点现场实测数据验证了研究结果。     

Seismic stability analysis of a rock block using the block theory and Newmark method

Seismic stability analysis of a rock block is an important issue in the field of rock mechanics and rock engineering. To solve this problem, the block theory and the Newmark method are combined, and a general method for seismic response of a rock block is introduced. First, the formation method of a three-dimensional rock block, which includes establishing a topological relationship among the block-polygon face-edge-vertex and dividing a complex block into convex subblocks, is presented, and the simplex integration method is employed to calculate the volume of a rock block and the areas of the polygonal faces. Second, the assumptions and algorithms of the general method for seismic response of a rock block are detailed. The dynamic analysis is carried out in time step. In each time step, the key technologies including analysis of the seismic force and motion mode, trial of the incremental displacement, check for the block entrance, and update of the motion parameters are performed in order. Last, two verification examples and three application examples including a wedge, a rock block of slope, and a combined rock block are used to analyze the correctness and practicality of the general method. The results show that, for a given ground motion record, the Newmark program can effectively simulate the dynamic response process of the motion mode, velocity, and safety factor of the rock block, and the permanent displacement under the earthquake action is obtained, which provides a quantitative parameter to evaluate the dynamic stability of a rock block.     

水力和超载条件下锚固岩石边坡动态稳定性拟静力分析

基于极限平衡理论,综合考虑水力条件、坡顶超载、地震荷载效应和锚固效应对岩石边坡进行了全面的稳定性分析。计算给出了多影响因素条件下岩石边坡稳定性安全系数的表达式,并重点分析了几种相关参数组合对岩石边坡稳定性的影响。分析表明,坡顶张拉裂缝积水、地下水渗流作用、滑面出流缝被堵塞、地震影响效应不利于岩石边坡抗滑稳定性,而锚索锚固效应则对提高边坡抗滑稳定性有积极作用;坡顶张拉裂缝积水、滑面出流缝被堵塞、水平向地震影响效应都不利于岩石边坡抗倾覆稳定性,但锚索锚固效应、坡顶超载、与竖直方向地震效应则对提高边坡抗倾覆稳定性有益。最后针对工程实际,提出了相应的工程建议。     

某公路桥桥基区岩质边坡稳定性评价

该公路桥桥基区位于高山峡谷地区,边坡稳定性评价问题尤为重要。本文选择具有代表性的两类典型地质剖面,岩土体分层和结构面切割控制滑移模式。设计了结构面不同切割厚度、不同剪出口位置和不同剪出角度等计算方案,对该区高陡边坡的稳定性进行了探讨。根据计算得到的安全系数,确定了其最不利滑移模式。在此基础上,对其自然状态、自然＋地震、饱水状态和饱水＋地震等工况下的稳定性进行了计算分析,发现存在两类典型最不利失稳模式,即浅层滑移模式和结构面切割滑移模式。前者规模有限,危害不大;后者规模相对较大。对工程危害较大,建议对其作锚固和护面处理,也应对坡脚相对软弱层作补强处理。     

Comparative study of Sarma's method and the discontinuous deformation analysis for rock slope stability analysis

This paper presents a comparative study of two methods, Sarma's method and the discontinuous deformation analysis (DDA), for rock slope stability analysis. The comparison concerns the stability analysis of two classic rock slopes. The study shows that the DDA, which accounts for the block kinematics, provides a very different factor of safety as compared with Sarma's method. More realistic reaction forces around each rock block can be obtained by the DDA, including the thrust forces between rock blocks and the forces between the base and the blocks. The DDA's result shows two possible directions for the relative movement between two contiguous blocks at the initiation of slope failure. It also indicates that the limit equilibrium condition may not occur along the interfaces of rock blocks at the initiation of slope failure. The determination of realistic interaction forces around each block will be very important in rock slope stability analysis if nonlinear failure criteria are considered.     

层状岩体开挖洞室围岩块体稳定分析及锚固方法

由于层状岩体的稳定性受层面控制,在该类岩体中进行开挖常常导致块体的失稳,给工程建设带来巨大的危害.本文从层面与结构面组合形成的块体系统稳定性分析入手,运用改进的块体理论,进行了块体稳定分析程序的开发,对定位、半定位块体的系统稳定性分析方法进行了探讨.以西龙池抽水蓄能电站地下厂房为例,对围岩中的块体进行了系统稳定分析.通过实际开挖验证,表明了分析结果的合理性,开发的程序可供同类工程参考使用.本文所提出的方法可为地下工程施工期的超前预报、围岩的系统锚固支护设计提供重要依据.     

向家坝水电站地下厂房围岩稳定的黏弹塑性有限元分析

考虑流变作用,建立三维有限元模型进行数值计算,以洞室变形和点抗滑安全系数为指标,针对向家坝水电站地下厂房围岩的特殊性进行稳定性研究,结果表明,随着围压的增高,流变速率逐渐减小,初始应变逐渐减小;软弱夹层处流变速率较其他岩体减小缓慢,且开挖后流变达到稳态状态时软弱夹层最终流变位移较大;黏弹塑性下围岩位移分布及变化规律与弹塑性一致,但黏弹塑性下计算位移明显要比弹塑性大;流变效应对岩体变形和稳定性,以及对支护结构有重要影响;黏弹塑性情况下,洞室围岩特征点抗滑安全系数比弹塑性条件下小,软弱夹层出露处和拱顶点抗滑安全系数较低,点抗滑安全系数分析还表明,软弱夹层对其稳定性影响明显,验证了位移分析结果。