3D key‐group method for slope stability analysis

Because of the simplicity and the speed of execution, methods used in static stability analyses have yet remained relevant. The key‐block method, which is the most famous of them, is used for the stability analysis of fractured rock masses. The KBM method is just based on finding key blocks, and if no such blocks are found to be unstable, it is concluded that the whole of the rock mass is stable. Literally, though groups of ‘stable’ blocks are taken together into account, in some cases, it may prove to be unstable. An iterative and progressive stability analysis of the discontinuous rock slopes can be performed using the key‐group method, in which groups of collapsible blocks are combined. This method is literally a two‐dimensional (2D) limit equilibrium approach. Because of the normally conservational results of 2D analysis, a three‐dimensional (3D) analysis seems to be necessary. In this paper, the 2D key‐group method is developed into three dimensions so that a more literal analysis of a fractured rock mass can be performed. Using Mathematica software, a computer program was prepared to implement the proposed methodology on a real case. Then, in order to assess the proposed 3D procedure, its implementation results are compared with the outcomes of the 2D key‐group method. Finally, tectonic block No.2 of Choghart open pit mine was investigated as a case study using the proposed 3D methodology. Results of the comparison revealed that the outcomes of the 3D analysis of this block conform to the reality and the results of 2D analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

弹粘塑性块体单元法在龙滩水电站右坝肩边坡稳定分析中的应用

介绍了三维弹粘塑性块体单元法的基本原理。该方法假定岩石块体为刚体,只考虑结构面的变形和强度特性。在建立块体系统的平衡方程、结构面的变形与块体位移的几何相容方程以及结构面上的弹粘塑性本构方程的基础上,出块体系统位移与稳定的基本方程。针对龙滩水电站右坝肩边坡地质条件复杂,块体稳定问题较为突出的情况,采用块体单元法计算了边坡中典型结构面切割形成的特定块体在不同工况下的强度储备安全系数,并针对结构面的几何参数和力学参数等重要影响因素进行了敏感性分析,为工程设计提供了依据。应用表明,作为一种新型的水工结构数值方法,块体单元法应用于复杂地质条件下的岩石高边坡的稳定和变形分析具有准确、适用和简便的特点。     

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.     

乌东德水电站左岸拱肩槽边坡稳定性

在对拱肩槽自然边坡工程地质条件详细调查的基础上,采用宏观地质分析和极限平衡法、数值模拟法相结合的研究手段,分层次对乌东德水电站左岸拱肩槽人工边坡整体稳定和局部稳定性进行了系统研究。研究表明乌东德水电站左岸拱肩槽边坡整体稳定性较好,三维离散元数值模拟结果显示,人工边坡变形以少量回弹变形为主,变形特征不突出,稳定性系数为1.4~1.6。在分析边坡开挖后可能形成的块体边界条件基础上,提出了人工边坡可能出现的块体失稳模式,以影响块体稳定性的结构面几何特征、结构面性状和结构面卸荷松弛张开特征入手,建立块体稳定性工程地质评价标准,对块体稳定性进行了宏观地质分析,并采用三维刚体极限平衡方法对可能产生的块体模型进行了计算分析,得到块体开挖后的稳定系数。结果表明,人工边坡可能出现块体多处于基本稳定状态。综合整体稳定性和局部稳定性研究成果,提出人工边坡加固方案建议。研究成果为工程设计与施工提供了重要依据,并对类似工程提供了可以借鉴的经验。     

一般块体方法理论解验证

裂隙岩体一般块体方法能够解决任意大小裂隙、任意形状工程岩体的岩石块体识别及稳定性计算问题。它在块体识别的过程中,将复杂的块体分解为若干个简单的凸形块体,从而使复杂块体的一系列问题大大简化。边坡和地下硐室是野外最常见的岩体建筑物,本文分别选择了一个边坡和一个地下硐室,从块体识别、块体规模、下滑力、摩擦力、粘滞力、稳定性系数等角度对该方法进行了验证。通过解析的方法求得上述两种模型中各个物理量的解,然后把求得的这些解析解与一般块体算法和程序的求解结果进行了比较。结果表明,一般块体方法的算法与程序是正确的。     

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

Quantification of mass and heat transport in fractured porous rocks is important to areas such as contaminant transport, storage and release in fractured rock aquifers, the migration and sorption of radioactive nuclides from waste depositories, and the characterization of engineered heat exchangers in the context of enhanced geothermal systems. The large difference between flow and transport characteristics in fractures and in the surrounding matrix rock means models of such systems are forced to make a number of simplifications. Analytical approaches assume a homogeneous system, numerical approaches address the scale at which a process is operating, but may lose individual important processes due to averaging considerations. Numerical stability criteria limit the contrasts possible in defining material properties. Here, a hybrid analytical–numerical method for transport modeling in fractured media is presented. This method combines a numerical model for flow and transport in a heterogeneous fracture and an analytical solution for matrix diffusion. By linking the two types of model, the advantages of both methods can be combined. The methodology as well as the mathematical background are developed, verified for simple geometries, and applied to fractures representing experimental field conditions in the Grimsel rock laboratory.     

锦屏一级水电站引渠内侧自然边坡的稳定性

层状岩体顺层滑动但却存在反倾的后缘结构面的边坡稳定性研究尚未见到具体讨论。本文采用了数值模拟方法对锦屏一级水电站引渠内侧边坡的稳定性进行了分析,通过结构面参数折减法,求得该边坡稳定性系数为1.191,后端岩体对前端不稳定体不存在推力。通过数值分析方法和极限平衡法对结构面相关参数的敏感性进行了分析对比,对比表明采用参数折减法的数值分析方法结果可靠。本文为类似复杂岩体边坡稳定性判定提供参考。     

山地旅游景区岩质边坡稳定性分析及其防治措施

山地旅游景区中因块体失稳和边坡失稳造成的人员伤亡事件不断发生,严重影响着旅游景区的安全运营。为保障旅游安全,本文以浙江某山地旅游景区进出口边坡为研究背景,通过三维激光扫描仪扫描边坡岩体,结合基于坐标投影法已开发的岩质边坡工程块体稳定性评价及可视化软件(CPG程序)对岩质边坡块体稳定性进行分析,并采用FLAC3D数值分析手段,对岩质边坡整体稳定性进行分析,最后利用有限元分析所提出的相应防治措施。研究结果表明,部分典型块体稳定性系数低于安全系数1.2,且受软弱夹层影响,边坡坡脚处有较大的剪应力及横向应力;钢栈桥最大拉应力区域较小,值均在1 MPa左右。在此基础上,提出清除块体、排水、锚喷、避让等多项综合措施,形成了具有山地旅游景区特色的防治对策。     

Extension of numerical manifold method for coupled fluid flow and fracturing problems

The present study extends the numerical manifold method to include the hydro‐mechanical model to investigate the effect of water flow in fractures on the stability of rock structures, particularly slopes. The proposed flow model is verified by a simple 2‐D flow problem in a homogeneous aquifer. Combining the water flow model with the earlier developed fracture evolution technique, the entire failure process of the rock slope due to a heavy rain is simulated. The results illustrate that the developed numerical manifold method can not only determine the trigger factor of the crack initiation but also model the failure processes related to crack initiation, propagation, block formation, detachment and sliding due to the water effect successfully. Copyright © 2014 John Wiley & Sons, Ltd.     

岩质边坡关键块体的搜索方法及工程应用

工程边坡开挖所揭露的某些结构面组合块体在破坏原有静力平衡状态后,进行应力重新分配,进而块体会发生失稳、滑动等变形,甚至影响到整个边坡发生破坏,因此,结构面组合块体的稳定性是决定岩质边坡稳定的重要因素。本文通过对某工程开挖边坡地形和结构面三维实体模型的建立,实现了边坡结构面与开挖地形实体模型在AutoCAD平台上的可视化操作,剖切不同位置的二维图形预测分析了边坡开挖后可能存在的结构面组合块体,采用块体计算程序(Swegde)验证关键块体并进行稳定性评价。结果表明:三维实体模型及剖切技术与块体计算方法的结合,易于搜索关键块体。事实证明,该方法操作简便,计算结果准确,搜索方法具备可行性。     

三维极限平衡理论及其在块体稳定分析中的应用

岩体与土体失稳的滑稳面形状大多具有三维特征，用二维极限平衡理论难以得到与实际相应的分析结果。通过将滑动块体离散为一系列柱体，对每一条柱体，分析作用于条柱上的作用力和力矩平衡条件，提出块体稳定分析的三维极限平衡分析方法。该方法不需要对滑裂面作形状的假定，运用迭代解法，可以方便地求出可能滑动块体稳定系数。应用三维极限平衡分析方法对某电站坝基深层滑动块体的稳定性进行了分析，得到了一些有益的结论。     

工程荷载作用下缓倾角反倾似层状岩质边坡变形稳定性分析

在反倾层状边坡的破坏机制和稳定性分析方面,由于其稳定性一般较好,系统深入地研究其破坏机制和稳定性的反而不多。以火山岩地层多次火山喷发旋回形成的缓倾角反倾似层状岩质边坡为研究对象,利用有限元分析其位移矢量图,揭示边坡的变形破坏机制和稳定性控制要素,利用极限平衡法、矢量和法,评价其稳定性,利用强度折减法分析塑性区的扩展规律,揭示滑动面发展的时间空间规律,结果表明,（1）类似层状反倾岩质边坡的潜在破坏模式为剪切–张拉破坏,滑面形态表现为近似折线状：顺坡向穿过凝灰岩夹层和强风化岩体,后缘通过陡倾结构面;（2）极限平衡法、矢量和法的边坡稳定性综合评价表明边坡浅层稳定性不满足工程稳定性要求,深层稳定性满足工程稳定性要求,且三维矢量和安全系数大于二维结果,是三维效应造成;（3）塑性区扩展揭示滑面的空间发展序列为滑面4、5、3。文中的技术路线和分析方案可用于缓倾角反倾层状岩质边坡稳定性评价。     

复杂边坡稳定性的二维与三维分析

目前,在边坡稳定性分析中广泛地采用二维极限平衡分析方法进行研究。但是对于地形、地层、地下水、岩体结构等条件复杂的边坡,仅用二维极限平衡分析方法进行研究是不够的,二维分析忽略了边坡的三维效应,而复杂边坡往往受三维效应影响大。但至今三维极限平衡方法还不是很完善。因此,本文结合一工程实例,采用二维与三维极限平衡分析相结合的方法对其边坡的稳定性进行了分析。研究结果表明,对于复杂边坡,应用二维和三维稳定性分析相结合的方法进行研究是一种较为恰当的选择。     

裂隙岩体三维柔度张量的数值试验方法

在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。     

某反倾页岩边坡破坏面确定及其稳定性分析

破坏面确定是边坡稳定性分析的基础,存在各级滑动面。不同结构类型边坡,其确定方法也随之不同。对于反倾软岩边坡,不能通过不连续面空间展布分析确定其破坏面。联合FLAC3D和极限平衡方法分析具有节理块体切割破坏模式的某反倾页岩边坡稳定性。在野外调查基础上分析边坡的变形破坏机制,应用FLAC3D研究其应力、应变等值线及相应增量等值线图确定边坡潜在最危险滑动面和次级滑动面,计算其稳定性系数。在防护设计中考虑次级滑动面,针对边坡危险区域分析其防护效果。应用强度折减计算两危险区域稳定性系数,表明防护后边坡整体稳定性较好。该方法对反倾软岩边坡的稳定性分析有一定的借鉴价值,在防护设计中考虑次级滑动面的影响具有一定的实际指导意义。     

Assessment of discontinuous rock slope stability with block theory and numerical modeling: a case study for the South Pars Gas Complex,Assalouyeh, Iran

In this study, a geotechnical model has been used to analyze the stability of a discontinuous rock slope. The main idea behind block theory is that it disregards many different combinations of discontinuities and directly identifies and considers critical rock blocks known as “key blocks”. The rock slope used as a case study herein is situated in the sixth phase of the gas flare site of the South Pars Gas Complex, Assalouyeh, Iran. In order to analyze the stability of discontinuous rock slopes, geotechnical modeling which was divided into geometrical sub-modeling and mechanical sub-modeling has been utilized. This model has been established upon the KGM (key-group method) algorithm which was based on the limit equilibrium method and block theory and prepared and coded by the Mathematica software. According to the results of the stability analysis, the analyzed slope was determined to be in the category of “needs attention,” and the security level, calculated through the FORM (first-order reliability method) analysis, was estimated to be 1.16. In order to verify the model, the results obtained from the model were compared with those of the UDEC software, which is a numerical method based on distinct components. As a conclusion, it was determined that the results of the model agreed well with those of the numerical method.     

岩质古滑坡体稳定性研究--以宝泉抽水蓄能电站龟山古滑坡体为例

龟山古滑坡体体积约2100万立方米,其稳定性直接影响电站的运行安全。首先分析了古滑坡体的边界条件和滑裂带力学参数取值,并指出岩质古滑坡稳定性分析中应注意的问题,然后分别使用极限平衡法和三维Flac方法分析了龟山古滑坡体的稳定性。最后根据稳定性分析结果提出了对龟山古滑坡体的处理建议。     

A generalized procedure to identify three‐dimensional rock blocks around complex excavations

This paper presents a generalized procedure for the identification of rock blocks formed by finite‐sized fractures around complex excavations. It was assumed that the study domain could be partitioned into a finite number of subdomains, where each either was, or could be, approximated by a convex polyhedron, and the fractures were finite in size and disc shaped and were defined using the location of the disc center, orientation, radius, cohesion coefficient, and friction angle. These may be either deterministic fractures obtained from a field survey or random fractures generated by stochastic modeling. In addition, the rock mass could be heterogeneous; i.e. the rock matrix and individual fractures could have different parameters in different parts. The procedure included: (1) partitioning of the model domain into convex subdomains; (2) removing noncontributive fractures. A fracture was deemed contributive when it played a part in block formation; i.e. it formed at least one surface with some of the blocks; (3) decomposing the subdomains into element blocks with fractures; (4) restoring the infinite fractures to finite discs; and (5) assembling the modeling domain. Our procedure facilitates robust computational programming, and is flexible in dealing with the problem of a complex study domain and with rock heterogeneity. A computer code was developed based on the algorithm developed in this study. The algorithm and computer program were verified using an analytical method, and were used to solve the problem of block prediction around the underground powerhouse of the Three Gorges Project. Copyright © 2008 John Wiley & Sons, Ltd.     

佛子岭抽水蓄能水电站地下厂房施工开挖过程的FLAC3D数值模拟

选取佛子岭抽水蓄能水电站地下厂房区,采用三维快速拉格朗日法（FLAC3D）模拟施工开挖过程,研究了洞室群围岩的开挖变形形态和应力状态,分析了围岩和调压井高边坡在自重荷载作用下的开挖稳定性。通过对地下厂房洞室群区的加固处理,分析了围岩在加固后的力学特性。利用FLAC3D程序的Ubiquitous模型,引入了一组主要节理裂隙,分析了此组节理裂隙对地下洞室群围岩的开挖变形及整体稳定性的影响,并与无节理裂隙的数值模拟结果进行对比,综合评价了节理裂隙对洞室群围岩稳定性的影响。     

3D stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method

A convenient approach to performing stability analysis of concrete gravity dams is the so-called two-dimensional “gravity method.” However, concrete gravity dams located in valleys with sloped rock foundation abutments behave as three-dimensional (3D) structures and are often able to share compressive and shear loads between adjacent monoliths, especially when shear keys are present. A general 3D limit equilibrium method was developed in this study to compute global sliding safety factors (SSF_g) by considering sequential load redistribution among adjacent monoliths when individual monoliths have mobilized their sliding strength. Two validation examples of the sliding safety assessment of existing dams are presented to illustrate the accuracy and efficiency of the proposed approach compared to that of the full 3D numerical analyses conducted using the distinct element method. It is shown that gravity dams may be formed by individual monoliths on sloped rock foundations that will slide if considered as isolated structures but will constitute a stable assembly when the load-sharing capabilities of monoliths are recognized in the analysis.