Stability Analysis and the Stabilisation of Flexural Toppling Failure

Flexural toppling is a mode of failure that may occur in a wide range of layered rock strata in both rock slopes and large underground excavations. Whenever rock mass is composed of a set of parallel discontinuities dipping steeply against the excavated face plane, the rock mass will have the potential of flexural toppling failure as well. In such cases, the rock mass behaves like inclined superimposed cantilever beams that bend under their own weight while transferring the load to the underlying strata. If the bending stress exceeds the rock column’s tensile strength, flexural toppling failure will be initiated. Since the rock columns are “statically indeterminate,” thus, their factors of safety may not be determined solely by equations of equilibrium. The paper describes an analytical model with a sequence of inclined superimposed cantilever rock columns with a potential of flexural topping failure. The model is based on the principle of compatibility equations and leads to a new method by which the magnitudes and points of application of intercolumn forces are determined. On the basis of the proposed model, a safety factor for each rock column can be computed independently. Hence, every rock column will have a unique factor of safety. The least factor of safety that exists in any rock column is selected as the rock mass representative safety factor based on which simple equations are proposed for a conservative rock mass stability analysis and design. As a result, some new relations are established in order to design the length, cross-sectional area and pattern of fully grouted rock bolts for the stabilisation of such rock mass. Finally, the newly proposed equations are compared with the results of existing experimental flexural toppling failure models (base friction and centrifuge tests) for further verification.     

坡后土体推力作用下反倾节理岩质边坡次生倾倒机理分析

次生倾倒破坏是层状反倾岩质边坡的一种主要破坏模式,极限平衡理论是分析倾倒破坏的常用方法,研究反倾节理岩质边坡次生倾倒破坏机理对边坡工程众多的西南山区基础设施建设具有重要的工程指导意义。在Goodman和Bray块体倾倒破坏极限平衡分析方法的基础上,建立了考虑地下水压力、节理连通率、岩体黏聚力等影响因素的反倾岩质边坡在坡后土体推力作用下的次生倾倒地质力学模型,提出了坡后土体推力作用下的反倾节理岩质边坡次生倾倒破坏的解析分析方法,推导出了边坡各岩层下推力的解析表达式,提出了边坡倾倒破坏的综合安全系数,并编写了对应的matlab计算程序,为该类边坡的设计和加固提供了理论依据。通过算例分析表明,与单纯岩质边坡块体倾倒破坏相比,该类边坡次生倾倒破坏形式的特点是破坏基准面以上岩层自上而下依次分为滑移区、倾倒区和稳定区3个部分;地下水压力、节理连通率、底裂面岩体黏聚力对各岩层的破坏形式、稳定安全系数大小都具有明显影响,尤其是在坡体中下部及坡脚部分最为敏感;而各岩层稳定安全系数最小的区域集中于边坡中上部。     

Investigation of rainfall-induced failure processes and characteristics of cataclinal and anaclinal slopes using physical models

In this study, two types of small-scale physical modeling tests have considered the impact of the infiltration of rainfall and groundwater level in order to investigate the processes involved in rock slope deformation and failure. The study conducted the physical tests under controlled conditions of groundwater level with rock block shape for two rock slope types (cataclinal and anaclinal slopes). Observations obtained during each stage of deformation and failure were used to explain how gravity deformation varies with groundwater conditions on cataclinal and anaclinal slopes, and infer how rainfall and groundwater influence slope failure. Our results indicate that groundwater level is a crucial factor in the deformation failure of slopes. The failure mechanisms of cataclinal slopes differ considerably from those of anaclinal slopes. The infiltration of surface water and groundwater can have a significant influence on rock layer deformation and the speed of failure. Different shapes of rock block have two toppling types of rock slope, the spherical rock model relatively close to flexural toppling type and the triangular rock model relatively similar to block flexural toppling type, respectively. Details of the failure characteristics of cataclinal and anaclinal slope models are discussed in this paper.     

Stability Analysis of Rock Slopes Against Block-Flexure Toppling Failure

Block-flexure is the most common type of toppling failure in rock slopes. In this case, some rock blocks fail due to tensile bending stresses and some overturn under their own weights. In this paper, first, a literature review of toppling failures is summarized. Then, a theoretical model is proposed for rock slopes with a potential for block-flexure toppling instability. Next, a new analytical approach is presented for the stability analysis of such slopes. Finally, a special computer code is developed for a quick stability assessment of the failures based on the proposed method. This code receives the rock slope parameters from the user as the input data and predicts its stability, along with the corresponding factor of safety against the failure, as the output. In addition, two case studies are used for practical verification of the proposed approach and the corresponding computer code as well.     

雅砻江上游互层斜坡倾倒变形破坏机制与演化

以甲西倾倒体为典型实例,从赋存环境、发育特征、形成条件等基础层面上分析雅砻江上游互层斜坡倾倒变形破坏机制及演化过程。研究表明:区内大型倾倒体是斜坡岩体在叠加有残余构造应力的自重应力场中长期演化的产物,软硬相间的岩性组合、陡倾内的岸坡结构,加之垂直层面密集节理的切割是斜坡发生倾倒变形的控制性因素;斜坡倾倒是受节理面和层面控制的复合倾倒模式,即:硬岩发生块状-弯曲倾倒,而软岩发生弯曲倾倒;受河谷演化控制,斜坡变形破坏主要经历了4个演化阶段:卸荷回弹陡倾面拉裂阶段,初始变形阶段,板梁根部折断、剪切面贯通阶段以及破坏阶段,并最终转化为蠕滑-拉裂模式形成滑坡。该滑动面受倾向坡外破裂面控制,而并非沿最大弯折带发育。     

反倾软硬互层岩质边坡倾倒变形破坏机理与影响因素研究

倾倒变形常见于反倾结构边坡,特别在具有软硬互层结构边坡中,甚至可发育为深度上百米的大型滑坡.为进一步探明此类反倾边坡倾倒变形的破坏机制,以及边坡形态结构及岩体力学参数等因素的影响规律,以离心模型试验为原型,结合离散元数值模拟,分析了倾倒变形的形成过程以及在外界扰动下的破坏机制.并通过单因素分析法、正交设计法等,研究了多...     

基于底摩擦试验的硬岩岩质边坡变形过程及破坏机制研究

针对不同倾向、不同倾角条件下,边坡变形破坏特征不同但缺乏相互对比分析研究的现状,在充分考虑硬岩岩质边坡变形破坏特征的基础上,配制硬岩相似材料,采用底摩擦试验方法,分析不同倾向、不同倾角边坡变形破坏模式,并借助PIVlab技术进行分析。结果表明:顺倾和反倾边坡变形破坏模式和破坏范围有明显区别。在45°坡度条件下,当顺倾边坡倾角由30°→45°→60°→80°转换时,变形破坏模式由滑移-拉裂→轻微滑移-弯曲（或滑移-剪切）→未有明显变形（整体稳定）→浅表部倾倒-拉裂逐渐演化。在45°坡度、反倾边坡条件下,变形破坏模式由岩层倾角30°和45°条件下无明显变形,逐渐向60°和80°条件下的倾倒-拉裂演化。当岩层倾角较陡时,反倾边坡破坏范围相对顺倾边坡更大,倾倒弯曲转折端更深。PIVlab结果反映出不同结构边坡条件下,不同位置的速度和位移矢量特征不同,且与宏观观察结果相吻合。研究成果能够为同类边坡的稳定性评价和治理设计提供一定参考。     

Toppling and stabilization of the intake slope for the Fengtan Hydropower Station enlargement project, Mid-South China

The intake slope for the Fengtan Hydropower Station enlargement project is composed of thickly bedded sedimentary rock. During excavation of the intake slope and tunnels, toppling was observed in the rock masses of the intake slope. Research was conducted to study the engineering geological conditions and the deformation characteristics of the slope during excavation. The in situ monitoring data and possible causes for toppling were analyzed. A method for analyzing monitoring data was proposed, which can be used to calculate the depth and rotation angle of block toppling. The monitoring results showed that toppling occurred only at a shallow depth, and induced local instability of the slope. Deformation had been controlled and the slope tended to be stable after reinforcement. Through this case study, it can be seen that the stability of the slope and underground openings during and after excavation is variable, especially when the loading conditions and topography are changed. A proper construction sequence is essential, i.e., excavation from the inside toward the free slope surface; excavating the slope above the tunnel after the tunnel lining is in place. This is particularly important for the excavation of multiple tunnels at the slope toe.     

岩体结构稳定分析原理和方法

工程实践表明,在边坡、地基或地下工程岩体中几组地质结构面和临空面的组合往往构成可能失稳的岩石结构体、存在向临空面运动的可能性、影响到工程岩体的稳定性。这时必须针对这种可能失稳的结构体进行分析,采取必要的加固或处理。关于岩石结构体的稳定分析,文献中已有一些报导,但偏重于图解和计算方法、一般是针对特定单一块体的解析,仅应用于边坡工程。     

斜坡倾倒变形的工程地质分析

近10年来,在山区,尤其是西部山区的工程建设和灾害防治实践中,我们发现越来越多的以“倾倒”为特征的岩质边坡变形破坏和稳定性问题,其出现的频度和造成的危害大有比肩“滑动”破坏这一边坡失稳的传统主题,成为困扰地质工程师和岩石力学工作者的又一难题。这类问题之所以难,是因为建立在以“滑动”为基础的传统边坡稳定性分析方法不再适用这类边坡。本文在大量工程实例的基础上,分析了边坡倾倒变形和破坏的基本特征,从“倾倒”变形破坏的地质过程和变形稳定性分析的基本理念出发,建立了描述倾倒边坡不同变形程度的工程地质模型,这个模型将倾倒边坡分为倾倒-坠覆、倾倒-错动、倾倒-张裂、倾倒-松弛4个区,分别对应不同的变形程度和稳定性状况,提出了各个区的具体特征和定性指标与量化指标相结合的描述指标体系,从而将倾倒的地质显现、力学机理和变形稳定性有机统一,实现了对倾倒边坡稳定性的工程地质评价。与传统的“滑动”问题不同的是,本文没有强调对这类问题采用强度稳定性的评价思路,而建议采用变形稳定性评价的理念,这似乎更适合倾倒变形这类问题的分析和评价。     

Modelling of Progressive and Instantaneous Failures of Foliated Rock Slopes

Summary Mechanisms of flexural toppling failure of slopes in foliated rock masses are investigated both experimentally by testing small scaled models in a centrifuge and theoretically by using a limiting equilibrium model and a finite element model based on the Cosserat theory. Both theoretical models include bending moments of rock layers in their formulation. Two main failure mechanisms are observed: (1) instantaneous failure involving a large volume of failed material and (2) progressive failure where the fracture initially localises near the toe region and then progresses further into the rock mass with increasing load. These two mechanisms of slope failure are observed to be controlled by the magnitude of the joint friction angle. The joint friction angles of about 20° and above are most likely to cause instantaneous failure while the lesser friction angles result in a progressive failure. Joint cohesion is not found to have a similar effect on the failure mechanisms, provided that it is low enough to allow sliding between the rock layers – a prerequisite for flexural toppling.     

Dynamic and Static Stability Assessment of Rock Slopes Against Wedge Failures

Summary ?The stability of slopes during and after excavation is always of great concern in the field of rock engineering. One of the structurally controlled modes of failure in jointed rock slopes is wedge failure. The limiting equilibrium methods for slopes under various conditions against wedge failure have been previously proposed by several investigators. However, these methods do not involve dynamic assessments and have not yet been validated by experimental results. In this paper, the tests performed on model wedges under static and dynamic loading conditions are described and the existing limiting equilibrium methods are extended to take into account dynamic effects. The applicability and validity of the presented method are checked through model tests carried out under well controlled conditions and by actual cases studied by the authors, both in Turkey and Japan.     

Deep-seated toppling deformations of rock slopes in western China

Toppling is the foremost failure pattern of anaclinal rock slopes, and deep-seated toppling deformations (DSTDs) are common on high anaclinal slopes on the sides of gorges in western China. The DSTDs can develop to depths of more than 200 m, and may show distinct signs of zonal failure. Many DSTDs undergo transformation to large landslides involving rock volumes of more than 10⁶ m³. However, the conditions for the formation and the basic evolving processes of DSTDs remain unclear. This study seeks to develop an inventory to classify the distribution, and the conditioning factors which govern the formation and deformation modes of DSTDs in western China and to analyze the effect of the geological and geomorphological variables on the toppling intensities. To this end, forty-nine DSTDs were analyzed. The results indicate that DSTDs in western China are commonly distributed along large deeply incised rivers in the southeastern margin of the Qinghai-Tibet plateau. The steep-dip anaclinal metamorphic soft or soft-hard-interbedded strata with near parallel strikes in the river channel, V-shaped deeply incised river channels, and convex slopes are favorable conditions for the formation of DSTDs in these settings. The dip angle, the gradient, and the height of most slopes which develop DSTDs are 60–90°, 30–50°, and 200–800 m, respectively. There is a highly positive relationship between the depth of toppling and the height of the slope. The toppled rock masses can be classed as extremely intense, intense, moderate, and weak toppling zones characterized by complete block detachment, tensile-shear fracture, tensile fracture, and reverse slip along foliations, respectively. Each zone corresponds to a specific range of the dip angle of the toppled strata, the aperture of the tensile cracks, the P-wave velocity, the state of rock weathering, and the degree of unloading. The extremely intense and the intense toppling zones tend to evolve into sliding failures. Overall, 94% of the DSTDs were derived from flexural toppling and 33% have developed into large landslides.

     

坡顶荷载作用下岩质边坡弯曲倾倒破坏分析

车辆、坡顶堆载等造成的坡顶荷载是影响边坡稳定性的一个重要因素。首先,基于叠合悬臂梁模型和极限平衡理论,建立了坡顶荷载作用下岩质反倾边坡的力学分析模型,推导了坡顶荷载作用下边坡的剩余倾倒力和剩余滑移力计算公式,给出了岩层破坏模式判别条件,并通过大型数学分析软件Matlab将分析方法程序化;然后,通过与离散元模拟结果进行对比分析,验证了所提分析模型的准确性;最后,基于所提分析方法,进行了不同参数的敏感性分析。研究结果表明,坡顶荷载对岩层剩余力的影响较大,但对岩层破坏模式的影响不大;对边坡稳定性较为敏感的切坡角度为50°和岩层倾角为58°,当小于该值时,边坡稳定性将显著提高;层间黏聚力对自重边坡稳定性影响较大;数值模拟与理论分析得到的安全系数较为一致,验证了考虑坡顶荷载作用下弯曲倾倒破坏分析理论解的正确性,可为类似工程稳定性分析提供参考。     

A study of the mechanism of flexural toppling failure of rock slopes

Summary The mechanism of flexural toppling failure of jointed rock slopes has been investigated through a series of centrifuge experiments conducted on models manufactured from two types of materials (brittle: a sand-gypsum mixture; and ductile: fibre-cement sheeting). The basal failure plane observed in the centrifuge models, has been found to emanate from the toe of the slope, and orient at an angle of 12 to 20° upward from the normal to the discontinuities. A theoretical model based on a limiting equilibrium approach (Aydan and Kawamoto, 1992) has been adopted to analyse the centrifuge test data. After calibration, the model was found to accurately predict the failure load for all the tests reported in this study. Using this model, a set of charts has been prepared to assist with the analysis of slopes susceptible to flexural toppling.     

SMR geomechanics and kinematic analysis near Rasulpur,Fatehpur Sikri,Uttar Pradesh

Slope stability of mine slopes is often associated with safety and economics during excavation. Sandstone is excavated from Rasulpur area of Fatehpur Sikri in Uttar Pradesh for the purpose of crushed, decorative and dimension stones. In the present paper an attempt has been made to characterize the rock slope faces into different stability classes. Characterization is based on geological and geotechnical parameters recorded on the outcrop during field investigation and supplemented by geomechanical properties by the laboratory test for strength of the rock intact. SMR Geomechanics classification is used to identify the stability class and remedial measures are also suggested to reduce any possible hazard. Kinematic analysis of slope was also investigated to determine the probability of any possible structurally controlled failure. On the basis of SMR Geomechanics calculations slope under investigation lies under good stability class i.e. 2a and 2b. Installation of nets during excavation can be done and for better safety spot and systematic rock bolting can be done. Kinematic study reveals that toppling failures may occur, special care must be given to the joint set which can trigger toppling failure.     

含软弱夹层岩质边坡稳定性研究现状及发展趋势

含软弱夹层岩质边坡在自然环境和工程实践中都比较常见，稳定性差，边坡失稳产生了大量的滑坡灾害，造成大量人员伤亡和经济损失。因此，含软弱夹层岩质边坡稳定性研究一直是工程地质和岩土工程领域的研究重点之一。在收集整理国内外相关资料的基础上，从自重工况、开挖工况、暴雨和蓄水工况、地震工况方面总结了目前含软弱夹层岩质边坡稳定性的研究现状及进展，取得如下主要认识:(1)软弱夹层对岩质边坡稳定性有显著不利影响，含软弱夹层岩质边坡的稳定性比均质岩质边坡、不含软弱夹层的层状岩质边坡都差；(2)含软弱夹层岩质边坡的稳定性系数、变形特征和破坏模式与软弱夹层的含水状态、抗剪强度、倾角、厚度、间距、层数和边坡坡度有关；(3)开挖容易诱发坡体沿软弱夹层滑坡，含软弱夹层岩质边坡开挖后需要及时支护；(4)爆破层裂效应改变了软弱夹层与围岩的接触状态，减小了它们之间的凝聚力和摩擦力，导致边坡稳定性降低；(5)暴雨和蓄水都不利于含软弱夹层岩质边坡稳定；(6)岩质边坡地震动力响应和变形破坏特征受软弱夹层参数(厚度、倾角、含水状态)、地震波特性(地震波的类型、幅值、频率、激振方向)和边坡结构(顺层或反倾)共同影响；(7)在软弱夹层对水平向动力响应的放大或减弱作用及厚层软弱夹层的消能减震作用方面仍然存在不同观点。在此基础上，分析了研究方法的优缺点，指出当前含软弱夹层岩质边坡稳定性研究存在的问题。最后，针对该领域的研究现状，提出了未来的研究重点和方向，主要包括:含多层软弱夹层岩质边坡的渐进性变形破坏过程和稳定性；全面深入研究单因素作用(开挖卸荷、爆破、地震、暴雨、库水位变化、地下水等)对含软弱夹层岩质边坡稳定性的影响机制；多因素耦合作用下含软弱夹层岩质边坡稳定性；支挡结构体系对含多层软弱夹层高陡岩质边坡的加固机制。     

岩质边坡滑动-倾倒组合破坏模式稳定性分析

在岩质边坡滑动-倾倒组合破坏地质力学模型的基础上,采用改进的传递系数法,提出了岩质边坡滑动-倾倒组合破坏的解析分析方法,并对初始下滑推力及岩块底部的凝聚力进行敏感性分析。与传递系数法相似,将边坡体几何力学参数及潜在倾倒岩块编号作为变量,使得每个倾倒岩块的稳定性分析具有统一的表达式,并易于采用Microsoft excel进行程序化分析。分析结果表明：岩块底面的凝聚力对下部潜在倾倒区域的破坏模式影响较大,随着岩块底面凝聚力的增加,潜在倾倒区域发生倾倒破坏的块体呈逐渐增加的趋势,而发生滑动破坏的块体则明显较少,岩块底面倾角对坡体整体稳定性影响较大;随着岩块底面倾角的增大,整个坡体的稳定性逐渐降低。     

危岩主控结构面变形破坏的扩展有限元法模拟分析

危岩是三峡库区典型的地质灾害类型之一,主要分为坠落式危岩和倾倒式危岩两种失稳形式,危岩主控结构面受荷断裂扩展是其发育成灾的关键核心。将危岩主控结构面类比为宏观裂纹,运用扩展有限元方法（XFEM）,求解结构面扩展过程的移动非连续问题,探索在荷载作用下危岩主控结构面的断裂扩展行为,以重庆万州太白岩危岩为例,考虑岩石的抗拉强度、主控结构面的几何位置与倾角对危岩的变形破坏模式与稳定性的影响。结果表明,随着岩石抗拉强度的降低,危岩的稳定性程度降低;随着主控结构面倾角的减小,危岩的稳定性程度提高,同时结构面开裂路径也明显改变;危岩体两种失稳模式的破坏机制都为拉剪机制,相对于倾倒式危岩,同等条件下坠落式危岩的稳定性更差。     

基于断距-层厚特征统计的反倾边坡S型破坏演化数值模拟

三峡库区巫峡龚家坊至独龙一带存在大量反倾不稳定边坡,多具有薄厚互层和软硬相间的岩体结构,边坡高度普遍在500 m以上。现场调查表明独龙7#边坡(D7)具有明显的“S”型柔性变形现象。为探明反倾边坡“S”型变形破坏机制,以独龙段反倾边坡为依托,从边坡的岩体结构调查、破坏模式概化、监测资料分析、变形破坏模拟等角度对软硬互层反倾高边坡的破坏机制进行研究。通过现场调查与无人机倾斜摄影,建立了边坡的三维模型,进而提取航拍数据,获得了岩层厚度、断距等的统计规律;基于断距-层厚统计规律,通过离散元软件UDEC对库水软化作用下D7边坡“S”型变形机理进行了模拟分析。研究表明:(1)独龙段边坡普遍具有陡倾内逆向层状结构,发育3组结构面,岩体被切割成块;(2)根据软岩占比,可将独龙段边坡分为2类:A类边坡软岩层占约20%,断距/层厚值分布于0.7~2.8区间,并集中于1.2~1.8;B类边坡软岩层占比约10%,断距/层厚值分布于0.5~3.3区间,并集中于0.6~1.5;A类边坡岩体长细比更大;(3)长期监测表明,边坡在库水位低值时位移量大,D7边坡位移持续增大,潜在整体失稳;(4)离散元模拟表明,边坡破裂面自坡脚延伸,中部硬岩区起到支撑并抑制上部变形的作用,边坡硬岩区与软岩区的差异变形以及变形体不同部位惯性的差异是导致岩层“S”型变形的主因,最终分别过“S”形岩层两个反弯点形成两条剪切带,形成自下而上的柔性弯曲-滑移型破坏。(5)断距-层厚比(S/T)可影响边坡破坏模式,比值越大,反折变形区与坡脚垮塌区越小,当S/T≥2时,S型变形不再发育。