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.     

层状边坡倾倒变形多级折断面分布深度计算模型

针对反倾层状岩质斜坡倾倒变形折断面空间展布缺乏定量判断的问题,以地质原型和变形机制分析为基础,考虑岩层自重、上覆岩层盖重、侧向压力、岩层间的摩擦力等作用,提出了岩板倾倒折断的独立悬臂梁模型和独立简支梁模型。采用板梁的最大拉应力破坏准则,推导出了倾倒变形各阶段岩层的临界折断深度公式。利用地质原型对推导的公式进行了验证,并通过离心试验获取了倾倒变形各阶段的坡形参数,对边坡各阶段折断深度进行了定量评价。研究表明：理论模型可计算倾倒变形层间剪切错动、弱倾倒破坏、强倾倒破坏等各阶段岩层的折断长度;岩层折断长度与岩层分布高程、拉应力、岩梁自身重度呈负相关,与岩层内摩擦角、岩层厚度、抗拉强度呈正相关;根据倾倒变形各阶段力学参数,计算倾倒体各级折断面分布位置,结果与地质原型和离心试验结果吻合。该研究成果对倾倒变形边坡稳定性评价具有一定的理论和实际意义。     

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.     

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.     

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...     

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。     

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。     

黄河上游某倾倒体的时效变形研究

黄河上游某巨型倾倒体主要由反倾层状砂岩和板岩相间分布构成,砂岩层以倾倒拉裂为主,板岩层以弯曲变形为主,两种不同的时效变形组合导致整个倾倒体的演化具有长期性、累进性和阶段性的特征。基于岩体组合模式和变形破坏表现形式,研究两种岩层的时效变形空间分布特征,总结整个坡体的时空演化规律,并探究其成因机理,论述岩体组合模式、岩体结构、卸荷裂隙以及地形地貌等因素对倾倒体演化的影响。     

层状岩石边坡倾倒破坏过程的数值流形方法模拟

层状岩石边坡的倾倒破坏是岩石边坡失稳破坏的主要形式之一.本文利用数值流形方法对一层状岩石边坡的倾倒破坏过程进行了模拟.模拟结果表明:在不考虑块体间粘结力的情况下,块体间的摩擦角决定着岩石边坡的稳定性.随着摩擦角的增加,块体间的摩擦系数增大,岩石边坡的稳定性增强,并出现相应的滑动区、倾倒区和稳定区.模拟结果与相应的理论预测结果相吻合.     

上硬下软反倾边坡开挖变形响应的物理模拟

现有上硬下软边坡的研究大都集中在压缩挤出变形的近水平泥岩、页岩基座型边坡变形演化过程,针对倾倒变形的板岩基座型边坡开挖响应研究甚少,本文以西藏玉曲河某水电站厂址边坡为研究对象,根据现场地质调查建立符合坡体实际情况的地质结构模型,采用物理试验的方法模拟原型边坡开挖。通过试验揭示上硬下软反倾边坡在开挖条件下的变形响应特征及破坏模式。研究结果表明:（1）开挖条件下上硬下软型边坡变形破坏过程分为a）下部软岩倾倒弯曲加剧;b）软岩倾倒折断,上部卸荷硬岩沿已有裂隙剪切;c）倾倒软岩滑移,卸荷硬岩剪断岩性分界部位,折断面贯通3个阶段。其变形破坏模式为下部软岩倾倒—上部硬岩剪断组合滑移型破坏;（2）开挖强倾倒区岩体会使下部软岩迅速失稳并促使上部硬岩剪切破坏;开挖引起的反倾上硬下软边坡大变形在短时间内完成,前期变形和能量积累是一个较长的过程;（3）开挖时需避免对坡脚倾倒岩体“大开挖”施工。     

Terrestrial laser scanning for rockfall stability analysis in the cultural heritage site of Pitigliano (Italy)

Traditional surveying methods are often not sufficient to achieve a complete geomechanical characterization of the rock mass, to analyze the instability mechanisms threatening the cultural heritage of hilltop historic towns. In Pitigliano (Tuscany, Central Italy), terrestrial laser scanning was employed complementarily to conventional geomechanical techniques. The overall 3D survey of the exposed surfaces was combined with scanlines of the inner walls of the subterranean cavities running underneath the historic centre. The rock mass discontinuities geometry was extracted, and the most critical instability mechanisms were mapped, with particular interest in the potential impacts on the ancient buildings located along the cliff edge. The geomechanical analysis of the surveyed joint sets confirmed a structural control on the cliff morphology by two main joint sets. Thanks to the laser scanner-based kinematic analysis, flexural toppling and wedge failure were found as the main hazardous instability mechanisms in Pitigliano. Finally, the conservation criticalities were identified and a pilot monitoring system was installed in a sector highly susceptible to block detachment.     

逆层岩质边坡地震动力破坏过程FLAC/PFC耦合数值模拟分析

建立含有非贯通层面和正交次级节理的逆层岩质边坡FLAC/PFC2D耦合计算模型,进行地震动力破坏过程模拟试验,研究了逆层岩质边坡地震动力破坏机理。试验结果证明,在地震动力破坏过程中,边坡内部层面主要产生剪切破坏,少量张拉破坏集中于逆层边坡顶部位置并且总是发生在坡体已经产生动力失稳之后,因此层面的抗拉强度并不影响逆层边坡的地震动力稳定性。坡顶正交次级节理只能产生张拉破坏,形成宏观的岩层倾倒趋势,而坡底的正交次级节理既会产生张拉破坏,也会产生剪切破坏,破坏面滑动趋势明显。动力响应坡顶放大效应和破坏面发育位置深度导致坡顶岩体的张拉倾倒早于坡底岩体的剪切滑动,与逆层边坡静力倾倒破坏顺序相反。     

The stability of slopes and underground openings against flexural toppling and their stabilisation

Summary The stability of slopes and underground openings during and after excavation is always of great concern in the field of rock engineering. Depending upon the geologic conditions and material properties of rock and discontinuities, and the geometry of excavations and topography, various kinds of instabilities are likely to be encountered. One of these is the flexural toppling failure which has become to be known recently. A stability analysis method for slopes and underground openings under various loading conditions against the flexural toppling failure is proposed. In addition, for the stabilisation of structures, a method is suggested to take into account the reinforcement effect of fully grouted rockbolts. The applicability and validity of the proposed method is checked through model tests carried out in laboratory under well controlled conditions.     

节理网络有限元在倾倒斜坡稳定分析中的应用

节理网络有限元是指具有节理网络模拟功能的有限元,它不但能将野外节理统计特征直接输入到模型中,同时允许节理按一定的破坏准则产生屈服,从而较好地模拟边坡的实际结构及破坏特征。论述了倾倒变形边坡的分析方法及存在的问题,介绍了节理网络有限元的功能及参数输入,说明了其在倾倒变形边坡应用中的优势,并以黄河上游茨哈峡电站Ⅰ号倾倒体为例,计算了该倾倒边坡的稳定性及破坏趋势,结果表明,节理网络有限元是倾倒变形边坡稳定分析的一种有效、可靠的方法。     

强度变化对崩坡积体堆积机制及稳定性影响研究

利用颗粒流PFC2D建立了岩土体物理模型,在此基础上设计了均以物理模型折减计算初始模型和以前一折减计算结果为下次折减计算初始模型两类计算条件,每一类又设计了只对凝聚力折减、仅对内摩擦角折减、强度参数同时折减3种计算方案,每种计算方案又包含折减1.0、0.50、0.10、0.01、0.0倍等5个计算工况。经对坡面演替、监测点x方向速度变化曲线等计算结果的对比分析发现：凝聚力对于岩土体的直立特性起控制作用,破坏模式多为崩塌倾倒模式;内摩擦角对于稳定坡角具有重要影响;强度参数同时衰减时,强度参数弱化幅度较大情况下岩土体呈散体物质破坏模式,为滑移渐进破坏模式,其中凝聚力弱化0.1倍前后（约10 kPa）后,破坏模式由崩塌破坏转变为滑移破坏。     

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。     

Centrifuge Modeling of Rock Slopes Susceptible to Block Toppling

Summary This paper presents the results of centrifuge tests that were aimed at validating the Goodman-Bray method for rock slope toppling analysis. The Goodman-Bray method was extended by the authors to accommodate non-persistent basal planes of rock columns. Two gypsum column models, with and without anchors were used to represent the failure modes. Measured critical centrifuge accelerations were in agreement with the results obtained from numerical modeling. A background of the toppling slope failures associated with a large hydropower project in China instigated the need for the centrifuge study. The centrifuge model tests used an artificial rock. The observed failure mode did not follow a straight failure plane as proposed by Goodman and Bray. The failures revealed a bi-planar slip surface with a deep-seated portion near the toe of the slope. The outcomes of the centrifuge tests illustrated the need to search for the critical failure surface when performing a toppling analysis. The search technique is similar to that usually performed in a conventional sliding analysis.     

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。     

含顺层断续节理岩质边坡地震作用下的破坏模式与动力响应研究

基于二维颗粒流软件PFC2D的人工合成岩体技术（SRM）,研究了岩桥倾角和节理间距不同组合形式的含顺层断续节理岩质边坡在地震作用下的破坏模式与动力响应规律。研究结果显示：在地震动力作用下,含单潜在滑动面的顺层断续节理岩质边坡呈现出滑移-倾倒的混合破坏特征,含多潜在滑动面的顺层断续节理岩质边坡则主要发生倾倒破坏;由顺层断续节理以及岩桥交替连接所组成的潜在滑动面是控制边坡动力稳定性的关键因素。在地震动力作用下,最靠近坡脚的岩桥段首先萌生翼裂纹,使得拉应力得到释放,随后各节理相继萌生裂纹并扩展、贯通,最终导致坡体发生阶梯状整体失稳。裂纹扩展受顺层断续节理控制,萌生裂纹中以张拉裂纹为主,且裂纹数量与输入地震波的加速度曲线具有同步性。另一方面,节理面的存在对边坡动力响应产生明显影响,沿坡表以及沿水平方向上的峰值速度、峰值位移随着岩桥倾角的增大、节理间距的减小而增大,同时节理间距和岩桥倾角对于峰值加速度（PGA）放大系数的影响范围主要集中在坡表、坡肩;沿竖直方向上,峰值位移随着岩桥倾角、节理间距的增大而减小,PGA放大系数曲线随高程变化总体呈现U型分布特征。     

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。