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.     

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.     

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,研究了多种因素对反倾边坡倾例变形的影响,通过极差分析获得了各因素的敏感性。通过在岩层内预置大量多边形随机裂隙,数值模拟较好地实现了对破裂面起裂及延展规律的模拟。结果表明:离心模型试验可较好地还原倾倒变形过程,而离散元数值模拟则可对实验结果进行有效的重现与扩展,两者吻合度良好;岩体变形过程存在3个阶段,即起始变形、稳态变形和失稳破坏等阶段;破裂面呈弧形,在变形积累到一定程度后快速形成;边坡可自下而上形成多级破裂面,并伴随岩层的强烈弯曲变形,在外界扰动下,倾倒变形体将由外到内沿不同破裂面形成渐进后退式破坏;多种影响因素中,边坡形态结构影响最大,层面参数次之,软硬岩岩石力学参数的差异影响较小;具体而言,边坡形态与坡体结构对倾倒变形的影响性大小表现为坡角＞倾角＞坡高＞坡形＞层厚比＞层厚,坡角、倾角、坡高越大,坡形越外凸,软硬岩层厚差越小,倾倒变形越容易发生;边坡变形规模主要受形态结构因素控制,倾角和坡角影响最显著。     

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。     

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.     

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.     

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。     

西藏玉曲河下游岸坡倾倒变形机制及稳定性分析

西藏玉曲河下游河谷由板岩组成的岸坡普遍发生倾倒变形,其变形特征在青藏高原东南部"三江"地区具有典型性。随着该地区水利水电项目的不断开发,倾倒变形边坡问题日益突出。本文根据在工程实践中遇到的倾倒变形边坡问题,采用现场调查、勘探和原位试验的方法,重点对边坡变形特征与板岩变形特性的相关性进行研究,并分析了3种倾倒类型：倾倒折断型呈脆性破坏,破坏模式主要为由前部向后部逐级后退式破坏,适合采用极限平衡方法进行稳定性分析;倾倒弯曲型属延性变形,破坏模式主要为边坡浅部的坠覆和松驰,适合采用建立在非连续介质模型基础上的应力应变分析方法;倾倒揉皱弯曲型与倾倒弯曲型类似,仅是在倾倒弯曲的基础上叠加了冰川的推覆作用而发生褶曲。     

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。     

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.

     

Application of distinct element analysis to three simple block models aimed at practical application to toppling failure of fissured rock slopes

To examine the accuracy and the chracteristics of the Distinct Element Method (DEM) which has non-deformable elements, the results simulated by the DEM were compared to the results of experiments and/or theories for three simple block models of a pillar, a mass and a toppling model. Consequently, it was elucidated that the DEM is a good numerical method which can be effectively applied to toppling failure of real fissured rock slopes.     

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。     

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.     

层状反倾-顺倾边坡倾倒变形形成条件及发育规模特征

以往研究中倾倒变形研究在反倾边坡较多而在顺倾边坡中很少,对两种不同结构的边坡形成倾倒体的异同点更是存在较多空白。在总结大量倾倒体实例基础上,对层状反倾和顺倾边坡倾倒变形形成条件及发育规模特征进行了详细研究。结果表明,顺倾边坡若发生倾倒,通常表现为坡高 100 m,边坡坡角 35°,岩层倾角 60°,岩性为薄层或薄层与中层互层的软岩、软硬相间的岩石;反倾边坡当坡角 30°及岩层倾角 30°就可能发生倾倒,其岩性为薄层～中厚层状的软岩、硬岩及具有似层状结构的坚硬岩石均可;提出层状岩质边坡“倾倒临界倾角 ”的概念,对于顺倾边坡, 60°,当 时边坡将可能产生倾倒破坏,当 时边坡通常产生顺层面的“滑移-弯曲”或“滑移-拉裂”型破坏;反倾边坡 30°,当 时边坡才可能演化成明显倾倒变形,当 时边坡不会倾倒或倾倒不明显;对于地质条件基本相同而坡体结构不同的两种边坡,反倾边坡形成的倾倒体无论是发育分布面积还是倾倒深度通常是大于顺倾边坡的,而且一旦形成倾倒体,二者的规模通常是深层的、大型或特大型的;倾倒体的分布面积和倾倒深度均呈现一种随坡高的增加而增加的趋势,坡高 250 m时其分布面积和倾倒深度表现为陡然增加,并且反倾边坡增加幅度大于顺倾边坡。     

Cut Slope Design Recommendations for Sub-Horizontal Hard Sedimentary Rock Units in Ohio, USA

Although most cut slopes in Ohio consist of inter-layered, sub-horizontal units of hard and soft sedimentary rocks (sandstone, limestone, dolostone, shale, claystone, mudstone), slopes consisting of relatively thick hard rock units are not uncommon. Design of stable cut slopes in hard rock units needs to consider rock mass strength and orientation of discontinuities with respect to slope face. Results of kinematic stability analyses show that hard-rock cut slopes are less likely to have conventional plane and wedge failures, caused by unfavorable orientation of discontinuities. The main cause of failure is identified to be the undercutting-induced toppling, which is not amenable to traditional kinematic or rock mass strength-based analyses. Therefore, to recommend a suitable slope angle, numerical models, using UDEC software, were employed to study how various slope angles affect the process of undercutting-induced toppling failures. The UDEC models showed a slope angle of 45° (1H:1 V) to be the most stable angle. However, a 63° (0.5H:1 V) slope angle can significantly reduce the potential for such failures and is therefore more appropriate than the widely used angle of 76° (0.25H:1 V).     

Regional extraction of flexural-toppled slopes in epicentral regions of subduction earthquakes along the Nankai Trough using DEMs

In the epicentral region of subduction earthquakes, large-scale landslides are triggered by strong shaking of slopes weakened by flexural toppling. The distribution of flexural-toppled slopes is the primary information for predicting and mitigating landslide damage beforehand. This study proposes and tests a simple algorithm for extracting flexural-toppled slopes on a regional basis from a 10-m resolution digital elevation model by windows of two sizes. Local relief is extracted with a large window (200 × 200 pixels), and microtopography is extracted with a small window (3 × 3 pixels). The algorithm was derived from the region of the Kanagi-kuzure landslide in Shikoku, and tested at Aka-kuzure landslide in Honshu in Japan. Both areas are underlain by strongly tilted sedimentary rocks in epicentral regions of subduction earthquakes along the Nankai Trough.     

Geometric model for toppling-prone deformation of layered reverse-dip slope

This paper presents the analyses of toppling response of layered reverse-dip slopes under the influence of geometric factors of slope angle, strata thickness and dip. The toppling response of reverse-dip slopes under different geometric factors is obtained by using the discrete element code UDEC. Then, a prediction model for toppling deformation is developed by utilizing support vector machine and the toppling-prone combinations of these geometric factors are determined from a total of 120 samples of reverse-dip slopes. The study has shown that the geometric model is a quarter of a spheroid with a slope angle of 80°, a strata dip of 80°, and a strata thickness of 0.19 m as the center. The length of the long equatorial radius of the spheroid is 31° (strata dip axial), that of the short equatorial radius is 21° (slope angle axial), and the polar radius is 0.075 m (strata thickness axial). And the ratio of long equatorial radius, short equatorial radius, and polar radius is 2.48:1.68:1.00.

     

高密度电法在倾倒变形分级中的应用研究

倾倒变形是水电边坡比较常见的一种倾倒变形现象,具有明显的分区性。利用地球物理属性对倾倒变形程度进行定量化分级比较少见。本文利用不同分区的岩体间电阻率值的差异采用高密度电阻率法对苗尾水电站右坝肩边坡倾倒变形进行分级。为了消除岩石自身形成的背景电阻率值影响对岩体质量分级定量化,本文对二维地质模型正演获得了背景电阻率的分布规律。在测量电阻率的基础上除以背景电阻率得到了与倾倒变形程度有关系数a。最后通过与地质调查的方法对比验证,证明了该方法的可靠性与准确性并成功获得倾倒变形等级定量化指标。     

陡倾煤层开采条件下上覆山体变形破坏物理模型试验研究

大型岩质滑坡是中国西南岩溶矿区的主要地质灾害类型,其破坏和成灾过程具有复合性。以我国重庆武隆鸡冠岭滑坡为例,通过离心物理模型试验研究了地下开采条件下陡倾灰岩斜坡的变形失稳机制。试验时随着煤层模型板被拔出,上覆岩层在拟重力作用下开始出现位移与层间错动,当煤层模型被拔出150 mm时,模型山体发生显著破坏。试验结果表明:陡倾灰岩斜坡在长期重力作用下,会出现弯曲倾倒的变形,随着地下煤层逐渐采空,上覆陡倾层状岩体失去支撑,岩层层面分离并产生拉张裂缝,岩体变形加剧发生倾倒破坏,并对煤层下部的稳定岩体形成挤压,下伏稳定岩体发生剪切破坏,最终导致鸡冠岭以倾倒-滑移的复合模式整体失稳。这一研究对中国西南山区大型岩质滑坡的早期识别与失稳机制分析具有指导意义。