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.     

A Methodology for Reliability-Based Design of Rock Slopes

Summary A reliability-based methodology for the design of rock slopes, that can easily be implemented by the practicing engineers is proposed. The advanced first-order second-moment (AFOSM) method is adopted as the reliability assessment model and its application is illustrated for the case of plane failure. A model is developed within the framework of first-order second-moment approach to analyze the uncertainties underlying the in situ shear strength properties of rock discontinuities. Here, particular emphasis is given on the assessment of uncertainties related to the shear characteristics of clean, unfilled rock discontinuities under low normal stress levels. An extensive literature survey on the shear characteristics of discontinuities is carried out in order to collect data for the quantification of uncertainties. The data extracted from this literature survey are classified and reprocessed so that they can be utilized in the uncertainty analysis model. A user friendly software called ROCKREL is developed to carry out the numerical computations and to make the proposed design format more practical. Received April 16, 2001; accepted June 10, 2002; Published online November 19, 2002 Authors' address: Prof. Celal Karpuz, Middle East Technical University, Faculty of Engineering, Department of Mining Engineering, 06531 Ankara, Turkey; e-mail: karpuz @metu.edu.tr     

反倾层状岩质边坡倾倒变形机理与影响因素的离散元模拟

为进一步研究层状反倾边坡的弯曲倾倒变形机制,以离心试验为原型,通过离散元数值模拟,研究了层状岩质反倾边坡的变形机理与影响因素。通过预置层内随机裂隙,实现了破裂面的形成和贯通。研究结果表明：模拟结果与试验吻合较好,边坡变形可分为起始蠕变、稳态变形和失稳破坏3个阶段;边坡破裂面在达到破坏荷载（G_f）后瞬间贯通,呈直线型,产状受岩层倾角控制,G_f值与坡角幂函数相关;反倾边坡的破坏需满足倾角和坡角启动条件,且变形破坏与岩层所受弯矩关系密切,当倾角为70°~80°、坡角大于60°时,最易破坏;典型破坏模式有倾倒-折断-块体式、倾倒-弯曲-折断式、倾倒-反折式3种,其受倾角、坡角组合控制;对材料参数的正交试验表明,各参数对G_f的敏感性从大到小依次为密度、层面内摩擦角、层厚、密度比、层面黏聚力,且G_f与层厚、层面内摩擦角及密度比具有良好的线性相关性;层面内摩擦角可影响破裂面产状,从而控制变形体规模,其他参数仅影响G_f的大小。     

反倾边坡影响倾倒稳定的几种因素探讨

倾倒破坏是岩石边坡主要的失稳类型之一,而分析岩石边坡倾倒破坏的极限平衡方法主要还是Goodman和Bray提出的G-B方法,尽管该方法采用的是一个比较理想化的模型,但其计算结果能够较好的反映出倾倒破坏的基本规律。本文主要讨论岩层倾角、厚度以及切坡角度对倾倒体稳定的影响。     

Estimation of Block Sizes for Rock Masses with Non-persistent Joints

Summary  Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified, the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support. In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19).     

反倾层状岩质边坡倾倒破坏力学模型

在地质调查基础上,将反倾边坡的各岩块概化为受自重弯矩及外力作用的悬臂梁,利用弯曲-拉裂模型研究其破坏模式。通过力学分析,建立了反倾层状岩质边坡各条块的力学模型。基于最大拉应力理论,给出条块倾倒失稳判据,以此判定边坡的稳定性,并定量分析了反倾边坡倾倒破坏的影响因素。结果表明:反倾边坡倾倒破坏发生在每个条块的上边界处,条块所受拉应力大小与其容重呈线性关系,与高度呈二次幂函数关系,与其宽度呈-1次幂函数关系,即板梁容重越大、高度越大、宽度越小,其倾倒破坏越明显。而当条块底面倾角满足一定条件时,才会发生倾倒破坏,其范围边界值与条块的高度和宽度有关。     

Modeling of a Multiply Jointed Voussoir Beam in the Centrifuge

Summary The mechanics and kinematics of a multiply jointed Voussoir beam have been studied based on the response of small scale beams tested in the centrifuge. The model beams were made up of six blocks, confined between fixed abutments. The tests included monitoring of beam deflection, development of axial thrust and distribution of strain within the beam. The models were subjected to accelerations of up to 90 g, depending upon the beam geometry. Two different beam geometries were considered. The test data were analysed in the light of pseudo analytical algorithms accepted in the analysis of singly jointed Voussoir beams. The data show that small translations and rotations of the block at the beam-abutment interface are required for a stable compression arch to set up in the beam. The computations and physical models indicate that the development of thrust is in linear proportion with the applied acceleration and is independent of beam thickness. The distribution of strains along the beam leads to the conclusion that the depth of the compression arch varies from the total beam thickness, to approximately one half of the beam thickness, under stable conditions. The data should be of considerable use to researchers looking to calibrate/validate numerical techniques used in describing the response of discontinuous rock masses.     

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。     

Stability of Asymmetric Roof Wedge Under Non-Symmetric Loading

Summary. An analytical method is presented for the calculation of the load carrying capacity of two-dimensional asymmetric rock wedges when the loading on the joint faces is non symmetric, such as the case of an asymmetric wedge formed in the roof of a circular tunnel in an inclined stress field. The pull out force that causes yield at one of the joint faces is evaluated from formulae based on the limiting equilibrium conditions assuming a purely frictional joint resistance. Next, the total pull out force required for the secondary face to yield is calculated. During this step, the wedge is further displaced and while the primary yielding face is plastically deformed, the other face is still in the elastic range until failure. Validation of the analytical procedure is obtained with the UDEC code, which provides an implementation of the Distinct Element Method in two dimensions. When the assumptions made in the analytical procedure are valid, the analytically calculated values for the pull out resistance of the wedge are computed to be close to the numerically obtained ones.     

Analysis of Critical Excavation Depth for a Jointed Rock Slope Using a Face-to-Face Discrete Element Method

Summary The critical excavation depth of a jointed rock slope is an important problem in rock engineering. This paper studies the critical excavation depth for two idealized jointed rock slopes by employing a face-to-face discrete element method (DEM). The DEM is based on the discontinuity analysis which can consider anisotropic and discontinuous deformations due to joints and their orientations. It uses four lump-points at each surface of rock blocks to describe their interactions. The relationship between the critical excavation depth D _s and the natural slope angle α, the joint inclination angle θ as well as the strength parameters of the joints c _r ,φ _r is analyzed, and the critical excavation depth obtained with this DEM and the limit equilibrium method (LEM) is compared. Furthermore, effects of joints on the failure modes are compared between DEM simulations and experimental observations. It is found that the DEM predicts a lower critical excavation depth than the LEM if the joint structures in the rock mass are not ignored.     

地震作用下岩质边坡倾倒破坏分析

倾倒破坏是陡倾层状岩体边坡一类主要的变形破坏形式,地震作用下岩质边坡块体倾倒破坏分析具有重要的工程指导意义。基于块体极限平衡,针对岩块长细比较大的情况,推导出了地震作用下岩质边坡倾倒破坏的一般解析解。对于简单的反倾边坡,给出了地震作用下倾倒破坏的显式解析解,并推导了岩块间法向力、破坏模式转变点和坡脚剩余下滑力计算公式。通过4个典型算例研究了地震作用对反倾边坡破坏模式、倾倒破坏时所允许的最大陡倾节理视倾角、破坏模式转变点和坡脚剩余下滑力的影响,为反倾边坡的抗震支护设计提供了理论基础。最后,根据地震影响系数与破坏模式转变点和坡脚剩余下滑力的定量关系对比分析了解析法与传递系数法,结果显示,当岩块长细比大于20时,解析法具有足够的计算精度。     

Physical Modeling of Landslide Mechanism in Oblique Thick-Bedded Rock Slope: A Case Study

The Jiweishan landslide illustrates the failure pattern of an apparent dip slide of an oblique thick-bedded rockslide. Centrifugal modeling was performed using a model slope consisting of four sets of joints to investigate the landslide initiation mechanism. Crack strain gauges pasted between the slide blocks and the base failed in sequence from the rear to the front as the centrifugal acceleration increased. When the acceleration reached 16.3g, the instantaneous failure of the key block in the front triggered the apparent dip slide of all blocks. The physical modeling results and previous studies suggest that the strength reduction in the weak layer and the failure of the key block are the main reasons for the Jiweishan landslide. The centrifuge experiment validated the previously proposed driving-blocks–key-block model of apparent dip slide in oblique with inclined bedding rock slopes. In addition, the results from limit equilibrium method and centrifuge test suggest that even though the failure of the key block in the front is instantaneous, a progressive stable–unstable transition exists.     

An Algorithmic 3D Rock Roughness Measure Using Local Depth Measurement Clusters

Summary. A computational algorithm which uses depth data from a reference plane to a rock fracture surface in calculating a new three-dimensional joint roughness coefficient is presented. Two independent sets of fracture data are investigated. The new coefficient is compared to Barton’s 2D joint roughness coefficient JRC. A measure indicating corrupt data is discussed. The algorithm is also used to show that, in general, rock roughness is only a local variable, not a directional one.     

厦门某岩质高边坡工程治理经验浅析

结合厦门某岩质高边坡治理工程实例,通过极限平衡法和有限元法对边坡稳定性进行分析,初步探讨节理裂隙的发育程度对岩质边坡稳定性的影响以及锚固件和边坡岩体之间的相互作用机理,在此基础上进行边坡工程支护方案的设计,得出的结论对类似工程有参考价值。     

重庆拉法基搅拌站岩质边坡稳定性分析

本文研究重庆拉法基长寿智深混泥土搅拌站岩质边坡稳定问题。针对该边坡所处的地形地貌、地层岩性、地质构造和气象水文条件,分析了影响岩质边坡稳定性的主要因素,归纳了该边坡可能的主要工况类型。在此基础上,采用块体极限平衡法对边坡进行了稳定性分析,并最终提出了以下综合治理措施：“表里排水”、“削坡减载”、“坡面防护”、“锚杆格构”以及“重力式挡墙支挡”。这些措施在后期施工中得到了应用,并取得了不错的效果,可为类似工程问题的分析评价提供借鉴。     

简化Bishop法的扩展及其在非圆弧滑面中的应用

在众多边坡稳定分析方法中，经典简化Bishop法的应用最为广泛，但此法只能求解圆弧滑面的安全系数。笔者提出了扩展简化Bishop法，它不仅保留了经典简化Bishop法精度高、易使用等优点，且能够计算非圆弧滑面的安全系数，是较为实用的边坡稳定分析方法。     

The Time-Dependent Reduction of Sliding Cohesion due to Rock Bridges Along Discontinuities: A Fracture Mechanics Approach

Summary In this paper, a fracture mechanics model is developed to illustrate the importance of time-dependence for brittle fractured rock. In particular a model is developed for the time-dependent degradation of rock joint cohesion. Degradation of joint cohesion is modeled as the time-dependent breaking of intact patches or rock bridges along the joint surface. A fracture mechanics model is developed utilizing subcritical crack growth, which results in a closed-form solution for joint cohesion as a function of time. As an example, a rock block containing rock bridges subjected to plane sliding is analyzed. The cohesion is found to continually decrease, at first slowly and then more rapidly. At a particular value of time the cohesion reduces to value that results in slope instability. A second example is given where variations in some of the material parameters are assumed. A probabilistic slope analysis is conducted, and the probability of failure as a function of time is predicted. The probability of failure is found to increase with time, from an initial value of 5% to a value at 100 years of over 40%. These examples show the importance of being able to predict the time-dependent behavior of a rock mass containing discontinuities, even for relatively short-term rock structures. Received November 5, 2001; accepted July 24, 2002; Published online November 19, 2002     

岩石边坡的危险滑动块体组合研究

在完善刚体极限平衡分析矢量法的基础上 ,采用树状结构深度优先的启发式搜索 ,建立了对岩石边坡寻找最危险滑动组合及相应整体抗滑稳定安全系数的方法。 该方法已用程序实现 ,并在小湾高拱坝坝肩稳定分析中成功地进行了应用。