Centroid sliding pyramid method for removability and stability analysis of fractured hard rock

This paper proposes a new method using centroid sliding pyramid (CSP) to identify the removability and stability of fractured hard rock in tunnel and slope engineering. The new method features two geometrical and topological improvements over the original key block method (KBM). Firstly, all the concave corners are considered as starting points of cutting process when a concave block is divided into a set of convex blocks in the original KBM. Only the concave corners formed by two joint planes are used for partitioning a concave block in the presented method and concave corners with free planes are excluded. Secondly, joint pyramid for removability computation in the original KBM is generated using all of the joint planes, while CSP is calculated only from the joint planes adjoining the free planes. The cone angle θ of CSP is the vectorial angle formed by the two candidate sliding surfaces of this CSP. Removability analysis of a block is transformed into calculating the cone angle of CSP. The geometrical relationship is simplified, and data size for removability computation is reduced compared with the original KBM. The provided method is implemented in a computer program and validated by examples of fractured rock slopes and tunnels.     

考虑岩桥破坏的块体稳定性分析方法

经典块体理论在进行块体可移动性分析和稳定性计算时是分步独立进行的,默认不可移动块体是稳定的,对不可移动块体不再进行稳定性分析。实际工程中,某些阻碍岩石块体运动的“岩桥”可能发生破坏,使得不可移动块体发生滑动。当块体的规模比较大时,在重力作用下破坏局部岩桥的可能性会增高。文中提出一种考虑岩桥破坏的块体稳定性分析方法,不再默认不可移动块体绝对稳定,计算块体稳定系数时,将阻碍块体移动的岩桥的抗剪切力纳入到块体的抗滑力中。该方法首先找出块体所有可能的滑动面和裂隙交线,识别块体沿每一个方向运动时需要破坏的岩桥,基于摩尔-库仑强度准则计算出块体沿每个方向运动时的稳定系数,然后,选取最小的稳定系数作为块体的实际稳定系数,最小稳定系数对应的方向即为块体最有可能的运动方向。     

基于自由面上环路对应节理无限切割的关键块体搜索

关键块体理论在评价工程裂隙岩体稳定性中得到了广泛应用。然而,一方面岩体中节理数量众多,关键块体的搜索将耗费较多机时;另一方面,极少数偶然出现的块体识别也会极大地增加计算量。因此,开发有针对性和灵活的关键块体搜索方法就非常重要。首先将研究区域分解成凸子区域,找出自由面上的闭合环路,然后利用环路的组成节理以及与其相交节理进行空间无限切割来识别该环路是否对应关键块体。该方法针对性强,能较好地适应人为规定的判别条件,如搜索楔形体以及后缘切割限定等,并能顺利实现凹面体的关键块体搜索,且编程实现简单。以某挂帮矿的顶柱为实例进行关键块体的搜索,验证了上述方法的可行性。     

A Morphological Visualization Method for Removability Analysis of Blocks in Discontinuous Rock Masses

Block theory has been successfully applied to solve practical problems in rock engineering associated with the stability of discontinuous rock masses. Traditional methods of block theory, which have not proposed detailed schemes for characterizing geometric features of arbitrary blocks with complex geometries, are difficult to simultaneously visualize the locations of blocks. To overcome the shortcomings of these traditional methods, this paper introduces the concept of block morphology to systematically represent the morphological characteristics of blocks. Morphological visualization analysis involves the classification, characterization and visualization of various blocks and the determination of their removability using the stereo-analytical method. The proposed morphological visualization method provides a basis for computer modeling and mechanical calculations of large-scale rock mass systems. Furthermore, examples are presented in this paper to verify the validity and demonstrate the exceptional performance of this method.     

A rigorous solution for the stability of polyhedral rock blocks

Block theory has been widely applied to stability analysis of rock engineering due to its clear concept and elegant geometrical theory. For a general block with multiple discontinuity planes, it is assumed that contact is only maintained on a single plane (single-plane sliding) or two intersecting planes (double-plane sliding) in block theory analysis. Since the normal forces and shear resistances acting on the other discontinuity planes are omitted, it can cause unreasonable estimations of block failure modes and incorrect calculation of factors of safety. In this study, a new method is presented that permits to consider the contribution of the normal forces and shear resistances acting on each discontinuity plane to the block stability. The proposed method meets all of the force-equilibrium and moment-equilibrium conditions and provides a rigorous solution for stability of general blocks with any number of faces and any shape. Some typical polyhedral blocks in rock slopes are analyzed using block theory and the proposed method. The results indicate that the traditional block theory may give a misleading conclusion for the predictions of stability and sliding direction of rock blocks when contact occurs on more than two discontinuity planes.     

含共面结构面岩体的岩桥贯通准则研究

块体理论是一种比较常用的岩土工程稳定性分析方法,但缺乏对非贯通结构面的研究,导致搜索出的关键块体不够精准和全面。如何处理非贯通结构面,判断其是否应该连通成为块体理论研究至关重要的一个问题。采用数值模拟的方法计算含两共面结构面岩体试样在不同岩桥倾角、结构面摩擦系数、围压和连通率情况下的贯通强度与峰值强度。引入贯通系数变量,定量描述贯通强度与峰值强度之间的关系。将贯通强度作为判断岩桥贯通与否的一个衡量指标,建立起贯通强度与岩桥倾角、结构面摩擦系数、围压和连通率之间的函数,即含两条共面结构面岩体的岩桥贯通准则。该准则可准确判断含两条共面结构面岩体的岩桥是否应该连通。基于岩桥贯通准则的块体理论能够准确搜索出因岩桥贯通而滑移的关键块体。     

变质片岩区边坡稳定性的块体理论分析

变质片岩区的边坡破坏与结构面和坡面的组合密切相关,块体理论在分析结构面和坡面组合方面有独特的优势。本文以秦岭北坡西安市黑河水库左岸108国道边坡为例,说明变质片岩区边坡稳定性的块体理论分析方法。作为准备工作,本文编制了块体理论相关程序和制作等密度图的相关程序。通过现场调查,本文将黑河库区108国道沿线边坡分成了15段,其中有4个潜在崩塌段。针对这4个潜在崩塌段,本文在每段中选取一个典型点,借助自编程序,使用块体理论分析方法寻找可动块体、关键块体并计算剩余下滑力。计算所得关键块体的结构面组合形式和实际相吻合,所得剩余下滑力计算结果表明4个潜在崩塌段中有3段崩塌危险性较高,且需要采取工程措施以防止崩塌阻断108国道。说明了变质片岩区边坡稳定性的块体理论分析方法,对变质片岩区其他工程具有一定借鉴意义。     

粉砂质板岩力学特性及各向异性特性

为研究鄂西北地区板岩的力学特性及各向异性特征,开展了志留系粉砂质板岩的单轴压缩和巴西劈裂试验,分析了试样的力学特性和各向异性特征以及在不同荷载作用下的变形破坏模式,揭示了不同破坏模式的力学机制,并通过数值分析研究了不同板理面角度板岩边坡破坏模式及力学机制。研究结果表明,粉砂质板岩中的板理面是影响岩体力学行为的弱面,使得粉砂质板岩表现出明显的各向异性的特征。在单轴压缩条件下,粉砂质板岩在垂直板理面方向比平行板理面方向更易变形,变形量更大;平行板理面方向加载时试样破坏类型为竖向劈裂型张拉破坏,其实质是压杆失稳;垂直板理面加载时试样的破坏类型为穿切板理面的劈裂型剪切破坏;所测得的力学参数各向异性也较明显。在劈裂荷载作用下,粉砂质板岩的破坏模式主要有张拉劈裂破坏和沿板理面剪切破坏两种,所得抗拉强度在平行板理面方向上最大,在垂直板理面方向上最小,两个方向上的抗拉强度均小于抗压强度。由于板理面间的抗拉强度极低,在受到与板理面呈小角度相交的劈裂荷载作用时,容易产生沿板理面的张拉劈裂或拉剪破坏,在实际工程中应尽量避免板理面间的受拉破坏和沿板理面的拉剪破坏。在边坡工程中,板理面倾向、倾角对边坡破坏模式及力学机制有较大影响,边坡防护治理需充分考虑这一影响。上述研究为粉砂质板岩区岩质边坡防护治理以及其他岩石工程设计与施工提供理论依据与技术基础。     

乌东德水电站右岸地下厂房随机块体特征研究

随机块体的几何特征和稳定性是水利水电工程中地下厂房支护设计的重要依据。对乌东德水电站右岸地下厂房随机块体的特征进行了深入研究。对研究区域内实测的裂隙参数进行了分组统计,确定了各组裂隙产状、迹长等参数的分布形式和大小。利用逆建模方法建立了三维裂隙网络模型,获取了各组裂隙的直径和三维密度。采用一般块体方法对地下厂房进行随机块体的识别和稳定性分析,利用GeneralBlock软件进行了10次随机实现,对10次计算结果进行了统计分析和讨论。研究结果表明,结构面与开挖面形成的随机块体集中在地下厂房的顶拱部位,10次随机实现中,地下厂房全长范围内平均每次形成的随机块体为414个;随机块体的平均体积为2.9 m³,最大块体的体积达152.0 m³;可移动块体中,大部分为稳定块体,不稳定块体均以坠落形式破坏;构成可移动块体的结构面多为3~4条,最多可达12条,其中倾W向的中等倾角裂隙是构成块体并可能造成块体失稳的最危险结构面;随机块体的平均深度为1.2 m,最大深度为8.8 m。建议支护锚杆应尽量穿透倾W向中等倾角的长大裂隙,且锚杆支护长度大于8.8 m。     

动荷载作用下隧道围岩块体稳定性分析及其应用

隧道围岩中的结构面将岩体切割成块体,块体在自然状态下的静力平衡因为隧道开挖而被打破,临空面的产生和动荷载的施加都可能导致块体的滑移,进而引起围岩失稳。以往应用块体理论寻找关键块体时,多只考虑纯重力的作用,而忽视了爆破振动、地震等动荷载对诱发失稳灾害的重要作用。将爆破振动荷载和地震荷载转化为等效静力,并通过数学计算求出使块体安全系数最低的动荷载方向,再利用关键块体理论矢量分析方法分析隧道围岩的稳定性。在长岗隧道中的应用表明,考虑动荷载作用下的块体安全系数明显小于只考虑重力作用时的安全系数,原本稳定的块体也可能在动荷载作用下变成关键块体导致围岩失稳,这与长岗隧道现场记录的破坏现象相符。     

Three-dimensional slope stability analysis of South Peak, Crowsnest Pass, Alberta, Canada

South Peak is a 7-Mm³ potentially unstable rock mass located adjacent to the 1903 Frank Slide on Turtle Mountain, Alberta. This paper presents three-dimensional numerical rock slope stability models and compares them with a previous conceptual slope instability model based on discontinuity surfaces identified using an airborne LiDAR digital elevation model (DEM). Rock mass conditions at South Peak are described using the Geological Strength Index and point load tests, whilst the mean discontinuity set orientations and characteristics are based on approximately 500 field measurements. A kinematic analysis was first conducted to evaluate probable simple discontinuity-controlled failure modes. The potential for wedge failure was further assessed by considering the orientation of wedge intersections over the airborne LiDAR DEM and through a limit equilibrium combination analysis. Block theory was used to evaluate the finiteness and removability of blocks in the rock mass. Finally, the complex interaction between discontinuity sets and the topography within South Peak was investigated through three-dimensional distinct element models using the code 3DEC. The influence of individual discontinuity sets, scale effects, friction angle and the persistence along the discontinuity surfaces on the slope stability conditions were all investigated using this code.     

基于系统评价的块体可靠度指标分析及应用

利用条件概率评价及系统工程理论,将关键块体作为块体系统一个重要组成部分,分析了关键块体可靠度指标评价办法,探讨了关键块体与次生关键块可靠度内在关系,由此类推,提出块体系统评价方法,推导出块体系统可靠度计算公式,实现对块体系统的失稳概率的评价计算。并选择一工程实例,对评价方法予以验证。结果表明：传统关键块体可靠度评价办法忽略块体间内在影响,结果偏向风险;而文中方法综合考虑块体之间影响,并建立了系统评价模型,对块体系统评价更接近实际情况,对块体系统理论的研究有一定借鉴意义。     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

复杂岩质高边坡半确定性块体三维稳定性研究

通过工程地质学中的赤平投影原理对各个结构面产状进行统计分析,找出优势结构面组合,再对非确定位置的结构面按一定间距进行搜索,利用运动学分析方法对各个块体进行分析,确定出可能从坡体上滑出的块体。结合三维刚体极限平衡法,计算出各个可能块体组合在不同工况下的稳定系数,找出最危险滑块,进而对边坡进行稳定性评价,通过具体的工程实例进行了验证。结果表明,将工程地质学方法、运动学分析方法与刚体极限平衡法结合起来分析复杂岩质边坡可以提高边坡稳定性评价的准确性,对工程具有很好的指导意义。     

节理岩体关键块体稳定的概率分析

基于地下岩体受节理面的控制,节理面的几何和力学参数随机分布,从而导致岩体系统具有高度不确定性,提出以关键块体理论为基础,考虑节理几何和力学参数随机性的岩体开挖可靠度分析方法,并给出了块体稳定的总失效概率评价模型。以澳大利亚阿德莱德地区一铜矿地质条件为例,以节理面倾角、倾向、摩擦系数和黏聚力为随机变量,通过Monte Carlo模拟和概率图方法,进行了岩体可靠度和失效概率的计算。最后,采用条件概率的分析方法,计算了单面滑动块体的总失效概率。计算结果表明,块体沿单面滑动并且出现的概率为11.0%,总的失效概率为3.85%,超过一般岩体工程可允许的风险水平,认为该方法可以作为评价块体可靠性的依据。     

Probabilistic block theory analysis for a rock slope at an open pit mine in USA

A new formulation is given to conduct a probabilistic block theory analysis. A new computer code (PBTAC) is developed to perform both deterministic and probabilistic block theory analysis. The variability of the discontinuity orientation and shear strength is incorporated in the probabilistic block theory analysis. Discontinuity orientation is treated as a bivariate random variable including the correlation that exists between the dip angle and dip direction. PBTAC code was applied to perform both deterministic and probabilistic block theory analyses for a part of an open pit mine in USA. Needed geological and geotechnical data for the analyses were obtained from field and laboratory investigations. The variability of the discontinuity orientations resulted in important differences between the probabilistic and deterministic block theory analyses results. The results confirmed that the design value selected for the maximum safe slope angle (MSSA) for a particular region in the open pit mine based on the deterministic block theory analysis can be on the unsafe side. In summary, the results showed clearly the superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtaining additional important information with respect to designing rock slopes. The calculated values agree very well with the existing almost stable bench face angles reported by the mining company.     

浅埋偏压隧道出口变形机理及稳定性分析

以皖南某公路浅埋偏压隧道出口段高边坡为研究对象,提出了零开挖进洞的施工方案,并结合洞口的工程地质条件,采取必要的加固措施。通过对该边坡现场工程地质条件的系统调查,首先对边坡的岩体结构类型及其成因机制、结构面与坡面组合特征进行细致研究,在此基础上通过FLAC3D数值模拟,结合工程地质条件分析,对其变形破坏机制进行深入探讨。研究结果表明,边坡的变形首先以隧道内侧存在的软弱岩体(挤压错动带、断层)的不均匀压缩为先导,进而引起上部岩体产生由NE向陡缓结构面构成的阶梯状滑动,这将会使隧道构筑物及隧道外壁承受较大的压应力,当压应力超过隧道构筑物及外壁的极限强度时将产生破坏,从而诱发上部岩体产生更大规模的地质灾害。基于此,隧道进洞开挖前首先应对上部岩体进行加固处理,避免隧道构筑物及隧道外壁产生应力集中现象。     

关键块体概率分析在复杂构造条件下大型地下工程开挖中的应用

锦屏一级水电站泄洪洞位于雅砻江右岸埋深大于100m的大理岩中,构造条件复杂,确定隧洞开挖面是否可能产生关键块体对工程安全具有重要意义。本文在对泄洪洞中导洞地质调查和研究基础上,将随机概率模型引入关键块体理论,分析关键块体的生成概率、体积大小与安全系数,得出关键块体形成概率服从负指数分布,主要取决于J②、J④组裂隙迹长的分布情况;关键块体的体积与主要结构面迹长成正比,最终收敛于结构面对关键块体完全切割时的关键块体体积;关键块体的安全系数随主要结构面迹长的增加而降低,但是同样收敛于结构面对关键块体的完全切割情况。为设计有效的加固方案提供了依据,具有积极的工程应用价值。     

The geometry and kinematics of flow perturbation folds

Minor folds formed synchronous with ductile deformation in high strain zones can preserve a record of the scale and kinematics of heterogeneous flow. Using structures associated with WNW-directed Caledonian thrusting in N Scotland, we show that localised perturbations in flow resulted in the generation of predominantly cylindrical minor folds with hinges lying at low angles to the transport direction. These define a series of larger-scale fold culminations (reflecting ‘surging flow’) or depressions (reflecting ‘slackening flow’) that are bisected by transport-parallel culmination and depression surfaces. The fold patterns suggest a dominance of layer-normal differential shearing due to gradients in shear strain normal to transport. Culmination surfaces are marked by along-strike reversals in the polarity of structural facing and vergence of minor folds which, contrary to classic fold patterns, define reverse asymmetric relationships. Culmination surfaces separate folding in to clockwise (Z folds) and anticlockwise (S folds) domains relative to the transport lineation. The dip of fold axial planes systematically increases as their strike becomes sub-parallel to transport resulting in a 3D statistical fanning arrangement centred about the transport direction. Thus, mean S- and Z-fold axial planes intersect precisely parallel to the transport lineation and potentially provide a means of determining transport directions in cases where lineations are poorly preserved. Culminations display convergent fold patterns with fold hinges becoming sub-parallel to transport towards the culmination surface and underlying detachment, whilst axial planes define overall concave up listric geometries which are bisected by the culmination surface. Thus, around culminations and depressions there are ordered, scale-independent relationships between transport direction, shear sense, fold facing, vergence and hinge/axial plane orientations. The techniques described here can be applied and used predictively within any kinematically coherent system of ductile flow.     

Faults and Source Parameters of Earthquakes in the Baikal Rift Zone: Dip Angles of Fault Planes

Analysis of gentle, intermediate, and steep dip angles of fault planes in earthquake sources of the Baikal region is carried out with the slips in seismic sources being taken into account. The areas where normal faulting slips at steep, intermediate, and gentle angles took place are distinguished, and this can be interpreted as transformation of a steep dip to gentle one. It is found that the increase in energy class is accompanied by the number of earthquakes with steep dip angles, whereas the proportion of earthquakes with intermediate angles decreases, and the fraction of earthquakes with gentle angles remains quasi-stable and small.