基于GIS边坡稳定三维极限平衡方法的开发及应用

由于GIS强大的功能从一般的数据存储到复杂的空间分析及图形显示,在岩土工程分析中亦必将成为一个常用工具。本文研究基于GIS栅格数据和4个边坡稳定三维极限平衡模型,开发了一个GIS扩展模块用于边坡三维安全系数计算。考题和实例计算表明了该模块的正确性和便利性。     

用有限元极限平衡法分析边坡的稳定性

用有限元分析为基础的极限平衡法计算了边坡安全系数,并将结果与摩尔-库仑屈服准则、外接圆D-P屈服准则强度折减法得到的结果、以及Spencer（极限平衡）法的结果进行了比较,结果表明,有限元极限平衡法计算的边坡安全系数与摩尔-库仑屈服准则强度折减法和Spencer法的结果很一致,而D-P准则强度折减法得到的结果偏差较大。叙述了存在已知滑动面和不存在滑动面时有限元极限平衡法的计算方法。用大型通用有限元软件,如ANSYS等,可方便地进行这种方法的边坡安全系数的计算,并有足够的精度。     

土体极限分析的基本方程与广义极限平衡法

对屈服条件与屈服函数的极值条件进行了讨论,在不需要流动法则的情况下建立了速度方程。平衡方程、屈服条件与屈服函数的极值条件、速度方程就是土体极限分析的基本方程。这样,对荷载、速度边界条件（包括荷载与速度边界同时存在）,均构成了完备的极限平衡问题。对边坡稳定问题的上、下限定理给出了严密的证明,并建立了求解极限平衡问题的广义极限平衡法,均质土的计算结果表明,圆弧滑动面的广义极限平衡法与对数螺旋面的上限解法基本一致。     

Approach to complete limit equilibrium analysis for rock wedges — the method of “artificial supports”

SummaryApproach to Complete Limit Equilibrium Analysis for Rock Wedges — The Method of Artificial Supports Since the movement of rock wedges or blocks is the primary phenomenon in rock mass failure, it is convenient to use limit equilibrium approaches for stability analysis. In spite of their wide use, limit equilibrium analysis is often restricted due to: 1) the usual procedural simplifications (regarding geometry, force application, failure modes), and 2) basic deficiencies of the limit equilibrium approach (the fundamentally indeterminate rigid body problem requires assumptions regarding the force reactions). The method of artificial supports intends to circumvent or reduce many of these restrictions. In particular, the problem of unknown force distribution on the supporting plane is reduced by specifically considering and optimizing a variety of reactions on these planes. All sliding modes of failure — i. e., translational, free and restrained rotational sliding — can be correctly modelled. Particularly significant is the result that the usual assumption oftranslational sliding can be incorrect andunsafe, if forces other than the weight are significant. The methodologies employed in the artificial support model can be extended to all modes of failure, i. e., lifting off and toppling in addition to the previously mentioned sliding modes; this is demonstrated with a procedure for a complete stability analysis for a 2-joint wedge.

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ZusammenfassungEin Weg zur vollständigen Gleichgewichtsberechnung für Felskörper — Die Methode der Künstlichen Auflager Da die Bewegung von Einzelblöcken das primäre Phänomen bei Felsstürzen ist, eignen sich Grenzgleichgewichtsbetrachtungen besonders gut für Stabilitätsuntersuchungen. Vor allem wegen der üblichen Vereinfachungen (Geometrie, Kräfteansätze, Versagensmechanismen) und grundlegender Unzulänglichkeiten (das grundsätzlich statisch unbestimmte Starrkörperproblem erfordert Annahmen bezüglich der Auflagerkräfte) sind solche Grenzgleichgewichtsbetrachtungen oft nur beschränkt anwendbar, obwohl sie häufig angewendet werden. Es wird versucht, mit der Methode der künstlichen Auflager viele dieser Einschränkungen zu umgehen. Vor allem wird das Problem der unbekannten Spannungsverteilung in den Auflageflächen dadurch reduziert, daß mögliche Kombinationen solcher Reaktionen in die Rechnung einbezogen und optimiert werden. Alle Gleitbewegungen, seien es Translationen oder freie bzw. beschränkte Rotationen auf den Auflageflächen, können korrekt behandelt werden. Besondere Bedeutung kommt aber der Tatsache zu, daß die übliche Annahme einer translatorischen Gleitung falsch ist bzw. daß man damit auf der unsicheren Seite liegt, wenn außer dem Eigengewicht noch andere Kräfte einwirken.Die Überlegungen, die der Modellvorstellung der künstlichen Auflager zugrunde gelegt wurden, können auf alle Instabilitätsfälle ausgedehnt werden, also auch auf Abheben und Kippen zusätzlich zu den vorhin genannten Gleitbewegungen; dies wird am Beispiel einer Rechenprozedur für eine vollständige Stabilitätsuntersuchung eines Gleitkeils gezeigt.

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RésuméTentative visant à compléter l'analyse par équilibre limite — la méthode des supports artificiels Le fait que le déplacement de blocs est le principal phénomène d'instabilité en massif rocheux suggère l'utilisation de méthodes d'équilibre limite à l'étude de sa stabilité. Bien qu'elles soient fréquemment utilisées, les analyses par équilibre limite sont souvent restreintes par suite 1) de simplifications opérationnelles (concernant la géométrie, les forces et les modes d'instabilité), et 2) des insuffisances fondamentales de cette approche (le problème des corps indéformables est en essence statiquement indéterminé et réclame en conséquence l'adoption d'hypothèses sur la teneur des réactions).L'intention de la méthode des supports artificiels est de réduire ou éviter plusieures de ces restrictions. En particulier le problème de la distribution inconnue des forces sur le plan d'assise est résolu en considérant et optimisant un certain nombre de réactions entre corps rigide et le plan de base. Tous les modes d'instabilité au glissement — à savoir translation, rotation restreinte et rotation libre — peuvent être correctement représentés. Spécialement digne d'intérêt est à cet égard le résultat concernant l'habituelle hypothèse de glissement en translation, puisque celui-ci peut s'avérer incorrect et exhiber des facteurs de sécurité supérieurs, par rapport à un glissement en rotation, lorsque des forces autres que le poids sont à considérer.La méthodologie servant de base à la méthode des supports artificiels peut être étendue à tous modes d'instabilité, à savoir: le soulèvement et le renversement venant compléter ceux précités; ceci est illustré par le développement d'une procédure d'analyse complète d'un bloc monolithique découpé par deux fissures.

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With 13 Figures     

Study on the action of the active earth pressure by variational limit equilibrium method

Within the framework of limiting equilibrium approach, the problem of active earth pressure on rigid retaining wall is formulated in terms of the calculus of variations by means of Lagrange multipliers. It is transcribed as the functional of extreme‐value problem by two undetermined function arguments, and is further transformed into determining the minimax solution of restrained functions incorporating the geometrical relations of the problem. The function of (fmincon) in the optimization toolbox of MATLAB 6.1 can be used to find the minimax solution. Computation results show there exist two kinds of modes of failure sliding along plane surface and rotating around log‐spiral cylinder surface when the soil behind the walls reaches the critical active state. The magnitude of active earth pressure in the case of translational mode is less than that in the case of rotational mode. The location of action point of earth pressure in the case of translational mode is at or below $\frac{1}{3}$ height of the wall, and in the case of rotational mode, is above $\frac{1}{3}$ height of the wall. Preliminary study indicates a pair of numbers by two theoretical modes can be regarded as an interval estimation of active pressure. Copyright © 2009 John Wiley & Sons, Ltd.     

基于有限元极限平衡法的尾矿坝坝体稳定分析

在平面应变条件下,采用基于弹塑性应力应变分析的有限元极限平衡法对尾矿坝坝体的稳定性进行研究。该方法可较好地结合极限平衡分析方法和有限元应力分析方法的特点。通过弹塑性有限元分析,合理准确地考虑结构整体应力场的影响,进而结合Hooke-Jeeves法优化搜索最危险滑动面的位置及其对应的最小安全系数。以某尾矿坝实际工程为例,比较分析了考虑正常、洪水以及特殊工况运行下有限元极限平衡法与极限平衡条分法和有限元强度折减法在安全系数大小及滑动面形状和位置的差异,重点运用有限元极限平衡法对尾矿坝坝体的稳定性进行验算并作出安全评价,为尾矿坝的安全设计施工提供可靠依据和技术支撑。     

基于GRASS GIS与TIN滑动面的边坡三维极限平衡方法研究

基于开源地理信息系统(GRASS GIS),建立三维极限平衡Hovland模型,研究了边坡稳定性计算方法。采用空间平面投影方法对椭球滑动面中各组成单元面积计算方法进行改进,提高了计算效率。考虑边坡主滑方向与各单元倾向之间的关系,给出了能反映正负变化的滑动面各单元安全系数表达式。通过引入约束Delaunay三角形剖分方法与网格优化算法来生成滑面不规则三角形格网(简称TIN)模型,弥补了Grid模型在滑动面边界准确表达方面的不足。相比Grid模型,在相同网格分辨率条件下,TIN滑动面获得的边坡整体安全系数更加接近正确解,能够有效提升计算精度。通过考题与工程实例,对所提方法与程序模块的正确性进行了验证。结果表明,通过分析滑动面上各单元的安全系数,可以进一步划分不稳定区域与阻滑区,能够为滑坡治理措施的制定提供重要参考。     

Seismic stability for landfills with a triangular berm using pseudo-static limit equilibrium method

This paper extends a previously developed three-part wedge method for the seismic stability analysis of the landfill with a triangular berm using pseudo-static method, and moreover, the translation failure condition of the landfill along under bottom of the berm is only presented. In the seismic impact zone, it is necessary to consider the impact of the seismic force on the stability of the landfill. Generally, apart from the horizontal seismic force, the landfill is also subjected to both upward and downward vertical seismic forces. The downward vertical seismic force has a positive impact on the seismic stability of the landfill, while the upward vertical seismic force is just opposite. Therefore, simply ignoring vertical seismic force, the seismic stability of the landfill will be overestimated or underestimated in the seismic condition. Besides, the seismic yield coefficient is calculated by assuming FS_V = 2FS and the ratio of vertical seismic coefficient to horizontal seismic coefficient is equal to 2/3.     

三维刚体极限平衡法中荷载的计算方法及工程应用

在三维刚体极限平衡矢量分析法的基础上,探讨了一些常用荷载的计算方法,给出了渗流荷载在不同假定下的算法,包括地下水位的结点设定法和滑块高度折减法。该法已应用于小湾电站进水口边坡的稳定分析,得到了有实用价值的结果。     

3D stability analysis of gravity dams on sloped rock foundations using the limit equilibrium method

A convenient approach to performing stability analysis of concrete gravity dams is the so-called two-dimensional “gravity method.” However, concrete gravity dams located in valleys with sloped rock foundation abutments behave as three-dimensional (3D) structures and are often able to share compressive and shear loads between adjacent monoliths, especially when shear keys are present. A general 3D limit equilibrium method was developed in this study to compute global sliding safety factors (SSF_g) by considering sequential load redistribution among adjacent monoliths when individual monoliths have mobilized their sliding strength. Two validation examples of the sliding safety assessment of existing dams are presented to illustrate the accuracy and efficiency of the proposed approach compared to that of the full 3D numerical analyses conducted using the distinct element method. It is shown that gravity dams may be formed by individual monoliths on sloped rock foundations that will slide if considered as isolated structures but will constitute a stable assembly when the load-sharing capabilities of monoliths are recognized in the analysis.     

基于滑动面应力假设下的三维边坡稳定性极限平衡法研究

基于滑动面法向应力的简单计算模式及Mohr-Coulomb强度准则,多个计算参数被使用对滑动面应力进行合理假设,并依据三维滑动体所满足的静力平衡条件,推导三维边坡稳定性极限平衡解答。同时,在三维边坡稳定性分析中,以往研究成果被采用对滑动面剪应力方向进行假定,且基于所采用极限平衡方程数目的不同,由此实现三维边坡极限平衡非严格法、准严格法和严格法。经与经典算例对比,验证了方法的可行性,并分析了三维非对称滑动体时非严格法、准严格法和严格法之间所得结果的差异。研究表明:非严格法所得计算结果偏小,其分析得到的边坡稳定性较为保守;准严格法与严格法计算所得结果接近,故采用不完全满足滑动体所有静力平衡条件的准严格法同样能得到较为可靠的安全系数。此外,所提方法构建了合理的滑动面应力假设,且求解过程简单,无需迭代计算,便于编程,从而利于工程应用。     

基于极限平衡有限元的岩质高边坡安全系数长期预测分析

引入基于Dijkstra算法的极限平衡有限元方法到岩质边坡长期稳定性研究中,得到边坡长期安全系数,并将该方法应用于糯扎渡工程坝肩高边坡,在弹塑性下比较刚体极限平衡和基于Dijkstra极限平衡有限元方法计算结果,认为该算法可信。基于糯扎渡水电站坝肩高边坡有限元流变分析中各时步应力场结果,采用基于Dijkstra极限平衡有限元方法得到各时步潜在滑动面和安全系数。由此判定该边坡长期稳定性,并给出安全系数随时间变化趋势和长期安全系数。     

滑面正应力近似方法对三维极限平衡法解的影响

采用楔形体与椭球滑面算例,研究了三维极限平衡法中滑面正应力近似方法对其计算结果的影响。使用线性插值近似滑面修正应力时,插值节点和网格数目的改变未对安全系数造成明显影响,但明显改变了修正应力的计算结果,网格交界处的修正应力易出现突变。采用移动最小二乘近似滑面修正应力后,安全系数基本不变,并且相对于线性插值,能在求解更少未知量的情况下获得更有规律的修正应力分布。算例表明,在采用线性插值和移动最小二乘近似计算滑面修正应力的情况下,安全系数基本不随滑面正应力的改变而变化,这与二维极限平衡法的相关研究结论基本相同,显示三维极限平衡法满足了平衡条件和合理性条件。     

Elastic solutions for a transversely isotropic half-space subjected to buried asymmetric-loads

Elastic closed-form solutions for the displacements and stresses in a transversely isotropic half-space subjected to various buried loading types are presented. The loading types include finite line loads and asymmetric loads (such as uniform and linearly varying rectangular loads, or trapezoidal loads). The planes of transverse isotropy are assumed to be parallel to its horizontal surface. These solutions are directly obtained from integrating the point load solutions in a transversely isotropic half-space, which were derived using the principle of superposition, Fourier and Hankel transformation techniques. The solutions for the displacements and stresses in transversely isotropic half-spaces subjected to linearly variable loads on a rectangular region are never mentioned in literature. These exact solutions indicate that the displacements and stresses are influenced by several factors, such as the buried depth, the loading types, and the degree and type of rock anisotropy. Two illustrative examples, a vertical uniform and a vertical linearly varying rectangular load acting on the surface of transversely isotropic rock masses, are presented to show the effect of various parameters on the vertical surface displacement and vertical stress. The results indicate that the displacement and stress distributions accounted for rock anisotropy are quite different for those calculated from isotropic solutions. Copyright © 1999 John Wiley & Sons, Ltd.     

冻融循环条件下碳质千枚岩物理力学性质研究

川藏铁路途经川西高海拔变质岩地区,岩石冻融风化强烈,地质灾害多发,开展典型岩石的室内冻融循环试验具有重要的理论意义和工程价值。将采集自金沙江桥位处的碳质千枚岩试样分为5组,选用-40~50 ℃的温差进行周期为8 h（冻、融分别4 h）的冻融循环模拟,每5次冻、融后观察岩样表观变化情况,称取质量并进行超声波波速测试,分别在冻融循环第22,42,65,85,105次后进行单轴抗压强度试验。对取得的各项物理力学指标进行计算分析,结果表明:随着冻融循环次数的增加,岩样表观无明显变化,质量稍有下降且下降速率逐渐降低;冻结后试样纵波波速震荡较大且无明显规律,融解后纵波波速呈下降趋势;试样单轴抗压强度逐渐减小并趋于稳定,岩石表现出脆性减弱而延性增强的特征;岩性对于冻融循环试验结果有重要影响,应当从微裂隙、岩石结构和岩石构造三方面入手进行更多试验以研究岩石冻融损伤机理。     

基于材料状态相关剪胀性的土坡稳定分析极限平衡法

土体剪胀性对土坡稳定性分析的结果有较大的影响,而在传统的极限平衡法中无法考虑土体的剪胀性。以Toyoura砂为例,通过基于材料状态相关临界状态理论的本构模型,确定了摩擦角与剪胀角之间的关系,然后将采用等效摩擦角的方式用于土坡稳定的极限平衡法分析中,提出了一种基于材料状态相关剪胀性的极限平衡法,并通过算例说明在极限平衡法中考虑剪胀角对正确评价土坡稳定性是很重要的。     

酸性环境下类砂岩材料物理性质的试验研究

采用酸性环境下的加速试验方法,研究了不同时段类砂岩材料-砂浆的物理性质,测试了试样的波速,监测了溶液中H+、Ca2+浓度变化,发现在不同腐蚀阶段砂浆表现出来的物理性质相差较大,其反应过程具有阶段性和Ca2+离子溶出具有滞后性的特点。同时,对不同尺寸试样受酸腐蚀的影响程度进行了对比分析,为酸雨地区岩石和混凝土性质的研究提供了可借鉴的思路。     

Elastic solutions for a transversely isotropic half-space subjected to a point load

We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd.     

Multiscale method for long tunnels subjected to seismic loading

A multiscale method for the dynamic analysis of underground structures is proposed, which involves the concurrent discretization of the entire domain with both coarse‐scale and fine‐scale finite element meshes. The coarse‐scale mesh is employed to capture seismic response characteristics of the integral system, whereas the fine‐scale mesh describes in detail the dynamic response in positions of potential damage or interest. For both the coarse‐scale and fine‐scale meshes to overlap, a bridging scale term is introduced so that compatibility of dynamic behavior between the coarse‐ and fine‐scale models is enforced. Both material and contact nonlinearities are considered in the multiscale model. As an application, the model is used for large‐scale seismic response of a newly built long‐distance shield tunnel. Results show that this multiscale method does not have spurious wave reflections at the fine/coarse interface and does not need filtering procedures, which is an advantage compared with the displacement coupling method. Stress and deformation response in lining segments and their connecting bolts are investigated and analyzed within the fine‐scale model, and the capacity of critical structural components, such as bolts and joints is evaluated. Copyright © 2011 John Wiley & Sons, Ltd.     

受酸腐蚀砂岩的物理力学性质探讨

考虑化学作用的岩土力学性质研究及其稳定性问题已成为国内外学者关注的焦点。采用酸性环境下的加速试验,研究了钙质胶结砂岩受酸腐蚀后在不同时段单轴压缩应力作用下表现出来力学特性,揭示了砂岩腐蚀过程和受酸腐蚀机制,其目的是为酸雨环境下,研究岩体的物理力学性质提供可以借鉴的思路和方法。