应用点安全系数分析基坑边坡三维稳定性

复杂基坑边坡具有明显的三维效应,目前计算方法尚不便准确计算其三维稳定性,不便于确定其空间失稳范围。在三维数值计算结果的基础上,选用Bezier双三次曲面对通过节点的位移等值面进行拟合,以位移等值面作为基坑边坡局部破坏面,据此计算出垂直破坏面的正应力和滑动方向的剪应力,提出新的点安全系数定义为该点抗剪强度与滑动方向上剪应力的比值,整体安全系数为等值面上点安全系数对面积的加权平均值。分析了某师范大学基坑边坡的稳定性,结果表明,点安全系数在剖面分布上呈中部小,内、外高的分布特征,小于1.06的区域从坡脚延伸至坡顶,揭示了滑动面的位置,最危险滑动面为15 mm的位移等值面。通过与刚体极限平衡法比较,验证了特定剖面上二者计算结果的一致性     

基于力平衡的三维边坡安全系数显式解及工程应用

将基于滑面正应力分布的二维极限平衡显式解法推广到三维边坡稳定性分析,提出适合一般形状空间滑面的三维边坡稳定性简便计算方法。首先,假设三维滑面正应力的初始分布,然后对其修正,使滑体满足所有力的平衡条件,导出关于安全系数的2次代数方程,最终得到三维边坡安全系数显式解。该方法克服了目前条柱法存在的一些难以解决的困难,不需要考虑条柱间作用力具体分布,满足主要平衡条件,计算过程简单。算例表明,该显式解与楔体三维极限平衡解析解完全一致,与对称三维边坡严格极限平衡解答接近。该方法已用于某重力坝坝肩三维滑体初步稳定性分析,计算结果有助于坝肩边坡的加固设计。     

填筑和开挖边坡的稳定性分析

在有限元应力应变分析的基础上,采用以剪应力定义的安全系数和模式搜索的方法确定边坡的安全系数及最危险滑动面。在平面应变条件下,对土层均质的填筑和开挖边坡的稳定性进行了较为全面的研究,并同天然边坡的安全系数和破坏面进行比较,计算结果表明,这3类边坡滑动面的形状基本一致,天然边坡安全系数要高于填筑和开挖边坡;同时比较了采用有限元稳定评价方法和采用极限平衡方法计算结果的差别;最后分析研究了计算参数变化对填筑和开挖边坡稳定性的影响。     

Modeling uncertainty in stability analysis for design of embankment dams on difficult foundations

A probabilistic 3-D slope stability analysis model (PTDSSAM) is developed to evaluate the stability of embankment dams and their foundations under conditions of staged construction taking into consideration uncertainty, spatial variabilities and correlations of shear strength parameters, as well as the uncertainties in pore water pressure. The model has the following capabilities: (1) conducting undrained shear strength analysis (USA) and effective stress analysis (ESA) slope stability analysis of staged construction, (2) incorporation of field monitored data of pore water pressure, and (3) incorporation of increase of undrained shear strength with depth, effective stress, and pore water pressure dissipation. The PTDSSAM model is incorporated in a computer program that can analyze slopes located in multilayered deposits, considering the total slope width.

The main outputs of the program are the geometric parameters of the most critical sliding surface (i.e., center of rotation/radius of rotation and critical width of failure), mean 2-D safety factor, mean 3-D safety factor, squared coefficient of variation of resisting moment, and the probability of slope failure. The program is applied to a case study, Karameh dam in Jordan. Monitored data of induced pore water pressure in the dam embankment and soft foundation were gathered during dam construction.

The stability of Karameh dam embankment and foundation was evaluated during staged construction using deterministic and probabilistic analysis. Foundation stability was evaluated based on the monitored data of pore water pressure.

The study showed that the mean values of the corrective factors which account for the discrepancies between the in situ and laboratory-measured values of soil properties and for the modeling errors have significant influence on the 2-D safety factor, 3-D safety factor, slope probability of failure, and on the expected failure width.

The degree of spatial correlation associated with shear strength parameters within a soil deposit also influences the probability of slope failure and the expected failure width. This correlation is quantified by scale of fluctuation. It is found that a larger scale of fluctuation gives an increase in the probability of slope failure and a reduction in the critical failure width.     

滑带土抗剪强度参数的三维反分析

以滑面正应力修正模式的三维边坡稳定性分析方法为基础,建立了确定滑带土抗剪强度参数的三维反分析模型。先对滑坡体的稳定性进行调查评估,确定滑坡的安全系数与三维滑面的几何尺寸;然后,通过对滑面正应力进行合理假定与修正,建立了平衡方程,以强度参数为未知数,利用数学方法并结合试验、经验等手段求解出抗剪强度参数。该模型克服了二维反分析将会高估滑带土的抗剪强度参数的缺陷,而且计算过程简单,易于编程实现。两个简单算例表明,三维反分析模型可以考虑三维滑体的空间效应,得到的抗剪强度参数更真实、更符合实际情况,为滑坡治理提供参考。     

膨胀变形对膨胀土边坡稳定性的影响

当采用合理的强度参数时,根据常规极限平衡或极限分析方法的计算结果,很难解释一些膨胀土边坡会在极缓的坡度下发生失稳破坏的原因。事实上,由于膨胀土遇水后会发生显著的变形,在饱和区与非饱和区交界面附近会出现很大的剪应力。因此,在膨胀土边坡的稳定分析中,需要考虑这种因素的影响。根据塑性力学的上限定理,严格地导出了考虑膨胀应力作功的功能平衡方程。根据强度储备定义的安全系数即隐含在这一方程中,它可以通过迭代方法求解。边坡稳定的上限分析在数值上是利用了单元集成法来完成的。这不仅能方便地利用应力分析的成果,而且能进行滑裂面的优化,从而找到最小的安全系数。对一个坡度为1:4的膨胀土边坡的稳定计算结果表明,膨胀变形会使边坡的安全系数显著减小。当考虑膨胀时,优化得到的破坏模式是在浅层出现一个局部的滑动,它会牵动其上部的土体也相继出现局部滑动,这正好符合膨胀土滑坡时所常见的牵引性的特征。     

基于聚类分析的边坡稳定性研究

在边坡稳定性分析中,滑面搜索方法对于得到边坡的稳定性系数至关重要。现今两种常用的边坡稳定性分析方法,极限平衡法以及强度折减法,可以得到极限应力状态下边坡的潜在滑面。而为了评价边坡在当前应力场下的稳定性,提出一种基于聚类分析概念的滑面搜索方法。这种方法综合考虑了边坡各点的位移以及点安全系数,采用K均值聚类法将具有相近性质的点进行分类,把边坡体分为潜在危险区以及稳定区。潜在危险区的边界即为边坡在当前应力状态下的潜在滑面,并运用矢量和方法计算得到其稳定性系数。采用上述方法对3个算例进行验算,并与极限平衡法以及强度折减法进行对比。结果表明：（1）基于聚类分析的边坡稳定性评价方法具有较好的合理性和可靠性;（2）当边坡处于临界状态附近,通过聚类分析得到的潜在滑面与其他两种方法得到的滑面基本一致;当边坡处于较稳定状态时,当前应力状态下的潜在滑面要比强度折减法得到的滑动带范围要更深更广,但求出的稳定性系数也较高;当存在软弱夹层时,矢量和计算出的滑面更为陡峻,稳定性系数比其他两种方法的结果要小。     

滑坡稳定性分析的点安全系数法

建立滑坡数值计算的三维模型,将滑带离散为薄层8节点六面体单元,采用基于摩尔-库仑强度准则的理想弹塑性本构模型模拟滑带材料,通过数值计算,可获得滑带单元的三维应力状态和滑动方向。定义单元点安全系数为滑带单元抗剪强度与滑面上平行滑动方向的剪应力之比,定义滑坡整体安全系数为单元点安全系数对滑带面积的加权平均值。采用点安全系数分析滑坡的空间滑动机制,采用整体安全系数评价滑坡稳定性。算例分析表明,分析结果符合现场实际情况。     

基于有限元计算的边坡三维滑裂面搜索

提出一种基于有限元计算的边坡三维滑裂面搜索的方法,根据有限元计算的应力结果,计算可能滑裂面的安全系数,然后用遗传算法搜索出最危险滑裂面,并得出相应的安全系数作为边坡的安全度评价指标。该方法的优越性是只需进行一次有限元计算,不需要假定滑裂面,可以用于具有复杂地貌和地质构造的三维边坡。通过算例,验证该方法的可行性和程序的正确性,以大岗山水电站库区边坡工程实例验证该方法的实用性。     

基于潘氏极大值原理的边坡稳定性的整体分析法

基于整体分析法和潘家铮最大值原理,建立了求解给定滑面安全系数的非线性优化模型。该模型将安全系数和滑面法向应力视为独立变量,目标函数就是安全系数本身,约束条件包括平衡方程、滑面法向应力和条间推力不负,以及推力线位于滑体之内。由于目标函数又仅是线性函数,且约束函数至多是二次多项式函数,所以该模型的非线性程度较低,具有良好的收敛性,可利用经典的优化算法进行求解。     

非线性破坏准则下边坡稳定性极限分析斜条分法

考虑坡顶均布荷载和地震效应典型情况下,将边坡滑体进行任意斜条块划分,建立了具有倾斜界面的多块体破坏模型。基于极限分析上限法和非线性摩尔-库仑破坏准则,考虑岩体内正应力的不均匀性,引入多点切线法和强度折减法推导得出边坡临界破坏状态下的安全系数Fs通用计算公式。采用序列二次规划法对安全系数Fs的目标函数进行最优化计算,并与既有研究成果进行对比分析,其结果具有较好的一致性,相对误差不超过3.565%,表明了该方法的正确性。同时对比传统单点切线法计算结果,多点切线法较单点切线法获得的边坡安全系数值偏小,表明了多点切线斜条分法偏于保守,是安全的。参数分析表明坡顶均布荷载、地震效应和非线性参数均对边坡安全系数及潜在临界滑裂面有重要影响。多点切线法引入非线性摩尔-库仑破坏准则对边坡进行稳定性极限分析,为相关研究人员提供了一种新的思路与方法。     

Determination of the critical slip surface in slope stability computations

The analysis of the stability of slopes using limiting equilibrium considerations necessitates the determination of the critical slip surface which yields the minimal factor of safety. The numerous methods currently available for slope stability analysis provide a procedure for assigning a factor of safety to a given slip surface, but do not consider the problem of identifying the critical conditions. This paper presents an effective minimization procedure based on dynamic programming by which the minimal factor of safety, and the corresponding surface, are determined simultaneously. This procedure SSDP (Slope Stability by Dynamic Programming), couples the minimization scheme with Spencer's method of slope stability analysis. It may be applied to slopes of any geometry, layering, pore pressure and external load distributions. No arbitrary restrictions are placed on the shape of the slip surfaces, and the analysis satisfies all equilibrium equations. Application of the procedure to slope stability problems reported in the literature shows that for a given slip surface the procedure yields factors of safety which are almost identical to those reported, but in every case a more critical slip surface, with a lower factor of safety, may be found.     

Sensitivity analysis applied to slope stabilization at failure

This article discusses how sensitivity analysis is a sound assessment tool for selecting the most efficient stabilization method of slopes at failure. A discretized form of the variational approach is used not only for performing sensitivity analysis but to locate the critical slip surface, i.e., the sensitivity analysis is carried out in the same way as it is done in optimization problems. This method supplies a robust formulation and methodology for obtaining the sensitivities of the safety factor with respect to both the soil parameters and the slope profile, stating the slope stabilization design as a relatively simple minimization problem. Two well known examples, as the Selset landslide and the Sudbury Hill slip are used to illustrate the application of the method and to highlight both its capabilities and limitations.     

地震效应下非线性抗剪强度参数对裂缝边坡稳定性影响的上限解析

基于非线性Mohr-Coulomb破坏准则,结合极限分析上限法和拟静力分析法,建立功能方程,推导了地震效应下裂缝边坡的安全系数计算方程。采用数学规划方法,计算了不同参数组合条件下的边坡安全系数值,详细分析了非线性条件下一系列参数对边坡稳定性的影响。研究表明,边坡安全系数随非线性参数和地震效应的增大而减小。对比分析可知,在非线性破坏准则下,裂缝深度较大时,裂缝对边坡稳定性影响显著,且边坡越陡影响越大;当裂缝深度超过某个值后,临界破坏面起始端可能不穿过裂缝最底端,而是从裂缝中间某部位穿过。在地震效应作用下,非线性抗剪强度参数对安全系数影响显著。研究成果进一步完善了裂缝边坡稳定性分析内容,所列图表为边坡的设计与施工提供有益参考。     

GIS-Based Probabilistic Mapping of Landslide Hazard Using a Three-Dimensional Deterministic Model

Based on a new Geographic Information Systems (GIS) grid-basedthree-dimensional (3-D) deterministic model and taking the slopeunit as the mapping unit, this study maps landslide hazard usingthe 3-D safety factor index and failure probability. Assuming theinitial slip to be the lower part of an ellipsoid, the 3-D critical slipsurface in the 3-D slope stability analysis is located by minimizingthe 3-D safety factor using the Monte Carlo random simulation.The failure probability of the landslide is calculated using anapproximate method in which the distributions of c, andthe 3-D safety factor are assumed to be in normal distribution.The method has been applied to a case study on three-dimensionallyand probabilistically mapping landslide hazard.     

A calculation method for the embedded depth of stabilizing piles in reinforced slopes

Embedded stabilizing piles are a significant optimization measure for traditional piles used to reinforce slopes or landslides. The determination of the embedded depth of the pile top is essential for engineering design. On the basis of the potential overtop-sliding failure mechanism for a piled slope, the corresponding overall slip surface is assumed to consist of the upper part from the original slip surface of the landslide, and the lower part occurs in the local slide mass upslope of the piles. The imbalanced thrust force method is used to determine the thrust force of the upper slide mass, and a variational calculus method within the framework of limit equilibrium for the lower slide mass is provided to calculate its limit resistance. According to the equilibrium relationship between the thrust force and the limit resistance under a design factor of safety of the piled slope, a closed-form solution to the piled-slope stability is specifically derived. It can quantitatively exhibit the influences of some important factors, including the embedded depth on the factor of safety and the corresponding slip surface of the slope. The analysis results of some practical examples show that the factor of safety decreases nonlinearly as the embedded depth increases. The proposed method can be applied in practical engineering.     

阻滑桩加固土坡稳定性分析的上限解法

从极限分析机动学方法出发,利用土的抗剪强度折减系数概念,建立了土坡的极限平衡状态方程,由此确定土坡的临界稳定安全系数及其相应的潜在破坏模式.对于典型问题,通过与现有极限平衡解和有限元数值解的对比分析,验证了这种上限解法的合理性.进而对于在给定的荷载条件下不能满足抗滑稳定性要求的土坡,考虑采用阻滑桩加固方式,根据桩侧有效土压力的合理分布模式确定桩体与滑动面相交的截面上等效抗滑力和抗滑力矩,利用极限分析上限定理建立了阻滑桩加固土坡的极限平衡状态方程,将桩侧土压力作为目标函数,运用数学规划方法确定了极限平衡状态时的临界桩侧土压力,以此为土坡加固中阻滑桩设计提供依据.通过数值计算与分析探讨了阻滑桩加固位置的优化布置等问题.     

多层边坡破坏机制数值模拟研究

通过大量的多层边坡算例来分析FLAC3D强度折减法在不同强度、坡比和层厚的情况下所得安全系数与滑动面位置的变化规律,并与极限平衡法进行对比,探究强度折减法和极限平衡法所得结果产生差异的原因,揭示多层边坡的破坏机制。数值模拟计算结果表明:①对于上层土体强度较软的边坡,当上下层强度相差到一定程度,表现为上层破坏,强度折减法与极限平衡法的安全系数相对差值最大,达5%~7%;上层土体厚度h增加时,安全系数逐渐减小;上层土体位于地表以下时,滑动面通过坡趾,安全系数保持不变。②对于下层土体强度较软的边坡,当上下层强度相差到一定程度,强度折减法所得安全系数基本保持不变,但极限平衡法仍保持增长趋势,最大相对差值可达12%;上层土体厚度h增加时,安全系数也相应增大,h位于9~12 m,边坡表现为深层破坏;而h=12 m时,极限平衡法的滑动面却通过坡趾,但安全系数相差很小。当h的变化范围在3~5 m,两种方法的安全系数相对差值最大,达6%~10%。破坏区分布分析表明,边坡呈拉伸-剪切复合破坏,对于下层土体强度较软的边坡,复合破坏模式更显著,与单一剪切破坏模式相比,最大有10%左右的相对差值。     

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。     

Improved finite element–based limit equilibrium method for slope stability analysis by considering nonlinear strength criteria and its application in assessing the anchoring effect

The shear strength envelope of most geotechnical materials is nonlinear. In this study, the finite element–based limit equilibrium method (FELE) is improved to assess the stability of a prescribed slip surface that obeys a nonlinear failure criterion. Two nonlinear failure criteria, namely, the Barton criterion and the generalized Hoek-Brown (GHB) criterion, are implemented. A power curve model that can perfectly fit the envelope of the GHB criterion is proposed to explicitly express the shear strength from the normal stress. The algorithm of the improved FELE, which includes a nonlinear criterion, is explained in detail, and the fast convergence of the method is checked by evaluating examples. The numerical examples show that, for a smooth slip surface, FELE can calculate a greater factor of safety (FOS) than that calculated using the Morgenstern-Price (MP) method when the strength criterion of slip surface is nonlinear. In addition, FELE can determine the bell-shaped distribution of the increase in normal stress caused by anchoring measures, which cannot be considered in the MP method.