极限平衡条件的拓展与土工结构稳定分析

与土体稳定有关的工程问题诸如挡土结构物上的土压力、地基承载力以及土坡稳定性都与土的极限平衡状态相关 联。将土体一点（单元）的极限平衡条件推广,给出土体沿滑动面的极限平衡条件,证明了该条件的充分必要性。依据该条件,提出了有限元应力分析与极限平衡结合的有限元极限平衡法及土体稳定的安全系数,并明确了安全系数的物理意义,以评价土工结构的稳定性。随后,列举了该方法在土工结构稳定分析中的一些具有代表性的应用,证明了该法是有效的,可以用于分析岩土工程中的稳定问题。     

非线性破坏准则下的边坡稳定塑性极限分析

利用塑性分析上限定理,考虑岩土介质本身的非线性破坏准则,对各种不同破裂面边坡稳定性分析进行研究。针对破坏边坡破裂面不同,采用外切直线法来分析其上限解,推导出非线性破坏准则下的边坡稳定性系数计算公式,并对较复杂的对数螺旋线破裂面边坡提出初始切线法,较好地求出塑性极限分析上限解。将在非线性破坏准则下按对数螺旋线破裂面推导出的塑性极限分析上限解运用于实际边坡工程,其结果与精确塑性分析结果非常接近,为非线性破坏准则下的边坡稳定塑性极限分析提供了一条新的思路与方法。     

基于Hoek-Brown准则的三维边坡变形稳定性分析

采用Hoek-Brown准则,分析三维边坡在开挖扰动下的变形稳定性。以某露天矿边坡为工程背景,利用快速拉格朗日差分法(FLAC3D)建立三维数值分析模型,并在边坡中布置若干监测点,利用FISH语言编制相应位移插值程序,探讨边坡开挖引起的动静态位移响应,从宏观角度揭示出边坡开挖后,不同区域的变形,为工程实践提供指导;介绍了强度折减技术在Hoek-Brown准则中的实施方法,采用计算不收敛失稳判据,计算边坡安全系数,从而进一步推广Hoek-Brown强度折减法在三维边坡稳定性分析中的应用。     

Limit analysis of 2-D and 3-D structures based on an ellipsoid yield criterion

In this paper, a nonlinear numerical technique is developed to calculate the limit load and failure mode of structures obeying an ellipsoid yield criterion by means of the kinematic limit theorem, nonlinear programming theory and displacement-based finite element method. Using an associated flow rule, a general yield criterion expressed by an ellipsoid equation can be directly introduced into the kinematic theorem of limit analysis. The yield surface is not linearized and instead a nonlinear purely kinematic formulation is obtained. The nonlinear formulation has a smaller number of constraints and requires less computational effort than a linear formulation. By applying the finite element method, the kinematic limit analysis with an ellipsoid yield criterion is formulated as a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the dissipation power which is to be minimized and an upper bound to the plastic limit load of a structure can then be calculated by solving the minimum optimization problem. An effective, direct iterative algorithm has been developed to solve the resulting nonlinear programming formulation. The calculation is based purely on kinematically admissible velocities. The stress field does not need to be calculated and the failure mode of structures can be obtained. The proposed method can be used to calculate the bearing capacity of clay soils in a direct way. Some examples are given to illustrate the validity and effectiveness of the proposed method.     

一种基于安全因子判据的坝肩裂隙岩体动力抗滑稳定分析方法

基于某混凝土拱坝,结合现行拱坝设计规范,研究提出了一种基于安全因子判据的坝肩岩体动力抗滑稳定安全度分析方法。该方法综合利用有限元和（刚体）极限平衡两种方法的优点,考虑了凝聚力和摩擦力是不同的抗力,其不确定性具有较大差异性,定义了抗滑稳定安全因子,据此来判别坝肩岩体的抗滑稳定安全度,安全因子随着凝聚力与摩擦力所占权重不同而变化,这种方法既考虑了坝肩岩体与坝体的联动作用,又能够反映拱坝体系真实的工作性态。通过某混凝土高拱坝工程实例,分析了坝肩裂隙岩体的抗震稳定性,结果表明,该方法具有较高的实用价值。     

Upper bound finite element analysis of slope stability using a nonlinear failure criterion

In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly.     

计算边坡安全系数的坡向离心法

边坡稳定分析方法发展最引人注目,它是经典土力学最早试图解决而至今仍未圆满解决的课题。在常用边坡分析方法的基础上,从边坡失稳机制出发,提出一种更方便的安全系数计算方法--坡向离心法。该法通过不断增大水平加速度,直至边坡失稳为止,依据水平加速度与重力加速度失稳影响机制求得安全系数。通过算例与传统极限平衡法和有限元强度折减法相比较,并对各物理参数进行敏感性分析。结果表明,坡向离心法在边坡工程稳定分析中的应用是切实可行的,其弹性模量和泊松比对该法所求安全系数影响不大。     

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。     

采用不同Drucker-Prager屈服准则得到的边坡安全系数的转换

研究了边坡稳定分析的有限元强度折减过程中（平面应变条件下）Drucker-Prager（简称D-P）屈服面的变化特点,从而提出了有限元强度折减法采用不同屈服准则计算得到的边坡安全系数之间的转换关系式。在利用有限元强度折减法计算边坡稳定安全系数时,ANSYS有限元软件采用的岩土材料屈服准则为Mohr-Coulomb（简称M-C）六边形外接圆D-P准则,可先求出外接圆D-P准则条件下的安全系数,然后利用所提出的安全系数转换公式就可直接计算出各D-P准则条件下的安全系数。因此,通过转换就可以在ANSYS程序中实现不同M-C准则,而不需要进行二次开发。采用ANSYS软件通过算例分析,比较了由转换关系式得到的安全系数与实际计算的结果,讨论了转算结果的误差。算例结果表明：通过转换关系式得到的安全系数与计算得到的结果非常接近,具有比较高的计算精度,同时也证明所提出的方法是可行的。     

有限元强度折减法边坡失稳判据的统一性

目前有限元强度折减法边坡稳定性分析中广泛使用的边坡失稳判据主要有3类,即有限元数值迭代不收敛判据、特征部位位移突变判据、广义塑性应变或等效塑性应变贯通判据。对于上述3类判据的选用,一直以来存在较大的分歧。而从本质上看,3类边坡失稳判据具有一致性和统一性。之所以使用不同判据时计算结果表现出差异,是由于人为误判和有限元数值计算误差造成的。在具有足够计算精度的情况下,3类判据所得结果一致。     

边坡安全系数的多解性讨论

边坡安全系数计算结果直接影响边坡工程设计,而极限平衡法不能给出唯一的安全系数值,研究边坡安全系数的多解性,有助于对边坡稳定性计算结果有一个合理地判断与取舍。先假定滑面正应力的初始分布,然后采用含有3个待定参数的拉格朗日函数对其修正,保证滑体满足所有的力与力矩平衡条件;设定一系列安全系数分别求解平衡方程组,得到对应的待定参数值;最后根据滑面正应力分布的合理性判断边坡安全系数的合理范围。算例表明,圆弧滑面合理安全系数范围在5 %以内,而任意形状滑面安全系数最大取值范围可达15 %。     

Stability analysis of rock slopes with a modified Hoek–Brown failure criterion

The original Hoek–Brown (HB) failure criterion was used to analyse the stability of rock slopes. For highly fractured rock, the original HB failure criterion has been modified, but its effect on the stability of rock slopes has not been studied. Within the framework of the kinematical approach of limit analysis, this paper computes the rigorous upper bounds of stability factors of homogeneous rock slopes with the modified HB failure criterion under the plane strain condition, by employing a ‘generalized tangential’ technique. In such technique, instead of using the modified HB failure criterion, a series of linear failure surfaces tangent to the actual non-linear failure surface are utilized to derive the upper bound solutions, incorporating a new parameter n ranging from 0.5 to 0.65. The numerical results are compared with other published solutions for the case of n=0.5. The effects of the n on the stability factors of rock slopes are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

加筋土边坡地震稳定性动点安全系数分析方法

对于地震作用下的土工合成材料加筋土边坡,边坡内部结构的动力响应十分复杂,按照已有的安全系数的方法评价比较困难。结合安全储备系数的原理,并考虑到水平方向和竖直方向地震荷载的共同作用,提出求解加筋土边坡地震稳定性的动点安全系数时程分析方法。在理论分析的基础上,分别定义加筋土边坡土体、土工合成材料和筋-土界面的动点安全系数,并建立数值模型。根据所定义的动点安全系数,在计算过程中使用开发的计算工具对动力响应过程中的动力特性数据进行记录、计算和存储,得到加筋土边坡数值模型在地震荷载作用下的动点安全系数。分析结果表明：动点安全系数时程分析方法具有良好的工程适用性;动点安全系数时程分析方法对复杂的加筋土边坡工程进行的地震稳定性分析考虑了加筋土边坡不同结构的综合稳定性,比现有的分析方法更明确地反应出加筋土边坡工程中相对薄弱的结构,对加筋土边坡工程的抗震设计提供一定参考价值;相比水平方向的地震,竖直方向的地震作用对加筋土边坡中筋材和筋-土界面的稳定性影响较大,但对加筋土边坡土体稳定性影响较小。     

基于系列Drucker-Prager破坏准则评述土坡的稳定性

各种在? 平面上等效面积的Drucker-Prager屈服准则,如DP4(Drucker-Prager与Mohr-Coulomb两屈服准则在? 平面上的投影面积相等)、DP5(Drucker-Prager与Matsuoka-Nakai两屈服准则在? 平面上的投影面积相等)和DP6(Drucker-Prager与Lade-Duncan两屈服准则在? 平面上的投影面积相等)等模型都不同程度地模拟了平面应变条件下土体的破坏强度,这就是为什么等效面积的Drucker-Prager屈服准则在二维土坡稳定分析中被推广应用的原因。结合砂土的真三轴强度破坏试验结果,从量化角度论证了DP4模型求出的土坡安全系数可能会保守一些,而DP5和DP6两模型求出的土坡安全系数可能会更真实一些,能更好地发挥材料的承载潜力,因而进一步改善了土坡稳定安全系数的计算精度。     

关于滑坡稳定性在滑坡安全系数取值中的作用讨论

在工程界存在着滑坡安全系数取值应考虑滑坡稳定性高低、对稳定系数较低的滑坡应采用较大的安全系数的思想。考虑滑坡稳定性的具体方式有两种:①考虑滑坡的实际稳定状态或变形情况;②考虑设计工况下的稳定系数。考虑滑坡稳定性的理由也有两种:①变形急剧势必危害较大;②滑坡在治理后的安全储备可用"安全储备系数"(即下滑力按安全系数放大后的剩余下滑力与下滑力不作改变时的剩余下滑力之比)来衡量,而"安全储备系数"存在着随稳定系数的减小而减小的规律。文章的研究表明,滑坡变形越急剧滑坡危害越大的规律是不存在的,滑坡"安全储备系数"既不能衡量滑坡在治理后的安全储备,也不随滑坡稳定系数的减小而减小,滑坡安全系数与稳定系数无关,将安全系数取值与稳定系数大小挂钩会导致诸多不合理现象产生。因此,滑坡安全系数取值不应考虑稳定系数大小。     

Three-dimensional undrained tunnel face stability in clay with a linearly increasing shear strength with depth

The undrained tunnel face stability in clay with a linearly increasing shear strength with depth was investigated by three-dimensional finite element analysis. Three parametric studies were performed to study the effects of the cover depth ratio, overburden stress factor and linear strength gradient ratio on the load factor of the undrained tunnel face stability. The influence of the linear strength gradient ratio on the predicted failure mechanism of the undrained face stability was discussed and examined. An approximate closed-form solution was proposed for three-dimensional undrained tunnel face stability in clays with constant or linearly increasing shear strength profiles with depth.     

Limit equilibrium method based on an approximate lower bound method with a variable factor of safety that can consider residual strength

In this paper, the factor of safety for a prescribed slip surface will be determined from an equivalent lower bound method (extremum principle), which can satisfy all equilibrium conditions without an interslice force function. This approach will give an overall factor of safety close to that from the classical methods for normal problems, while the thrust line, the local factor of safety for individual slice/block and the progressive yielding phenomenon can be estimated, which will be useful for some special cases. The force and moment equilibrium of every slice will be satisfied, while the location of the thrust line will always be acceptable in the present formulation. To solve the difficult optimisation problem, an innovative coupled particle swarm/harmony search algorithm is proposed in this paper, and a practical engineering problem for which the factor of safety is close to 1.0 is used to illustrate the consideration of the residual strength in the limit equilibrium slope stability analysis.     

Slope stability analysis by means of finite element limit analysis and finite element strength reduction techniques. Part II: Back analyses of a case history

This paper deals with a back analysis of a slope failure. The case history investigated is located in an alpine environment in central Europe and is characterized by a very steep original terrain, indicating in situ soil with high strength. To study the factor of safety, two different approaches applying the so-called φ′/c′ reduction are used, namely finite element limit analysis and strength reduction finite element analysis. Comparison of a strength reduction technique with rigorous finite element limit analysis confirms that the factors of safety (FoS) obtained are very similar for associated plasticity, an intrinsic assumption of limit analysis. For non-associated plasticity, a modified version of the so-called Davis approach has been applied because it has been shown that the original formulation proposed by Davis works well when the FoS is defined in terms of loads but is not appropriate when the FoS is defined in terms of soil strength. The results show that, with the modified Davis parameter, both strength reduction finite element analyses and finite element limit analyses provide very similar factors of safety. The key advantage of limit analysis, however, is that the value of the FoS can be bracketed from above and below with upper and lower bound calculations.     

Limit equilibrium analysis of seismic stability of slopes reinforced with a row of piles

An approach based on the category of limiting equilibrium analysis is proposed to consider the reinforcing effect of one row of vertical piles on slope under seismic conditions. The approach is based on an uncoupled formulation in which the pile response and slope stability are considered separately. Closed‐form equations are derived, allowing the yield acceleration coefficient to be determined for giving pile characteristics. Results were compared with those obtained using another limit equilibrium method. The effects of pile location on the effectiveness of increasing seismic stability of the slope–pile system were elucidated. It was found out that the piles should be installed in the middle–upper part of the slope to achieve greatest safety, but the pile length and other possible failure modes should be checked carefully in design. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of factor of safety for vegetated and barren soil slopes with limit equilibrium computations

Limit equilibrium method (LEM) is the most conventional and popular technique in slope stability analysis. Location of the unique failure surface and the determination of corresponding critical factor of safety (critical-FOS) of the soil slope requires a lot of trial and research. With this amount of trial and research results, we evaluate the field of factor of safety (FOS-field), which represents the critical-FOS at a point within the domain of all possible failure surfaces. Such a field can be very important for the precise judgment of the most critical-FOS of the slope and its perturbation. This paper also presents the evaluation of the FOS-field of vegetated slopes, thus providing an analytical way to examine the effect of vegetation on the soil slope stability. We evaluated the stability of vegetated and barren soil slopes under dry and fully saturated conditions. With dry and fully saturated conditions, the behaviour of slopes in most favourable and worst conditions can be simulated. Evaluation of FOS-field for various slope geometries and conditions show that the more unstable the slope becomes, the more difficult it will be to pinpoint the location of the critical failure surface with the unique least FOS. We verified the LEM codes with finite element method (FEM) and spectral element method (SEM) codes considering a sample problem from Smith and Griffiths’ book (Smith and Griffiths 2003).