基于最小二乘法的边坡稳定性分析

利用经典土压力理论设定合理土条推力线范围,根据静力平衡及力矩平衡条件建立以条块界面安全系数 为变量的线性超定方程组,应用MATLAB软件基于最小二乘方法对此方程组求解,依据极大值原理及合理性条件： ,最终获得边坡整体安全系数 。经算例验证得出如下结论：当条块界面与条块整体安全系数相等时,边坡抗剪能力发挥最大;安全系数随推力线位置的升高而减小,但影响并不大;由于考虑了极大值原理,该法求得的安全系数略微偏大于其他方法。     

Slope stability analysis based on the direct comparison of driving forces and resisting forces

The paper disproves a commonly accepted concept that the slope stability problem cannot be correctly solved without invoking the auxiliary static assumptions. The given slope stability analysis is based on the direct comparison of the driving force tending to induce a movement of the slope mass and the mobilized resisting force. A problem of separating the driving forces from the resisting forces is resolved by subdividing an area of the assumed slide mass into two segments wherein the driving forces dominate over the resisting forces at the first segment and vice versa at the other. The slope stability is assessed by the stability index that is equal to a ratio between the resisting forces and driving forces. The stability problem is reduced to determining and analyzing a distribution of the interslice force along the slip line length. A system of recurrence dependencies involving the components of the interslice force and the vertical coordinates of the thrust line is derived from the complete system of the slice equilibrium equations (equilibrium of the horizontal and vertical forces and the force moment equilibrium). This system falls into two subsystems of relations one of which involves only the components of the interslice force. From this it follows that a distribution of the interslice force does not depend on the thrust line position. The slope safety factor regulated by the design manuals for mobilizing the soil shear strength along the slip line is prescribed in advance. A computer program is developed for solving the governing recurrence relations and computing the slope stability index. The applicability of the program is confirmed by solving the problem on a calculation of the critical safety factor for three shapes of the slip line (a circular arc, and a cubic and quadratic parabola) and the stability problem of the real inhomogeneous slope consisting of four layers. Copyright © 2008 John Wiley & Sons, Ltd.     

边坡稳定性分析的条块稳定系数法

鉴于传统条分法对边坡安全系数定义和使用的局限性,引入了条块稳定系数的概念。分析了条间力推力线高度的影响因素,假定条间力传递时都具有相同的条间力稳定系数 ,并考虑了条块重力偏心矩的影响。根据条块的力和力矩平衡关系以及条间力假定,建立了求解条块稳定系数的四元方程组。在此基础上,求得条块稳定系数随滑动面的分布状况。根据条块稳定系数随滑动面的分布规律划分了滑体的主滑段、抗滑段和牵引段,大致判断滑坡的滑动模式。根据滑面上抗滑力和下滑力之比的定义,求解边坡整体稳定系数。采用传统条分法和所建立的条块分析法分别以圆弧滑动和折线形滑动的两个实例进行了验算,说明了条块分析法的优越性和可靠性。     

一般条分法的安全系数显示解

对于边坡稳定性分析中的安全系数方案,根据条底法向力方程,对条底法向力进行假定,使得假定后的条底法向力具有两个待定参数.与传统的条间力假定相比,该假定理论根据更充分,物理意义更明确.通过假定后的条底法向力,化简三个整体极限平衡方程(水平方向、垂直方向力的平衡及力矩平衡),得到安全系数Fs的三次代数方程,其有意义的根为严格满足可能滑动体整体平衡条件的一般条分法的安全系数Fs的显示解.参与计算的有关参数尽管偏多,但都是简单的代数求和.因此,在不损失计算精度的同时,大大简化了一般条分法计算安全系数Fs的过程.算例分析表明,所给一般条分法的安全系数显示解是正确的.     

滑坡稳定分析剩余推力法的改进研究

首先介绍了刚体极限平衡法的基本原理,然后分析了剩余推力法存在的问题,进而提出了一种改进剩余推力法,其基本思想是：在出现屈服的条分面上,改用Sarma法确定条分面之间的作用力,即假定该条分面上的水平推力不变,但剪切力由摩尔-库仑准则确定。最后对改进剩余推力法进行了算例考核,并介绍了三板溪工程应用情况。     

双排抗滑桩加固滑坡的前桩后侧推力算法

为了在求解双排全长桩和后排沉埋-前排全长桩中前桩后侧坡体推力的同时也可得到其分布模式,以便更合理确定前排桩受力特征,针对双排桩加固的基岩-覆盖层式滑坡,采用斜条分法将排间滑体分割成若干斜向平行滑面的土条;对所形成的在不同深度位置的4类典型土条,根据静力平衡条件,推导了其作用于前桩受荷段后侧的推力计算公式,进而可确定出前排桩受荷段后侧坡体推力分布模式及其合力。实例分析表明,本文方法所确定的前桩后侧坡体推力呈不规则抛物线形分布,其峰值点接近于滑面;后排桩沉埋模式时前桩后侧坡体推力比后排桩全长模式时的值小8.6%～10.6%;本文方法比传递系数法的计算值偏大10.6%～13.4%,且相对更接近于FLAC3D模拟结果。     

土坡等圆心角斜条分稳定性分析法

在土坡稳定性计算中,条分法作为一种简单而又实用的方法在实际工程中得到了广泛的应用。传统的条分法大多采用垂直条分,等圆心角斜条分法以斜条分代替垂直条分,使得条间力的假设更为合理。在斜条分的基础上,结合重新定义的应力水平安全系数,使问题的求解也更为简单、迅速,并且求解的结果还可以反映出土条应力状态的差异。     

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.     

边坡稳定分析条块力-位移法及其应用

在现行条分法的基础上,建立了一种全新的边坡条块力-位移分析方法。现行条分法中条块底边的力学参数采用极限平衡状态力学参数,即每个条块底边均处于极限平衡状态,这种极限平衡状态对于残余应力是较为适宜的。采用理想弹塑性模型和一种全新的本构模型描述土条块底边力学特性,并以不平衡推力法为例,提出了临界状态条块的确定方法,针对可能的破坏模式进行了分析,并提出了边坡整体破坏各条块的应力和位移的确定方法,计算出相应的稳定系数,如传统强度折减法、综合下滑力-抗滑力法、主推力法、综合位移法和富余位移法稳定系数。通过计算分析论证了理想弹塑性模型在不改变力学参数的情况下是难以描述边坡渐近破坏过程的,而一种全新的本构模型可以描述渐近破坏各条块的力学行为。提出的条块力-位移法可以确定边坡在不同荷载和位移条件下的稳定性,也可以获得边坡的推力变化和滑面移动特征,进而实施边坡的应力、位移和稳定性的初步预测预报。     

简化Bishop法的剩余下滑推力计算方法研究

简化Bishop法是评价圆弧形滑动面滑坡稳定性的"严格"方法,计算方法简便、精确,已有相关学者研究了其严格性,但却没有与之相适应的滑坡剩余下滑推力解析法,给滑坡（边坡）的综合治理带来了一定困难。本文从简化Bishop法计算原理出发,考虑坡体自重、外力、水平地震力、滑动面处的孔隙水压力等,利用力多边形法则,得到了两类简化Bishop法剩余下滑推力分析模型,即:Ⅰ型（T_i ≥ 0）和Ⅱ型（T_i < 0）;针对两类模型推导出了第i-1条块的下滑推力,然后,使F_i-1参与到第i条块的力多边形受力模型中,从上往下逐条块计算下滑推力,进而推导出条块i的剩余下滑推力解析计算公式。该解析法与传递系数法隐式解所计算的剩余下滑推力进行比较,总体上呈现出简化Bishop法剩余下滑推力高于传递系数法隐式解,两者的剩余下滑推力差值随着安全储备的增大而减小,且该解析法适用于安全储备要求较高的滑坡（边坡）,该解析法为圆弧形滑动面滑坡（边坡）治理设计提供了一定的理论依据。     

降雨入渗非饱和黏土边坡稳定性的极限平衡条分法研究

考虑非饱和黏土边坡的基质吸力和渗流力,根据水位线位于滑面上、下的临界平衡状态,分别建立了滑体条块极限平衡状态下力和力矩平衡式,获得了降雨条件下非饱和黏土边坡稳定性的极限平衡条分法计算式。通过试验、参量变换以及作用力的位置关系可以确定相关参量,并采用数值计算求解临界平衡状态下滑体条块的相互作用力系数和非饱和边坡安全系数。案例结果表明：考虑渗流力时的非饱和黏土边坡安全系数比不考虑渗流力的安全系数降低约13.8%,且考虑渗流力作用的条间力作用系数变化率明显大于不考虑渗流力的结果;当降雨强度超过一定值时,坡面径流很快形成,边坡出现不稳定的时间基本相同。     

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。     

Extremum solutions to the limit equilibrium method subjected to physical admissibility

In the slope stability analysis, the interslice force calculated by the method of slices is the internal force of the slope in the limit equilibrium state, which is vital to the design of reinforcement. However, none of the existing methods can guarantee a priori the interslice force is reasonable. Starting from the global analysis procedure, an optimization problem for maximizing the factor of safety is posed under the constraints that the system of forces in the sliding body is physically admissible. In the problem, both the factor of safety and the normal stress along the slip surface are taken as the independent variables. With weak nonlinearity and no numerical problems inherent in the methods of slices, the optimization problem can be solved by those conventional optimization techniques. No assumption is made regarding the interslice forces, but the system of forces from the optimization problem is physically admissible. To bracket the factor of safety, meanwhile, the minimum of the factor of safety is calculated through a minimization process under the same constraints as the maximization process. It is illustrated that for smooth slip surfaces, the solutions to the maximum and the minimum almost coincide, and for non-smooth slip surfaces, the interval of the solution is very narrow.     

两种滑动面型式下边坡稳定性计算方法的研究

基于圆弧和任意曲线两种滑动面型式,对边坡稳定性计算方法中的瑞典法、简化Bishop法、简化Janbu法、严格Janbu法、Morgenster-Price法、Sarma法和不平衡推力法进行研究。对上述各种方法的研究成果进行了总结,并对Morgenster-Price法中的条间力函数 选择了4种形式（即 为常数0.1、0.5、1.0及半正弦函数）,对不平衡推力法中的公式进行了改进。通过算例对比,及当条分数不同、边坡坡角和坡高变化时,分析了这些方法的特点,由分析结果可知：（1）瑞典法和简化Janbu法计算得的安全系数最小,简化Bishop法和不平衡推力法与严格法得到的结果颇为接近;（2）任意曲线滑动面方法较圆弧滑动面方法计算得的安全系数稍小,且得到的临界滑动面与临界圆弧滑动面相接近,因而表明,圆弧滑动面作为一种近似的临界滑动面能够满足实际工程需要;（3）均质边坡采用较少条分数即可获得较高的安全系数计算精度,非均质边坡需一定数量的条分保证结果的可靠性;（4）Sarma法对土条侧面法向力和剪切的假设,使得其在均质边坡计算得的安全系数比其他方法要大,有偏于不安全的考虑,但Sarma法能够考虑边坡非均质对条分法的影响;（5）当边坡外形（如坡角、坡高）变化时,严格Janbu法在两种滑动面型式下计算得的安全系数相差很小,而其他方法稍大一些;（6）Morgenster- Price法中,条间力函数 对计算得到的结果影响很小。     

基于通用条分原理的锚框支护边坡地震动力稳定分析

考虑水平地震力作用与锚框支护作用,分析微分形式的土条受力平衡,推导积分形式的滑体极限平衡,编程搜索求解相应方程组,提出一套基于通用条分原理的锚框支护边坡地震动力稳定分析方法。利用本文所述方法与数值模拟方法,分别计算了某高速公路锚框支护边坡的动力稳定安全系数,两者结果基本相同。进一步探讨了平均锚固力和地震作用系数对该边坡动力稳定安全系数的影响。本文所述基于通用条分原理的锚框支护边坡地震动力稳定分析方法,具有考虑因素全面、计算工作量小的优点,能够为边坡工程的初步设计,包括坡形设计、锚杆优化、抗震验算等,提供一种较为准确的简便计算手段。     

加筋土边坡稳定性分析的水平条分法

加筋土是一种新型的经济可靠的边坡加固方式。针对新型加筋土边坡带来的问题和基于垂直条块划分的极限平衡方法的不足,提出了一种严格满足力与力矩的平衡的极限平衡分析方法。基于水平条块的严格条分法将滑体水平的划分成若干条块,边坡中的加筋材料产生的抗力作为附加外力作用于条块上,再应用极限平衡的思想和假设对典型条块的受力状态进行分析。根据极限平衡条件推导了边坡安全系数的隐式表达式,再通过力矩的平衡,求解条间力待定系数,进而叠代求解安全系数。说明了利用本文公式计算坡顶极限承载力的方法。该方法计算结果较经典极限平衡法结果稍大。     

Improved Bell's method for the stability analysis of slopes

A new procedure based on the approximation to the total normal pressure along the slip surface is developed to compute the factor of safety of slopes for slip surfaces of all shapes. By taking the whole sliding body, instead of an individual slice, as the loaded object, all the equilibrium equations are formulated according to the three‐moment equilibrium conditions rather than the two force equilibrium conditions and one‐moment equilibrium condition. The system of nonlinear equations deduced in this way is well‐scaled and enjoys excellent numerical properties such as the existence of solution with a positive factor of safety, a nearly unlimited scope of convergence and a rapid convergence rate associated with the Newton method. In the case of ?_u =0—the situation where no drainage and no consolidation are involved, furthermore, the system has a unique solution and the factor of safety has an explicit expression. Some typical examples are analyzed to demonstrate the numerical properties of the proposed procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Limiting equilibrium method for slope/drilled shaft system

The use of drilled shafts to stabilize an unstable slope has been a widely accepted practice. There are two basic design and analysis issues involved: one is to determine the global factor of safety of the drilled shafts stabilized slope and the other one is to determine the design earth thrust on the drilled shafts for structural design of the shafts. In this paper, a limiting equilibrium method of slices based solution for calculating global factor of safety (FS) of a slope with the presence of a row of drilled shafts is developed. The arching mechanisms due to the presence of the drilled shafts on slope were taken into account by a load transfer factor. The method for calculating the net force applied to the drilled shaft from the soil mass was also developed. The interrelationships among the drilled shaft location on the slope, the load transfer factor, and the global FS of the slope/shaft system were derived utilizing the developed numerical closed‐form solution. An illustrative example is presented to elucidate the use of the solution in optimizing the location of the drilled shafts on slope to achieve the desired global factor of safety of the slope/shaft system. Copyright © 2009 John Wiley & Sons, Ltd.     

基于M-P法的抗滑桩支护边坡稳定性分析

为评价采用抗滑桩支护后的边坡稳定性,从设计和验算两个角度着手,基于Morgenstern-Price（M-P）法建立了抗滑桩支护边坡的分析模型,进而得到了抗滑桩下滑力和边坡安全系数的表达式;通过引入自适应遗传优化算法,建立边坡稳定性分析优化模型,搜索采用抗滑桩支护边坡的非圆弧最危险滑动面;从确定安全系数求抗滑桩所受下滑力和确定抗滑桩抗力求边坡最小安全系数两种情况出发,探讨了抗滑桩位置对边坡稳定性的影响。结果表明：该方法可搜索出更加符合实际情况的边坡非圆弧最危险滑动面,并且能够得到抗滑桩的下滑力或边坡的最小安全系数,相同条件下抗滑桩应设置在边坡中部较为适合,才能最大发挥抗滑桩的加固作用。     

Debris slope stability analysis using three-dimensional finite element method based on maximum shear stress theory

How to evaluate debris slope stability reasonably is yet an urgent problem. The paper presents an applied method evaluating debris slope stability, using three-dimensional (3D) finite element contact algorithm based on the maximum shear stress theory. The Guanjia debris slope is located between K9 + 940 and K10 + 200 of Longli First-class Highway in Zhejiang, China. On its left slope, some cracks appeared at the end of 2002 and these were immediately backfilled, overlying a plastic membrane. However, many new cracks appeared on the slope during the rainfall in April 2003. Meanwhile, some small collapses and springs occurred in the front of the slope, and many cracks appeared on the middle part. The stability of the Guanjia debris slope was analyzed using the method proposed in the paper, the strength reduction finite element method, the imbalance thrust force method, Fellenius method, Janbu simplified method, Spencer’s method, Morgenstern–Price method and generalized limit equilibrium (GLE) method. The results show that: (1) the safety factors of the debris slope obtained using the imbalance thrust force method is the minimum in all limit equilibrium methods; (2) 1.07 and 1.06 are the safety factors of Section CC′ and DD′ (the middle part of this slope) of the Guanjia debris slope obtained using the method proposed (FEM with shear strength reduction technique based on the maximum shear stress theory) in this study, respectively, which reflect the slope actual condition in critical failure status; (3) the method proposed in this study may take into account the spatial effect of the debris slope, which makes the results of slope stability analysis more reasonable and reliable than other methods that can be used as a reference for the evaluation of stability of the same type of debris slope; and (3) further study should be done to confirm whether the proposed method in this study is suitable for other types of slopes.