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1.
Conventional methods of slices used for slope stability analysis satisfying all equilibrium conditions involves generally solving two highly non‐linear equations with respect to two unknowns, i.e. the factor of safety and the associated scaling parameter. To solve these two equations, complicated numerical iterations are required with non‐convergence occasionally occurring. This paper presents an alternative procedure to derive the three equilibrium equations (horizontal and vertical forces equations and moment equation) based on an assumption regarding the normal stress distribution along the slip surface. Combination of these equations results in a single cubic equation in terms of the factor of safety, which is explicitly solved. Theoretical testing demonstrates that the proposed method yields a factor of safety in reasonable agreement with a closed‐form solution based on the theory of plasticity. Example studies show that the difference in values of factor of safety between the proposed method, the Spencer method and the Morgenstern–Price method is within 5%. Application of the proposed method to practical slope engineering problems is rather straightforward, but its solution is of the same precision as those given by the conventional rigorous methods of slices since it is still within the rigorous context. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
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一般条分法的安全系数显示解 总被引：2，自引：1，他引：2
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. 相似文献
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边坡安全系数的多解性讨论 总被引：4，自引：0，他引：4
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 %。 相似文献
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R. Baker 《国际地质力学数值与分析法杂志》1980,4(4):333-359
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. 相似文献
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临界滑动面搜索是边坡稳定分析中很重要的内容,针对现有方法的不足,提出了一种新的搜索方法。基于边坡稳定性的整体分析法,建立了确定临界滑面的非线性优化模型。该模型将滑面离散点的纵坐标和安全系数都视为独立变量,目标函数取为安全系数本身,约束条件是平衡方程组和滑面凸性。由于目标函数是线性函数,约束条件至多是二次多项式,非线性程度较低,可采用经典优化算法和常见的非线性优化工具求解,比如Matlab。通过实例分析并与传统的滑面搜索方法进行对比表明,所建议的方法在数值稳定性及收敛性方面均具有优势。 相似文献
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在边坡稳定性分析中宜采用严格极限平衡条分法,特别是对于任意形状滑动面。由于条间力假设的不同,产生了不同的边坡稳定安全系数求解格式,既造成计算及应用的不方便,又掩盖了各自方法的优劣。首次将现有严格极限平衡条分法对条间力的假定表示成统一形式,根据力和力矩的平衡,导出简单明了的条间力递推方程和条间力矩递推方程。根据这2个方程,通过Newton-Raphson法建立了传统意义下基于严格平衡的安全系数统一求解格式。所需有关导数均可用递推公式计算,其性质为解析解,因而计算格式具有良好的稳定性与收敛性。所有公式均为代数式,便于在工程中推广应用。 相似文献
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扩展简化Bishop法的取矩中心对安全系数的影响 总被引：3，自引：0，他引：3
扩展简化Bishop法的提出,为非圆弧滑面安全系数的求解提供了一个简便的途径。然而,在建立滑体总体力矩平衡方程时选择不同的取矩中心会得到不同的计算结果,这在某种程度上限制了该法的应用推广。为此,针对不同类型的滑面（组合滑面、折线滑面）,较为系统地研究了取矩中心对安全系数的影响规律,并提出了确定取矩中心的原则。算例分析表明：无论哪种类型的滑面,只要选择合适的取矩中心扩展简化Bishop法便可得到与严格法（Morgenstern-price法）相当的计算精度,且该法数值计算简便,具有较高的实用价值。 相似文献
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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。 相似文献
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基于力平衡的三维边坡安全系数显式解及工程应用 总被引：9，自引：2，他引：7
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。 相似文献
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Determination of the critical failure surface for slope stability analysis using ant colony optimization 总被引：3，自引：0，他引：3
Slope stability analysis of any natural or artificial slope aims at determining the factor of safety of the slip surface that possesses the lowest factor of safety. In this study, an ant colony optimization (ACO) algorithm is developed to solve this factor-of-safety minimization problem. Factors of safety of slip surfaces are found by using the Morgenstern–Price method, which satisfies both force and moment equilibrium. Nonlinear equations from the Morgenstern–Price method are solved numerically by the Newton–Raphson method. In the proposed ACO algorithm, the initiation point and the shape of the slip surface are treated as the search variables. The proposed heuristic algorithm represents slip surfaces as piecewise-linear curves and solves for the optimal curve yielding the minimum factor of safety. To demonstrate its applicability and to investigate the validity and effectiveness of the algorithm, four examples with varying complexity are presented. The obtained results are compared with the available literature and are found to be in agreement. 相似文献
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A numerical model to predict landslide movements along pre‐existing slip surfaces from rainfall data is presented. The model comprises: a transient seepage finite‐element analysis to compute the variations of pore water pressures due to rainfall; a limit equilibrium stability analysis to compute the factors of safety along the slip surface associated with transient pore pressure conditions; an empirical relationship between the factor of safety and the rate of displacement of the slide along the slip surface; an optimization algorithm for the calibration of analyses and relationships based on available monitoring data. The model is validated with reference to a well‐monitored active slide in central Italy, characterized by very slow movements occurring within a narrow band of weathered bedrock overlaid by a clayey silt colluvial cover. The model is conveniently divided and presented in two parts: a groundwater model and a kinematic model. In the first part, monthly recorded rainfall data are used as time‐dependent flow boundary conditions of the transient seepage analysis, while piezometric levels are used to calibrate the analysis by minimizing the errors between monitoring data and computed pore pressures. In the second part, measured inclinometric movements are used to calibrate the empirical relationship between the rate of displacement along the slip surface and the factor of safety, whose variation with time is computed by a time‐dependent stability analysis. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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关于强度折减有限元方法中边坡失稳判据的讨论 总被引：100，自引：18，他引：82
在边坡稳定性分析中采用强度折减弹塑性有限元方法时,所得到的总体安全系数在一定程度上依赖于所采用的失稳评判标准,通常以数值计算的收敛性作为边坡失稳判据。而有限元计算的数值收敛性受多种因素的影响,因而由此所得到的安全系数的合理性及其唯一性受到了质疑。为了考查目前各种失稳判据的合理性及其适用性,分别依据计算的收敛性、特征部位位移的突变性和塑性区的贯通性等3个失稳判据,针对某一典型边坡算例,采用强度折减弹塑性有限元方法进行稳定性分析,并与Spencer极限平衡法所得到的总体安全系数进行了对比。对比分析表明,以有限元数值计算的收敛性作为失稳判据在某些情况下所得到的安全系数可能误差较大,而采用特征部位位移的突变性或塑性区的贯通性作为失稳判据所得到的边坡安全系数与Spencer极限平衡法的计算结果比较接近,考虑到实用性与简便性,建议在边坡稳定性分析的强度折减有限元方法中联合采用特征部位位移的突变性和塑性区的贯通性作为边坡的失稳判据。 相似文献
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K. T. Chau 《国际地质力学数值与分析法杂志》1999,23(15):1835-1855
This paper further examines the possibility of modelling landslide as a consequence of the unstable slip in a steadily creeping slope when it is subject to perturbations, such as those induced by rainfall and earthquakes. In particular, the one-state variable friction law used in the landslide analysis by Chau is extended to a two-state variable friction law. According to this state variable friction law, the shear strength (τ) along the slip surface depends on the creeping velocity (V) as well as the two state variables (θ1 and θ2), which evolve with the ongoing slip. For translational slides, a system of three coupled non-linear first-order ordinary differential equations is formulated, and a linear stability analysis is applied to study the stability in the neighbourhood of the equilibrium solution of the system. By employing the stability classification of Reyn for three-dimensional space, it is found that equilibrium state (or critical point) of a slope may change from a ‘stable spiral’ to a ‘saddle spiral with unstable plane focus’ through a transitional state called ‘converging vortex spiral’ (i.e. bifurcation occurs), as the non-linear parameters of the slip surface evolve with its environmental changes (such as those induced by rainfall or human activities). If the one-state variable friction law is used in landslide modelling, velocity strengthening (i.e. dτss/dV > 0, where τss is the steady-state shear stress) in the laboratory always implies the stability of a creeping slope containing the same slip surface under gravitational pull. This conclusion, however, does not apply if a two-state variable friction law is employed to model the sliding along the slip surface. In particular, neither the region of stable creeping slopes in the non-linear parameter space can be inferred by that of velocity strengthening, nor the unstable region by that of velocity weakening. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
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Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi1 and ψ2, where ψ1 and ψ2, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Development of robust numerical solutions for poro‐elasticity is an important and timely issue in modern computational geomechanics. Recently, research in this area has seen a surge in activity, not only because of increased interest in coupled problems relevant to the petroleum industry, but also due to emerging applications of poro‐elasticity for modelling problems in biomedical engineering and materials science. In this paper, an original mixed least‐squares method for solving Biot consolidation problems is developed. The solution is obtained via minimization of a least‐squares functional, based upon the equations of equilibrium, the equations of continuity and weak forms of the constitutive relationships for elasticity and Darcy flow. The formulation involves four separate categories of unknowns: displacements, stresses, fluid pressures and velocities. Each of these unknowns is approximated by linear continuous functions. The mathematical formulation is implemented in an original computer program, written from scratch and using object‐oriented logic. The performance of the method is tested on one‐ and two‐dimensional classical problems in poro‐elasticity. The numerical experiments suggest the same rates of convergence for all four types of variables, when the same interpolation spaces are used. The continuous linear triangles show the same rates of convergence for both compressible and entirely incompressible elastic solids. This mixed formulation results in non‐oscillating fluid pressures over entire domain for different moments of time. The method appears to be naturally stable, without any need of additional stabilization terms with mesh‐dependent parameters. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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在平面应变条件下,从考虑强度折减的滑动土体极限平衡方程出发,推导出一般情况下均质土坡稳定分析的泛函极值等周模型。依据泛函取极值时必须满足的欧拉方程,通过坐标变换对变分问题求解,得到滑裂面函数及其上分布的法向应力函数。对于给定的边界条件及横截条件,土坡稳定问题转化为求解以两个拉格朗日乘子、安全系数和滑裂面一个端点的x坐标为4个未知量的函数极值问题,可以通过数值计算得到最小安全系数及所对应的最危险滑裂面。考虑坡顶拉裂缝,通过算例分析了不同的滑裂面位置及对应的安全系数。通过对ACADS边坡考题算例分析,在不考虑坡顶开裂的条件下,采用该方法的分析结果与依据极限平衡法得到的各裁判答案非常接近,在考虑坡顶开裂时,安全系数略有减小。 相似文献
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数值分析方法（有限元、有限差分等）可计算边坡应力、变形和破坏,但直接计算边坡安全系数比较困难;而极限平衡法需对边坡体内力作出假设,计算精度受到限制。利用数值分析方法计算得到的应力场,重新定义推力最大原理中推力的含义,将常规边坡临界滑动场数值模拟方法作进一步的改进,提出基于数值应力场的边坡临界滑动场方法。该方法可充分发挥两大方法的优势,能够准确、方便地搜索出边坡临界滑动面位置,并给出更合理的边坡安全系数。通过两个算例的稳定性分析,并与其他方法进行比较,验证了该方法的准确性和合理性。 相似文献