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S. W. Sloan 《国际地质力学数值与分析法杂志》1989,13(3):263-282
This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive-frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory. The computational procedure uses three-noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem. Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure. 相似文献
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非线性破坏准则下的边坡稳定塑性极限分析 总被引：3，自引：0，他引：3
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。 相似文献
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A plane strain yield design approach to stability analysis of a column‐reinforced soil foundation under inclined loading 
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下载免费PDF全文 The ultimate bearing capacity problem of column‐reinforced foundations under inclined loading is investigated within the framework of static and kinematic approaches of yield design theory. The configuration of a native soft clayey soil reinforced by either a group of purely cohesive columns (lime‐column technique) or a group of purely frictional columns (stone‐column technique) is analyzed under plane strain conditions. First, lower bound estimates are derived for the ultimate bearing capacity by considering statically admissible piecewise linear stress distributions that comply with the local strength conditions of the constitutive materials. The problem is then handled by means of the yield design kinematic approach of limit analysis through the implementation of several failure mechanisms, allowing the formulation of upper bound estimates for the ultimate bearing capacity. A series of finite element limit load solutions obtained from numerical elastoplastic simulations suggests that the predictions derived from the kinematic approach appear to be more accurate than the estimates obtained from the static approach. Comparison with available results obtained in the context of yield design homogenization demonstrates the accuracy of the proposed direct analysis, which may therefore be viewed as complementary approach to homogenization‐based approaches when a small number of columns is involved. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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重力坝的深层抗滑稳定分析多采用刚体极限平衡法和非线性有限元法,但刚体极限平衡法不能反映坝基岩体渐进失稳过程和破坏的力学机制,非线性有限元法模拟岩体不连续效率低,且还未有统一的失稳判据。基于离散块体边界应力计算结果,提出重力坝坝基多滑面抗滑稳定安全系数计算公式,并探讨了以坝体-坝基系统能量突变作为坝基失稳判据的物理意义。通过与非线性有限单元法、刚体极限平衡法计算结果的比较,验证了所提方法及判据的可靠性及合理性。结合向家坝水电站重力坝泄12#坝段进行计算分析,结果表明：基于离散元强度储备系数法搜索的坝基失稳通道由坝基岩体屈服区和结构面滑移带组成,所提计算方法与判据适用于实际工程的坝基深层抗滑稳定计算分析,且计算结果偏安全。 相似文献
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In geomechanics, limit analysis provides a useful method for assessing the capacity of structures such as footings and retaining walls, and the stability of slopes and excavations. This paper presents a finite element implementation of the kinematic (or upper bound) theorem that is novel in two main respects. First, it is shown that conventional linear strain elements (6‐node triangle, 10‐node tetrahedron) are suitable for obtaining strict upper bounds even in the case of cohesive‐frictional materials, provided that the element sides are straight (or the faces planar) such that the strain field varies as a simplex. This is important because until now, the only way to obtain rigorous upper bounds has been to use constant strain elements combined with a discontinuous displacement field. It is well known (and confirmed here) that the accuracy of the latter approach is highly dependent on the alignment of the discontinuities, such that it can perform poorly if an unstructured mesh is employed. Second, the optimization of the displacement field is formulated as a standard second‐order cone programming (SOCP) problem. Using a state‐of‐the‐art SOCP code developed by researchers in mathematical programming, very large example problems are solved with outstanding speed. The examples concern plane strain and the Mohr–Coulomb criterion, but the same approach can be used in 3D with the Drucker–Prager criterion, and can readily be extended to other yield criteria having a similar conic quadratic form. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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A new method for computing rigorous upper bounds on the limit loads for one‐, two‐ and three‐dimensional continua is described. The formulation is based on linear finite elements, permits kinematically admissible velocity discontinuities at all interelement boundaries, and furnishes a kinematically admissible velocity field by solving a non‐linear programming problem. In the latter, the objective function corresponds to the dissipated power (which is minimized) and the unknowns are subject to linear equality constraints as well as linear and non‐linear inequality constraints. Provided the yield surface is convex, the optimization problem generated by the upper bound method is also convex and can be solved efficiently by applying a two‐stage, quasi‐Newton scheme to the corresponding Kuhn–Tucker optimality conditions. A key advantage of this strategy is that its iteration count is largely independent of the mesh size. Since the formulation permits non‐linear constraints on the unknowns, no linearization of the yield surface is necessary and the modelling of three‐dimensional geometries presents no special difficulties. The utility of the proposed upper bound method is illustrated by applying it to a number of two‐ and three‐dimensional boundary value problems. For a variety of two‐dimensional cases, the new scheme is up to two orders of magnitude faster than an equivalent linear programming scheme which uses yield surface linearization. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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This contribution is addressing the ultimate limit state design of massive three-dimensional reinforced concrete structures based on a finite-element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state-of-the-art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures. 相似文献
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S. W. Sloan 《国际地质力学数值与分析法杂志》1988,12(1):61-77
This paper describes a technique for computing lower bound limit loads in soil mechanics under conditions of plane strain. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow rule. Using a suitable linear approximation of the yield surface, the procedure computes a statically admissible stress field via finite elements and linear programming. The stress field is modelled using linear 3-noded traingles and statically admissible stress discontinuities may occur at the edges of each triangle. Imposition of the stress-boundary, equilibrium and yield conditions leads to an expression for the collapse load which is maximized subject to a set of linear constraints on the nodal stresses. Since all of the requirements for a statically admissible solution are satisfied exactly (except for small round-off errors in the optimization computations), the solution obtained is a strict lower bound on the true collapse load and is therefore ‘safe’. A major drawback of the technique, as first described by Lysmer,1 is the large amount of computer time required to solve the linear programming problem. This paper shows that this limitation may be avoided by using an active set algorithm, rather than the traditional simplex or revised simplex strategies, to solve the resulting optimization problem. This is due to the nature of the constraint matrix, which is always very sparse and typically has many more rows that columns. It also proved that the procedure can, without modification, be used to derive strict lower bounds for a purely cohesive soil which has increasing strength with depth. This important class of problem is difficult to tackle using conventional methods. A number of examples are given to illustrate the effectiveness of the procedure. 相似文献
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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. 相似文献
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基于非线性规划的有限元塑性极限分析下限法研究 总被引：1，自引：0，他引：1
在分析Sloan建立的有限元塑性极限分析线性规划数学模型存在的局限性基础上,提出了基于非线性规划的有限元塑性极限分析下限法数学模型。采用非线性屈服条件构建了下限法静力容许应力场,建立了求解超载系数、强度储备系数的下限法数学模型,并提出了针对塑性极限分析非线性规划数学模型的求解策略;最后对一个经典算例进行了深入分析,验证了方法的正确性。 相似文献
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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. 相似文献
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对于平面应变条件下岩土稳定性分析,基于线性规划的上限有限元需对常用的摩尔-库仑屈服准则形成的二阶锥约束进行线性化,直接地处理方法是以外接多边形替代锥体投影形成的圆域。为了提高线性化精度往往需直接增加外接多边形边数,从而造成线性规划模型中决策变量包含大量的塑性乘子变量,使计算难度大为增加甚至变得不可行。为此,引入Ben-Tal和Nemirovsky提出的一种二阶锥线性化方法,并将其嵌入到自编的上限有限元程序。经算例分析发现,该法与外接多边形线性化方法所获计算结果相互印证,且其通过适量的增加决策变量和等式约束数目,能保证摩尔-库仑屈服准则线性化精度,同时形成的线性规划规模更小,可望应用于基于线性规划模型的上限有限元中。 相似文献
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Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming 下载免费PDF全文
下载免费PDF全文 In this paper, the formulation of the lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming is described. The finite element concept was used to discretize the soil mass into 3‐noded triangular elements. The stress field was modeled using a linear interpolation within the elements while stress discontinuities were permitted to occur at the shared edges of adjacent elements. An elliptical yield criterion was adopted to model the anisotropic undrained strength of the clay. A statically admissible stress field was defined by enforcing the equilibrium equations within all triangular elements and along all shared edges of adjacent elements, stress boundary conditions, and no stress violation of the anisotropic strength envelope cast in the form of a conic quadratic constraint. The lower bound solution of the proposed formulation was solved by second‐order cone programming. The proposed formulation of the anisotropic undrained strength criterion was validated through comparison of the model's predictions with the known exact solutions of strip footings, and was applied to solve undrained stability of a shallow unlined square tunnel. Computational performance between the proposed approach of second‐order cone programming and linear programming was examined and discussed. 相似文献
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流变场分配(flow field partitioning)现象在自然界高应变岩石中十分常见。传统的基于固体连续变形机制理论的变形分析中,流变场分配问题往往被忽略,致使应变带中流变场如何分配一直都缺乏深入认识。Eshelby阐述了嵌入均匀介质中的椭球体内流变场的数学方法,为探讨流变场的分配奠定了理论基础。本文从固体连续变形机制入手,重点介绍基于Eshelby理论的多尺度数值模拟思路和方法,探讨流变场分配问题。模拟结果表明:嵌入基质中的椭球体内分布的流变场主要取决于椭球体与基质间的相对流变强度,椭球体的相对流变强度越低,其变形越接近于简单剪切,且有限应变积累越快。模拟还揭示,不同流变强度的椭球体内模拟拉伸线理和面理产状的总体格局反映基质流变场特征。由此得到以下结论:(1)在流变场分配现象显著的区域,局部小尺度上应变、涡度测量分析结果无法直接揭示区域流变场运动学边界条件,对这些区域的构造变形分析必须是多尺度的;(2)基于Eshelby理论的以实质变形组构为约束的多尺度数值模拟分析,能更为合理地揭示高应变岩石中流变场的分配。 相似文献
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Alain Corfdir 《国际地质力学数值与分析法杂志》2004,28(6):543-561
Application of yield design to porous media usually requires a preliminary calculation of the fluid flow net. The stability analysis is then carried out with seepage forces associated with the flow. We assume here that the flow is steady and that the yield criterion is defined by a function of the effective stress tensor. The formulation that we propose here allows taking into account seepage force in the expression of the kinematic stability conditions by means of hydraulic boundary conditions without calculation of the fluid flow. One obtains a formulation of the kinematic condition similar to the case of classic, non-porous media. The method is illustrated by two examples: a cylinder subjected to fluid flow and a vertical cut. It can be adapted to various boundary conditions and to the case of a criterion defined by a function of a generalized effective stress tensor. We also give a method to derive rigorous lower bounds using approximate fluid pressure field. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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基于三维非线性有限元的边坡稳定分析方法 总被引：3，自引：0，他引：3
刚体极限平衡法不能反映岩体中实际的应力分布,而基于有限元的强度折减系数法在判断收敛性方面存在一些问题。为了解决这些问题,采用多重网格法,分别建立用于有限元计算的结构网格和用于计算滑面稳定安全系数的滑面网格,可以方便地获得任意滑面或滑块的稳定安全系数,从而将非线性有限元和极限平衡分析结合起来。为了提高计算规模和计算精度,采用有限元并行计算程序TFINE.Pfem进行计算,分析了网格密度对计算结果精度的影响,并应用于锦屏高边坡的稳定分析中。与刚体极限平衡法结果的对比分析表明,由于考虑了计算过程中的非线性应力调整,该方法的计算结果比刚体极限平衡法偏大,而且更符合实际情况。 相似文献