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1.
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
2.
极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法（smoothed finite element method,简称SFEM）的基础上,提出了一种基于新型混合常应力−光滑应变单元的极限分析方法（mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法）。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划（second order cone programming,简称SOCP）问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。 相似文献
3.
极限分析方法是土边坡稳定性分析的重要方法之一。刚体有限元上限法是其中的一类,此类方法仍旧存在一些关键问题需要完善。由于单元的刚性假设,系统的塑性变形内能耗散仅发生在单元间的界面上,故此类方法的性能主要取决于界面的布局,即采用非结构化三角形单元计算往往精度较差。为此,提出了基于滑动面摄动的刚体有限元上限法及临界滑动面的搜索方法。首先,在考虑刚体转动的基础上构造刚体有限元上限法的二阶锥规划模型,用于确定在给定试滑动面条件下的运动许可速度场。其次,将试滑动面的控制参数视为决策变量,建立搜索临界滑动面的非线性非凸优化问题模型,并采用非线性单纯形方法和粒子群方法求解此优化问题找出临界滑动面。通过经典边坡稳定问题的分析求解,验证了所提出的新方法,进一步证实了网格类型（即界面的布局）是影响刚体有限元上限法计算精度的主要因素。经过计算结果的对比发现,在刚体有限元上限法中考虑刚体转动是非常必要的,不仅可以提高刚体有限元上限法的计算精度,还可以克服此方法对界面布局的依赖性。 相似文献
4.
基于线性规划模型的极限分析上限有限元的实现 总被引：2，自引：0，他引：2
极限分析上限有限元法常利用三角形常应变率单元和摩尔-库仑屈服函数线性化的方法,以形成较易求解的线性规划模型。然而为满足计算精度,需引入大量的优化变量,增加了计算和存储的难度。为此,基于线性规划模型,利用MATLAB编制极限分析上限有限元程序,针对线性规划模型等式约束矩阵的高度稀疏性的特点,以稀疏矩阵的方式存储,从而在一定程度上解决了上述问题,使得上限有限元法能处理较大规模的岩土工程稳定性问题。以条形基础地基承载力课题为例进行算例分析,验证该方法的有效性,同时讨论了模型网格单元和塑性乘子数目对计算结果精度的影响。 相似文献
5.
Similar to plane strain, axisymmetric stress problem is also highly kinematics constrained. Standard displacement‐based finite element exhibits volumetric locking issue in simulating nearly/fully incompressible material or isochoric plasticity under axisymmetric loading conditions, which severely underestimates the deformation and overestimates the bearing capacity for structural/geotechnical engineering problems. The aim of this paper is to apply variational multiscale method to produce a stabilized mixed displacement–pressure formulation, which can effectively alleviate the volumetric locking issue for axisymmetric stress problem. Both nearly incompressible elasticity and isochoric J2 elastoplasticity are investigated. First‐order 3‐node triangular and 4‐node quadrilateral elements are tested for locking issues. Several representative simulations are provided to demonstrate the performance of the linear elements, which include the convergence study and comparison with closed‐form solutions. A comparative study with pressure Laplacian stabilized formulation is also presented. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
6.
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
7.
D. T. BergadoJ. C. ChaiN. Miura 《Computers and Geotechnics》1995,17(4):447-471
The behavior of a reinforced embankment on soft Bangkok clay has been analyzed by plane strain finite element method. The finite element analysis considers the selection of proper soil/reinforcement properties according to the relative displacement pattern of upper and lower interface elements. The large deformation phenomenon is simulated by updating the node coordinates, including those of the embankment elements above the current construction level, which ensures that the applied fill thickness simulates the actual field value. A full scale test reinforced embankment with a vertical face (wall) on Bangkok clay has been analyzed by the proposed finite element method, and the numerical results are compared with the field data. The response of a reinforced embankment on soft ground is principally controlled by the interaction between the reinforced soil mass and soft ground and the interaction between the grid reinforcement and the backfill soil. The tension in reinforcement and lateral displacement of the wall face varied during consolidation of foundation soil. The maximum tension force occurred in the reinforcement layer placed at the base of reinforced mass, due to bending of the reinforced mass resulting from differential settlements. It is considered necessary to account for the permeability variation of the soft ground foundation in the finite element analysis. 相似文献
8.
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
9.
Lower bound limit analysis of an anisotropic undrained strength criterion using second‐order cone programming 
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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
10.
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
11.
It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
12.
The paper presents closed‐form solutions for stress and displacement influence functions for stress discontinuity (SD) and displacement discontinuity (DD) elements, for a two‐dimensional plane‐strain elastic, transversely anisotropic medium. The solutions for SD elements are based on Kelvin's problem and for DD elements on the concept of dipoles. Stress and displacement influence functions are derived for the following elements: constant SD, linear SD, constant DD, linear DD, square root DD, parabolic DD, constant DD surface, and linear DD surface elements. The formulations are incorporated into FROCK, a hybridized boundary element method code, and are validated by providing comparisons between the results from FROCK and the finite element code ABAQUS. A limited parametric analysis shows the effects of slight anisotropy on the stress field around the tip of a crack and of the orientation of the crack with respect to the axes of elastic symmetry. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
13.
地基极限承载力分析是土力学研究中的一个经典课题。基于Hellinger-Reissner混合变分原理和有限元方法,将岩土体弹塑性问题构造成基于有限元框架的二阶锥规划（second-order cone programming,SOCP）问题,进而提出一种基于二阶锥规划理论的增量有限元法,即FEM-SOCP法。将岩土体弹塑性问题构造成二阶锥规划的数学优化问题,可以避免采用传统弹塑性计算中复杂的应力点积分等算法和屈服面棱角的平滑处理。此外,对于二阶锥规划问题,可以采用具有原始?对偶内点求解法的标准数学规划求解器MOSEK进行求解。将增量加载FEM-SOCP法应用于经典的基底粗糙的条形浅基础地基极限承载力分析中,分别考虑了关联和非关联塑性条件下的Mohr-Coulomb屈服准则。数值结果表明：所提出的增量加载FEM-SOCP法获得的地基承载力系数及地基承载力与传统FEM计算结果基本一致,而与常规有限元计算结果相比,基于增量加载的FEM-SOCP法所获得的屈服区更加平滑。 相似文献
14.
为研究浅埋隧道掌子面稳定性及获取精细化的破坏模式,提出了一种上限有限元非结构化网格自适应加密策略。以单元耗散能权重指标作为网格自适应加密评判准则,该策略同时兼顾了单元尺度与塑性应变。应用高阶的6节点三角形单元并建立上限有限元线性规划模型,以多次反复计算和网格加密的方式实现了二维自适应上限有限元分析并编制了计算程序。利用条形基础地基极限承载力课题,从上限解精度和网格加密形态方面验证了该程序的有效性。针对浅埋隧道掌子面稳定性问题,展开多参数条件下的自适应上限有限元计算,分析了网格加密过程中单元总数与上限解精度的关系,列出不同隧道埋深和内摩擦角对应的隧道掌子面稳定性临界值的上限解,揭示出掌子面稳定性变化规律及精细化的破坏模式。 相似文献
15.
Measurement of small strain behavior of a local soil by fiber Bragg grating-based local displacement transducers 总被引：1，自引：0，他引：1
The small strain stiffness of soils has a significant role in geotechnical design and analysis. In laboratory, the small strain behavior is examined by different techniques including the bender element method for measuring the maximum shear modulus and local displacement transducer (LDT) for measuring Young’s modulus at small strains. However, most commonly used LDTs are based on electrical components and have limitations, such as electromagnetic interference and possibility of short circuit in the presence of water. To overcome these limitations, in the present study, a conventional triaxial apparatus has been modified to measure and study the stress–strain behavior of soils at small strains. The major modifications include addition of piezoceramic sensors (bender elements) for measuring the maximum shear modulus and fiber Bragg grating (FBG) sensor-based local displacement transducers (FBG–LDTs) for measuring the stress–strain behavior at small strains. The modified triaxial apparatus has been used to conduct several tests on a completely decomposed granite soil from a site in Hong Kong. The stress–strain behaviors measured by the newly developed FBG–LDTs and an external displacement transducer are compared and discussed. In particular, the shear modulus values obtained using the bender elements, FBG–LTDs, and the external displacement transducer are also compared, discussed, and evaluated. The comparison and assessment show that the FBG–LTDs are more suitable for measuring the small strain behavior of soils. 相似文献
16.
ANSYS三维地应力场数值模拟方法应用研究 总被引：2，自引：1，他引：1
初始地应力场由自重应力场和构造应力场叠加而成,是深部地下工程分析必须考虑的重要因素。针对目前常用的三维地应力场数值模拟方法在维持地应力场分布规律和避免附加位移方面存在的缺陷,进行了ANSYS地应力场模拟方法的比较研究。用java语言编写了针对不同ANSYS版本的初始应力文件合并程序,提出了高版本ANSYS初始应力文件合并的EXCEL简易方法,实现了不需编写任何其他程序、对所有类型单元通用的ANSYS初始应力平衡等效节点反力法,构建了一套实用的ANSYS三维地应力场模拟方法流程。 相似文献
17.
It is a well-known fact that addressing hydromechanical problems in saturated soils with the finite element method and equal-order interpolation formulations in displacements and pore pressures produces unstable results. Classically, stabilization has been achieved by increasing the interpolation degree of displacement with respect to pore pressure, hence fulfilling the Babuska–Brezzi condition. However, the use of quadratic elements involves high computational costs. From that point of view, the use of stabilized low-order elements is a more desirable option. Much research has been carried out in different directions in the stabilization of low-order formulations for saturated soils in quasistatic conditions, among others with the technique based on strain field enhancement through internal degrees of freedom. This article presents an alternative displacement–pore pressure formulation for saturated soil dynamics based on the enhancement of the displacement field through incompatible modes. 相似文献
18.
The aim of this study is to arrive at a better understanding of the phenomenon of locking of low‐order compatible displacement type of finite elements in particular for the hour‐glass mode of the plane four‐node element and dilative materials. To this end the properties of finite elements are investigated in an analytical way, where a finite element is considered as a plane boundary value problem with prescribed boundary displacement (Dirichlet problem). In this paper for the sake of simplicity the simplest possible linear comparison solid, namely isotropic linear elasticity, is applied, although recognizing fully that for a dilative material elasto‐plasticity would be more realistic. From the study described in this paper it is concluded that locking of the four‐node element is not due to any particular numerical formulation of this compatible finite element since, even the analytical solution suffers from this problem. The locking of this element is not related to incompressibility of the material either as the analytical solution shows locking to occur at a parameter set which differs significantly from the one in case of incompressibility. It is shown that locking is a consequence of the combination of the dilative material behaviour and the compatible displacement type of boundary conditions, which leads to infinite isotropic stresses in the element. These infinite isotropic stresses occur at the limit of uniqueness of the solution, which for this element is shown to occur outside the parameter range of the sufficiency of uniqueness. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
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20.
In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. 相似文献