三维塑性极限分析下限法原理及应用

介绍了三维塑性极限分析下限法的基本原理。将计算区域离散为有限个三维空间单元,利用极限分析中的下限定理,借助有限元思想建立数学规划模型,并引入非线性规划的数值方法寻求问题的下限解。以均匀土质边坡的极限荷载作为算例,比较了所得数值解与经典塑性力学理论解,论证了该方法的正确性。     

不排水双层粘性土地基极限承载力的数值分析

采用弹塑性有限元分析了条形基础作用下不排水条件的双层粘性土地基极限承载力性状。采用修正的地基承载力系数表征,并将不同的几何与土层参数条件下的数值解与上下限解和经典的经验解进行比较。表明弹塑性位移有限元法可以很好地求解地基的极限承载力问题,其求解得到的修正地基承载力系数与基于下限原理的有限元解很接近,而上限解高估了地基的极限荷载值,传统的经验解在某些条件下却偏小。     

下限分析有限单元法的非线性规划求解

下限分析有限单元法将下限定理这一数学变分问题转化为一个数学规划问题,克服了人为构造可静应力场的困难,在实际工程中具有广阔的应用前景。通过有限元离散得到的非线性下限规划模型中包含大量的优化变量与约束条件,常规优化算法难以求解。为此,在分析非线性下限规划模型自身特点的基础上,引入可行弧技术和Wolfe非精确搜索技术改进其优化求解效率。算例分析表明,基于可行弧技术和Wolfe非精确搜索技术,下限分析有限单元法优化求解程序的收敛速度和步长搜索效率得到明显的提升,并且其数值稳定性良好、计算精度较高,可以较好地适应实际工程问题的计算。     

线性与非线性强度的土石坝坝坡稳定分析下限法

土石坝的坝坡稳定是影响土石坝安全的重要因素,传统的土石坝坝坡稳定采用的是瑞典圆弧法或者毕肖普法,其计算结果既不是下限解也不是上限解。在Sloan的工作基础上,基于有效应力的方式, 用有限单元思想离散结构物,建立满足平衡条件、间断条件、应力边界条件以及屈服条件的极限分析下限法的非线性规划模型,并且编制了相应的程序,应用到土石坝坝坡稳定性的计算中。考虑了地震荷载和渗流作用,采用迭代算法对土石坝进行非线性强度指标的坝坡稳定计算。最后,以几个典型土坡和具体的土石坝工程为算例,与多种方法的分析结果比较,表明了该方法的可行性。     

青藏高原多年冻土区天然气水合物的形成及地球化学勘查

高原冻土带是天然气水合物生成和保存的潜在源区.对青藏高原西大滩-安多长达556 km的多年冻土区烃类有机地球化学剖面的测量结果表明,土壤样品的酸解氢、酸解甲烷、酸解乙烷、酸解丙烷和热释汞异常明显,其异常下限远高于背景值,其中酸解甲烷的背景值为395.54 μL/kg,异常下限为883.84 μL/kg,可见该区天然气水合物成藏具有很好的远景.通过统计学分析和综合地球化学对比分析,指出烃类"负异常"是地下赋存天然气水合物的重要标志.据此初步建立了多年冻土区天然气水合物的形成及地球化学勘查模式.     

基于极限分析法求解基坑支护墙入土深度下限解

基于极限分析下限法构建满足一定规则的静力许可应力场,以极限平衡方程与屈服准则为基础,确定坑底土体的下限极限承载力,并根据其与基坑支护墙入土深度的关系推导出支护墙入土深度的下限解,并提出了基坑抗隆起稳定性分析的计算式。采用工程实例验证了支护墙入土深度的下限解及基坑抗隆起稳定性分析计算的可行性。     

考虑孔隙水压力的土坡稳定性的有限元下限分析

以极限分析下限法理论为基础,应用有限单元思想离散结构物,建立了同时满足平衡条件、应力边界条件、屈服条件和应力间断条件的静力许可应力场,其中孔隙水压力被当作一种类似于重力的外力荷载。引入线性数学规划手段后,得到了考虑孔隙水压力的边坡稳定的下限法数学规划模型,由此可以求出安全系数的下限解及其对应的应力场。最后,以2个经典的土坡为算例,与多种方法的分析结果比较,论证了该方法的正确性。     

非均质土坡的有限元塑性极限分析

在评价现有边坡稳定分析方法的基础上,提出了边坡稳定的有限元塑性极限分析方法。借助有限单元思想和线性规划,建立了边坡稳定的数学规划模型,由此可以求出安全系数的上下限解,从而,界定了边坡的安全范围,同时,可以给出下限状态下的应力场和上限状态下的速度场。以一个经典非均质土坡的边坡稳定作为算例,比较了多种方法的分析结果,论证了本方法的正确性。     

抽汲地下水引起地面沉降的水-土耦合三维有限元数值模拟

建立了抽汲地下水非稳定流定解问题的三维数学模型,利用现有承压含水层非稳定流定解问题数值方程求解,重点讨论了源汇项的具体数学表达式.根据土的有效应办原理和压密原理推导出抽水沉降非线性弹性压密方程,结合武汉新业大厦水文地质与工程地质条件,利用已研制的三维有限元计算程序LCYXY3D.F90对该环境岩土工程问题进行了分析和评价,计算结果与实测结果符合较好.     

偏心荷重下转动浅基承载力的严密解法

根据偏心荷载作用下地基失稳的特征,构建了偏心荷重下地基极限状态时土体中不连续应力场和速度场,分析了土体中不连续应力场和速度场的特点。基于上、下限原理的推论,建立计算模型,构建求解地基极限承载力的算法,通过解三类边值问题,求得偏心荷重下转动浅基极限承载力的严密解,该解满足刚性基础转动的速度边界和其他已知的边界条件。算例表明解垂直偏心荷载下地基极限平衡问题的解法是可行的,且结论可靠。     

Finite-element method in modeling geologic transport processes

Deterministic mathematical modeling of complex geologic transport processes may require the use of odd boundary shapes, time dependency, and two or three dimensions. Under these circumstances the governing transport equations must be solved by numerical methods. For a number of transport phenomena a general form of the convective-dispersion equation can be employed. The solution of this equation for complicated problems can be solved readily by the finite-element method. Using quadrilateral isoparametric elements or triangular elements and a computational algorithm based on Galerkin's procedure, solutions to unsteady heat flux from a dike and seawater intrusion in an aquifer have been obtained. These examples illustrate that the finite-element numerical procedure is well suited for solving boundary-value problems resulting from modeling of complex physical phenomena.     

A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.     

An experimentally verified model of the seepage progress due to dissolution of soluble particles in foundations subject to intergranular flow

The foundations of dams containing soluble material, typically gypsum and limestone, undergo a dissolving process as a consequence of reservoir seepage. In due course, such dissolution of soluble material increases the volume of holes through which water may flow, in turn involving an increase in flow rate through the dam foundation. To adapt dam design to the particular conditions of these foundations, especially in foundations containing gypsum, with the main aims of delaying the dissolution process and avoiding damage or loss of functionality during dam lifespan, a procedure that models the dissolution process coupled with seepage phenomena is necessary. The objective of this paper is to provide this procedure and test it under experimental conditions. This entails coupling a conventional code for calculation of seepage networks, by means of the finite-element method, with a code developed by the authors to calculate the solution front advance (the zone where the dissolution is taking place). The procedure is verified by performing permeameter testing using sand and soluble material mixtures, with the tests being numerically modelled.     

Numerical upper bounds to the ultimate load bearing capacity of three-dimensional reinforced concrete structures

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.     

土石坝横向裂缝的土工离心机模型试验研究

岸坡突变所产生的不均匀沉降变形常常是导致土石坝心墙发生横向裂缝的主要原因。使用糯扎渡高心墙堆石坝心墙混合土料进行了模拟心墙发生横向裂缝的土工离心机模型试验。试验中再现了由于岸坡坡度变化导致坝顶发生横向裂缝的现象。采用工程中常用的3种裂缝分析方法：倾度法、Leonards法和有限元应力法对试验结果进行了分析。结果表明,前两种方法仅在测点较多时才是适用的,而有限元应力法对土石坝心墙横向裂缝问题更为有效。     

3D coupled scaled boundary finite-element/finite-element analysis of ground vibrations induced by underground train movement

When trains move through the tunnels, vibrations are generated and transmitted to the surrounding ground causing vibrations and noises in adjacent structures. The vibrations and noises can sometimes reach such a high level that can hardly be tolerated by the neighboring residents especially in densely populated urban environments. Consequently, the problem of train-induced vibrations has received increasing attention from both engineers and researchers. This paper presents the application of the scaled boundary finite-element method (SBFEM) to the 3D analysis of ground vibrations induced by underground trains. The media around the tunnel is simulated by the SBFEM. The train track is modeled using the finite-element method. 3D examples in both frequency and time domains are addressed to validate the accuracy and applicability of the method.     

An element for modeling potential channel flows between impervious underground structures in an urban regional groundwater flow field

In an urban regional groundwater flow field, the presence of thousands of channels between impervious structures makes the field difficult to simulate using the finite-element method (FEM), because the scale of the field is usually several orders of magnitude larger than that of the channels. To overcome this problem, a simple element for the simulation of potential channel flows has been developed. This element works with linear triangular elements and can be easily implemented in a finite-element code to simulate the channel flows with a sparse mesh without a loss of global accuracy. The transmissivity matrix of this element is deduced from the analytical solution for channel flow. The application of the element is discussed, and the accuracy of the element is assessed. The element makes it easy to merge small structures that are close to each other into a larger one that can be modeled with a sparse mesh.     

Numerical simulation of ground anchors

A procedure of finite-element modeling and beam-column modeling of ground anchors was proposed in this study to investigate the load transfer mechanism in ground anchors. The procedure included the modeling of soil, grout, and strand tendon and the interface modeling of soil–grout and grout–strand in ground anchors. A series of finite element analyses and beam-column analyses were performed using the proposed models on ground anchors. The numerical predictions were compared with observed measurements in a field load test. The results indicated that the numerical simulation of load transfer mechanism on ground anchors can provide reasonable predictions.     

人工填土高边坡爆破振动动力响应分析研究

通过现场测试,利用频谱分析方法,得到了生产爆破引起的地震波在人工填土高边坡中传播特性和基本规律的研究成果;利用有限元软件,结合实测数据采用模态叠加法,对研究边坡进行了动力响应分析,分析了该边坡表面的加速度及位移分布规律、边坡破坏的形式。     

济南泉域岩溶地下水三维等参有限元数值模拟

基于济南泉群研究区域岩溶水贮存和运动特征,建立了三维有限元数学模型,并利用等参有限元方法求解,再根据2001年、2002年的水文资料,识别模型参数,进一步对济南泉域内岩溶地下水的开采方案进行评价,探讨了济南市“保泉”与“供水”的可行性,为科学管理济南市泉群区域内地下水资源提供依据。