多块体接触有限元法及其对不连续面围岩的模拟

给出了一种求解多块体接触的有限元解法,即将接触面条件精确引入并以节点接触力为基本未知量,把高度接触非线性问题凝缩在可能接触面上进行。首先从两块体三维接触力学模型着手,从整体有限元方程导出增量形式的协调方程,在此基础上详细讨论了多块体接触协调方程的建立方法。随后以广义Mohr-Coulomb准则为摩擦力条件,给出了增量形式的定解和判定条件。程序实施时,针对三维接触问题滑动方向无穷的问题,同时对接触状态及滑动摩擦力分量进行判定,使得迭代收敛快速准确;对于多块体常见的非光滑接触,即角点问题,将角点分类,并根据角点实际的接触状态分情况给出了更为合理的处理方法。通过算例验证后的程序应用于不连续面地下洞室开挖模拟,取得了满意的结果。     

Non-linear analysis of geomechanical problems using coupled finite and infinite elements

In modeling of many geomechanics problems such as underground openings, soil-foundation structure interaction problems, and in wave propagation problems through semi-infinite soil medium the soil is represented as a region of either infinite or semi-infinite extent. Numerical modeling of such problems using conventional finite elements involves a truncation of the far field in which the infinite boundary is terminated at a finite distance. In these problems, appropriate boundary conditions are introduced to approximate the solution of the infinite or semi-infinite boundaries as closely as possible. However, the task of positioning the finite boundary in conventional finite element discretization and the definition of the boundary and its conditions is very delicate and depends on the modeller's skill and intuition. Moreover, such a choice is influenced by the size of the domain to be discretized. Consequently, the dimensions of the global matrices and the time required for solution of the problem will increase considerably and also selection of the arbitrary location of truncated boundary may lead to erroneous result. In order to over come these problems, mapped infinite elements have been developed by earlier researchers (Simoni and Schrefier, 1987). In the present work the applicability of infinite element technique is examined for different geomechanics problems. A computer program INFEMEP is developed based on the conventional finite element and mapped infinite element technique. It is then validated using selected problems such as strip footing and circular footing. CPU time taken to obtain solutions using finite element approach and infinite element approach was estimated and presented to show the capability of coupled modeling in improving the computational efficiency. Mesh configurations of different sizes were used to explore the enhancement of both computational economy and solution accuracy achieved by incorporation of infinite elements to solve elastic and elasto-plastic problems in semi-infinite/finite domain as applied to geotechnical engineering. © Rapid Science Ltd. 1998     

Finite element analysis of two cylindrical expansion problems involving nearly incompressible material behaviour

The displacement formulation of the finite element method is well suited to the analysis of elasto-plasticity problems involving compressible material behaviour, but it is well known that numerical difficulties occur when the material is incompressible or nearly incompressible. The effect of these additional constraints depends on both element formulation and mesh topology. A two-dimensional plane strain finite element formulation suitable for the solution of problems involving large strains and displacements (but small rotations) based on the isoparametric approach is described. The kinematics of deformation are defined in terms of the Eulerian strain rates that are invariably used in small strain analysis; the formulation therefore retains some of the character of small strain theory but includes additional geometrically non-linear terms. The results of a series of plane strain finite element analyses of two cylindrical expansion problems are presented. These results confirm the previously observed trend that as Poisson's ratio approaches 0·5 then the quality of the calculated stress deteriorates. The study also indicates that the solution quality depends increasingly on mesh topology as perfect incompressibility is reached.     

动力固结流—固耦合模型的求解方法

以三维多孔介质中基本方程为基础，提出了动力固结问题的力学模型，给出了相应的变分原理及其有限元格式，用轴对称问题的有限单元法模拟了单点单次夯击过程，给出了详细的求解方法及算例，并将计算结果与现场实测资料作了比较。     

Parametric variational principle for elastic–plastic consolidation analysis of saturated porous media

Finite element procedures for numerical solution of various engineering problems are often based on variational formulations. In this paper, a parametric variational principle applicable to elastic-plastic coupled field problems in consolidation analysis of saturated porous media is presented. This principle can be used to solve problems where materials are inconsistent with Drucker's postulate of stability, such as in non-associated plasticity flow or softening problems. The finite element formulation was given, and it can be solved by either the conventional method or a parametric quadratic programming method.     

一种适用于岩土力学无界域的有限元与边界元耦合法的具体实现

针对有限元与边界元耦合法在岩土力学无异域中应用的具体实现问题进行了研究，提出了在微机上实现的具体措施和需建立的程序模块，将有限元与边界元耦合法计算结果、有限元计算结果与理论解析解进行了比较。     

求解非稳定对流占优水质模型的非标准Galerkin有限元法

在求解非稳定地下水溶质运移模型时,若对流项占优,则模型表现出双曲方程的特性。针对这种特性,采用非标准Galerkin有限元方法进行求解是解决这类问题的有效途径。分别采用Wavelet-Galer-kin有限元方法、迎风有限元方法和特征有限元方法对强对流溶质运移模型进行了求解,并将其结果与标准Galerkin有限元和解析解进行对比。结果表明:标准Galerkin有限元方法会产生强烈的数值振荡;Wavelet-Galerkin有限元方法的时空定位效果好;迎风有限元方法能够有效降低数值振荡现象,但迎风因子对解的影响较大,而且会带来时间延迟;特征有限元方法能够提高解的精度,故可以认为特征有限元方法是求解强对流地下水溶质运移模型的首选方法。     

On the use of infinite elements in the analysis of two-dimensional layered elastic systems via discretized integral equations

A boundary integral equation approach is presented for the two-dimensional plane strain analysis of horizontally layered elastic systems resting on a rough and rigid base. The validity of Somigliana identity for unbounded layers is discussed and an Infinite Boundary Element is proposed in order to take into account the lateral unboundedness of the physical problem in the discretized equations. This element is implemented in a computer code based on a successive stiffness solution procedure. A series of numerical tests concerning single- and multi-layered problems is illustrated, and the performance of the proposed solution method is compared with that of more traditional boundary element and finite element techniques.     

Influence of a wall system on the interaction between soil and foundation plates

The paper considers the influence of a building wall system on the interaction between the soil and the foundation plate. A simplified semi-analytical finite element method gives an economical solution for large three-dimensional soil-structure interaction problems. The simplified method appears to be sufficiently accurate for engineering purposes. Numerical results presented show significant influence of building walls on the foundation-plate-soil interaction.     

An approximate F.E. analysis of seepage with a free surface

An approximate step-by-step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non-approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint.     

Finite element methods for variable density flow and solute transport

Saltwater intrusion into coastal freshwater aquifers is an ongoing problem that will continue to impact coastal freshwater resources as coastal populations increase. To effectively model saltwater intrusion, the impacts of increased salt content on fluid density must be accounted for to properly model saltwater/freshwater transition zones and sharp interfaces. We present a model for variable density fluid flow and solute transport where a conforming finite element method discretization with a locally conservative velocity post-processing method is used for the flow model and the transport equation is discretized using a variational multiscale stabilized conforming finite element method. This formulation provides a consistent velocity and performs well even in advection-dominated problems that can occur in saltwater intrusion modeling. The physical model is presented as well as the formulation of the numerical model and solution methods. The model is tested against several 2-D and 3-D numerical and experimental benchmark problems, and the results are presented to verify the code.     

Three dimensional FEM of moving coordinates for the analysis of transient vibrations due to moving loads

This paper is concerned with the transient vibration analysis of railway-ground system under fast moving loads. A 3D finite element method in a convected coordinate system moving with the load is formulated, together with viscous-elastic transmitting boundary conditions in order to limit the finite element mesh. A method is proposed to introduce Rayleigh type material damping in the finite element formulation in the moving coordinate system, while measures have also been taken to improve the numerical stability of the solution procedure. The performance of the transmitting boundary and the entire solution procedure are assessed via comparison with the ordinary finite element solution of some relatively simple problems and through a comparison with field measurements. The reasonable agreement found from these comparisons demonstrates the validity of the proposed method.     

Finite element seepage flow nets

A variational principle and the corresponding finite element equations for determination of the stream function for soil seepage problems is given using the standard finite element potential solution as data. The procedure is very simple and independent of the element type employed. Generalization of the method to multiply connected domains is included.     

Comparative analysis of some geomechanics problems using finite and infinite element methods

Four classical geomechanics problems involving semi-infinite linear elastic media have been solved numerically using recently developed mapped infinite elements coupled to finite elements.The effect of the remoteness of the truncated boundary and the location of infinite element coupling on solution accuracy has been studied. The results of conventional analyses using finite elements over a relatively large but restricted region are compared to the coupled analyses. Comparison of the results shows that for the same number of degrees of freedom the performance of the coupled solutions is superior to the conventional approach with respect to accuracy of solution and computational efficiency. Finally, some general guidelines are proposed for the efficient numerical solution of these types of problems using the coupled finite/infinite element approach.     

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.     

基于粗细网格的有限元并行分析方法

并行计算己成为求解大规模岩土工程问题的一种强大趋势。探讨了粗细网格与预处理共轭梯度法结合的并行有限元算法。从多重网格刚度矩阵推得有效的预处理子。该算法在工作站机群上实现。用地基处理时土体强夯的数值模拟分析进行了数值测试,对其并行性能进行了详细分析。计算结果表明：该算法具有良好的并行加速比和效率,是一种有效的并行算法。     

Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method

The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd.     

Three-dimensional heat,moisture and air transfer in unsaturated soils

A new three-dimensional numerical model of coupled heat, moisture and air transfer in unsaturated soil is presented. In particular, the model accommodates moisture transfer in the form of liquid and vapour flow and heat transfer arising from conduction, convection and latent heat of vaporization. The bulk flow of dry air and the movement of air in a dissolved state are also included. The theoretical basis of the model, the finite element solution of the spatial terms and finite difference solution of the temporal terms are briefly presented. Attention is focused on the verification of the new numerical solution. This is achieved via comparisons with independent solutions of heat, moisture and air transfer in an unsaturated soil. The physical problem considered includes the highly non-linear hydraulic properties of sand. Thermal conductivity is also included as a function of soil moisture content. Excellent correlation of results is shown thus providing confidence in the new model. The new model is also applied to a number of test cases which illustrate the need for the development of a model which can fully include three-dimensional behaviour. In particular, three applications are presented each increasing in complexity. The first application illustrates three-dimensional heat transfer. This particular application is verified against existing commercial finite element software. Subsequent applications serve to illustrate how the coupled processes of heat moisture and air transfer combine to yield three-dimensional problems even within a simple geometric domain. Visualization of three-dimensional results is also addressed. © 1998 by John Wiley & Sons, Ltd.     

浅埋隧道掌子面稳定性二维自适应上限有限元分析

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。     

饱和模型非定常渗流的数值求解方法

提出了饱和模型非稳定流的有限元算法，并对自由面流量补给项提出一种简单的处理方法，从而避免了在迭代中求解自由面的位置，最后给出了计算实例。