Use of the finite element method in modelling a static earth pressure problem

Results obtained with the finite element method are greatly affected by the overall dimensions of the mesh and the number and size of the elements used. Proper choice of the boundary conditions is also necessary to obtain an accurate estimate of the unknowns of the problem. This paper discusses some factors that influence the results of a finite element idealization of the problem of earth pressure behind a gravity wall with a dry, cohesionless backfill.     

Finite volume approach for finite strain consolidation

The paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Fully deformable discrete element analysis using a finite element approach

A method of analysis is presented for problems in which the deformation of the individual blocks play a significant role. The blocks are modeled as single quadrilateral elements and a constitutive model has been presented for computing the contact forces. In order to illustrate the influence of the deformation of the individual blocks two examples have been presented. The results of the analysis with deformable blocks and with rigid blocks are compared. These examples clearly demonstrate the importance of the deformation of blocks in the class of problems represented by these two examples.     

固结问题有限元法时步自适应研究

关于提高有限元法解的精度和稳定性问题已受到不少学者的重视。基于Biot固结理论,为提高有限元法计算的精度和稳定性,研究了固结过程中的时步自适应。采用基本原理推导出时步控制公式,从而全面控制应力和孔隙压力场。研究结果有助于准确模拟应力应变的发展,对粘土心墙土石坝等建筑物的设计及施工有重要意义。     

Variational principles and finite element simulations for thermo-elastic consolidation

In this paper, a general variational principle for the initial boundary value problem of quasi-static thermoelastic consolidation is developed by assuming infinitesimal deformation and an incompressible fluid flowing through a linearly elastic solid. By manipulating the coupling operators, an extended form of the variational pronciple is derved. The associated finite element formulation based on this principle is presented and numerical applications for plane strain thermo-elastic consolidation are revealed.     

波浪作用下某防沙堤的动力固结有限元分析

基于饱和土动力固结理论,采用SWANDYNE II有限元分析,程序预测一个梯形沉箱防沙堤在某设计波浪作用下的响应。采用Pastor-Zienkiwicz Mark III广义塑性模型模拟了海床土的循环应力-应变行为。通过动三轴试验,确定了主要的模型参数,分析中只考虑了波浪对结构的作用,忽略行波对海床表面的作用。动力固结有限元分析的结果定性上与常规的拟静力极限平衡分析方法一致,有限元分析定量给出了体系的位移、应力、孔隙水压力分布和结构位移随波浪持续时间的累积过程,其研究结果初步展现了动力固结有限元方法在近海和海岸岩土工程领域的广阔应用前景。     

Biot固结有限元方程组的病态规律分析

针对Biot固结有限元方程组的病态问题，采用正交试验和量纲分析法探讨病态性的变化规律及其影响因素。主要考虑单元平均尺寸、时间步长、压缩性和渗透性等4个因素的影响。分别提出2组相互独立的相似准则，在此基础上得到2个新的无量纲量，并将其用于分析Biot固结有限元方程组系数矩阵的条件数的变化规律。结合算例进行参数分析结果表明，对病态程度的敏感性由大到小依次为单元平均尺寸、时间步长、压缩性和渗透性；单元平均尺寸太小会使病态加剧；随着2个无量纲量的增大，病态程度呈现单调增加的趋势。其结果为深化对Biot固结数值分析病态问题的认识提供有益参考。     

Numerical performance of projection methods in finite element consolidation models

Projection, or conjugate gradient like, methods are becoming increasingly popular for the efficient solution of large sparse sets of unsymmetric indefinite equations arising from the numerical integration of (initial) boundary value problems. One such problem is soil consolidation coupling a flow and a structural model, typically solved by finite elements (FE) in space and a marching scheme in time (e.g. the Crank–Nicolson scheme). The attraction of a projection method stems from a number of factors, including the ease of implementation, the requirement of limited core memory and the low computational cost if a cheap and effective matrix preconditioner is available. In the present paper, biconjugate gradient stabilized (Bi‐ CGSTAB) is used to solve FE consolidation equations in 2‐D and 3‐D settings with variable time integration steps. Three different nodal orderings are selected along with the preconditioner ILUT based on incomplete triangular factorization and variable fill‐in. The overall cost of the solver is made up of the preconditioning cost plus the cost to converge which is in turn related to the number of iterations and the elementary operations required by each iteration. The results show that nodal ordering affects the perfor mance of Bi‐CGSTAB. For normally conditioned consolidation problems Bi‐CGSTAB with the best ILUT preconditioner may converge in a number of iterations up to two order of magnitude smaller than the size of the FE model and proves an accurate, cost‐effective and robust alternative to direct methods. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of element size on the static finite element analysis of steep slopes

The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher‐order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd.     

Direct,partitioned and projected solution to finite element consolidation models

Direct, partitioned, and projected (conjugate gradient‐like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi‐CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi‐CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two‐dimensional (2‐D) and three‐dimensional (3‐D) coupled consolidation problems. Copyright © 2002 John Wiley & Sons, Ltd.     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

Guidelines for using the finite element method to predict one-dimensional consolidation behaviour

Several finite element schemes, based both on the diffusion and coupled approaches, have been implemented in computer programs and a comparative study carried out to investigate the numerical performance of each scheme. Factors such as stability, convergency, accuracy, computational time and the effects of wide variations in soil parameters (eg laminated soils) have been examined. The study indicates that the numerical performance of each scheme is controlled by a non-dimensional parameter and guidelines have been suggested which allow accurate and economic solutions to be obtained.     

竖井地基的粘弹—粘塑性固结及有限元解

用1个带双屈服面的粘弹-粘塑性模型来描述软土的流变性状，并结合Biot固结理论对软土地基的固结沉降进行有限元分析。对竖井预固结地基进行计算，以预压所产生的沉降量及所引起的附加有效应力分别大于设计载荷所引起的最终沉降量和附加应力为终止预压的依据，计算取得了合理结果。     

断裂问题的扩展有限元法研究

扩展有限元（extended finite element method,XFEM）是近年来发展起来的、在常规有限元框架内求解不连续问题的有效数值计算方法,其基于单位分解的思想,在常规有限元位移模式中加入能够反映裂纹面不连续性的跳跃函数及裂尖渐进位移场函数,避免了采用常规有限元计算断裂问题时需要对裂纹尖端重新加密网格造成的不便。在推导扩展有限元算法的基础上,分析了应力强度因子的J积分计算方法及积分区域的选取。采用XFEM对I型裂纹进行了计算,有限元网格独立于裂纹面,无需在裂纹尖端加密网格;分析了积分区域、网格密度对应力强度因子计算精度的影响,指出了计算应力强度因子的合适参数,验证了此方法的可靠性和准确性。     

无压渗流问题分析的多节点有限元方法

采用基于平均值插值的多节点有限元方法分析有自由面渗流问题。在自由面附近采用多节点单元逼近自由面,利用平均值插值建立多节点单元的形函数,在远离自由面的区域采用四边形/三角形单元剖分。给定一个初始自由面位置,通过对渗流控制方程的多节点有限元求解,根据自由面上节点水头值判断自由面节点的调整方向和大小,最终迭代求出自由面的位置。土坝渗流问题的数值分析表明了所提方法的有效性和足够的计算精度。     

Computations with finite element methods for the Brinkman problem

Various finite element families for the Brinkman flow (or Stokes–Darcy flow) are tested numerically. Particularly, the effect of small permeability is studied. The tested finite elements are the MINI element, the Taylor–Hood element, and the stabilized equal order methods. The numerical tests include both a priori analysis and adaptive methods.     

Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system

A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd.     

A consistent formulation of a dilatant interface element

The paper considers a plane joint or interface element suitable for implementation into a standard non-linear finite element code. The element is intended to model discontinuities with rough contact surfaces, such as rock joints, where dilatant behaviour is present. Of particular concern is the formulation of a constitutive model which fully caters for all possible histories of opening, closing and sliding (accompained by dilation or contraction) in any direction. The non-linear incremental constitutive equations are formulated in a manner appropriate for a back-ward difference discretization in time along the path of loading. The advantage of such an approach is that no essential distinction need be drawn between opening, closing and sliding. Further, a convenient formulation of the constitutive equations is facilitated by representing the different contact conditions in relative displacement space. The state diagram in relative displacement space, however, changes from one time step to the next, and evolution equations for the updating must be formulated. These concepts are illustrated for two rock-joint models: a sawtooth asperity model and a limited dilation model. The models are based on a penalty formulation to enforce the contact constraints, and explicit equations for the tangent stiffness matrix and for the corrector step of the standard Newton–Raphson iterative algorithm are derived. These equations have been implemented as an user element into the finite element code ABAQUS⁷. Three examples are presented to illustrate the predictions of the formulation.