A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

A mixed finite element approach for viscoelastic wave propagation

In this paper, we are interested in the modeling of wave propagation in viscoelastic media. We present a family of models which generalize the Zeners model. We achieve its mathematical analysis: existence and uniqueness of solutions, energy decay and propagation with finite speed. For the numerical resolution, we extend a mixed finite element method proposed in [8]. This method combines mass lumping with a centered explicit scheme for time discretization. For the resulting scheme, we prove a discrete energy decay result and provide a sufficient stability condition. For the numerical simulation in open domains we adapt the perfectly matched layers techniques to viscoelastic waves [23]. Various numerical results are presented.     

基于线性规划模型的极限分析上限有限元的实现

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。     

UH模型在有限元分析中的应用

由姚仰平等提出的超固结土统一硬化模型(UH模型)能够描述超固结土的硬化、软化、剪缩和剪胀等应力应变特性以及应力路径对它的影响。通过改进,直线型的Hvorslev线由抛物线型的Hvorslev线代替,UH模型的参数与剑桥模型(Cam-clay模型)的参数相同。应用该模型,对三轴试验进行有限元模拟,分析了与应用Cam-clay模型所得应力应变关系曲线的异同点;针对刚性承压板试验,进行了地基承载力的三维有限元分析,比较了与应用Cam-clay模型和摩尔库仑模型(Mohr-Coulomb模型)等所得p-s曲线的不同,分析了地基中不同点处的应力-应变关系曲线,并与Boussinesq弹性理论计算的应力做了比较;进行了地基固结沉降数值分析,比较了孔压、沉降的变化规律,体现了UH模型的优越性。     

A finite element model for the analysis of tailored pulse stimulation of boreholes

A constitutive model is described for the prediction of dynamic crack formation in geological media. The model includes a simple tensile failure criterion for crack formation and a soil plasticity model for both deviatoric and volumetric plasticity. Numerical results are presented which show that the model reproduces the observed dependence of fracture formation on loding rate for dynamic pressure loading of boreholes. The use of the model as a numerical tool for design is demonstrated through two example parameter studies.     

带相变瞬态温度场问题的扩展有限元解析

带相变瞬态传热问题是寒区工程多场耦合问题求解的关键.在剖析常规有限元法在求解带相变瞬态温度场问题的不足的基础上,结合冻土冻融温度变化的特点,提出采用扩展有限元法求解冻土工程带相变瞬态传热问题的新方法,以四边形单元为例推导了冻土工程温度场的求解格式,详细剖析了瞬态传热过程中移动界面水平集函数的构造、单元刚度矩阵的形成及高斯积分的求解.据此编写了相应的扩展有限元程序,通过经典Stefan问题全面验证了程序的正确性与合理性.     

A finite element porothermoelastic model for dual-porosity media

An existing dual-porosity finite element model has been extended to include thermo-hydro-mechanical coupling in both media. The model relies on overlapping distinct continua for the fluid and solid domains. In addition, conductive and convective heat transfers are incorporated using a single representative thermodynamics continuum. The model is applied to the problem of an inclined borehole drilled in a fractured formation subjected to a three-dimensional state of stress and, a temperature gradient between the drilling fluid and the formation. A sensitivity analysis has been carried out to study the impact of thermal loading, effect of heat transport by pore fluid flow and, the effect of parameters of the secondary medium used to represent the fractures. Copyright © 2004 John Wiley & Sons, Ltd.     

A novel finite element method for seepage analysis

A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately. The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.     

A finite element method for studying the transient non-linear thermal creep of geological structures

A finite element theory, suitable for describing the long-term transient thermal creep of geomechanical structures where the material obeys an arbitrary type of creep law, is presented. The method takes into account large deformation effects, is stable for the large time steps required to model geophysical phenomena and accurately simulates changing, incompressible, plastic flow fields. Applications of the theory to the prediction of long-term creep and creep rupture of simple engineering structures, are given. The theory is also applied to predict the thermal creep of layered media to study the mechanics of folding and rift formation.     

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。     

Sensitivity analysis applied to finite element method model for coupled multiphase system

Today multiphysics problems applied to various fields of engineering have become increasingly important. Among these, in the areas of civil, environmental and nuclear engineering, the problems related to the behaviour of porous media under extreme conditions in terms of temperature and/or pressure are particularly relevant. The mathematical models used to solve these problems have an increasing complexity leading to increase of computing times. This problem can be solved by using more effective numerical algorithms, or by trying to reduce the complexity of these models. This can be achieved by using a sensitivity analysis to determine the influence of model parameters on the solution. In this paper, the sensitivity analysis of a mathematical/numerical model for the analysis of concrete as multiphase porous medium exposed to high temperatures is presented. This may lead to a reduction of the number of the model parameters, indicating what parameters should be determined in an accurate way and what can be neglected or found directly from the literature. Moreover, the identification parameters influence may allow to proceeding to a simplification of the mathematical model (i.e. model reduction). The technique adopted in this paper to performing the sensitivity analysis is based on the automatic differentiation (AD), which allowed to develop an efficient tool for the computation of the sensitivity coefficients. The results of the application of AD technique have been compared with the results of the more standard finite difference method, showing the superiority of the AD in terms of numerical accuracy and execution times. From the results of the sensitivity analysis, it follows that a drastic simplification of the model for thermo‐chemo‐hygro‐mechanical behaviour of concrete at high temperature, is not possible. Therefore, it is necessary to use different model reduction techniques in order to obtain a simplified version of the model that can be used at industrial level. Copyright © 2012 John Wiley & Sons, Ltd.     

三个因素对缓冲层饱和过程影响的二维有限元分析

在参与高放射性核废料地质处置库的缓冲层饱和过程的诸多因素中,初始的水头、渗透系数和饱和度最为关键。作者使用THM耦合问题的二维有限元方法分析了以上三个因素对缓冲层饱和过程的影响。由计算结果可知,初始的水头、渗透系数和饱和度的数值越大,缓冲材料达到饱和的时间越快,反之亦然。     

高填石路堤动力响应的室内模型试验及弹塑性有限元分析

高填石路堤在工后运营过程中,长期受到动力荷载的作用。基于相似比理论建立高填石路堤动力响应的室内试验模型,以简谐振动荷载和冲击荷载模拟高填石路堤实际受到的复杂动力荷载,采用动土压力盒和加速度计拾取模型路堤在振动器作用下的响应波形,利用Drucker-Prager弹塑性本构模型进行模型路堤的动力响应有限元分析。分析结果表明,有限元分析值与实测值比较接近,即使在较大的动力荷载作用下,高填石路堤内部产生的塑性区也只是暂时的和局部的,仍可维持其整体稳定,且表现出应变硬化的动力特性。     

一种双重孔隙-裂隙岩体流变模型及其在地下洞室有限元分析中的应用

用西原模型描述双重孔隙-裂隙介质的流变特性,在理论上给出了其流变参数及强度指标的确定方法,建立了瞬弹-黏弹-黏塑性平面有限元求解格式和研制了相应的计算程序。针对一个矩形地下洞室围岩为裂隙岩体和完整岩体的两种工况进行数值分析,对比了围岩中的位移、应力及塑性区。其结果显示:相比于单一介质的情况,双重介质因其变形模量、凝聚力和内摩擦角减小,故洞室围岩中随时发展的位移和塑性区有明显的增长,两种工况的围岩应力分布亦存在较大的不同,特别是双重介质围岩中最大主应力σ_1和最小主应力σ_3的差值较大,因此,提高了围岩破坏的可能性。     

边坡稳定分析的非线性有限元混合解法

在对有限元强度折减法和有限元迭代解法的优缺点分析的基础上,提出了边坡稳定分析的非线性有限元混合解法,该法将有限元强度折减法和有限元迭代解法联合运用于边坡稳定分析,充分利用了两种方法的优点。即由有限元强度折减法搜索边坡可能滑动面,将可能滑动面在网格中画出,由迭代解法逐步迭代求得其滑动面的安全系数。并以算例和工程实例说明了此种方法的正确性和合理性。     

边坡稳定的非线性有限元分析

基于有限元强度折减法,进行了边坡的弹塑性材料非线性及大变形几何非线性分析,并考虑了边坡的三维变形情况。在有限元分析中采用的是莫尔-库仑理想弹塑性模型,大变形分析采用的是更新的拉格朗日法。均质边坡的算例分析表明,有限元法与简化的毕肖普法的安全系数计算结果具有相同的规律,即安全系数都随着黏聚力及内摩擦角的增加而增加,随着重度的增加而减小,但是,各种有限元法的计算结果都比相应的毕肖普法的解要大,亦即毕肖普法偏于安全。各种方法对应的安全系数由大到小的顺序依次是：三维小变形有限元分析、二维大变形有限元分析、二维小变形有限元分析,简化的毕肖普法,前二者能更好地反映实际的边坡变形情况,二者的安全系数值也十分接近,因而是较好的方法。     

A new finite element formulation for one-dimensional analysis of elastic-plastic materials

It is well accepted that severe numerical difficulties arise when using the conventional finite element displacement method to analyse incompressible, or nearly incompressible, solids. These effects are caused by the kinematic constraints imposed on the nodal velocities by the constant volume condition. In elastic-plastic analysis, these effects are due to a conflict between the plastic flow rule and the finite element discretization. Although several methods have been proposed to cope with this problem, none has been based on the appropriate choice of displacement interpolation to minimise the constraints. In this paper, a new displacement interpolation, which is able to reduce the imposed constraints, is adopted. Comparisons of the results with those from a conventional linear displacement interpolation are made for predictions of cylindrical and spherical cavity expansion limit pressures in elastic-plastic solids. This study suggests that the proposed displacement interpolation is preferable to the conventional one in the elastic-plastic finite element analysis of one dimensional-axisymmetric problems which involve nearly incompressible material behaviour.     

A finite element analysis of direct shear tests on stiff clays

A finite element analysis is presented of some direct shear tests carried out on samples of a stiff, heavily overconsolidated clay. The effects of softening are accounted for through a simple material model which views this phenomenon as a consequence of an intrinsic loss of strength of the material taking place when plastic strains increase. After illustrating the main characteristics of the finite element approach, with particular reference to the correct determination of the non-reversible strains, its use in the interpretation of the mentioned shear tests is discussed. Some comments are also presented on the mesh dependence of the numerical results, and on the use of a relation between material parameters and element size which reduces this negative effect. Finally, the solution procedure is applied to the simulation of a compression test in order to investigate the possibility of numerically detecting the ‘spontaneous’ (i.e. not directly induced by the boundary conditions) formation of shear zones within the specimen.     

A finite element approach for the analysis of active slow-moving landslides

In the present paper, a finite element approach is proposed to analyse the mobility of active landslides which are controlled by groundwater fluctuations within the slope. These landslides are usually characterised by low displacement rates with deformations that are essentially concentrated within a narrow shear zone above which the unstable soil mass moves with deformations of no great concern. The proposed approach utilises an elasto-viscoplastic constitutive model in conjunction with a Mohr-Coulomb yield function to describe the behaviour of the soil in the shear zone. For the other soils involved by the landslide, an elastic model is used for the sake of simplicity. A significant advantage of the present method lies in the fact that few constitutive parameters are required as input data, the most of which can be readily obtained by conventional geotechnical tests. The rest of the required parameters should be calibrated on the basis of the available monitoring data concerning the change in the piezometric levels and the associated movements of the unstable soil mass. After being calibrated and validated, the proposed approach can be used to predict future landslide movements owing to expected groundwater fluctuations or to assess the effectiveness of drainage systems which are designed to control the landslide mobility. The method is applied to back-predict the observed field behaviour of three active slow-moving landslides documented in the literature.