非共轴本构模型的数值计算问题

应用角点非共轴本构模型结合有限元方法分析浅基础的受力沉降问题。当非共轴塑性模量较小时,包含非共轴模型子程序的ABAQUS的非线性计算可能不收敛。深入地分析表明,不收敛问题是由于在塑性变形刚开始时,非共轴的塑性应变增量明显大于共轴的塑性应变增量。为了克服数值不收敛问题,对原有的角点非共轴模型加以改进。在改进的模型中,非共轴塑性模量是累加塑性剪应变的函数。计算结果表明,这个改进的非共轴模型提高了非线性计算的收敛性,同时保持了原有非共轴模型的功能。     

An adaptive finite element model for wellbore breakout simulation

A finite element formulation is proposed and implemented for analysing the stability of excavated wells using the DiMaggio-Sandler constitutive elastoplastic model with a typical carbonate reservoir configuration. The quality of the finite element approximation is ensured by applying smooth curved elements adapted to the wellbore geometry, and h − p adaptive finite element meshes in the plastic zone. General purpose procedures are defined to transfer the elastoplastic deformation history to newly created integration points. A breakout damage criterion is proposed based on the second invariant of the deviatoric plastic deformation tensor. This damage criterion is used to apply a mesh movement algorithm to represent material collapse. The automatic successive application of the breakout damage criterion results in elliptical realistically looking geometries obtained in experiments reported in the literature.     

A two‐mechanism elastoplastic model for shakedown of unbound granular materials and DEM simulations

An elastoplastic model has been developed for the finite elements modelling of repeated load triaxial tests. This model is based on the shakedown theory established by Zarka for metallic structures. To the previous works, which were based on the Drucker–Prager yield surface and the plastic potential of Von Mises, a compression cap has been added to each one. The model straightforwardly determines the purely elastic state or the elastic shakedown state or the plastic shakedown state and calculates the deviatoric and the volumetric plastic strains. The calibration of the elastoplastic model has been carried out with DEM simulations and an unbound granular material for roads under repeated load triaxial tests using finite element method. The calculations underline the capabilities of the model to take into account, with a unique formalism, the accumulation of the deviatoric and volumetric plastic strains along the loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of stone-column reinforced foundations

A numerical model is proposed to analyse elastic as well as elastoplastic behaviour of stone-column reinforced foundations. The stone-columns are assumed to be dispersed within the in situ soil and a homogenization technique is invoked to establish equivalent material properties for in situ soil and stone-column composite. The difficulties encountered in carrying out elastoplastic analyses of composite materials are overcome by adopting a separate yield function for each of the constituent materials and a sub-iteration procedure within an implicit backward Euler stress integration scheme. In the proposed procedure, equilibrium as well as kinematic conditions implied in the homogenization procedure are satisfied for both elastic as well as elastoplastic stress states. The proposed model is implemented in an axi-symmetric finite element code and numerical prediction is made for the behaviour of model circular footings resting on stone-column reinforced foundations. This prediction indicates good agreement with experimental observation. Finally, a new scheme in which the length of stone-column is variable is proposed and its behaviour is examined through a numerical example. © 1998 John Wiley & Sons, Ltd.     

Numerical aspects of non-coaxial model implementations

This paper ascertains the reasons for the numerical problems when the yield vertex non-coaxial model is implemented in the finite element analysis to predict the behaviour of complicated geotechnical engineering problems. The numerical problem, reflected in the failure of convergence in the non-linear solutions in ABAQUS, is likely to happen when a smaller non-coaxial plastic modulus is used. It is found that a large non-coaxial influence at the start of elastoplastic loading, which causes the predominance of non-coaxial plastic strain rate over the coaxial plastic strain rate in stress–strain responses, is the reason for the numerical problem. The original yield vertex non-coaxial model is modified to overcome the numerical problem. Instead of a constant non-coaxial plastic modulus in the original yield vertex non-coaxial model, the non-coaxial modulus is made a function of cumulative deviatoric plastic strain. It shows that the modified non-coaxial model retains the functions of the original non-coaxial model. Meanwhile, it overcomes the non-convergence problem when a smaller non-coaxial plastic modulus, representing a larger non-coaxial influence, is used.     

Numerical modeling of the flow and transport of radionuclides in heterogeneous porous media

This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion–dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion–convection–reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations.      

Implicit and explicit procedures for the yield vertex non-coaxial theory

The yield vertex non-coaxial model is different from classical elastoplastic models, in that there is an additional plastic strain rate tangential to yield surfaces, as well as the plastic strain rate normal to yield surfaces, when orientations of principal stress change. This feature raises concerns on its finite element implementations. In nonlinear finite element numerical iterations, a large tangential plastic strain rate is likely to make the trial total strain rate direct inside a yield surface, which entails convergence difficulty. Some modifications are introduced on the non-coaxial model itself to make numerical convergence easier in the work published in Yang and Yu (2010) [20]. This paper is an extension of the previous work. Instead of modifying the non-coaxial model itself, this paper concerns the use of finite element explicit procedure, which is suitable for highly discontinuous problems. The simulations of shallow foundation load-settlement responses indicate that the finite element explicit procedure, assisted with a robust and explicit automatic substepping integration scheme of the non-coaxial model, does not encounter numerical difficulty. In addition, the overall trends of implicit and explicit simulations are similar.     

Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay

This paper presents a numerical model for the analysis of cone penetration in soft clay based on the finite element method. The constitutive behaviour of the soil is modelled by modifying an elastic, perfectly-plastic soil model obeying Von-Mises yield criterion to take into account the strain-softening, rate dependent behaviour of soft clay. Since this is a problem involving large soil deformations, the analysis is carried out using an Arbitrary Lagrangian Eulerian method where the quality of the mesh is preserved during penetration. The variation of cone resistance is examined with various parameters such as rigidity index of the soil, in situ stress anisotropy and roughness at the cone–soil interface, which influence the penetration resistance of the cone. A theoretical correlation has been developed incorporating these parameters and the results have been compared with previous correlations based on the cavity expansion theory, finite element method and strain path method. With the increase in strain-softening, relative brittleness of the soil increases and the penetration resistance is significantly reduced. With the rising strain-rate dependency, penetration resistance increases but this increase is independent of the degree of brittleness of the soil.     

极限分析有限元法讲座--Ⅱ有限元强度折减法中边坡失稳的判据探讨

边坡失稳,滑体滑出,滑体由稳定静止状态变为运动状态,同时产生很大的且无限发展的位移,这就是边坡破坏的特征。有限元中通过强度折减使边坡达到极限破坏状态,滑动面上的位移和塑性应变将产生突变,且此位移和塑性应变的大小不再是一个定值,有限元程序无法从有限元方程组中找到一个既能满足静力平衡又能满足应力-应变关系和强度准则的解,此时,不管是从力的收敛标准,还是从位移的收敛标准来判断有限元计算都不收敛。塑性区从坡脚到坡顶贯通并不一定意味着边坡破坏,塑性区贯通是破坏的必要条件,但不是充分条件,还要看是否产生很大的且无限发展的塑性变形和位移,有限元计算中表现为塑性应变和位移产生突变。在突变前计算收敛,突变之后计算不收敛,表征滑面上土体无限流动,因此可把有限元静力平衡方程组是否有解,有限元计算是否收敛作为边坡破坏的依据。-     

Explicit stress integration of complex soil models

In this paper, two complex critical‐state models are implemented in a displacement finite element code. The two models are used for structured clays and sands, and are characterized by multiple yield surfaces, plastic yielding within the yield surface, and complex kinematic and isotropic hardening laws. The consistent tangent operators—which lead to a quadratic convergence when used in a fully implicit algorithm—are difficult to derive or may even not exist. The stress integration scheme used in this paper is based on the explicit Euler method with automatic substepping and error control. This scheme employs the classical elastoplastic stiffness matrix and requires only the first derivatives of the yield function and plastic potential. This explicit scheme is used to integrate the two complex critical‐state models—the sub/super‐loading surfaces model (SSLSM) and the kinematic hardening structure model (KHSM). Various boundary‐value problems are then analysed. The results for the two models are compared with each other, as well with those from standard Cam‐clay models. Accuracy and efficiency of the scheme used for the complex models are also investigated. Copyright © 2005 John Wiley & Sons, Ltd.     

双重孔隙-裂隙岩体中洞室变形及强度各向异性的三维有限元分析

将确定双重孔隙-裂隙介质凝聚力及内摩擦角的方法与描述介质强度各向异性的微结构-无迹张量方法相结合,引入到三维有限元程序中。以简单的算例,通过解析解与数值解的比较,验证了所开发的有限元程序的可靠性。针对一个假定的位于被3组正交裂隙所切割的围岩中的矩形洞室,使用Mohr-Coulomb准则进行弹塑性数值模拟,就不同的工况分析了围岩中的位移、应力及塑性区的状态。计算结果显示：裂隙组的不同展布及组合使得岩体的变形及强度性质有着不同的各向异性,从而相应地导致围岩中的位移、应力及塑性区的分布与量值产生明显的差异。     

龙滩水电站航道座滑边坡平面弹塑性有限元分析

基于弹塑性有限元（FEM）模型和Mohr-Coulomb屈服准则,采用平面有限元法对龙滩水电站航道1+016～ 1+080段座滑后边坡在开挖处理过程中的稳定性进行了数值模拟研究,分析了开挖中岩坡的应力场、位移场、塑性屈服区及支护效应。模拟结果表明,边坡在开挖过程中存在连续变形,局部出现塑性屈服,地下水位升降对边坡影响较大,但边坡整体仍处于稳定状态,开挖过程中有效的支护措施对改善边坡的稳定性至关重要。     

New Viscoplastic Model for Design Analysis of Tunnels in Squeezing Conditions

Summary  This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis of tunnels in squeezing conditions. Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy     

Elastic–plastic analysis of geotechnical problems by mathematical programming

A numerical technique, based on a mathematical programming algorithm, is presented for the solution of geotechnical problems where elastic-plastic material behaviour is considered. The proposed approach can be adopted for geotechnical media characterized by any suitable yield condition, accounting, if necessary, for workhardening behaviour. The loading process is subdivided into a series of steps applied to a finite element mesh with geometry and material properties constant along each step, but with possible changes between subsequent steps. As an application some typical geotechnical problems are analysed by means of the proposed algorithm and a comparison is made between the available in situ measurements and the numerical results.     

顺层路堑边坡锚杆支护稳定性的有限元模拟分析

基于理想弹塑性本构模型和Drucker-Prager准则,运用ANSYS软件和有限元数值模拟技术,建立了顺层岩体边坡的有限元分析模型。结合沪蓉国道主干线宜昌至恩施公路白氏坪-榔坪段顺层路堑高边坡工程实例,对顺层岩体路堑边坡布设锚杆支护前后的应力、变形和稳定性进行了模拟分析。分析比较表明,锚杆支护结构可以减小边坡临界状态下的最大位移、增大最危险接触面的摩擦力和提高边坡的稳定性系数,从而能有效地提高边坡的稳定性以防止顺层滑坡的发生。     

单轴压缩非贯通节理岩石尖端塑性区及弹塑性断裂模型研究

基于Drucker-Prager（下简称D-P）准则,建立压缩载荷作用下的非贯通节理岩石的弹塑性断裂模型。针对节理岩石小范围屈服翼裂纹尖端塑性区,推导了D-P屈服准则的纯I、纯II及I、II复合型3种翼裂纹无量纲塑性区径长函数,并与Mises准则的塑性区进行对比;结果表明,D-P准则的I型和复合型塑性区较Mises屈服准则的塑性区大,且其II型及I、II复合型塑性区在翼裂纹上下表面不连续。进一步,引入断裂软化因子以表征节理岩石裂隙断裂扩展后的断裂软化规律,考虑非贯通节理岩石复合型断裂软化,是由于节理尖端翼裂纹应变能密度超过最小应变能密度导致其成核扩展引起的,提出用应变能密度的指数函数形式表征断裂软化变量的演化;塑性屈服函数采用Borja等的应力张量3个不变量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;建立节理岩石的弹塑性断裂本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性断裂模型的程序。以单轴压缩下非贯通节理岩石为例,分析岩石断裂韧度、节理摩擦系数和节理倾角等参数的影响,结果表明,所提出的弹塑性断裂模型与数值和试验结果比较吻合。     

Simplified numerical modelling of pile penetration – the press‐replace technique

This paper presents a simplified finite element analysis technique, the ‘Press‐Replace’ technique, to model pile penetration problems in geotechnical engineering, particularly, pile jacking. The method is employed in standard finite element analysis software. The method involves a straining and a consequent geometry update phase. First, a cone penetration test in (undrained) clay is modelled and compared with the results of analytical, semi‐analytical and more advanced finite element techniques. The model sensitivity for the step size and mesh is investigated using a hypoplastic constitutive model. An optimum way of modelling based on the numerical performance is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Extended Barcelona Basic Model for unsaturated soils under cyclic loadings

The Barcelona Basic Model (BBM) is an extension of the Cam clay model that has become popular in applications involving unsaturated soils and, in particular, in simulations using the finite element method. Partially saturated soils can be loaded in different ways, for instance, mechanically and/or hydraulically. In addition, cycles of loading and unloading can be applied. The present work introduces a modification of the BBM in order to simplify its computer implementation and also to allow the simulation of elastoplastic behaviour during cycles of both mechanical and hydraulic loading. A unique smooth yield surface is introduced and a two-yield surfaces concept is applied in order to represent the cyclic behaviour. The influence of the intermediate principal stress on the strength is also accounted for. Finally, the numerical integration (stress update) of the extended BBM is briefly discussed.     

Micromechanical viscoelasto‐plastic models and finite element implementation for rate‐independent and rate‐dependent permanent deformation of stone‐based materials

This paper presents parallel and serial viscoelasto‐plastic models to simulate the rate‐independent and the rate‐dependent permanent deformation of stone‐based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto‐plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement‐based incremental formulation for the viscoelastic part and an elastic predictor—plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto‐plastic model employed a viscoelastic predictor—plastic corrector algorithm. The stone‐based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto‐plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto‐plastic matrix models. The simulation results showed that the serial viscoelasto‐plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto‐plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate‐independent and rate‐dependent viscoelasto‐plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto‐plastic behaviors of the stone‐based materials. Copyright © 2009 John Wiley & Sons, Ltd.     

A fully coupled thermo-hydro-mechanical nonlinear model for a frozen medium

This paper describes a nonlinear elasto-plastic simulation of freezing and thawing of rock. A mathematical formulation is described in which deformation, fluid flow and heat flow are fully coupled. A non-linear elasto-plastic constitutive relationship is presented and a two dimensional (plane stress) numerical modeling is performed based on the finite element method applied to thermo-poro-elastoplasticity. It is assumed that the Mohr-Coulomb's failure criterion is valid for yield locus and plastic potential. The numerical scheme employed in the code accommodates phase change of pore-water from liquid to solid (ice). The primary aim of this paper is to compare the temperature transfer and deformation prediction obtained from the numerical code with those obtained from the freezing and thawing experiments. It is found from the numerical simulation that a relatively good prediction can be made of temperature transfer and deformation behavior. The numerical code has also been applied to a hypothetical cavern problem to demonstrate its applicability.