Preconditioned IDR(s) iterative solver for non‐symmetric linear system associated with FEM analysis of shallow foundation     

H.H.T. Tran  K.C. Toh  K.K. Phoon 《国际地质力学数值与分析法杂志》2013,37(17):2972-2986

Non‐associated flow rule is essential when the popular Mohr–Coulomb model is used to model nonlinear behavior of soil. The global tangent stiffness matrix in nonlinear finite element analysis becomes non‐symmetric when this non‐associated flow rule is applied. Efficient solution of this large‐scale non‐symmetric linear system is of practical importance. The standard Krylov solver for a non‐symmetric solver is Bi‐CGSTAB. The Induced Dimension Reduction [IDR(s)] solver was proposed in the scientific computing literature relatively recently. Numerical studies of a drained strip footing problem on homogenous soil layer show that IDR(s = 6) is more efficient than Bi‐CGSTAB when the preconditioner is the incomplete factorization with zero fill‐in of global stiffness matrix K_ep (ILU(0)‐K_ep). Iteration time is reduced by 40% by using IDR(s = 6) with ILU(0)‐K_ep. To further reduce computational cost, the global stiffness matrix K_ep is divided into two parts. The first part is the linear elastic stiffness matrix K_e, which is formed only once at the beginning of solution step. The second part is a low‐rank matrix Δ, which is re‐formed at each Newton–Raphson iteration. Numerical studies show that IDR(s = 6) with this ILU(0)‐K_e preconditioner is more time effective than IDR(s = 6) with ILU(0)‐K_ep when the percentage of yielded Gauss points in the mesh is less than 15%. The total computation time is reduced by 60% when all the recommended optimizing methods are used. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction     

Konstantinos I. Andrianopoulos  Achilleas G. Papadimitriou  George D. Bouckovalas 《国际地质力学数值与分析法杂志》2010,34(15):1586-1614

This paper presents a new plasticity model developed for the simulation of monotonic and cyclic loading of non‐cohesive soils and its implementation to the commercial finite‐difference code FLAC, using its User‐Defined‐Model (UDM) capability. The new model incorporates the framework of Critical State Soil Mechanics, while it relies upon bounding surface plasticity with a vanished elastic region to simulate the non‐linear soil response. Stress integration of constitutive relations is performed using a recently proposed explicit scheme with automatic error control and substepping, which so far has been employed in the literature only for constitutive models aiming at monotonic loading. The overall accuracy of this scheme is evaluated at element level by simulating cyclic loading along complex stress paths and by using iso‐error maps for paths involving change of the Lode angle. The performance of the new constitutive model and its stress integration scheme in complex boundary value problems involving earthquake‐induced liquefaction is evaluated, in terms of accuracy and computational cost, via a number of parametric analyses inspired by the successful simulation of the VELACS centrifuge Model Test No. 2 studying the lateral spreading response of a liquefied sand layer. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

不规则水体断面面积及体积的计算—兼论多面函数内插模型的精度     

黄谟涛 《武汉大学学报(信息科学版)》1988,(2)

本文以吕言的三次曲面函数内插模型为基础,推出一套计算不规则水体断面面积及其体积的封闭公式,并用实例加以验证。最后从另一侧面探讨了多面函数模型的内插精度问题。本文得到的公式同样适用于工程上的土方量及断面面积的计算。  相似文献   

ACMEG‐TS: A constitutive model for unsaturated soils under non‐isothermal conditions     

Bertrand François  Lyesse Laloui 《国际地质力学数值与分析法杂志》2008,32(16):1955-1988

This paper introduces an unconventional constitutive model for soils, which deals with a unified thermo‐mechanical modelling for unsaturated soils. The relevant temperature and suction effects are studied in light of elasto‐plasticity. A generalized effective stress framework is adopted, which includes a number of intrinsic thermo‐hydro‐mechanical connections, to represent the stress state in the soil. Two coupled constitutive aspects are used to fully describe the non‐isothermal behaviour. The mechanical constitutive part is built on the concepts of bounding surface theory and multi‐mechanism plasticity, whereas water retention characteristics are described using elasto‐plasticity to reproduce the hysteretic response and the effect of temperature and dry density on retention properties. The theoretical formulation is supported by comparisons with experimental results on two compacted clays. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar     

Xiao‐Ting Chen  J. F. Shao  C. A. Davy  F. Skoczylas 《国际地质力学数值与分析法杂志》2010,34(4):357-382

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

Elasto‐plastic analysis of block structures through a homogenization method     

G. de Felice  A. Amorosi  M. Malena 《国际地质力学数值与分析法杂志》2010,34(3):221-247

The paper describes the development and numerical implementation of a constitutive relationship for modeling the elasto‐plastic behavior of block structures with periodic texture, regarded at a macroscopic scale as homogenized anisotropic media. The macroscopic model is shown to retain memory of the mechanical characteristics of the joints and of the shape of the blocks. The overall mechanical properties display anisotropy and singularities in the yield surface, arising from the discrete nature of the block structure and the geometrical arrangement of the units. The model is formulated in the framework of multi‐surface plasticity. It is implemented in an finite element (FE) code by means of two different algorithms: an implicit return mapping scheme and a minimization algorithm directly derived from the Haar–Karman principle. The model is validated against analytical and experimental results: the comparison between the homogenized continuum and the original block assembly shows a good agreement in terms of ultimate inelastic behavior, when the size of the block is small as compared with that of the whole assembly. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

Creep of saturated materials as a chemically enhanced rate‐dependent damage process     

Liang Bo Hu  Tomasz Hueckel 《国际地质力学数值与分析法杂志》2007,31(14):1537-1565

Material behaviour that exhibits characteristics of creep induced by a spontaneous mineral dissolution enhanced by material damage is studied. It is believed that the characteristic rates of the chemical processes involved determine the time‐rate dependence of the resulting strain. A basic model of a combined chemo‐plastic softening and chemically enhanced deviatoric strain hardening for saturated geomaterials is presented. Chemical softening is postulated to occur as a consequence of the net mass removal resulting from dissolution and precipitation of specific minerals occurring at the damage‐generated inter‐phase interfaces. Closed and open systems are discussed. In the former case, deformation at constant stress results entirely from a local compensation mechanism between the chemical softening and strain hardening. The classical three stages of creep are interpreted in terms of mechanisms of dissolution and precipitation, as well as the variation in the reaction surface areas involved in the mass exchange. In an open system, the above local mechanism is enhanced by the removal of mass via diffusion of species affecting the mass balance. Such a system is addressed via a boundary value problem as shown in an example. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

Finite elements modelling of the long‐term behaviour of a full‐scale flexible pavement with the shakedown theory     

Cyrille Chazallon  Fatima Allou  Pierre Hornych  Saida Mouhoubi 《国际地质力学数值与分析法杂志》2009,33(1):45-70

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真空预压联合电渗加固高塑性软土的试验研究   总被引：1，自引：0，他引：1  

曹永华  侯晋芳  高志义 《岩土工程技术》2010,24(6):290-293

为处理常规排水固结法难以处理的高塑性软土,进行了真空预压联合电渗加固的大比尺室内模型试验研究。试验首先对塑性指数为26～29的高塑性软土进行真空预压的加固,待固结度达到80%后启动电渗进行加固。试验中对电流、电势和表层沉降等进行了全面的监测。试验结果表明电极反转、间歇通电技术有利于提高电能的利用率。土体强度由加固前的0～7.1kPa增长到加固后的18.2～26.2kPa。后期电渗对强度增长的贡献十分明显。  相似文献   

Computational study on the modification of a bounding surface plasticity model for sands     

《Computers and Geotechnics》2014

The accurate simulation of complex dynamic phenomena requires the availability of advanced constitutive models capable of simulating a wide range of features of soil behaviour under cyclic loading. One possible strategy is to improve the capabilities of existing bounding surface plasticity models, as this framework is characterised by its modularity and flexibility. As a result, specific components of the formulation of this type of model may be adjusted to improve the reproduction of any aspect of soil behaviour deemed essential to the problem being analysed. In this paper, a series of computational studies are performed in order to establish the impact of expanding a bounding surface plasticity model for sands on its modelling capabilities and to suggest ways of mitigating the associated increase in complexity. Changes to three distinct aspects of the selected constitutive model are examined: the shape of the Critical State Line in p′ − e space, the expression used for calculating the hardening modulus and the form of the yield surface. It is shown that the introduced changes have the potential to increase significantly the ability to control how certain aspects of soil response, such as degradation of stiffness and flow liquefaction with limited deformation, are reproduced by the model. Moreover, this paper presents a systematic approach to the expansion of this type of constitutive model, establishing how alterations to the formulation of a model may be assessed in terms of improved accuracy and potential benefits.  相似文献