Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation

Finite element analysis of non-isothermal elasto-plastic multiphase geomaterials is presented. The multiphase material is modelled as a deforming porous continuum where heat, water and gas flow are taken into account. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The modified effective stress state is limited by the Drucker-Prager yield surface for simplicity. Small strains and quasi-static loading conditions are assumed. Numerical results of strain localization in globally undrained samples of dense, medium dense and loose sands and isochoric geomaterial are presented. A biaxial compression test is simulated assuming plane strain condition during the computations. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A case of strain localization induced by a thermal load where evaporation takes place is also analysed. Dedicated to Professor S. Valliappan in occasion of his retirement     

A thermo‐hydro‐mechanical model for multiphase geomaterials in dynamics with application to strain localization simulation

In this paper, the non‐isothermal elasto‐plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo‐hydro‐mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the hybrid mixture theory. A computationally efficient reduced formulation of the macroscopic balance equations that neglects the relative acceleration of the fluids, and the convective terms is adopted. The modified effective stress state is limited by the Drucker–Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non‐linear set of equations is solved by the Newton method with a monolithic approach. Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A numerical study of the regularization properties of the finite element model is shown and discussed. A non‐isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed. Copyright © 2016 John Wiley & Sons, Ltd.     

A formulation for an unsaturated porous medium undergoing large inelastic strains

 This paper presents a formulation for a saturated and partially saturated porous medium undergoing large elastic or elastoplastic strains. The porous material is treated as a multiphase continuum with the pores of the solid skeleton filled by water and air, this last one at constant pressure. This pressure may either be the atmospheric pressure or the cavitation pressure. The governing equations at macroscopic level are derived in a spatial and a material setting. Solid grains and water are assumed to be incompressible at the microscopic level. The isotropic elastoplastic behaviour of the solid skeleton is described by the multiplicative decomposition of the deformation gradient into an elastic and a plastic part. The effective stress state is limited by the Drucker-Prager yield surface, for which a particular “apex formulation” is advocated. The water is assumed to obey Darcy's law. Numerical examples of strain localisation of dense and loose sand conclude the paper. Received 15 March 2001     

Pore pressure response of earth dams in random seismic environment

The progressive development of pore water pressure due to earthquake loading and associated loss of strength may be a major cause of instability in earth dams consisting of low to medium dense saturated sands and hydraulic fill materials.In this study a procedure is developed for the analysis of pore pressure response of an earth dam subjected to a random seismic environment. The ground motion is modelled as a portion of the stationary random process which may be defined alternatively by (a) Kani—Tajimi spectral density function, or (b) a design response spectrum. The earth dam is modelled as a series of shear slices and is considered to be homogeneous. The nonlinearity in shear modulus and damping are incorporated by using an equivalent linear model for the stress-strain behavior of soils. The dynamic response to vertically propagating shear waves is formulated in the frequency domain providing the transfer functions for various parameters, viz, stress, strain and acceleration, etc. The power spectra of these parameters are then readily obtained.Using a simple linear model for the generation of pore water pressure the expected value of associated damage is obtained. Numerical results of an example analysis and a parametric study are presented.     

Influence of n-alkanes on wettability and zeta potential of quartz

Contact angles were measured in the following systems: quartz/water droplet/saturated vapor of water + n-alkane and quartz/water droplet/saturated vapor of n-alkane. The alkanes tested were from hexane to pentadecane. In both systems non-smooth changes of contact angle as a function of the chain length were observed. These changes are similar to the zeta-potential changes measured previously for two different samples of quartz in the quartz/n-alkana/water system. On the basis of the results and calculations it is suggested that the observed non-smooth changes of contact angle are due to similar changes in film pressures of the water and n-alkanes.     

A mixture model for the compaction of saturated sand

Free draining water saturated sands and dry sands compact progressively under cyclic shear loading, and the rate of compaction increases as the shear strain amplitude increases, independent of the confining stress magnitude. As the sand grains are relatively incompressible, this compaction is essentially an irreversible porosity decrease induced by rearrangement of the granular structure. We present a constitutive model of differential type for porosity variation which has the minimal ingredients necessary to reflect the observed cyclic loading phenomena, and determine the associated material functions of a particular form by correlation with cyclic loading data. A hypoelastic shear response is also correlated to cyclic loading data to complete an isotropic constitutive model. Pore pressure generation under cyclic loading in undrained conditions is evaluated to illustrate the predictions of the model.     

饱和砂土基于相变状态的不排水本构模型

饱和砂土基于相变状态的改进本构模型能较好地描述砂土不排水情况下的应力-应变关系。通过改进模型中相变状态参量的计算方法,将e-lgp°表达式加以改进,通过详细的阐述,提出e_pt-lgp的关系式,并通过三轴压缩试验的数据对提出的关系式加以验证。应用新的关系式计算不排水条件下试样的相变孔隙比e_pt,进而计算出模型中的相变状态参量。改进后的不排水本构模型的计算结果与不排水三轴压缩的试验结果能较好地吻合,即验证了本构模型的有效性,也验证了e_pt-lgp关系式的合理性,使原有的边界面本构模型更好地描述不排水的情况下、不同密度和围压状态下饱和砂土的力学行为。     

基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

Effect of cyclic shearing on shear localisation in granular bodies

Cyclic shearing of an infinite narrow layer of dry and cohesionless sand between two very rough boundaries under constant vertical pressure is numerically modelled with the finite element method using a polar hypoplastic constitutive relation. The constitutive relation was obtained through an extension of a non-polar model by polar quantities, viz. particle rotations, curvatures, couple stresses using the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. The material constants can be easily determined from granulometric properties and laboratory tests. The attention of numerical simulations is laid on the influence of number of cycles on the thickness of an induced shear zone for both an initially dense and loose granular specimen. In addition, the effect of a stochastic distribution of the initial void ratio on shear localisation is demonstrated.KeywordsGranular material, Cyclic shearing, Polar hypoplasticity, Finite element method, Shear localisation     

Modeling of multiphase flow with phase change in porous media – a case study

A general numerical model developed to simulate the time‐dependent changes of moisture content, temperature and pore pressures is proposed for a porous material. The model is based on a coupled heat and mass transfer mathematical formulation. The model’s validation is conducted using experimental data for concrete. The gravimetric technique is used to obtain the experimental data on moisture content in cylinders made up of fully saturated concrete exposed to drying. Further to demonstrate the applicability of the model, it is also studied the moisture migration, temperature development and thermal stresses in a concrete element exposed to fire. The obtained results indicate that during fire, several degradation phenomena are taking place at the same time. Thermal stresses developed by the temperature differential, especially when temperature‐dependent material properties are taken into the account, along with the increase of pore pressures, may contribute to structural failure.     

平面应变条件下饱和土体分叉后的力学性状

土坡和挡土墙的应变局部化和渐进破坏分析的一个关键问题是如何合理描述土体分叉后的力学性状,而从试验得到的峰后应力应变关系实际上并不是土体本身的一种真实本构反应。为此,提出了一种描述含剪切带土体宏观力学特性的改进后的复合体理论(或均匀化理论)。结合干密砂以及饱和松砂、中密砂、密砂的平面应变试验结果,验证了该理论框架的合理性。     

A fully coupled finite element analysis of water‐table fluctuation and land deformation in partially saturated soils due to surface loading

A fully coupled numerical model is presented for the water‐table fluctuation and land deformation in partially saturated soils due to surface loading. This numerical model is developed based on the poroelastic governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. The numerical model is verified and validated against a one‐dimensional consolidation problem concerning surface loading on a soil column which has six different initial water‐table elevations. The numerical model is then applied to a two‐dimensional consolidation problem of surface loading on a partially saturated soil at a construction site. Results from the numerical simulations of both problems show that the water table fluctuates in the partially saturated soils, and the unsaturated zone above the water table has significant effects on the consolidation behaviour of the partially saturated soils under surface loading. Such effects are caused by the permanent absorption of a portion of the mechanical loading stress and the weak hydromechanical coupling between the solid skeleton deformation field and the groundwater flow field in the unsaturated zone due to its partial saturation. Copyright © 2000 John Wiley & Sons, Ltd.     

Significance of formation factor in sand structure characterization

The formation factor F, obtained by electrical conductivity measurements of saturated sand samples, has been recently correlated with the liquefaction behavior of sands (2). The significance of F as a parameter obtained by nondestructive technique is discussed here, showing its capability to characterize the structure of anisotropic sand aggregates.     

A nonlinear mixture theory representation of saturated sand

Nonlinear constitutive equations for saturated sands are proposed. They exhibit the interaction of dilatation and shear stress observed in sands in its small strain range. The equations are based on a continuum theory derived from a Newtonian approach to a mixture of a nonlinear solid and compressible fluid. The determination of the constitutive parameters from common soil mechanics experiments is discussed and illustrated by qualitatively valid numerical results.     

三维各向异性砂土UH模型

为了全面地描述砂土在三维空间不同方向上的本构特性,应当综合考虑各向异性和中主应力的影响。该文在砂土UH（统一硬化）模型的基础上,采用各向异性的变换应力方法,发展了三维各向异性砂土UH模型。该方法通过调整不同方向应力分量的相对大小,将各向异性砂土等效为各向同性砂土,并且在变换应力空间将偏平面上的破坏或屈服包线变成圆形。用各向异性的变换应力张量代替真实应力张量,能够方便地得到同时考虑各向异性和中主应力影响的砂土UH模型。与试验数据的对比表明,三维各向异性UH模型能够合理地预测真三轴应力状态下各向异性砂土的应力-应变关系。     

考虑相变状态的较密实饱和砂土弹塑性模型

在三轴试验中,较密实砂土是很难最后到达临界状态的。该文在Yu等提出的CASM模型基础上,提出了适合模拟较密实饱和砂土的弹塑性模型。该模型有两方面的改进:一方面,模型将剪胀应力比M_d引入剪胀方程;另一方面,模型中硬化参数采用与应力路径无关的参数来替代CASM模型中的塑性体应变增量。经试验结果验证,该模型较适合模拟饱和中密或密实砂土的剪胀特性,同时也能较好地体现中密或密砂剪切过程中的硬化及软化现象。模型共10个参数,用常规三轴试验就可获取。     

Capturing strain localization in dense sands with random density

This paper presents a three‐invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density. A recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation. The new three‐invariant constitutive model, similar to its two‐invariant predecessor, is capable of accounting for meso‐scale inhomogeneities as well as material and geometric nonlinearities. Details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed‐form expression for the consistent tangent operator, whose spectral form is used in the strain localization analyses, is derived. An algorithm based on the spectral form of the so‐called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop. The aforementioned framework is utilized in a series of boundary‐value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso‐scale and the intrinsic uncertainty associated with them. Copyright © 2006 John Wiley & Sons, Ltd.     

堤防地基地震液化的数值模拟

基于Biot动力耦合理论,采用一个经过广泛验证的砂土循环弹塑性本构模型,建立了平面应变条件下土堤地基的地震液化数值模拟方法。以某河流堤防的实际工程为例,应用该方法对土堤地基的地震液化进行了数值模拟,并对地震作用下的超孔隙水压力、加速度、位移等动力反应进行了计算分析,得到了一些对于抗震分析有用的结果。     

Horizontal pneumatic conveying: a 3d distinct element model

Pneumatic conveying is widely used for transporting bulk solids in chemical, process and agricultural industries. It is environmentally friendly, flexible and can be fully automated. But it can also involve high power consumption, wear, abrasion, blockage and particle degradation. Hence understanding the physics can help to optimise design and operation. Conveying in a horizontal pipe involves complex multiphase flows, potentially with lean and dense phase regions, stationary particles and blockage.The Distinct Element Method (DEM) is a powerful tool to study granular dynamics. It models interactions at the particle level and reproduces the assembly physics. This paper presents a 3D DEM model to predict pressure drop, flowrate and flow patterns in pneumatic conveying. The inter-particle forces are modelled using the spring-dashpot-slider analogy. A novel gas flow model is developed. The pipe is divided into sections. In each section a lean and dense region is determined on a voidage criterion based on particle positions. Given the pressure at the boundaries, the fluid flow is determined assuming steady state conditions. This uses the Ergun equation for the flow through the dense phase and the equations of Wen and Yu for modified single spheres and wall resistance for the lean phase. It uses an iterative algorithm adjusting the fluid flowrate so that the pressure in each section is the same in the dense phase and lean phase and maintaining the boundary pressures. Once the fluid flow profile has been calculated the fluid drag on each particle can be determined. The results compare well with experimental data relating pressure gradient and solid and gas flowrates from Molerus (1993), Molerus (1996). Flow patterns for all the flow regimes, fully suspended flow, strand flow, slug flow, and conveying over stationary layer are observed.     

脉石英矿制备高纯石英砂工艺的试验研究

为了使天然脉石英达到高纯石英砂的标准,通过煅烧—水淬—浮选—酸洗—乙醇-去离子水洗等工艺提纯石英砂,采用光学显微镜、扫描电镜、X射线衍射、激光粒度仪、电感耦合等离子体光谱仪等手段分析石英砂试样的显微结构、形貌、物相、粒度和成分。结果表明,脉石英矿粗砂粒径分布较均匀,浮选精砂及高温煅烧精砂的粒径明显增大,比表面积明显减小;浮选后精砂的大颗粒为纯石英;筛分、高温处理对石英砂杂质元素去除不明显,浮选、酸浸去除杂质效果显著,脉石英矿经处理后的石英砂中SiO2的质量分数达到99.99%以上。