A general approach to the modelling of contaminant transport through composite landfill liners with intact or leaking geomembranes

Finite‐element models of contaminant transport through composite landfill liners require highly refined meshes around the interface between the geomembrane and the clay layer, especially if leakage through holes in the geomembrane is considered. In addition, no general formulation for transport through leaking geomembranes can be found in the literature. The paper develops a general approach to time‐dependent contaminant migration through composite liners with intact or leaking geomembranes. Equations are derived for various combinations of system conditions including Dirichlet and Neumann boundary conditions in the waste, constant mass of contaminants in the waste, steady state or transient transport in the geomembrane, and steady state or transient seepage velocities in the mineral liner. The effect of the geomembrane on transport in the soil is converted into an equivalent boundary condition applicable at the top of the clay layer. Hence, only the media underlying the top geomembrane are explicitly represented in the numerical model, yielding a computationally efficient algorithm. The new formulation is validated in conjunction with finite‐layer, finite‐element and boundary‐element methods, by comparing its predictions to those of more conventional approaches which represent the geomembrane explicitly. The scope of the method is illustrated by modelling a landfill liner with a geomembrane leaking in five locations. Copyright © 2007 John Wiley & Sons, Ltd.     

Theoretical investigation of the effects of consolidation on contaminant transport through clay barriers

Consolidation of clayey contaminant barriers such as landfill liners has been postulated as a cause of early breakthrough of contaminants. In this paper we theoretically investigate this proposition. For this purpose a sophisticated one‐dimensional, large‐deformation model of coupled mechanical consolidation and solute transport is employed. This new model is a generalization of existing coupled consolidation and solute transport models described in the literature. It takes into account both non‐linearities in geometry as well as constitutive relations. The latter relate the compressibility, hydraulic conductivity and coefficient of effective diffusivity to the deformation of the soil. The model is applied to a case study of a clay liner and geomembrane system. Results obtained from numerical solution of the model equations are compared with those from various simplified models, including a ‘diffusion only’ (i.e. a rigid soil) model traditionally used in contaminant barrier design. For barriers incorporating low compressibility soils (as for many well compacted clays), there is little difference between contaminant transit (i.e. breakthrough) times predicted by the two models. However, for contaminant barriers incorporating more compressible soils, consolidation is shown to significantly accelerate transport. These results indicate the potential importance of accounting for the effects of soil consolidation and highlight the limitations of existing models when modelling solute transport through composite barriers utilizing soft soils. Based on these limited results, we suggest a possible way of taking into account soil consolidation using simplified models. Copyright © 2008 John Wiley & Sons, Ltd.     

非平衡-非线性吸附情况下填埋场污染物运移分析

采用Langmuir等温吸附线方程描述非线性吸附性能, 基于改进的混合元方法，通过数值计算与分析，探讨了非平衡吸附条件下污染物运移过程及其机理。计算结果表明: 当考虑非平衡、非线性吸附性能时, 污染物穿透曲线即浓度的时程变化曲线尖锐而狭窄、峰值点前移, “拖长尾”现象不明显, 由此说明，土颗粒对污染物的非平衡、非线性吸附使得污染物的穿透能力增强, 滞留能力下降。进一步的变动参数比较分析表明：Langmuir等温线方程中的参数B、压实粘土衬里的渗透性及地下水渗流速度对污染物运移过程具有显著的影响。     

衬垫中污染物运移的一维概率分析

衬垫中污染物的运移分析一般采用确定性方法。为了研究渗透系数变异性对污染物运移的影响,基于土层剖面随机场理论,将渗透系数模拟成服从对数正态分布的空间随机场,利用Monte-Carlo和数值积分两种方法进行分析。两种方法得到的结果有很好的一致性。衬垫渗透系数的空间变异性对污染物运移有重要影响。变异系数较大时,衬垫失效概率在前期较大而后期较小,但衬垫底部出现高浓度(相对浓度0.9～1.0)的几率也较高。衬垫的可靠性要综合考虑渗透系数的变异性和渗透系数数值范围的影响。     

复合衬层中变系数有机污染物迁移规律分析

土工膜和下伏压实黏土组成的复合衬层已被广泛用作填埋场的防渗屏障系统。有机污染物在复合衬层中迁移时,其主要运移机制是扩散作用。假设有机污染物在土工膜中稳态扩散,并假设在下伏衬层中扩散系数为迁移距离的线性函数,且考虑降解作用的影响,建立了有机污染物在复合衬层中的一维扩散模型,针对零浓度下边界条件,获得了模型解析解。基于该解析解,分析讨论了相关参数的敏感性。结果表明,相关参数对计算结果影响很大,降解半衰期对污染物运移同样存在较大影响。该解析模型仅适用于有机污染物在两层复合衬垫中的迁移问题,可为填埋场的初步设计提供参考     

裂隙岩体中污染物运移过程的数值模拟

基于双重介质理论模型建立了污染物在地下环境中运移的耦合数学模型,给出了有限元离散的数值格式。并以核废料储存过程中核素90Sr为例,采用所建立的数值模型模拟其在裂隙岩体中运移过程,预测了污染物的浓度分布范围和发展趋势。模拟结果表明:核素90Sr在处置库中运行40年后,下游地区的抽水井的浓度可达到3 100 Bq/m3,超出了国家规定的标准,为固体废物场址的选择以及污染的控制提供了决策依据。     

One‐dimensional contaminant transport through a deforming porous medium: theory and a solution for a quasi‐steady‐state problem

Contaminant migration through soil is usually modelled mathematically using the dispersion–advection equation. This type of model finds application when planning the remediation of contaminated land, predicting the movement of polluted groundwater and designing engineered landfills. Usually the analysis assumes that the porous media through which the contaminant migrates is stationary. However, the construction of landfills on clay soils means that the soil beneath the landfill will undergo time‐dependent deformation as the soil consolidates. To date, there are no published data on the effect a deforming porous media may have on contaminant transport beneath a landfill; indeed, there appears to be no theory of contaminant migration through a deforming soil. In this paper, a one‐dimensional theory of contaminant migration through a saturated deforming porous media is developed based on a small and large strain analysis of a consolidating soil and conservation of contaminant mass. By selection of suitable parameters, the new transport equation reduces to the familiar one‐dimensional dispersion–advection equation for a saturated soil with linear, reversible, equilibrium controlled sorption of the contaminant onto the soil skeleton. Analytic solutions to a quasi‐steady‐state contaminant transport problem for a deforming media are presented, and a preliminary assessment made of the potential importance of soil deformation on the results of a contaminant migration analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

考虑土体固结变形的污染物运移模型

土体的固结压缩变形对污染物的运移具有重要的影响,而目前国内关于污染物在变形多孔介质中运移规律的研究尚处于空白,在国外也是近几年才有人开始这方面的研究工作。在Biot固结理论和污染物运移理论相结合的基础上,提出了污染物在黏土防渗层中迁移转化的一维数学模型,该模型的最大特点是考虑了土体受力变形对污染物运移的影响,在合理简化的基础上给出了模型的解析解,并将计算结果与太湖疏浚污染底泥堆场的实测结果进行了比较分析,模拟计算的结果在一定程度上能够反映实际土层中污染物的运移情况。     

含单个孔洞岩盐路基稳定性的无网格分析

用无网格伽辽金法计算了孔洞边缘危险点的应力。对含单个孔洞岩盐路基的稳定性进行了分析,给出了针对不同孔洞埋深的临界载荷。数值结果表明,EFGM对于解决含有单个孔洞的应力集中问题,是有效且灵活的。     

Weak discontinuity in porous media: an enriched EFG method for fully coupled layered porous media

In this paper, a series of multimaterial benchmark problems in saturated and partially saturated two‐phase and three‐phase deforming porous media are addressed. To solve the process of fluid flow in partially saturated porous media, a fully coupled three‐phase formulation is developed on the basis of available experimental relations for updating saturation and permeabilities during the analysis. The well‐known element free Galerkin mesh‐free method is adopted. The partition of unity property of MLS shape functions allows for the field variables to be extrinsically enriched by appropriate functions that introduce existing discontinuities in the solution field. Enrichment of the main unknowns including solid displacement, water phase pressure, and gas phase pressure are accounted for, and a suitable enrichment strategy for different discontinuity types are discussed. In the case of weak discontinuity, the enrichment technique previously used by Krongauz and Belytschko [Int. J. Numer. Meth. Engng., 1998; 41:1215–1233] is selected. As these functions possess discontinuity in their first derivatives, they can be used for modeling material interfaces, generating only minor oscillations in derivative fields (strain and pressure gradients for multiphase porous media), as opposed to unenriched and constrained mesh‐free methods. Different problems of multimaterial poro‐elasticity including fully saturated, partially saturated one, and two‐phase flows under the assumption of fully coupled extended formulation of Biot are examined. As a further development, problems involved with both material interface and impermeable discontinuities, where no fluid exchange is permitted across the discontinuity, are considered and numerically discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

大变形黏土防渗层中的污染物迁移和转化规律研究

国内湖泊疏浚污染底泥堆场一般以较厚的黏土层作为主要防渗层,由于在上覆底泥作用下黏土层会发生较大的固结变形,因此,在研究黏土防渗层中的污染物运移和转化规律时,应该考虑土体变形的影响。基于Gibson一维大变形固结理论和饱和多孔介质中的污染物对流扩散方程,建立了二者耦合的可变形多孔介质中污染物的运移和转化模型,其中首次考虑了土体自重和生物降解作用的影响。利用所建立模型的数值解,研究了在可变形黏土防渗层中的污染物运移和转化规律,同时分析了模型中不同项和主要参数的作用和影响。研究结果表明,土体大变形对黏土防渗层中污染物的运移有着较复杂的影响,一方面土体变形会加速污染物的运移;另一方面土体固结带来的渗透性减小会增加污染物的穿透时间,二者的不同作用取决于众多的影响因素,如土层厚度和吸附作用等。研究结果对于评估天然黏土防渗层对污染物的阻隔作用有重要的指导意义。     

Semi-analytical solutions of a contaminant transport equation with nonlinear sorption in 1D

A new method to determine semi-analytical solutions of one-dimensional contaminant transport problem with nonlinear sorption is described. This method is based on operator splitting approach where the convective transport is solved exactly and the diffusive transport by finite volume method. The exact solutions for all sorption isotherms of Freundlich and Langmuir type are presented for the case of piecewise constant initial profile and zero diffusion. Very precise numerical results for transport with small diffusion can be obtained even for larger time steps (e.g., when the Courant-Friedrichs-Lewy (CFL) condition failed).     

我国北方型裂隙岩溶水流及污染物运移数值模拟研究进展

简要回顾了近几十年来我国北方型裂隙岩溶水流及污染物运移数值模拟方面的研究成果,评述了裂隙岩溶水资源评价和污染物运移模拟的计算方法和模拟技术,其中对一些与数值模拟相关的重要问题、近年来研究的热点问题,如模型参数识别及其尺度效应问题、数值弥散和数值振荡问题、Non-Darcy流和Non-Fickian运移问题以及随机方法研究等进行了重点评述,对已有的解决办法进行了比较和对照,并探讨了今后的研究趋势.     

Numerical study of soil heterogeneity effects on contaminant transport in unsaturated soil (model development and validation)

The movement of chemicals through soil to groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. The study of the effects of different factors involved in transport phenomena can provide valuable information to find the best remediation approaches. Numerical models are increasingly being used for predicting or analyzing solute transport processes in soils and groundwater. This article presents the development of a stochastic finite element model for the simulation of contaminant transport through soils with the main focus being on the incorporation of the effects of soil heterogeneity in the model. The governing equations of contaminant transport are presented. The mathematical framework and the numerical implementation of the model are described. The comparison of the results obtained from the developed stochastic model with those obtained from a deterministic method and some experimental results shows that the stochastic model is capable of predicting the transport of solutes in unsaturated soil with higher accuracy than deterministic one. The importance of the consideration of the effects of soil heterogeneity on contaminant fate is highlighted through a sensitivity analysis regarding the variance of saturated hydraulic conductivity as an index of soil heterogeneity. Copyright © 2011 John Wiley & Sons, Ltd.     

悬浮颗粒的浓度对其在饱和多孔介质中迁移和沉积特性的影响

多孔介质中悬浮颗粒迁移和沉积特性的研究对地下污染物净化、石油开采、核废料处置、水土保持等有很重要的意义。对4种不同浓度的悬浮颗粒在3种不同的渗流速度下进行室内试验,研究悬浮颗粒的浓度对其迁移和沉积特性的影响。结果表明,在一定的悬浮颗粒浓度下,随着渗流速度的增加,穿透曲线中的悬浮颗粒的相对浓度也增大。同时,渗流速度一定时,悬浮颗粒的浓度存在一个临界值,小于该临界值,穿透曲线中的相对浓度随悬浮颗粒的浓度增大而增大;大于该临界值时,相对浓度随悬浮颗粒的浓度增大而减小。另外,悬浮颗粒的临界浓度是与渗流速度相关的,随着渗流速度增加,悬浮颗粒的临界浓度也逐渐增大     

Numerical model of contaminant transport through conduit-porous matrix system

A mathematical model for determining solute concentrations at a point within a cylindrically symmetrical conduit-porous matrix system is described. Both convection and diffusion are considered within the conduit subsystem, whereas only diffusion is considered within the porous matrix subsystem. The two subsystems are coupled through continuity conditions imposed at their interface boundary. The transport equations are solved utilizing an alternating-direction implicit-method technique. The solute concentration profiles resulting from this model are then sketched and discussed.     

Theoretical and numerical study of the steady‐state flow through finite fractured porous media

This paper investigates the two‐dimensional flow problem through an anisotropic porous medium containing several intersecting curved fractures. First, the governing equations of steady‐state fluid flow in a fractured porous body are summarized. The flow follows Darcy's law in matrix and Poiseuille's law in fractures. An infinite transversal permeability is considered for the fractures. A multi‐region boundary element method is used to derive a general pressure solution as a function of discharge through the fractures and the pressure and the normal flux on the domain boundary. The obtained solution fully accounts for the interaction and the intersection between fractures. A numerical procedure based on collocation method is presented to compute the unknowns on the boundaries and on the fractures. The numerical solution is validated by comparing with finite element solution or the results obtained for an infinite matrix. Pressure fields in the matrix are illustrated for domains containing several interconnected fractures, and mass balance at the intersection points is also checked. Copyright © 2013 John Wiley & Sons, Ltd.     

Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method

In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

多孔介质中非均匀流动特性的染色示踪试验研究

通过土壤染色剂进行的4组试验,对不同介质结构条件下的水流和溶质非均匀运动规律,非均匀流动变异信息分布特征关系以及全局性非均匀流动示踪方法进行了研究。结果表明,即使在相对比较均匀的介质条件下,流动也表现出明显的非均匀特性;对数正态分布能够较好的反映水流的运动分布模式,相比水流运动,溶质的运动和分布规律明显不同,表现出更多的不确定性和变异性。     

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

A time‐domain viscous‐spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u–U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous‐spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed ‘drained’ boundary. For general two‐dimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscous‐spring or viscous boundaries established for u–U formulation. Copyright © 2015 John Wiley & Sons, Ltd.