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.     

基于混合物理论的水力-化学-力学污染物输运模型研究

由于废弃物的堆积以及填埋场上覆盖层的重量,衬垫因此承受一定的压力,发生力学固结;由于黏土本身的结构特性,当污染物通过黏土垫层时可能会发生化学固结,而固结作用可直接对污染物的对流输运产生影响,也会引起土层体积和结构的变化,从而改变其固有的输运性质。从混合物理论出发,建立了水力-化学-力学作用下的溶质输运理论框架,统一地描述了水力-化学-力学作用下变形、水的吸附或解吸附、对流和扩散现象。将输运系数考虑为有效孔隙率的函数,由此反映固结对输运参数的影响。对所建立的数学模型进行无量纲化处理,并使用有限元软件COMSOL Multiphysics进行求解,最后进行了参数分析。研究结果表明,垫层土体中吸附水和自由水之间的化学势差异越大,层间吸附水的解吸附量越大;当土体的软硬性质不同时,当层间吸附水解吸附后,土体固结程度不同,从而对污染物输运过程的影响不同。而当垫层上覆荷载增大时,土体宏观孔隙的扩张的限制作用增强,从而对土体产生一种修复作用,抑制污染物在土体中的输运。     

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     

An analytical solution for one-dimensional contaminant diffusion through multi-layered system and its applications

An analytical solution for one-dimensional contaminant diffusion through multi-layered media is derived regarding the change of the concentration of contaminants at the top boundary with time. The model accounts for the arbitrary initial conditions and the conditions of zero concentration and zero mass flux on the bottom boundary. The average degree of diffusion of the layered system is introduced on the basis of the solution. The results obtained by the presented analytical solutions agree well with those obtained by the numerical methods presented in the literature papers. The application of the analytical solution to the problem of landfill liner design is illustrated by considering a composite liner consisting of geomembrane and compacted clay liner. The results show that the 100-year mass flux of benzene at the bottom of the composite liner is 45 times higher than that of acetone for the same composite liner. The half-life of the contaminant has a great influence on the solute flux of benzene diffused into the underlying aquifer. Results also indicates that an additional 2.9–5.0 m of the conventional (untreated) compacted clay liner under the geomembrane is required to achieve the same level of protection as provided by 0.60 m of the Hexadecyltrimethylammonium (HDTMA)-treated compacted clay liners in conjunction with the geomembrane. Applications of the solution are also presented in the context of a contaminated two-layered media to demonstrate that different boundary and initial conditions can greatly affect the decontamination rate of the problem. The method is relatively simple to apply and can be used for performing equivalency analysis of landfill liners, preliminary design of groundwater remediation system, evaluating experimental results, and verifying more complex numerical models.     

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。     

Flow and transport through clay membrane barriers

Flux equations for liquid and solute migration through clay barriers that behave as semi-permeable membranes used in waste containment and remediation applications, known as clay membrane barriers (CMBs), are discussed. The results of a simplified analysis of flow through a geosynthetic clay liner (GCL) using measured values for the chemico-osmotic efficiency coefficient (ω) of the GCL indicate a total liquid flux that counters the outward Darcy (hydraulic) flux due to chemico-osmosis associated with clay membrane behavior of the GCL. Also, the solute (contaminant) flux through the GCL is reduced relative to the solute flux that would occur in the absence of membrane behavior due to chemico-osmotic counter advection and solute restriction. Since diffusion commonly controls solute transport through GCLs and other low-permeability clay barriers, the implicit (empirical) correlation between ω and the effective salt-diffusion coefficient of the migrating contaminant is an important consideration with respect to contaminant restriction in CMBs.     

CCL吸附特性及孔隙率降低对污染物运移的影响

假定孔隙均匀地分布于土体的物质空间内和土骨架对污染物的吸附特性服从平衡线性,对基本体积质量关系进行分析,提出了由于土体对污染物的吸附而引起的孔隙率降低的估算公式。在考虑土体孔隙率变化的条件下,建立了污染物一维运移的控制方程,并考虑垃圾生物降解效应、压实黏土衬里（CCL）防渗层、下覆有限厚度含水层等实际情况,确定了初始条件和边界条件。对所建立的初边值问题进行了数值求解,且对某假想填埋场情况进行了变动参数与对比计算,结果表明,由于土颗粒对污染物的吸附所引起的孔隙率降低,显著地降低了污染物对压实黏土衬里的穿透能力。与常孔隙率情况相比,CCL中污染物的峰值浓度降低近10 %,含水层中污染物浓度降低更显著。当考虑土体孔隙率变化时,弥散对污染物运移具有控制作用,分布系数对污染物的运移具有重要影响。     

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.     

Multi-dimensional chemo-osmotic consolidation of clays

A model of chemo-osmotic consolidation of clays in multi-dimensional domains is presented, with volumetric strains induced by both changes in the chemistry and osmotically driven pore water flow considered. Three fully coupled governing equations considering force equilibrium, pore water transport and chemical transport are presented and solved using the transient finite element method. The proposed approach is verified via consideration of chemo-osmotic consolidation of a compacted clay landfill liner and then applied to investigation of a hypothetical case with a local leachate leak in the compacted clay liner. An assessment of the impact of the two-dimensional nature of the system is made. The consolidation process is found to be dominated by osmotic consolidation in the early stages and subsequently by chemical consolidation. It is found that the surface settlement and the leachate concentration in the compacted clay liner may be highly overestimated by a one-dimensional analysis. Moreover, the peak negative excess pore pressure predicted by the two-dimensional solution remains in a shallow region under the leak while in the one-dimensional solution it moves progressively downwards.     

Landfill Base Liners: Assessment of Material Equivalency and Impact to Groundwater

This paper gathered available flow and transport solutions and used them for two composite liners, consisting of geomembrane (GM) overlying either a compacted clay liner (CCL) or a geosynthetic clay liner (GCL). Its aim is to provide a guiding framework for the possible choices of (a) approaches to bottom liner design, (b) respective analytical solutions to flow and transport equations, as well as (c) parameters required for each type of solution. On the basis of the obtained results, the following recommendations are made. When the goal of analysis is to determine material equivalency, leachate flow rate is an adequate key parameter for GM-CCL composite liners. For GM-GCL composite liners, it is necessary to compute contaminant concentration or mass flux, considering (a) transport through defects for inorganic contaminants and (b) diffusion and the contribution of any available attenuation layer for organic contaminants. When the goal of analysis is to assess impact to groundwater, it is advised to calculate both discharge rate and contaminant mass flux regardless of liner type. The critical parameter for the transport calculations is the retardation factor of the contaminant, for the case of CCLs, while the results for GCLs are much less sensitive to this parameter.     

The 14-year Performance of a Compacted Clay Liner used as Part of a Composite Liner System for a Leachate Lagoon

The migration of contaminants through a 2.9 m thick compacted clay liner (CCL) for a landfill leachate lagoon is examined 14 years after construction. The clay liner formed the lower portion of the composite liner system but the geomembrane (GM) was found to have defects that had allowed leachate to migrate between the GM and CCL. Chloride, sodium, potassium, calcium and magnesium pore water profiles through the CCL are examined. It is shown that chloride migrated approximately 1.7 m into the CCL during the 14 years of the lagoon operation, sodium approximately 1.2 m, and potassium 0.7 m. Diffusion and sorption data from laboratory diffusion testing are utilized in combination with a finite layer contaminant transport model to predict field contaminant migration profiles through the composite liner system and to establish the time of ‘failure’ of the geomembrane at sometime between 0 and 6 years after installation. Relatively high sorptive uptake of potassium by the CCL soil is observed from batch testing and diffusion testing with field data suggesting an even larger amount of sorption. It is hypothesized that organic sludge matter at the base of the lagoon is responsible for potassium uptake from the leachate. This field case highlights the importance of the compacted clay liner as part of the composite liner system in acting as a diffusion barrier during the lifetime of the lagoon as well as using relatively non-conservative contaminants such as chloride and sodium to estimate geomembrane ‘failure’ times     

Failure probability assessment and parameter sensitivity analysis of a contaminant’s transit time through a compacted clay liner

This paper presents failure probability assessment and parameter sensitivity analysis of a contaminant’s transit time through a compacted clay liner. Monte Carlo simulation (MCS) was used to assess failure probability, and the failure samples generated in the MCS were used to investigate the sensitivity of various uncertain parameters to the failure probability. To facilitate the MCS, a database on various transport parameters was developed by collecting and analyzing measurement data reported in literature. Failure probability assessment and parameter sensitivity analysis showed that the uncertainties in adsorption parameters, longitudinal dispersivity, and hydraulic conductivity have the most significant effects on failure probability.     

有机污染物在完好复合衬垫中的迁移分析

在复合衬垫中,有机污染物除了在土工膜缺陷处发生迁移外,在完好土工膜中的迁移也是主要方式。考虑有机污染物在土工膜边界处的浓度跳跃现象,建立了有机污染物在完好复合衬垫中迁移的一维模型,得到了解析解。通过与有限差分解的比较,验证了解答的合理性。应用该解答分析了GCL复合衬垫和CCL复合衬垫防止有机污染物渗漏的效果。结果表明,CCL复合衬垫的效果较好,可以通过黏土改性和增加黏土厚度的方法来提高其有效性。有机污染物类型的选择对GCL复合衬垫的分析结果影响较大,而阻滞系数的变化对分析结果影响较小。     

GCL与CCL复合衬垫的等效性分析

土工合成材料粘土衬垫(GCL)与土工膜(GM)形成的复合衬垫在垃圾填埋场中的应用日益广泛。我国规范中允许在特殊情况下用GCL代替压实粘土(CCL)做垃圾填埋场的衬垫,但是对于“特殊情况”没有明确说明。本文采用数值方法对复合衬垫中无机污染物的对流和扩散进行了计算,从衬垫底部污染物通量和累积量两个角度对GCL复合衬垫和CCL复合衬垫阻滞污染物运移的效果进行了比较,分析两种复合衬垫的等效性,并研究了GCL复合衬垫的适用范围。结果表明,当渗滤液水头较高时,GCL复合衬垫体现出其优势。     

Solute transport through a deforming porous medium

Solute transport through a porous medium is typically modelled assuming the porous medium is rigid. However, many applications exist where the porous medium is deforming, including, municipal landfill liners, mine tailings dams, and land subsidence. In this paper, mass balance laws are used to derive the flow and transport equations for a deforming porous medium. The equations are derived in both spatial and material co‐ordinate systems. Solute transport through an engineered landfill liner is used as an illustrative example to show the differences between the theory for a rigid porous medium, and small and large deformation analysis of a deforming porous medium. It is found that the large deformation model produces shorter solute breakthrough times, followed by the small deformation model, and then the rigid porous medium model. It is also found that it is important to include spatial and temporal void ratio variations in the large deformation analysis. It is shown that a non‐linear large deformation model may greatly reduce the solute breakthrough time, compared to a standard transport analysis typically employed by environmental engineers. Copyright © 2002 John Wiley & Sons, Ltd.     

渗透系数的变异性对压实黏土衬垫性能的影响

压实黏土衬垫是填埋场等环境岩土工程中常用的屏障材料,其厚度和渗透系数是主要的设计参数。考虑渗透系数的变异性,用衬垫底部污染物相对浓度和通量等指标分析了设计参数对衬垫有效性的影响。研究表明,渗透系数的变异性对衬垫性能有很大的影响：当衬垫厚度较小或渗透系数均值较大时,衬垫底部出现高浓度（接近于1）的概率很大,这个浓度区间可能比相对浓度的均值高很多,对周围环境污染有较大的威胁。从非反应性溶质的运移来看,我国规范中对衬垫厚度和渗透系数的规定是合理的。相对于污染物的通量,厚度和渗透系数对衬垫底部相对浓度的影响更为显著,相对浓度更适合作为评价衬垫性能的指标。     

Solute transfer during consolidation based on a solid‐fluid‐solute coupling model

The migration of contaminant through soil is usually modeled using the advection‐dispersion equation and assumes that the porous media is stationary without introducing a constitutive equation to represent soil structure. Consequently, time‐dependent deformation induced by soil consolidation or physical remediation is not considered, despite the need to consider these variables during planning for the remediation of contaminated ground, the prediction of contaminated groundwater movement, and the design of engineered landfills. This study focuses on the numerical modeling of solute transfer during consolidation as a first step to resolve some of these issues. We combine a coupling theory‐based mass conservation law for soil‐fluid‐solute phases with finite element modeling to simulate solute transfer during deformation and groundwater convection. We also assessed the sensitivity of solute transfer to the initial boundary conditions. The modeling shows the migration of solute toward the ground surface as a result of ground settlement and the dissipation of excess pore water pressure. The form of solute transport is dependent on the ground conditions, including factors such as the loading schedule, contamination depth, and water content. The results indicate that an understanding of the interaction between coupling phases is essential in predicting solute transfer in ground deformation and could provide an appropriate approach to ground management for soil remediation.     

Sensitivity Analysis of a Combined Groundwater Flow and Solute Transport Model Using Local-Grid Refinement: A Case Study

Combining groundwater flow models with solute transport models represents a common challenge in groundwater resources assessments and contaminant transport modeling. Groundwater flow models are usually constructed at somewhat larger scales (involving a coarser discretization) to include natural boundary conditions. They are commonly calibrated using observed groundwater levels and flows (if available). The groundwater solute transport models may be constructed at a smaller scale with finer discretization than the flow models in order to accurately delineate the solute source and the modeled target, to capture any heterogeneity that may affect contaminant migration, and to minimize numerical dispersion while still maintaining a reasonable computing time. The solution that is explored here is based on defining a finer grid subdomain within a larger coarser domain. The local-grid refinement (LGR) implemented in the Modular 3D finite-difference ground-water flow model (MODFLOW) code has such a provision to simulate groundwater flow in two nested grids: a higher-resolution sub-grid within a coarse grid. Under the premise that the interface between both models was well defined, a comprehensive sensitivity and uncertainty analysis was performed whereby the effect of a parameter perturbation in a coarser-grid model on transport predictions using a higher-resolution grid was quantified. This approach was tested for a groundwater flow and solute transport analysis in support of a safety evaluation of the future Belgian near-surface radioactive waste disposal facility. Our reference coarse-grid groundwater flow model was coupled with a smaller fine sub-grid model in two different ways. While the reference flow model was calibrated using observed groundwater levels at a scale commensurate with that of the coarse-grid model, the fine sub-grid model was used to run a solute transport simulation quantifying concentrations in a hypothetical well nearby the disposal facility. When LGR coupling was compared to a one-way coupling, LGR was found to provide a smoother flow solution resulting in a more CPU-efficient transport solution. Parameter sensitivities performed with the groundwater flow model resulted in sensitivities at the head observation locations. These sensitivities identified the recharge as the most sensitive parameter, with the hydraulic conductivity of the upper aquifer as the second most sensitive parameter in regard to calculated groundwater heads. Based on one-percent sensitivity maps, the spatial distribution of the observations with the highest sensitivities is slightly different for the upper aquifer hydraulic conductivity than for recharge. Sensitivity analyses were further performed to assess the prediction scaled sensitivities for hypothetical contaminant concentrations using the combined groundwater flow and solute transport models. Including all pertinent parameters into the sensitivity analysis identified the hydraulic conductivity of the upper aquifer as the most sensitive parameter with regard to the prediction of contaminant concentrations.     

Diffusion and sorption experiments using a DKS permeameter

The analysis of contaminant transport through clay liner is a relevant aspect in the design of industrial, urban and mining waste disposal systems, since these areas must be designed and operated to prevent contaminating substances from reaching underground water systems in unacceptable concentrations. The design requires an estimate of the potential contaminant transport rate. However, before any attempt at quantification can be made, values for transport mechanism control parameters must be established. Clayey materials are frequently used as contaminant barriers. In these materials, which have low hydraulic conductivity, the main contaminant transport mechanism is molecular diffusion. Parameters controlling transport for these conditions are the diffusion coefficient and sorption parameters. These parameters depend on soil constituents and characteristics as well as on the chemical constitution of the contaminant. The great complexity of the factors involved makes it necessary to determine the parameters of each type of soil. This paper discusses an equipment called DKS permeameter (diffusion, convection, sorption), for the study of soil-contaminant transport mechanisms, designed at the Institute for Soil Mechanics of the Ruhr-University Bochum, and some results obtained from its use at COPPE/Federal University of Rio de Janeiro (UFRJ), Brazil. This equipment determines the effective diffusion coefficient and sorption parameter with a better reflection of field conditions. The soil under study is a mix of sodium–bentonite that has low hydraulic conductivity (k=10⁻⁹ cm/s) with adequate liner characteristics. The result indicated the relevance of determining sorption parameters for structured soils, since the sorption perceived from batch test results using pulverised soil represents maximum soil capacity. Designs based on this parameter would overestimate the attenuation capacity of the liner.     

考虑非等温环境下污染物在黏土中的运移解析模型

利用广义积分变换法推导了非等温条件下污染物在压实黏土衬垫中的运移解析解。所提出的解析解考虑了分子扩散、对流、吸附和热扩散的耦合效应,并考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化。通过与热扩散试验结果、已有的解析解和基于COMSOL软件的数值模型的对比,验证了所提出的解析解。利用经过验证的解析解,研究了非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数3个参数随温度的变化对甲苯在压实黏土衬垫系统中迁移的影响。结果表明,非等温环境以及压实黏土的渗透系数、有效扩散系数和分布系数随温度的变化均对甲苯在压实黏土衬垫中迁移有着显著的影响。不考虑非等温环境的影响将极大低估污染物的溢出量和污染物的击穿时间。既有解析解忽略压实黏土的渗透系数和有效扩散系数随温度的变化会极大低估甲苯的流出速率,而忽略压实黏土分布系数随温度的变化会极大高估甲苯击穿衬垫系统的时间和达到稳态的时间。所提出的解析解能够考虑热扩散作用,同时考虑了压实黏土的渗透系数、分布系数和有效扩散系数3个参数随温度的变化,较既有解析解更贴近工程实际,能够为压实黏土衬垫系统的设计和服役性能评价提供指导和借鉴。