This paper presents analytical solutions for predicting one-dimensional diffusion of an organic contaminant through a triple-layer composite liner system comprising a geomembrane (GM), a geosynthetic clay liner (GCL), and a compacted clay liner (CCL). We consider two different bottom boundary conditions, i.e., fixed-concentration bottom boundary and semi-infinite bottom boundary, for which the methods of separation of variables and Laplace transform, respectively, are used to obtain the analytical solutions. The proposed analytical solutions are then verified against the CST3 numerical model and an analytical solution available in the literature. Using the verified analytical solutions, a series of parametric studies is conducted to investigate the effect of several relevant parameters on contaminant transport through the GM/GCL/CCL liner system. The results indicate that the CCL thickness, the CCL distribution coefficient, and the effective diffusion coefficient of CCL have significant impact on contaminant diffusion in the GM/GCL/CCL liner system, whereas the effective diffusion coefficient of the GCL, the diffusion coefficient of the GM, and the partition coefficient of the GM have negligible effect on contaminant diffusion in the GM/GCL/CCL liner system. The analytical solutions presented herein can be used to aid the design of a triple-layer composite liner system and the verification of other numerical models.

中文翻译：

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考虑降解效应的三层复合内衬系统中有机污染物扩散的解析解

本文提出了用于预测有机污染物通过包括土工膜（GM），土工合成粘土衬里（GCL）和压实粘土衬里（CCL）的三层复合衬里系统的一维扩散的分析解决方案。我们考虑了两个不同的底边界条件，即固定浓度底边界和半无限底边界，分别使用变量分离和拉普拉斯变换的方法来获得解析解。然后，针对CST3数值模型和文献中提供的分析解决方案对提出的分析解决方案进行验证。使用经过验证的分析解决方案，进行了一系列参数研究，以研究几个相关参数对通过GM / GCL / CCL衬管系统进行的污染物传输的影响。结果表明，CCL厚度，CCL分布系数和CCL有效扩散系数对GM / GCL / CCL衬里系统中的污染物扩散有显着影响，而GCL的有效扩散系数，CCL扩散系数GM和GM的分配系数对GM / GCL / CCL内衬系统中的污染物扩散影响可忽略不计。本文介绍的分析解决方案可用于协助三层复合衬里系统的设计和其他数值模型的验证。GM的扩散系数和GM的分配系数对GM / GCL / CCL内衬系统中污染物的扩散影响可忽略不计。本文介绍的分析解决方案可用于协助三层复合衬里系统的设计和其他数值模型的验证。GM的扩散系数和GM的分配系数对GM / GCL / CCL内衬系统中污染物的扩散影响可忽略不计。本文介绍的分析解决方案可用于协助三层复合衬里系统的设计和其他数值模型的验证。