Analytical solutions for organic contaminant diffusion in triple-layer composite liner system considering the effect of degradation

  • Hefu Pu
  • Jinwei Qiu
  • Rongjun ZhangEmail author
  • Junjie Zheng
Research Paper


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.


Analytical solutions Degradation Diffusion Geomembrane Geosynthetics Landfill composite liner Organic contaminant 

List of symbols


Contaminant concentration in leachate


Effective diffusion coefficient for CCL


Effective diffusion coefficient for GCL


GM diffusion coefficient


Contaminant mass flux


Steady-state contaminant mass flux


Distribution coefficient


Distribution coefficient for CCL


Partition coefficient between GM and GCL


Partition coefficient for the organic contaminant and GM


Thickness of CCL


Thickness of GCL


Thickness of GM


Porosity of CCL


Porosity of GCL


Retardation factor for CCL


Contaminant half-life


First-order decay constant


Dry density


Dry density of CCL



Financial support for this investigation was provided by the National Key R&D Program of China (Grant No. 2016YFC0800200), the National Natural Science Foundation of China (Grant No. 51678268), and the Fundamental Research Funds for the Central Universities of China (Grant No. HUST-2016YXMS101). This support is gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Geotechnical and Underground EngineeringHuazhong University of Science and TechnologyWuhanChina

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