Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer

Zou Qi; Chao Chunfeng; Sun Xinpo

doi:10.12052/gdutxb.250077

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer

更新时间：2026-05-27

- Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer
- Vol. 42, Issue 5, Pages: 39-48(2025)
- 作者机构：
  
  四川轻化工大学土木工程学院,四川,自贡,643002
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.250077
  CLC： X505
- Published：2025
- 稿件说明：
移动端阅览
邹棋, 晁春峰, 孙新坡. 污染物通过破损土工膜在下伏非饱和土层中的运移解析解[J]. 广东工业大学学报, 2025, 42(5): 39–48.

Zou Qi, Chao Chunfeng, Sun Xinpo. Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer[J]. 2025, 42(5): 39-48.
邹棋, 晁春峰, 孙新坡. 污染物通过破损土工膜在下伏非饱和土层中的运移解析解[J]. 广东工业大学学报, 2025, 42(5): 39–48. DOI： 10.12052/gdutxb.250077

Zou Qi, Chao Chunfeng, Sun Xinpo. Analytical Solution for Contaminant Transport Through a Damaged Geomembrane into the Underlying Unsaturated Soil Layer[J]. 2025, 42(5): 39-48. DOI： 10.12052/gdutxb.250077.

摘要

本文建立了一种一维分析模型，以模拟有机污染物通过破损土工膜进入下伏非饱和土层中的运移情况。该模型不仅考虑了土工膜的破损情况，还引入了土体的非饱和特性，从而更准确地描述污染物在非饱和土层中的运移机制。通过边界转换、位移定理、拉普拉斯变换及其逆变换公式，推导出污染物浓度随时间和深度变化的解析解。同时，将非饱和土层退化为饱和土层，并采用典型算例计算污染物浓度分布，所得结果与现有研究数据进行对比，验证结果高度吻合。随后，系统分析了3种因素(即土工膜的褶皱率和破损孔洞数以及土体的非饱和指数)对非饱和土层归一化污染物浓度随时间和深度变化的影响规律。研究结果表明：在给定的非饱和土层深度下，土工膜的褶皱率和破损孔洞数与非饱和土层中污染物运移速率呈正相关，而土体的非饱和指数则与其呈负相关。在给定的时间下，非饱和土层中归一化污染物浓度为零的临界深度，会随土工膜的褶皱率和破损孔洞数的增加而加深，随土体的非饱和指数增加而变浅。土工膜的破损对污染物运移的影响远大于土体的非饱和特性。该研究为非正规垃圾填埋场优化、天然非饱和土层中污染物浓度演变预测及相关污染防控措施提供了理论参考。

Abstract

A one-dimensional analytical model was developed to simulate the transport of organic contaminants through a defective geomembrane into the underlying unsaturated soil layer. This model accounted for geomembrane defects and incorporated the unsaturated properties of the soil

providing a more accurate representation of contaminant migration mechanisms in unsaturated soil. By applying boundary transformation

the displacement theorem

the Laplace transform

and its inverse

an analytical solution describing the variation of contaminant concentration with time and depth was derived. Additionally

the unsaturated soil layer was reduced to a saturated soil layer

and typical case studies were conducted to calculate contaminant concentration distributions. The obtained results were compared with existing research data

demonstrating a high degree of consistency. A systematic analysis was then conducted to investigate the effects of three key factors (i.e.

geomembrane wrinkle rate

the number of perforations

and the soil unsaturated index) on the temporal and spatial evolution of normalized contaminant concentration in the unsaturated soil layer. The results indicate that

at a given depth

the geomembrane wrinkle rate and the number of perforations are positively correlated with the contaminant migration rate

whereas the soil unsaturated index exhibits a negative correlation. Similarly

at a given time

the critical depth at which the normalized contaminant concentration becomes zero deepens with the increase of the geomembrane wrinkle rate and the number of perforations

but shallows with the increase of the soil unsaturated index. Moreover

the impact of geomembrane defects on contaminant migration is significantly greater than that of soil unsaturated properties. This study provides a theoretical reference for the optimization of informal landfills

the prediction of contaminant concentration evolution in natural unsaturated soil layers

and the related contamination prevention and control measures.

关键词

Keywords

references

INTERNATIONAL SOLID WASTE ASSOCIATION. Global waste management outlook 2024: beyond an age of waste, turning rubbish into a resource[R]. Nairobi: UNEP, 2024.

FANG D Z, LI K X. An overview of power generation from municipal solid waste incineration plants at home and abroad[J]. Power Generation Technology, 2019, 40(4): 367.

ZHANG Y M, SHANG X B, LI K M, et al . Technologies status and management strategies of municipal solid waste disposal in China[J ] . Ecology and Environment Sciences, 2011, 20(2): 389.

RENOU S, GIVAUDAN J G, POULAIN S, et al . Landfill leachate treatment: review and opportunity[J ] . Journal of Hazardous Materials, 2008, 150(3): 468-493.

SAWHNEY B L, KOZLOSKI R P. Organic pollutants in leachates from landfill sites[J]. Journal of Environmental Quality, 1984, 13(3): 349-352.

KAZA S, YAO L, BHADA-TATA P, et al . What a waste 2.0: a global snapshot of solid waste management to 2050[M ] . Washington: World Bank Publications, 2018: 295.

MARTTINEN S K, KETTUNEN R H, RINTALA J A. Occurrence and removal of organic pollutants in sewages and landfill leachates[J]. Science of the Total Environment, 2003, 301(1-3): 1-12.

ROWE R K, PRIYANTO D, PONNAN R. Factors affecting the service-life of HDPE geomembranes in an LLW disposal facility-19320[C]//WM2019: Proceedings of the 45th Annual Waste Management Conference. Phoenix, Ariz: [s.n.], 2019: 3-7.

ZHU M Z, YANG Y M, XU Y, et al . Discussion on repair technologies of high-density polyethylene membrane leaks in landfill anti-seepage system[J ] . Journal of Environmental Engineering Technology, 2022, 12(5): 1647-1652.

ROWE R K, FAN J. A general solution for leakage through geomembrane defects overlain by saturated tailings and underlain by highly permeable subgrade[J]. Geotextiles and Geomembranes, 2022, 50(4): 694-707.

QIU Z C, PENG M Q, XU H, et al . Analytical analysis of one-dimensional transport of organic contaminants through composite cut-off walls with defective geomembranes[J ] Acta Scientiae Circumstantiae, 2025, 45(2): 226-238.

HUANG J, WANG J J, HUANG S Y, et al . Study on the working characteristics of core wall rockfill dam considering geomembrane permeation[J ] . Water Resources and Power, 2024, 42(8): 142-146.

CEN W J, BOLANHAN K K, LIU F R. Experimental study on tensile properties of defective and damaged geomembranes[J]. Advances in Science and Technology of Water Resources, 2021, 41(1): 69-73.

LI T Y, SUN D A, NI P P, et al . Semi-analytical model for axisymmetric transport of contaminant through flawed geomembrane[J ] . Geosynthetics International, 2023, 31(5): 728-740.

LI T Y, SUN D A, CHEN Z, et al . Semi-analytical solution for two-dimensional contaminant transport through composite l iner with strip defects[J ] . Construction and Building Materials, 2024, 440: 137404.

LI T Y, SUN D A, FU X L, et al . Two-dimensional migration characteristics of contaminants considering time-dependent contaminant sources and GM defects[J ] . Chinese Journal of Geotechnical Engineering, 2024, 46(11): 2450-2456.

EI-ZEIN A. A general approach to the modelling of contaminant transport through composite landfill liners with intact or leaking geomembranes[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(3): 265-287.

EI-ZEIN A, MCCARROLL I, TOUZE-FOLTZ N. Three-dimensional finite-element analyses of seepage and contaminant transport through composite geosynthetics clay liners with multiple defects[J]. Geotextiles and Geomembranes, 2012, 33: 34-42.

ROWE R K, ABDELATTY K. Leakage and contaminant transport through a single hole in the geomembrane component of a composite liner[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2013, 139(3): 357-366.

XIE H J, CHEN Y M, LOU Z H. An analytical solution to contaminant transport through composite liners with geomembrane defects[J]. Science China Technological Sciences, 2010, 53: 1424-1433.

XIE H J, JIANG Y S, ZHANG C H, et al . An analytical model for volatile organic compound transport through a composite liner consisting of a geomembrane, a GCL, and a soil liner[J ] . Environmental Science and Pollution Research, 2015, 22: 2824-2836.

SUN D A, LI T Y, PENG M Q, et al . Semi-analytical solution for the two-dimensional transport of organic contaminant through geomembrane with strip defects to the underlying soil liner[J ] . International Journal for Numerical and Analytical Methods in Geomechanics, 2023, 47(3): 392-409.

LI T Y, SUN D A, CHEN Z, et al . Two-dimensional migration characteristics of contaminant through composite liner with arbitrarily distributed defects[J ] . Computers and Geotechnics, 2024, 174: 106652.

LIU T F, HU L M. Organic acid transport through a partially saturated liner system beneath a landfill[J]. Geotextiles and Geomembranes, 2014, 42(5): 428-436.

GUAN C, XIE H J, CHEN Y M, et al . Analytical solution for one dimensional contaminant diffusion through unsaturated soils beneath landfills[J ] . Journal of Civil, Architectural Environmental Engineering, 2012, 34(S2): 93-98.

PHAM T A, HASHEMI A, SUTMAN M, et al . Effect of temperature on the soil-water retention characteristics in unsaturated soils: analytical and experimental approaches[J ] . Soils and Foundations, 2023, 63(3): 101301.

ZHOU T, LI T Y, WANG L, et al . Analytical solution for the consolidation of unsaturated vertical drain foundation under depth-dependent initial conditions[J ] . International Journal for Numerical and Analytical Methods in Geomechanics, 2022, 46(14): 2754-2769.

ZHANG J L, YANG Q, LI Z G, et al . Comprehensive analysis of contaminant migration in two layers of unsaturated soils[J ] . Journal of Dalian University of Technology, 2011, 51(4): 574-580.

HUANG Y C, LI T Y, FU X L, et al . Analytical solutions for the consolidation of unsaturated foundation with prefabricated vertical drain[J ] . International Journal for Numerical and Analytical Methods in Geomechanics, 2020, 44(17): 2263-2282.

CHEN K, WANG C, LIANG F Y, et al . A new SWRC model of unsaturated soil considering the coupling of hydraulic hysteresis and volume deformation[J ] . Rock and Soil Mechanics, 2024, 45(12): 3694-3704.

ZHAI Q, SHEN T L, TIAN G, et al . Prediction of the coefficient of permeability for unsaturated soil by considering the film flow[J ] . Chinese Journal of Geotechnical Engineering, 2024, 46(2): 291-298.

FITYUS S G, SMITH D W, BOOKER J R. Contaminant transport through an unsaturated soil liner beneath a landfill[J]. Canadian Geotechnical Journal, 1999, 36(2): 330-354.

DIAW E B, LEHMANN F, ACKERER P. One-dimensional simulation of solute transfer in saturated-unsaturated porous media using the discontinuous finite elements method[J]. Journal of Contaminant Hydrology, 2001, 51(3-4): 197-213.

LIN Y C, YEH H D. A simple analytical solution for organic contaminant diffusion through a geomembrane to unsaturated soil liner: considering the sorption effect and Robin-type boundary[J]. Journal of Hydrology, 2020, 586: 124873.

CHEN R, GE Y H, CHEN Z K, et al . Analytical solution for one-dimensional contaminant diffusion through unsaturated soils beneath geomembrane[J ] . Journal of Hydrology, 2019, 568: 260-274.

ROWE R K, BRACHMAN R W I. Assessment of equivalence of composite liners[J]. Geosynthetics International, 2004, 11(4): 273-286.

ROWE R K. Protecting the environment with geosynthetics: 53rd Karl Terzaghi lecture[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146(9): 04020081.

CHEN Y M, XIE H J, KE H, et al . An analytical solution for one-dimensional contaminant diffusion through multi-layered system and its applications[J ] . Environmental Geology, 2009, 58: 1083-1094.

FENG S J, PENG M Q, CHEN Z L, et al . Transient analytical solution for one-dimensional transport of organic contaminants through GM/GCL/SL composite liner[J ] . Science of the Total Environment, 2019, 650: 479-492.

CHEN J S, LIU Y H, LIANG C P, et al . Exact analytical solutions for two-dimensional advection-dispersion equation in cylindrical coordinates subject to third-type inlet boundary condition[J ] . Advances in Water Resources, 2011, 34(3): 365-374.

VAN GENUCHTEN M T. Analytical solutions of the one-dimensional convective-dispersive solute transport equation[M]. Washington: US Department of Agriculture, Agricultural Research Service, 1982: 157.

ROWE A. Effect of drainage layers on water retention of potting media in containers[J]. PloS One, 2025, 20(2): e0318716.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

An Optimal Operation Strategy for Community Microgrid Alliances Considering Power Exchange under Multi-package Shared Energy Storage Model

Research on Foreign Object Detection in Power Transmission Lines Based on the AAGV-YOLOX Model

Multi-Scale Contrastive Embedding Enhanced Adaptive Intrusion Detection Model

Robust Design for Artificial Noise-assisted UAV Terahertz Secure Communication

Modeling of 3D NAND Memory Cells with Taper Angle and Programming Strategy Optimization

Related Author

No data

Related Institution

No data

AI问答

⁰