Analytical Solutions for Axisymmetric Diffusion of Organic Pollutants in a Circular‐Shaped Cutoff Wall System

IF 3.4 2区工程技术 Q2 ENGINEERING, GEOLOGICAL International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-10-22 DOI:10.1002/nag.3875

Wenhao Jiang, Shangqi Ge, Jiangshan Li

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Abstract

Through the variable substitution and separated variable methods, this study develops a two‐dimensional (2‐D) axisymmetric diffusion analytical solution for organic pollutants in a circular‐shaped cutoff wall (CCW) system for the first time, which can more precisely and reasonably simulate the diffusion behaviors in “circular‐shaped” vertical barriers. Then, the proposed analytical solution's reasonableness is verified by comparing it with an existing analytical solution and a corresponding finite‐difference solution. Meanwhile, the comparison suggests that this solution will degrade to a 2‐D diffusion analytical solution when the pollution source radius is large enough. Furthermore, the presented analytical solution can also be simplified to a one‐dimensional axisymmetric diffusion analytical solution, or to the axisymmetric diffusion analytical solutions in a single‐layered medium. These exact analytical solutions can not only be applied to study axisymmetric diffusion behaviors under specific scenarios, but also be used to validate other complex numerical models. Last, a case study is conducted to investigate the impacts of pollution source concentration distribution, CCW horizontal thickness, and defined equivalent diffusion coefficient on the barrier performance. Overall, the proposed analytical solutions and obtained diffusion laws in this study can provide guidance for the service effect assessment and the engineering design of cutoff walls.

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有机污染物在环形截壁系统中轴对称扩散的分析解决方案

本研究通过变量替换法和分离变量法，首次建立了有机污染物在圆弧形截流壁（CCW）系统中的二维（2-D）轴对称扩散解析解，可以更精确、更合理地模拟 "圆弧形 "垂直屏障中的扩散行为。然后，通过与现有的解析解和相应的有限差分解进行比较，验证了所提出的解析解的合理性。同时，比较结果表明，当污染源半径足够大时，该解决方案将退化为二维扩散分析解决方案。此外，所提出的解析解还可以简化为一维轴对称扩散解析解，或单层介质中的轴对称扩散解析解。这些精确的分析解不仅可用于研究特定情况下的轴对称扩散行为，还可用于验证其他复杂的数值模型。最后，还进行了一项案例研究，探讨污染源浓度分布、CCW 水平厚度和定义的等效扩散系数对屏障性能的影响。总之，本研究中提出的分析方案和获得的扩散规律可为截流墙的使用效果评估和工程设计提供指导。

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来源期刊

International Journal for Numerical and Analytical Methods in Geomechanics 工程技术-材料科学：综合

CiteScore

6.40

自引率

12.50%

发文量

160

审稿时长

9 months

期刊介绍： The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.