Laplace变换求解成层土中污染物一维扩散问题

成层土中污染物的迁移规律较为复杂,将其简化为一维扩散模型。运用Laplace变换和Laplace数值逆变换方法进行了求解,编制了计算程序。计算结果可以退化到单层土的情况,结论与经典的理论解完全一致。通过与现有用数值软件计算结果的对比,检验了解答的正确性;采用的计算方法对一室内试验结果进行了模拟,计算结果和实测数据较为吻合,证明所提方法的可靠性。求解方法可用于求解更为复杂的边界条件下的污染物迁移问题。

Solution for One-Dimensional Contaminant Diffusion in Layered Clayey Soils Using Laplace Transforms

Contaminant diffusion in layered soil is very complex. The diffusion process is simplified as a one-dimensional diffusion mode. The Laplace transformation and Laplace numerical inverse transformation are adopted. The proposed solution can be degraded to a single layer case. The obtained results are well consistent with those obtained by the classic theory. The correctness of the presented solution is verified by comparing the calculation results with the results generated by existing numerical software. One case study is conducted and the calculation results have a good agreement with measured data, which prove the reliability of the proposed method. The presented method can be used to solve more complex boundary conditions of contaminant migration.