一维对流-扩散试验各种边界条件及其统一形式解析解

发布时间：2018-05-30 15:36

本文选题：对流-扩散 + 土柱试验　；参考：《岩土力学》2015年10期

【摘要】：黏土系材料广泛应用于各种污染防治工程,扩散系数是其关键参数之一,实验室一般通过拟合一维土柱对流-扩散试验数据来确定土的扩散系数。探讨了常用的零浓度边界、零浓度梯度边界和半无限边界对应的试验条件,给出了各边界条件的统一形式,通过引入变换式和辅助问题,求解得到各边界条件下统一的有限厚度土层中对流-扩散-吸附解析解,分析了各解析解之间的差异和用于数据拟合产生的误差。结果表明,每一种底边界条件都与土柱试验底部的实际情况相对应,柯西边界可看作各种边界条件的统一形式;土柱未被击穿时各边界条件解析解无差别;土柱击穿后,越靠近土柱底面,各种边界条件解析解计算结果差异越大,底面处浓度值随柯西参数?/?的增大而减小,?/?越大,代表底边界处扩散在溶质迁移中所占比例越大,同时底部浓度梯度越大;算例中对底部为半无限边界的试验数据进行拟合,若采用零浓度边界和零浓度梯度边界,计算结果分别偏大15%和偏小9%,根据土柱底部的对流-扩散比例和浓度梯度具体情况选择相应边界条件下的解析解,是保证数据拟合正确性的基本要求。
[Abstract]:Clay materials are widely used in various pollution prevention and control projects, and diffusion coefficient is one of its key parameters. In general, the diffusion coefficient of soil is determined by fitting one-dimensional soil column convection-diffusion test data. The test conditions corresponding to zero concentration boundary, zero concentration gradient boundary and semi infinite boundary are discussed, and the unified form of each boundary condition is given. The analytical solution of convection-diffusion-adsorption in the finite thickness soil is obtained under the boundary conditions. The differences between the analytical solutions and the errors caused by the data fitting are analyzed. The results show that each bottom boundary condition corresponds to the actual condition at the bottom of the soil column test, the Cauchy boundary can be regarded as a unified form of various boundary conditions, the analytical solutions of each boundary condition have no difference when the soil column is not broken down, The closer the soil column is to the bottom surface, the greater the difference between the analytical solutions of various boundary conditions is, and the concentration at the bottom of the soil column varies with the Cauchy parameter. Increase and decrease /? The larger the bottom boundary is, the larger the proportion of diffusion in solute migration is and the bigger the bottom concentration gradient is. The experimental data with semi-infinite boundary at the bottom are fitted with zero concentration boundary and zero concentration gradient boundary. The calculated results are larger than 15% and 9% smaller, respectively. According to the concrete conditions of convection-diffusion ratio and concentration gradient at the bottom of the soil column, the analytical solution under the corresponding boundary conditions is the basic requirement to ensure the accuracy of the data fitting.
【作者单位】：上海大学土木工程系;
【基金】：国家自然科学基金资助项目(No.51178260,No.51478256) 上海市教委科研创新项目(No.14YZ005)
【分类号】：TU411

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