时变降雨条件下非饱和植被土中水分瞬态渗流解析解及应用分析

    Analytical solutions and application analysis of transient seepage of water in the unsaturated vegetated soil under a time-varying rainfall condition

    • 摘要: 针对时变降雨条件下非饱和植被土中水分瞬态渗流问题,基于几点假定,采用变量代换、Green函数运算和Fourier级数变换等方法发展得到了相应解析解。该解析解还考虑了两类典型底边界和任意初始含水率分布形式。进一步,给出了几种常见降雨模式下解析解的表达式。在此基础上,通过两方面对比,验证了所发展解析解的可靠性。最后,以一类填埋场植被盖层为研究对象,应用解析解,分析了多个因素对其底部水分渗漏影响。结果表明:在降雨总量相同时,总体上,前期降雨速率较大降雨模式下的累计渗漏量CQb较大;对于初始总储水量相等的不同含水率分布形式,底部含水率较大的形式会导致较大的CQb,且其影响主要发生在降雨入渗前期;对于所考虑的四种典型根系形状,均布形根系下植被盖层阻隔底部水分渗漏效果最好,指数形根系最差,但根系形状产生的影响相对较小;蒸腾速率增大可明显降低CQb,且这种影响会随降雨入渗过程的进行逐渐变得更显著。总的来说,所得解析解和相关应用分析有助于指导非饱和植被土中水分渗流相关工程实践。

       

      Abstract: Aiming at the issue of transient seepage of water in the unsaturated vegetated soil under a time-varying rainfall condition, based on several assumptions, the corresponding analytical solutions are obtained by using methods such as variable substitution, Green's function operation, and Fourier series transformation. The analytical solutions also consider two types of typical bottom boundaries and the arbitrary initial water content distribution form. Furthermore, the expressions of analytical solution under several common rainfall patterns are provided. On this basis, the developed analytical solutions'reliability is verified through comparisons in two aspects. Eventually, taking a class of vegetation cover of landfill as the research object, the analytical solutions are applied to analyze the impacts of several factors on its bottom water leakage. The results show that when the total rainfall is the same, overall, the cumulative leakage amount CQb is larger under the rainfall pattern with a larger rainfall rate in the early stage. For different forms of water content distribution with the equal initial total water storage, the form with a larger bottom water content leads to a larger CQb, and its impact mainly occurs in the early stage of rainfall infiltration. Among four typical root shapes considered, the vegetation cover with a uniform root shape has the best effect in blocking the bottom water leakage, and the exponential root shape has the worst effect, but the effect of root shape is relatively small. An increase in the transpiration rate can obviously reduce the CQb, and this effect will gradually become more significant as the rainfall infiltration process proceeds. Generally, the obtained analytical solution and the relevant application analysis are helpful for guiding the engineering practices related to the seepage of water in unsaturated vegetated soils.

       

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