| 非饱和土中水平入渗方程显式求解 |
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| 引用本文： | 李纪伟,林法力,韦昌富,汪华斌,陈盼,朱赞成,刘子振.非饱和土中水平入渗方程显式求解[J].岩土力学,2021(1):203-210. |
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| 作者姓名： | 李纪伟 林法力 韦昌富 汪华斌 陈盼 朱赞成 刘子振 |
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| 作者单位： | ;1.台州学院建筑工程学院;2.中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室;3.华中科技大学土木与水利工程学院 |
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| 基金项目： | 国家自然科学基金重点项目(No.41931286);国家自然科学基金面上项目(No.41877269);浙江省自然科学基金一般项目(No.LY19E080008,No.LY19E080007)。 |
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| 摘 要： | 在求解非饱和态土中水分入渗问题时,水力函数是体积含水率或者吸力的函数,致使其控制方程呈现出强非线性的特征,进而使得其求解变得十分困难。基于水分在土体介质中流动耗时取极值路径的选择这一假定,引入时间泛函,基于变分法原理将水平入渗问题转化为泛函极值问题。通过求解Euler–Lagrange方程,结合边界条件,得到非线性瞬态水平入渗问题的显式解析解。结合Brooks-Corey型水力函数,显式地求解出该类型非饱和态土的体积含水率发展分布规律。通过计算4种不同类型土体的水平入渗规律,将求解结果与已有结果以及数值结果进行对比,验证了该方法的有效性。结果表明:体积含水率分布与位置距离和湿润峰距离比值呈幂函数关系,指数取决于土-水特征曲线的形状参数;初始条件与边界条件会对体积含水率分布造成不同程度的影响。
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| 关 键 词： | 水平入渗 变分法 Euler–Lagrange方程 Brooks-Corey模型 |
Explicit solution of horizontal infiltration equation in unsaturated soils |
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| LI Ji-wei,LIN Fa-li,WEI Chang-fu,WANG Hua-bin,CHEN Pan,ZHU Zan-cheng,LIU Zi-zhen.Explicit solution of horizontal infiltration equation in unsaturated soils[J].Rock and Soil Mechanics,2021(1):203-210. |
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| Authors: | LI Ji-wei LIN Fa-li WEI Chang-fu WANG Hua-bin CHEN Pan ZHU Zan-cheng LIU Zi-zhen |
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| Institution: | (School of Architecture and Civil Engineering,Taizhou University,Taizhou,Zhejiang 318000,China;State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;School of Civil and Hydraulic Engineering,Huazhong University of Science and Technology,Wuhan,Hubei 430074,China) |
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| Abstract: | When solving the water infiltration problem in unsaturated soils, the hydraulic function is a function of water content or suction, which makes the equation governed by hydraulic function exhibits strong nonlinear characteristics resulting in the difficulty of solving the horizontal infiltration problem. Based on the assumption that the water flow in soil medium follows the path of time-consuming extreme value, a time functional was introduced, and the horizontal infiltration problem was transformed into a functional extreme value problem based on a variational principle. By solving Euler-Lagrange equation and combining with the boundary conditions, the explicit analytical solution of the nonlinear transient horizontal infiltration problem was obtained. Combined with the Brooks-Corey hydraulic function, the distribution of volume water content of this type of soils in the unsaturated state was explicitly solved. By calculating the water horizontal infiltration laws of four different types of soil samples through theoretical and numerical methods, the results obtained by the solution matched well with the existing results and numerical results, verifying the effectiveness of the method. The results show that the distribution of volume water content has a power function against location distance and wetting peak distance ratio, and the power exponent depends on the shape parameter of soil water characteristic curve. Initial conditions and boundary conditions had different effects on the distribution of volumetric water content. |
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| Keywords: | horizontal infiltration variational method Euler-Lagrange equation Brooks-Corey model |
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