排水期沟渠附近潜水非稳定流解析解及参数反演

Analytical solution and parameter inversion of transient seepage model of groundwater near ditch during drainage period

将潜水蒸发等垂向水量补排作用离散成逐日的阶梯函数,将排水沟渠概化为水位稳定不变的第一类边界,建立含阶梯函数型源汇项的沟渠附近潜水非稳定渗流模型。依据Boussinesq方程第一线性化方法,应用Laplace变换的"积分性质"、阶梯函数的Laplace变换性质,求出模型解析解,利用数值法验证解析解的可靠性,并讨论特定解及其物理意义。利用模型解的反问题研究方法,根据潜水位变动速度随时间变化的数学规律,建立求模型参数的拐点法和配线法。结合实例演算表明,相对于现行正演的试算法,反演算法直接、简明。

In this paper,the vertical replenishment and drainage effects of phreatic water such as evaporation are discretized into daily step functions, and the ditch is generalized as the first kind of boundary with stable water level,and the phreatic unsteady seepage model near the drainage ditches with step function source and sink term is established. According to the first-linearization method of Boussinesq equation,the analytical solution of the model is given by using the "integral property" of Laplace transform and the Laplace transformation property of step function. The reliability of the analytical solution has been verified by numerical method, and the specific solution and its mathematical significance are discussed. According to the mathematical law that the fluctuation rate of groundwater level varying with time,the methods of inflection points and matching line are established to calculate the model parameters by using the method of solving the inverse problem of model. An actual calculated example shows that the inversion algorithm is more direct and concise than the current forward trial method.