河渠水位线性变化条件下河渠-潜水非稳定流模型及其解

Solution of the Transient Stream-Groundwater Model With Linearly Varying Stream Water Levels

在河渠水位迅速变化后再缓慢变化的条件下,建立了河渠半无限潜水含水层中非稳定渗流模型.利用Boussinesq第一线性化方法及Laplace变换,并注意应用Laplace变换中的"积分性质",给出形式相对简单、由常用函数表达的解,阐述特定解及其相应的物理意义.由解所揭示的潜水位变化规律表明,含水层任一点处潜水位变动速度的时间变化曲线形态是固定的,与河渠边界水位变动速率λ无关;潜水最大变速发生的时间,随λ呈非线性位移.依据潜水位变化规律,建立利用潜水位变动速度求含水层参数的方法,并用实例演示了拐点法求参数的过程.

Based on the first linearized Boussinesq equation,the analytical solution of the transient groundwater model for description of phreatic flow in a semi-infinite aquifer bordered by a linear stream with linearly varying stream water levels,was derived through the Laplace transform and in view of the integral property of the Laplace transform. The solution is composed of some common functions and its expression form is relatively simple. According to the mathematical characteristics of the solution,its corresponding physical meaning was discussed. The variation rule of the phreatic level revealed by the solution shows that the temporal variation curve of the aquifer at any point is fixed and has nothing to do with the change rate of the water level of the river channel. The time of the maximum speed change of the phreatic aquifer nonlinearly varies with λ. Based on the variation rule of the phreatic level,the method determining the aquifer parameters with the changing velocity of the phreatic level was established,and the process of obtaining the parameter with the inflection point method was demonstrated through an example.