库水波动下库岸边坡地下水浸润线解析解及误差分析

解析法是库岸边坡地下水浸润线计算中便于实际应用的方法,但该方法须基于若干假定并对潜水运动基本方程线性化后才能求解。针对各假定和线性化过程建立不同的地下水渗流数学模型,用解析法和有限元法解答上述数学模型,分析各误差大小及其规律。结果表明:库岸垂直处理带来的误差要小于方程线性化处理和不考虑非饱和渗流带来的误差,而且它们都随渗透系数变大而减小;在三峡库区库水调度情况下,假定库水位等速变化带来的误差对大多岸坡而言可以忽略;计算库岸边坡地下水浸润线时,解析法只适用于水位变化幅度相比含水层厚度较小,且几何边界规则、岩土结构简单、岩土体渗透性较好时的情况。

Analytic Solutions and Their Errors of Groundwater Phreatic Line in Bank Slope under Reservoir Water Level Fluctuation

Although analytical method is a practical method in the calculation of phreatic line of groundwater in reservoir bank slope, it is based on certain assumptions and the linearization of the Boussinesq's equation. Different mathematical models for the seepage of groundwater were established and then solved by analytical method or finite element method. By comparing the solutions to these different models, the errors caused by these assumptions and the linearization were analyzed. Results showed that both the errors caused by the linearization and the neglect of unsaturated seepage were greater than the error caused by assuming the  reservoir bank is vertical, and all of them decreased with the increase of permeability coefficient. The error caused by the assumption of uniform water level changes could be ignored in the case of Three Gorges reservoir water scheduling. When calculating the groundwater phreatic line in reservoir bank slope, analytical method only applies to the case when the water level fluctuation amplitude is smaller than 30% of the aquifer thickness, the geotechnical structure is regular, and the soil has good permeability and simple structure.