第29卷第2期 2015年4月
现代地质 GEOSCIENCE
Vol.29No.2
Apr.2015
时变补给条件下河渠间潜水的一维非稳定运动
夏强，许模，邓英尔，李晓
（成都理工大学地质灾害防治与地质环境保护国家重点实验室，四川成都610059）
摘要：针对河渠间潜水的一维非稳定运动，考虑了补给强度的时变性，根据Boussinesq方程的第一线性化方法，应用 Duhamel原理得到了方程的解析解，进一步得出补给强度为指数函数和三角函数的潜水位计算公式。通过算例分析补给强度指数增加、指数衰减和正弦函数变化条件下潜水面的变化特征，指数增加条件下潜水位单调增加，分水岭从高水位一侧向河间地块中部移动；指数衰减条件下潜水位先增大，后减小，具有一个峰值，分水岭先从高水位一侧向河间地块中部移动，之后随补给强度减弱返回到高水位河渠；正弦函数变化条件下潜水位表现出周期性起伏变化，且水位对补给的响应具有明显的时滞性，分水岭在高水位河渠与河间地块中部之间往复移动。研究结果可为量化分析地下水
系统对气候变化的响应以及地表水地下水转化规律等问题提供理论依据。关键词：潜水；河间地块；非稳定运动；时变补给
中图分类号：P641.132
文献标志码：A
文章编号：10008527(2015)02027906
Water TableFluctuationBetween Two ParallelDitchesInduced
by Time-varyingRecharge XIA Qiang, XU Mo, DENG Ying-er, LI Xiao
(ospeuaooafoaaeodaaouaadeoafoooays) Abstract: Taking account of exponentially and periodically time-varying recharge, water table fluctuation be-tween two parallel ditches was studied. The analytical solution was derived based on the first linearization method of Boussinesq equation, and Duhamel principle. This paper analyzed the characteristics of phreatic water move-ment by using three kinds of recharge rate functions including exponent-increase, exponent-decay, and sine func-tion. In the first case, water table rises monotonously with the increasing recharge rate; and watershed between the two ditches moves from the higher level side towards the other sides, but will never cross the middle line of the aquifer. In the exponent-decay case, water table goes up at the beginning, then falls after reaching a peak value; watershed firstly moves towards the middle of the aquifer, then turns back to the higher level side due to the decli-ning recharge rate. In the last case, water table periodically fluctuates corresponding to the sine function recharge; and there is a significant time lag between the stimulator and the respond; watershed sways back and forth between the higher level ditch and the middle of the aquifer. The results can be a clue to study the response of groundwate
system to climate change, in addition to the transition rule between surface and ground water. Key words: phreatic water; parallel ditch; unsteady flow; time-varying recharge
0引言
源评价、人工排水和灌溉等具有重要意义，国内外经典的地下水动力学教材以此问题为重要内
研究河渠附近地下水运动规律，对地下水资容[1-4]。河渠边界条件和河间补给条件是河渠间收稿日期：2014-11-10；改回日期：2014-12-02：责任编辑：威开静。
（0000国作者简介：夏强，男，博士，讲师，1982年出生，水文地质学专业，主要从事水文地质的教学与科研工作。
Email: xiaqiang2012@ edut. cn。