ISSN 1000-3665 CN 11-2202/P

    Dupuit模型的改进——具入渗补给

    Improvement of Dupuit model:with infiltration recharge

    • 摘要: Dupuit(1863年)提出的模型是“圆岛状含水层稳定井流模型”,这个模型只有侧向湖海边界条件,而不涉及上边界降水入渗补给条件。因此,Dupuit模型只能在旱季用于地下水井流试验求取含水系统的参数,而不能够用于预测。文章发展Dupuit潜水井流模型,考虑地面均匀稳定入渗补给(蒸发排泄示为其负值)作用。以质量守衡原理为基础,假定渗流服从Darcy定律并满足Dupuit徦定,建立极坐标下的地下水流微分方程,再依边界条件建立相应的流量方程和水位方程。这些方程为具地面入渗补给条件下井流试验求取水文地质参数以及预测相应条件下地下水抽水的效果,提供了基础条件。讨论了引入Dupuit假定对本问题解析研究可以降维(略去z变量)带来好处的同时,在地下水分水岭附近及抽水井附近可能出现偏离Dupuit假定,建议在抽水试验求取含水层参数时,观测孔的部署要尽量回避这些区段。

       

      Abstract: The model proposed by Dupuit (1863) is a “steady well flow model of Round Island aquifer”. The Dupuit model only considers lateral boundary conditions, and the upper boundary precipitation infiltration recharge condition is not considered. Therefore,Dupuit model can only be used in the dry season to obtain the parameters of aquifer system by groundwater well flow test,but can't be used to predict groundwater dynamic. In this paper,the Dupuit model of groundwater well flow is developed to consider the effect of uniform and steady infiltration recharge (evaporation and discharge shows negative value). Based on the principle of mass balance,assuming that the groundwater flow obeys Darcy's law and satisfies Dupuit's assumption,the differential equation of groundwater flow in polar coordinates is established, and then the corresponding discharge equation and water level equation are established according to the boundary conditions. These equations can be used to calculate hydrogeological parameters by well flow test under the condition of precipitation infiltration recharge,and to predict the effect of groundwater pumping under the corresponding conditions. It is discussed that the introduction of Dupuit hypothesis can bring benefits to the analytical study of this problem, which can reduce the dimension (omitting z variables). At the same time, it may deviate from the Dupuit assumption near the groundwater ridge and the pumping well. It is suggested that these areas should be avoided in the arrangement of observation holes when the aquifer parameters are obtained by pumping test.

       

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