Theory on Coupling of Radial Flow in a Confined Aquifer and Bending of Confining Unit
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摘要: 指出承压含水层盖层的弯曲变形与开采井周围的径向地下水运动存在相互作用, 而这一效应在传统的井流理论中没有被认识到.通过引入弹性薄板理论, 建立了无越流的承压含水层井流-顶板弯曲效应的解析模型, 同时考虑了含水层和水的压缩性, 结果表明Theis井流方程给出的抽水降深偏小.在此基础上推导了有越流承压含水层井流-盖层弯曲效应的偏微分方程, 求出了解析解, 并与传统理论的结果进行了对比, 表明Hantush-Jacob公式计算的降深也是偏小的.在抽水井附近和抽水初期, 传统理论可能导致显著的相对误差.Abstract: The non-steady radial flow surrounding a pumping well in a fully confined or leaky confined aquifer will induce the bending of confining unit, and then the radial flow patterns are affected by the bending effect through reducing of total stress.However, in conventional theory of groundwater flow, this interaction was omitted. In this study, the elastic plate theory was introduced to establish the analytical models of coupling of radial flow in a confined aquifer and bending of the confining unit, and meanwhile both of non-leaky and leaky conditions were considered as well as the compressibility of skeleton and water. It was indicated by the analytical solutions of the new theory that Theis equation underestimated the drawdown for fully confined aquifers. For leaky confined aquifers, the drawdown simulated by Hantush-Jacob equation was less than that evaluated by the new theory which considered the bending effect of confining unit. The relative errors would be remarkable in the beginning of pumping and/or near the pumping well.
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Key words:
- radial flow /
- bending /
- confined aquifer /
- leaky /
- analytical solution
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图 1 无越流承压含水层-井孔模型概化图(箭头表示水流方向)
Fig. 1. Schematic for a fully confined aquifer-well system
图 2 当rD=0.1时, 无越流承压含水层单井定流量抽水的sD-tD曲线
Fig. 2. sD-tD curve for the fully confined aquifer-well systems while rD=0.1
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