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標題: 降雨及潮汐衍生之非拘限含水層地下水位變化
The variation of groundwater level in an unconfined aquifer induced by rainfall and tidal waves
作者: 徐筱婷
Hsu, Hsiao-Ting
Contributors: 謝平城
水土保持學系所
關鍵字: 地下水位;潮汐波動;降雨;傾斜含水層。
groundwater level;tidal fluctuation;rainfall;sloping aquifer
日期: 2013
Issue Date: 2013-11-07 13:16:57 (UTC+8)
Publisher: 水土保持學系所
摘要: 在沿海地區含水層內地下水位會受到降雨、潮汐和地形的影響,而產生不同的波傳速率和水位變化。目前地下水位的資料取得,以採用觀測井進行觀測為主,然而受限於儀器的昂貴與開挖觀測井的成本過高,因此利用控制方程式與邊界條件進行求解,能幫助我們更了解地下水位的波動。
本文考量非拘限含水層具不透水底床傾角、海岸邊坡傾角、以及降雨量隨著空間的變化,基於Dupuit-Forchheimer的假設,將沿海含水層分為兩個區域,沿海地區設為降雨區,內陸地區則為無降雨區。接著引用Chapman(1980)提出的Boussinesq方程式為控制方程式,將其線性化後,並利用Li et al.(2000)提出的移動邊界法探討海岸邊坡傾角的影響,進行地下水位波動之解析。
文中分為一維與二維的地下含水層,分別探討潮汐及降雨造成非拘限含水層具傾斜底床的地下水位變動,於非降雨區之解加入e^(-p(X-1))因子以滿足邊界條件後再進行求解,經與前人研究的解進行比較後,亦獲得相當不錯的結果。受到潮汐及降雨的影響,當不透水底床向上傾角越大時,地下水位會越快到達最大值後下降,直至無降雨區不再有明顯的波動產生;當底床向下傾角越大時,地下水位會以線性增加的方式逐漸抬升至內陸更遠處;而當海岸邊坡傾角越小時,地下水位會上升。
The influence of rainfall, tide waves and landforms on water table will cause different fluctuations and wave celerity on coastal aquifers. The data of groundwater level are mainly obtained from the observation wells. However, it is very expensive to set up the instrument and wells. Therefore, by means of solving governing equations with boundary conditions, we can better understand the groundwater level fluctuations.
The present study considers the unconfined aquifer with an impervious sloping bed, a beach slope, and various rainfalls. Therefore, based on the Dupuit-Forchheimer assumptions two zones of a coastal aquifer are defined. One zone near the coast is with rainfall and the other inland zone is without rainfall. Next, the study employed the Chapman’s(1980) modified Boussinesq equation as governing equations. After linearization of these equations and applying the moving boundary method proposed by Li et al.(2000) to the beach slopes, the analytic solutions of groundwater table fluctuations are presented.
The analysis of one-dimensional and two-dimensional models of groundwater fluctuations are carried out respectively. We discuss the effects of tidal waves and rainfall on the groundwater fluctuations in a coastal unconfined sloping aquifer. The solutions of the non-rainfall area satisfy the boundary conditions by adding the factor e^(-p(X-1)). In comparison with previous analytical solutions, the results agree very much. The groundwater level increases quickly with the upward inclined angle of the impermeable bed to maximum and then decreases until reaching to the non-rainfall area. The groundwater level induced by tidal waves and rainfall increases linearly with the downward inclined angle of the impermeable bed to further inland gradually. Moreover, the groundwater level also increases as the beach angle becomes small.
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