- 學位論文
應用有限元素法探討非拘限含水層之抽水量
Simulation Studies of the Pumping Rate in Unconfined Aquifers by Finite Element Method
摘要
地下水流動是一個複雜的物理現象，由於數值方法及電子計算機的快速發展，多數學者以數學模型來模擬地下水流。以往在二維非拘限地下水流動，大都以水平（X-Y面）作為討論的對象，其控制方程式為非線性之偏微分方程式，而垂直斷面又涉及非飽和孔隙介質流之物理現象，使控制方程式更複雜，參數更多且不易確立。本文之目的，為減少非飽如孔隙介質流參數之推估，而不需引用非飽和層的理論。將單位時間內抽水量視為含水層排水量及孔隙壓縮效應所產生排水量二者之和，以有限元素法將非拘限含水層中之自由水面作為模擬區域的變動邊界，針對非拘限含水層之飽和部份，以有限元素法推估自由水面。 控制方程式應用有限元素法離散後，可獲得一線性聯立方程式。於穩態時以水頭值當作其自由水面高程進行疊代，直到二者差值絕對值小於允許誤差值E即為模擬自由水面高程。於抽水實驗時，本研究首先藉由調整孔隙壓縮產生之排水量，即為模式中之抽水量，使觀測井對應節點之洩降與實驗觀測井洩降之差值小於給定之允許誤差值EA。進而計算含水層中之有效孔隙率使孔隙壓縮產生之排水量與含水層洩降之排水量二者之總和等於實際抽水量。而本文模擬結果與利用雙對數標準曲線比對法及半對數分析法所求得之有效孔隙率，亦在同一個數階之內，顯示本模式之可靠性及可行性。
並列摘要
Due to the rapid development of numerical analysis and computer, scholars employ mathematical model to simulate the groundwater flow, a complex physical phenomenon. It is used to discuss the flow in a two-dimensional unconfined aquifer in the horizontal (x-y) plane. The governing equation is a nonlinear partial differential one, and the vertical section involves the phenomenon of unsaturated porous media flow which has a more complex phenomenon and more uncertain parameters. Therefore, the purpose of the article is to reduce the estimate of parameters in an unsaturated porous media flow, and not to quote some theories of an unconfined aquifer. We calculate the total volume of water released from storage in the aquifer per unit time due to the elastic storage and the actual drainage of water from the aquifer, take the free surface as a moving boundary in a simulated region, and estimate the groundwater stage in the saturated region of unconfined aquifer by using the Finite Element Method. A linear system can be obtained by solving the governing equation using the Finite Element Method. We use iteration method and take head as groundwater stage until the absolute value of the difference is under the allowed value. This study makes sum of the drainage in this mode and drawdown cone equal to the total pumping rate by adjusting the effective porosity after making the absolute value of the difference between the stage of the observation well and the corresponding node under the allowed value EA by adjusting the drainage in this mathematical model. By comparing with the values of effective porosity obtained from normal logarithm curves and semilog curves analysis method, the result is in a same order, which confirms the reliability and feasibility of the method propose in this paper.