山區地下水與質量傳輸模式

The Mountain Groundwater and Mass Transport Model

王元亨(Yuan-Heng Wang)

指導教授 ： 黃良雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.02174

摘要

地下水分布區域極為廣大，水平距離與垂向深度之尺度差異懸殊，數值模擬使用上，常造成計算量龐大或精度不高等問題。因此，本研究延續蔡東霖(2001)使用垂向二次內插函數及水平有限解析法以建立擬三维地下水流模式，此可將模擬三維水頭變化之問題簡化。於原蔡東霖之模式中，張正緯(2007)進一步引入自由液面方程式(Eagleson, 1970)，改良非拘限含水層處理自由液面之非線性問題。而本研究將承接上述前人研究之計算方法，開發山區地下水流與質量傳輸模式。

山區中，地形起伏以及不規則自由液面位置之問題，將導致數值計算上面臨網格點不隨地形變化分布，為了避免計算網格與地形無法對應造成計算上之誤差，本研究將 -轉換技巧套入自由液面方程式(Eagleson, 1970)處理山區非拘限含水層，並整合詹景帆(2011)以 轉換發展山區地下水之計算中拘限含水層之計算，使山區地下水模式更趨完備。同時根據山區地下水流於水平與垂直上之計算方法，引入 轉換開發山區質量傳輸之計算，簡化郭遠錦(2004)之模式於垂向上之計算。

本研究於山區地下水流控制方程式，延續詹景帆(2011)拆解為抽水擾動與地形重力效應兩部分進行計算，並將山區複雜之地形與自由液面利用 轉換為水平座標不變，垂直座標各層厚度與自由液面至下底床距離為1之土層。計算中，引入每層土層之孔隙水壓與污染物濃度，於垂向深度皆為二次內插函數分布下進行垂向積分，將三維地下水流方程式與三維質量傳輸方程式簡化為水平二維方程式，於層與層介面邊界分別滿足孔隙水壓、水流通量連續；濃度連續、汙染物通量連續之條件下，再依據土壤性質做垂直分層與水平分區，聯立垂直與水平二維之計算，完成本文之擬三維山區地下水流與山區質量傳輸模式。

本研究山區地下水流方面，針對平地區域、平地區域之虛擬分層與不連續土層、斜坡區域，以及緩坡區域進行測試與驗證。山區質量傳輸方面，則針對解析解、不連續土層，以及斜坡進行測試與驗證，檢測本研究兩模式之合理性與適用範圍。並在最後提供一簡易斜坡抽水傳輸案例，將兩模式做一聯合應用測試。

關鍵字

山區地下水流模式 ； 山區質量傳輸模式 ； 有限解析法 ； 二次內插函數 ； σ -轉換

並列摘要

Groundwater has a wide range distribution in all kinds of terrain. A large order difference between the horizontal distance and vertical depth scale in computing three dimensional groundwater flow often causes the problems of massive computation and low accuracy. In dealing with such large areas, this study follows and improves upon the development of the groundwater flow, computation model of Tung-Lin Tsai (2001) by using a semi-three dimensional groundwater model. Doing so, this model can be efficiently applied to large areas and can more accurately represent the simulation of small ranges to enhance the computation accuracy of unconfined aquifers, Cheng-Wei Chang (2007) combined the free surface equation (see, Eagleson (1970)) with the groundwater flow computation model of Tung -Lin Tsai (2001). This corrected the error of dominated non-linear variation on free surface. This study combines those previous studies to develop the mountain groundwater and mass transport model.

In mountain areas, the terrain varies dramatically and the elevation of free surface is difficult to predict, causing inaccuracies in numerical computing. To avoid computation grid mismatch with the mountain terrain and free surface elevation, using transform to calculate mountainous terrain and free surface elevation can overcome the computational shortcomings caused by complex free surface elevation and the terrain of mountain. In this study, transform was applied to (see, Eagleson (1970)) the free surface equation, so that the mountain unconfined aquifer can be better computed. Then by integrating the mountain confined aquifer study of Jing-Fan Jan (2011) allowing the mountain groundwater model be more complete. On the other hand, this study simplifies the vertical computation part of groundwater mass transport model of Yuan-Ching Kuo(2004) and expect to apply in mountain areas. It adapts the same horizontal and vertical computation way of the mountain groundwater model and transform to develop the mountain mass transport model.

In this study, first, the mountain groundwater flow governing equation follows Jing-Fan Jan (2011) divided into two parts considered individually, that are dismantling the slope disturbance for the non-pumping effect of gravity and pumping disturbance without considering the slope effect of gravity, and then transform the complicated mountainous terrain and free surface elevation into a unchanged horizontal coordinate and the thickness of the vertical coordinates of the aquifer layers are 1 by coordinates. In computation, the governing equation of the mountain groundwater model and the mountain mass transport model for every layer is assumed to satisfy quadratic polynomial function. At the interface between each of the two layers, the continuity of pore pressure, pollutants concentration and theirs continuity of flux must be satisfied. According to soil properties, doing the vertical and horizontal two-dimensional calculations, complete mountainous area of the proposed semi-three dimensional groundwater flow and mass transport model

Some simple cases will be tested and verified to see the applicability of both models. The mountain groundwater model is tested with reasonable parameter settings and is verified with the semi-three dimensional groundwater model of Tung-Lin Tsai (2001). These cases include flat plane pumping case, virtual horizontal decomposition of flat plane pumping case, non-continuous horizontal aquifer pumping case, pure slope pumping case and mild slope pumping case. In addition those cases with slopes are aim both at no pumping effect to consider the mountain groundwater of slope gravitational perturbation and the pumping disturbance. The mountain mass transport model is tested with reasonable parameter settings and verified with simple two dimensional analytical solutions. These cases include flat plane concentration with diffusion transport case, flat plane concentration with diffusion-advection transport case, flat plane line source concentration with uncontinuous diffusion-advection transport case, and pure slope concentration with diffusion-advection transport case. Finally, the mountain groundwater and mass transport model are combined to give and show a pure slope pumping transport case.

並列關鍵字

the mountain groundwater model ； the mountain mass transport model ； finite analytical method ； quadratic polynomial function ； σ -transform

參考文獻

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