以σ-轉換發展山區地下水之計算

Developing the Computation of Mountain Groundwater with σ-Transform

詹景帆(Jan, Jing-Fan)

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(2011年)

https://doi.org/10.6342/NTU.2011.02327

摘要

山區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，因此在處理如此大範圍區域，本研究延續蔡東霖(2001)開發之地下水流模式，引用擬三维地下水模式著手，使得模式可有效率地應用於大區域之模擬且亦可精確地用於小範圍之模擬。為克服地形高低起伏，進而利用σ-轉換技巧計算山區地形，補足無法反應山區複雜地形之不足。
本研究先將山區地下水流控制方程式拆解為無抽水擾動考慮斜坡重力效應與考慮抽水擾動無斜坡重力效應兩部份個別考慮，再將極為複雜之山區地形利用σ-轉換為水平座標不變，垂直座標各層厚度皆為1之土層。計算中，引入每個土層之孔隙水壓於垂向深度皆為二次多項式函數分布下作垂向積分，將三維地下水流方程式簡化為水平二維方程式，層與層間介面邊界滿足孔隙水壓、水流通量連續之條件下，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計算，完成本文之擬三維山區地下水流模式。
本文以簡單案例進行模式驗證，針對無抽水擾動考慮斜坡重力效應之山區地下水與加入考慮抽水擾動之山區地下水進行驗證，顯示本模式之合理性。此外，本研究設計兩概念模型以模擬實際山區地形，分別為緩坡地形與高山地形之不同情況進行模擬探討。

關鍵字

擬三维地下水模式 ； σ-轉換 ； 垂向積分 ； 二次多項式內插函數 ； 孔隙水壓連續 ； 水流通量連續 ； 有限解析法

並列摘要

Groundwater distribution in the mountain area is very wide. The tremendous order difference of the horizontal distance and vertical depth scales in completing three dimensional groundwater flow often causes the problem of massive computation or low accuracy. Therefore, in dealing with such large areas, this study continues and improves the development of groundwater flow computation model of Tung-Lin Tsai (2001) by using semi-three dimensional groundwater model, that making models can be efficiently applied to large area and can be accurately simulated the simulation for a small range. To overcome the undulating terrain, using σ- transform to calculate mountainous terrain will supplement the shortcoming that complex terrain of the mountain can’t be presented.

In this study, firstly mountain groundwater flow governing equation are 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 a very complicated mountainous terrain into a unchanged level coordinate and the thickness of the vertical coordinates of the soil layers are 1 by σ-coordinates. In computation, the governing equation for every layer is assumed to satisfy quadratic polynomial function. At the interface between two layers the continuity of pore pressure and the continuity of flux must be satisfied. According to soil properties﹐ doing the vertical stratification and horizontal partitions, the simultaneous vertical and horizontal two-dimensional calculations, complete this mountainous area of the proposed semi-three dimensional groundwater flow model.

In this study, a simple case of the model is validated. Aiming at no pumping effect to consider the mountain groundwater of slope gravitational perturbation and the pumping disturbance of the mountain groundwater, verify and display the model reasonable. In addition, the study designs two conceptual models to simulate the actual mountainous terrain, high mountain terrain and gentle slope respectively, discussing the simulation of different mountainous terrain situation.

並列關鍵字

semi-three dimensional groundwater flow model ； σ-transform ； vertical integration ； quadratic polynomial function ； the continuity of pore pressure ； the continuity of flux ； finite analytic method

參考文獻

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