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研究生:蕭惠如
研究生(外文):Huei-Ru Shiau
論文名稱:潮汐衍生之海岸含水層地下水位波動
論文名稱(外文):The Fluctuations of Water Level in Coastal AquifersInduced by Tidal Waves
指導教授:謝平城謝平城引用關係
指導教授(外文):Ping-Cheng Hsieh
口試委員:蔡清標黃清哲
口試日期:2013-01-23
學位類別:碩士
校院名稱:國立中興大學
系所名稱:水土保持學系所
學門:農業科學學門
學類:水土保持學類
論文種類:學術論文
論文出版年:2013
畢業學年度:101
語文別:中文
論文頁數:66
中文關鍵詞:潮汐海岸含水層傾斜不透水底床微擾法
外文關鍵詞:tidecoastal aquiferinclined impervious bedperturbation method
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沿海地區的含水層常會受到潮汐的影響,而導致地下水位波動,連帶著
會影響地下水含水層內的生物活動、化學物質轉換及海岸沉積物沖蝕。一般
地下水位變動資料是由地下水觀測井所得,但地形陡峭或偏遠地區,並不易
挖井,且所費不貲。而了解海岸地下含水層內的水流分布情形,可以提供正
確的預測及管理。
一般探討地下水流運動之控制方程式,多以Boussinesq 方程式為主,傳
統的Boussinesq 方程式假設不透水底床為水平,在本研究前,已有多位學者
以此方程式推演出不同地層狀況的解析解(如:海岸邊坡傾斜問題、含水層
內有滲漏現象)。但現實的海岸含水層因為地層的擠壓,含水層內的不透水
底床有可能呈現傾斜的狀態。針對此現象,本研究引用Chapman (1980)修正
之Boussinesq 方程式作為含水層內水流運動的控制方程式,並以微擾法
(perturbation method)推導出二階非線性解。
本研究加入不透水底床的角度變化,探討不同邊坡角度以及不透水底床
傾斜角度影響地下水位隨時間及空間的變化。當不透水底床為水平時,本研
究與前人提出之解析解以及室內實驗資料比較,皆得到良好的結果。而隨著
不透水底床角度變化,往上傾斜角度越大時,地下水位往下的震盪量也隨之
變大,但下游端地下水位會逐漸變小。並發現在不透水底床往下傾斜變化時,
傾斜角度在-25˚~-35˚間,下游端地下水位會有先上升後下降之情形發生。
二維解析解部份,加入河川水位起伏的影響,在不透水底床往上傾斜大
於10˚時,會增加地下水位波動的頻率。而在不透水底床往下傾斜時,河川
水位起伏的影響,會增大地下水位往下的震盪量,下游端地下水位也隨之降
低。

Tide-induced water table fluctuations in coastal aquifers have a great impact on biological activities, chemical transformations and coastal sediment erosions.
The data of groundwater level changes are usually obtained by the groundwater observation wells. It is not easy to dig wells in the steep terrain or remote areas and also it costs a lot. Understanding water table fluctuations in coastal aquifers can provide the correct prediction and management.
The Boussinesq equation is usually employed to govern the flow in coastal aquifers. The traditional Boussinesq equation supposes that the impervious bed is flat. Before this study, there are a number of scholars using this equation to deduce analytical solutions of different stratigraphic situations. (e.g., the problem of inclined coastal slope, the leakage phenomenon of aquifers). Impervious beds within the coastal aquifers may be inclined because of squeezing ground. For this phenomenon, the study employed the Chapman’s (1980) modified Boussinesq equation to govern the flow in coastal aquifers and solved it by the perturbation method. Then, second-order nonlinear solutions were obtained.
This study added the change of the inclined angle of the impervious bed,and then the groundwater level fluctuations varying with time and space in different slopes angle and impervious bed angles were discussed. When the impervious bed is flat, this study compared with the previous nalytical solutions and the indoor experimental data, the results are in a good agreement. With the change of impermeable bed angle, the larger the inclined angle, the larger the
downward vibration of groundwater level. But the downstream groundwater level will gradually become smaller. It is also found that if the impervious bed slopes downward, the inclined angle between -25 ° ~ -35 °, the downstream
groundwater level will first rise and then descend.
As to the two-dimensional analytical solutions, the impact of river water level fluctuations was investigated. When the impervious bed slopes upward, the angle greater than 10 °, it will increase the frequency of groundwater level fluctuations. When the impervious bed slopes downward, the influence of the river water level fluctuations will increase the downward vibration of groundwater level, but the downstream groundwater level will decrease.

第一章 前言 ......................................... 1
第二章 文獻回顧.............................. ........ 3
2-1 潮汐影響海岸含水層之一維研究 ........................ 3
2-2 潮汐影響海岸含水層之二維研究 ........................ 4
第三章 潮汐影響海岸含水層地下水位波動之一維分析 ............ 5
3-1 數學模式 ........................................ 5
3-1-1 潮汐影響海岸含水層之一維示意圖 .................... 5
3-1-2 水流運動控制方程式 .............................. 6
3-1-3 邊界條件 ...................................... 6
3-1-4 無因次化 ...................................... 6
3-1-5 引入新變數 .................................... 7
3-1-6 微擾法 ........................................ 8
3-1-7 解析解......................................... 9
第四章 潮汐影響海岸含水層地下水位波動之二維分析 ............ 13
4-1 數學模式 ........................................ 13
4-1-1 潮汐影響海岸含水層之二維示意圖 .................... 13
4-1-2 水流運動控制方程式 .............................. 14
4-1-3 邊界條件 ...................................... 14
4-1-4 無因次化 ...................................... 15
4-1-5 引入新變數 .................................... 16
4-1-6 微擾法 ....................................... 17
4-1-7 解析解 ....................................... 17
第五章 結果與討論 .................................... 22
5-1 潮汐影響海岸含水層地下水位波動之一維分析 .............. 22
5-1-1 與前人研究比較 ................................. 22
5-1-2 一維不透水底床傾斜之變化 ......................... 28
5-2 二維分........................................... 39
5-2-1 與前人研究比較 ................................. 39
5-2-2 二維不透水層傾斜之變化 ........................... 40
第六章結論與建議 ...................................... 55
6-1 結論 ............................................ 55
6-2 建議 ............................................ 57
參考文獻 ............................................. 59
附錄A 一維解析解之Matlab 程式 .......................... 61
附錄B 二維解析解之Matlab 程式 .......................... 64

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dansce canal des vitesses sensiblement pareilles de la surface au,” Journal of
Mathematical Pure et Application, 2nd Series, 17:55-108.
2. Cartwright N, P. Nielsen, L. Li, 2004, “Experimental observations of watertable waves in an unconfined aquifer with a sloping boundary,” Advances in Water Resources, 27:991–1004.
3. Chapman, T.G., 1980, “Modeling groundwater flow over sloping beds”, Water Resources Research, 16:1114–1118.
4. Dagan, G, 1967, “Second-order theory of shallow free-surface flow in porous media,” Quart, Journ. Mech. And Applied Math., Vol. XX, Pt.4.
5. Ingersoll, L. R. and O. J. Zobel, 1913, “An Introduction to The Mathematical Theory of Heat Conduction with Engineering and Geological Applications,” Ginn and Company, Boston.
6. Jeng, D.S., B. R. Seymour , H. T. Teo, D. A. Barry and L. Li, 2003,“New approximation for tide-induced water table fluctuations at a sloping beach,” MODSIM 2003.
7. Knight, J.H., 1981. “Steady period flow through a rectangular dam,” Water Resources Research, 17:1222–1224.
8. Li, L., D.A. Barry, C. Cunningham, F. Stagnitti and J.Y. Parlange, 2000, “A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean,” Advances in Water Resources, 23:825–833.
9. Li, H., J. J. Jiao, 2002, “Tidal groundwater level fluctuations in L-shaped leaky coastal aquifer system,” Journal of Hydrology, 268:234–243.
10.Li, H., J. J. Jiao, M. Luk and K. Cheung, 2002, “Tide-induced groundwater level fluctuation in coastal aquifers bounded by L-shaped coastlines,” Water Resources Research, 38(3) :10.1029.
11.Liu P.L.F. and W. Jiangang, 1997, “Nonlinear diffusive surface waves in porous media,” J. Fluid Mech., 347:119–139.
12.Nielsen P, 1990,“Tidal dynamics of the water table in beaches,” Water Resource Research, 26:2127–2134.
13. Parlange, J.Y., F. Stagnitti, J.L. Starr and R.D. Braddock, 1984, “Free-surface flow in porous media and periodic solution of the shallow-flow approximation,” Journal of Hydrology, 70:251-263.
14. Philips, J.R., 1973, “Periodic nonlinear diffusion: an integral relation and its
physical consequences,” Aust. J. Phys, 26:513–519.
15. Su, N., F. Liu and V. Anh, 2003, “Tides as phase-modulated waves inducing periodic groundwater flow in coastal aquifers overlaying a sloping impervious base,” Environmental Modeling & Software, 18:937–942.
16. Sun, H., 1997, “A two dimensional analytical solution of groundwater response to tidal loading in an estuary” Water Resource Research, 33:1429–1435.

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