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研究生:蕭永明
研究生(外文):Yeong-Ming Shiau
論文名稱:均勻入滲時坡面地下水流之理論解析
論文名稱(外文):Analytical solutions for groundwater flow on sloping bed with uniform recharge
指導教授:周憲德
指導教授(外文):Hsien-Ter Chou]
學位類別:碩士
校院名稱:國立中央大學
系所名稱:土木工程研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:75
中文關鍵詞:非線性理論解地下水斜坡滲流
外文關鍵詞:nonlinear solutiongroundwatersloping bedseepage
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  • 被引用被引用:2
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摘 要
早期推求均勻降雨條件下,斜坡上地下水滲流之解析解時,為了解決非線性之問題,常須限制其邊界條件,故只能應用於特殊之案例。本文以Childs之理論為基礎,假設流線平行坡面,並沿斜坡計算勢能梯度,推導過程中利用變數轉換,並結合牛頓-羅弗森之疊代方法,可求得自由水面之座標為水面斜率之參數式。利用此解之特性,可直接求得最大正向水深及其發生位置,結果與前人之實驗結果相當符合。本研究之理論解不僅不受邊界條件之限制,亦可用來求解mixed邊界值問題。
本研究著重於非線性地下水方程式之理論解析,並將利用所得之理論解,分析入滲強度因子與坡度因子對斜坡上地下水滲流之影響。此外,針對地下水面可能對斜坡造成之破壞,也將透過土石流發生之案例加以討論。
Abstract
The major purpose of this study is to obtain a new approximation for seepage flow over a sloping bed. This study is based on Childs’ theory. The streamlines are assumed to be nearly pararell to the sloping bed, and coordinate s pararell to the bed is used to calculate the hydraulic gradient. In the process, variables translation and the Newton-Raphson interation method are applied to obtain the solution of phreatic surface, which is in form of the function of the derivative of free surface, P.
The maximum water table height hmax and its location smax could be easily obtained, and are well coincident with previous published studies. The solution developed here could not only deal with problems with various upstream and downstream depths, but also could be used to explore mixed boundary value problems.
The analytical results can be used to evaluate the effects of slope, replenishment, and hydraulic conductivity on the preatic surface. The solution is applied to a case study of a debris flow event.
目 錄
頁次
中文摘要…………………………………………………………Ⅰ
英文摘要…………………………………………………………Ⅱ
目錄………………………………………………………………Ⅲ
圖目錄……………………………………………………………Ⅴ
表目錄……………………………………………………………VII
符號表…………………………………………………………… VIII
第一章 前言………………………………………………………1
1.1 關於地下水滲流之研究……………………………1
1.2 研究動機與目的…………………………………… 1
1.3 研究方法…………………………………………… 1
1.4 本文結構……………………………………………2
第二章 文獻回顧…………………………………………………3
2.1 傳統之Dupuit地下水理論假設……………………4
2.2 Dupuit地下水理論之修正………………………… 4
2.3 斜坡上無降雨情形下地下水面之研究……………5
2.4 斜坡上均勻降雨情形下地下水面之研究…………6
第三章 理論推導.………………………………………………12
3.1 地下水問題之描述…………………………………12
3.1.1 地下水問題之相關參數……………………12
3.1.2 本文探討之地下水問題邊界條件…………12
3.2 地下水控制方程式之推導…………………………13
3.3 地下水非線性方程式之理論解析………………… 14
3.3.1無因次化方程式之推導………………………14
3.3.2 待疊代之函數推導…………………………15
3.4 邊界值問題之理論解………………………………18
3.4.1 Dirichlet邊界值問題………………………18
3.4.2 Mixed邊界值問題……………………………19
3.5 牛頓-羅弗森(Newton-Raphson)疊代法……………20
3.6 理論解之應用…………………….…………………22
3.6.1 求解最大水深之位置及其水深……………22
3.6.2 求解最高點之位置及其水深………………23
第四章 結果與討論…………………………………………… 24
4.1 理論解之驗證……………………………………… 24
4.2 臨界入滲強度 之討論………………………………25
4.3 Dirichlet邊界值問題之結果分析…………………27
4.3.1 參數範圍之設定……………………………27
4.3.2 坡度因子之影響…………………………… 28
4.3.3 入滲強度因子之影響……………………… 29
4.3.4 坡長因子之影響…………………………… 30
4.4 Mixed邊界值問題之結果分析………………………………31
4.4.1 Mixed邊界值問題之特性……………………31
4.4.2 參數範圍之設定……………………………32
4.4.3 坡度因子之影響……………………………32
4.4.4 入滲強度因子之影響………………………33
4.5馬槽橋土石流案例研究………………………………………34
4.5.1 案例說明……………………………………34
4.5.2 案例分析……………………………………35
第五章 結論與建議………………………………………………37
5.1 結論…………………………………………………………37
5.2 建議…………………………………………………………38
參考文獻…………………………………………………………39
參考文獻1. Abramowitz, M., and Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York, pp. 12, 1970.2. Bredehoeft, J. D., “Finite Difference Approximations to the Equations of Groundwater Flow”, Water Resoursces Research, 5(2), 531-534, 1969.3. Childs, E. T., “Drainage of Groundwater Resting on a Sloping Bed”, Water Resoursces Research, 7(5), 1256-1263, 1971.4. Chapman, T. G., “Modeling Groundwater Flow Over Sloping Beds”, Water Resources Research, 16(6), 1114-1118, 1980.5. Choi, E. C. C., “A Finite Element Study of Steady State Flow in an Unconfined Aquifer Resting on a Sloping Bed”, Water Resoursces Research, 14(3), 391-394, 1978.6. Harr, M. E., “Groundwater and Seepage”, McGraw-Hill, New York, pp. 40-59, 1962.7. Henderson, F. M., and Wooding, R. A., “Overland Flow and Groundwater Flow from a Steady Rainfall of Finite Duration”, J. Geophysical Research, 69(8), 1531-1540, 1964.8. Jaiswal, C. S., and Chauhan, H. S., “A Hele-Shaw Model Study of Steady State Flow in an Unconfined Aquifer Resting on a Sloping Bed”, Water Resources Research, 11(4), 595-600,1975.9. Liggett, J. A., “Location of Free Surface in Porous Media”, Journal of the Hydraulics Division, 103(4), 353-365, 1977.10.Luthin, J. N., and Guitjens, J. C., “Transient Solutions for Drainage of Sloping Land”, J. Irrigation and Drainage Division, 93(3), 43-51, 1967.11.Marei, S. M., and Towner, G. D., “A Hele-Shaw Analog Study of the Seepage of Groundwater Resting on a Sloping Bed”, Water Resources Research, 11(4), 589-59412.Ram, S., and Chauhan, H. S., “Drainage of Sloping Lands with Constant Replenishment”, J. Irrigation and Drainage Engineering, 113(2), 213-223 , 1987. 13.Ram, S., and Chauhan, H. S., “Analytical and Experimental Solutions for Drainage of Sloping Land With Time-Varying Recharge”, Water Resources Research, 23(6), 1090-1096 , 1987. 14.Schmid, P., and Luthin, J. N., “The Drainage of Sloping Lands”, J. Geophysical Research, 69(8), 1525-1529, 1964. 15.Singh, S. T., and Jacob, C. M., “Transient Analysis of Phreatic Aquifers Lying Between Two Open Channels”, Water Resources Research, 13(2), 411-419, 1977.16.Towner, G. D., “Drainage of Groundwater Resting on a Sloping Bed with Uniform Rainfall, Water Resources Research, 11(1), 144-147, 1975. 17.Wooding, R. A., and Chapman, T. G., “Groundwater Flow over a Sloping Impermeable Layer, part 1 , Application of the Dupuit-Forchheimer Assumption”, J. Geophysical Research, 71(12), 2895-2902, 1966.18.Yates, S. R., and Warrick, A. W. , and Lomen, D. O., “Hillside Seepage: An Analytical Solution to a Nonlinear Dupuit-Forchheimar Problem”, Water Resources Research, 21(3), 331-336, 1985.19.高銘伸,『宏觀收斂迭代法速度比較』,國立中央大學土木研究所,碩士論文,pp. 8-11,2001。20.姚善文,『土石流發生之水文特性探討』,國立中央大學土木研究所,碩士論文,pp. 63,2001。21.張石角,『陽明山國家公園馬槽橋災變及其鄰近地區之環境地質研究』,工程環境會刊,pp. 21-39,1987。
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