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 本文探討入射波通過局部透水彈性底床所產生波浪變化及底床內孔隙水壓及應力變化之問題，並提出理論解析解。文中波浪運動採用線性波浪理論，而透水彈性底床考慮為均質、等向透水均勻彈性介質所組成，並且引用Biot 理論之動量方程式及配合Verruijt 提出之Storage 方程式，所推導出高階偏微分控制方程式來描述。為能求得解析解故依求解領域之幾何形狀分區且建立各區通解，其中對於含有非齊性邊界條件之邊界值問題，則分離成齊性邊界條件之邊界值問題分別求解，各區之通解再利用各交界面之運動及動力邊界條件，配合正交函數之特性，聯立求解整個問題之解析解。 在驗證本文理論解正確性上，則比較前人所研究波浪通過有限寬度沙質底床之孔隙水壓試驗結果，及具有壕溝底床所引起波浪變形之數值結果，比較結果均得到良好的一致性。進一步利用本文理論討論，局部透水彈性底床之寬度、厚度、透水性及彈性對入射波與底床內孔隙水壓及應力影響。由討論結果顯示，當透水彈性底床越寬及越厚或底床材質透水性越佳及較具彈性時會減少波浪透過率，而其中透水性對波浪變形影響最大。當透水彈性底床寬度大於兩倍波長，底床中間位置孔隙水壓之變化相當於在無限寬度底床條件；而當寬度減小會造成孔隙水壓增加，底床內之垂直有效應力減少，和兩側水平有效應力及剪應力增加，但底床透水性較差時寬度減少會造成孔隙水壓先增加而後減少至零的現象。當底床透水性較佳時，會造成孔隙水壓增加尤其是在底床兩側。而當底床透水性較差時，孔隙水壓之變化受到彈性影響會較明顯，而導致底床中間位置孔隙水壓大於底床兩側。
 In this study, the problem of incident wave passing a finite-width poro-elastic bed, and effects on incidence waveform, pore pressure and effective stresses are considered, and an analytic solution is proposed. The wave motion is described using the linear wave theory. The poro-elastic bed is considered as homogeneous, isotropic, and elastic, and a high-order partial different governing equation, derived from using the momentum equation of Biot’s theory and the storage equation present by Verruijt is adopted. In order to obtain the analytic solution, the problem domain is divided into sub-regions and general solutions are derived for each region. Finally, the analytic solution is completed for the entire problem by utilizing kinematic and dynamic conditions on the interface between neighboring regions. The present analytic solution is verified by comparing with previous experiments of waves passing finite–width sand beds, and waves propagating over a bottom trench. The present analytic solution is used to study effects of finite-width poro-elastic beds on waves. The results show that wider, thicker, higher permeability and higher flexibility of rectangular bed can induce less wave transmission. And permeability produces the most effect. For finite-width beds with widths wider then twice of wave length, the pore pressures in the middle of beds are the same as those of infinite-width beds. The narrower beds have higher pore pressures, lower vertical effective stresses, and higher horizontal and shear stresses on both sides of beds. Higher permeability induces higher pore pressure especially on the both sides of the bed. On the other hand, beds with lower permeability pore pressures are affected mainly by flexibility, and pore pressures in the middle of beds are larger than those on both sides.
 目錄摘要iAbstractii誌謝iii目錄iv圖目錄vi表目錄xi符號說明xii第一章 緒論11-1 前言11-2 文獻回顧21-3 研究方法41-4 內容組織4第二章 問題描述與理論解析62-1 問題描述62-2 透水彈性體理論描述72-3 邊界條件122-4 波浪場及透水彈性體通解之建立162-4-1 波浪場通解推導162-4-2 透水彈性體通解推導192-5 待定係數求解232-5-1 將通解代入透水彈性體底床側邊及底部之邊界條件232-5-2 將通解代入透水彈性體底床及波浪場交界面之邊界條件272-5-3 將通解代入波浪場交界面之邊界條件30第三章 驗證與討論343-1 理論驗證343-1-1 與Yamamoto et al. (1978) 實驗結果之比較343-1-2 與 李(1994) 試驗之比較353-1-3 與 吳(1994) 海底壕溝數值模式之比較373-1-4 延伸討論，不同孔隙率底床對入射波浪的影響383-2波浪通過局部透水彈性底床之波浪場變化403-2-1 透水彈性底床寬度及厚度對波浪場影響403-2-2 透水彈性底床剪力係數對波浪場影響413-2-3 透水彈性底床滲透性對波浪場影響423-3 波浪通過透水彈性底床之透水彈性底床內部變化433-3-1 透水彈性底床特性對孔隙水壓振幅影響443-3-1-1 透水彈性底床中間表面壓力與寬度變化443-3-1-2 透水彈性底床寬度變化對內部孔隙水壓影響453-3-1-3 透水彈性底床剪力係數變化對內部孔隙水壓影響483-3-1-4 透水彈性底床滲透係數變化對內部孔隙水壓影響483-3-2 透水彈性底床特性對垂直有效應力影響493-3-2-1 透水彈性底床寬度變化對垂直有效應力影響493-3-2-2 透水彈性底床剪力係數變化對垂直有效應力影響503-3-2-3 透水彈性底床滲透係數變化對垂直有效應力影響513-3-3 透水彈性底床特性對水平有效應力影響513-3-3-1 透水彈性底床寬度變化對水平有效應力影響513-3-3-2 透水彈性底床剪力係數變化對水平有效應力影響523-3-3-3 透水彈性底床滲透係數變化對水平有效應力影響523-3-4 透水彈性底床特性對剪應力影響533-3-4-1 透水彈性底床寬度變化對剪應力影響533-3-4-2 透水彈性底床剪力係數變化對剪應力影響543-3-4-3 透水彈性底床滲透係數變化對剪應力影響54第四章 結論與建議55參考文獻R-1附錄A 透水彈性體基本方程式之推導A-1附錄B 第Ⅱ區波浪場通解之推導B-1附錄C 第Ⅳ區透水彈性體通解之推導C-1附錄D 第Ⅳ區透水彈性體特徵值通解為零之推導D-1附錄E 求解待定係數內之積分式及積分常E-1
 參考文獻1.Biot, M.A., “General Theory of Three-Dimensional Consolidation,” Journal of Applied Physics, Vol. 12, pp. 155-164, 1941.2.Biot, M.A., “Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid: 1. Low-Frequency Range,” The Journal of the Acoustical Society of America, Vol. 28, No. 2, pp. 168-178, 1956.3.Biot, M.A., “Mechanics of Deformation and Acoustic Propagation in Porous Media,” Journal of Applied Physics, Vol. 33, No. 4, pp. 1482-1498, 1962.4.Darcy, H., Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856.5.Das, B.M., Advanced Soil Mechanics, Hemisphere Pub. Corp., McGraw-Hill, New York, 1983.6.Hsu, J.R.C., Jeng D.S. and Tsai, C.P., “Short-Crested Wave-Induced Soil Response in a Porous Seabed of Infinite Thickness,” International Journal for Numerical and Analytical Methods in Geomechanics Vol. 17, pp. 553-576, 1993.7.Liu, Philip L-F., “Damping of Water Waves over Porous Bed,” Journal of the Hydraulics Division, ASCE, Vol. 99 (HY12), pp. 2263-2271, 1973.8.Liu, Philip L-F., “On Gravity Waves Propagated Over a Layered Permeable Bed,” Coastal Engineering, Vol. 1, pp. 135-148, 1977.9.Madsen, O.S., “Wave-Induced Pore Pressures and Effective Stresses in a Porous Bed,” Geotechnique, Vol. 28, No. 4, pp. 377-393, 1978.10.Maeno, Y. H. and Hasegawa, T., “Evaluation of wave-induced pore pressure in sand layer by wave steepness.” Coastal Engineering in Japan, 28,pp. 33-44, 198511.Putnam, J.A., “Loss of Wave Energy Due to Percolation in a Permeable Sea Bottom,” Transaction of American Geophysical Union, Vol. 30, pp. 349-356, 1949.12.Terzaghi, K., Theoretical Soil Mechanics, J. Wiley and Sons, inc., New York, 1954.13.Tsai, C.P. and Lee, T.L. (1995), "Standing wave Induced Pore Pressures in a Porous Seabed," Ocean Engineering, Vol. 22, No. 6, pp. 505-51714.Thomas, S.D., “A finite element Model for the analysis of wave induced stresses, displacements and pore pressures in an unsaturated seabed I: theory.” Computers and Geotechnics, Vol 8,pp. 1-38, 198915.Thomas, S.D., “A finite element Model for the analysis of wave induced stresses, displacements and pore pressures in an unsaturated seabed II: Model verification.” Computers and Geotechnics, Vol 17, pp. 107-132, 199516.Verruijt, A., “Elastic Storage of Aquifers,” Flow through Porous Media, edited by De Wiest, R.J.M., Academic, New York, pp. 331-376, 1969.17.Yamamoto, T., “Wave-Induced Pore Pressures and Effective Stresses in In homogeneous Seabed Foundations,” Ocean Engineering, Vol. 8, pp. 1-16, 1981.18.Yamamoto, T., “On the Response of a Coulomb-damped Poroelastic Bed to Water Waves,” Marine Geotechnology, Vol. 5, No. 2, pp. 93-130, 1983.19.Yamamoto, T., Koning, H.L., Sellmeiher, H. and Van Hijurn, E.V., “On the Response of a Poro-elastic Bed to Water Waves,” Journal of Fluid Mechanics,Vol. 87, pp. 193-206, 1978.20.宋長虹, 水波作用下多孔彈性底床動力反應之研究, 國立台灣大學土木工程研究所博士論文, 1993。21.李兆芳、劉正琪, 波浪通過透水潛堤之新理論解析, 第十七屆海洋工程研討會論文集, 台南, 593頁-605頁, 1995。22.李柏宏, 波浪下作用可透水底床之孔隙水壓及流場之變化, 國立成功大學水利及海洋工程研究所碩士論文, 1994。23.李宗霖, 波浪與海床土壤交互作用之解析, 國立中興大學土木工程學系博士論文, 1999。24.吳永照、王瑋、徐虎嘯, 海底壕溝引致二階表面波的變形, 第十六屆海洋工程研討會論文集,A-122頁 – A141頁, 1994。24.張興漢, 波浪通過剛性多孔介質底床特性之研究, 國立成功大學水利及海洋工程研究所碩士論文, 1997。25.藍元志, 波浪與可透水彈性體相互作用之分析, 國立成功大學水利及海洋工程研究所博士論文, 2000。
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 1 水波作用下多孔彈性底床動力反應之研究 2 波浪與可透水彈性體互相作用之分析 3 波浪作用下可透水底床之孔隙水壓及流場之變化 4 波浪與海床土壤交互作用之解析 5 波浪通過剛性多孔介質底床特性之研究 6 波浪通過孔隙底床之傳播特性 7 波浪作用於透水彈性物體之研究分析

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