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.

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