長時間尺度之水下底床變形

Under Water Bed Form Deformation of Long Time Scale

郭中閔(Jhong-Min Guo)

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(2013年)

https://doi.org/10.6342/NTU.2013.00845

摘要

在河川及海洋中有許多水利工程建設，如橋墩、海底油管等等，底床變形會對其結構物安全產生危害，像是橋墩會因底床變形崩塌、海底油管會因底床變形破裂；在水庫方面，臺灣地區坡陡流急，因此水庫泥沙淤積問題嚴重，研究底床變形機制，對水庫清淤或許有所助益。臺灣四面環海，底床變形對於國土保育及國土規劃亦有關連，透過研究底床變形，將可預測出海岸線的增長與後退。本研究主要目的即為研究在長時間水流與水波作用下之軟質孔隙彈性介質底床變形，延續郭遠錦(2011)之研究。因在郭遠錦(2011)，其數值模擬僅為簡單情境之邊界條件與實際物理問題尚有差異，並且其水體設置數值海綿層(sponge layer)將擾動流速吸收以防止水波反射回內部水體導致數值發散，但在實際問題中，並無設置海綿層這類機制，故需考慮這樣的處理方式對數值模擬的影響。又在郭遠錦(2011)展示之結果中，其底床變形模擬時間略短，其原因可歸咎於時距設定偏短上的限制，故尚無法有效模擬較真實底床變形之問題。研究中，水體主要根據勢流理論建立其控制方程式與邊界條件，而土體之控制方程式則採用 Biot(1956a、1956b、1962) 所建立之多孔隙彈性介質理論加以描述。底床固體位移以流函數(stream function)表示其底床固體位移，並以量階(order)分析簡化土體控制方程式為拉普拉斯方程式(Laplace Equation)與雙調和方程式(Biharmonic Equation)，提出水波與沙波間時間尺度差異顯著關係，並利用邊界元素法(boundary element method)模擬水流與水波作用下之軟質孔隙彈性介質底床變形。

本研究之主要貢獻敘述如下：(1.) 利用水波分散關係式與沙波分散關係式，繪製週波數與角頻率之關係圖，探討時間尺度差異顯著關係。(2.) 提出一無因次參數，為控制底床變形參數，其主要控制因子為流速與拉美第一彈性常數。(3.) 改善計算時距，使較能反應出在水流與水波作用下軟質孔隙彈性介質底床之變形趨勢，並運用數值技巧在水體上下游設置可使擾動流速通過之邊界條件，免除數值海綿層的影響使結果較貼近實際物理現象，並對其原邊界條件計算上之處理進行改善，以減小數值運算上的誤差。(4.) 在研究中亦建構不同情境之邊界條件，諸如土體透水與不透水邊界、加入懸浮載(suspended load)以及加入底床載(bed load)，使模擬結果在實際面上更具參考價值。最後，本研究之數值模擬結果與施宛平(1998)之數值模擬結果，以及李鴻源等人(1990)之實驗結果進行比對，驗證底床變形趨勢一致。

關鍵字

多孔隙彈性介質理論 ； 邊界元素法 ； 底床變形 ； 長時間尺度

並列摘要

There are lots of hydraulic engineering buildings in rivers and the oceans, such as bridge pier and the seabed oil pipes, etc. Bed form deformation will destroy the hydraulic engineering buildings safety, like bridge pier will collapse and the seabed oil pipes will crack by bed form deformation. On the part of reservoir, Taiwan area is high gradient slope and large flow velocity, thus, there is serious impact of sediment deposition for Taiwan reservoirs, studying the problem of bed form deformation may have benefit for Taiwan reservoirs desilting. Taiwan is a small island surrounded by seas, bed form deformation relates to territory protection and plan. Through studying bed form deformation can predict that coastline grow and reduce. The aim of this research is to study the flow and water waves effects on bed form deformation of porous elastic media in the long time scale situation, and follow Kuo (2011)’s study. Because of Kuo (2011), the numerical simulation is only for simple situations of boundary conditions, there still have differences between actual physical problems. Furthermore, Kuo(2011) sets numerical sponge layer in water body on downstream for absorbing disturbance flow velocity to avoid water waves reflexing to inner water body which can lead to numerical divergence. However, there has no sponge layer mechanism in real problem; therefore, this process should be considered what effect for numerical simulation. In Kuo (2011), the bed form deformation time seems too short, and it can impute to the limitation of small time step; so that can’t be effective in simulating the actual bed form deformation problem. In this research, water body is based on potential theory to build up the governing equations and boundary conditions, and the soil body is based on Biot(1956a, 1956b, and 1962) which build up the porous elastic media theory to set up the governing equations. Utilizing the stream function to express the bed solid displacement, and using order analysis to simplify the soil body’s governing equations to Laplace equation and biharmonic equation. Bring up the significant difference between time scale of water waves and soil waves, and using boundary element method to simulate soft porous elastic media bed form deformation which is affected by flow and water waves.
There are followings the main contribution of this study : (1.) Utilizing the dispersion relation of water waves and soil waves to plot angular frequency and wave number diagram, and investigating significant difference between time scales. (2.) Proposed a dimensionless parameter for the control of bed form deformation, the main controlling factors are flow velocity and shear modulus of the soil. (3.) Improved calculation of time step, that can be able to reflect soft porous elastic media bed form deformation trends on the flow and water waves affect. Using numerical skill to set up boundary condition which can let disturbance flow velocity pass in water body on upstream and downstream, in order to eliminate the impact of numerical sponge layer to make the results closer to actual physical phenomenon. And the calculation of its original boundary conditions of the process to make improvements to reduce the error of numerical simulation. (4.) Constructed different situations boundary conditions in this study, such as soil body permeable and impermeable boundary on upstream and downstream, adding suspended load, and adding bed load, so that numerical simulations are useful in reality. Finally, numerical simulation results of this study will verify with Shi (1998) and Li, et al (1990).

並列關鍵字

porous elastic media theory ； boundary element method ； bed form deformation ； long time scale

參考文獻

42. 郭遠錦，2011，水下長時間尺度之底床變形研究，國立臺灣大學土木工程學研究所博士論文。

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5. Biot, M. A., 1962, “Mechanics of deformation and acoustic propagation in porous media”, The Journal of the Acoustical Society of America, Vol. 33, pp. 1482-1498.

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