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  • 學位論文

顆粒流湧浪於動床渠道之流動結構:理論及實驗方法

Vertical structure of liquid-granular surges over erodible beds: experiments and theory

指導教授 : 卡艾瑋

摘要


本論文致力於探討礫石流在狹長山谷中之發展機制。透過小尺度的長渠道試驗,模擬在高流量之供給條件下,引致顆粒流湧浪行經鬆軟底床之運動行為。透過影像分析方法可同步計算實驗量測值,主要分為流速及礫石濃度。 我們採用雷射條紋濃度法計算實驗濃度值,在濕顆粒流中,建立礫石濃度與光線可穿透距離之關係,進而得到沿深度變化之濃度曲線;流速方面,則是採用質點軌跡測速法,計算自由液面以下之實驗流速值。以實驗量測值作為基礎,透過控制體積法推算底床剪應力,並比較其與流速、礫石濃度、礫石通量、底床載厚度、正向應力,及顆粒有效應力等參數。結果顯示,邊界磨損效應對濕顆粒流的影響相當有限。當底床剪應力增加時,其對顆粒運動造成影響之變化率約與深度呈拋物線關係。 理論方面,我們以應力平衡為基礎,採用垂直擴散理論,推導在顆粒流湧浪中,礫石濃度隨深度變化之情形。將理論模式應用至實驗,當水位、運動層厚度,及初始底床高程為已知變數時,可預測礫石濃度及應力分布隨深度之變化,並能成功表現在實驗結果中所發現之應力關係。透過實驗比較,可驗證模式準確性,並檢視理論與實驗之間之現象差異。

並列摘要


The purpose of the study is to explore the transport mechanism of the debris flow developing in a narrow valley. We conduct small-scale laboratory experiments to simulate the behavior of the flood-induced liquid-granular surge flowing over the loose erodible bed. Via image processing methods, the experimental measurements of velocities and grain concentrations can be simultaneously calculated from the same footage. Grain concentrations are calculated adopting the laser distance-to-wall measurements, based on the relation between the grain concentration and the mean maximum travelling distance of laser beam. Velocities below the free surface are calculated adopting particle tracking velocimetry (PTV). The experimental basal shear stresses are solved via control volume analysis. The results show that when basal shear stresses increase, the wall abrasion behavior can be neglected, which intensifies following a cubic relationship with depth. In theory, we adopt the diffusive flux approach with a diffusivity in terms of the granular pressure to derive the analytical solution for grain concentration profile. The model requires the water level, the bed-load layer thickness, and the initial deposited bed level, as known variables. Besides, the analytical solution can be used to described the relations of stresses with depth earlier found in experiments. The model are compared with experimental measurements to observe the difference between the theory and experiments.

參考文獻


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