由海底地震所引發之海嘯常導致沿海地區受創嚴重，而海嘯湧潮所夾帶之洪水亦會於建築物周圍產生局部沖刷災害，此外豪雨或強降雨形成之高濃度泥沙流，如泥流 (Mudflow)或夾帶大量泥沙之洪水 (Mud Flood)，亦會造成人命傷亡、建築物及橋梁等公共建設毀損。在探討局部沖刷與高濃度泥流時，由於泥沙之運動特性與賓漢流體之流動特性相似，本研究發展一流變模式來模擬山崩及海嘯或洪水所引發之局部沖刷，此模式源於包含壓密現象 (Phenomenon of Compaction) 之傳統賓漢模式，然而此壓密現象存在於許多泥沙及沉積物問題中，且通常由沉降或壓密作用所造成。此效應對於山崩滑移之表面形狀及局部沖刷之沖刷剖面至關重要。然而傳統賓漢模式缺乏描述此種機制之名詞。因此本文將賓漢模式轉換為賓漢雙黏性流模式 (Bingham constitutive model) ，並加入額外參數〖τ_y〗^' 、(γ_y ) ̇來表達壓密作用，〖τ_y〗^'表示夯實材料之降伏應力 (Compacted yield stress) ，(γ_y ) ̇為降伏應變，若無壓密，〖τ_y〗^'則轉為降伏應力τ_y，且模式將還原為傳統賓漢模式。當考慮壓密作用時，τ_y將會增加並轉為〖τ_y〗^'，造成流變曲線不連續，此模式稱為非連續之賓漢雙黏性流模式 (Discontinuous Bi-viscous Model) ，簡稱DBM。本模式求解三維Navier-Stokes方程式，並以VOF法追蹤流體介面之運動。模式所需提供之參數有降伏應力τ_y、黏滯係數μ_b及夯實降伏應力〖τ_y〗^'。由於降伏應力與黏滯係數尚無系統之決定方式，且需仰賴流變儀進行流變分析，此不僅在試體採樣過程中容易破壞原有之結構，在應用上亦有不便之處。為此，本研究參考Raudkivi (1998) 所提供之賓漢流變參數經驗公式發展流變參數決定法 (Rheological Parameter Determining Method , RPDM)。在提供泥沙粒徑與比重後，即可求得一組適當之流變參數，掌握適切之初始猜值。由於傳統賓漢模式中並無探討夯實土砂之降伏應力，因此本文則透過經驗式得出適當之初始猜值。本研究並進行三維泥流型山崩與局部沖刷模擬。在三維泥流型山崩方面，模擬1966年發生於美國德州之石膏尾礦潰壩之真實案例。首先，本文藉由 Jeyapalan (1983) 利用流變儀分析求得之降伏應力、黏滯係數等流變參數進行三維模擬，並探討夯實土砂之降伏應力對於山崩行為機制之影響。模擬結果顯示夯實之降伏應力將改變潰壩流體潰壩之時間點、流動過程、堆積型態與溢淹距離。其後藉由模式結果進一步分析該案例中賓漢流體之流動行為，包含流速、強剪區與弱剪區之分布等，由結果中可以清楚看出賓漢流體於強剪區與弱剪區之分布情形與速度之關係，顯示本研究所發展之非連續賓漢雙黏性流模式(DBM)可模擬複雜之三維高濃度泥沙流問題。而由模擬結果亦可得知本模式能適切表達泥流之運動過程及堆積現象，並與觀測結果對照有良好之一致性。接著，本研究透過 Jeyapalan (1983) 所提供之泥沙比重與中值粒徑，利用流變參數決定法推得模式所需之降伏應力與黏滯係數，進行三維泥流運動之動態模擬。本文並將模擬結果與 Jeyapalan (1983) 提供之流變參數所得之數值結果進行比較與討論分析。由探討中發現，利用流變參數決定法求得之流變參數帶入模式後，其潰壩流體之堆積型態、溢淹距離與實例照片及觀測數據更加接近，顯示該法之實用性及模式之準確性。在局部沖刷與沖刷坑發展方面，本研究模擬半圓柱之沖刷實驗 (Dey and Barbhuiya, 2005) ，透過文中所提供之泥沙粒徑與比重，計算出流變參數之初始猜值。模擬結果顯示本研究推得之參數亦可適切地模擬底床沖淤之過程並預測沖刷坑之最大深度，且誤差在10%以內，突顯本研究方法之實用性。

The tsunami caused by an undersea earthquake often leads to coastal areas hit seriously, and the flood entrained by tsunami surges often brings local scour around the buildings. Moreover, the high concentrations of sediment flow formed by heavy rain, such as Mudflow or Mud flood, often causes live losses or damages on structures during typhoon season. The flood induced by heavy rainfalls may result in local scour around the bridge. In order to understand more about the movement characteristics of sediment, which are similar to ones of the Bingham fluid, we newly developed a rheology model for simulating the natural hazards of landslide and local scour induced by a tsunami or severe floods in this study. The model originated from the conventional Bingham constitution model included tamping effect, which exists in most of the mud or sediment problems and usually is caused by the settlement and compaction processes.
The tamping effect is crucial to the shape of the slip surface and scour profile in the landslide and local scour problems, respectively. However, the conventional Bingham model lacks the mechanism of describing this prenominal. Hence, we converted the Bingham model into the Bi-viscous model, adding additional parameters, Yield_solid and Gamma_yield, to present the tamping effect. Yield_solid indicated the yield stress of compacted material; Gamma_yield indicated the yield strain rate. Without the tamping effect, the Yield_solid went to the yield stress, and the model went back to the conventional Bingham model. While the tamping effect was taken into account, the Yield_solid increased and made the rheology curve discontinuous. The novel model is called Discontinuous Bi-viscous Model, shorten as DBM. It solves 3D Navier-Stokes equation and tracking the movement of fluid interface with Volume of the Fluid method. The provided parameters in the model are Bingham yield stress、Bingham viscosity and yield strain rate. However, there is no systematical method for determining these parameters and need to rely on rheometer. For this reason, the present study developing Rheological Parameter Determining Method (RPDM) by way of the empirical formula of Raudkivi (1998) . It can be inquired into reasonable rheological parameters after providing sediment grain size and proportion, and grasp the appropriate initial value. The traditional models do not investigate yield strain rate, in this paper, we can get the appropriate initial value by numerical method.

The present study carrying out three-dimensional Mudflow landslides and local scour simulation on the cylinder. In three-dimensional Mudflow landslides, we apply our model to simulate one real case, 1966 dam break of gypsum tailing in Texas. First, we use yield stress and viscosity analyzed by Jeyapalan (1983) to simulate, and discuss the influence of yield strain to the mechanisms of landslides. The results show that yield strain will change the time of dam break, the process of mobile, stacking patterns and inundation distance.
From the simulation results, we know that DBM is not only express the movement of the process and the accumulation of mud flow but also has a good consistency with observations. With the grain size and proportion of sediment which provided by Jeyapalan (1983) , we can obtain the rheological parameters through the rheological parameter determining a method to carry out the dynamic simulation of three-dimensional mudflow motions. To verify our methods with Jeyapalan (1983) . Simulation results show that the parameters calculated by the present study could express the motion of mudflow and accumulation phenomenon appropriately, and well compare with experimental results. Regarding the issue of local scour, we study on the Turbulent flow field in a scour hole at a semicircular abutment (Dey and Barbhuiya, 2005) . The simulation result shows that the parameters calculated by our study could also describe the seabed erosion and the final development of scouring pit, and the maximum depth of scouring pit of error less than 10%, in addition to the good comparison with scouring pit patterns.

摘要 iii
Abstract vi
誌謝 viii
目錄 ix
第一章 緒論 1
1-1 研究背景 1
1-2 沖刷文獻回顧 3
1-3 泥流型山崩文獻回顧 9
1-4 賓漢流變參數之文獻回顧 12
1-5本文架構 18
第二章 研究方法與模式介紹 19
2-1 研究方法 19
2-2 賓漢流理論 20
2-3 模式介紹 25
2-3-1 控制方程式 (Governing Equation) 25
2-3-2 有限體積法 (Finite Volume Method) 25
2-3-3 流體體積法 (Volume of Fluid) 26
2-4 流變參數之定義與計算 32
第三章 泥流潰壩案例模擬與分析 38
3-1 數值模式設定 39
3-2 模擬結果 44
3-3 流變參數決定法(應用於石膏潰壩) 88
第四章 沖刷案例模擬 113
4-1 半圓柱橋墩沖刷實驗驗證 113
第五章 結論與建議 128
5-1 結論 128
5-2 建議 129
參考文獻 130
附錄A 非連續賓漢雙黏性流模式之解析解驗證 138
附錄B 新增石膏潰壩案例之數值結果與網格收斂性分析 142
B.1 夯實降伏應力τ_0'=1.0×109 (Pa) 之數值結果 142
B.2 石膏潰壩案例(網格收斂性分析) 149
B.3 石膏潰壩案例(賓漢雙黏性流) 154
附錄C 實際案例之沖刷坑動態模擬 161
附錄D 小型沖刷實驗 167
附錄E 口試書面答覆表 177

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