豪雨或颱風降雨造成之高濃度泥沙流（Hyperconcentrated Sediment Flow），如土石流（Debris Flow）、泥流（Mudflow）及挾帶大量泥沙之洪流（Mud Flood），常導致人命傷亡及建築物、橋梁、公共建設毀損。此外海嘯湧潮（Bore）及大雨來襲後形成之洪水亦會於海堤、房屋等結構物周圍產生局部沖刷災害。本研究旨在發展一三維多相流變模式，結合賓漢雙黏性流流變模式之NS-VOF數值模式，以描述上述問題之流場行為。於局部沖刷問題之部份，本研究中以賓漢流變模式降伏應力，及流體之黏滯性參數描述泥沙受水流沖刷之運動行為。本流變模式與Bird et al.（1983）所推導之賓漢流解析解驗證結果相當符合，證明本模式於程式發展有高度正確性。其後將本模式用於模擬雙園橋倒塌案例，該案例之底床為泥質底床，模擬結果與實測沖刷深度亦有相當良好之一致性。然而真實情形中之底床常包含粒徑較大之泥沙，越往河川上游底床所含大顆粒之泥沙比例越高，此時以傳統賓漢流體之概念進行模擬之準確性便會下降。為解決此問題，本研究於賓漢雙黏性流模式導入顆粒碰撞之效應，並以水流沖刷半圓形橋墩周圍沙質底床之實驗為驗證對象。模擬結果顯示導入顆粒碰撞項後，模式可更精準描述於結構物周圍沙質底床之沖刷坑發展及下游方堆積之高度與型態。此外本文亦探討模式於高濃度泥沙流問題之應用。本研究以1989年Liu與Mei 推導出之斜板上賓漢流理論解進行驗證，證明本模式可精準模擬泥流之現象，並將此模式應用於1966年德州石膏尾礦潰壩之真實案例，模擬結果之流況、流體堆積之分佈、型態及距離皆與實例照片及觀測提供之數據相當接近。其後藉由模式結果進一步分析此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，由模式結果中可以清楚看出賓漢流體於強剪區及弱剪區之分布情形及與速度之關係，此案例之結果顯示本模式可模擬複雜之三維高濃度泥沙流問題，並可藉由模擬結果更加了解賓漢流體之運動特性。Hyperconcentrated sediment flows, such as debris flows, mudflows, and mud floods, induced by heavy rainfalls or typhoons frequently cause live losses and damages on structures. In addition, tsunami bores or river floods may result in sever local scour. The present study aims at developing a 3D multi-phase rheological model that incorporates Bingham bi-viscous model to characterize flow fields in the above-mentioned scenarios. Regarding the issue of local scour, the present study adopts the parameters of Bingham yield stress and Bingham viscosity in the rheological model to describe the fluid motions around the structures. We validate the numerical model with the analytical solution derived by Bird et al.（1993）. Highly consistency can be observed. We then implement this model to simulate the failure of Shuang-Yuan bridge. Muddy riverbed is applied. Good agreement can be seen in terms of the scour depth. However, the constitution of riverbed changes toward the upstream direction with large grain size which cannot fully describe by the Bingham model. For this, we present a quadratic rheological model to incorporate the effect of particle collision. The quadratic rheological model is validated by simulating the local scour around a semicircular abutment with sandy bed. The result shows that the model is capable of describing not only the scour profile around the cylinder, but also the sediment deposition in the downstream area.As for the hyperconcentrated sediment flows, we study the mudflow on an incline plane. The result is validated with the theoretical solution and experimental measurement provided by Liu and Mei（1989）. Very good agreement can be seen. We then apply our model to simulate one real case, 1966 dam break of gypsum tailing in Texas. Our simulation result presents very good agreement in terms of the flooding distance, propagation ceasing time, and propagation speed. We also find that our result presents many detail appearances of the stopped gypsum which are extremely close to those observed on the historical photo. We further analyze the flow characteristics, such as the time-dependence shear and plug areas, which can rarely be seen in the literatures. We concluded that the newly developed rheological model is capable of simulating complex hyperconcentrated sediment flows as well as the local scour problems.
