運動波模型模擬可變寬度與複合性渠道中潰壩洪水之傳遞

Abstract

本論文延伸運動波模型，使其可應用於複合式斷面或可變斷面參數的渠道上的洪水演算。本論文提出洪水在可變斷面之渠道上的傳遞行為可藉由變數變換法轉換為在固定斷面之渠道上的洪水波，可透過解析解進行模擬。而洪水在複合式斷面渠道中的傳遞則可透過有限體積法以數值解的方式進行模擬。本論文以1976年美國Teton Dam潰壩下游洪水水位歷史資料和2008年中國唐家山堰塞湖潰壩下游水位站監測之流量歷線進行準確性之對比驗證和效率評估。由驗證結果可知，本模型可以準確模擬洪水波大尺度的行為，有效降低過去運動波模型在複雜渠道上的顯著誤差。並且，本模型所需要的演算時間以及下游地形資料並未增加，因此可以極大地保留運動波模型的高效率特性。在得到良好的模擬結果的同時，避免如二維動力波模型因數值方法演算需時過長而造成可疏散時間被壓縮等問題。此外，本模型可以清楚的呈現各種因素，包含複合式斷面、寬度、坡度、糙度以及潰壩洪水歷線的型態對洪水波的各別影響效果。

An extended kinematic wave model is proposed for the simulation of flood propagation in the simple or compound channels with variable cross-sectional properties, including channel width, bed slope, and friction coefficient. The model considers the distinctive effects and multiple wave types induced by the compound channel and variable cross-sectional properties but disregards the multi-dimensional and dynamic flood motions. First, the study derives an explicit analytical kinematic wave model for regular channels with variable cross-sectional properties by changed variable method. It implies that the flood propagation can be solved as in the channel with constant cross-sectional properties primarily and then transformed into the solution for variable cross-sectional properties. The analytical model is applied to the well-documented flood due to the Tangjiashan Landslide Dam failure, Sichuan, in 2008 and presents satisfactory agreements with the recorded data. Second, the study derives an explicit numerical kinematic wave model for compound channels by HLL Finite Volume numerical method. The numerical model is validated and assessed by the analytical model and the historical data of the flood due to the failure of Teton Dam in Idaho, in 1976. Based on these comparisons, the model is shown capable of performing dam failure flood simulations with good efficiency and accuracy. Last, the model is used to simulate different dam failure scenarios for the Shihmen Dam in Taiwan. This application shows clearly how flood behavior is affected by compound channel geometry, width and slope changes, and the gradual or sudden character of the dam failure.