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研究生： 吳正義
Wu, Cheng-Yi
論文名稱： 土石流運動及堆積行為之數值模擬
Numerical Modeling on the Motion and Deposition Behaviors of Debris Flow
指導教授： 常正之
Charng, Jeng-Jy
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年： 2003
畢業學年度： 91
語文別： 英文
論文頁數： 168
中文關鍵詞： 有限差分 、土石流 、運動 、堆積
外文關鍵詞： FDM, Debris Flow, Deposition, Motion
相關次數： 點閱：101  下載：10 
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    • 本研究將土石流視為連續且不可壓縮之層流流體，以連體力學中質量守恆與動量守恆的觀點，推導二維土石流平均流深控制方程式，並建立一適用流經固定床底之土石流數值模式。且以磨擦－碰撞流變模式模擬台灣常見之礫石型土石流流變行為，藉以探討該型土石流的流動與堆積行為。

    本數值模式應用馬科麥克(MacCormack)顯式差分法模擬土石流流動及堆積行為，不僅可大幅節省計算時間，並可有效應用在一維的現地土石流（銅門及豐丘土石流）與二維的室內水槽試驗。此外，模擬的結果顯示溪床坡度與土石流量對土石流流動行為有顯著的影響，且在磨擦碰撞流變模式所需之參數中，降伏應力在土石流流動距離及堆積高度之預測上為一相當重要的輸入參數。

    A 2-D numerical model capable of capturing the motion and deposition behaviors of debris flow was proposed in the present study. The friction-collision model was successfully introduced to the numerical model to reflect the realistic rheology of granular debris flow which occurred frequently in Taiwan. The governing equations were derived on the basis of mass and momentum conservation and the achievement of mathematical formulation was largely relied on the simplification of problem being solved and some assumptions were also made for the ingredient and flow pattern of debris flow such as continuum, homogeneous, monophase, cohesionless granular material and incompressible laminar flow and shallow water flow.

    The proposed numerical model was solved by explicit finite difference scheme based on MacCormack’s method and capable of performing 1-D simulation of full-scale debris flow events in Tung-Men and Feng-Chiou field site while 2-D simulation of flume experiments. According to the simulation results, the bed slope and inflow discharge exhibits strong influences on the debris flow behavior. And the yield stress in friction-collision model plays a very influential role on the prediction of the movement of flowing distance and deposition thickness of debris flow.

    Chapter Title Page Abstract i Acknowledgments iii Table of Contents iv List of Tables viii List of Figures ix List of Symbols xiii Ⅰ Introduction 1.1 General 1 1.2 Objective and Scope of the Study 2 1.3 Methodology 3 Ⅱ Literature Review 2.1 General 4 2.2 The Debris Flow Problem 4 2.3 Debris Flows – Current Knowledge 5 2.3.1 Definition 5 2.3.2 Characteristics 6 2.3.3 Types 7 2.3.4 Influence Factors 8 2.4 Interpretations of Debris Flow Behavior 9 2.4.1 Initiation 9 2.4.2 Force Applied on Debris Flow 10 2.4.3 Main Features of Flow Motion 10 2.4.3.1 Velocity Distribution 11 2.4.3.2 Path of Grain Movement 11 2.4.3.3 Sediment Concentration Distribution 12 2.4.3.4 Flow Zone 12 2.4.3.5 Boundary Layer 13 2.5 Mathematical Model of Debris Flow 13 2.5.1 General 13 2.5.2 Theoretical Assumption 13 2.5.3 Governing Equation 14 2.5.3.1 Continuity Equation 14 2.5.3.2 Momentum Conservation Equation 16 2.5.3.3 Comment 17 2.5.4 Rheology of Debris Flow 17 2.5.4.1 Dispersive Model 19 2.5.4.2 Bingham Model 20 2.5.4.3 Viscous-Plastic-Collision Model 21 2.5.4.4 Comment 22 2.5.5 Sediment Concentration 22 2.5.5.1 Erosion process 23 2.5.5.2 Deposition process 24 2.5.6 Bed Shear Stress 24 2.5.7 Excess Pore Pressure 25 2.5.8 Initial and Boundary Conditions 25 2.5.8.1 Initial condition 25 2.5.8.2 Boundary condition 26 2.6 Demonstrative Studies on Numerical Modeling of Debris Flows 27 2.7 MATLAB Program 45 2.7.1 Introduction to MATLAB 45 2.7.2 Programming with MLTLAB 46 Ⅲ Methodology 3.1 General 47 3.2 Mathematical Formulation 47 3.2.1 Depth-Average Continuity Equation 47 3.2.2 Momentum Equation 49 3.2.2.1 Internal Stress Analysis 49 3.2.2.2 Depth-Average Equation 52 3.2.3 Comment 54 3.3 Numerical Algorithm—Finite Difference Method 56 3.4 Grid System 56 3.5 Discretization of Governing Equation 57 3.5.1 Discretization of the Continuity Equation 57 3.5.2 Discretization of the Momentum Equation 59 3.5.2.1 X-momentum component 59 3.5.2.2 Y-momentum component 61 3.6 Initial and Boundary Condition for Numerical Model 64 3.7 Stability and Convergence of Numerical Solution 64 3.7.1 Stability Analysis 64 3.7.2 Convergence Analysis 65 3.8 Numerical Scheme 65 3.9 Numerical Experiments of Numerical Model 66 3.9.1 Flow Boundary at Upstream 66 3.9.2 Geometry Boundary of Hillslope 67 Ⅳ Implementation of Numerical Modeling of Case Studies 4.1 General 68 4.2 One Dimensional Numerical Modeling 68 4.2.1 Case1: Tung-Men Debris Flow 68 4.2.2 Case2: Feng-Chiou Debris Flow 72 4.3 Two Dimensional Numerical Modeling 73 4.3.1 Equipments for Flume Experiment and Arrangement 74 4.3.2 Geometry Condition 74 4.3.3 Initial and Boundary Condition 74 4.3.4 Physical and Numerical Parameters 74 Ⅴ Results and Discussions 5.1 Numerical Experiment 76 5.1.1 Inflow Condition 76 5.1.2 Geometry Boundary of Hillslope 76 5.1.3 Comment 77 5.2 Tung-Men Debris Flow 77 5.2.1 Mesh Density 77 5.2.2 Yield Stress 78 5.2.3 Comparison between Numerical Result and Previous 78 5.3 Feng-Chiou Debris Flow 78 5.3.1 General 78 5.3.2 Comparison between Numerical Result and Field Observations 78 5.4 Numerical Modeling of Flume Experiment 79 5.4.1 Flume Channel 79 5.4.2 Alluvial Fan in Flood Basin 79 Ⅵ Conclusion and Recommendations 6.1 Conclusion 81 6.2 Recommendations 82 Reference 83 Tables and Figures 87

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