本研究中使用耦合歐拉-拉格朗日(CEL)技術進行數值分析探討挾帶現象對顆粒流之影響，此技術能有效避免顆粒流模型於遭遇大變形時發生網格畸變問題，結合賓漢流變組成律描述顆粒流與可侵蝕層由靜止狀態至流動狀態之行為，研究內容主要分為顆粒流挾帶模型驗證與顆粒流挾帶模型尺度分析。
顆粒流挾帶模型驗證中以數值分析結果與實驗室顆粒流挾帶實驗進行流動型態與流動速度驗證，首先以網格收斂性分析選擇出最適用之網格尺寸，接著以參數敏感度分析取得賓漢組成律參數，並同時探討賓漢組成律參數對顆粒流流動行為之影響，最後以取得之賓漢組成律參數搭配不同可侵蝕層條件進行數值分析與結果驗證。
顆粒流挾帶模型尺度分析使用上述已驗證之模型進一步調整模型尺度進行數值分析，探討模型在不同尺度下挾帶現象對於顆粒流流動距離與流動速度之影響，其中提出了尺度正規化參數Lpercent、Lscale、Vscale幫助進行結果分析，最後將分析結果中之流動速度與常用經驗公式計算結果進行比較，討論經驗公式之準確性與適用條件。
藉由以上一系列之數值分析本研究取得良好的成果，於顆粒流挾帶模型驗證中，數值分析結果與實驗結果於不同可侵蝕層厚度模型之最終流動距離最小差距約為0.5%，且流動型態皆相當接近，於流動階段之流動速度亦表現相當高之一致性，證實了以CEL搭配賓漢組成律建立之模型能有效還原實驗結果。顆粒流挾帶模型尺度分析釐清了隨著尺度放大流動距離受挾帶之影響並非等比例放大，且在尺度放大至一程度開始影響開始減緩，於流動速度部分亦有此現象。流動速度經驗公式適用性分析中指出了不同經驗公式與經驗參數所適用之尺度大小與可侵蝕層條件。

In this study, CEL technique was used to explore the effect of entrainment on granular flow. This technique can effectively avoid the problem of mesh distortion when the granular flow model encounters large deformation. The research is divided into two parts, model validation and model scale analysis. In model validation, the results of numerical analysis and granular flow entrainment experiment are used to validate the flow pattern and velocity. The influence of Bingham parameters on the analysis results is also discussed. In the part of model scale analysis, the validated model is changed into different scales, and the effect of the entrainment on the flow distance and flow velocity of the granular flow at different scales is discussed. Through the above series of numerical analyses, good results have been achieved in this study. The numerical analysis results are quite close to the experimental results in the flow pattern and flow velocity in the flow stage, which proves that the CEL technique can effectively restore the experiment results. It is found that the effect of entrainment of flow distance and flow velocity is not proportional to increased and is convergent at larger scales.

李根政。八八風災的山林啟示錄：一場制度和公權力形成的系統性破壞。天下雜誌出版社。(2019)。
行政院農業委員會水土保持局。水土保持手冊。南投市。(2017)。
徐采筠。「驗證與應用耦合歐拉－拉格朗日技術：以顆粒流試驗為例」。碩士論文，國立成功大學土木工程學系。(2019)。
Breien, Hedda, et al. "Erosion and morphology of a debris flow caused by a glacial lake outburst flood, Western Norway." Landslides 5.3 (2008): 271-280.
Berger, C., B. W. McArdell, and Fritz Schlunegger. "Direct measurement of channel erosion by debris flows, Illgraben, Switzerland." Journal of Geophysical Research: Earth Surface 116.F1 (2011).
Costa, John E. "Physical geomorphology of debris flows." Developments and applications of geomorphology. Springer, Berlin, Heidelberg, 268-317. (1984).
Chhabra, Raj and J. F. Richardson. “Non-Newtonian flow in the process industries : fundamentals and engineering applications.” (1999).
Calvo, L., et al. "Runout and deposit morphology of Bingham fluid as a function of initial volume: implication for debris flow modelling." Natural Hazards 75.1: 489-513. (2015).
Chen, H. X., and Li Min Zhang. "EDDA 1.0: integrated simulation of debris flow erosion, deposition and property changes." Geoscientific Model Development 8.3: 829-844. (2015).
Cao, Chen, et al. "An approach to predict debris flow average velocity. " Water 9.3: 205. (2017).
Du, R. H., et al. "A comprehensive investigation and control planning for debris flow in the Xiaojiang River basin of Yunnan Province." Sichuan Science and Technology Press, Chongqing Branch 33 (1987).
Dai, Zili, et al. "3D numerical modeling using smoothed particle hydrodynamics of flow-like landslide propagation triggered by the 2008 Wenchuan earthquake." Engineering Geology 180: 21-33. (2014)
Debelak, Aliena Marie, Christopher Bareither, and Hussam Mahmoud. Coupled Numerical Simulation of Debris Flow-Soil-Structure Interactions for Flexible Barrier Mitigation Systems. No. MPC 21-438. (2021).
Fink, Jonathan H., et al. "Rheological properties of mudflows associated with the spring 1980 eruptions of Mount St. Helens volcano, Washington." Geophysical research letters 8.1: 43-46. (1981).
Fraccarollo, L., and M. Papa. "Numerical simulation of real debris-flow events." Physics and Chemistry of the Earth, Part B: Hydrology, Oceans and Atmosphere 25.9: 757-763. (2000).
Han, Guoqi, and Deguan Wang. "Numerical modeling of Anhui debris flow." Journal of Hydraulic Engineering 122.5: 262-265. (1996).
Hungr, Oldrich, Scott McDougall, and Michael Bovis. "Entrainment of material by debris flows." Debris-flow hazards and related phenomena. Springer, Berlin, Heidelberg, 135-158. (2005).
Haas, Tjalling de, and Teun van Woerkom. "Bed scour by debris flows: experimental investigation of effects of debris‐flow composition." Earth Surface Processes and Landforms 41.13: 1951-1966. (2016).
Iverson, Richard M. "The physics of debris flows." Reviews of geophysics 35.3: 245-296. (1997)
Iverson, Richard M. "The debris-flow rheology myth." Debris-flow hazards mitigation: mechanics, prediction, and assessment 1: 303-314. (2003).
Iverson, Richard M. "Debris-flow mechanics." Debris-flow hazards and related phenomena: 105-134. (2005).
Iverson, Richard M., et al. "The perfect debris flow? Aggregated results from 28 large‐scale experiments." Journal of Geophysical Research: Earth Surface 115.F3 (2010).
Iverson, Richard M. "Elementary theory of bed‐sediment entrainment by debris flows and avalanches." Journal of Geophysical Research: Earth Surface 117.F3 (2012).
Iverson, Richard M. "Scaling and design of landslide and debris-flow experiments." Geomorphology 244: 9-20. (2015).
Johnson, Arvid M. Physical processes in geology: A method for interpretation of natural phenomena; intrusions in igneous rocks, fractures, and folds, flow of debris and ice. Freeman, Cooper, (1970)
Jian, Li, and Luo Defu. "The formation and characteristics of mudflow and flood in the mountain area of the Dachao River and its prevention." Zeitschrift für Geomorphologie 25.4: 470-484. (1981).
Jakob, Matthias, Oldrich Hungr, and Dr Matthias Jakob. Debris-flow hazards and related phenomena. Vol. 739. Berlin: Springer, (2005).
Kang, Chao, and Dave Chan. "Numerical simulation of 2D granular flow entrainment using DEM." Granular Matter 20.1: 1-17. (2018).
Kavinkumar, C., S. Sureka, and J. Pillai Rakesh. "Influence of erodible layer on granular column collapse using discrete element analysis." Geomechanics and Geoengineering: 1-13. (2021).
Lee, Kwangwoo, and Sangseom Jeong. "Large deformation FE analysis of a debris flow with entrainment of the soil layer." Computers and Geotechnics 96: 258-268. (2018).
Lin, Cheng-Han, Ching Hung, and Tsai-Yun Hsu. "Investigations of granular material behaviors using coupled Eulerian-Lagrangian technique: From granular collapse to fluid-structure interaction." Computers and Geotechnics 121: 103485. (2020).
Morton, D. M., and R. H. Campbell. "Spring mudflows at Wrightwood, southern California." Quarterly Journal of Engineering Geology 7.4: 377-384. (1974).
Mizuyama, Takahisa. "Technical standard for the measures against debris flow (draft)." Technical memorandum of PWRI 2632: 48. (1988).
Major, Jon J., and Thomas C. Pierson. "Debris flow rheology: Experimental analysis of fine‐grained slurries." Water resources research 28.3: 841-857. (1992).
Mangeney, A., et al. "Erosion and mobility in granular collapse over sloping beds." Journal of Geophysical Research: Earth Surface 115.F3 (2010).
McCoy, S. W., et al. "Sediment entrainment by debris flows: In situ measurements from the headwaters of a steep catchment." Journal of Geophysical Research: Earth Surface 117.F3 (2012).
Prochaska, Adam B., et al. "A study of methods to estimate debris flow velocity." Landslides 5.4: 431-444. (2008).
Qiu, Gang, Sascha Henke, and Jürgen Grabe. "Application of a Coupled Eulerian–Lagrangian approach on geomechanical problems involving large deformations." Computers and Geotechnics 38.1: 30-39. (2011).
Parsons, Jeffrey D., Kelin X. Whipple, and Alessandro Simoni. "Experimental study of the grain-flow, fluid-mud transition in debris flows." The Journal of Geology 109.4: 427-447. (2001).
Rickenmann, Dieter. "Empirical relationships for debris flows." Natural hazards 19.1: 47-77. (1999).
Remaître, Alexandre, Jean‐Philippe Malet, and Olivier Maquaire. "Morphology and sedimentology of a complex debris flow in a clay‐shale basin." Earth surface processes and landforms: the journal of the British Geomorphological Research Group 30.3: 339-348. (2005).
Reid, Mark E., et al. "Entrainment of bed sediment by debris flows: results from large-scale experiments." Italian journal of engineering geology and environment: 367-374. (2011).
Shirole, D., C. Moormann, and K. G. Sharma. "A new continuum based model for the simulation of a seismically induced large-scale rockslide." Procedia engineering 173: 1755-1762. (2017).
Tecca, Pia R., et al. "Development of a remotely controlled debris flow monitoring system in the Dolomites (Acquabona, Italy)." Hydrological processes 17.9: 1771-1784. (2003).
Tian, Shuwen, Changming Wang, and Zhimin Zhang. "A hybrid method of debris flow velocity estimation based on empirical equation." International Journal of Heat and Technology 35.1: 147-152. (2017).
Varnes, David J. "Slope movement types and processes." Special report 176: 11-33. (1978).
Venutelli, Maurizio. "A constitutive explanation of Manning’s formula." Meccanica 40.3: 281-289. (2005).
Wang, Zhaoyin, Peter Larsen, and Wei Xiang. "Rheological properties of sediment suspensions and their implications." Journal of Hydraulic Research 32.4: 495-516. (1994).
Wang, Xiaobo, Norbert R. Morgenstern, and Dave H. Chan. "A model for geotechnical analysis of flow slides and debris flows." Canadian geotechnical journal 47.12: 1401-1414. (2010).