臺灣博碩士論文加值系統

台灣地區山坡地及高山林地約佔全島面積四分之三，地勢可謂相當陡峻，因此大多數之河川呈現源短流急之特性，且雨量豐沛、地質脆弱，造成河川含砂量特別高。因此崩塌、土石流等山地災害頻傳，造成嚴重的生命財產損失，且崩塌土體及高含砂水流堵塞河道形成堰塞湖之事件也時有所聞。因此崩塌土體或高含砂水流挾帶大量泥砂入匯主河河道，對入匯口附近之水流形態造成影響，並進而引起當地河床突變，甚至於主河下游河段之河相亦可能發生改變。由於高含砂水流入匯主流所形成之交匯行為在台灣山區是十分常見的現象，但是因為其交匯機制牽涉到太多複雜之因素，致使相關文獻十分有限。
本研究分別由三個主軸，包括交匯型態之分類、室內水槽實驗及數值模擬等，對此課題進行探討。首先蒐集前人相關研究及配合現地調查，以基本之泥砂運移物理概念建立台灣地區河岸崩塌及高含砂支流與主河水流交匯模式之初步分類及型態描述。交匯型態主要可分為完全堵河與不完全堵河兩大類：其中完全堵河以崩塌造成的居多，可分為六種型態；而不完全堵河則包括崩塌與土石流支流入匯等情形，根據其相對於主河之作用強弱可分為四種類型。文中並舉出數個實例應用於此分類型態，包括土石流與主河交匯之例及河岸崩塌阻斷主河形成堰塞湖之例，以說明其交匯現象，增加對此機制更深一層之認識。
接著利用數位影像處理技術進行室內渠槽試驗，主要工作為探討高含砂支流入匯主河之交匯行為，其量測方法確實可行且已有初步成果。實驗量測主要可分為兩大部份：一是針對主支流交匯時流場之量測，係採用Voronoï影像追蹤法，於試驗區放置示踨球，將拍攝之交匯影像處理後取得流場分析；另一是使用雷射光筆投射於交匯後形成之泥砂堆積體，以擷取之各剖面經由座標轉換得出數位地形資料，所獲得之相關結果均可作為數值模擬之參考。
最後則利用二層流體之淺水流方程建立可模擬交匯現象之數值模式，以有限體積法之顯式均勻網格離散控制方程式，數值方法以HLL型數值格式為主要架構，利用lateralisation of momentum flux來處理坡度效應，最後再使用Strang splitting的方式計算含有摩擦力之源項部份。本研究已成功地建立一維及二維定床二層流體之數值模式，可模擬高含砂支流入匯主河時深度及流場之變化。冀望透過本研究能增進對此現象的了解，並可於未來進一步探討泥砂在主河水流中堆積或沖刷之過程及對河床變形之演變，作為日後研究的基礎或工程規劃設計上能有所幫助。

This study examines various ways in which flow slides and river currents interact, including blocking of rivers due to either accumulated debris or to the formation of landslide dams across the channel width. In other situations, local narrowing of a channel can occur due to partial invasion by a debris fan. At the outlets of debris flow gullies, thick deposits may be left for water currents to slowly transport downstream. The study is composed of three parts: (1) systematic field observations; (2) laboratory experiments; (3) computational simulations. The purpose of this work is to study this confluence behavior of a hyperconcentrated tributary inflowing the main river.
In the first part, it collects numerous previous studies and field investigations in order to study confluence modes of debris slides and river flows in Taiwan. A preliminary classification is established according to the basic concepts of sediment transport. We have analyzed several examples further and applied them to our catalogue to illustrate the classification method in detail. The confluence mechanism can be realized through this classification but it still needs more study, including of experimental research, as well as field investigation to better establish the classification framework.
In the second part, it uses digital image processing to survey the confluence behavior of a tributary with hyperconcentrated flow entering the main river. The experiment has two parts: in the first, digital terrain data were computed via coordinate transformation from profiles extracted by laserlines; in the second, velocity fields were obtained by using Voronoï imaging method to analyze the images through low-pass and high-pass filters when trace-particles were added. The measurement approach is described and preliminary results are presented. Through the discussion of alluvial fan morphology, we can better understand the interaction of this mechanism.
Finally, we proposed a numerical scheme to simulate the confluence phenomenon by using two-layer shallow water equations. The rheology behavior of mudflow or debris flow was regarded as the Herschel and Bulkley or Bingham fluid. Thus the shear stress on rigid bed can be derived from the constitutive equation. The computational approach uses the HLL scheme as a basic building block, treats the bottom slope by lateralizing the momentum flux, then refines the scheme using the Strang splitting to deal with the frictional source term. This study successfully set up 1D and 2D two-layer shallow water computations on rigid bed. The numerical model can describe the variety of depths and velocities, including water and mud, when the hyperconcentrated tributary flows into the main river. The results in this study will be helpful for advanced research sequentially and design or plan of hydraulic engineering structures.

TABLE OF CONTENTS
Acknowledgements I
Chinese abstract II
Chinese summary IV
English abstract VII
Table of contents IX
List of figures XIII
List of tables XX
List of english-chinese locations XXI
Chapter 1 1
Introduction 1
1.1 Motives 1
1.2 Objectives 1
1.3 Overview of dissertation 2
References 5
Chapter 2 6
Classification of confluence mode between debris slides and river flows in Taiwan 6
2.1 Introduction 6
2.2 Landslide dam events in Taiwan 7
2.3 Classification of confluence mode 13
2.3.1 Entirely blocking river 15
2.3.2 Partially blocking river 21
2.3.3 The condition of entirely blocking river 21
2.4 Case study 23
2.4.1 Confluence of Chiacholiao Creek and Chinshui Creek 23
2.4.2 Landslide dam in Shinwulu Creek 24
2.4.3 Other cases 28
2.5 Discussion 32
2.5.1 Essentials of complete landslide-damming river 32
2.5.2 Minimum volume of the entire blockage 33
2.5.3 Erosion phase of landslide deposit 34
2.6 Concluding remarks 36
References 37
Chapter 3 40
Experiments of alluvial fans formed by hyperconcentrated tributaries 40
3.1 Introduction 40
3.2 Experiments 41
3.2.1 Experimental device 41
3.2.2 Methods of measurement 43
3.2.2.1 Survey of topography 43
3.2.2.2 Measurement of velocity field 46
3.2.3 Experimental materials and conditions 49
3.3 Results 52
3.3.1 Morphology of alluvial fan 52
3.3.2 Results of velocity field 55
3.4 Discussion 59
3.4.1 Centroids of alluvial fans 59
3.4.2 Shapes of alluvial fan 60
3.5 Concluding remarks 65
References 65
Chapter 4 67
Two-layer shallow water computation of mud flow intrusion into quiescent water 67
4.1 Introduction 67
4.2 Governing equations and physical description 70
4.3 Computational scheme 74
4.3.1 Basic HLL scheme 74
4.3.2 Continuity equations 76
4.3.3 Lateralised momentum flux 77
4.3.4 Frictional source term 79
4.4 Single layer model validation 82
4.4.1 Single water layer 82
4.4.2 Single mud layer 88
4.4.3 Sensitivity analysis 89
4.5 Two-layer model validation 93
4.5.1 Superposed layers of identical density 93
4.5.2 Internal hydraulic jumps 98
4.6 Intrusion of mud surges into quiescent water 100
4.7 Concluding remarks 108
References 108
Chapter 5 112
Two-dimensional numerical model of two-layer shallow water equations 112
5.1 Introduction 112
5.2 Governing equations 113
5.3 Computational scheme 115
5.4 Numerical modeling results 121
5.4.1 2D partial breach modeling for top layer 121
5.4.2 Deposition of mud flow on 2D plane 126
5.4.3 Numerical simulation of confluence 131
5.5 Concluding remarks 143
References 144
Chapter 6 146
Conclusions 146
Appendixes 149
A. Derivation of governing equations 149
A.1 Continuity equations 149
A.2 Momentum equations 150
B. Rheological relationship of Herschel and Bulkley model 152
C. Bottom friction of Bingham fluid for two-layer flows 157
References 159

Chapter 1
Chien, N. and Z.H. Wan (1991), Mechanics of sediment transport, Science Press. (in Chinese)
Jan, C.D. (2000), Introduction to debris flow, Scientific & Technical Publishing Co., Ltd. (in Chinese)
O’Brien, J.S. (2003), FLO-2D users manual, FLO Engineering, Inc.
Chapter 2
Bookhagen, B., Haselton, K. and M.H. Trauth (2001), “Hydrological modeling of a Pleistocene landslide-dammed lake in the Santa Maria Basin, NW Argentina,” Palaeogeography, Palaeoclimatology, Palaeoecology, 169: 113-127.
Chai, H.J., Liu, H.C. and Z.Y. Zhang (1996), “The main conditions of landslide dam,” Journal of Geological Hazards and Environment Preservation, 7(1): 41-46. (in Chinese)
Chai, H.J., Liu, H.C. and Z.Y. Zhang (1998), “Study on the categories of landslide-damming of rivers and their characteristics,” Journal of Chengdu University of Technology, 25(3): 411-416. (in Chinese)
Chen, D.M., Wang, Z.Y. and Y. He (2002), “Experimental study on the fluvial process of debris flow discharging into a river,” Journal of Sediment Research, June 2002(3): 22-28. (in Chinese)
Chen, S.C. (1999), “Failure mechanism and disaster mitigation on landslide-dammed lakes,” Journal of Chinese Soil and Water Conservation, 30(4): 299-311. (in Chinese)
Chen, S.C. (2000), “From landslide-dammed lake in Dongpurui Creek review series of landslide-dammed lakes in Chichi Earthquake,” Soil & Water Newsletter, 44: 1-6. (in Chinese)
Chen, S.C. and C.M. Wu (2002), “Effects on concentration on hillslope development,” Journal of Chinese Soil and Water Conservation, 33(2): 141-150. (in Chinese)
Chen, S.C. and S.H. Peng (2003a), “Confluence of debris slides and river flows in Taiwan,” In: Lee CF, Tham LG (eds) Proceedings of the international conference on slope engineering, Hongkong, 8-10 December 2003, pp. 757-762.
Chen, S.C. and S.H. Peng (2003b), “Experiment of confluence between main river and tributary by applying digital image processing,” Journal of Chinese Soil and Water Conservation, 34(2): 195-205. (in Chinese)
Chow, V.T., Maidment, D.R. and L.W. Mays (1988), Applied hydrology, McGraw-Hill.
Costa, J.E. and R.L. Schuster (1988), “The formation and failure of natural dams,” Geological Society of America Bulletin, 100: 1054-1068.
Liang, Z.Y., Liu, X., Xu, Y.N. and Z.C. Sui (2001), “River channel changes due to convergence of debris flow,” Journal of Natural Disasters, 10(1): 45-50. (in Chinese)
Reid, L.M. and T. Dunne (1996), Rapid evaluation of sediment budgets, CATENA VERLAG GMBH, Germany.
Schuster, R.L. (2000), “Outburst debris-flows from failure of natural dams,” In: Wieczorek GF, Naeser ND (eds) debris-flow hazards mitigation: mechanics, prediction, and assessment: proceedings of the second international conference on debris-flow hazards mitigation, Taipei, 16-18 August 2000, pp. 29-42.
Schuster, R.L. (eds) (1986), Landslide Dams, Processes, Risk and Mitigation, ASCE, New York.
Schuster, R.L. and J.E. Costa (1986), “A perspective on landslide dams,” In: Schuster RL (eds) Landslide Dams, Processes, Risk and Mitigation, ASCE, pp.1-20.
Schuster, R.L. and L.M. Highland (2003), “Impact of landslides and innovative landslide-mitigation measures on the natural environment,” In: Lee CF, Tham LG (eds) Proceedings of the international conference on slope engineering, Hongkong, 8-10 December 2003, pp. 50-95.
Smith, D.G. and C.M. Pearce (2002), “Ice jam-caused fluvial gullies and scour holes on northern river flood plains,” Geomorphology, 42: 85-95.
Takahashi, T. (1991), Debris flow, Published for the International Association for Hydraulic Research by A. A. Balkema, Rotterdam, Netherlands.
Tang, B.X. (eds) (2000), Debris flows in China, Institute of Mountain Hazards & Environment, Chinese Academy of Sciences, Beijing. (in Chinese)
Trauth, M.H. and M.R. Strecker (1999), “Formation of landslide-dammed lakes during a wet period between 40,000 and 25,000 yr B.P. in northwestern Argentina,” Palaeogeography, Palaeoclimatology, Palaeoecology, 153: 277-287.
Water Conservancy Agency (1999), September 21 Chichi earthquake Tsaoling landslide treatment report, Report, Ministry of Economic Affairs, Taiwan. (in Chinese)
Water Resources Planning Institute (2002), Study on the disaster mitigation strategies for landslide dams, Research Report, Water Resources Agency, MOEA, Taiwan. (in Chinese)
Zhu, P.Y., Cheng, Z.L. and Y. You (2000), “Research on causes of river blocking by sediment delivery of Peilonggou Gully debris flow in the Sichuan-Xizang Highway,” Journal of Natural Disasters, 9(1): 80-83. (in Chinese)
Chapter 3
Capart, H., Young, D.L. and Y. Zech (2002), “Voronoï imaging methods for the measurement of granular flows,” Experiments in Fluids, 32: 121-135.
Chen, D.M. (2000), Mechanism of confluence between debris flow and the main river, Ph.D. thesis, China Inst. of Water Resources and Hydropower Research, China. (in Chinese)
Chen, S.C. (1999), “Failure mechanism and disaster mitigation on landslide-dammed lakes,” J. Chin. Soil Water Conserv., 30(4): 299-311. (in Chinese)
Chen, S.C. and S.H. Peng (2003a), “Confluence of debris slides and river flows in Taiwan,” In C.F. Lee and L.G. Tham (eds), Proceedings of the International Conference on Slope Engineering: 757-762. Hongkong: University of Hong Kong.
Chen, S.C. and S.H. Peng (2003b), “Experiment of confluence between main river and tributary by applying digital image processing,” J. Chin. Soil Water Conserv., 34(2): 195-205. (in Chinese)
Hsu, C.C., Lee, W.J. and C.H. Chang (1998), “Subcritical open-channel junction flow,” J. of Hydraulic Engineering, ASCE, 124(8): 847-855.
Jähne, B. (2002), Digital image processing, Berlin: Springer.
Kao, P.S. (2003), The effects in main river morphology from hyperconcentrated tributary flow, MSc thesis, Dept. of Soil and Water Conservation, National Chung-Hsing University, Taiwan. (in Chinese)
Ni, W.J. (2004), Small scale sapping experiment and topography measurement by laser scan, MSc thesis, Dept. of Civil Engineering and Hydrotech Research Institute, National Taiwan University. (in preparation)
Parker, G. et al. (1998a), “Alluvial fans formed by channelized fluvial and sheet flow. I: theory,” J. of Hydraulic Engineering, ASCE, 124(10): 985-995.
Parker, G. et al. (1998b), “Alluvial fans formed by channelized fluvial and sheet flow. II: application,” J. of Hydraulic Engineering, ASCE, 124(10): 996-1004.
Spinewine, B., Capart, H., Larcher, M. and Y. Zech (2003), “Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows,” Experiments in Fluids, 34: 227-241.
Tsai, Y.F. and C.L. Shieh (1997), “Experimental and numerical studies on the morphological similarity of debris-flow fans,” Journal of the Chinese Institute of Engineers, 20(6): 629-642.
Zhu, P.Y., Cheng, Z.L. and Y. You (2000), “Research on causes of river blocking by sediment delivery of Peilonggou Gully debris flow in the Sichuan-Xizang Highway,” Journal of Natural Disasters, 9(1): 80-83. (in Chinese)
Chapter 4
Abbott, M.B. (1979), Computational hydraulics: elements of the theory of free surface flows, Pitman.
Capart, H. and D.L. Young (2002), “Two-layer shallow water computations of torrential geomorphic flows,” In Proceedings of the International Conference on Fluvial Hydraulics, Bousmar & Zech (eds), pp. 1003-1012.
Castro, M., Macias, J. and C. Pares (2001), “A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system,” Math. Modell. and Numer. Anal., 35(1): 107-127.
Chen, S.C. (1999), “Failure mechanism and disaster mitigation on landslide-dammed lakes,” J. Chin. Soil Water Conserv., 30(4): 299-311. (in Chinese)
Chen, S.C. and S.H. Peng (2003a), “Confluence of debris slides and river flows in Taiwan,” In Proceedings of the International Conference on Slope Engineering, Hongkong, China, pp. 757-762.
Chen, S.C. and S.H. Peng (2003b), “Experiment of confluence between main river and tributary by applying digital image processing,” J. Chin. Soil Water Conserv., 34(2): 195-205. (in Chinese)
Chien, N. and Z.H. Wan (1991), Mechanics of sediment transport, Science Press. (in Chinese)
Fraccarollo, L., and E.F. Toro (1995), “Experimental and numerical assessment of the shallow water model for two-dimensional dam-break type problems,” J. Hydr. Res., 33(6): 843-864.
Fraccarollo, L., Capart, H. and Y. Zech (2003), “A Godunov method for the computation of erosional shallow water transients,” Int. J. Numer. Meth. Fluids, 41: 951-976.
Gerald, C.F. and P.O. Wheatley (1999), Applied numerical analysis, Addison Wesley Longman.
Harten, A., Lax, P.D. and B. van Leer (1983), “On upstream difference and Godunov-type schemes for hyperbolic conservation laws,” SIAM Review, 25: 35-61.
Hsu, C.T. and K.C. Yeh (2002), “Iterative explicit simulation of 1D surges and dam-break flows,” Int. J. Numer. Meth. Fluids, 38: 647-675.
Huang, X. and M.H. Garcia (1997), “A perturbation solution for Bingham-plastic mudflows,” J. Hydr. Engrg., ASCE, 123(11): 986-994.
Huang, X. and M.H. Garcia (1998), “A Herschel-Bulkley model for mud flow down a slope,” J. Fluid Mech., 374: 305-333.
Imran, J., Parker, G., Locat, J. and H. Lee (2001), “A 1-D numerical model of muddy subaqueous and subaerial debris flows,” J. Hydr. Engrg., ASCE, 127(11): 959-968.
Jin, M. and D.L. Fread (1999), “1D modeling of mud/debris unsteady flows,” J. of Hydraulic Engineering, ASCE, 125(8): 827-834.
Laigle, D. and P. Coussot (1997), “Numerical modeling of mudflows,” J. Hydr. Engrg., ASCE, 123(7): 617-623.
Leveque, R.J. (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge Univ. Press.
Liu, K.F. and C.C. Mei (1989), “Slow spreading of a sheet of Bingham fluid on an inclined plane,” J. Fluid Mech., 207: 505-529.
Liu, K.F. and M.C. Huang (2002), “The numerical simulation of debris flows and its application in Shen-Mu Village,” J. Chin. Soil Water Conserv., 33(3): 215-221. (in Chinese)
Montgomery, P.J. and T.B. Moodie (2003), “Generalization of a relaxation scheme for systems of forced nonlinear hyperbolic conservation laws with spatially dependent flux functions,” Studies in Applied Mathematics, 110(1): 1-19.
O’Brien, J.S., Julien, P.Y. and W.T. Fullerton (1993), “Two-dimensional water flood and mudflow simulation,” J. Hydr. Engrg., ASCE, 119(2): 244-261.
Salmon, R. (2002), “Numerical solution of the two-layer shallow water equations with bottom topography,” Journal of Marine Research, 60(4): 605-638.
Saurel, R. and R. Abgrall (1999), “A multiphase Godunov method for compressible multifluid and multiphase flows,” J. Comput. Phys., 150: 425-467.
Stoker, J.J. (1957), Water waves, Interscience.
Toro, E.F. (1999), Riemann solvers and numerical methods for fluid dynamics: a practical introduction, 2nd ed., Springer, Berlin.
Wang, Z.L. and H.T. Shen (1999), “Lagrangian simulation of one-dimensional dam-break flow,” J. Hydr. Engrg., ASCE, 125(11): 1217-1221.
Chapter 5
Capart, H. and D.L. Young (2002), “Two-layer shallow water computations of torrential geomorphic flows,” In Proceedings of the International Conference on Fluvial Hydraulics, Bousmar & Zech (eds), pp. 1003-1012.
Chaudhry, M.H. (1993), Open-Channel Flow, Prentice-Hall, Inc.
Fennema, R.J. and M.H. Chaudhry (1989), “Implicit methods for two-dimensional unsteady free-surface flows,” J. Hydr. Res., 27(3): 321-332.
Fennema, R.J. and M.H. Chaudhry (1990), “Explicit methods for 2-D transient free-surface flows,” J. Hydr. Engrg., ASCE, 116(8): 1013-1034.
Fraccarollo, L., Capart, H. and Y. Zech (2003), “A Godunov method for the computation of erosional shallow water transients,” Int. J. Numer. Meth. Fluids, 41: 951-976.
Harten, A., Lax, P.D. and B. van Leer (1983), “On upstream difference and Godunov-type schemes for hyperbolic conservation laws,” SIAM Review, 25: 35-61.
Jeyapalan, J.K., Duncan, J.M. and H.B. Seed (1983), “Investigation of flow failures of tailings dams,” J. Hydr. Engrg., ASCE, 109(2): 172-189.
Julien, P.Y. and Y. Lan (1991), “Rheology of hyperconcentrations,” J. Hydr. Engrg., ASCE, 117(3): 346-353.
Liu, K.F. and M.C. Huang (2002), “The numerical simulation of debris flows and its application in Shen-Mu Village,” J. Chin. Soil Water Conserv., 33(3): 215-221. (in Chinese)
O’Brien, J.S., Julien, P.Y. and W.T. Fullerton (1993), “Two-dimensional water flood and mudflow simulation,” J. Hydr. Engrg., ASCE, 119(2): 244-261.
Pastor, M., Quecedo, M., González, E., Herreros, M.I., Fernádez Merodo, J.A. and P. Mira (2004), “Simple approximation to bottom friction for Bingham fluid depth integrated models,” J. Hydr. Engrg., ASCE, 130(2): 149-155.
Saurel, R. and R. Abgrall (1999), “A multiphase Godunov method for compressible multifluid and multiphase flows,” J. Comput. Phys., 150: 425-467.
Tsai, Y.F. and C.L. Shieh (1997), “Experimental and numerical studies on the morphological similarity of debris-flow fans,” Journal of the Chinese Institute of Engineers, 20(6): 629-642.
Young, D.L. and H. Capart (2001), Development and validation of a geomorphic flood routing framework, Research Report, Council of Agriculture Executive Yuan, Taiwan, ROC.
Zhao, D.H., Shen, H.W., Tabios III, G.Q., Lai, J.S. and W.Y. Tan (1994), “Finite-volume two-dimensional unsteady-flow model for river basins,” J. Hydr. Engrg., ASCE, 120(7): 863-883.
Zhao, D.H., Tabios III, G.Q. and H.W. Shen (1995), RBFVM-2D model, river basin two-dimensional flow model using finite volume method: program documentation, University of California, Berkeley, California USA.
Appendixes
Abbott, M.B. (1979), Computational hydraulics: elements of the theory of free surface flows, Pitman.
Bagnold, R.A. (1954), “Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear,” Proc. R. Soc. London, Ser. A, 225: 49-63.
Batchelor, G.K. and J.T. Green (1972), “The determination of the bulk stress in a suspension of spherical particles to order c2,” J. Fluid Mech., 56, 375.
Chien, N. and Z.H. Wan (1991), Mechanics of sediment transport, Science Press. (in Chinese)
Chong, J.S., Christiansen, E.B. and A.D. Baer (1971), “Rheology of concentrated suspension,” J. Appl. Polymer Sci., 15: 2007-2021.
Coussot, P. (1994), “Steady, laminar, flow of concentrated mud suspensions in open channel,” J. Hydr. Res., 32(4): 535-559.
Einstein, H.A. and N. Chien (1956), “Effect of heavy sediment concentration near the bed on the velocity and sediment distribution,” Missouri River Div. Sediment Series, No. 8, U.S. Corps of Engrs., pp. 76.
Jan, C.D. (2000), Introduction to debris flow, Scientific & Technical Publishing Co., Ltd. (in Chinese)
Krieger, I.M. and T.J. Doughery (1986), “A mechanism for non-Newtonian flow in suspensions of rigid spheres,” Transactions of the Society of Rheology, 3: 137-152.
Krone, R.B. (1986), “The significance of aggregate properties to transport processes,” Lecture Note on Estuarine Cohesive Sediment Dynamics, ed. By A. J. Mehta, pp. 66-84.
O’Brien, J.S. (2003), FLO-2D users manual, FLO Engineering, Inc.
Pastor, M., Quecedo, M., González, E., Herreros, M.I., Fernádez Merodo, J.A. and P. Mira (2004), “Simple approximation to bottom friction for Bingham fluid depth integrated models,” J. Hydr. Engrg., ASCE, 130(2): 149-155.
Takahashi, T. (1991), Debris flow, Published for the International Association for Hydraulic Research by A. A. Balkema, Rotterdam, Netherlands.
Thomas, D.G. (1965), “Transport characteristics of suspensions, Pt. VIII a note on the viscosity of Newtonian suspensions of uniform spherical particles,” J. Colloid Sci., 20: 267-277.