Abstract
A depth-averaged quasi single-phase mixture model is proposed for debris flows over inclined bed slopes based on the shallow water hydrosediment-morphodynamic theory with multi grain sizes. The stresses due to fluctuations are incorporated based on analogy to turbulent flows, as estimated using the depth-averaged k − ε turbulence model and a modification component. A fully conservative numerical algorithm, using wellbalanced slope limited centred scheme, is deployed to solve the governing equations. The present quasi single-phase model using four closure relationships for the bed shear stresses is evaluated against USGS experimental debris flow and compared with traditional quasi single-phase models and a recent physically enhanced two-phase model. It is found that the present quasi single-phase model performs much better than the traditional models, and is attractive in terms of computational cost while the two-phase model performs even better appreciably.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ancey C (2001) Debris flows and related phenomena. In: Balmforth NJ and Provenzale A (eds.), Geomorphological Fluid Mechanics. Springer, Heidelberg Germany. pp 528–547.
Armanini A, Capart H, Fraccarollo L, et al. (2005) Rheological stratification in experimental free-surface flows of granular–liquid mixtures. Journal of Fluid Mechanics 532: 269–319. https://doi.org/10.1017/S0022112005004283
Armanini A, Fraccarollo L, Rosatti G (2009) Two-dimensional simulation of debris flows in erodible channels. Computers & Geosciences 35(5): 993–1006. https://doi.org/10.1016/j.cageo.2007.11.008
Aureli F, Maranzoni A, Mignosa P, et al. (2008) A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography. Advances in Water Resources 31(7): 962–974. https://doi.org/10.1016/j.advwatres.2008.03.005
Balmforth NJ, Liu JJ (2004) Roll waves in mud. Journal of Fluid Mechanics 519: 33–54. https://doi.org/10.1017/s0022112004000801
Beeler NM, Tullis TE, Goldsby DL (2008) Constitutive relationships and physical basis of fault strength due to flash heating. Journal of Geophysical Research -Solid Earth 113(B1): B01401. https://doi.org/10.1029/2007JB004988
Berti M, Genevois R, Simoni A, et al. (1999) Field observations of a debris flow event in the Dolomites. Geomorphology 29(3-4): 265–274. https://doi.org/10.1016/s0169-555X(99)00018-5
Berzi D, Jenkins JT (2008) A theoretical analysis of free-surface flows of saturated granular–liquid mixtures. Journal of Fluid Mechanics 608: 393–410. https://doi.org/10.1017/S0022112008002401
Berzi D, Larcan E (2013) Flow resistance of inertial debris flows. Journal of Hydraulic Engineering 139(2): 187–194. https://doi.org/10.1061/(asce)hy.1943-7900.0000664
Berger C, McArdell BW, Schlunegger F (2011) Direct measurement of channel erosion by debris flows, Illgraben, Switzerland. Journal of Geophysical Research-Earth Surface 116(F1): F01002. https://doi.org/10.1029/2010jf001722
Bouchut F, Fernandez-Nieto ED, Mangeney A, et al. (2015) A two-phase shallow debris flow model with energy balance. ESAIM-Mathematical Modelling and Numerical Analysismodelisation Mathematique ET Analyse Numerique 49(1): 101–140. https://doi.org/10.1051/m2an/2014026
Brufau P, Garcia-Navarro P, Ghilardi P, et al. (2000) 1D mathematical modelling of debris flow. Journal of Hydraulic Research 38(6): 435–446. https://doi.org/10.1080/00221680009498297
Cao Z, Pender G, Wallis S, et al. (2004) Computational dambreak hydraulics over erodible sediment bed. Journal of Hydraulic Engineering 130(7): 689–703. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:7(689)
Cao Z, Li Z, Pender G, et al. (2012) Non-capacity or capacity model for fluvial sediment transport. Proceedings of the Institution of Civil Engineers -Water Management 165(4): 193–211. https://doi.org/10.1680/wama.10.00035
Cao Z, Hu P, Hu K, et al. (2015) Modeling roll waves with shallow water equations and turbulent closure. Journal of Hydraulic Research 53(2): 161–177. https://doi.org/10.1080/00221686.2014.950350
Cao Z, Hu P, Pender G, et al. (2016) Non-capacity transport of non-uniform bed load sediment in alluvial rivers. Journal of Mountain Science 13(3): 377–396. https://doi.org/10.1007/s11629-015-3710-8
Cao Z, Xia C, Pender G, et al. (2017) Shallow water hydrosediment-morphodynamic equations for fluvial processes. Journal of Hydraulic Engineering 143(5): 02517001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001281
Cardoso-Landa G (2009) Associated disasters to the debris flows. In: Starrett S (ed.), Proceedings of the 2009 World Environmental and Water Resources Congress, Kansas City, Missouri, USA. pp 5833–5844. https://doi.org/10.1061/41036(342)590
Cascini L, Cuomo S, Pastor M, et al. (2008) Geomechanical modelling of triggering mechanisms for rainfall-induced triangular shallow landslides of the flow type. In: Sanchez-Marre M, Bejar J, Comas J, et al. (eds), International Environmental Modelling and Software Society (iEMSs), Manno. pp 1516–1523.
Cascini L, Cuomo S, Pastor M (2013) Inception of debris avalanches: remarks on geomechanical modelling. Landslides 10(6): 701–711. https://doi.org/10.1007/s10346-012-0366-0
Chiang SH, Chang KT, Mondini AC, et al. (2012) Simulation of event-based landslides and debris flows at watershed level. Geomorphology 138: 306–318. https://doi.org/10.1016/j.geomorph.2011.09.016
Cozzolino L, Cimorelli L, Covelli C, et al. (2014) A novel numerical approach for 1D variable density shallow flows over uneven rigid and erodible beds. Journal of Hydraulic Engineering 140(3): 254–268. https://doi.org/10.1061/(asce)hy.1943-7900.0000821
Coussot P, Meunier M (1996) Recognition, classification and mechanical description of debris flows. Earth-Science Reviews 40(3-4): 209–227. https://doi.org/10.1016/0012-8252(95)00065-8
Cui YT, Paola C, Parker G (1996) Numerical simulation of aggradation and downstream fining. Journal of Hydraulic Research 34(2): 185–204. https://doi.org/10.1080/00221689609498496
Cui P, Zhou GGD, Zhu XH, et al. (2013) Scale amplification of natural debris flows caused by cascading landslide dam failures. Geomorphology 182: 173–189. https://doi.org/10.1016/j.geomorph.2012.11.009
D'Aniello A, Cozzolino L, Cimorelli L, et al. (2015) A numerical model for the simulation of debris flow triggering, propagation and arrest. Natural Hazards 75(2): 1403–1433. https://doi.org/10.1007/s11069-014-1389-8
Denlinger RP, Iverson RM (2001) Flow of variably fluidized granular masses across three-dimensional terrain: 2. Numerical predictions and experimental tests. Journal of Geophysical Research - Solid Earth 106(B1): 553–566. https://doi.org/10.1029/2000jb900330
Di Silvio G, Gregoretti C (1997) Gradually varied debris flow along a slope. In: Chen CL (ed), Debris-Flow Hazards Mitigation: Mechanics, Prediction & Assessment, San Francisco, California, USA. pp 767–776.
Di Cristo C, Iervolino M, Vacca A (2014) Applicability of Kinematic, Diffusion and Quasi-Steady dynamic wave models to shallow mud flows. Journal of Hydrologic Engineering, 19(5): 956–965. https://doi.org/10.1061/(asce)he.1943-5584.0000881
Di Cristo C, Iervolino M, Vacca A (2015) On the stability of gradually-varying mud flows in open channels. Meccanica 50(4): 963–979. https://doi.org/10.1007/s11012-014-0075-y
Di Cristo C, Greco M, Iervolino M, et al. (2016) Twodimensional two-phase depth-integrated model for transients over mobile bed. Journal of Hydraulic Engineering 142(2): 04015043. https://doi.org/10.1061/(asce)hy.1943-7900.0001024
Di Cristo C, Iervolino M, Vacca A (2018) Applicability of Kinematic and Diffusive models for mud-flows: a steady state analysis. Journal of Hydrology 559: 585–595. https://doi.org/10.1016/j.jhydrol.2018.02.016
Egashira S (2011) Prospects of debris flow studies from constitutive relations to governing equations. Journal of Disaster Research 6(3): 313–320. https://doi.org/10.20965/jdr.2011.p0313.
George DL, Iverson RM (2014) A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests. Proceedings of the Royal Society A -Mathematical Physical and Engineering Sciences 470(2170): 20130820. https://doi.org/10.1098/rspa.2013.0820
Gray JMNT, Wieland M, Hutter K (1999) Gravity-driven free surface flow of granular avalanches over complex basal topography. Proceedings of the Royal Society A -Mathematical Physical and Engineering Sciences 455(1985): 1841–1874. https://doi.org/10.1098/rspa.1999.0383
Greco M, Iervolino M, Leopardi A, et al. (2012) A two-phase model for fast geomorphic shallow flows. International Journal of Sediment Research 27(4): 409–425. https://doi.org/10.1016/s1001-6279(13)60001-3
Gregoretti C, Degetto M, Boreggio M (2016) GIS-based cell model for simulating debris flow runout on a fan. Journal of Hydrology 534: 326–340. https://doi.org/10.1016/j.jhydrol.2015.12.054
Guadagno FM, Forte R, Revellino P, et al. (2005) Some aspects of the initiation of debris avalanches in the Campania Region: the role of morphological slope discontinuities and the development of failure. Geomorphology 66: 237–254. https://doi.org/10.1016/j.geomorph.2004.09.024
Hirano M (1971) River bed degradation with armouring. Proceedings of Japan Society of Civil Engineers, Tokyo, Japan. pp 55–65. (In Japanese)
Hoey TB, Ferguson R (1994) Numerical simulation of downstream fining by selective transport in gravel bed rivers: Model development and illustration. Water Resources Research 30(7): 2251–2260. https://doi.org/10.1029/94wr00556
Hotta N, Tsunetaka H, Suzuki T (2015) Interaction between topographic conditions and entrainment rate in numerical simulations of debris flow. Journal of Mountain Science 12(6): 1383–1394. https://doi.org/10.1007/s11629-014-3352-2
Hu K, Pu L, Wang X (2016) Experimental study of entrainment behavior of debris flow over channel inflexion points. Journal of Mountain Science 13(6): 971–984. https://doi.org/10.1007/s11629-015-3749-6
Huang W, Cao Z, Carling P, et al. (2014) Coupled 2D hydrodynamic and sediment transport modeling of megaflood due to glacier dam-break in Altai Mountains, Southern Siberia. Journal of Mountain Science 11(6): 1442–1453. https://doi.org/10.1007/s11629-014-3032-2
Hunt B (1994) Newtonian Fluid Mechanics Treatment of Debris Flows and Avalanches. Journal of Hydraulic Engineering 120(12): 1350–1363. https://doi.org/10.1061/(asce)0733-9429(1994)120:12(1350)
Hutter K, Svendsen B, Rickenmann D (1994) Debris flow modeling: A review. Continuum Mechanics and Thermodynamics 8(1): 1–35. https://doi.org/10.1007/s001610050026
Hürlimann M, Rickenmann D, Graf C (2003) Field and monitoring data of debris-flow events in the Swiss Alps. Canadian Geotechnical Journal 40(1): 161–175. https://doi.org/10.1139/t02-087
Hürlimann M, McArdell BW, Rickli C (2015) Field and laboratory analysis of the runout characteristics of hillslope debris flows in Switzerland. Geomorphology 232: 20–32. https://doi.org/10.1016/j.geomorph.2014.11.030
Imaizumi F, Tsuchiya S, Ohsaka O (2016) Field observations of debris-flow initiation processes on sediment deposits in a previous deep-seated landslide site. Journal of Mountain Science 13(2): 213–222. https://doi.org/10.1007/s11629-015-3345-9
Imran J, Parker G, Locat J, et al. (2001) 1D numerical model of muddy subaqueous and subaerial debris flows. Journal of Hydraulic Engineering 127(11): 959–968. https://doi.org/10.1061/(asce)0733-9429(2001)127:11(959)
Iverson RM (1997) The physics of debris flows. Reviews of Geophysics 35(3): 245–296. https://doi.org/10.1029/97rg00426
Iverson RM (2000) Landslide triggering by rain infiltration. Water Resources Research 36(7):1897–1910. https://doi.org/10.1029/2000wr900090
Iverson RM, Logan M, LaHusen RG, et al. (2010) The perfect debris flow? Aggregated results from 28 large-scale experiments. Journal of Geophysical Research -Earth Surface 115(F3): F03005. https://doi.org/10.1029/2009jf001514
Iverson RM, Reid ME, Logan M, et al. (2011) Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nature Geoscience 4: 116–121. https://doi.org/10.1038/ngeo1040
Jeng CJ, Sue DZ (2016) Characteristics of ground motion and threshold values for colluvium slope displacement induced by heavy rainfall: a case study in northern Taiwan. Natural Hazards and Earth System Sciences 16(6):1309–1321. https://doi.org/10.5194/nhess-16-1309-2016
Laigle D, Coussot P (1997) Numerical modeling of mudflows. Journal of Hydraulic Engineering 123(7): 617–623. https://doi.org/10.1061/(asce)0733-9429(1997)123:7(617)
Li J, Cao Z, Hu K, et al. (2017a) A depth-averaged two-phase model for debris flows over fixed beds. International Journal of Sediment Research, in press. https://doi.org/10.1016/j.ijsrc.2017.06.003
Li J, Cao Z, Hu K, et al. (2017b) A depth-averaged two-phase model for debris flows over erodible beds. Earth Surface Processes and Landforms 43(4): 817–839. https://doi.org/10.1002/esp.4283
Liu K, Huang M (2006) Numerical simulation of debris flow with application on hazard area mapping. Computational Geosciences 10(2): 221–240. https://doi.org/10.1007/s10596-005-9020-4
Luca L, Hutter K, Kuo CY, et al. (2009) Two-layer models for shallow avalanche flows over arbitrary variable topography. International Journal of Advances in Engineering Sciences and Applied Mathematics 1(2-3): 99–121. https://doi.org/10.1007/s12572-010-0006-7
Lucas A, Mangeney A, Ampuero JP (2014) Frictional velocityweakening in landslides on Earth and on other planetary bodies. Nature Communications 2014 5:417. https://doi.org/10.1038/ncomms4417
Mangeney A, Roche O, Hungr O, et al. (2010) Erosion and mobility in granular collapse over sloping beds. Journal of Geophysical Research-Earth Surface 115(F3): F03040. https://doi.org/10.1029/2009jf001462
McArdell BW, Bartelt P, Kowalski J (2007) Field observations of basal forces and fluid pore pressure in a debris flow. Geophysical Research Letters 34(7): L07406. https://doi.org/10.1029/2006gl029183
Meng X, Wang Y (2016) Modelling and numerical simulation of two-phase debris flows. Acta Geotechnica 11(5): 1027–1045. https://doi.org/10.1007/s11440-015-0418-4
Meng X, Wang Y, Wang C, et al. (2017) Modeling of unsaturated granular flows by a two-layer approach. Acta Geotechnica 12(3): 677–701. https://doi.org/10.1007/s11440-016-0509-x
Ni H (2010) Turbulence simulation and application in modern hydraulics engineering. China Water Power Press, Beijing. (In Chinese)
O’Brien JS (1986) Physical processes, rheology and modeling of mudflows. PhD thesis, Colorado State University.
Okuda S, Suwa H, Okunishi K, et al. (1977) Synthetic observation on debris flow, Part 3. Observation at valley Kamikamihorizawa of Mt. Yakedake in 1976. Annuals of Disaster Prevention Research Institute, Kyoto University 20B-1: 237–263. (In Japanese)
Ouyang C, He S, Tang C (2015) Numerical analysis of dynamics of debris flow over erodible beds in Wenchuan earthquakeinduced area. Engineering Geology 194: 62–72. https://doi.org/10.1016/j.enggeo.2014.07.012
Pailha M, Pouliquen O (2009) A two-phase flow description of the initiation of underwater granular avalanches. Journal of Fluid Mechanics 633: 115–135. https://doi.org/10.1017/S0022112009007460
Parker G (1991) Selective sorting and abrasion of river gravel. I: Theory. Journal of Hydraulic Engineering 117(2): 131–149. https://doi.org/10.1061/(asce)0733-9429(1991)117:2(131)
Parsons JD, Whipple KX, Simoni A (2001) Experimental Study of the Grain-Flow, Fluid-Mud Transition in Debris Flows. Journal of Geology 109(4): 427–447. https://doi.org/10.1086/320798
Pelanti M, Bouchut F, Mangeney A (2008) A Roe-Type scheme for two-phase shallow granular flows over variable topography. ESAIM-Mathematical Modelling and Numerical Analysis-modelisation Mathematique ET Analyse Numerique 42(5): 851–885. https://doi.org/10.1051/m2an:2008029
Pitman EB, Le L (2005) A two-fluid model for avalanche and debris flows. Philosophical Transacitions of the Royal Society A-Mathematical Physical and Engineering Sciences 363(1832): 1573–1601. https://doi.org/10.1098/rsta.2005.1596
Pudasaini SP, Wang Y, Hutter K (2005) Modelling debris flows down general channels. Natural Hazards and Earth System Science 5(6): 799–819. https://doi.org/10.5194/nhess-5-799-2005
Pudasaini SP (2012) A general two-phase debris flow model. Journal of Geophysical Research-Earth Surface 117(F3): F03010. https://doi.org/10.1029/2011JF002186
Rastogi AK, Rodi W (1978) Predictions of heat and mass transfer in open channels. Journal of the Hydraulics Division 104(3): 397–420.
Rengers FK, McGuire LA, Kean JW, et al. (2016) Model simulations of flood and debris flow timing in steep catchments after wildfire. Water Resources Research 52(8): 6041–6061. https://doi.org/10.1002/2015WR018176
Rice RJ (2006) Heating and weakening of faults during earthquake slip. Journal of Geophysical Research -Solid Earth 111(B5): B05311. https://doi.org/10.1029/2005JB004006
Richardson JF, Zaki WN (1954) Sedimentation and fluidisation: Part 1. Chemical Engineering Research and Design 75: s82–s99. https://doi.org/10.1016/S0263-8762(97)80006-8
Rickenmann D, Zimmermann M (1993) The 1987 debris flows in Switzerland: documentation and analysis. Geomorphology 8(2-3): 175–189. https://doi.org/10.1016/0169-555X(93)90036-2
Rosatti G, Begnudelli L (2013) Two-dimensional simulation of debris flows over mobile bed: Enhancing the TRENT2D model by using a well-balanced Generalized Roe-type solver. Computers & Fluids 71: 179–195. https://doi.org/10.1016/j.compfluid.2012.10.006
Rodi W (1993) Turbulence models and their applications in Hydraulics-a State of the Art Review, 3rd edn. IAHR Monograph, Balkema, Rotterdam, The Netherlands.
Santi PM, de Wolfe VG, Higgins JD, et al. (2008) Sources of debris flow material in burned areas. Geomorphology 96(3-4): 310–321. https://doi.org/10.1016/j.geomorph.2007.02.022
Sarno L, Carravetta A, Martino R, et al. (2013) Pressure coefficient in dam-break flows of dry granular matter. Journal of Hydraulic Engineering 139 (11): 1126–1133. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000772
Sarno L, Carravetta A, Martino R, et al. (2014) A two-layer depth-averaged approach to describe the regime stratification in collapses of dry granular columns. Physics of Fluids 26(10): 103303. https://doi.org/10.1063/1.4898563
Sarno L, Carravetta A, Martino R, et al. (2017) Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models. Advances in Water Resources 100: 183–198. https://doi.org/10.1016/j.advwatres.2016.12.014
Savage SB, Hutter K (1989) The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199: 177–215. https://doi.org/10.1017/s0022112089000340
Shieh CL, Jan CD, Tsai YF (1996) A numerical simulation of debris flow and its application. Natural Hazards 13(1): 39–54. https://doi.org/10.1007/bf00156505
Takahashi T (1991) Debris Flow. Balkema, Rotterdam.
Takahashi T (2007) Debris Flow Mechanics, Prediction and Countermeasures. Taylor & Francis, London.
Toro-Escobar C, Parker G, Paola C (1996) Transfer function for the deposition of poorly sorted gravel in response to streambed aggradation. Journal of Hydraulic Research 34(1): 35–53. https://doi.org/10.1080/00221689609498763
Wei FQ, Xie H, Lopez JL, et al. (2000) Extraordinarily serious debris flow disasters in Venezuela in 1999 Mountain Research 18(6): 580–582. (In Chinese)
Wu W, Wang SSY, Jia Y (2000) Nonuniform sediment transport in alluvial rivers. Journal of Hydraulic Research 38(6): 427–434. https://doi.org/10.1080/00221680009498296
Wu W, Wang SSY (2008) One-dimensional explicit finitevolume model for sediment transport. Journal of Hydraulic Research 46(1): 87–98. https://doi.org/10.1080/00221686.2008.9521846
Xia C, Cao Z, Pender G, et al. (2017) Numerical Algorithms for Solving Shallow Water Hydro-Sediment-Morphodynamic Equations. Engineering Computations 34(8): 28366–286. https://doi.org/10.1108/ec-01-2016-0026
Xia J, Lin B, Falconer RA, et al. (2010) Modelling dam-break flows over mobile beds using a 2D coupled approach. Advances in Water Resources 33(2): 171–183. https://doi.org/10.1016/j.advwatres.2009.11.004
Zanuttigh B, Lamberti A (2007) Instability and surge development in debris flows. Reviews of Geophysics 45(3): RG3006. https://doi.org/10.1029/2005rg000175
Zhang R, Xie J (1993) Sedimentation research in Chinasystematic selections. China Water and Power Press, Beijing, China. (In Chinese)
Zhang S, Duan J (2011) 1D finite volume model of unsteady flow over mobile bed. Journal of Hydrology 405(1-2): 57–68. https://doi.org/10.1016/j.jhydrol.2011.05.010
Acknowledgments
The work reported in this manuscript is funded by Natural Science Foundation of China (Grants Nos. 51279144 and 11432015).
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Xia, Cc., Li, J., Cao, Zx. et al. A quasi single-phase model for debris flows and its comparison with a two-phase model. J. Mt. Sci. 15, 1071–1089 (2018). https://doi.org/10.1007/s11629-018-4886-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11629-018-4886-5