Abstract
To simulate debris flow run-out, the governing equations for free-surface shallow flow are corrected by setting the basal flow resistance coefficients with the quadratic rheological friction model. A well-balanced numerical scheme is developed for its run-out simulation over irregular topography. A linear reconstruction is adopted for improving the spatial accuracy of the numerical scheme. Considering the complex friction terms of governing equations of debris flow, they are estimated with a full implicit scheme for ensuring stability of the numerical scheme. The validity check of run-out simulation is implemented based on general knowledge of fluid, and a well-studied case occurred in the Xiezi Gully in Yingxiu Town, Sichuan Province of China. For practical purpose, the present numerical scheme is used for run-out prediction of debris flow in Xiaojia Gully of Panzhihua City, Sichuan Province of China. Our work aims to present a well-balanced numerical scheme for debris flow run-out simulation prediction, which can be applied quite conveniently to solve other kinds of debris flow models and helpful to promote the development in debris flow numerical calculation.
Similar content being viewed by others
References
Abancó C, Hürlimann M (2014) Estimate of the debris-flow entrainment using field and topographical data. Nat Hazards 71(1):363–383
Bermudez A, Vazquez ME (1994) Upwind methods for hyperbolic conservation laws with source terms. Comput Fluids 23:1049–1071
Bisantino T, Fischer P, Gentile F, Liuzzi GT (2010) Rheological properties and debris-flow modeling in a southern Italy watershed. WIT Trans Eng Sci 67:237–248
Chen HX, Zhang LM (2015) EDDA: integrated simulation of debris flow erosion, deposition and property changes. Geosci Model Dev 8:829–844
Chen HX, Zhang LM, Zhang S, Xiang B, Wang XF (2013) Hybrid simulation of the initiation and runout characteristics of a catastrophic debris flow. J Mt Sci 10(2):219–232
Chen HX, Zhang LM, Gao L, Yuan Q, Lu T, Xiang B, Zhang WL (2017) Simulation of interactions among multiple debris flows. Landslides 14(2):1–21
Cuomo S, Pastor M, Cascini L, Castorino GC (2014) Interplay of rheology and entrainment in debris avalanches: a numerical study. Can Geotech J 51(11):1318–1330
Cuomo S, Sala MD, Novità A (2015) Physically based modelling of soil erosion induced by rainfall in small mountain basins. Geomorphology 243:106–115
Frank F, Mcardell BW, Huggel C, Vieli A (2015) The importance of entrainment and bulking on debris flow runout modeling: examples from the Swiss Alps. Nat Hazards Earth Syst Sci 15(11):2569–2583
George DL, Iverson RM (2014) A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests. Proc R Soc A Math Phys Eng Sci 470(2170):20130820–20130820
Gregoretti C, Degetto M, Boreggio M (2016) GIS-based cell model for simulating debris flow runout on a fan. J Hydrol 534:326–340
Hu K, Mingham CG, Causon DM (2000) Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations. Coast Eng 41(4):433–465
Hungr O (1995) A model for the runout analysis of rapid flow slides, debris flows and avalanches. Can Geotech J 32:610–623
Iverson RM (1997) The physics of debris flows. Rev Geophys 35:245–296
Iverson RM, George DL (2014) A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis. Proc R Soc A Math Phys Eng Sci 470(2170):20130819–20130819
Iverson RM, Reid ME, Logan M, Lahusen RG, Godt JW, Griswold JP (2011) Positive feedback and momentum growth during debris-flow entrainment of wet bed sediment. Nat Geosci 4:116–121
LeVeque RJ (2002) Finite volume methods for hyperbolic problems. Cambridge University Press, Cambridge
Liang QH (2010) Flood simulation using a well-balanced shallow flow model. J Hydraul Eng 136(9):669–675
Liang Q, Borthwick AGL (2009) Adaptive quadtree simulation of shallow flows with wet–dry fronts over complex topography. Comput Fluids 38(2):221–234
Liang Q, Marche F (2009) Numerical resolution of well-balanced shallow water equations with complex source terms. Adv Water Resour 32(6):873–884
Liu KF, Wu YH (2012) Comparison between FLO-2D and Debris-2D on application of assessment of granular debris flow. Kyoto Conference Proceeding (The Tenth International Symposium on Mitigation of Geo-disasters in Asia) http://hdl.handle.net/2433/180432
Liu Y, Zhou J, Song L, Zou Q, Liao L, Wang Y (2013) Numerical modelling of free-surface shallow flows over irregular topography with complex geometry. Appl Math Model 37(23):9482–9498
Liu J, You Y, Chen X, Liu J, Chen X (2014) Characteristics and hazard prediction of large-scale debris flow of Xiaojia gully in Yingxiu town, Sichuan Province, China. Eng Geol 180:55–67
Nakatani K, Wada T, Satofuka Y, Mizuyama T (2008) Development of “Kanako 2D (Ver.2.00)”, a user-friendly one- and two-dimensional debris flow simulator equipped with a graphical user interface. Int J Erosion Control Eng 1(2):62–72
O’Brien JS, Julien PY (1988) Laboratory analysis of mudflow properties. J Hydraul Eng 114(8):877–887
O’Brien JS, Julien PY, Fullerton WT (1993) Two-dimensional water flood and mudflow simulation. J Hydrol Eng 119(2):244–261
Ouyang C, He S, Xu Q, Luo Y, Zhang W (2013) A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain. Comput Geosci-UK 52(1):1–10
Pongsanguansin T, Maleewong M, Mekchay K (2016) Shallow-water simulations by a well-balanced WAF finite volume method: a case study to the great flood in 2011, Thailand. Comput Geosci 20:1269–1285
Rickenmann D, Laigle D, Mcardell BW, Hübl J (2006) Comparison of 2d debris-flow simulation models with field events. Comput Geosci 10(2):241–264
Song L, Zhou J, Guo J, Zou Q, Liu Y (2011) A robust well-balanced finite volume model for shallow water flows with wetting and drying over irregular terrain. Adv Water Resour 34(7):915–932
Takahashi T (2014) Debris flow: mechanics, prediction and countermeasures, 2nd edn. CRC Press, London
Toro EF (2001) Shock-capturing methods for free-surface shallow flows. John Wiley & Sons Press, Chichester
Wu NJ, Chen C, Tsay TK (2016) Application of weighted-least-square local polynomial approximation to 2D shallow water equation problems. Eng Anal Bound Elem 68:124–134
Zhang H (2014) Research on mathematical model and hydrodynamic characteristics of flow field in lakes. Hydraulic and hydro-power engineering department. Huazhong University of Science & Technology, Wuhan (in Chinese)
Zhang P, Ma J, Shu H, Han T, Zhang Y (2014) Simulating debris flow deposition using a two-dimensional finite model and soil conservation service-curve number approach for Hanlin gully of southern Gansu (China). Environ Earth Sci 73(10):6417–6426
Zhou BF, Li DJ, Luo DF (1991) Guide to prevention of debris flow. Science Press, Beijing (in Chinese)
Zia A, Banihashemi MA (2008) Simple efficient algorithm (SEA) for shallow flows with shock wave on dry and irregular beds. Int J Numer Methods Fluids 56(11):2021–2043
Acknowledgements
This work was supported by the State Key Program of the National Natural Science Fund of China (Grant No. 41330636), the National Natural Science Fund of China (Grant Nos. 41302218 and 41402243) and Special Fund for Scientific Research of China Ministry of Lands and Resources (CMLR) (Grant No. 201211095).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Han, X., Chen, J., Xu, P. et al. A well-balanced numerical scheme for debris flow run-out prediction in Xiaojia Gully considering different hydrological designs. Landslides 14, 2105–2114 (2017). https://doi.org/10.1007/s10346-017-0850-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10346-017-0850-7