Application of Bed Load Formulations for Dam Failure and Overtopping

Seyed Alireza Hosseinzadeh-Tabrizi, Mahnaz Ghaeini-Hessaroeyeh


The Enhanced HLLC scheme as a robust approximate Riemann solver is used for numerical modeling of three different test cases of mobile bed and stepped mobile bed in dam failure and dam overtopping conditions. The current research has been done in the frame of the finite volume method using shallow water equations along with the Exner equation for sediment continuity. The Ribberink, Wong and Parker formulations have been used for the modelling of bed load movement. A convenient approach based on the Boussinesq hypothesis is deployed for considering turbulence effects in the second case. The affections of stepped and slope condition for the flow bed are considered through a corrected version of the HLLC flux components. Finally, the model is applied for modelling overtopping in the third case. The results of the present model are relatively reasonable by comparing with the experimental data.


HLLC Scheme; Stepped Bed; Shallow Water Equations; Sediment; Overtopping.


Harten, A. and Lax, P.D. and van Leer, B., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, Siam Review, 1983, 25(1): 35-61.

Toro, E. F. and Spruce, M. and Speares, W., Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 1994, 4 (1): 25–34.

Fraccarollo, L. and Capart, H. and Zech, Y., A Godunov method for the computation of erosional shallow water transients, International journal for numerical methods in fluids, 2003, 41: 951-976.

Simpson, G. and Castelltort, S., Coupled model of surface water flow, sediment transport and morphological evolution, Journal of computers and geosciences, 2006, 32:1600-1614.

Vásquez, J. A. and Leal João, G. A. B., Two-dimensional dam-break simulation over movable beds with an unstructured mesh, International conference on fluvial hydraulics, River flow 2006, Lisbon, Portugal, 2006, C-II:1483-1492.

Castro, M. J., Garcıa-Rodrıguez, J.A., Gonzalez-Vida J.M., Pares C., Solving shallow-water systems in 2D domains using finite volume methods and multimedia SSE instructions, Journal of computational and applied mathematics, 2008, 221:16-32.

Goutière, Laurent, Sandra Soares-Frazão, C. Savary, T. Laraichi, and Yves Zech. "One-dimensional model for transient flows involving bed-load sediment transport and changes in flow regimes." Journal of Hydraulic Engineering 134, no. 6 (2008): 726-735.

Soares-Frazão, S. and Zech Y., HLLC scheme with novel wave-speed estimators appropriate for two-dimensional shallow-water flow on erodible bed, International journal for numerical methods in fluids, 2011,66: 1019–1036.

Soares-frazão, S. Dam-break flows over mobile beds: experiments and benchmark tests for numerical models, Journal of Hydraulic Research, 2012, 50(4): 364–375.

Talukdar, S., kumar, B., Dutta, S., Predictive capability of bed load equations using flume data, Journal of Hydrology and Hydromechanics, 2012, 60(1):45-56.

Liu, X., Mohammadian, A., Sedano, J.A.I., A Well-Balanced 2-D Model for Dam-Break Flow with Wetting and Drying, Journal of Fluid Flow, Heat and Mass Transfer, 2014, 1(1): 30-37.

Liu, X., Mohammadian, A., Kurganov, A., Sedano, J.A.I., Well-balanced central-upwind scheme for a fully coupled shallow water system modeling flows over erodible bed, Journal of Computational Physics, 2015, 300: 202-218.

Caviedes-Voullième D., Morales-Hernández M., Juez C, Lacasta A., García-Navarro P., Two-Dimensional Numerical Simulation of Bed-Load Transport of a Finite-Depth Sediment Layer: Applications to Channel Flushing, Journal of Hydraulic Engineering, 2017, 143(9): 04017034.

Van Emelen, S., Zech Y., & Soares-Frazão S., Impact of sediment transport formulations on breaching modelling, Journal of Hydraulic Research, 2014, 53(1): 60–72.

Zhiguo H., Peng H., Liang Z., Gangfeng W., Thomas P, Modelling of Breaching Due to Overtopping Flow and Waves Based on Coupled Flow and Sediment Transport, journal of water, 2015, 7:4283-4304.

Saberi, O., Zenz G., Numerical Investigation on 1D and 2D Embankment Dams Failure Due to Overtopping Flow, International Journal of Hydraulic Engineering 2016, 5(1): 9-18.

Xia, J., Lin, B., Falconer, R. A. and Wang, G., Modelling dam-break flows over mobile beds using a 2D coupled approach, Advanced in water resources, 2010,33: 171-183.

Ribberink, Jan S. "Bed-load transport for steady flows and unsteady oscillatory flows." Coastal Engineering 34, no. 1 (1998): 59-82.

Wong, Miguel, and Gary Parker. "Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database." Journal of Hydraulic Engineering 132, no. 11 (2006): 1159-1168.

Parker, Gary. "Discussion of “Lateral Bed Load Transport on Side Slopes” by Syunsuke Ikeda (November, 1982)." Journal of Hydraulic Engineering 110, no. 2 (1984): 197-199.

Soares-Frazão, S., Lories, D., Taminiau, S. and Zech, Y., Dam-break flow in a channel with a sudden enlargement, 30th IAHR Congress, Thessaloniki, Greece, 2003, C-II: 221-228.

Toro, Eleuterio F. Shock-capturing methods for free-surface shallow flows. John Wiley, 2001.

Spinewine, B., and Y. Zech. "Dam-break waves over movable beds: a “flat bed” test case." In EC Contract EVG1-CT-2001-00037 IMPACT Investigation of Extreme Flood Processes and Uncertainty, Proceedings 2nd Project Workshop, Mo-i-Rana, Norway, pp. 12-13. 2002.

Leal, J. G. A. B., Rui ML Ferreira, and ANTÓNIO H. Cardoso. "Dam-break wave propagation over a cohesionless erodible bed." In Proc. 30rd IAHR Congress, vol. 100, pp. 261-268. 2003.

Schmocker, L., and W. H. Hager. "Overtopping and breaching of dikes—breach profile and breach flow." In River Flow 2010 (Proceedings on 5th International Conference on Fluvial Hydraulics,), pp. 515-522. 2010.

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DOI: 10.28991/cej-030932


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