Application of a weakly compressible smoothed particle hydrodynamics multi-phase model to non-cohesive embankment breaching due to flow overtopping

Abstract

The subject of present study is the application of mesh free Lagrangian two-dimensional non-cohesive sediment transport model applied to a two-phase flow over an initially trapezoidal-shaped sediment embankment. The governing equations of the present model are the Navier-Stocks equations solved using Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method. To simulate the movement of sediment particles, the model considers a powerful two-part technique; when the sediment phase has rigid behavior, only the force term due to shear stress in the Navier-Stokes equations is used for simulation of sediment particles’ movement. Otherwise, all the Navier-Stokes force terms are used for transport simulation of sediment particles. In the present model, the interactions between different phases are calculated automatically, even with considerable difference between the density and viscosity of phases. Validation of the model is performed using simulation of available laboratory experiments, and the comparison between computational results and experimental data shows that the model generally predicts well the flow propagation over movable beds, the induced sediment transport and bed changes, and temporal evolution of embankment breaching.

Keywords

WCSPH method / non-cohesive sediment transport / rheological model / two-part technique / two-phase dam break

References

[1] Basco D R, Shin C S. A one-dimensional numerical model for storm-breaching of barrier islands. Journal of Coastal Research, 1999, 15(1): 241–260

[2] Tingsanchali T, Chinnarasri C. Numerical modeling of dam failure due to flow overtopping. Hydrological Sciences Journal, 2001, 46(1): 113–130

[3] Wang Z, Bowles D S. Three-dimensional non-cohesive earthen dam breach model. Part 1: theory and methodology. Advances in Water Resources, 2006, 29(10): 1528–1545

[4] Faeh R. Numerical modeling of breach erosion of river embankments. Journal of Hydraulic Engineering, 2007, 133(9): 1000–1009

[5] Pontillo M, Schmocker L, Greco M, Hager W H. 1D numerical evaluation of dike erosion due to overtopping. Journal of Hydraulic Research, 2010, 48(5): 573–582

[6] Volz C, Rousselot P, Vetsch D, Faeh R. Numerical modelling of non-cohesive embankment breach with the dual-mesh approach. Journal of Hydraulic Research, 2012, 50(6): 587–598

[7] Wu W, Marsooli R, He Z. Depth-averaged two-dimensional model of unsteady flow and sediment transport due to noncohesive embankment break/breaching. Journal of Hydraulic Engineering, 2012, 138(6): 503–516

[8] Kuiry S N, Ding Y, Wang S S Y. Numerical simulations of morphological changes in barrier islands induced by storm surges and waves using a supercritical flow model. Frontiers of Structural and Civil Engineering, 2014, 8(1): 57–68

[9] Lucy L B. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, 1977, 82(12): 1013–1024

[10] Monaghan J J. Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics, 1992, 30(1): 543–574

[11] Altomare C, Crespo A J C, Domínguez J M, Gómez-Gesteira M, Suzuki T, Verwaest T. Applicability of smoothed particle hydrodynamics for estimation of sea wave impact on coastal structures. Coastal Engineering, 2015, 96: 1–12

[12] Husain S M, Muhammed J R, Karunarathna H U, Reeve D E. Investigation of pressure variations over stepped spillways using smooth particle hydrodynamics. Advances in Water Resources, 2014, 66: 52–69

[13] Ataie-Ashtiani B, Shobeyri G. Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 2008, 56(2): 209–232

[14] Capone T, Panizzo A, Monaghan J J. SPH modelling of water waves generated by submarine landslides. Journal of Hydraulic Research, 2010, 48(sup1): 80–84

[15] Memarzadeh R, Hejazi K. ISPH numerical modeling of nonlinear wave run-up on steep slopes. Journal of the Persian Gulf (Marine Science), 2012, 3(10): 17–26

[16] Vacondio R, Rogers B D, Stansby P K, Mignosa P. Shallow water SPH for flooding with dynamic particle coalescing and splitting. Advances in Water Resources, 2013, 58: 10–23

[17] Bui H H, Fukagawa R. An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore-water pressure. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(1): 31–50

[18] Hosseini S M, Manzari M T, Hannani S K. A fully explicit three-step SPH algorithm for simulation of non-Newtonian fluid flow. International Journal of Numerical Methods for Heat & Fluid Flow, 2007, 17(7): 715–735

[19] Manenti S, Sibilla S, Gallati M, Agate G, Guandalini R. SPH simulation of sediment flushing induced by a rapid water flow. Journal of Hydraulic Engineering, 2012, 138(3): 272–284

[20] Razavitoosi S L, Ayyoubzadeh S A, Valizadeh A. Two-phase SPH modelling of waves caused by dam break over a movable bed. International Journal of Sediment Research, 2014, 29(3): 344–356

[21] Ran Q, Tong J, Shao S, Fu X, Xu Y. Incompressible SPH scour model for movable bed dam break flows. Advances in Water Resources, 2015, 82: 39–50

[22] Memarzadeh R, Barani G, Ghaeini-Hessaroeyeh M. Numerical modeling of sediment transport based on unsteady and steady flows by incompressible smoothed particle hydrodynamics method. Journal of Hydrodynamics, 2017, (in press)

[23] Asadi Kalameh H, Karamali A, Anitescu C, Rabczuk T. High velocity impact of metal sphere on thin metallic plate using smooth particle hydrodynamics (SPH) method. Frontiers of Structural and Civil Engineering, 2012, 6(2): 101–110

[24] Shao S, Lo E. Incompressible SPH method for simulating Newtonian and non Newtonian flows with a free surface. Advances in Water Resources, 2003, 26(7): 787–800

[25] Ata R, Soulaimani A. A stabilized SPH method for inviscid shallow water flows. International Journal for Numerical Methods in Fluids, 2005, 47(2): 139–159

[26] Crespo A J C, Gómez-Gesteira M, Dalrymple R A. Modeling dam break behavior over a wet bed by a SPH technique. Journal of Hydraulic Engineering, 2008, 134(6): 313–320

[27] Lee E S, Moulinec C, Xu R, Violeau D, Laurence D, Stansby P. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. Journal of Computational Physics, 2008, 227(18): 8417–8436

[28] Khayyer A, Gotoh H. On particle-based simulation of a dam break over a wet bed. Journal of Hydraulic Research, 2010, 48(2): 238–249

[29] Ferrari A, Fraccarollo L, Dumbser M, Toro E F, Armanini A. Three-dimensional flow evolution after a dam break. Journal of Fluid Mechanics, 2010, 663: 456–477

[30] Chang T J, Kao H M, Chang K H, Hsu M H. Numerical simulation of shallow-water dam break flows in open channels using smoothed particle hydrodynamics. Journal of Hydrology (Amsterdam), 2011, 408(1-2): 78–90

[31] Shakibaeinia A, Jin Y C. A weakly compressible MPS method for modeling of open-boundary free-surface flow. International Journal for Numerical Methods in Fluids, 2010, 63(10): 1208–1232

[32] Fourtakas G, Rogers B D. Modelling multi-phase liquid-sediment scour and resuspension induced by rapid flows using Smoothed Particle Hydrodynamics (SPH) accelerated with a Graphics Processing Unit (GPU). Advances in Water Resources, 2016, 92: 186–199

[33] Jánosi I M, Jan D, Szabó K G, Tél T. Turbulent drag reduction in dam-break flows. Experiments in Fluids, 2004, 37(2): 219–229

[34] Schmocker L, Hager W H. Modelling dike breaching due to overtopping. Journal of Hydraulic Research, 2009, 47(5): 585–597

[35] Lo E Y M, Gotoh H, Shao S D. Simulation of near-shore solitary wave mechanics by an incompressible SPH method. Applied Ocean Research, 2002, 24(5): 275–286

[36] Rabczuk T, Belytschko T, Xiao S P. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12-14): 1035–1063

[37] Chen C L, Ling C H. Granular-flow rheology: role of shear-rate number in transition regime. Journal of Engineering Mechanics, 1996, 122(5): 469–480

[38] Ken-Ichi K. A plasticity theory for the kinematics of ideal granular materials. International Journal of Engineering Science, 1982, 20(1): 1–13

[39] Monaghan J J. Simulating free surface flows with SPH. Journal of Computational Physics, 1994, 110(2): 399–406

[40] Shakibaeinia A, Jin Y C. A mesh-free particle model for simulation of mobile-bed dam break. Advances in Water Resources, 2011, 34(6): 794–807

[41] Coleman S E, Andrews D P, Webby M G. Overtopping breaching of noncohesive homogeneous embankments. Journal of Hydraulic Engineering, 2002, 128(9): 829–838

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg