Numerical Simulation of Sub-Surface Landslide Waves Using an explicit three-step compressible SPH algorithm

Document Type : Research Article


Water engineering group, Water engineering college, Razi university, kermanshah,Iran


The coastal waves that are produced by a landslide in the lake of reservoir dams can threaten the dam safety. Therefore, the exact recognition of hydraulic flow due to coastal waves has always been of interest to researchers. So far, extensive laboratory and numerical research have been conducted. In this research, a completely lagrangian numerical method which is based on particle and non-grid called the Smoothed Particle Hydrodynamic Method (SPH) was used to simulate coastal waves due to landslide. In the present study, a new three-step SPH algorithm based on the prediction and correction method was solved by governing equations. To validate the method, the laboratory data of the dam break problem on dry bed has been used. The results of this study approximated the analytical solution well, and the current model result was close to the analytical solution for the depth of flow in the break site. Also, the correlation coefficient of 0.9998, the mean absolute error of 0.5426 and the efficiency coefficient of the Nash-Sutcliff model 0.974 for the calculated parameters indicated that the model is accurately calibrated and the model can simulate the depth and discharge of water. Also, the results showed that the ability of the present model in the numerical simulation of sub-surface landslide wave in the production region and run-up region is high, and it stimulates the propagation region very well with an accuracy of 95%. With the comparison of measured and laboratory results, the correlation coefficient and the root mean square error were 0.95 and 0.0071 respectively, which indicates the high accuracy of the model in calculating the surface water profile due to subsurface landslide.


Main Subjects

[1]. B. Ataie ashtiani, B. Shobeyri, Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics, International Journal for numerical methods in fluids, Vol. 56, No. 2, pp. 232-209, 2008.
[2]. L. B. Lucy, A numerical approach to the testing of the fission hypothesis, The astronomical journal, Vol. 82, pp. 1024-1013, 1977.
[3]. R. A. Gingold, J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly notices of the royal astronomical society, Vol. 181, No. 3, pp. 389-375, 1977.
[4]. T. Capone, A. Panizzo, J.J. Monaghan, SPH modelling of water waves generated by submarine landslides, Journal of Hydraulic Research, Vol.48 , pp. 84-80, 2010.
[5]. S.A. Rzadkiewicz, C. Mariotti, P. Heinrich, Numerical simulation of submarine landslides and their hydraulic effects, Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol.123 , pp. 157-149, 1997.
[6]. A. Leroy, D. Violeau, M. Ferrand, Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH, Journal of Computational Physics, Vol. 261, pp.-106 129, .4102
[7]. E. Napoli, M. De Marchis, C. Gianguzzi, Milici, A coupled Finite Volume–Smoothed Particle Hydrodynamics method for incompressible flows, Computer Methods in Applied Mechanics and Engineering, Vol. 310, pp. -674 693, 2016.
[8]. D. Nomeritae, S. Grimaldi, Explicit incompressible SPH algorithm for free-surface flow modelling: A comparison with weakly compressible schemes, Advances in Water Resources, Vol. 97, pp. 167-156, 2016.
[9]. C. Shi, Y. An, Q. Wu, Q. Liu, Numerical simulation of landslide-generated waves using a soil–water coupling smoothed particle hydrodynamics model, Advances in Water Resources, Vol 92, pp. 141-130, 2016.
[10]. Y. An, Q. Wu, Q. Liu, Three-dimensional smoothed-particle hydrodynamics simulation of deformation characteristics in slope failure, Advances in Water Resources, Vol 92, pp.11-1, 2016.
[11]. S. Viroulet, D. Cébron, o. Kimmoun, Ch. Kharif, Shallow water waves generated by subaerial solid landslides, Geophysical Journal International, Vol.193 , pp.762-747, 2013.
[12]. H.M. Fritz, F. Mohammed, J. Yoo, Lituya Bay landslide impact generated mega-tsunami 50 th Anniversary, in: Tsunami Science Four Years after the 2004 Indian Ocean Tsunami, Springer, pp.175-153, 2009.
[13]. M. Khanpour, A. R. Zarrati, M. Kolahdoozan, A. Shakibaeinia, and S. Jafarinik, Numerical modeling of free surface flow in hydraulic structures using Smoothed Particle Hydrodynamics. Applied Mathematical Modelling, vol. 40, pp. 9834-9821, 2016.
[14]. F. Rouzbahani, K. Hejranfar, A truly incompressible smoothed particle hydrodynamics based on artificial compressibility method, Computer Physics Communications, vol. 210, pp. 28-10, 2016.
[15]. V. Khoolosi, S. Kabda┼čli, Numerical Simulation of Impulsive Water Waves Generated by Subaerial and Submerged Landslides Incidents in Dam Reservoirs, Civil Engineering Journal, Vol. 2, No. 10, pp. 519-497, 2016.
[16]. L.-c. Qiu, F. Jin, P.-z. Lin, Y. Liu, Y. Han, Numerical simulation of submarine landslide tsunamis using particle based methods, Journal of Hydrodynamics, Vol.29 , pp. -542 551, .7102
[17]. L. Gui-Rong, L. Moubin, Smoothed particle hydrodynamics: a meshfree particle method, World Scientific, 2003.
[18]. R. Xu, An improved incompressible smoothed particle hydrodynamics method and its application in free-surface simulations, PhD, University of Manchester, UK, 2010.
[19]. J. Monaghan, R. Gingold, Shock simulation by the particle method SPH, Journal of computational physics, Vol.52, pp. 389-374, 1983.
[20]. S. Cummins, M. Rudman, An SPH projection method.  Journal of computational physics, Vol.152, pp.607-584, 1999.
[21]. S. Hosseini, M. Manzari, S. Hannani, A fully explicit threestep SPH algorithm for simulation of non-Newtonian fluid flow, International Journal of Numerical Methods for Heat & Fluid Flow, Vol.17, pp.735-715, 2007.
[22]. J. Morris, P. Fox, J. Zhu, Modeling low Reynolds number incompressible flows using SPH, Journal of computational physics, Vol.136, pp. 226-214, 1997.
[23]. S. Shao, E. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Advances in water resources, Vol.26, pp.800-787, 2003.
[24]. D. Komatina, M. Jovanovic, Experimental study of steady and unsteady free surface flows with water-clay mixtures. Journal of Hydraulic Research, Vol.35, pp.590-579, 1997.
[25]. J. Martin, W. Moyce, An experimental study of the collapse of liquid columns on a rigid horizontal plane, Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Vol.244, pp.324-312, 1952.
[26]. P. Heinrich, Nonlinear water waves generated by submarine and aerial landslides, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol. 118, pp. 266-249, 1992.