The Performance of the SPH Method in Simulating Surface Runoff Along a Saturated Soil Slope

The Performance of the SPH Method in Simulating Surface Runoff Along a Saturated Soil Slope

L.M. Dakssa I.S.H. Harahap 

Civil Engineering Department, Universiti Teknologi PETRONAS, Malaysia

30 June 2013
| Citation



Rainfall-induced slope failures are one of the most disastrous and frequently occurring natural hazards. Hence, it is indispensible to predict their occurrence and their post-failure velocity in order to save lives and properties in mountainous areas. The rain that falls on a soil slope results in either infiltration or surface runoff, depending on the site characteristics. For saturated soil slopes, the amount of rain that goes as infiltration is usually less than the amount that goes as runoff. As a result, surface runoff scours the slope surface, thereby removing the soil slope protecting covers and eventu-ally putting the slope, at least, in a marginally stable condition. This article reports the performance of the smoothed particle hydrodynamics numerical scheme in simulating runoff along a saturated soil slope with emphasis on predicting the velocity of flow. The average velocity of flow using the smoothed particle hydrodynamics method was compared with the average value obtained using a standard open-channel hydraulics empirical equation. The results show that the smoothed particle hydrodynamics method could be used as an alternative method for predicting the runoff velocity along a soil slope in hilly areas.


Compressible fl uid, incompressible fl uid, infi ltration, meshless numerical methods, runoff, SPH


[1] Ng, W.C.C. & Shi, Q., A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage. Computers and Geotechnics, 22(1), pp. 1–28, 1998. doi:

[2] Tsaparas, I., Rahardjo, H., Toll, D.G. & Leong, E.C., Controlling parameters for rainfall-induced landslides. Computers and Geotechnics, 29, pp. 1–27, 2002. doi: http://dx.doi. org/10.1016/S0266-352X(01)00019-2

[3] Kjekstad, O. & Highland, L., Economic and social impact of landslides. Landslides — Disaster Risk Reduction, eds K. Sossa & P. Canuti, Springer: Berlin and Heidelberg,

pp. 573–587, 2009. doi:

[4] Borja, R.I., Landslides and debris flow induced by rainfall. Insights. Institute of Advanced Study, Vol. 2, No. 3, Durham University, 2009.

[5] Abay, A. & Barbieri, G., Landslide susceptibility and causative factors evaluation of the landslide area of Debresina, in the southwestern Afar escarpments. Ethiopia. Journal of Earth Science and Engineering, 2, pp. 133–144, 2012.

[6] Liu, G.R. & Liu, M.B., Smoothed particle hydrodynamics — a meshfree particle method, World Scientific Publishing, Singapore, 2003.

[7] Bui, Ha H., Sako, K. & Fukagawa, R., Numerical simulation of soil–water interaction using smoothed particle hydrodynamics (SPH) method. Journal of Terramechanics, 44, pp. 339–346, 2007. doi:

[8] Gesteira, M.G., Rogers, B.D., Dalrymple, R.A., Crespo, A.J.C. & Narayanaswamy, M., User Guide for the SPHysics Code v2.0, 2010.

[9] Narsilio, G.A., Buzzi, O., Fityus, S., Yun, T.S. & Smith, D.W., Upscaling of Navier–Stokes equations in porous media: theoretical, numerical and experimental approach. Computers and Geotechnics, 36, pp. 1200–1206, 2009. doi: compgeo.2009.05.006

[10] Jiang, F. & Sousa, A.C.M., Smoothed particle hydrodynamics modelling of trans-verse flow in randomly aligned fibrous porous media. Transport in porous media, 75, pp. 17–33, 2008. doi:

[11] Morris, J.P., Zhu, Y. & Fox, P.J., Parallel simulations of pore-scale flow through porous media. Computers and Geotechnics, 25, pp. 227–246, 1999. doi: S0266-352X(99)00026-9

[12] Pereira, G.G., Prakash, M. & Cleary, P.W., SPH modelling of fluid at the grain level in a porous medium. Applied Mathematical Modelling, 35, pp. 1666–1675, 2011. doi:

[13] Shao, S., Incompressible SPH flow model for wave interactions with porous media. Coastal Engineering, 57, pp. 304–316, 2010. doi:

[14] Monaghan, J.J., Simulating free surface flows with SPH. Journal of Computational Physics, 110, pp. 399–406, 1994. doi:

[15] Morris, J.P., Fox, P.J. & Zhu, Y., Modelling low Reynolds number incompressible flows using SPH. Journal of Computational Physics, 136, pp. 214–226, 1997. doi: http://

[16] Bui, Ha H., Fukagawa, R. & Sako, K., Smoothed particle hydrodynamics for soil me-chanics. Numerical Methods in Geotechnical Engineering (eds.), Taylor & Francis, 2006.

[17] Tennessee Department of Transportation (TDOT), design division, drainage manual, roadside ditches and streams, May 15, 2011.