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Smoothed Particle Hydrodynamics for modelling landslide–water interaction problems

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Abstract

This work aims to develop a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) in-house code for modelling landslide–water interaction problems. While we consider the landslide phase as a non-Newtonian fluid-like mass, governed under the Generalized Newtonian Fluids (GNFs) Navier–Stokes model, we deal with the water phase as a Newtonian fluid. For this purpose, we propose a new constitutive law to handle simultaneously the landslide and the water dynamics behavior that subsequently guarantees strong and natural coupling between both phases. Namely, this constitutive law is based on a rheological model of visco-plastic Casson fluid combined with a pressure-dependent Mohr–Coulomb yield criterion. For the validation of the proposed code, we reproduce numerically the experimental benchmarks scenarios relating to subaerial and submarine landslides previously available in the literature. Good agreements between our numerical results and the reference data are obtained.

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References

  • Abadie S, Morichon D, Grilli ST, Glockner S (2010) Numerical simulation of waves generated by landslides using a multiple-fluid Navier–Stokes model. Coast Eng 57(9):779–794. https://doi.org/10.1016/j.coastaleng.2010.03.003

  • Adami S, Hu XY, Adams NA (2010) A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation. J Comput Phys 229(13):5011–5021. https://doi.org/10.1016/j.jcp.2010.03.022

  • Ataie-Ashtiani B, Najafi Jilani A (2007) A higher-order Boussinesq-type model with moving bottom boundary: applications to submarine landslide tsunami waves. Int J Numer Methods Fluids 53(6):1019–1048. https://doi.org/10.1002/fld.1354

  • Ataie-Ashtiani B, Najafi-Jilani A (2008) Laboratory investigations on impulsive waves caused by underwater landslide. Coast Eng 55(12):989–1004. https://doi.org/10.1016/j.coastaleng.2008.03.003

  • Ataie-Ashtiani B, Nik-Khah A (2008) Impulsive waves caused by subaerial landslides. Environ Fluid Mech 8(3):263–280. https://doi.org/10.1007/s10652-008-9074-7

  • Ataie-Ashtiani B, Shobeyri G (2008) Numerical simulation of landslide impulsive waves by incompressible smoothed particle hydrodynamics. Int J Numer Methods Fluids 56(2):209–232. https://doi.org/10.1002/fld.1526

  • Ataie-Ashtiani B, Yavari-Ramshe S (2011) Numerical simulation of wave generated by landslide incidents in dam reservoirs. Landslides 8(4):417–432. https://doi.org/10.1007/s10346-011-0258-8

  • Bercovier M, Engelman M (1980) A finite-element method for incompressible non-Newtonian flows. J Comput Phys 36(3):313–326. https://doi.org/10.1016/0021-9991(80)90163-1

  • Biscarini C (2010) Computational fluid dynamics modelling of landslide generated water waves. Landslides 7(2):117–124. https://doi.org/10.1007/s10346-009-0194-z

  • Bungartz H, Schäfer M (2006) Fluid-structure interaction modelling, simulation, optimisation, vol 53. Springer Science & Business Media

  • Byron Bird R, Armstrong RC, Hassager O (1987) Dynamics of polymer liquids: Vol. 1 Fluid mechanics. Wiley-Interscience

  • Canelas R, Ferreira R, Domínguez J, Crespo A (2014) Modelling of wave impacts on harbour structures and objects with SPH and DEM. In: Proceedings of the 9th SPHERIC International Workshop, Paris, France. pp 313–320. https://doi.org/10.13140/RG.2.1.1217.7045

  • Casson N (1959) A flow equations for pigment-oil suspensions of the printing ink type. In: Mill CC (ed) Rheology of Disperse Systems Pergamon Press, Oxford. pp 84–104

  • Clous L, Abadie S (2019) Simulation of energy transfers in waves generated by granular slides. Landslides 16(9):1663–1679. https://doi.org/10.1007/s10346-019-01180-0

  • Colagrossi A, Landrini M (2003) Numerical simulation of interfacial flows by smoothed particle hydrodynamics. J Comput Phys 191(2):448–475. https://doi.org/10.1016/S0021-9991(03)00324-3

  • Dai Z, Huang Y, Cheng H, Xu Q (2017) SPH model for fluid-structure interaction and its application to debris flow impact estimation. Landslides 14(3):917–928. https://doi.org/10.1007/s10346-016-0777-4

  • Dutykh D, Kalisch H (2013) Boussinesq modeling of surface waves due to underwater landslides. Nonlinear Process Geophys 20(3):267–285. https://doi.org/10.5194/npg-20-267-2013

  • Elsaady W, Oyadiji SO, Nasser A (2020) A review on multi-physics numerical modelling in different applications of magnetorheological fluids. J Intell Mater Syst Struct 31(16):1855–1897. https://doi.org/10.1177/1045389X20935632

  • Evers FM, Heller V, Fuchs H, Hager WH, Boes RM (2019) Landslide generated impulse waves in reservoirs: basics and computation. 2nd edn. VAW Mitteilung 254, ETH Zurich, Switzerland. https://doi.org/10.3929/ethz-b-000413216

  • Farhadi A, Emdad H, Rad EG (2016) Incompressible SPH simulation of landslide impulse-generated water waves. Nat Hazards 82(3):1779–1802. https://doi.org/10.1007/s11069-016-2270-8

  • Fritz HM (2002) Initial phase of landslide generated impulse waves. PhD thesis, ETH Zurich, Zurich, 14871

  • Fritz HM, Hager WH, Minor H-E (2001) Lituya bay case: Rockslide impact and wave run-up. Sci Tsunami Haz 19(1):03–22

    Google Scholar 

  • Fritz HM, Hager WH, Minor H-E (2003) Landslide generated impulse waves. 1. Instantaneous flow fields. Exp Fluids 35:505–519. https://doi.org/10.1007/s00348-003-0659-0

  • Fu L, Jin Y-C (2015) Investigation of non-deformable and deformable landslides using meshfree method. Ocean Eng 109:192–206. https://doi.org/10.1016/j.oceaneng.2015.08.051

  • Ghaïtanellis A (2017) Modelling bed-load sediment transport through a granular approach in SPH. Dynamique, vibrations. PhD thesis, Université Paris-Est, English. NNT: 2017PESC1087

  • Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181(3):375–389. https://doi.org/10.1093/mnras/181.3.375

  • Grilli ST, Watts P (2005) Tsunami generation by submarine mass failure. I: modeling, experimental validation, and sensitivity analyses. J Waterw Port Coast Ocean Eng 131(6):283–297. https://doi.org/10.1061/(ASCE)0733-950X(2005)131:6(283)

  • Grilli ST, Shelby M, Kimmoun O, Dupont G, Nicolsky D, Ma G, Kirby JT, Shi F (2017) Modeling coastal tsunami hazard from submarine mass failures: Effect of slide rheology, experimental validation, and case studies off the US East Coast. Nat Hazards 86:353–391. https://doi.org/10.1007/s11069-016-2692-3

  • Heidarzadeh M, Ishibe T, Sandanbata O, Muhari A, Wijanarto AB (2020) Numerical modeling of the subaerial landslide source of the 22 December 2018 Anak Krakatoa volcanic tsunami, Indonesia. Ocean Eng 195:106733. https://doi.org/10.1016/j.oceaneng.2019.106733

  • Heinrich P (1992) Nonlinear water waves generated by submarine and aerial landslides. J Waterw Port Coast Ocean Eng 118(3):249–266. https://doi.org/10.1061/(ASCE)0733-950X(1992)118:3(249)

  • Heller V, Spinneken J (2013) Improved landslide-tsunami prediction: Effects of block model parameters and slide model. J Geophys Res Oceans 118(3):1489–1507. https://doi.org/10.1002/jgrc.20099

  • Heller V, Bruggemann M, Spinneken J, Rogers BD (2016) Composite modelling of subaerial landslide-tsunamis in different water body geometries and novel insight into slide and wave kinematics. Coast Eng 109:20–41. https://doi.org/10.1016/j.coastaleng.2015.12.004

  • Hosseini K, Omidvar P, Kheirkhahan M, Farzin S (2019) Smoothed particle hydrodynamics for the interaction of Newtonian and non-Newtonian fluids using the \(\mu (I)\) model. Powder Technol 351:325–337. https://doi.org/10.1016/j.powtec.2019.02.045

  • Ionescu IR, Mangeney A, Bouchut F, Roche O (2015) Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J Non-Newtonian Fluid Mech 219:1–18. https://doi.org/10.1016/j.jnnfm.2015.02.006

  • Ishikawa T, Oshima S, Yamane R (2000) Vortex enhancement in blood flow through stenosed and locally expanded tubes. Fluid Dyn Res 26(1):35–52. https://doi.org/10.1016/s0169-5983(98)00047-1

  • Krimi A, Khelladi S, Nogueira X, Deligant M, Ata R, Rezoug M (2018a) Multiphase smoothed particle hydrodynamics approach for modeling soil-water interactions. Adv Water Resour 121:189–205. https://doi.org/10.1016/j.advwatres.2018.08.004

  • Krimi A, Rezoug M, Khelladi S, Nogueira X, Deligant M, Ramírez L (2018b) Smoothed Particle Hydrodynamics: A consistent model for interfacial multiphase fluid flow simulations. J Comput Phys 358:53–87. https://doi.org/10.1016/j.jcp.2017.12.006

  • Lee C-H, Huang Z (2021) Multi-phase flow simulation of impulsive waves generated by a sub-aerial granular landslide on an erodible slope. Landslides 18(3):881–895. https://doi.org/10.1007/s10346-020-01527-y

  • Lin C, Pastor M, Li T, Liu X, Qi H, Lin C (2019) A SPH two-layer depth-integrated model for landslide-generated waves in reservoirs: application to Halaowo in Jinsha River (China). Landslides 16(11):2167–2185. https://doi.org/10.1007/s10346-019-01204-9

  • Lindstrøm EK (2016) Waves generated by subaerial slides with various porosities. Coast Eng 116:170–179. https://doi.org/10.1016/j.coastaleng.2016.07.001

  • Liu MB, Liu GR, Lam KY (2003) Constructing smoothing functions in smoothed particle hydrodynamics with applications. J Comput Appl Math 155(2):263–284. https://doi.org/10.1016/S0377-0427(02)00869-5

  • Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82:1013–1024. https://doi.org/10.1086/112164

  • Lynett P, Liu P L-F (2002) A numerical study of submarine-landslide-generated waves and run-up. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 458(2028):2885–2910. https://doi.org/10.1098/rspa.2002.0973

  • Ma G, Kirby JT, Hsu T-J, Shi F (2015) A two-layer granular landslide model for tsunami wave generation: Theory and computation. Ocean Model 93:40–55. https://doi.org/10.1016/j.ocemod.2015.07.012

  • Meng Z (2018) Experimental study on impulse waves generated by a viscoplastic material at laboratory scale. Landslides 15(6):1173–1182. https://doi.org/10.1007/s10346-017-0939-z

  • Miller DJ (1960) Giant waves in Lituya Bay, Alaska. Geol Surv Prof Pap 354-C. https://doi.org/10.3133/pp354C

  • Mitsoulis E (2007) Flows of viscoplastic materials: models and computations. Rheology Reviews 135–178

  • Mohr O (1914) Abhandlungen aus dem Gebiete der technischen Mechanik. Wilhelm Ernst & Sohn

  • Molteni D, Colagrossi A (2009) A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH. Comput Phys Commun 180(6):861–872. https://doi.org/10.1016/j.cpc.2008.12.004

  • Monaghan JJ (2005) Smoothed particle hydrodynamics. Rep Prog Phys 68(8):1703–1759. https://doi.org/10.1088/0034-4885/68/8/R01

  • Monaghan JJ (2012) Smoothed Particle Hydrodynamics and its diverse applications. Annu Rev Fluid Mech 44:323–346. https://doi.org/10.1146/annurev-fluid-120710-101220

  • Morris JP (1996) Analysis of smoothed particle hydrodynamics with applications. PhD thesis, Monash University Australia

  • Najafi-Jilani A, Ataie-Ashtiani B (2008) Estimation of near-field characteristics of tsunami generation by submarine landslide. Ocean Eng 35(5-6):545–557. https://doi.org/10.1016/j.oceaneng.2007.11.006

  • Nomeritae, Daly E, Grimaldi S, Bui HH (2016) Explicit incompressible SPH algorithm for free-surface flow modelling: A comparison with weakly compressible schemes. Adv Water Resour 97:156–167. https://doi.org/10.1016/j.advwatres.2016.09.008

  • Pastor M, Haddad B, Sorbino G, Cuomo S, Drempetic V (2009) A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. International Int J Numer Anal Methods Geomech 33(2):143–172. https://doi.org/10.1002/nag.705

  • Pastor M, Blanc T, Haddad B, Drempetic V, Morles MS, Dutto P, Merodo JAF (2014) Depth averaged models for fast landslide propagation: mathematical, rheological and numerical aspects. Arch Comput Meth Eng 22(1):67–104. https://doi.org/10.1007/s11831-014-9110-3

  • Pilvar M, Pouraghniaei MJ, Shakibaeinia A (2019) Two-dimensional sub-aerial, submerged, and transitional granular slides. Phys Fluids 31(11):113303. https://doi.org/10.1063/1.5121881

  • Qiu L-C (2008) Two-dimensional SPH simulations of landslide-generated water waves. J Hydraul Eng 134(5):668–671. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:5(668)

  • Qiu L-C, Jin F, Lin P-Z, Liu Y, Han Y (2017) Numerical simulation of submarine landslide tsunamis using particle based methods. J Hydrodyn 29(4):542–551. https://doi.org/10.1016/S1001-6058(16)60767-9

  • Rauter M, Hoße L, Mulligan RP, Take WA, Løvholt F (2021) Numerical simulation of impulse wave generation by idealized landslides with OpenFOAM. Coast Eng 165:103815. https://doi.org/10.1016/j.coastaleng.2020.103815

  • Romano A, Lara JL, Barajas G, Di Paolo B, Bellotti G, Di Risio M, Losada IJ, De Girolamo P (2020) Tsunamis generated by submerged landslides: numerical analysis of the near-field wave characteristics. J Geophys Res Oceans 125(7):e2020JC016157. https://doi.org/10.1029/2020JC016157

  • Ruffini G, Heller V, Briganti R (2019) Numerical modelling of landslide tsunami propagation in a wide range of idealised water body geometries. Coast Eng 153:103518. https://doi.org/10.1016/j.coastaleng.2019.103518

  • Rzadkiewicz A, Mariotti C, Heinrich P (1997) Numerical simulation of submarine landslides and their hydraulic effects. J Waterw Port Coast Ocean Eng 123(4):149–157. https://doi.org/10.1061/(ASCE)0733-950X(1997)123:4(149)

  • Schwaiger HF, Higman B (2007) Lagrangian hydrocode simulations of the 1958 Lituya Bay tsunamigenic rockslide. Geochem Geophys Geosyst 8(7). https://doi.org/10.1029/2007gc001584

  • Shi C, An Y, Wu Q, Liu Q, Cao Z (2016) Numerical simulation of landslide-generated waves using a soil-water coupling smoothed particle hydrodynamics model. Adv Water Resour 92:130–141. https://doi.org/10.1016/j.advwatres.2016.04.002

  • Si P, Shi H, Yu X (2018) A general numerical model for surface waves generated by granular material intruding into a water body. Coast Eng 142:42–51. https://doi.org/10.1016/j.coastaleng.2018.09.001

  • Snelling BE, Collins GS, Piggott MD, Neethling SJ (2020) Improvements to a smooth particle hydrodynamics simulator for investigating submarine landslide generated waves. Int J Numer Methods Fluids 92(7):744–764. https://doi.org/10.1002/fld.4804

  • Tajnesaie M, Shakibaeinia A, Hosseini K (2018) Meshfree particle numerical modelling of sub-aerial and submerged landslides. Comput Fluids 172:109–121. https://doi.org/10.1016/j.compfluid.2018.06.023

  • Tan H, Chen S (2017) A hybrid DEM-SPH model for deformable landslide and its generated surge waves. Adv Water Resour 108:256–276. https://doi.org/10.1016/j.advwatres.2017.07.023

  • Tappin DR, Watts P, Grilli ST (2008) The Papua New Guinea tsunami of 17 July 1998: anatomy of a catastrophic event. Nat Hazards Earth Syst Sci 8(2):243–266. https://doi.org/10.5194/nhess-8-243-2008

  • Vacondio R, Mignosa P, Pagani S (2013) 3D SPH numerical simulation of the wave generated by the Vajont rockslide. Adv Water Resour 59:146–156. https://doi.org/10.1016/j.advwatres.2013.06.009

  • Viroulet S, Cébron D, Kimmoun O, Kharif C (2013) Shallow water waves generated by subaerial solid landslides. Geophys J Int 193(2):747–762. https://doi.org/10.1093/gji/ggs133

  • Viroulet S, Sauret A, Kimmoun O (2014) Tsunami generated by a granular collapse down a rough inclined plane. EPL (Europhysics Letters) 105(3):34004. https://doi.org/10.1209/0295-5075/105/34004

  • Wang W, Chen G, Zhang H, Zhou S, Liu S (2016) Analysis of landslide-generated impulsive waves using a coupled DDA-SPH method. Engineering Analysis with Boundary Elements 64:267–277. https://doi.org/10.1016/j.enganabound.2015.12.014

  • Xenakis AM, Lind SJ, Stansby PK, Rogers BD (2015) An incompressible SPH scheme with improved pressure predictions for free-surface generalised Newtonian flows. J Non-Newtonian Fluid Mech 218:1–15. https://doi.org/10.1016/j.enganabound.2015.12.014

  • Xenakis AM, Lind SJ, Stansby PK, Rogers BD (2017) Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment. Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences 473(2199):20160674. https://doi.org/10.1098/rspa.2016.0674

  • Xiao T, Qin N, Lu Z, Sun X, Tong M, Wang Z (2017) Development of a smoothed particle hydrodynamics method and its application to aircraft ditching simulations. Aerosp Sci Technol 66:28–43. https://doi.org/10.1016/j.ast.2017.02.022

  • Yavari-Ramshe S, Ataie-Ashtiani B (2016) Numerical modeling of subaerial and submarine landslide-generated tsunami waves–recent advances and future challenges. Landslides 13(6):1325–1368. https://doi.org/10.1007/s10346-016-0734-2

  • Yavari-Ramshe S, Ataie-Ashtiani B (2017) A rigorous finite volume model to simulate subaerial and submarine landslide-generated waves. Landslides 14(1):203–221. https://doi.org/10.1007/s10346-015-0662-6

  • Yeylaghi S, Moa B, Buckham B, Oshkai P, Vasquez J, Crawford C (2017) ISPH modelling of landslide generated waves for rigid and deformable slides in Newtonian and non-Newtonian reservoir fluids. Adv Water Resour 107:212–232. https://doi.org/10.1016/j.advwatres.2017.06.013

  • Yu M-L, Lee C-H (2019) Multi-phase-flow modeling of underwater landslides on an inclined plane and consequently generated waves. Adv Water Resour 133:103421. https://doi.org/10.1016/j.advwatres.2019.103421

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  1. Department of Mechanics Engineering, Faculty of Technology, Blida-1 University, BP 270 road, Soumaa Blida, Algeria

    Abderrahmane Mahallem, Mohamed Roudane & Sid Ahmed Gouri

  2. Department of Civil, Geological and Mining Engineering, Polytechnique Montréal, Montréal, Canada

    Abdelkader Krimi

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  1. Abderrahmane Mahallem
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Mahallem, A., Roudane, M., Krimi, A. et al. Smoothed Particle Hydrodynamics for modelling landslide–water interaction problems. Landslides 19, 1249–1263 (2022). https://doi.org/10.1007/s10346-021-01807-1

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