Advertisement

Kinematics of flow mass movements on inclined surfaces

  • Ilaria Rendina
  • Giacomo ViccioneEmail author
  • Leonardo Cascini
Original Article

Abstract

Flow mass movements are catastrophic events occurring all over the world and may result in a great number of casualties and widespread damages. The analysis of the time–space evolution of the kinematic quantities is a useful tool to understand the propagation stage of these phenomena as well as for control works design. In order to compare the kinematic effects in terms of adopted rheology, the paper deals with the flow regime of Newtonian and non-Newtonian fluids on inclined surfaces and provides a contribution to this topic through the use of numerical procedures based on a finite volume (FV) scheme. The flow kinematic is analyzed through the Froude number, which is able to provide a unique overall description of flow behavior, including the temporal–spatial variability of the propagation heights and flow velocities. Case studies concern a 1D/2D dam break of Newtonian (water flow) and non-Newtonian flows (in particular based on a viscoplastic law). The analysis of Newtonian flows aims to validate the adopted FV scheme against available analytical solutions of a dam break problem.

Keywords

Flow movements Viscoplastic flows FV model Froude number 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Egashira, S., Miyamoto, K., Takahito, I.: Constitutive equations of debris flow and their applicability. In: 1st Int. Conf. on Debris-Flow Hazards Mitigation, pp. 340–349. ASCE (1997)Google Scholar
  2. 2.
    Iverson, R.M.: The debris-flow rheology myth. In: Rickenmann, D., Chen, C.L. (Eds.), Debris-Flow Hazards Mitigation: Mechanics, Prediction, and Assessment, pp. 304–313 (2003)Google Scholar
  3. 3.
    Montserrat, S., Tamburrino, A., Roche, O., Niño, Y.: Pore fluid pressure diffusion in defluidizing granular columns. J. Geophys. Res. 117(F2), 2156–2202 (2012)Google Scholar
  4. 4.
    Coussot, P., Meunier, M.: Recognition, classification and mechanical description of debris flow. Earth Sci. Rev. 40, 209–227 (1996).  https://doi.org/10.1016/0012-8252(95)00065-8 Google Scholar
  5. 5.
    Costa, J.E.: Rheologic, geomorphic, and sedimentologic differentiation of water floods, hyperconcentrated flows, and debris flows. In: Baker, V.R., Kochel, R.C., Patton, P.C. (eds.) Flood Geomorphology, pp. 113–122. Wiley, New York (1988)Google Scholar
  6. 6.
    Cruden, D.M., Varnes, D.J.: Landslide types and process. In: Turner, A.T., Schuster, R.L. (eds.) “Landslides—Investigation and Mitigation”, Trasportation Research Board Special Report No. 247, pp. 36–75. National Academy Press, Washington DC (1996)Google Scholar
  7. 7.
    Hungr, O., Evans, S.G., Bovis, M.G., Hutchinson, J.N.: A review of the classification of landslides of the flow type. Environ. Eng. Geosci. 6(3), 1–18 (2001).  https://doi.org/10.2113/gseegeosci.7.3.221 Google Scholar
  8. 8.
    Richardson, J.R., Julien, P.Y.: Suitability of simplified overland flow equations. Water Resour. Res. 30(3), 665–671 (1994).  https://doi.org/10.1029/93WR03098 Google Scholar
  9. 9.
    Savage, S.B., Hutter, K.: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215 (1989).  https://doi.org/10.1017/S0022112089000340 MathSciNetzbMATHGoogle Scholar
  10. 10.
    Iverson, R.M.: The physics of debris flows. Rev. Geophys. 35(3), 245–296 (1997).  https://doi.org/10.1029/97RG00426 Google Scholar
  11. 11.
    Ng, C.W.W., Choi, C.E., Law, R.P.H.: Longitudinal spreading of granular flow in trapezoidal channels. Geomorphology 194, 84–93 (2013).  https://doi.org/10.1016/j.geomorph.2013.04.016 Google Scholar
  12. 12.
    Campbell, C.S., Brennen, C.E., Sabersky, R.H.: Flow regimes in inclined open-channel flows of granular materials. Powder Technol. 41, 77–82 (1985).  https://doi.org/10.1016/0032-5910(85)85077-4 Google Scholar
  13. 13.
    Pouliquen, O.: Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542 (1999).  https://doi.org/10.1063/1.869928 MathSciNetzbMATHGoogle Scholar
  14. 14.
    Pouliquen, O., Chevoir, F.: Dense flows of dry granular material. C. R. Phys. 3, 163–75 (2002).  https://doi.org/10.1016/S1631-0705(02)01309-9 Google Scholar
  15. 15.
    Forterre, Y.E., Pouliquen, O.: Flows of dense granular media. Ann. Rev. Fluid Mech. 40(1), 1–24 (2008).  https://doi.org/10.1146/annurev.fluid.40.111406.102142 MathSciNetzbMATHGoogle Scholar
  16. 16.
    Choi, C.E., Ng, C.W.W., Au-Yeung, S.C.H., Goodwin, G.R.: Froude characteristics of both dense granular and water flows in flume modelling. Landslides 12, 1197–1206 (2015).  https://doi.org/10.1007/s10346-015-0628-8 Google Scholar
  17. 17.
    Pudasaini, S.P., Hutter, K., Hsiau, S.S., Tai, S.C., Wang, Y., Katzenbach, R.: Rapid flow of dry granular materials down inclined chutes impinging on rigid walls. Phys. Fluids 19, 053302 (2007).  https://doi.org/10.1063/1.2726885 zbMATHGoogle Scholar
  18. 18.
    Ugarelli, R., Di Federico, V.: Transition from supercritical to subcritical regime in free surface flow of yield stress fluids. Geophys. Research Lett. 34, L21402 (2007).  https://doi.org/10.1029/2007GL031487 Google Scholar
  19. 19.
    Coussot, P.: Steady, laminar, flow of concentrated mud suspensions in open channel. J. Hydraul. Res. 32(4), 535–559 (2012).  https://doi.org/10.1080/00221686.1994.9728354 Google Scholar
  20. 20.
    Johnson, C.G., Gray, J.M.N.T.: Granular jets and hydraulic jumps on an inclined plane. J. Fluid Mech. 675, 87–116 (2011).  https://doi.org/10.1017/jfm.2011.2 MathSciNetzbMATHGoogle Scholar
  21. 21.
    Gray, J.M.N.T., Tai, Y.C., Noelle, S.: Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161–181 (2003).  https://doi.org/10.1017/S0022112003005317 MathSciNetzbMATHGoogle Scholar
  22. 22.
    Haldenwang, R., Slatter, P.T., Chhabra, R.P.: An experimental study of non-Newtonian fluid flow in rectangular flumes in laminar, transition and turbulent flow regimes. J. S. Afr. Inst. Civ. Eng. 52(1), 11–19 (2010)Google Scholar
  23. 23.
    Viccione, G., Rossi, F., Guida, D., Lenza, T.L.L.: Physical modelling of laboratory debris flows by using CMC WSEAS. Trans. Fluid Mech. 10, 164–174 (2015)Google Scholar
  24. 24.
    Iverson, R.M., George, D.L., Logan, M.: Debris flow runup on vertical barriers and adverse slopes. J. Geophys. Res. Earth Surf. 121, 2333–2357 (2016).  https://doi.org/10.1002/2016JF003933 Google Scholar
  25. 25.
    Viccione, G., Ferlisi, S., Marra, E.: A numerical investigation of the interaction between debris flows and defense barriers. In: Advances in Environmental and Geological Science and Engineering, Proceedings of the 8th International Conference on Environmental and Geological Science and Engineering (EG’15), Salerno, pp. 332–342 (2015). ISBN: 978-1-61804-314-6Google Scholar
  26. 26.
    Armanini, A., Scotton, P.: On the dynamic impact of a debris flow on structures. In: Proceedings of XXV Congress of IAHR, Tokyo, 30 Aug–3 Sept, 1993; Tech. Sess. B, III, pp. 203-210 (1993)Google Scholar
  27. 27.
    Faug, T.: Macroscopic force experienced by extended objects in granular flows over a very broad Froude-number range. Eur. Phys. J. E 38, 10 (2015).  https://doi.org/10.1140/epje/i2015-15034-3 Google Scholar
  28. 28.
    Law, R.P.H., Choi, C.E., Ng, C.W.W.: Discrete element investigation of the influence of debris flow baffles on rigid barrier impact. Can. Geotech. J. 53(2), 179–185 (2015).  https://doi.org/10.1139/cgj-2014-0394 Google Scholar
  29. 29.
    Ng, C.W.W., Choi, C.E., Koo, R.C.H., Kwan, J.S.H.: Dry granular flow interaction with dual-barrier systems. Géotechnique 68(5), 386–399 (2018).  https://doi.org/10.1680/jgeot.16.P.273 Google Scholar
  30. 30.
    Choi, C.E., Ng, C.W.W., Song, D., Law, R.P.H., Kwan, J.S.H., Ho, K.K.S.: A computational investigation of baffle configuration on the impedance of channelized debris flow. Can. Geotech. J. 52(2), 182–197 (2014).  https://doi.org/10.1139/cgj-2013-0157 Google Scholar
  31. 31.
    Kwan, J.S.: H. Supplementary technical guidance on design of rigid debris-resisting barriers. Technical Note No. TN 2/2012. Geotechnical Engineering Office, Civil Engineering and Development Department, The HKSAR Government, Hong Kong (2012).  https://doi.org/10.1016/j.jnnfm.2012.03.001
  32. 32.
    Domnik, B., Pudasaini, S.P.: Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations. J. Non-Newton. Fluid Mech. 173, 72–86 (2012).  https://doi.org/10.1016/j.jnnfm.2012.03.001 Google Scholar
  33. 33.
    Domnik, B., Pudasaini, S.P., Katzenbach, R., Miller, A.S.: Coupling of full two-dimensional and depth-averaged models for granular flows. J. Non-Newton. Fluid Mech. 201, 56–68 (2013).  https://doi.org/10.1016/j.jnnfm.2013.07.005 Google Scholar
  34. 34.
    Di Cristo, C., Iervolino, M., Vacca, A.: Applicability of kinematic and diffusive models for mud-flows: a steady state analysis. J. Hydrol. 559, 585–595 (2018).  https://doi.org/10.1016/j.jhydrol.2018.02.016 Google Scholar
  35. 35.
    Evangelista, S., De Marinis, G., Di Cristo, C., Leopardi, A.: Dam-break dry granular flows: experimental and numerical analysis. WSEAS Trans. Environ. Dev. 10(1), 382–392 (2014)Google Scholar
  36. 36.
    Di Cristo, C., Evangelista, S., Leopardi, A., Greco, M., Iervolino, M.: Numerical simulation of a dam-break with a wide range of shields parameter. In: Proceedings of the International Conference on Fluvial Hydraulics, RIVER FLOW 2014. 1679–1687 (2014).  https://doi.org/10.13140/2.1.2068.4485
  37. 37.
    Cornelius, E.A., Bernt, L.: Numerical solution of the Saint Venant equation for non-Newtonian fluid. In: The 55th Conference on Simulation and Modelling (SIMS 55), Aalborg (2014)Google Scholar
  38. 38.
    Sarno, L., Carravetta, A., Martino, R., Tai, Y.-C.: A two-layer depth averaged approach to describe the regime stratification in collapses of dry granular columns. Phys. Fluids 26, 10330 (2014).  https://doi.org/10.1063/1.4898563 Google Scholar
  39. 39.
    Sarno, L., Carravetta, A., Martino, R., Papa, M.N., Tai, Y.-C.: Some considerations on numerical schemes for treating hyperbolicity issues in two-layer models. Adv. Water Resour. 100, 183–198 (2017).  https://doi.org/10.1016/j.advwatres.2016.12.014 Google Scholar
  40. 40.
    Pastor, M., Haddad, B., Sorbino, G., Cuomo, S., Drempetic, V.: A depth-integrated, coupled SPH model for flow-like landslides and related phenomena. Int. J. Numer. Anal. Methods Geomech. 33, 143–184 (2009).  https://doi.org/10.1002/nag.705 zbMATHGoogle Scholar
  41. 41.
    Pugliese Carratelli, E., Viccione, G., Bovolin, V.: Free surface flow impact on a vertical wall: a numerical assessment. Theor. Comput. Fluid Dyn. 30(5), 403–414 (2016).  https://doi.org/10.1007/s00162-016-0386-9 Google Scholar
  42. 42.
    Cozzolino, L., Cimorelli, L., Covelli, C., Morte, R.D., Pianese, D.: Novel numerical approach for 1D variable density shallow flows over uneven rigid and erodible beds. J. Hydraul. Eng. 140(3), 254–268 (2014).  https://doi.org/10.1061/(ASCE)HY.1943-7900.0000821 Google Scholar
  43. 43.
    D’Aniello, A., Cozzolino, L., Cimorelli, L., Della Morte, R., Pianese, D.: A numerical model for the simulation of debris flow triggering, propagation and arrest. Nat. Hazards 75(2), 1403–1433 (2015).  https://doi.org/10.1007/s11069-014-1389-8 Google Scholar
  44. 44.
    D’Aniello, A., Cozzolino, L., Cimorelli, L., Covelli, C., Della Morte, R., Pianese, D.: One-dimensional simulation of debris-flow inception and propagation. Procedia Earth Planet. Sci. 9, 112–121 (2014).  https://doi.org/10.1016/j.proeps.2014.06.005 Google Scholar
  45. 45.
    Cozzolino, L., Pepe, V., Della Morte, R., Cirillo, V., D’Aniello, A., Cimorelli, L., Pianese, D.: One-dimensional mathematical modelling of debris flow impact on open-check dams. Procedia Earth Planet. Sci. 16, 5–14 (2016).  https://doi.org/10.1016/j.proeps.2016.10.002 Google Scholar
  46. 46.
    Rickenmann, D.: Hyperconcentrated flow and sediment transport at steep slopes. J. Hydraul. Eng. 117(11), 1419–1439 (1991).  https://doi.org/10.1061/(ASCE)0733-9429(1991)117:11(1419) Google Scholar
  47. 47.
    Di Cristo, C., Evangelista, S., Iervolino, M., Greco, M., Leopardi, A., Vacca, A.: Dam-break waves over an erodible embankment: experiments and simulations. J. Hydraul. Res. 56(2), 196–210 (2017).  https://doi.org/10.1080/00221686.2017.1313322 Google Scholar
  48. 48.
    Evangelista, S., Greco, M., Iervolino, M., Leopardi, A., Vacca, A.: A new algorithm for bank-failure mechanisms in 2D morphodynamic models with unstructured grids. Int. J. Sediment Res. 30(4), 382–391 (2015).  https://doi.org/10.1016/j.ijsrc.2014.11.003 Google Scholar
  49. 49.
    Evangelista, S., Altinakar, M., Di Cristo, C., Leopardi, A.: Simulation of dam-break waves on movable beds using a multi-stage centered scheme. Int. J. Sediment Res. 28(3), 269–284 (2013)Google Scholar
  50. 50.
    Martino, R., Papa, M.N.: Variable-concentration and boundary effects on debris flow discharge predictions. J. Hydraul. Eng. 134(9), 1294–1301 (2008).  https://doi.org/10.1061/(ASCE)0733-9429(2008)134:9(1294) Google Scholar
  51. 51.
    Naef, D., Rickenmann, D., Rutschmann, P., Mcardell, B.W.: Comparison of flow resistance relations for debris flows using a one-dimensional finite element simulation model. Nat. Hazards Earth Syst. Sci. 6(1), 155–165 (2006).  https://doi.org/10.5194/nhess-6-155-2006. (Copernicus Publications on behalf of the European Geo-sciences Union) Google Scholar
  52. 52.
    Shao, S., Lo, E.Y.M.: Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface. Adv. Water Resour. 26, 787–800 (2003).  https://doi.org/10.1016/S0309-1708(03)00030-7 Google Scholar
  53. 53.
    Manenti, S., Amicarelli, A., Todeschini, S.: WCSPH with limiting viscosity for modeling landslide hazard at the slopes of artificial reservoir. Water (Switzerland) 10(4), 515 (2018).  https://doi.org/10.3390/w10040515 Google Scholar
  54. 54.
    Hammad, K., Vradis, G.C.: Flow of a non-Newtonian Bingham plastic through an axisymmetric sudden contraction: effects of Reynolds and yield numbers. Numer. Methods Non-Newton. Fluid Dyn. ASME 179, 63–9 (1994)Google Scholar
  55. 55.
    Martinez, C.E., Miralles-Wilhelm, F., Garcia Martinez, R.: Quasi-three dimensional two-phase debris flow model accounting for boulder transport. In: 5-th International Conference on Debris Flow Hazards. Mitigation, Mechanics, Prediction and Assessment, pp. 457- 466 (2011)Google Scholar
  56. 56.
    Flow-3D User Manual v9.4Google Scholar
  57. 57.
    Fiorentino, A., De Luca, G., Rizzo, L., Viccione, G., Lofrano, G., Carotenuto, M.: Simulating the fate of indigenous antibiotic resistant bacteria in a mild slope wastewater polluted stream. J. Environ. Sci. 69, 95–104 (2018).  https://doi.org/10.1016/j.jes.2017.04.018 Google Scholar
  58. 58.
    Carreau, P.J., DeKee, D., Chhabra, R.P.: Rheology of Polymeric Systems: Principles and Applications. Hanser, Munich (1997)Google Scholar
  59. 59.
    Friedrichs, K.O., Lax, P.D.: Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. USA 68, 1686–1688 (1971).  https://doi.org/10.1073/pnas.68.8.1686 MathSciNetzbMATHGoogle Scholar
  60. 60.
    Courant, R., Friedrichs, K., Lewy, H.: On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11(2), 215–234 (1967).  https://doi.org/10.1147/rd.112.0215 MathSciNetzbMATHGoogle Scholar
  61. 61.
    Stoker, J.J.: Water Waves: The Mathematical Theory with Applications. Wiley, New York (1992).  https://doi.org/10.1002/9781118033159 zbMATHGoogle Scholar
  62. 62.
    Guinot, V.: Godunov-Type Schemes. An Introduction for Engineers. Elsevier, Amsterdam (2003)Google Scholar
  63. 63.
    Lanzini, A.: Modellistica del fronte d’avanzamento di fenomeni franosi. Master thesis, 118 (2012)Google Scholar
  64. 64.
    Pastor, M., Blanc, T., Pastor, M.J., Sanchez, M., Haddad, B., Mira, P., Fernandez Merodo, J.A., Herreros, M.I., Drempetic, V.: A SPH depth-integrated model with pore pressure coupling for fast landslides and related phenomena. In: Ho, Li (eds.) 2007 International Forum on Landslides Disaster Management (2007). ISBN 978-962 7619-30-7Google Scholar
  65. 65.
    Pokhrel, P.R.: General phase-eigenvalues for two-phase mass flows: supercritical and subcritical states. PhD thesis. 77 (2014)Google Scholar
  66. 66.
    Cascini, L., Cuomo, S., Pastor, M., Rendina, I.: Modelling of debris flows and flash floods propagation in storage basins of Italian Alps. Eng. Geol. Under ReviewGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of SalernoFiscianoItaly

Personalised recommendations