Journal of Mountain Science

, Volume 16, Issue 2, pp 364–382 | Cite as

Numerical simulation of mud-flows impacting structures

  • Massimo Greco
  • Cristiana Di CristoEmail author
  • Michele Iervolino
  • Andrea Vacca


The study of the interaction of mud-flows with obstacles is important to define inundation zones in urban areas and to design the possible structural countermeasures. The paper numerically investigates the impact of a mud-flow on rigid obstacles to evaluate the force acting on them using two different depth-integrated theoretical models, Single-Phase Model (SPM) and Two-Phase Model (TPM), to compare their performance and limits. In the first one the water-sediment mixture is represented as a homogeneous continuum described by a shear-thinning power-law rheology. Alternatively, the two-phase model proposed by Di Cristo et al in 2016 is used, which separately accounts for the liquid and solid phases. The considered test cases are represented by a 1D landslide flowing on a steep slope impacting on a rigid wall and a 2D mud dam-break flowing on a horizontal bottom in presence of single and multiple rigid obstacles. In the 1D test case, characterized by a very steep slope, the Two-Phase Model predicts the separation between the two phases with a significant longitudinal variation of the solid concentration. In this case the results indicate appreciable differences between the two models in the estimation of both the wave celerity and the magnitude of the impact, with an overestimation of the peak force when using the Single-Phase Model. In the 2D test-cases, where the liquid and solid phases remain mixed, even if the flow fields predicted by the two models present some differences, the essential features of the interaction with the obstacles, along with the maximum impact force, are comparable.


Mud-Flow Impact force Two-phase model Power-law 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The work described in the present paper was realized in the framework of the project MISALVA, financed by the Italian Minister of the Environment, Land Protection and Sea. CUP H36C18000970005.


  1. Aureli F, Dazzi S, Maranzoni A, et al. (2015) Experimental and numerical evaluation of the force due to the impact of a dambreak wave on a structure. Advances in Water Resources 76: 29–42. Google Scholar
  2. Bukreev VI (2009) Force action of discontinuous waves on a vertical wall. Journal Applied Mechanics and Technical Physics. 50(2): 278–283. Google Scholar
  3. Burger J, Haldenwang R, Alderman N (2010) Friction factor- Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes. Chemical Engineering Science 85: 3549–3556. Google Scholar
  4. Campomaggiore F, Di Cristo C, Iervolino M, et al. (2016) Development of roll waves in power-law fluids with non-uniform initial conditions. Journal of Hydraulic Research 54(3): 289–306. Google Scholar
  5. Canelli L, Ferrero AM, Migliazza M, et al. (2012) Debris flow risk mitigation by means of rigid and flexible barriers–experimental tests and impact analysis. Natural Hazard and Earth System Science 12: 1693–1699. Google Scholar
  6. Carotenuto C, Merola MC, Ãlvarez-Romero M, et al. (2015) Rheology of natural slurries involved in a rapid mudflow with different soil organic carbon content. Colloids and Surfaces A 466: 57–65. Google Scholar
  7. Chanson H, Jarny S, Coussot P (2006) Dam Break Wave of Thixotropic Fluid. Journal of Hydraulic Engineering 132 (3): 280–293. Google Scholar
  8. Chiou MC, Wang Y, Hutter K (2005) Influence of obstacles on rapid granular flows. Acta Mechanica 175: 195–122. Google Scholar
  9. Coussot P (1994) Steady, laminar, flow of concentrated mud suspensions in open channel. Journal of Hydraulic Research 32(4): 535–559. Google Scholar
  10. Cui P, Gray JMNT (2013) Gravity driven granular free-surace flow around a circular cylinder. Journal of Fluid Mechanics 720: 314–337. Google Scholar
  11. Cui P, Hu K, Zhuang J, et al. (2011) Prediction of debris-flow area by combining hydrological and inundation simulation methods. Journal of Mountain Science 8: 1–9. Google Scholar
  12. Cui P, Chao Z, Lei Y (2015) Experimental analysis on the impact force of viscous debris flow. Earth Surface Process and Landforms 40:1644–1655. Google Scholar
  13. Dent JD, Lang TE (1983) A biviscous modified Bingham model of snow avalanche motion. Annals Glaciology 4: 42–46. Google Scholar
  14. Di Cristo C, Iervolino M, Vacca A (2006) Linear stability analysis of a 1-D model with dynamical description of bed load transport. Journal of Hydraulic Research 44: 480–487. Google Scholar
  15. Di Cristo C, Iervolino M, Vacca A (2013) Gravity-driven flow of a shear-thinning power-law fluid over a permeable plane. Applied Mathematical Sciences 7(33-36): 1623–1641. Google Scholar
  16. Di Cristo C, Iervolino M, Vacca A (2014) Simplified wave models applicability to shallow mud flows modeled as power-law fluids. Journal of Mountain Sciences 19: 956–965. Google Scholar
  17. Di Cristo C, Greco M, Iervolino M, Leopardi A, Vacca A (2016) Twodimensional two-phase depth-integrated model for transients over mobile bed. Journal of Hydraulic Engineering 142(2), 04015043. Google Scholar
  18. Di Cristo C, Iervolino M, Vacca A (2018a) Applicability of kinematic and diffusive models for mud flows: a steady state analysis. Journal of Hydrology 559: 585–595. Google Scholar
  19. Di Cristo C, Evangelista S, Iervolino M, et al. (2018b) Dam-break waves over an erodible embankment: experiments and simulations Journal of Hydraulic Research 56(2): 196–210. Google Scholar
  20. Dressler RF (1952) Hydraulic resistance effect upon the dam-break functions. Journal of Research of the National Bureau Standards 49(3): 217–225.Google Scholar
  21. Evangelista S, Greco M, Iervolino M, et al. (2015) A new algorithm for bank-failure mechanisms in 2D morphodynamic models with unstructured grids. International Journal of Sediment Research 30(4): 382–391. Google Scholar
  22. Faug T (2015) Depth-average analytical solution for free-surface granular flow impacting rigid walls down inclines. Physical Review E 92(6).
  23. Fernandez-Nieto ED, Bouchut F, Bresch D, et al. (2008) A new Savage-Hutter type model for submarine avalanches and generated tsunami. Journal of Computational Physic 227(16): 7720–7754. Google Scholar
  24. Fernández-Nieto ED, Noble P, Vila JP (2010) Shallow water equations for non-Newtonian fluids. Journal of Non-Newtonian Fluid Mechanics 165(13-14): 712–732. Google Scholar
  25. Gao L, Zhang LM, Chen HX (2017) Two dimensional simulation of debris flow impact pressure on buildings. Engineering Geology 226: 236–244. Google Scholar
  26. Gavrilov AA, Rudyak VY (2016) Reynolds-averaged modeling of turbulent flows of power-law fluids. Journal of Non-Newtonian Fluid Mechanics 227: 45–55. Google Scholar
  27. Gavrilov AA, Rudyak VY (2017) Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes. Fluid Dynamics 52(3): 363–374. Google Scholar
  28. Gori F, Boghi A (2011) Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids. International Communications in Heat and Mass Transfer 38(6): 696–703. Google Scholar
  29. Gori F, Boghi A (2012) A three dimensional exact equation for the turbulent dissipation rate of Generalised Newtonian Fluids. International Communications in Heat and Mass Transfer 39(4): 477–485. Google Scholar
  30. Greco M, Iervolino M, Leopardi A, et al. (2012a) A Two-Phase Model for Fast Geomorphic Shallow Flows. International Journal of Sediment Research 27(4): 409–425. Google Scholar
  31. Greco M, Iervolino M, Vacca A, et al. (2012b) Two-phase modelling of total sediment load in fast geomorphic transients. River Flow 2012, Proc., Int. Conf. on Fluvial Hydraulics, 1, Colegio de Ingenieros Civiles de Costa Rica (CiC): 643–648.Google Scholar
  32. Greco M, Iervolino M, Vacca A (2018) Analysis of bedform instability with 1-D two-phase morphodynamical models. Advances in Water Resources 120: 50–64. Google Scholar
  33. Harten A, Lax PD, van Leer B (1983) On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Review 25(1): 35–61. Google Scholar
  34. He S, Liu W, Ouyang C, et al. (2014) A two-phase model for numerical simulation of debris flow. Natural Hazard and Earth System Science 2: 2151–2183. Google Scholar
  35. Hewitt DR, Balmforth NJ (2013) Thixotropic gravity currents. Journal of Fluid Mechanics 727: 56–82. Google Scholar
  36. Hubl J, Steinwendtner H (2001) Two-dimensional simulation of two viscous debris flows in Austria. Physics and Chemistry of the Earth-Part C 26(9): 639–644. Google Scholar
  37. Huang X, Garcia MH (1998) A Herschel-Bulkley model for mud flow down a slope. Journal of Fluid Mechanics 374: 305–333. Google Scholar
  38. Hung O, Morgan GC, Kelerhals R (1984) Quantitative analysis of debris torrent hazard for design of remedial measures. Canadian Geothecnical Journal 21: 663–677. Google Scholar
  39. Hutter C, Svendsen B, Rickenmann D (1996) Debris flow modelling: A review, Continuum Mechanics and Thermodynamics 8(1): 1–35. Google Scholar
  40. Hwang CC, Chen JL, Wang JS, et al. (1994) Linear stability of power law liquid film flowing down an inclined plane. Journal of Physics D: Applied Physics 27: 2297–2301. Google Scholar
  41. Imran J, Harff P, Parker G (2001) A numerical model of submarine debris flows with graphical user interface. Computers & Geosciences 27(6): 717–729. Google Scholar
  42. Iervolino M, Carotenuto C, Gisonni C, et al. (2017) Impact Forces of a Supercritical Flow of a Shear Thinning Slurry Against an Obstacle. In: Mikoš M, Casagli N, Yin Y, et al. (eds), Advancing Culture of Living with Landslides. WLF 2017. Springer, Google Scholar
  43. Iverson RM (1997) The physics of debris flows. Review of Geophysics 35(3): 245–296. Google Scholar
  44. Iverson RM, Denlinger RP (2001) Flow of variably fluidized granular masses across three-dimensional terrain: 1. Coulomb mixture theory. Journal of Geophysical Research, Solid Earth 106(B1): 537–552. Google Scholar
  45. Iverson RM, George DL (2014) A depth-averaged debris-flow model that includes the effect of evolving dilatancy. I Physical basis. Proceeding of Royal Society A Mathematical Physical and Engineering Sciences 470: 1–31. Google Scholar
  46. Jóhannesson T, Gauer P, Issler P, et al. (2009) The design of avalanche protection dams-Recent practical and theoretical developments. Project Report EUR23339. Climate Change and Natural Hazard Research Area. Series2. European Commission (Available online at: Scholar
  47. Kattel P, Kafle J, Fischer JT, et al. (2018) Interaction of two-phase debris with obstacles. Engineering Geology 242: 197–217. Google Scholar
  48. Kolesnichenko O, Shiriaev AS (2002) Partial stabilization of underactuated Euler–Lagrange systems via a class of feedback transformations. Systems & Control Letters 45(2): 121–132. Google Scholar
  49. Laigle D, Labbe M (2017) SPH-based numerical study of the impact of mudflows on obstacles. International Journal of Erosion Control Engineering 10(1): 56–65. Google Scholar
  50. Leopardi A, Oliveri E, Greco M (2002) Two-dimensional modeling of flood to map risk prone areas. Journal of Water Resources Planning and Management 128(3): 168–178. Google Scholar
  51. Li J, Cao ZX, Hu KH, et al. (2018a) A depth-averaged two-phase model for debris flows over fixed beds. International Journal of Sediment Research 33(4): 462–477. Google Scholar
  52. Li J, Cao ZX, Hu KH, et al. (2018b) A depth-averaged two-phase model for debris flows over erodible beds. Earth Surface Processes and Landform 43(4): 817–839. Google Scholar
  53. Liu KF, Mei CC (1989). Slow spreading of a sheet of Bingham fluid on an inclined plane. Journal of Fluid Mechanics 207: 505–529. Google Scholar
  54. Longo S, Di Federico V, Chiapponi L (2015) Non-Newtonian powerlaw gravity currents propagating in confining boundaries. Environmental Fluid Mechanics 15: 515. Google Scholar
  55. Meng X, Wang Y (2016) Modelling and numerical simulation of twophase debris flows. Acta Geotechnica 11: 1027–1045. Google Scholar
  56. Mizuyama T (2008) Structural Countermeasures for debris flow disaster. International Journal of Erosion Control Engineering 1(2): 38–43. Google Scholar
  57. Morabito F, Teel AR, Zaccarian L (2004) Nonlinear anti-wind-up applied to Euler-Lagrange systems. IEEE Transactions on Robotics and Automation 20(3): 526–537. Google Scholar
  58. Ng C, Mei CC (1994) Roll waves on a shallow layer of mud modeled as a power-law fluid. Journal of Fluid Mechanics 263: 151–184. Google Scholar
  59. Ng CWW, Choi CE, Song D, et al. (2015) Physical modelling of baffled influence on landslide debris mobility. Landslide 12(1): 1–18. Google Scholar
  60. Noble P, Vila JP (2013) Thin power-law film flow down an inclined plane: consistent shallow-water models and stability under largescale perturbations. Journal of Fluid Mechanics 735: 29–60. Google Scholar
  61. O’Brien JS, Julien PY, Fullerton WT (1993) Two-dimensional water flood and mudflow simulation. Journal of Hydraulic Engineering 119(2): 244–261. Google Scholar
  62. Pelati M, Bouchut F, Mangeney A (2008) A Roe-type scheme for two-phase shallow granular flows over variable topography. ESAIM Mathematical Modelling and Numerical Analysis, 42: 851–885. Google Scholar
  63. Perazzo CA, Gratton J (2004) Steady and traveling flows of a power–law liquid over an incline. Journal of Non-Newtonian Fluid Mechanics 118: 57–64. Google Scholar
  64. Pitman EB, Le L (2005) A two-fluid model for avalanche and debris flows. Philosophical Transactions of the Royal Society A. Mathematical Physical and Engineering Sciences 363: 1573–1601. Google Scholar
  65. Pudasaini SP, Wang Y, Hutter K (2005) Modelling debris flows down general channels. Natural Hazard and Earth System Science 5(6): 799–819. Google Scholar
  66. Pudasaini SP (2012) A general two-phase debris flow model. Journal of Geophysical Research 117 F03010. Google Scholar
  67. Rudman M, Blackburn HM, Graham LJW, et al. (2004) Turbulent pipe flow of shear-thinning fluids. Journal of Non-newtonian Fluid Mechanics 118(1): 33–48. Google Scholar
  68. Rudman M, Blackburn HM (2006) Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method. Applied Mathematical Modelling 30(11): 1229–1248. Google Scholar
  69. Sharma R, May J, Alobaid F, et al. (2017) Euler-Euler CFD simulation of the fuel reactor of a 1 MWth chemical-looping pilot plant: Influence of the drag models and specularity coefficient. Fuel 200: 435–446. Google Scholar
  70. Scheidl C, Chiari M, Kaitna R, et al. (2013) Analysing debris-flow impact model, based on small scale modelling approach. Survey of Geophysics 34(1): 121–140. Google Scholar
  71. Shige-eda M, Akiyama J (2003) Numerical and experimental study on two-dimensional flood flows with and without structures. Journal of Hydraulic Engineering 129(10): 817–821. Google Scholar
  72. Soares-Frazão S, Canelas R, Cao Z, et al. (2012) Dam-break flows over mobile beds: experiments and benchmark tests for numerical models. Journal of Hydraulic Research 50(4): 364–375. Google Scholar
  73. Sonder I, Zimanowski B, Buttner R (2006) Non-Newtonian viscosity of basaltic magma. Geophysical Research Letter 33: L02303. Google Scholar
  74. Sovilla B, Faug T, Kohler A, et al. (2016) Gravitational wet avalanche pressure on pylon-like structures. Cold Regions Science and Technology 126: 66–75. Google Scholar
  75. Tai YC, Gray JMN, Hutter C, et al. (2001) Flow dense avalanches past obstructions. Annals of Glaciology 32: 281–284 Google Scholar
  76. Takahashi T (2007) Debris Flow: Mechanics, Prediction and Countermeasures. Taylor and Francis, New York, USA.Google Scholar
  77. Teufelsbauer H, Wang Y, Chou C, et al. (2009) Flow obstacleinteraction in rapid granular avalanches: DEM simulation and comparison with experiments. Granular Matter 11(4): 209–220. Google Scholar
  78. Tiberghien D, Laigle D, Naaim M, et al. (2007) Experimental investigation of interaction between mudflow and on obstacle. Proceeding of the International Conference on Debris-Flow Hazard Mitigation: Mechanics, Prediction and Assessment, Chengdu. China. pp 281–292.Google Scholar
  79. Turnbull B, Bowman ET, McElwaine JN (2015) Debris flows: experiments and modelling. Comptes Rendus Physique 16(1): 86–96.Google Scholar
  80. Vagon F, Segalini A (2016) Debris flow impact estimation on a rigid barrier. Natural Hazard and Earth System Science 16: 1691–1697. Google Scholar
  81. Wang Y, Williams KC, Jones MG, et al. (2010) CFD simulation of gas-solid flow in dense phase bypass pneumatic conveying using the Euler-Euler model. Applied Mechanics and Materials 26-28: 1190–1194. Google Scholar
  82. Wang F, Chen X, Chen J, et al. (2017) Experimental study on a debris-flow drainage channel with different types of energy dissipation baffles. Engineering Geology 220: 43–51. Google Scholar
  83. Wu W, Wang SS-Y (2007) One dimensional modeling of dam-break flow over movable beds. Journal of Hydraulic Engineering 133(1): 48–58. Google Scholar
  84. Xia CC, Li J, Cao ZX, et al. (2018) A quasi single-phase model for debris flows and its comparison with a two-phase model. Journal of Mountain Science 15(5): 1071–1089. Google Scholar
  85. Zhang X, Bai Y, Ng CO (2010) Rheological Properties of Some Marine Muds Dredged from China Coasts. Proceedings of the 28 International Offshore and Polar Engineering Conference, Beijing, China. pp 455–461.Google Scholar

Copyright information

© Science Press, Institute of Mountain Hazards and Environment, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DICEAUniversità di Napoli Federico IINapoliItaly
  2. 2.DIUniversità della Campania Luigi VanvitelliAversa (CE)Italy

Personalised recommendations