Coupled Effects of Energy Dissipation and TravellingVelocity in the Run-Out Simulation of High-SpeedGranular

ABSTRACT

The run-out of high speed granular masses or avalanches along mountain streams, till their arrest, is analytically modeled. The power balance of a sliding granular mass along two planar sliding surfaces is written by taking into account the mass volume, the slopes of the surfaces, the fluid pressure and the energy dissipation. Dissipation is due to collisions and displacements, both localized within a layer at the base of the mass. The run-out, the transition from the first to the second sliding surface and the final run-up of the mass are described by Ordinary Differential Equations (ODEs), solved in closed form (particular cases) or by means of numerical procedures (general case). The proposed solutions allow to predict the run-up length and the speed evolution of the sliding mass as a function of the involved geometrical, physical and mechanical parameters as well as of the simplified rheological laws assumed to express the energy dissipation effects. The corresponding solutions obtained according to the Mohr-Coulomb or Voellmy resistance laws onto the sliding surfaces are recovered as particular cases. The run-out length of a documented case is finally back analysed through the proposed model.

The run-out of high speed granular masses or avalanches along mountain streams, till their arrest, is analytically modeled. The power balance of a sliding granular mass along two planar sliding surfaces is written by taking into account the mass volume, the slopes of the surfaces, the fluid pressure and the energy dissipation. Dissipation is due to collisions and displacements, both localized within a layer at the base of the mass. The run-out, the transition from the first to the second sliding surface and the final run-up of the mass are described by Ordinary Differential Equations (ODEs), solved in closed form (particular cases) or by means of numerical procedures (general case). The proposed solutions allow to predict the run-up length and the speed evolution of the sliding mass as a function of the involved geometrical, physical and mechanical parameters as well as of the simplified rheological laws assumed to express the energy dissipation effects. The corresponding solutions obtained according to the Mohr-Coulomb or Voellmy resistance laws onto the sliding surfaces are recovered as particular cases. The run-out length of a documented case is finally back analysed through the proposed model.

Cite this paper

nullF. Federico and G. Favata, "Coupled Effects of Energy Dissipation and TravellingVelocity in the Run-Out Simulation of High-SpeedGranular,"*International Journal of Geosciences*, Vol. 2 No. 3, 2011, pp. 274-285. doi: 10.4236/ijg.2011.23030.

nullF. Federico and G. Favata, "Coupled Effects of Energy Dissipation and TravellingVelocity in the Run-Out Simulation of High-SpeedGranular,"

References

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[2] S. Straub,“Predictability of Long Run-Out Landslide Motion: Implications from Granular Flows Mechanics,” Geologische Rundschau, Vol. 86, No. 2, 1997, pp. 415-425. doi:10.1007/s005310050150

[3] A. Musso, F. Federico and G. Troiano, “A Mechanism of Pore Pressure Accumulation in Rapidly Sliding Submerged Porous Blocks,” Computers and Geotechnics, Vol. 31, No. 3, 2004, pp. 209-226. doi:10.1016/j.compgeo.2004.02.001

[4] S. B. Savage and K. Hutter, “The Motion of a Finite Mass of Granular Material Down a Rough Inclined Plane,” Journal of Fluid Mechanics, Vol. 199, 1989, pp. 177-215. doi:10.1017/S0022112089000340

[5] K. T. Chau, “Onset of Natural Terrain Landslides Modelled by Linear Stability Analysis of Creeping Slopes with a Two-State Variable Friction Law,” International Journal for Numerical and Analytical Method in Geomechanics, Vol. 23, No. 15, 1999, pp. 1835-1855. doi:10.1002/(SICI)1096-9853(19991225)23:15<1835::AID-NAG2>3.0.CO;2-2

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[7] D. Zhang and M. A. Foda, “An instability Mechanism for the Sliding Motion of Finite Depth of Bulk Granular Materials,” Acta Mechanica, Vol. 121, No. 1-4, 1997, pp. 1-19. doi:10.1007/BF01262520

[8] J. Corominas, “The Angle of Reach as Mobility Index for Small and Large Landslides,” Canadian Geotechnical Journal, Vol. 33, No. 2, 1996, pp. 260-271. doi:10.1139/t96-005

[9] Y. S. Fang and Z. Y. Zhang, “Kinematic Mechanism of Catastrophic Landslides and Prediction of Their Velocities and Travelling Distance,” Landslides, Lausanne, 1988.

[10] D. Rickenmann, “Empirical Relationships for Debris Flows,” Natural Hazards, Vol. 19, No. 1, 1999, pp. 47-77. doi:10.1023/A:1008064220727

[11] A. E. Scheidegger, “On the Prediction of the Reach and Velocity of Catastrophic Landslides,” Rock Mechanics, Vol. 5, No. 4, 1973, pp. 231-236. doi:10.1007/BF01301796

[12] D. Zhang and M. A. Foda, “Internal Wave - Granular Temperature Interaction: An Energy Balance Study on Granular Flow,” Acta Mechanica, Vol. 136, No. 3-4, 1999, pp. 155-170. doi:10.1007/BF01179255

[13] N. Mitarai, H. Nakanishi, “Velocity Correlations in the Dense Granular Shear Flows: Effects on Energy Dissipation and Normal Stress,” Physical Review E, Vol. 75, 2007.

[14] R. A. Bagnold, “Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear,” Proceeding of the Royal Society, Vol. 225, No. 1160, 1954, pp. 49-63. doi:10.1098/rspa.1954.0186

[15] B. Salm, “Contribution to Avalanche Dynamics,” in Proceeding of International Symposium on Scientific Aspects of Snow and Ices Avalanches, Davos, 5-10 April 1965, pp. 199-214.

[16] M. Pirulli and A. Mangeney, “Results of Back-Analysis of the Propagation of Rock Avalanches as a Function of Assumed Rheology,” Rock Mechanics and Rock Engineering, Vol. 41, No. 1, 2008, pp. 59-84. doi:10.1007/s00603-007-0143-x

[17] A. Musso, F. Federico and M. Palmieri, “Proguex–A Code to Estimate the Run-Out Length of Granular Debris Flows,” in Italian, in Manuale di Ingegneria Civile ed Ambientale, Vol. 1, 2003.

[18] D. Ayotte, O. Hungr, “Assessment of Natural Terrain Landslide Debris Mobility,” Geotechnical Engineering Office, Hong Kong, 1998.

[19] H. Chen and C. F. Lee, “Numerical Simulation of Debris Flow,” Canadian Geotechnical Journal, Vol. 37, No. 1, 2000, pp. 146-160. doi:10.1139/t99-089

[20] T. H. Erismann and G. Abele, “Dynamics of Rockslides and Rockfalls,” Springer-Verlag, Berlin, 2001.

[21] R. J. Fannin and T. P. Rollerson, “Debris flows: Some Physical Characteristics and Behaviour,” Canadian Geo- technical Journal, Vol. 30, No. 1, 1993, pp. 71-81. doi:10.1139/t93-007

[22] A. Helmstetter, D. Sornette, J. R. Grasso, J. V. Andersen, S. Gluzman and V. Pisarenko, “Slider Block Friction Model for Landslides: Applications to Vaiont and La Clapière Landslides,” Journal of Geophysical Research, Vol. 109, 2004. doi:10.1029/2002JB002160

[23] O. Hungr, “Model for the Run-Out Analysis of Rapid Flow Slides, Debris Flows, and Avalanches,” Canadian Geotechnical Journal, Vol. 32, No. 4, 1995, pp. 610-623. doi:10.1139/t95-063

[24] O. Hungr and S. G. Evans, “Rock Avalanche Run out Prediction Using a Dynamic Model,” Proceeding of 7th International Symposium on Landslides, Vol. 1, Trondheim, 1996, pp. 233-238.

[25] H. J. Melosh, “The Mechanics of Large Rock Avalanches,” Reviews in Engeneering Geology, Vol. 7, 1987, pp. 41-49

[26] M. Pirulli and G. Sorbino, “Effetto della Reologia sull’ Analisi della Propagazione di Flussi di Detrito,” Incontro Annuale dei Ricercatori di Geotecnica, Pisa, 2006.

[27] P. Revellino, O. Hungr, F. Guadagno and S. G. Evans, “Velocity and Run-out Simulation of Destructive Debris Flows and Debris Avalanches in Pyroclastic Deposits Cam- pania Region, Italy,” Environmental Geology, Vol. 45, No. 3, 2003, pp. 295-311. doi:10.1007/s00254-003-0885-z

[28] S. B. Savage, “Flows of Granular Materials with Applica- Tions to Geophysical Problems,” International Summer School on Mechanics, Udine, 1992.

[29] M. Tiande, L. Zhougyu, N. Yonghang and M. Chongwu, “A Sliding Block Model for the Run-out Prediction of High-Speed Landslides,” Canadian Geotechnical Journal, Vol. 38, No. 2, 2001, pp. 217-226. doi:10.1139/t00-092

[30] J. Vaunat, S. Leroueil, “Analysis of Post-Failure and Slope Movements within the Framework of Hazard and Risk Analysis,” Natural Hazards, Vol. 26, No. 1, 2002, pp. 83-109. doi:10.1023/A:1015224914845

[1] D. M. Cruden and D. J. Varnes, “Landslides Types and Processes,” In A. K. Turner and R. L. Schuster Eds., Landslides: Investigation and Mitigation, National Academy Press, Washington, 1996, pp. 36-75.

[2] S. Straub,“Predictability of Long Run-Out Landslide Motion: Implications from Granular Flows Mechanics,” Geologische Rundschau, Vol. 86, No. 2, 1997, pp. 415-425. doi:10.1007/s005310050150

[3] A. Musso, F. Federico and G. Troiano, “A Mechanism of Pore Pressure Accumulation in Rapidly Sliding Submerged Porous Blocks,” Computers and Geotechnics, Vol. 31, No. 3, 2004, pp. 209-226. doi:10.1016/j.compgeo.2004.02.001

[4] S. B. Savage and K. Hutter, “The Motion of a Finite Mass of Granular Material Down a Rough Inclined Plane,” Journal of Fluid Mechanics, Vol. 199, 1989, pp. 177-215. doi:10.1017/S0022112089000340

[5] K. T. Chau, “Onset of Natural Terrain Landslides Modelled by Linear Stability Analysis of Creeping Slopes with a Two-State Variable Friction Law,” International Journal for Numerical and Analytical Method in Geomechanics, Vol. 23, No. 15, 1999, pp. 1835-1855. doi:10.1002/(SICI)1096-9853(19991225)23:15<1835::AID-NAG2>3.0.CO;2-2

[6] R. M. Iverson, M. E. Reid and R. G. Lahusen, “Debris- flow Mobilization from Landslides,” Journals of Earth and Planetary Sciences, Vol. 25, 1997, pp. 85-138. doi:10.1146/annurev.earth.25.1.85

[7] D. Zhang and M. A. Foda, “An instability Mechanism for the Sliding Motion of Finite Depth of Bulk Granular Materials,” Acta Mechanica, Vol. 121, No. 1-4, 1997, pp. 1-19. doi:10.1007/BF01262520

[8] J. Corominas, “The Angle of Reach as Mobility Index for Small and Large Landslides,” Canadian Geotechnical Journal, Vol. 33, No. 2, 1996, pp. 260-271. doi:10.1139/t96-005

[9] Y. S. Fang and Z. Y. Zhang, “Kinematic Mechanism of Catastrophic Landslides and Prediction of Their Velocities and Travelling Distance,” Landslides, Lausanne, 1988.

[10] D. Rickenmann, “Empirical Relationships for Debris Flows,” Natural Hazards, Vol. 19, No. 1, 1999, pp. 47-77. doi:10.1023/A:1008064220727

[11] A. E. Scheidegger, “On the Prediction of the Reach and Velocity of Catastrophic Landslides,” Rock Mechanics, Vol. 5, No. 4, 1973, pp. 231-236. doi:10.1007/BF01301796

[12] D. Zhang and M. A. Foda, “Internal Wave - Granular Temperature Interaction: An Energy Balance Study on Granular Flow,” Acta Mechanica, Vol. 136, No. 3-4, 1999, pp. 155-170. doi:10.1007/BF01179255

[13] N. Mitarai, H. Nakanishi, “Velocity Correlations in the Dense Granular Shear Flows: Effects on Energy Dissipation and Normal Stress,” Physical Review E, Vol. 75, 2007.

[14] R. A. Bagnold, “Experiments on a Gravity-Free Dispersion of Large Solid Spheres in a Newtonian Fluid under Shear,” Proceeding of the Royal Society, Vol. 225, No. 1160, 1954, pp. 49-63. doi:10.1098/rspa.1954.0186

[15] B. Salm, “Contribution to Avalanche Dynamics,” in Proceeding of International Symposium on Scientific Aspects of Snow and Ices Avalanches, Davos, 5-10 April 1965, pp. 199-214.

[16] M. Pirulli and A. Mangeney, “Results of Back-Analysis of the Propagation of Rock Avalanches as a Function of Assumed Rheology,” Rock Mechanics and Rock Engineering, Vol. 41, No. 1, 2008, pp. 59-84. doi:10.1007/s00603-007-0143-x

[17] A. Musso, F. Federico and M. Palmieri, “Proguex–A Code to Estimate the Run-Out Length of Granular Debris Flows,” in Italian, in Manuale di Ingegneria Civile ed Ambientale, Vol. 1, 2003.

[18] D. Ayotte, O. Hungr, “Assessment of Natural Terrain Landslide Debris Mobility,” Geotechnical Engineering Office, Hong Kong, 1998.

[19] H. Chen and C. F. Lee, “Numerical Simulation of Debris Flow,” Canadian Geotechnical Journal, Vol. 37, No. 1, 2000, pp. 146-160. doi:10.1139/t99-089

[20] T. H. Erismann and G. Abele, “Dynamics of Rockslides and Rockfalls,” Springer-Verlag, Berlin, 2001.

[21] R. J. Fannin and T. P. Rollerson, “Debris flows: Some Physical Characteristics and Behaviour,” Canadian Geo- technical Journal, Vol. 30, No. 1, 1993, pp. 71-81. doi:10.1139/t93-007

[22] A. Helmstetter, D. Sornette, J. R. Grasso, J. V. Andersen, S. Gluzman and V. Pisarenko, “Slider Block Friction Model for Landslides: Applications to Vaiont and La Clapière Landslides,” Journal of Geophysical Research, Vol. 109, 2004. doi:10.1029/2002JB002160

[23] O. Hungr, “Model for the Run-Out Analysis of Rapid Flow Slides, Debris Flows, and Avalanches,” Canadian Geotechnical Journal, Vol. 32, No. 4, 1995, pp. 610-623. doi:10.1139/t95-063

[24] O. Hungr and S. G. Evans, “Rock Avalanche Run out Prediction Using a Dynamic Model,” Proceeding of 7th International Symposium on Landslides, Vol. 1, Trondheim, 1996, pp. 233-238.

[25] H. J. Melosh, “The Mechanics of Large Rock Avalanches,” Reviews in Engeneering Geology, Vol. 7, 1987, pp. 41-49

[26] M. Pirulli and G. Sorbino, “Effetto della Reologia sull’ Analisi della Propagazione di Flussi di Detrito,” Incontro Annuale dei Ricercatori di Geotecnica, Pisa, 2006.

[27] P. Revellino, O. Hungr, F. Guadagno and S. G. Evans, “Velocity and Run-out Simulation of Destructive Debris Flows and Debris Avalanches in Pyroclastic Deposits Cam- pania Region, Italy,” Environmental Geology, Vol. 45, No. 3, 2003, pp. 295-311. doi:10.1007/s00254-003-0885-z

[28] S. B. Savage, “Flows of Granular Materials with Applica- Tions to Geophysical Problems,” International Summer School on Mechanics, Udine, 1992.

[29] M. Tiande, L. Zhougyu, N. Yonghang and M. Chongwu, “A Sliding Block Model for the Run-out Prediction of High-Speed Landslides,” Canadian Geotechnical Journal, Vol. 38, No. 2, 2001, pp. 217-226. doi:10.1139/t00-092

[30] J. Vaunat, S. Leroueil, “Analysis of Post-Failure and Slope Movements within the Framework of Hazard and Risk Analysis,” Natural Hazards, Vol. 26, No. 1, 2002, pp. 83-109. doi:10.1023/A:1015224914845