A Two-Phase Debris Flow Model with Boulder Transport

A Two-Phase Debris Flow Model with Boulder Transport

C. Martinez R. Garcia-Martinez F. Miralles-Wilhelm 

Department of Civil and Environmental Engineering, Florida International University

Florida International University and FLO-2D Software, Inc

Department of Earth and Environment, Florida International University

Page: 
389-402
|
DOI: 
https://doi.org/10.2495/SAFE-V1-N4-389-402
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

We present a quasi three-dimensional numerical model to simulate debris flows that considers a con-tinuum non-Newtonian fluid phase for water and fine sediments, and a non-continuum phase for large particles such as boulders. Particles are treated in a Lagrangian frame of reference using the 3D Discrete Element Method. The fluid phase is implemented in the RiverFLO-2D model, which solves the 2D depth-averaged shallow water equations with the Finite Element Method on a triangular non-structured mesh. The model considers particle–particle and wall–particle collisions, taking into account that particles are immersed in a fluid and subject to gravity, friction and drag forces. Bingham and Cross rheological models are used for the continuum phase providing very stable results, even in the range of very low shear rates. Results show that Bingham formulation proves better able to simulate the stopping of the fluid when the applied shear stresses are low. Comparing numerical results with analytical solutions and data from flume-experiments demonstrates that the model is capable of replicating the motion of large particles moving in the fluid flow. An application to simulate debris flows that occurred in Northern Venezuela in 1999 shows that the model can replicate the main boulder accumulation reported for that event.

Keywords: 

boulder accumulation, debris flow, discrete element method, finite element method, Lagrang-ian formulation

  References

[1] Iverson, R.M., The physics of debris fl ows, Rev. of Geophysics, 35, pp. 245–296, 1997. doi:http://dx.doi.org/10.1029/97RG00426

[2] Johnson, A.M., A Model for Debris fl ow, Ph.D. dissertation. Pennsylvania State University: University Park, 1965.

[3] Bingham, E.C. & Green, H., Paint a plastic material and not a viscous liquid; the mea-surement of its mobility and yield value. Proceedings of American Society of Testing Materials, 19, pp. 640–664, 1919.

[4] Barnes, H.A., Hutton J.F. & Walters, K., An introduction to rheology, Elsevier: Amsterdam, 1989.

[5] O’Brien, J.S. & Julien, P.Y., Physical properties and mechanics of hyperconcentrated sediment fl ows. ASCE Specialty Conference on the Delineation of Landslides, Debris Flows Hazards, pp. 260–279, 1985.

[6] Bagnold, R.A., Experiments on a gravity-free dispersion of large solid spheres in a N ewtonian fl uid under shear. Proceedings of the Royal Society of London, 225, pp. 49–63, 

1954. doi:http://dx.doi.org/10.1098/rspa.1954.0186

[7] Takahashi, T., Debris Flows, Balkema: Rotterdam, 1991.

[8] Asmar B.N., Langston, P.A. & Ergenzinger, P., The potential of the discrete element method to simulate debris fl ow. Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment, 1, pp. 435–445, 2003.

[9] O’Brien, J.S. & Julien, P.Y., Laboratory analysis of mudfl ows properties.  Journal of  Hydraulic Eng, 114(8), pp. 877–887, 1988. doi:http://dx.doi.org/10.1061/ (ASCE)0733-9429(1988)114:8(877)

[10] García-Martínez, R., Espinoza, R., Valera, E. & González, M., An explicit two-dimensional fi nite element model to simulate short and long term bed evolution in alluvial rivers. Journal of Hydraulic Research, 44(6), pp. 755–766, 2006. doi:http://dx.doi.org/

10.1080/00221686.2006.9521726

[11] Martinez, C., Miralles-Wilhelm, F. & Garcia-Martinez, R., A 2D fi nite element debris fl ow model based on the cross rheology formulation. Fourth International Conference on Debris-Flow Hazards Mitigation: Mechanics, Prediction and Assessment, Chendu: China, 2007.

[12] Huang, X. & Garcia, M.H., Asymtotic solution for Bingham debris fl ows. Debris-fl ow hazards mitigation: mechanics, prediction and assessment. Proceedings of the First  International Conference, ASCE: New York, pp. 561–575, 1991.

[13] Garcia-Martinez, R., Gonzalez, N. & O’Brien, J., Dam-break fl ood routing (Chapter 5). Dam-Break Problems, Solutions and Case Studies, ed. D. de Wrachien. & S. Mambretti, WIT Press, 2009. ISBN: 978-1-84564-142-9.

[14] Wieczorek, G.F., Larsen, M.C., Eaton, L.S., Morgan, B.A. & Blair, J.L., Debris-fl ow and fl ooding hazards associated with the December 1999 storm in coastal Venezuela and strategies for mitigation, U.S. Geological Survey, Open File Report 01–0144, 1991.

[15] Garcia-Martinez, R., Mud Flow Hazard Maps for Vargas State. Final Report for the Avila Project, Fluid Mechanics Institute: University Central of Venezuela (In Spanish), 2008.