A Perturbation Solution for Bingham-Plastic Mudflows
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 11
Abstract
An analytical solution is proposed for laminar mudflows and debris flows that can be modeled by a Bingham-plastic law. Two-dimensional, unsteady, nonuniform, Bingham flows released from a point source or a source of finite size (dam-break problem or mudslide problem) on a steep slope are considered. The method of matched asymptotic expansions was implemented to get a first-order solution. For the dam-break problem, the proposed model is found to be valid when the shock wave has advanced three reservoir lengths downstream. Also, it is found that the Bingham flow only propagates a finite distance downstream, with the shock depth asymptotically approaching the yield depth and the shock velocity asymptotically falling to zero. The hydrograph produced by a Bingham flow is seen to have a slower and lower flood peak and a longer and higher flow tail than that produced by Newtonian flow having the same dynamic viscosity. Comparison of the model predictions with laboratory observations shows reasonable agreement.
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References
1.
Aguirre-Pe, J., Quisca, S., and Plachco, F. P.(1995). “Tests and numerical one-dimensional modeling of a high-viscosity fluid dam-break wave.”J. Hydr. Res., Delft, The Netherlands, 33(1), 17–26.
2.
Arattano, M., and Savage, W. Z. (1992). “Kinematic wave theory for debris flows.”Open-File Rep. 92-290, U.S. Dept. of the Interior, Geological Survey, Denver, Colo.
3.
Chen, C. L.(1988a). “Generalized viscoplastic modeling of debris flow.”J. Hydr. Engrg., ASCE, 114(3), 237–258.
4.
Chen, C. L.(1988b). “General solution for viscoplastic debris flow.”J. Hydr. Engrg., ASCE, 114(3), 259–282.
5.
Choi, S. U., and Garcia, M. H. (1993). “Kinematic wave approximation for debris flow routing.”Proc. XXV Congr. of Int. Assoc. Hydr. Res., Tokyo, Japan.
6.
Coussot, P.(1994). “Steady, laminar flow of concentrated mud suspensions in open channel.”J. Hydr. Res., Delft, The Netherlands, 32(4), 535–559.
7.
Crochet, M. J., Davies, A. R., and Walters, K. (1984). Numerical simulation of non-Newtonian flow. Elsevier, New York, N.Y.
8.
Crochet, M. J., and Walters, K.(1983). “Numerical methods in non-Newtonian fluid mechanics.”Annu. Rev. Fluid Mech., 15, 241–260.
9.
Davies, T. R. H. (1988). Debris flow surges—a laboratory investigation. Report No. 96, ETH, Zurich, Switzerland.
10.
Dent, D. J., and Lang, T. E.(1983). “A biviscous modified Bingham model of snow avalanche motion.”Ann. Glaciol., 4, 42–46.
11.
Hungr, O. (1988). “Notes on dynamic analysis of flowslides.”Landslides, C. Bonnard, ed., Vol. 1, A. A. Balkema Publishers, Brookfield, Vt., 679–683.
12.
Hunt, B.(1994). “Newtonian fluid mechanics treatment of debris flows and avalanches.”J. Hydr. Engrg., ASCE, 120(12), 1350–1363.
13.
Krone, R. B. (1963). “A study of rheologic properties of estuarial sediments.”Ser. Rep. No. 63-8, Hydr. Engrg. Lab. and Sanitary Res. Lab., Univ. of Calif., Berkeley, Calif.
14.
Krone, R. B., and Wright, V. (1987). “Laboratory and numerical study of mud and debris flow, Vol. 1 and 2.”Rep. of Dept. Civ. Engrg., Univ. of Calif., Davis, Calif.
15.
Jeyapalan, J. K., Duncan, J. M., and Seed, H. B.(1983). “Analysis of flow failures of mine tailings dams.”J. Geotech. Engrg., ASCE, 109(2), 150–189.
16.
Jiang, L., and LeBlond, P. H. (1993). “Numerical modeling of an underwater Bingham plastic mudslide and the wave which it generates.”J. Geophys. Res., 98(C6), 10303–10317.
17.
Johnson, A. M. (1970). Physical processes in geology. Freeman, San Francisco, Calif.
18.
Li, J., Yuan, J., Bi, C., and Luo, D.(1983). “The main features of the mudflow in Jiang-Jia Ravine.”Z. Geomorph. N. F., 27(3), 325–341.
19.
Liu, K. F., and Mei, C. C.(1989). “Slow spreading of a sheet of Bingham fluid of an inclined plane.”J. Fluid Mech., Cambridge, U.K., 207, 505–529.
20.
MacArthur, R. C., and Schamber, D. R. (1985). “Numerical methods for simulating mudflows.”Third Int. Symp. on River Sedimentation, Jackson, Miss.
21.
Mainali, A., and Rajaratnam, N. (1991). “Hydraulics of debris flows—a review.”Tech. Rep. No. WRE91-2, Dept. Civ. Engrg., Univ. of Alberta, Edmonton, Alberta, Canada.
22.
Mainali, A., and Rajaratnam, N.(1994). “Experimental study of debris flows.”J. Hydr. Engrg., ASCE, 120(1), 104–123.
23.
Migniot, P. C. (1968). “A study of the physical properties of various forms of very fine sediment and their behavior under hydrodynamic action.” La Houille Blanche, No. 7, 591–620 (in French).
24.
Nayfeh, A. H. (1973). Perturbation methods. John Wiley & Sons, Inc., New York, N.Y.
25.
Sabersky, R. H., Acosta, A. J., and Hauptmann, E. G. (1989). Fluid flow: a first course in fluid mechanics, 3rd Ed., Macmillan Publishing Co., New York, N.Y.
26.
Takahashi, T. (1991). “Debris flows.”International Association for Hydraulic Research Monogr. Ser., Balkema Publishers, Brookfield, Vt., USA.
27.
Wan, Z. (1982). “Bed material movement in hyperconcentrated flow.”Ser. Paper No. 31, Inst. of Hydrodyn. and Hydraul. Engrg., Tech. Univ. of Denmark, Lyngby, Denmark.
28.
Wan, Z., and Wang, Z. (1994). Hyperconcentrated flow, International Association for Hydraulic Research monograph series, Balkema Publishers, The Netherlands.
29.
Wang, M., Duan, W., Tan, G., and Zhan, Y. (1985). “On the structure and movement mechanism of flow with hyperconcentration of sediment.”Paper presented at Int. Workshop on Flow at Hyperconcentrations of Sediment, Int. Res. and Training Ctr. on Erosion and Sedimentation (IRTCES), Beijing, People's Republic of China.
30.
Whitham, G. B. (1974). Linear and nonlinear waves. Wiley-Interscience, New York, N.Y.
31.
Wright, V., and Krone, R. (1987). “Laboratory and numerical study of mud and debris flows.”Proc., 22nd International Association for Hydraulic Research Congress, Lausanne, Switzerland.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 123 • Issue 11 • November 1997
Pages: 986 - 994
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
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