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Abstract

We present a mathematical model for movement of debris flows, based on kinematic wave theory, and apply our model to published data from two debris flows that occurred in 1981 on Mount St. Helens, Washington, U.S.A. The model, which is based on a relationship originally developed for water flow in open channels, shows good agreement with the field data.

Résumé

Un modèle mathématique est présenté, qui concerne la dynamique des «laves torentielles», basé sur la théorie de l'onde cinématique. Le modèle est appliqué aux données publiées se rapportant à deux phénomènes de laves torrentielles qui ne sont produits en 1981 sur le Mont St. Helens, Etat de Washington, aux Etats-Unis. Le modèle qui est basé sur une équation développée à l'origine pour le flux d'eau en canal ouvert, laisse apparaître une bonne correspondance avec les données expérimentales.

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References

  • ABBOTT M.B., 1966: An introduction to the method of characteristics. New York, American Elsevier, 243 p.

    Google Scholar 

  • ARATTANO M. and SAVAGE W.Z., 1992: Kinematic wave theory for debris flows: U.S. Geological Survey Open-File Report, 92–290, 39 p.

  • BAGNOLD R.A., 1954: Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid near shear. Proceedings, Royal Society of London, ser. A. v. 225, p. 49–63.

    Article  Google Scholar 

  • BINGHAM E.C., 1922: Fluidity and plasticity: McGraw-Hill, New York, 440 p.

    Google Scholar 

  • CHEN C.L., 1987: Comprehensive review of debris flow modeling concepts in Japan, in Costa J.E., and Wieczorek, G.F., eds., Debris flow/avalanches—Process, recognition and mitigation: Geological Society of America, Reviews in Engineering Geology, v. 7, p. 13–29.

  • CHEN C.L., 1988: Generalized viscoplastic modeling of debris flows. American Society of Civil Engineers, Journal of Hydraulic Engineering, v. 114, no. 3, p. 237–258.

    Article  Google Scholar 

  • CHOW V.T., 1959: Open-channel hydraulics: McGraw-Hill, New York, 680 p.

    Google Scholar 

  • COSTA J.E. and WILLIAMS G.P., 1984: Debris-flow dynamics: U.S. Geological Survey Open-File Report 84–606, Video Tape, 23 min.

  • GALLINO G.L. and PIERSON T.C., 1984: The 1980 Polallie creek debris flow and subsequent dam-break flood, east Fork Hood river basin, Oregon: U.S. Geological Survey Open-File Report, 84–587, 39 p.

  • HENDERSON F.M., 1966: Open channel flow: MacMillan Publishing Co. Inc., New York, 522 p.

    Google Scholar 

  • HUNT B., 1982: Asymptotic solution for dam-break problem: Journal of the Hydraulics division, Proceedings of the American Society of Civil Engineers, v. 108, no. HY1, p. 115–126.

    Google Scholar 

  • JOHNSON A.M., 1970: Physical processes in geology: W.H. Freeman, San Francisco, 577 p.

    Google Scholar 

  • LAENEN A. and HANSEN R.P., 1988: Simulation of three lahars in the mount St. Helens area, Washington, using a one-dimensional, unsteady-state streamflow model: U.S. Geological Survey Water-Resources Investigation Report 88–4004, 20 p.

  • LIGHTHILL M.J. and WHITHAM G.B., 1955: On kinematic waves I. Flood movement in long rivers. Proceedings of the Royal Society of London, v. A 229, p. 281–316.

    Article  Google Scholar 

  • MAIONE U., 1977: Appunti di idrologia. Le piene fluviali: La Goliardica Pavese, Pavia, Italy, v. 3, 224 p.

    Google Scholar 

  • MILLER J.E., 1984: Basic concepts of kinematic-wave models. U.S. Geological Survey Professional Paper 1302:32 p., Washington.

  • PIERSON T.C., 1986: Flow behavior of channelized debris flows, Mount St. Helens, Washington, in Abrahms A.D., ed., Hillslope Processes: Allen & Unwin, Boston, p. 269–296.

    Google Scholar 

  • PIERSON T.C., JANDA R.J., THOURET J. and BORRERO C.A., 1990: Perturbation and melting of snow and ice by the 13 November 1985 eruption of Nevado del ruiz, Colombia, and consequent mobilization, flow and deposition of lahars: Journal of Volcanology and Geothermal Research, v. 41, p. 17–66.

    Article  Google Scholar 

  • RODINE J.M. and JOHNSON A.M., 1976: The ability of debris, heavily freighted with coarse clastic materials, to flow on gentle slopes: Sedimentology, v. 23, p. 213–234.

    Article  Google Scholar 

  • ROUSE H., 1938: Fluid mechanics for hydraulic engineers: McGraw-Hill, New York, 422 p.

    Google Scholar 

  • TAKAHASHI T., 1978: Mechanical characteristics of debris flow: Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, v. 104, no. HY8, p. 1153–1169.

    Google Scholar 

  • TAKAHASHI T., 1980: Debris flow on primatic open channel: Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers, v. 106, no. HY3, p. 381–398.

    Google Scholar 

  • TAKAHASHI T., 1991: Debris Flows: Rotterdam, AHR/AIRH monograph, A.A. Balkema, 165 p.

  • WEIR G.J., 1982: Kinematic wave theory for Ruapehu lahars: New Zealand Journal of Science, v. 25, p. 197–203.

    Google Scholar 

  • WEIR G.J., 1983: The asymptotic behavior of simple kinematic waves of finite volume: Proceedings of the Royal Society of London, vol. A 387, p. 459–467.

    Article  Google Scholar 

  • WHITHAM G.B., 1955: The effects of hydraulic resistance in the dam-break problem: Proceedings of the Royal Society of London. v. A 227, p. 399–407.

    Article  Google Scholar 

  • YANO K. and DAIDO A., 1965: Fundamental study on mud-flow: Kyoto, Japan, Kyoto University, Bulletin of the Disaster Prevention Research Institute, V. 14, p. 69–83.

    Google Scholar 

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Arattano, M., Savage, W.Z. Modelling debris flows as kinematic waves. Bulletin of the International Association of Engineering Geology 49, 3–13 (1994). https://doi.org/10.1007/BF02594995

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