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Mud and debris flows are natural phenomena representing serious hazard for population and structures in mountain zones, because of their rapid occurrence and the diffi culty in forecasting the phenomena initiation. Numerical models can however be useful in predicting the peak discharge and the strength of flowing mass, helping administrations in preparing risk mitigation measures. In this work, a numerical model for hyperconcentrated flows is presented. It is based on shallow water equations, with a particular source terms treatment which translates into an increased numerical stability and makes the model highly versatile. The test case applications focus on some fundamental characteristics necessary for debris- and mud-flow representation. In particular, classic dam-break problems have been used to test wave celerity and wet-dry fronts propagation, while a mud-flow dam-break problem has been chosen to investigate model sensibility to different rheological schemes. Then, the model has been applied to two real events that occurred in Northern Italy. The first one is a debris flow which took place at Acquabona, near Cortina d’Ampezzo. This event is extensively documented, since it has been observed by a monitoring station prepared by the University of Padua. The second one is a tragic event, during which the little town of Stava has been stricken by a destructive mud flow caused by the collapse of two earth dams.
debris flow, mud flow, numerical simulation, source terms
[1] Julien, P.Y. & Lan Y.Q., Rheology of hyperconcentrations. Journal of Hydraulic Engineering, 117(3), pp. 346–353, 1991. doi:http://dx.doi.org/10.1061/(ASCE)07339429(1991)117:3(346)
[2] Johnson, A.M., Physical Processes in Geology, W.H. Freeman: San Francisco, Calif., 1970.
[3] Chen, C.L., Generalized viscoplastic modelling of debris fl ow. Journal of Hydraulic Research, ASCE, 114(3), 1988.
[4] Takahashi, T., Debris fl ow, IAHR Monograph Series, A.A. Balkema: Rotterdam Brookfi eld, p. 165, 1991.
[5] Iverson, R.M., Hydraulic modelling of unsteady debris-fl ow surges with solid-fl uid interaction. Debris Flow Hazards Mitigation: Mechanics, Prediction and Assessment, ASCE, New York, NY, 1997.
[6] Rickenmann, D. & Koch, T., Comparison of debris fl ow modelling approaches. Debris Flow Hazards Mitigation: Mechanics, Prediction and Assessment, ASCE, New York, NY, 1997.
[7] Takahashi, T., Debris fl ow on prismatic open channel. Journal of the Hydraulics Division, 106(HY3), pp. 381–396, 1980.
[8] Vrijling, J.K., Hengel, W. & Houben, R.J., A framework of risk evaluation. Journal of hazardous materials, 43, pp. 245–261, 1995. doi:http://dx.doi.org/10.1016/ 0304-3894(95)91197-V
[9] Schippa, L. & Pavan, S., Analytical treatment of source terms for complex channel geometry. Journal of Hydraulic Research, 46(6), pp. 753–763, 2008.
[10] Schippa, L. & Pavan, S., Bed evolution numerical model for rapidly varying fl ow in natural streams. Computer & Geosciences, 35, pp. 390–402, 2009. doi:http://dx.doi. org/10.1016/j.cageo.2008.08.004
[11] Toro, E.F., Riemann Solvers and Numerical Method for Fluid Dynamics, Springer-Verlag: Berlin Heidelberg New York, 1999.
[12] Cunge, J.A., Holly, F.M. & Verswey, A., Practical aspects of computational river hydraulics, The Pitman Advanced Publishing Program, 1980.
[13] Hutter, K., Svendsen, B. & Rickenmann, D., Debris-fl ow modelling: a review. Continuum Mechanics and Termodynamics, 8, pp. 1–35, 1996. doi:http://dx.doi.org/10.1007/ BF01175749
[14] Ying, X. & Wang, S.S.Y., Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel fl ows. Journal of Hydraulic Research, 46(1), pp. 21–34, 2008. doi:http://dx.doi.org/10.1080/00221686.2008.9521840
[15] Brufau, P., Garcia-Navarro, P., Ghilardi, P., Natale, L. & Savi, F., 1D Mathematical modelling of debris fl ow. Journal of Hydraulic Research, 38(6), pp. 435–446, 2000. doi:http://dx.doi.org/10.1080/00221680009498297
[16] Fraccarollo, L. & Papa, M., Numerical simulation of real debris-fl ow events. Physics and Chemistry of the Earth, 25(9), pp. 757–763, 2000. doi:http://dx.doi.org/10.1016/ S1464-1909(00)00098-8
[17] Laigle, D. & Coussot, P., Numerical modelling of mudfl ows. Journal of Hydraulic Engineering, 123(7), pp. 617–623, 1997. doi:http://dx.doi.org/10.1061/(ASCE)07339429(1997)123:7(617)
[18] Zanuttigh, B. & Lamberti, A., Analysis of debris wave development with one- dimensional shallow-water equations. Journal of Hydraulic Engineering, 130(4), pp. 293–303, 2004. doi:http://dx.doi.org/10.1061/(ASCE)0733-9429(2004)130:4(293)
[19] Naef, D., Rickenmann, D., Rutschmann, P. & McArdell, B.W., Comparison of fl ow resistance relations for debris fl ow using a one-dimensional fi nite element simulation model. Natural Hazards and Earth System Sciences, 6, pp.155–165, 2006. doi:http:// dx.doi.org/10.5194/nhess-6-155-2006
[20] Mambretti, S., Larcan, E. & De Wrachien, D., 1D modelling of dam-beak surges with fl oating debris. Biosystems Engineering, 100, pp. 297–308, 2008. doi:http://dx.doi. org/10.1016/j.biosystemseng.2008.02.011
[21] Garcia-Navarro, P. & Vazquez-Cendon, M.E., On numerical treatment of the source terms in the shallow water equations. Computer & Fluids, 29, pp. 951–979, 2000. doi:http://dx.doi.org/10.1016/S0045-7930(99)00038-9
[22] Stoker, J.J., Water waves. The Mathematacal Theory with Applications. John Wiley and Sons, Toronto, Canada, 1992.
[23] Goutal, N. & Maurel, F., Proceedings of the 2nd workshop on dam-break wave simulation, Direction des études et recherches, Electricité de France, Rep. HE43/97/016/B, 1997.
[24] Hungr, O., A model for the run-out analysis of rapid fl ow slides, debris fl ow, and avalanches. Canadian Geothecnical Journal, 32(4), pp. 610–623, 1995. doi:http://dx.doi. org/10.1139/t95-063
[25] Berti, M., Geneovis, R., Simoni, A. & Tecca, P.R., Field observations of a debris fl ow event in the Dolomites. Geomorphology, 29, pp. 265–274, 1999. doi:http://dx.doi. org/10.1016/S0169-555X(99)00018-5
[26] C. Embleton & J. Thornes, Brunsden, D., Mass movements. Process and geomorphology, ed. E. Arnold, London, pp. 131–186, 1979.
[27] Costa, J.E. & Williams, G.P., Debris fl ow dynamics, Film, Open File Report 84/606. U.S. Geological Survey, Water Resources Division: USA, 1984.
[28] Orlandini, S. & Lamberti, A., Effect of wind precipitation intercepted by steep mountain slopes. Journal of the hydrologic engineering, 5(4), pp. 346–354, 2000. doi:http:// dx.doi.org/10.1061/(ASCE)1084-0699(2000)5:4(346)