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Influence of rheology on debris-flow simulation

Systems of partial differential equations that in- clude the momentum and the mass conservation equations are commonly used for the simulation of debris flow initia- tion, propagation and deposition both in field and in labora- tory research. The numerical solution of the partial differ- ential equations can be very complicated and consequently many approximations that neglect some of their terms have been proposed in literature. Many numerical methods have been also developed to solve the equations. However we show in this paper that the choice of a reliable rheological model can be more important than the choice of the best approximation or the best numerical method to employ. A simulation of a debris flow event that occurred in 2004 in an experimental basin on the Italian Alps has been carried out to investigate this issue. The simulated results have been com- pared with the hydrographs recorded during the event. The rheological parameters that have been obtained through the calibration of the mathematical model have been also com- pared with the rheological parameters obtained through the calibration of previous events, occurred in the same basin. The simulation results show that the influence of the inertial terms of the Saint-Venant equation is much more negligible than the influence of the rheological parameters and the ge- ometry. A methodology to quantify this influence has been proposed. flow events, but it cannot give more detailed predictions of their effects (Suwa and Yamakoshi, 2000; Ayotte and Hungr, 2000). The application of mathematical models is employed to obtain more quantitative estimations of the dynamic char- acteristics of debris flows (velocity, flow depth, discharge, flow duration, etc.). The estimation of the dynamic character- istics of debris flows is in fact needed by administrators, deci- sion makers and practitioners who have to protect the life, the property and the economical activities of people who live in debris flows prone areas and to forbid anthropic activities in these latter (Regione Piemonte, 2002; Petrascheck and Kien- holz, 2003). Sometimes different boundary conditions (e.g. water-sediment hydrograph, peak discharge) are taken into account in order to test the sensitivity of the results and the adequacy of the designed/existing countermeasures. When a more detailed hazard assessment is needed, especially for re- location of settlements and human activities, more complex mathematical models can be used (2-D models, two phase models, movable bed models that can incorporate deposi- tions and erosions along the torrent) (Ghilardi and Natale, 2000; Pudasaini et al., 2003, 2005). However the estimation of the parameters to be used in the simulations is often not straightforward and the choice of the more apt rheological model can be very difficult. In this paper the simulation of a debris flow event occurred in 2004 in an instrumented torrent will be presented and the influence on results of the rheolog- ical parameters will be discussed. A one-phase Saint-Venant model has been used for the simulation because the avail- able field data allowed to calibrate only 2 parameters: the calibration of 2-D models would have required more param- eters. At the moment, in the field practice, 1-D models are still more commonly employed than 2-D models. This paper should offer an help to practitioners to better understand the performances of 1-D models.