# Numerical simulation of debris flows using a two phase model: application to debris flows in Iceland

Narbona-Reina, G.; Mangeney, A.; Castro-Díaz, M.; Fernández-Nieto, E.; Conway, S.; Mangold, N. and Bouchut, F. (2011). Numerical simulation of debris flows using a two phase model: application to debris flows in Iceland. In: AGU Fall Meeting 2011, 5-9 Dec 2011, San Francisco, CA, USA.

## Abstract

Debris flows play a significant role in erosion processes at the surface of the Earth and represent a threat to population and infrastructure in volcanic, mountainous, seismic and coastal areas. Natural flows generally involve a fluid phase mixed up with a granular phase. However, most of the current models only deal with the granular phase due to the mathematical and numerical difficulties related to the description of two phase flows. We present here a numerical model that describes the flow of a mixture of granular material and its interstitial fluid over a complex topography following the work of Pitman and Le (2005). In contrast to the approach that solves mass and momentum equations for the total mixture, this model considers mass and momentum equations for both the liquid and the solid phase separately, making it possible to take into account different velocities for the two phases. We use here a numerical discretization of the depth-averaged equations derived by Pelanti et al. (2008) that takes into account a Coulomb friction law for the solid phase, buoyancy effects, friction between the two phases and complex topography effects. We performed sensitivity analysis on some simple cases which has shown that the water content and the interaction between the two phases affect the flow dynamics and the morphology of the deposit. Finally, we will use this model to simulate debris flows occurring in Iceland that threaten the North-West coastal villages. Thanks to the high resolution data obtained by aerial lidar survey, by the NERC ARSF, the local 3D local topography is accounted for. Comparison between simulated and observed deposits makes it possible to calibrate the friction coefficient of the granular material involved and to provide first estimate of the water content in these debris flows. References: E.B. Pitman, L. Le. A two-fluid model for avalanche and debris flows. Phil. Trans. R. Soc. A 363, 1573-1601, 2005. M. Pelanti, F. Bouchut, A. Mangeney. A Roe-type scheme for two-phase shallow granular flows over variable topography. M2AN 42, 851-885, 2008.