Abstract. This paper describes a one-dimensional finite element code for debris flows developed to model the flow within a steep channel and the stopping conditions on the fan. The code allows the systematic comparison of a wide variety of previously proposed one-phase flow resistance laws using the same finite element solution method. The onedimensional depth-averaged equations of motion and the numerical model are explained. The model and implementation of the flow resistance relations was validated using published analytical results for the dam break case. Reasonable agreement for the front velocities and stopping location for a debris-flow event in the Kamikamihori torrent in Japan can be achieved with turbulent flow resistance relations including "stop" terms which allow the flow to come to rest on a gently sloping surface. While it is possible to match the overall bulk flow behavior using relatively simple flow resistance relations, they must be calibrated. A sensitivity analysis showed that the shape of the upstream input hydrograph does not much affect the flow conditions in the lower part of the flow path, whereas the event volume is much more important.

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Sediment loads have been measured in six Swiss mountain torrents over several decades. Most of these torrent catchments are situated in the prealpine belt. They have catchment areas of between 0·5 and 1·7 km 2 . Bedslopes at the measuring sites vary between 5 and 17 per cent, and peak discharges up to 12 m 3 s −1 have been recorded. Geophone sensors installed in the Erlenbach stream allow bedload transport activity to be monitored and sediment volumes associated with each flood event to be determined. A detailed analysis of the measurements in this stream results in an empirical equation in which the sediment load per flood event is expressed as a function of the effective runoff volume (discharges above the threshold for bedload motion) and of the normalized peak discharge. For the total of 143 investigated flood events in the Erlenbach stream, the deviation of the predicted from the measured value is within a factor of two for more than two-thirds of all events. A distinction can be made between summer and winter events in analysing the bedload transport events. The summer events, mainly caused by thunderstorms, transport comparatively larger sediment loads than the winter events. For the other investigated streams, the periods of the deposited sediment volume surveys cover in general several flood events. An analysis is performed analogous to that for the Erlenbach stream. The sediment loads show a similar dependency on the two factors effective runoff volume and normalized peak discharge. However, the exponents of these factors in the power law expressions differ from stream to stream. A comparison of the investigated stream shows that some of the variation can be explained by considering the bedslope above the measuring site. The inclusion of a bedslope factor is in agreement with laboratory investigations on bedload transport.

A debris flow represents a mixture of sediment particles of various sizes and water flowing down a confined, channel-shaped region (e.g., gully, ravine or valley) down to its end, at which point it becomes unconfined and spreads out into a fan-shaped mass. This review begins with a survey of the literature on the physical-mathematical modeling of debris flows. Next, we discuss the basic aspects of their phenomenology, such as dilatancy, internal friction, fluidization, and particle segregation. The basic characterization of a debris flow as a mixture motivates the application of the continuum thermodynamical theory of mixtures to formulate a model for a debris flow as a viscous fluid-granular solid mixture. A major advantage of such a formulation, which goes beyond the most general models in the literature, e.g., Takahashi (1991), is that it can be used to expose and better understand the assumptions underlying existing models, as well as to derive new, more sophisticated models. Finally, we delve into the issue of how such models have been or can be implemented numerically, as well as general boundary conditions for debris flows.