This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by Pudasaini and Hutter (2003). It is a generalisation of the Savage and Hutter (1989, 1991) equations based on simple channel topography to a two-phase fluid-solid mixture of debris material. Important terms emerging from the correct treatment of the kinematic and dynamic boundary condition, and the variable basal topography are systematically taken into account. For vanishing fluid contribution and torsion-free channel topography our new model equations exactly degenerate to the previous Savage-Hutter model equations while such a degeneration was not possible by the Iverson and Denlinger (2001) model, which, in fact, also aimed to extend the Savage and Hutter model. The model equations of this paper have been rigorously derived; they include the effects of the curvature and torsion of the topography, generally for arbitrarily curved and twisted channels of variable channel width. The equations are put into a standard conservative form of partial differential equations. From these one can easily infer the importance and influence of the pore-fluid-pressure distribution in debris flow dynamics. The solid-phase is modelled by applying a Coulomb dry friction law whereas the fluid phase is assumed to be an incompressible Newtonian fluid. Input parameters of the equations are the internal and bed friction angles of the solid particles, the viscosity and volume fraction of the fluid, the total mixture density and the pore pressure distribution of the fluid at the bed. Given the bed topography and initial geometry and the initial velocity profile of the debris mixture, the model equations are able to describe the dynamics of the depth profile and bed parallel depth-averaged velocity distribution from the initial position to the final deposit. A shock capturing, total variation diminishing numerical scheme is implemented to solve the highly non-linear equations. Simulation results present the combined effects of curvature, torsion and pore pressure on the dynamics of the flow over a general basal topography. These simulation results reveal new physical insight of debris flows over such non-trivial topography. Model equations are applied to laboratory avalanche and debris-flow-flume tests. Very good agreement between the theory and experiments is established.

We performed laboratory experiments of dry granular chute flows impinging an obstructing wall. The chute consists of a 10cm wide rectangular channel, inclined by 50° relative to the horizontal, which, 2m downslope abruptly changes into a horizontal channel of the same width. 15l of quartz chips are released through a gate with the same width as the chute and a gap of 6cm height, respectively. Experiments are conducted for two positions of the obstructing wall, (i) 2m below the exit gate and perpendicular to the inclined chute, and (ii) 0.63m into the horizontal runout and then vertically oriented. Granular material is continuously released by opening the shutter of the silo. The material then moves rapidly down the chute and impinges on the obstructing wall. This leads to a sudden change in the flow regime from a fast moving supercritical thin layer to a stagnant thick heap with variable thickness and a surface dictated by the angle of repose typical for the material. We conducted particle image velocimetry (PIV) experiments by recording the moving material from the side with charge coupled devices (CCD) cameras. The experiment was also video recorded. From the CCD data velocities were also deduced using the PIV technique. In order to compare the results here we describe the experiments for the same material and the same gap width of the silo gate but for the two positions of the obstructing wall. Analysis of the shock front formation and propagation upslope, evolution of the height of the supercritical flow, impact velocity and momentum are presented and discussed in detail. Computed and derived shock front heights match well.