Modelling debris flows down general channels

Abstract

Abstract. This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by . It is a generalisation of the Hutter (1989, 1991) equations based on simple channel topography to a twophase 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 pressureCorrespondence to: S. P. Pudasaini (pudasain@mechanik.tu-darmstadt.de) 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.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

“…More recently, depthaveraged equations in more general surface-following curvilinear coordinate systems have been derived using asymptotic analysis (e.g. [24][25][26][27][28]). …”

“…Deriving improved depth-averaged models that more accurately accommodate the physical effects of complex topography is an active research pursuit (e.g. [24,[26][27][28]). Because our model is tested in §4 with the simple basal surface of the concrete flume, we postpone this issue for future studies.…”

Correction to “Experimental study of bedrock erosion by granular flows”

“…Many models assume that changes in z direction momentum are small compared to the static weight of the mass, such that vertical stresses other than the static normal stress are neglected [e.g., Savage and Hutter, 1989]. In terrain-fitted coordinates, centripetal acceleration accounts for much, but not all, of the vertical acceleration Pudasaini et al, 2005]. In Cartesian coordinates, an estimation of vertical stresses over an irregular bed has been accomplished by modeling stresses on the bed from basal sliding as the sum of a normal component from weight and an additional term associated with vertical acceleration due to the topography of the channel .…”

Numerical Modeling of Two-Phase Gravitational Granular Flows with Bottom Topography

“…Iverson [Ive97] and Iverson and Denlinger [ID01] first addressed the need of accounting for interstitial fluid effects in the flowing mass, and developed a solid-fluid mixture theory based on the simplifying assumptions of constant porosity and equality of fluid and solid velocities. See also later extensions [DI04] and similar approaches [PWH05]. Making a step forward, Pitman and Le [PL05] have recently presented a depth-averaged two-phase model for debris flows and avalanches that contains mass and momentum equations for both the solid and fluid component, thus providing equations for porosity and velocity of both phases.…”