[1] This paper presents a new, generalized two-phase debris flow model that includes many essential physical phenomena. The model employs the Mohr-Coulomb plasticity for the solid stress, and the fluid stress is modeled as a solid-volume-fraction-gradient-enhanced non-Newtonian viscous stress. The generalized interfacial momentum transfer includes viscous drag, buoyancy, and virtual mass. A new, generalized drag force is proposed that covers both solid-like and fluid-like contributions, and can be applied to drag ranging from linear to quadratic. Strong coupling between the solid-and the fluid-momentum transfer leads to simultaneous deformation, mixing, and separation of the phases. Inclusion of the non-Newtonian viscous stresses is important in several aspects. The evolution, advection, and diffusion of the solid-volume fraction plays an important role. The model, which includes three innovative, fundamentally new, and dominant physical aspects (enhanced viscous stress, virtual mass, generalized drag) constitutes the most generalized two-phase flow model to date, and can reproduce results from most previous simple models that consider single-and two-phase avalanches and debris flows as special cases. Numerical results indicate that the model can adequately describe the complex dynamics of subaerial two-phase debris flows, particle-laden and dispersive flows, sediment transport, and submarine debris flows and associated phenomena.

Geomorphic mass flows are often complex in terms of material composition and its evolution in space and time. The simulation of those hazardous phenomena would strongly benefit from a multi‐phase model, considering the motion and—importantly—interaction of phases characterized by different physical aspects including densities, frictions, viscosities, fractions, and their mechanical responses. However, such a genuine multi‐phase model is still lacking. Here, we present a first‐ever, multi‐mechanical, multi‐phase mass flow model composed of three different phases: the coarse solid fraction, fine‐solid fraction, and viscous fluid. The coarse solid component, called solid, represents boulders, cobbles, gravels, or blocks of ice. Fine‐solid represents fine particles and sand, whereas water and very fine particles, including colloids, silt, and clay, constitute the viscous fluid component in the mixture. The involved materials display distinct mechanical responses and dynamic behaviors. Therefore, the solid, fine‐solid, and fluid phases are described by Coulomb‐plastic, shear‐ and pressure‐dependent plasticity‐dominated viscoplastic, and viscosity‐dominated viscoplastic rheologies. They are supposed to best represent those materials. The new model is flexible and addresses some long‐standing issues of multi‐phase mass flows on how to reliably describe the flow dynamics, runout, and deposition morphology of such type of phenomena. With reference to some benchmark simulations, the essence of the model and its applicability are discussed.

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.

Abstract. r.avaflow represents an innovative open-source computational tool for routing rapid mass flows, avalanches, or process chains from a defined release area down an arbitrary topography to a deposition area. In contrast to most existing computational tools, r.avaflow (i) employs a two-phase, interacting solid and fluid mixture model (Pudasaini, 2012); (ii) is suitable for modelling more or less complex process chains and interactions; (iii) explicitly considers both entrainment and stopping with deposition, i.e. the change of the basal topography; (iv) allows for the definition of multiple release masses, and/or hydrographs; and (v) serves with built-in functionalities for validation, parameter optimization, and sensitivity analysis. r.avaflow is freely available as a raster module of the GRASS GIS software, employing the programming languages Python and C along with the statistical software R. We exemplify the functionalities of r.avaflow by means of two sets of computational experiments: (1) generic process chains consisting in bulk mass and hydrograph release into a reservoir with entrainment of the dam and impact downstream; (2) the prehistoric Acheron rock avalanche, New Zealand. The simulation results are generally plausible for (1) and, after the optimization of two key parameters, reasonably in line with the corresponding observations for (2). However, we identify some potential to enhance the analytic and numerical concepts. Further, thorough parameter studies will be necessary in order to make r.avaflow fit for reliable forward simulations of possible future mass flow events.