Historical Account to the State of the Art in Debris Flow Modeling

In this contribution, I present a historical account of debris flow modelling leading to the state of the art in sim-ulations and applications. A generalized two-phase model is presented that unifies existing avalanche and debris flow theories. The new model (Pudasaini, 2012) covers both the single-phase and two-phase scenarios and in-cludes many essential and observable physical phenomena. In this model, the solid-phase stress is closed by Mohr-Coulomb plasticity, while the fluid stress is modeled as a non-Newtonian viscous stress that is enhanced by the solid-volume-fraction gradient. A generalized interfacial momentum transfer includes viscous drag, buoy-ancy and virtual mass forces, and a new generalized drag force is introduced to cover both solid-like and fluid-like drags. Strong couplings between solid and fluid momentum transfer are observed. The two-phase model is fur-ther extended to describe the dynamics of rock-ice avalanches with new mechanical models. This model explains dynamic strength weakening and includes internal fluidization, basal lubrication, and exchanges of mass and mo-mentum. The advantages of the two-phase model over classical (effectively single-phase) models are discussed. Advection and diffusion of the fluid through the solid are associated with non-linear fluxes. Several exact solutions are constructed, including the non-linear advection-diffusion of fluid, kinematic waves of debris flow front and deposition, phase-wave speeds, and velocity distribution through the flow depth and through the channel length. The new model is employed to study two-phase subaerial and submarine debris flows, the tsunami generated b