| In this contribution, I present a historical account of debris flow modelling leading to the state
of the art in simulations 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 includes 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, buoyancy 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 further 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 momentum. 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 by the debris impact at lakes/oceans, and rock-ice avalanches. Simulation
results show that buoyancy enhances flow mobility. The virtual mass force alters flow
dynamics by increasing the kinetic energy of the fluid. Newtonian viscous stress substantially
reduces flow deformation, whereas non-Newtonian viscous stress may change the
overall flow dynamics. Strong non-linear dynamics of the fluid fraction demonstrates
the typical state of the two-phase debris flow. An innovative formulation provides
a unique opportunity, within a single framework, to simultaneously simulate the
sliding debris, the water lake or ocean, the debris impact, the tsunami generation and
propagation, and the sediment transport and deposition process in the bathymetric
surface. The simulation results demonstrate the applicability of the model equations to
adequately describe the complex dynamics of two-phase debris flows, avalanches,
particle-laden, dispersive flows, turbidity currents, landslide and debris-induced
tsunami and the associated applications to hazard mitigation, geomorphology and
sedimentology.
Reference:
Shiva P. Pudasaini (2012): A general two-phase debris flow model. J. Geophys. Res., 117,
F03010,doi: 10.1029/2011JF002186. |