Takaaki ABE, Yoshifumi SATOFUKA and Takahisa MIZUYAMA
Abstract
A modified particle method for simulating highly concentrated granular flows
is proposed based on a constitutive equation considering inter]particle stress.
The particle method we use is based on the Moving Particle Semi]implicit iMPSj
method, which has been originally proposed for calculation of incompressible
viscous fluid flows with free surfaces. The MPS method is capable of simulating
a wide variety of hydraulic problems such as solid]liquid two]phase flows, the
blocking of a bridge by driftwood, and river embankment erosion. In spite of
being a flexible tool for numerically simulating intense behavior of water and
other types of fluids, original MPS is applicable only to Newtonian fluid flows.
Some modifications are necessary in order to calculate highly concentrated granular
flows with dilatant properties. First, the inter]particle stress term is introduced
to the momentum equations by taking the divergence of inter]particle stress
tensor derived by Tsubaki et al. i‚P‚X‚W‚Qj. The equations are further modified
by adding a bed friction corrective term to take into account the effects of
bed roughness and energy dissipation on the movable bed of debris flow. The
proposed method is then applied to the simulation of debris flow experiments.
A quantitative comparison is made between the velocity distributions predicted
in the present method and the experimental and theoretical results for granular
flow with a movable bed. Velocity profiles of modified MPS with an inflexion
point are similar in shape to those measured and calculated by Tsubaki et al.,
while standard MPS encounters limitations in attaining appropriate profile curves.
Key wordsFdebris flow, particle method, MPS method, granular flows, constitutive
equation