抄録
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 (MPS) 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. (1982). 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.
