Disaster Mitigation of Debris Flows, Slope Failures and Landslides 129 Resistance of the Debris Flow on the Roughness Boundary

The constitutive equations for debris flows that are presently generally used are arrived at by evaluating the interactions in the flow, the particle to particle displacements and collisions, and turbulence generating within the pore fluid. The other hand, although the beds of mountain rivers are covered with large particles as an armor coat, the existing constitutive equations do not take boundary conditions, such as riverbed roughness, into consideration. When we will discuss about the boundary conditions, we would evaluate the particle-particle and particle-fluid interactions in the closed area of the bed. Channel experiments under various conditions of riverbed roughness were conducted based on the above concept. To investigate the influence of riverbed roughness on debris flows, the coefficient f ′ was defined by modifying the coefficient of resistance, f, which is the ratio of the energy gradient to the friction loss. The modified resistance coefficient f ′ takes the same value when sediment concentration is the same and there is no consideration about boundary condition of riverbed roughness. Experimental results indicate that f ′ increases as riverbed roughness increases with larger riverbed particle. Moreover, f ′ increases as the relative flow depth, which is the ratio of the flow depth, h, to roughness height, ks, becomes small and the sediment concentration, c, becomes dense. That is, the excess flow resistance appears due to large riverbed roughness. This suggest