A new physically based impact model for debris flow

A new analytical model is proposed to estimate the peak impact pressure of debris flow exerted on a rigid barrier. The new model consists of two terms, p = α₁ρ₀gh₀ + 0·5ρ₀u₀², accounting for static and dynamic impacting effects, respectively. The static coefficient α₁ is determined according to equations governing the mass and momentum conservation and energy conservation, and the dynamic coefficient 0·5 is adopted on the basis of the Bernoulli equation. The new analytical model is validated for a wide range of Froude number (Fr) with data collected from past studies on small-scale experiments and field observations and numerical simulations of debris flow as a particle–fluid mixture performed by coupled computational fluid dynamics–discrete-element method (CFD–DEM, for wide-range coverage of Fr). Based on equivalence with the new model, the empirical coefficients involved in conventional pure hydrostatic (k) and pure hydrodynamic (α) impact models are found positively and negatively correlated to Fr, respectively. A unique relationship between k and α is further derived: (cos θ/k) + (1/α) = 1, where θ denotes slope angle. The underlying physics of this relationship is interpreted. According to the proposed model, a design chart in terms of Fr is further recommended for practical design of debris-resisting barriers. The new analytical model offers a possible improvement on robust and reliable estimation of debris flow impact on a rigid barrier.