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.

中文翻译：

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一种新的基于物理的泥石流冲击模型

提出了一种新的分析模型来估计施加在刚性屏障上的泥石流的峰值冲击压力。新模型由两项组成，p  =  α ₁ ρ ₀ g h ₀  + 0·5 ρ ₀ u ₀ ²，分别考虑静态和动态冲击效应。静态系数α ₁根据控制质量和动量守恒和能量守恒的方程确定，并在伯努利方程的基础上采用动力学系数0·5。新的分析模型在广泛的弗劳德数 (Fr) 范围内得到验证，数据来自过去的小规模实验和现场观察研究，以及由耦合计算流体动力学-离散执行的作为颗粒-流体混合物的泥石流的数值模拟。 -元素方法（CFD-DEM，用于 Fr 的大范围覆盖）。基于与新模型的等效性，发现传统纯流体静力（k）和纯流体动力（α）冲击模型中涉及的经验系数分别与 Fr 正相关和负相关。之间的独特关系k和α进一步推导出：(cos θ / k ) + (1/ α ) = 1，其中θ表示倾斜角。解释了这种关系的基础物理学。根据所提出的模型，进一步推荐了以 Fr 为单位的设计图表，用于防碎片屏障的实际设计。新的分析模型可能对泥石流对刚性屏障的影响进行稳健可靠的估计。