In the design of multiple rigid barriers, the height of the first barrier governs the impact dynamics of debris flow on the next barrier in a channel. However, current design approaches neglect the height of the first barrier, and no specific guideline is given on the design of the impact load on the second barrier. In this study, a new impact equation that explicitly considers the effects of the height of the first barrier on the impact dynamics is proposed. This is achieved by adopting the barrier Froude number Fr_b, which is the ratio of inertia to barrier potential. Thereby, the new impact equation accounts for the static load as a function of the first barrier height. The equation is evaluated using physical experiments carried out in a 5-m-long flume. The experiments modelled dry sand and water flows impacting dual rigid barriers. These two idealised flow types represent extreme cases of frictional and viscous flows, which exhibit entirely different impact mechanisms. A comparison of the experimental results from this study shows that the proposed impact model using the barrier Froude number provides a reasonably conservative estimate for the normalised impact force on the first rigid barrier with overflow. Furthermore, a bilinear design envelop for the impact force exerted on the second barrier is proposed based on the barrier Froude number of the first barrier.

在多个刚性屏障的设计中，第一个屏障的高度决定着碎屑流对通道中下一个屏障的冲击动力学。然而，当前的设计方法忽略了第一屏障的高度，并且在第二屏障上的冲击载荷的设计上没有给出具体的指导。在这项研究中，提出了一个新的冲击方程，该方程明确考虑了第一道障碍物的高度对冲击动力学的影响。这可以通过采用势垒弗劳德数Fr _b来实现，即惯性与势垒势之比。由此，新的冲击方程式将静载荷作为第一屏障高度的函数加以考虑。使用在5 m长的水槽中进行的物理实验评估该方程式。实验模拟了干砂和水流对双重刚性障碍的影响。这两种理想的流动类型代表了摩擦流动和粘性流动的极端情况，它们表现出完全不同的冲击机理。这项研究的实验结果进行了比较，结果表明，使用屏障Froude数的拟议冲击模型为带溢流的第一个刚性屏障上的标准化冲击力提供了合理的保守估计。此外，