New impact equation using barrier Froude number for the design of dual rigid barriers against debris flows

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.