Effects of cylindrical-obstacle spacing on granular shock wave interactions in gravity-driven flows

Hazardous geophysical granular flows, such as debris flows and rock avalanches, can exert intense impact forces on obstacles and threaten downstream structures located in their paths. Installing protective structures can mitigate damage, but quantifying their influence on flow evolution and impact loading remains challenging. This study investigates the interactions of granular shock waves (GSWs) generated in front of two cylindrical obstacles with varying spacings through chute experiments and discrete element modeling. Impact pressure sensors were mounted on the upstream surface of each cylinder and on the chute bed to measure dynamic impact pressures in the GSW region. Granular flow velocity and depth were obtained using image processing. Results demonstrate that cylinder spacing significantly influences the geometric characteristics of GSWs. Runup increases with steady-state Froude number ( Fr steady ) but decreases as spacing narrows. The granular vacuum length grows with bed slope but decreases significantly with decreasing cylinder spacing. Impact pressures on the cylinders and the chute bed increase linearly with Fr steady . Low-frequency power spectral density (PSD) is positively correlated with Fr steady , whereas centroid frequency and pressure impulse counts exhibit low sensitivity to Fr steady . The dimensionless impact pressure coefficient ( α ) decreases nonlinearly with increasing Froude number ( Fr ). At low Fr , α values for dry granular flows are lower than those for debris flows, but the difference diminishes at higher Fr . These findings may improve our understanding of granular flow–obstacle interactions and might help to design protective structures.