Vertical chutes and pipes are a common component of many industrial apparatus used in the transport and processing of powders and grains. Here, a typical arrangement is considered first in which a hopper at the top feeds the chute and a converging outlet at the bottom controls the mass flux. Discrete element method (DEM) simulations reveal that steady uniform flow is only observed for intermediate flow rates, with jamming and unsteady waves dominating slow flows and non-uniform wall detachment in fast flow. Focusing on the steady uniform regimes, a progressive idealisation is carried out by matching with equivalent DEM simulations in periodic cells. These investigations justify a one-dimensional continuum modelling of the problem and provide key test data. Novel exact solutions are derived here for vertical flow using a linear version of the ‘ $\mu(I),\varPhi(I)$ -rheology’, for which the bulk friction $\mu$ and steady solid volume fraction $\varPhi$ depend on the inertial number I. Despite not capturing the full nonlinear complexities, the solutions match important aspects of the DEM flow fields and reveal simple scaling laws linking many quantities of interest. In particular, this study clearly demonstrates a linear relation between the chute width and the size of the shear zones at the walls. This finding contrasts with previous works on purely quasi-static flow, which instead predict a roughly constant shear zone width, a difference which implies that finite-size effects are minimal for the inertial flows studied here.

Earthquake-induced landslides can result in serious property damage and significant casualties. Although extensive research has been conducted to investigate their extraordinarily long runout, the underlying mechanism remains a very challenging open problem. In this paper, we explore the effect of vibration on landslide runout through simulations of simplified granular chute flows using the discrete element method with a focus on surface-normal vibration. We show that the mobility of the flows is enhanced by low-frequency vibration for inclination angles of both 19° and 24°. The flows are, however, strikingly different -solid-like for the former and liquid-like for the latter, as revealed by their microstructure and stress states. The vibration enhances the mobility through reduction in the normal load and in the solid volume fraction for the 19° and the 24° flows respectively. This work reveals complexities in the rheological states and the dynamic responses of inclined-surface granular flows under vibration, serving as an initial step to unravelling the full dynamic mechanisms of the long runout of earthquake-induced landslides.