Shock waves, dead zones and particle-free regions form when a thin surface avalanche of granular material flows around an obstacle or over a change in the bed topography. Understanding and modelling these flows is of considerable practical interest for industrial processes, as well as for the design of defences to protect buildings, structures and people from snow avalanches, debris flows and rockfalls. These flow phenomena also yield useful constitutive information that can be used to improve existing avalanche models. In this paper a simple hydraulic theory, first suggested in the Russian literature, is generalized to model quasi-two-dimensional flows around obstacles. Exact and numerical solutions are then compared with laboratory experiments. These indicate that the theory is adequate to quantitatively describe the formation of normal shocks, oblique shocks, dead zones and granular vacua. Such features are generated by the flow around a pyramidal obstacle, which is typical of some of the defensive structures in use today.

One means of preventing areas from being hit by avalanches is to divert the flow by straight or curved walls or tetrahedral or cylindrical-type structures. Thus, there arises the question how a given avalanche flow is changed regarding the diverted-flow depth and flow direction. In this paper a report is given on laboratory experiments performed for gravity-driven dense granular flows down an inclined plane obstructed by plane wall and tetrahedral wedge. It was observed that these flows are accompanied by shocks induced by the presence of the obstacles. These give rise to a transition from super-to subcritical flow of the granular avalanche, associated with depth and velocity changes. It is demonstrated that with an appropriate shock-capturing integration technique for the Savage-Hutter theory, the shock formation for a finite-mass granular flow sliding from an inclined plane into a horizontal run-out zone is well described, as is the shock formation of the granular flow on either side of a tetrahedral protection structure.