Notions on Granular Materials

This chapter has quite modest ambitions. We limit ourselves to the introduction of a few fundamental notions about granular materials, in order to facilitate access to this field of mechanics, and to setting out what distinguishes a granular material from a fluid medium. These differences will be illustrated by two important applications  

The pressure distribution in a granular material at static equilibrium within the gravity field, which differs from the one that estabhshes itself in a fluid. The case of tanks/silos will be discussed. 

The flow of a granular material, for example in an hourglass, which differs from that of a fluid. The reasons for this will be explained. 

Flows of cohesive granular materials will not be discussed, setting aside the notion of powder flowability whose introduction requires to be complemented by drawing on examples from continuum mechanics. For non-cohesive granular materials, we shall propound a macroscopic approach, which describes phenomena within the framework of continuum mechanics. This approach, with the highly classical Janssen model (1895), enables the silo effect in pressure distribution to be 

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This result is readily understood if one reverts to the notion of pressnre field satnration set ont in section 18.4. The pressure exerted on the granular material in the vicinity of the orifice is given by the width of the orifice as established by [18.20] if the height of the grannlar material is sufficient. The pressnre is a local data, and it is this pressure value that sets the velocity. Relation [18.21] is classically converted into the well-known form of Beverloo s law which expresses the flow rate as a function of the same quantities ... 

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