Grain size dependence of yielding in granular soils interpreted using fracture mechanics, breakage mechanics and Weibull statistics

The macroscopic yield pressure of brittle granular soils is experimentally known to depend on the size of the particles. In this paper this connection is established theoretically within a unified framework that integrates principles of fracture mechanics, breakage mechanics and Weibull's weakest link theory. In particular, the work input at which a granular continuum begins to comminute is linked to the specific fracture energy at which a single particle fails, which reveals an intrinsic length scale in the form of the mean grain size of the initial assembly. The macroscopic yield pressure is then connected with both grain size and the specific fracture process developing at the grain scale. The impacts on macroscopic yield pressure of various grain fracture mechanisms are explored, discussed and assessed against a wide set of data at both particle and assembly scale. This work provides a new theoretical basis to estimate the effect of widely variable particle sizes in large-scale applications for which direct testing is not feasible, such as rockfill engineering and mining technologies.