Evolution of shear bands in sand

Localisation of deformation in narrow shear bands is a fundamental phenomenon of granular material behaviour. When modelling granular materials, shear localisation has therefore to be considered. The model must include an adequate constitutive law with an intrinsic length determining the thickness of the localised shear zones, and a representation of microscopic inhomogeneities triggering shear localisation. In the framework of a Cosserat continuum the behaviour of non-cemented granular material can be described by a hypoplastic law including the evolution of non-symmetric stresses and couple stresses. Void ratio fluctuations are introduced by a physically justified probability density function. The assumption is that fluctuations are minimal in the densest state, and maximal in the critical state. It is shown that shear bands can evolve spontaneously in the interior of a granular body even under homogeneous stress or displacement boundary conditions. Experimental verifications are given. Numerical results are compared with laboratory tests performed with a Cornforth and a Hamblytype biaxial apparatus. Shear localisation in the experiment is visualised by means of an optical method called particle image velocimetry. Further numerical results are compared with experimental results taken from publications.