Stress-strain relations for sand based on particulate considerations

Particulate, discrete and frictional systems such as sand constitute a separate class of materials. In order to derive stress-strain relations for these materials, their key features have to be identified and incorporated into the theoretical formulations. The presence of voids, the ability to undergo continuous and systematic spatial rearrangement of particles, the existence of bounds for the developed ratio of tangent and normal contact forces and the systematic variations of the tangent and normal contact force distributions during general loading, are identified as key features of particulate, discrete and frictional systems. The contact normal and the contact branch length distribution functions describe the spatial arrangement of particles mathematically. The distribution of contact normals exhibit mutually orthogonal principal directions which coincide with the principal stress directions. Most contacts in frictional systems do not develop limiting friction during general loading. Sliding of a few suitably oriented contacts followed by rolling and rigid body rotations and displacements of a large number of particles is the main mechanism causing non-recoverable deformations in frictional systems. As a part of the rearranging process, dominant chains of particles are continuously constructed and destructed, the rates being different at different stages of loading. A change of loading direction is associated with a change of dominant chains of particles resulting in changes in strain magnitudes. Rate insensitive incremental stress-strain relations are derived here using the principle of virtual forces. The key features of frictional systems have been incorporated into the stress-strain relations following the theoretical framework proposed by Rothenburg(1980), for analysing bonded systems of uniform spherical particles. For frictional systems, the load-deformation response at particle contacts is assumed to be non-linear. The deformations resulting from all internal activity are quantified defining equivalent incrementally elastic stiffnesses in the tangent and normal directions at contacts and defining loading and unloading criteria. After each increment of loading, the incremental stiffnesses and contact normal distribution are updated to account for the changes resulting from rearrangement of particles. Laws that describe the spatial rearrangement of particles, changes in the ratio between the tangent and normal contact force distributions and the resistance to deformation resulting from changes in dominant chains of particles are established based on the information from laboratory experiments reported in the literature and numerical experiments of Bathurst(1985). The stress ratio and the state parameter (defined as the ratio of void ratios at the critical-state to the current state, computed for a given mean-normal stress) are identified as key variables that can be used to quantify the extent of particle rearrangements. The proposed formulations are capable of modelling the non-linear stress-strain response which is dependent on the inherent anisotropy, stress induced anisotropy, density of packing, stress level and stress path. To predict the stress-strain response of sand, a total of 24 model parameters have to be evaluated. All the model parameters can be evaluated from five conventional triaxial compression tests. The proposed stress-strain relations have been verified by comparing with laboratory measurements on sand. The data base consists of triaxial tests reported by Negussey(1984), hollow cylinder tests graciously carried out for the author by A. Sayao, and true triaxial and hollow cylinder tests made available for the Cleveland Workshop(1987).Applied Science, Faculty ofCivil Engineering, Department ofGraduat