Micro mechanics of elastic soil

This paper presents a review of the stress dependence for soil stiffness at very small strains. Previously published data for sands and clays are presented, and it is shown that in all cases, provided voids ratio is kept approximately constant, then the very small strain stiffness of soils is found to vary with mean effective stress p as p(1/2). The p(1/2) dependence of stiffness has long been established for more idealised aggregates comprising regular arrays of spherical particles, and published micro mechanical explanations for this behaviour are presented. A simple mean field approach based on Hertzian contact theory predicts that the dependence should be p(1/3), but highlights two possible reasons for the apparent discrepancy comparing with available data: (i) contacts may not be Hertzian and (ii) the number of contacts may increase with increasing stress level at approximately constant voids ratio. Two alternative previously published explanations for the p(1/2) dependence relate to conical contacts between particles and particle chain buckling mechanisms. These mechanisms are presented and discussed, and the paper shows that the p(1/2) dependence could arise due to one or other of these mechanisms, but not both simultaneously. It seems possible that in densely compacted or overconsolidated soils where voids ratio is approximately constant until yield occurs, contacts may be aspherical. and the number of contacts may simultaneously increase with increasing confining stress. In this case the conical contact and particle chain buckling mechanisms are not viable: a more rigorous analysis based on the contact of rough particles is required. It is proposed that such an analysis should allow for the simultaneous elastic squeeze down of surface asperities and increase in the number of asperity contacts under increasing confining stress.