Micromechanical modeling of granular soil at small strain by arrays of elastic spheres

The need for a micromechanical approach to modelling the stress-strain response of granular soil is discussed and justified. This work focuses on the small shear strain ({dollar}gamma{dollar} {dollar}leq{dollar}.01%) behavior, and investigates the validity of modelling analytically uniform, rounded-grained quartz sand by arrays of identical elastic, rough, quartz spheres. As a first step, the stress-strain properties of six regular arrays of spheres are studied in some detail, with focus on isotropic and transversely isotropic and biaxial boundary loading.; An analytical procedure is established for determining the elastic moduli of a random assemblage of equal, elastic, rough spheres of arbitrary mean porosity, subjected to isotropic confining pressure. The procedure uses the properties of the regular arrays already described, it accounts for the spatial distribution of porosity, and it calculates the macroscopic moduli through the Self Consistent Method. The procedure was applied to compute the shear and bulk moduli of assemblages of quartz spheres, which were then compared to static and dynamic measurements on uncycled and heavily precycled quartz sands from the literature. Although the theoretical sands are significantly stiffer than the actual soils, excellent agreement was found with resonant column measurements on heavily precycled Ottawa sand at small strains.; Finally, a new two-dimensional model of the stress-strain behavior of granular soil at small strains is presented. The model is based on an incremental solution to the contact problem of two equal, elastic, rough spheres and is implemented through nonlinear finite element techniques. The results of numerical experiments conducted on this idealized aggregate are compared to laboratory data on the static and cyclic small strain behavior of actual sand, as well as to recent compressional wave velocity measurements on anisotropically consolidated dry sands, with good agreement. These measurements, performed at the large cubic triaxial facility at the University of Texas, have shown that the P-wave velocity depends only on the principal stress parallel to the direction of wave propagation; this finding was also predicted by the simulation.; Concluding, the hypothesis that certain aspects of the behavior of granular soil are due to the particulate nature of the soil is justified. These aspects can not be interpreted and reproduced analytically unless this particulate nature is fully taken into account.