COMPUTATIONS OF DILATANCY AND YIELD SURFACES FOR ASSEMBLIES OF RIGID FRICTIONAL SPHERES

This paper is concerned with the Reynolds dilatancy and shear strength of idealized granular media. The first part of the paper offers a cal culation of dilatancy in rigid-sphere assemblies based on the theoreti cal estimate previously proposed by J. D. Goddard (Proc. 11th Int. Con gress of Rheology (ed. P. Moldenaers and R. Kuenings; Elsevier, Amster dam 1992) 141-142) as a generalization of the classical work of O. Rey nolds (Phil. Mag. 20 (1885) 469-481). This new estimate yields an anal ytical expression for the dilatancy of two-dimensional isotropic assem blies of disks with arbitrary size distribution. Only a few special ca ses of three-dimensional assemblies could be treated analytically, but a stochastic (Monte Carlo) calculation is readily implemented. The es timates of the present method are roughly three times those of Reynold s, and it is argued that the two types of estimate represent opposite bounds for the dilatancy and strength of frictionless sphere assemblie s. The second part of the paper summarizes results from a detailed par ticle-mechanics (discrete-element) computer simulation of rigid-sphere assemblies, based on the recently developed quasi-static method of Zh uang, Didwania and Goddard (J. Comput. Phys. 121 (1995) 331-346). Dila tancies and yield cones are computed for various mono-and polydisperse assemblies of rigid frictional spheres subject to simple monotonic de formations, of the type encompassed by the 'cubical triaxial' test of soil mechanics. At large plastic strains, the computed yield surfaces bear a striking resemblance to the empirical Lade-Duncan yield surface of soil mechanics, which is adopted as a convenient referential basis for presenting the simulations. Many of the computed yield cones exhi bit a lack of convexity at small strain, which may suggest a plastic i nstability that is suppressed in the current simulations, a matter pro posed for further investigation. The results presented here suggest th at frictional-sphere assemblies may mimic the shape and evolution of y ield surfaces at small confining pressures for certain real non-cohesi ve granular media, if not the absolute magnitudes of yield strength.