The strength and dilatancy of sands are continuously the research focus of soil mechanics. Further understanding of these mechanical properties depends on the insight view of the granular fabric of sands. The granular and discrete properties of materials make sands feasible to be studied by granular mechanics. Three strength indices including the critical state strength, the peak strength and the characteristic stress strength, dilatancy and shear modulus of sands in unconfined biaxial tests were investigated using the approach of granular mechanics. Micromechanical insights were obtained for the phenomenological behavior of sands observed in 2D discrete element simulations. The results presented in this paper indicated the friction coefficient of sand particles was crucial to the critical state strength of sands. This conformed to the theory of critical state soil mechanics. The other two strength indices correlated not only to the friction coefficient of sand particles but also the confining stress that sands were subject to and the relative density. The peak strength of sands was found to be irrespective of the stiffness of sand particles. A definite correlation of the characteristic stress strength with the stiffness of sand particles was unable to determine. The shear modulus of sands primarily correlated with the stiffness of sand particles, but its correlation with the relative density of sands was insignificant as far as the present situations were considered. The dilatancy of sands remained difficult to be understood as it correlated with many parameters such as the friction coefficient of sand particles, the mean stress that sands were subject to, the relative density, the Poisson’s ratio of sand particles as well as the stiffness of sand particles. At last, the calibrated model of granular mechanics developed was employed to investigate the Prandel problem in which a limit equilibrium solution was obtained for the bearing capacity of weightless foundations subject to surcharges. Agreements and disagreements of these two solutions were observed which enriched the understanding of bearing capacity of foundations.