Spatial heterogeneity prevails in soils, even in remolded specimens formed in the laboratory under carefully controlled conditions. Spatial variability prompts the emergence of mechanical phenomena that are not encountered in homogeneous media. The purpose of this study is to explore phenomena associated to spatial variability in soils, taking into consideration their particulate nature. We focus on the effect of variability in soil stiffness on the load-deformation response under zero-lateral strain conditions, using complementary finite element simulations (correlated random media) and experiments (rubber-sand mixtures). Results show the development of non-homogeneous stress and strain fields, intricate load transfer and stress concentration along percolating stiff zones, the reduction in K0 values, more complex interpretation of wave propagation traces for the characterization of small strain stiffness, and suggest judicious use of mixture formulas.