Understanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.