Overexploitation, rising prices and decreasing reserves of construction sand have prompted the need to develop sustainable alternatives. Crushed waste glass is a potential substitute, with geo-mechanical properties potentially comparable to natural aggregates. This study first investigates the morphological differences between a crushed glass and a natural sand at the particle scale. Particle shape analyses based on X-ray CT scanning indicate that the natural sand generally exhibits higher sphericity and convexity, although smaller crushed glass particles show greater shape variability and irregularity. Oedometer tests were conducted on these crushed glass and natural sand samples of the same particle size range, and a series of numerical simulations were performed using the discrete element method (DEM). Based on CT-derived particle geometries, together with spherical harmonic functions to simplify and reconstruct complex particle surfaces, direct inputs of realistic particle shapes were enabled in the DEM simulations. The impacts of particles’ surface roughness on one-dimensional compressibility where investigated by considering multiple contact constitutive models. These include the classical simplified Hert-Mindlin contact model and several user-defined rough contact models implemented in the C++ user-defined constitutive model of the PFC3D v7.0 software. Rough contact models, including the Greenwood & Tripp (1984) model, the Otsubo et al. (2015) rough contact model and its modified version, as well as the Yimsiri and Soga (2000) rough contact model and its modified version, were compared. Based on the consideration of real particle shape, this study investigated the influence of different contact models on one-dimensional compressive response, focusing on how best to realistically couple the effect of particle morphology and contact mechanics in modelling the macroscopic behaviour of different materials.