A discrete element method (DEM) was used to investigate the undrained behaviour of granular materials under a critical state soil mechanics (CSSM) framework. The laboratory works within CSSM framework are mostly confined to an isotropic condition; therefore, the experimental data for the same granular material under different consolidated conditions was limited in the literatures. The research employs DEM to investigate the effect of different consolidation conditions, i.e. isotropic (the principal stress ratio, K=σ′3/σ′1=1), anisotropic (K=0.5) and K0- conditions, on the same granular material. It was found that the consolidation condition influenced the micro- and macro- mechanical properties and so their undrained behaviour during shearing. However, a unique critical state line (CSL) was achieved regardless of consolidation condition. The state of granular material is often defined in terms of initial state parameter (ψ0) using the CSL. The instability stress ratio (ηIS), which characterizes the triggering of instability or liquefaction, showed good relation with ψ0 and the relation is known as the instability curve. Multiple instability curves were found depending on the consolidation condition. The particle contact at the onset of instability in terms of coordination number (CN) was almost the same for the same ψ0 for all consolidation conditions, however the fabric anisotropy in terms of von Mises fabric (FvM) showed similar correlation with ηIS as found for instability curves. This suggests that the difference in instability curves for different consolidation conditions may be related to fabric anisotropy.