This paper investigates the strength and critical state (CS) behaviours of granular materials via DEM simulations of true triaxial drained tests under three different loading modes including constant b (intermediate stress ratio) tests with constant σ1′ (major principal stress), constant p′ (mean pressure) and constant σ3′ (minor principal stress) respectively. To this end, a series of samples are generated with the same particle size distribution, and with the confining stresses ranging from 100 kPa to 900 kPa. The CS is achieved for all samples. Both the macroscopic behaviours and the microscopic behaviours are examined and compared considering different loading modes, confining stresses and intermediate stress ratios (b). The critical state lines (CSLs) are found to be unique and independent of the loading modes, but dependent on the b values. The CSLs with b=0 and b=1 form the two boundaries of CSLs respectively beyond which CSLs under all other b tests cannot go beyond. Si