It has been well recognised that principal stress rotation (PSR) can lead to non-coaxiality and can accelerate the liquefaction of granular materials such as soil, which poses a challenge for the safe design of geotechnical applications. Most of previous studies regarding PSR have focused on shearing along only one direction. However, in reality, shearing may be multi-directional, e.g., in earthquakes, with one shear being from the weight of geotechnical materials and the other shear being from that of the seismic waves of earthquakes. These two shears are likely to act at different angles. To replicate these two shears, a bi-directional simple shear apparatus has been developed and is used for the current research. This research work aims to investigate the mechanical behaviour of granular materials under various bi-directional simple shears from both macro- and micro-scale perspectives qualitatively. Specifically, drained monotonic, undrained monotonic, and undrained cyclic bi-directional simple shear tests on glass beads are conducted to obtain a basic understanding of the macro-scale mechanical responses of granular materials under various loading conditions. Numerical simulations based on the discrete element method (DEM) are conducted to reproduce these macro-scale mechanical responses so that the DEM simulations and experimentations are mutually validated. Further, DEM simulations provide more insights into macro-scale mechanical responses regarding lateral normal stresses and principal stress results. Meanwhile, the corresponding micro-mechanical features of bi-directional simple shear can also be revealed by DEM simulations. A greater emphasis is placed on the micro-mechanical features of granular material under bi-directional simple shear since these have not been previously investigated. Parametric studies with DEM simulations are conducted to determine the micro-mechanical parameters of granular assemblies by characterising the macro-scale mechanical behaviour of glass beads. With the micro-mechanical parameters determined by parametric studies, DEM results are in good agreement with experimental data for unidirectional simple shear cases. Thus, these determined parameters are used for DEM simulations of various bi-directional simple shear cases. For the drained monotonic bi-directional simple shear cases, shear loading consists of the first and second shear. As to the specific loading paths, loading angles from 0° to 180° with an interval of 30° are formed between these two shears. The loading angles of 0° and 180° in essence are unidirectional, as the basis of bi-directional simple shear. The vertical stress is maintained at 200kPa during drained monotonic shearing. The DEM simulations closely replicate the experimental conditions for each test. It is shown that the DEM results are in good agreement with experimental data. Both macro-scale and micro-scale responses of the granular material to bi-directional shear are influenced by the initial dense state of the specimens. From a macro-mechanical perspective, the shear stresses, lateral normal stresses, and principal stresses are all loading-angle dependent. At a relatively small shear strain, a higher loading angle generally leads to higher magnitudes of shear stress (τ_xz), lateral normal stress and principal stress. However, at a very large shear strain, the values of shear stress, normal stress, and principal stress are similar in magnitude for various loading angles. Non-coaxiality is observed at all loading angles and its evolution for bi-directional simple shear shares similarities with that for unidirectional simple shear. From a micro-mechanical perspective, the loading-angle dependence of the coordination number is influenced by the initial dense state of granular assemblies. A threshold coordination number may exist for undrained monotonic shearing, below which the instability of granular assemblies can occur. The loading-angle dependence of contact force chains is notable for a relatively small shear strain, despite being less evident towards the end of the shearing process. In general, the loading-angle dependence of rose diagrams follows that of contact force chains. The rose diagrams also show that the distribution of contact force magnitudes differs from that of contact normal, which suggests that stress anisotropy is more notable than fabric anisotropy. Furthermore, a higher loading angle leads to a higher degree of fabric anisotropy, which in turn corresponds to a higher shear stress (τ_xz). The orientation of the major principal fabric is found to be slightly lower than that of the major principal stress. For the undrained monotonic bi-directional simple shear cases, the first and second shear are also conducted at the loading angles from 0° to 180° with an interval of 30°. In the first shear, the vertical stress is maintained at 200kPa. However, in the second shear, the volume of the specimen remains unchanged while the effective stress is continuously dissipated. The results show that the ultimate shear stress (τ_xz) and shear strain (γ_xz ) are both loading-angle dependent. However, the angle dependence of the pore water pressure and principal stress is less evident. Similarly, the angle dependence of micro-mechanical features such as the coordination number is also less evident. The coordination number continuously decreases due to the loss of micro-contacts associated with the dissipation of effective stress. Rose diagrams suggest that the difference between stress anisotropy and fabric anisotropy is reduced for undrained monotonic shearing, which is attributed to the loss of micro-contacts. Meanwhile, the deviator fabric under undrained monotonic loading is also generally lower than that under drained monotonic loading. For the undrained cyclic bi-directional simple shear cases, the effects of the loading paths with and without static shear consolidation (SSC) are investigated. The initial- and post-liquefaction behaviour of glass beads are investigated. It is found that the mechanical responses are evidently loading-path dependent from both macro- and micro-scale perspectives. An initial SSC tends to increase the liquefaction resistance. The test material has a higher liquefaction resistance in the post-liquefaction stage than in the corresponding initial liquefaction stage. The loading paths in the initial liquefaction stage may further affect the material behaviour in the post-liquefaction stage. It is found that the packing density in terms of the relative density and the coordination number influences the liquefaction resistance of granular materials. The relationship between PSR and liquefaction resistance is demonstrated, and it is seen that a smaller variation in the amount of PSR corresponds to a higher liquefaction resistance. Fabric anisotropy is found to be loading-path dependent, and its relationship to liquefaction resistance is discussed. Lastly, the contributions of strong and weak contact force networks to the deviatoric stress and fabric anisotropy are discussed and compared with the findings in literature. It is found that the deviatoric stress is largely dependent on the strong contact force network. However, the strong and weak contact force networks are both indispensable for fabric anisotropy. The loading-angle dependence of the deviator stress and fabric anisotropy of strong and weak contact force networks has also been examined.