# Test Granular Materials Failure Using Bi-Directional Simple Shear Apparatus: A Review
## 4 Bi-Directional Simple Shear Tests with Complex Loading Stages
It was concluded that the large shear strain can be developed when  
Figure 8: Different levels of stress reversals in tests with varied stress paths, by [PERSON] (Reprinted from [37]). Figure 7: Multi-directional loadings considered the initial static driving force, tested by [PERSON] (Reprinted from [37]). Figure 9: Cyclic shear strain and permanent shear strain in a simple shear test (Reprinted from [37]). the excess pore water pressure is much smaller than the total vertical stress. It was found that the consolidation shear stress has a significant influence on both the shear strain development and the pore water pressure generation, and the effect is different in the different stress paths. Specifically, increasing the consolidation shear stress increases the liquefaction resistance by reducing the level of shear stress reversal. The shear strain in the tests with a small consolidation shear stress was greater than the tests without the consolidation shear stress. By systematically studying the effect of the consolidation shear stress on the liquefaction resistance, [PERSON] [37] concluded that the reduction factors, developed by [PERSON] et al. [57], and [PERSON] and [PERSON] [29], may not reflect the differences in liquefaction triggering between a uni-directional simple test and a corresponding uni-directional simple shear test under the same testing conditions. The reduction factors were defined as the difference between a cyclic shear stress ratio in a uni-directional simple shear test (\(CSR_{1D}\)) and its corresponding bi-directional simple shear test (\(CSR_{2D}\)), normalized by the cyclic shear stress ratio in an uni-directional simple shear test (\(CSR_{1D}\)), \(\frac{CSR_{1D}-CSR_{2D}}{CSR_{1D}}\). The reduction factor in the study conducted by [PERSON] [37] had a wider range, from 0.6 to 1.3, compared to that from 0.8 to 1.0 as recommended in previous studies. [PERSON] [37] concluded that the difference is due to the fact that less stress paths were considered in previous studies. It shows the cyclic shear strength in a bi-directional simple shear is more complex than a uni-directional simple shear test. To study the shear stress of sand with static shear stress during consolidation, [PERSON] et al. [52] conducted a group of bi-directional simple shear tests on Leighton Buzzard sand Fraction B, which shows dominant contractive behaviour. Similar to the stress paths used by [PERSON] et al. [56], as shown in Figure 11, the effect of the consolidation shear stresses on the undrained monotonic and cyclic shear behaviour was studied [52; 58; 59]. In the tests with different magnitudes and directions of the consolidation shear stresses, it has been shown that a smaller angle leads to a more brittle shear response and a higher peak strength. In the tests with a greater CSR (magnitude of consolidation shear stress), the most brittle response and the highest peak strength take place at a 0\({}^{\circ}\) angle, which is similar to results reported by [PERSON] et al. [56]. In the tests with a smaller CSR, the peak strength at all of the angles is greater than the tests without the consolidation shear stress, as shown in Figure 12, and the most brittle response and the highest peak strength take place at a 90\({}^{\circ}\) angle. It was concluded that the consolidation shear stress densifies the soil samples, and the role of densification is predominant over the role of angles under a smaller CSR. Figure 11: Stress paths on soil samples including the first consolidation shear stress, followed by undrained shear [52]. Figure 5:0 Limiting pore water pressure in a simple shear test (Reprinted from [37]). Using the same stress paths, [PERSON] et al. [60; 61] studied the non-coaxiality of sand during the shear. Non-coaxiality is analyzed based on the linear relation between \(\frac{\tau}{\sigma_{vc}}\) and \(\tan\psi\), which is found in the constant load simple shear tests [41].