# Test Granular Materials Failure Using Bi-Directional Simple Shear Apparatus: A Review
## 4 Bi-Directional Simple Shear Tests with Complex Loading Stages  
To study the foundation soil of an offshore Arctic gravity structure subjected to complex loading conditions, [PERSON] et al. [PERSON] et al. (2009) conducted a group of bi-directional simple shear tests that considered the effect of the consolidation shear stress. The bi-directional simple shear apparatus developed by [PERSON] et al. [PERSON] et al. (2009) was used, which is capable of measuring the pore water pressure. The tested material was normally consolidated resedimented Boston Blue clay. In the experiment, 35 cm\({}^{3}\) cylindrical clay samples were trimmed to the height of 2.3 cm, and placed into wire-reinforced membranes. The D/H was less than 1.91. In the tests conducted by [PERSON] et al. [PERSON] et al. (2009), the effect of the direction of consolidation shear stresses on the undrained monotonic shear behaviour was studied on clay. The consolidation shear stress presents the gravity loading induced initial shear stress within the foundation soil, and the undrained monotonic shear stress presents horizontal stress caused by external loads, such as an ice-loading force. In the consolidation stage, the samples were consolidated with a shear stress in directions from \(0^{\circ}\) to \(180^{\circ}\), with an interval of \(30^{\circ}\). Then, a secondary shear stress was applied in the \(0^{\circ}\) direction under the undrained conditions. The samples had a consolidation shear stress ratio (CSR, \(\frac{\tau_{c}}{\sigma_{vc}}\)) of 0.2, in which the consolidation shear stress ratio equalled the consolidation shear stress normalized by the effective vertical consolidation stress. The results show that the peak X shear strength decreases dramatically in tests with an angle from \(0^{\circ}\) to \(120^{\circ}\), and then increases in tests with an angle from \(120^{\circ}\) to \(180^{\circ}\), as shown in Figure 5. The shear strength is increased if one considers the total shear stress, in which the shear stress in the Y direction of the apparatus is included. The total shear strength is generally decreased by the increasing angle between these two shear stresses. In the tests with angles smaller than \(60^{\circ}\), brittle stress-strain behaviours are reported, and increasing the angles from \(60^{\circ}\) to \(180^{\circ}\) increases the ductility. The results indicate that the angles between the two shear stresses should be considered in foundation design, as the soil responses are significantly different in the soil with different angles. [PERSON] [47] and [PERSON] [46] tested the same stress paths as those used by [PERSON] et al. [56], and found similar relations between the angles and shear strength. However, there is a common limitation in these studies, only one CSR was considered, 0.2. The magnitude of the CSR is not well studied. [PERSON] et al. [50], and [PERSON] and [PERSON] [38] performed two-directional monotonic and cyclic simple shear tests using an apparatus developed at UC Berkeley [30]. In this apparatus, cell pressure can be exerted, and the pore water pressure can be measured. [PERSON] and [PERSON] [38] used this apparatus to study the seismic loading conditions on slopes. The slope conditions were represented by the consolidation shear stresses in the dip direction, and seismic loadings were applied parallel or perpendicular to the consolidation shear stresses, as shown in Figure 6a. The consolidation shear stresses were first added during the consolidation, and then the cyclic loadings were added perpendicular to the consolidation shear stresses, as shown in Figure 6c. For comparison, a second series of tests was also conducted, in which the consolidation shear stresses were in the same direction as the cyclic shear stresses, as shown in Figure 6b. In the tests conducted by [PERSON] et al. [30], and [PERSON] and [PERSON] [38], the specimens were prepared in a plain rubber membrane held tight against a vacuum mould. The specimens were in a cylindrical shape with a D/H of four.