# Test Granular Materials Failure Using Bi-Directional Simple Shear Apparatus: A Review
## 1 Introduction
Similar to the triaxial apparatuses, the hollow cylinder apparatuses use cell pressure to confine the sample through the membrane. In a hollow cylinder apparatus, there are two separate cell pressures, applied in the interior and exterior chambers. The two cell pressures can work independently or simultaneously to control the pressure on both the inner and outer surfaces of a sample. The complex load paths can be tested using a hollow cylinder apparatus [22]. However, because of the geometry of the sample, the apparatus can only add one shear stress. Although the uniformity of the strain of a sample is improved by using a hollow cylinder sample compared with a solid cylinder sample, end-restraint and sample curvature still cause non-uniformities of stress and strain. Non-uniformities in stress occur at the boundary of a sample. As a hollow cylinder sample increases the surface area-to-volume ratio of a sample, the non-uniformities are increased in another way compared with a solid cylinder specimen. Moreover, because of the large height of a sample, the lateral pressure within a sample increases from top to bottom, while the cell pressure is the intermediate value over the height of the sample. As a result, the cell pressure is higher than the lateral stress at the top, and is lower than that at the bottom, causing a non-uniform strain (thinner at the top and thicker at the bottom). The non-uniform strain is also the result of no lateral confinement. In addition, the resultant stresses are also non-uniform, and are greater at the top and less at the bottom. Another problem related to the sample height is the pore water pressure redistribution, particularly at a low strain rate. The redistribution of the pore water pressure and non-uniformity of the samples together cause the change in the local strain and density. Different from triaxial testing, the principal stresses rotate continuously during a torsional test, which replicates in situ stress conditions. A hollow cylinder apparatus also allows for the independent control of principal stresses and the rotation of the major principal stress axis, and is widely used in the simulation of principal stress rotation [20; 21; 23; 24]. However, [PERSON] [25] stated that a hollow cylinder apparatus allows for control over the principal axes instead of allowing the free rotation of the principal axes. Simple shear apparatuses have been developed for several decades [26; 27; 28; 29; 30]. The most commonly used type of simple shear apparatuses was developed by the Norwegian Geotechnical Institute (NGI). A short cylindrical sample is used in the simple shear testing, surrounded by a reinforced latex membrane or a latex membrane with a stack of rings. The two kinds of lateral confinement show a general agreement in the shear strength and volume change in the experimental results, using cohesive and non-cohesive soils [31; 32]. Physical constraints in the horizontal direction accurately maintain the \(K_{0}\) consolidation. However, the shape of a cylindrical specimen prevents the direct measurement of the forces on the constraints. Although numerous studies have been carried out to measure the lateral stress on rings and reinforced membrane with non-standard equipment that is no longer produced, to this day, there is still no easy way to make a reliable measurement [33; 34; 35]. Simple shear testing replicates the in situ stress, and has a smooth rotation of the principal axes during shearing. For bi-directional simple shear apparatuses, such as the VDDCSS, it is possible to apply shear stresses in two independent directions on the horizontal plane. In terms of uniformity, a large diameter-to-height ratio (D/H) and small height, where D/H is usually greater than four in tests, effectively reduces the non-uniformity of the stress, effectively within the active portion of the sample [28; 36].