In the hollow-cylindrical torsional shear apparatus, four independent stress parameters can be set optionally as vertical force, torque, inner pressure and outer pressure are controlled independently. However, the stress conditions are not absolutely fixed in this study because the importance lies not in the value of α itself but in the relative value of α between the shear history and the shear. Two sorts of stress conditions are generally considered, as follows.
1. α=45o conditions
The specimen has different boundary conditions in each direction -- torsional, vertical, radial and circumferential -- because of its shape. It is possible that the difference in the effect of the boundary conditions is minimized by using the same value of α in each experiment. Although simple shear conditions, where vertical, radial and circumferential strain are zero, are the best choice for removing the effect of the edge friction, it was impossible to maintain simple shear conditions during the test in this study. Therefore, α=45o conditions were chosen because it seemed that these conditions were closest to the simple shear conditions in this kind of experiment. However, it should be noted that these conditions generate stress non-uniformity as explained in the following.
2. pi=po conditions
Non-uniformity of stress distribution is generated due to the difference between inner pressure pi and outer pressure po. Although the mean value is calculated as an average, it is desirable to minimize the stress non-uniformity. If pi=po conditions are adopted, there is no stress non-uniformity of σr and σθ. However, the advantageous boundary conditions mentioned above, can not be selected because the relationship of b=sin2α is necessary in these conditions.
Figures 3 (a) and 4 (a) show the stress-strain relationships for virgin shear under α=45o and pi=po conditions, respectively. Figures 3 (b) and 4 (b) show the volumetric strain-shear strain relationships in the same case shown in Figs. 3 (a) and 4 (a), respectively. A very similar behaviour is obtained from both α=45o and pi=po conditions. It means that the effects of the stress non-uniformity and the boundary conditions were insignificant in the experiment. As the specimen, which was loaded under triaxial extension, was constricted at a slightly smaller strain level in the pi=po conditions than in the α=45o conditions, α=45o conditions have been adopted for the shear process in this study.
