Possible Stress Path of HCA for Cyclic Principal Stress Rotation under Constant Confining Pressures

Nowadays most hollow cylinder apparatus (HCA) in the world can only apply two dynamic loads, namely the axial load $\left(W\right)$ and torque $\left(M_T\right)$ , during cyclic principal stress rotation. The limitation of this loading mode is presented, and based on such limitation other possible and applicable loading modes are put forward: (1) On the premise of setting $W$ a special constant related to the inner $\left(p_i\right)$ and outer $\left(p_o\right)$ cell pressure, the stress path at which shear stress $\left(q\right)$ regularly changes with rotation angle $\left(\alpha \right)$ under the constant $b$ (Bishop parameter) and the constant mean principal stress $p$ can be achieved by adjusting $M_T$ ; (2) setting $b$ at a constant (not equal to 0.5), the linear relation between $p$ and $q$ can be realized under a regular changing $\alpha$ . In this case $W$ and $M_T$ should satisfy a certain equation and meanwhile the peak value of $q$ should be restricted within the $p-q$ critical state line; (3) without regarding the effect of intermediate principal stress, a stress path of $({\sigma }_1+{\sigma }_3)∕2$ monotonously changing with $\alpha$ can be achieved under constant $q$ . This implies that $W$ and $M_T$ should satisfy a combination of a number of simple trigonometric functions; and (4) the stress path of constant $b$ (with a random value between 0 and 0.5) and monotonous relation between $p$ and $R$ can be available under a regular changing $\alpha$ . In realizing this stress path, $W$ and $M_T$ should satisfy certain equations and the maximum $R$ should also be restricted by the critical state line. Results of this research can not only validate possible stress paths in cyclic principal stress rotation tests but can also provide a basis for further HCA improvement.