Anisotropic time-dependent behaviors of shale under direct shearing and associated empirical creep models

Understanding the anisotropic creep behaviors of shale under direct shearing is a challenging issue. In this context, we conducted shear-creep and steady-creep tests on shale with five bedding orientations (i.e. 0°, 30°, 45°, 60°, and 90°), under multiple levels of direct shearing for the first time. The results show that the anisotropic creep of shale exhibits a significant stress-dependent behavior. Under a low shear stress, the creep compliance of shale increases linearly with the logarithm of time at all bedding orientations, and the increase depends on the bedding orientation and creep time. Under high shear stress conditions, the creep compliance of shale is minimal when the bedding orientation is 0°, and the steady-creep rate of shale increases significantly with increasing bedding orientations of 30°, 45°, 60°, and 90°. The stress-strain values corresponding to the inception of the accelerated creep stage show an increasing and then decreasing trend with the bedding orientation. A semilogarithmic model that could reflect the stress dependence of the steady-creep rate while considering the hardening and damage process is proposed. The model minimizes the deviation of the calculated steady-state creep rate from the observed value and reveals the behavior of the bedding orientation's influence on the steady-creep rate. The applicability of the five classical empirical creep models is quantitatively evaluated. It shows that the logarithmic model can well explain the experimental creep strain and creep rate, and it can accurately predict long-term shear creep deformation. Based on an improved logarithmic model, the variations in creep parameters with shear stress and bedding orientations are discussed. With abovementioned findings, a mathematical method for constructing an anisotropic shear creep model of shale is proposed, which can characterize the nonlinear dependence of the anisotropic shear creep behavior of shale on the bedding orientation.