Fractional nonlinear creep constitutive theory considering bedding orientation and anchorage

This study develops a unified fractional nonlinear creep constitutive theory for bedded rocks under the coupled influence of bedding orientation and transverse anchorage. A full-stage one-dimensional framework is constructed by connecting an elastic spring, a fractional viscoelastic element, and a damage-coupled fractional viscoplastic element. A acceleration switch is introduced and generalized through an effective-stress measure based on the deviatoric stress invariant, enabling the onset of accelerated creep to be driven by the time-varying confinement provided by the anchorage system. To account for bedding-induced anisotropy, the model is extended to three dimensions using a compliance-substitution strategy and an explicit transversely isotropic compliance transformation, yielding a closed-form orientation–parameter mapping through the dimensionless matrix \(U(\theta )\). The anchorage effect is homogenized as an equivalent unidirectional lateral constraint stiffness \(K_{b}(t)\) that decays exponentially, leading to explicit expressions for axial strain, lateral confinement stress, and bolt force under constant axial stress. The accelerated creep initiation time shows an orientation-dependent decreasing trend from 0° to 90°. The fitting results show that the proposed model reproduces the instantaneous jump, steady-state creep and third-order acceleration across the stress level, and is superior to Burgers and Nishihara models in capturing non-stationary post-response.