The kinematic-constraint-inspired non-ordinary state-based peridynamics with fractional viscoelastic-viscoplastic constitutive model to simulating time-dependent deformation and failure of rocks.

• A novel fractional viscoelastic-viscoplastic (FVEVP) constitutive law is proposed. • A numerical implementation strategy of the FVEVP model by an explicit time integration scheme is proposed. • A unified progressive damage-rupture criterion is proposed. • A non-linear creep-damage-fracture kinematic-constraint-inspired non-ordinary state-based peridynamics (KC NOSBPD) formulation is proposed. • The time-dependent deformation and fracturing behaviors of intact, macrofractured, and surrounding rock mass around underground openings are reproduced. An in-depth understanding of the time-dependent deformation and failure behavior of rocks is essential for the long-term stability of surrounding rock mass around underground engineering. In this paper, the kinematic-constraint-inspired non-ordinary state-based peridynamic (KC NOSBPD) formulation is proposed to incorporate time dependence by adopting a fractional viscoelastic-viscoplastic (FVEVP) constitutive law to describe the non-linear creep deformation behavior and conjugating it with a time-independent progressive damage-rupture criterion to reproduce creep damage and subsequent creep fracture process. The FVEVP constitutive model is established by coupling a Hooke body, an Abel dashpot and a fractional viscoplastic body. Through the Grünwald-Letnikov (GL) definition of the fractional-order derivatives, finite increment formulations for the FVEVP constitutive model are derived to facilitate numerical implementation by an explicit time integration scheme. The unified progressive damage-rupture criterion is obtained by combining the damage criterion with the rupture criterion via a strain-dependent isotropic scalar damage variable. The novel model is employed to reproduce the time-dependent deformation and fracturing behaviors of intact salt rock, macrofractured sandstone specimens, and surrounding rock mass around the salt cavern gas storage. The proposed model agrees well with experimental data and numerical results from other published literature. To the authors' knowledge, the FVEVP model is first developed to simulate fracture behaviors. [ABSTRACT FROM AUTHOR]