Improved nonlinear Burger creep model for soft rocks based on the fractional-order theory and considering viscoplastic deformation

The significance of creep behavior in soft rocks is crucial in rock engineering, particularly when ensuring the time-dependent stability of underground structures. This study proposed a new nonlinear creep constitutive model to represent the soft rock’s creep behavior subjected to uniaxial and triaxial stress conditions. The Burger model was modified by substituting the traditional Newton dashpot with the fractional derivative Abel dashpot, and a viscoplastic body was introduced in series with the improved Burgers model to simulate the accelerating phase of rock creep. The model's efficacy was confirmed by fitting the parameters using creep test data from different soft rocks. The isochronous stress-strain curve approach was employed to calculate the long-term strength of rocks, and a sensitivity analysis was conducted to evaluate how the model parameters affect creep deformation. The high agreement between the predicted outcomes and the actual creep experimental data for salt, shale, and sandstone demonstrates the proposed model's accuracy and logic. These results indicate that the model reliably represents soft rocks' nonlinear creep characteristics and the whole creep process.