Step-variable-order fractional viscoelastic-viscoinertial constitutive model and experimental verification of cemented backfill

The focus of this study will be on the order of a fractional dashpot with 1 < beta < 2, which has the angible physical meaning of a viscoinertial element. The creep constitutive model based on fractional calculus shows its unique advantages in describing the creep characteristics and can well describe the creep mechanical behavior under different load conditions. The viscoelastic properties of the fractional dashpot have been well studied in the literature for the order 0 < beta < 1, and the viscoinertial element (1 < beta < 2) extends the theoretical content of the fractional dashpot. With the theoretical framework of the viscoinertial property, the disadvantages of the fractional constitutive model in describing the nonlinear acceleration stage can be circumvented without adding a new element. Based on the step-variable-order fractional dashpot (SVOFD), the creep constitutive models depending on different variables are constructed. Drawing support from the UGO algorithm of 1stOpt software, the parameters of the fractional constitutive models are determined by fitting with the graded loading and unloading creep tests. Summing up, it may be stated that the proposed variable-order fractional constitutive models can better describe the loading and unloading creep characteristics of cemented backfill.

Automated summary

This study focuses on the order of a fractional dashpot with 1 < beta < 2, which has the tangible physical meaning of a viscoinertial element. It presents the unique advantages of the creep constitutive model based on fractional calculus in describing creep characteristics and extends the theoretical content of the fractional dashpot with the viscoinertial element (1 < beta < 2).