A nonlinear creep model for transversely isotropic rock based on fractional calculus theory

Abstract

A nonlinear creep model based on fractional calculus theory is proposed to better describe the creep characteristics of transversely isotropic rock. The model includes a Hooke elastomer, a fractional Abel dashpot, a Kelvin body, and a nonlinear viscoplastic body, which effectively capture the three stages of creep (including the primary, steady-state, and accelerating creep stages) while also reflect the influence of different bedding angles on creep behavior. The parameters of the model are identified by the Levenberg–Marquardt algorithm. Compared to previous models assuming constant Poisson’s ratio for transversely isotropic rock, our nonlinear creep model demonstrates improved accuracy and rationality.

Keywords:

• Nonlinear creep model
• transversely isotropic rock
• fractional calculus theory

Author contributions

Yukun Li: Formal analysis, Data Curation, Writing-Original Draft, Investigation; Mingxuan Shen: Methodology, Writing - Review & Editing, Supervision, Funding acquisition; Bin Du: Conceptualization, Funding acquisition;

Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author ([email protected]) upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (No 52268022).