Creep constitutive model for damaged soft rock based on fractional-order nonlinear theory

Investigating the combined effects of mining damage and creep damage on slope stability is crucial, as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence. This study develops a fractional-order non-linear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the three-dimensional finite difference method on the FLAC^3D platform. Comparative analysis of the theoretical, numerical, and experimental results reveals that the fractional-order constitutive model, which incorporates the double damage effect, accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase. The numerical results show a fitting accuracy exceeding 97% with the creep test curves, significantly outperforming the 61% accuracy of traditional creep models.