A unified hardening/softening elastoplastic model for rocks undergoing brittle-ductile transition with strength-mapping and fractional plastic flow rule

A novel unified hardening/softening model is presented, addressing challenges in the constitutive modelling of rocks’ strain-hardening and strain-softening behaviours with brittle-ductile transition. The model highlights the impact of confining pressure on failure mode transition when capturing variations in initial yield, peak, and residual strength. The yield criterion and hardening/softening law are developed by a strength-mapping method, where the peak strength is considered the upper bound. The strength-mapping method relies on a mapping index formulated by plastic shear strains. The mapping index is then incorporated into the fractional plastic flow rule, leading to the proposed constitutive model with 9 easy-to-calibrate parameters. The model predictions have been validated by 4 series of rock samples on triaxial tests, where the brittle-ductile transitions have been well captured. The results indicate that it is reliable to capture the rocks’ complicated mechanical responses, particularly the brittle-ductile transition, with our proposed strength-mapping method and fractional plastic flow rule.