Fractional creep damage constitutive model of weakly cemented soft rock under unloading confining pressure

This study investigates the creep damage characteristics of weakly cemented soft rock induced by excavation and unloading in an underground chamber, focusing on specimens from the western mining area. A series of multi-stage unloading confining pressure creep tests on weakly cemented soft rock was conducted using GDS HPTAS. Under different water conditions, the creep characteristics and creep rate characteristics of weakly cemented soft rock were studied under confining pressure unloading. Based on the reciprocal steady creep rate method, the mathematical exponential function relationship between long-term strength and water content of weakly cemented soft rock was determined. A new method is proposed to determine the boundary point t₁ between attenuation creep and constant velocity creep and the boundary point t₂ between constant velocity creep and accelerated creep based on the characteristics of creep rate curve. By introducing the Riemann-Liouville fractional order integral operator and the negative time exponential damage evolution variable, nonlinear damage Abel clay pot was defined, and a six-element fractional order creep damage constitutive model, including elastic elements, viscoelastic damage elements, viscous damage elements and nonlinear viscoplastic damage elements, was established. Based on the experimental results, the Trust-Region algorithm in Matlab was used to identify the model parameters and analyze the sensitivity. The results show that the established model has clear physical significance and high agreement with the test values. It can accurately reflect the creep damage characteristics of weakly cemented soft rock under excavation and unloading confining pressure in underground engineering, which is significant for ensuring the long-term stability of underground engineering.