A four-element fractional creep model of weakly cemented soft rock

The creep model is the main form used to describe the creep behavior of weakly cemented soft rock (WCSR). To investigate the creep behavior of weakly cemented soft rock, multi-stage loading creep tests were performed by using GDS HPTAS creep triaxial apparatus. The creep curves, creep rates, and creep failure modes of weakly cemented soft rock under different water contents were obtained. A novel four-element fractional-order creep model to describe the three-stage creep behavior of weakly cemented soft rock was proposed using the Abel dashpot basing on the creep test results and fractional calculus theory. The formula of this model was developed according to the H-Fox special function. The trust-region method was used to obtain the model parameters, and the parameters were optimized using the ant colony optimization approach. The creep curves of weakly cemented soft rock under different water contents were calculated and compared with the experimental results, verifying the superiority of the four-element fractional-order creep model in describing the creep characteristics of weakly cemented soft rock. The calculated results were also in good agreement with the experimental results, which confirms that the four-element fractional order creep model can accurately reflect the complete creep behavior of weakly cemented soft rock.