The creep behaviors of red sandstone in northern Yunnan and its fractional order damage modelling considering relaxation time effect

The creep characteristics of rocks pose significant challenges to the construction and operation of tunnels. Triaxial compression tests were conducted on sandstone using the GCTS rock testing system, revealing the rheological properties of sandstone. A fractional-order creep model considering rock relaxation time was constructed, and the effectiveness and applicability of this model were validated through experimental data. The results indicate that: (1) With increasing confining pressure, the creep rate during the stable creep stage gradually decreases, while the creep rate during the accelerated creep stage gradually increases. The long-term strength of sandstone increases, and the fracture angle gradually decreases, transitioning from intergranular fracture to transgranular fracture. (2) Utilizing experimental data, a nonlinear damage constitutive model considering relaxation time was established to describe the creep characteristics of sandstone. The influence of various parameters in the constitutive equation on sandstone creep characteristics was analyzed. An increase in relaxation time τ results in reduced creep response. The damage parameters β and ζ determine the creep rate during the accelerated creep stage. (3) Comparative analysis between theoretical and experimental curves demonstrates that the proposed model provides a more accurate fit, with simple model parameters that facilitate ease of use and strong applicability. These methods contribute to a better understanding of the creep failure mechanisms and behaviors of sandstone.