Variable-Order Fractional Constitutive Model for Triaxial Fatigue Behavior of Freeze-Thaw Double-Fractured Red Sandstone

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• ¹Liaoning Technical University, Fuxin, Liaoning Province, China
• ²Shenmu Zhangjiamao Mining Co., Ltd., Shaanxi Coal Group, xi,an, China
• ³Xi'an University of Science and Technology, Xi'an, China

To explore the fatigue behavior of freeze-thaw fractured rocks, triaxial incremental cyclic loading tests were performed on double-fractured red sandstone under three freeze-thaw cycle conditions. A fatigue deformation constitutive model incorporating variable-order fractional derivatives was proposed. Results show that with increasing freeze-thaw cycles, peak stress under static and cyclic loads decreases linearly, while peak strain increases linearly. The fatigue failure process of freeze-thaw double-fractured sandstone follows the static full-process curve. The failure strain exceeds the static peak strain but remains below the control point strain. After multiple freeze-thaw cycles, rock samples exhibited triaxial fatigue failure with extensive and complex surface cracking. Surface deterioration resulted in particle detachment and powdering without fragment dispersion, indicating that freeze-thaw cycling softens the rock and enhances ductility. The fatigue strength of freeze-thaw double- fractured sandstone can be accurately determined by an incremental fatigue loading scheme, averaging the final two cycle stress values, and utilizing the fatigue threshold stress ratio from axial deformation. By modifying the Nishihara model’s third-stage Abel viscoelastic model to a variable-order fractional-order viscous pot, performing cyclic load equivalent substitution and introducing freeze-thaw damage variables can better reflect the three-stage deformation of double-fractured red sandstone under freeze-thaw and cyclic loading. These findings advance constitutive modeling of sandstone fatigue failure and support safety assessments of fractured rock masses in cold regions.