Analysis of Uniaxial Fatigue Mechanical Properties and Constitutive Modeling for Freeze- Thaw Cycled Red Sandstone with Double Fissures

Technical Summary: Analysis of Uniaxial Fatigue Mechanical Properties and Constitutive Modeling for Freeze-Thaw Cycled Red Sandstone with Double Fissures

Problem Statement
Rock mass engineering in cold regions, such as railways, tunnels, and slopes, faces significant safety threats from the coupling of freeze-thaw cycles and cyclic loading (e.g., traffic loads and construction disturbances). While the individual effects of freeze-thaw damage and fatigue deformation on rock have been studied separately, the specific mechanical behavior of fractured rock masses under the combined influence of these factors remains insufficiently understood. This study addresses the challenge of characterizing the fatigue mechanical properties and damage evolution of double-fissured red sandstone subjected to freeze-thaw cycling, aiming to provide a theoretical basis for quantitative damage description and stability assessment.

Methodology
The research employed a combination of experimental testing and theoretical modeling:

• Specimen Preparation: Standard cylindrical red sandstone samples ($\phi$50 mm $\times$ 100 mm) were prepared with two prefabricated fissures (dip angle 45°, length 20 mm) and a rock bridge (dip angle 120°, length 28.28 mm).
• Freeze-Thaw Cycling: Specimens were subjected to 0, 10, and 20 freeze-thaw cycles. Each cycle involved vacuum saturation followed by freezing at -30°C for 12 hours and thawing at 20°C for 12 hours.
• Mechanical Testing:
  • Static Testing: Conventional uniaxial compression tests were conducted to determine peak stress, elastic modulus, cohesion, internal friction angle, and characteristic stresses (crack initiation and dilatancy).
  • Fatigue Testing: Uniaxial step-incremental cyclic loading tests were performed under 0 MPa confining pressure. The loading scheme started at 0.3$\sigma_f$ (lower limit) and 0.8$\sigma_f$ (upper limit), with the upper limit increasing by 0.05$\sigma_f$ every 1,000 cycles until failure.
• Constitutive Modeling: A fatigue deformation constitutive model was developed based on the Nishihara model. The traditional Abel dashpot in the viscoplastic component was replaced with a variable-order fractional dashpot to better capture the dynamic changes in viscosity and deformation rates. A freeze-thaw damage variable ($D_n$) was introduced to account for pre-existing damage.

Key Results

• Degradation of Mechanical Properties: Freeze-thaw cycles significantly accelerated macroscopic damage. As the number of cycles increased (0 to 20), the peak stress decreased from 14.62 MPa to 8.22 MPa, and the elastic modulus dropped from 4.39 GPa to 1.73 GPa. Cohesion and internal friction angle also exhibited a sharp decline, particularly after 20 cycles.
• Characteristic Stress Evolution: The crack initiation stress and dilatancy stress decreased systematically with more freeze-thaw cycles. The normalized stress levels ($\sigma_{ci}/\sigma_f$ and $\sigma_{cd}/\sigma_f$) also declined, indicating a reduced resistance to crack initiation and volume dilatancy.
• Failure Mode Transition:
  • 0 Cycles: Failure was dominated by tensile splitting and wing crack coalescence.
  • 10-20 Cycles: The failure mode transitioned towards shear failure. Secondary cracks appeared more frequently at the tips of pre-existing flaws, and shear-type cracks emerged, suggesting that freeze-thaw damage weakens structural weak planes near the fissure tips.
• Fatigue Behavior: The fatigue life of the specimens decreased drastically with freeze-thaw damage. Specimens with 0 cycles failed after 837 cycles, while those with 20 cycles failed after only 35 cycles under the same loading scheme. The axial deformation curves shifted from Type B (linear accumulation) to Type C (rapid failure) as freeze-thaw damage increased.
• Dynamic Elastic Modulus: The dynamic elastic modulus generally decreased with an increasing number of loading-unloading cycles and freeze-thaw cycles, reflecting cumulative internal damage and pore compaction.

Constitutive Model Contributions
The study established a fatigue constitutive model that integrates:

1. Variable-Order Fractional Derivative Theory: Replacing the standard dashpot allows the model to flexibly describe the evolution of creep rates and viscoplastic responses at different strain stages.
2. Freeze-Thaw Damage Variable: The model incorporates a damage variable ($1-D_n$) to quantify the degradation of mechanical parameters due to freeze-thaw cycling.
3. Decomposition of Load: Cyclic loads were decomposed into static and alternating components to derive storage and loss compliances for the elastic, viscoelastic, and viscoplastic stages.

Verification and Significance
The proposed model was verified against experimental data from stepwise cyclic loading tests under three freeze-thaw conditions.

• Accuracy: The model successfully captured the three-stage evolution of axial strain (initial compaction, constant-rate deformation, and accelerated failure).
• Statistical Fit: The correlation coefficients ($R^2$) between the model predictions and experimental results exceeded 0.90 for all conditions (ranging from 0.971 to 0.998).
• Significance: The authors claim that this research provides a theoretical tool for quantitatively describing the freeze-thaw damage process and fatigue deformation of fractured rock masses. The established constitutive model offers a basis for assessing the long-term stability of engineering projects in cold, fractured rock environments. The study confirms that freeze-thaw damage significantly reduces the fatigue strength of rock masses, necessitating careful consideration in the design and monitoring of cold-region infrastructure.