• Stress holding significantly reduces fatigue life of Jintan salt rock, with stress level magnitude having a greater impact on peak strain than holding duration.
• Machine learning analysis quantifies that higher stress limits and stress holding adversely affect fatigue index, while lower stress limits and rate have a positive effect.
• A novel fatigue-creep composite damage constitutive model is developed, accurately capturing elasto-viscous behavior under complex cyclic loading including stress holding.
• Sensitivity analysis reveals that strain changes are influenced not only by stress variations but also by alterations in elasto-viscous parameters, providing new insights for mechanical assessment.