Objective As the core facility for large-scale natural gas storage, salt cavern gas storage experiences progressive damage to the surrounding rock due to the combined effects of cyclic injection–production loads and high temperatures. While the classical Burgers model captures the basic creep behavior of salt rock, it does not account for the coupled influence of temperature and stress fields on viscoelasticity, nor does it incorporate material stiffness degradation from damage accumulation. Consequently, the model cannot accurately represent thermo-mechanical coupling or damage evolution. Therefore, a more precise constitutive model is urgently needed to ensure the long-term safe operation of gas storage facilities.

Methods An improved Burgers damage constitutive model incorporating the temperature time-lag effect was developed. Temperature-dependent correction terms for the elastic modulus and viscosity coefficient were introduced, and a damage variable was incorporated based on Lemaitre’s Hypothesis of Strain Equivalence to derive the temperature–pressure coupling damage equation. For the unique trapezoidal-wave injection–production operations of salt cavern gas storage, a four-stage piecewise control equation and a damage evolution dynamic equation with decoupled stress amplitude and mean value were established. To validate the model’s accuracy, a triaxial cyclic loading test under multi-factor coupling was designed and conducted, and the relevant model parameters were determined through inverse calculation.

Results The improved model predicted axial strain of salt rock under varying temperature–pressure conditions with errors within 10％, significantly outperforming the classical model. Test results indicated that high temperature accelerated damage accumulation; as temperature rose from room temperature to 80 °C, the damage index increased from 3.22 to 3.92. Raising the average stress to 17.5 MPa increased the damage variable by 52％, confirming the amplifying effect of average stress on damage. The improved model demonstrated high simulation accuracy for three-stage damage, with an overall correlation coefficient (R²) exceeding 0.98.

Conclusion The improved model accurately analyzes the coupling of temperature, stress, and damage fields, including the average stress amplification effect under trapezoidal-wave loads. It excels in piecewise analysis of trapezoidal waves and characterization of the temperature time-lag effect, providing a reliable tool for assessing the long-term stability of gas storage surrounding rock. This model holds significant engineering value for operation optimization, damage monitoring and early warning, and long-term safety assessment of gas storage.