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• Completed graded upper stress limit interval fatigue (GUIF) tests and graded lower stress limit interval fatigue (GLIF) tests, comparing the effects of different time intervals and stress amplitudes on the fatigue failure characteristics of mudstone. • The fatigue life of mudstone shows an increasing trend with increasing time intervals. • The study found that the residual strain cycles before and after the time intervals exhibited opposite patterns in the GUIF tests compared to the GLIF tests. • In discontinuous graded fatigue tests, the impact of the fatigue stage on the damage to mudstone was smaller than the impact of the interval stage. During the operation of an underground salt cavern gas storage, Fatigue failure occurs in the surrounding rock of gas storage reservoirs under non-continuous gas injection and extraction loading. Due to the special layered salt rock structure in China, the mudstone interlayer is the weak part of the gas storage. It is necessary to study the effect of stress magnitude and interval time on the fatigue mechanical properties of mudstone. Graded upper stress limit interval fatigue (GUIF) test and graded lower stress limit interval fatigue (GLIF) test were carried out on mudstone respectively. And different interval times were set to investigate the effect of interval time on the mechanical properties of mudstone. With the increase in the interval time, the fatigue life and peak strain of the mudstone increased. Under the same interval time, the lower-limit interval test result showed a significantly higher fatigue life than the upper-limit interval test result. The stress–strain curve exhibited three stages: scattered–dense–scattered. During the unloading phase, the modulus of elasticity increased with increasing stress levels, indicating that the internal structure of the mudstone is extremely sensitive to the stress. In the (GUIF) test, the average residual strain increased with the increase in the interval time, and the residual strain during the cycle after the time interval under different grades was lower than the residual strain before the time interval; the results of the (GLIF) test showed the opposite trend. In the (GUIF) test, the average creep strain increased with increasing interval time under the same stress level, and the average creep strain was greater than the average residual strain, and the creep stage had a greater effect on mudstone damage than the fatigue stage. The post-fatigue creep strain was significantly greater than the pre-fatigue creep strain. The research results can be useful in ensuring the stable operation of gas storage in salt caverns. [ABSTRACT FROM AUTHOR]