With the development of salt cavern gas storage construction technology, the construction of large-scale gas storage salt caverns using sediment voids is expected to solve the problem of low effective volume formation rate and poor construction economy of high-impurity salt mines. There are few studies on the long-term operation mechanical behavior of salt cavern gas storage under the influence of sediment accumulation currently. This paper studies the influence of sediment accumulation height, particle gradation, and operating pressure on the stability of salt caverns by constructing a coupling model of sediment particle discontinuous medium and surrounding rock continuous medium. The continuous-discontinuous coupling algorithm is suitable for analyzing the influence of particle accumulation height and particle gradation on the creep shrinkage of salt caverns. The increase of sediment accumulation height slows down the creep shrinkage of the bottom of the salt cavern, strengthens the restraining effect on the surrounding rock of the cavern, and moves the position of the maximum displacement of the surrounding rock to the upper part of the cavern; the sediment particle gradation has little effect on the cavern volume shrinkage rate, and the greater the coarse particle content, the smaller the cavern volume shrinkage rate; the greater the operating pressure, the more conducive to maintaining the stability of the cavern, slowing down the upward movement of the sediment body and increasing the gas storage space in the upper part of the cavern. This research results can provide a reference for evaluating the long-term operation stability of sediment-type high-impurity salt cavern gas storage.