Abstract Salt rock is widely used as an excellent material for energy storage owing to its low permeability, high safety, and stable mechanical properties. In this study, salt rock was subjected to a gradual loading creep test through the conventional uniaxial compression test. The loading time of each stage was approximately 14 days, and the total creep time exceeded five months. The steady-state creep rate of salt rock under different stresses and the corresponding creep strain law were positively correlated with the increase in stress and time. In addition, the long-term strength of the salt rock, determined via the isochronous stress–strain curve inflection point method, was 12 MPa. Furthermore, the viscoelastic–plastic damage-creep model of salt rock was established based on the theory of fractional derivatives. This proposed model was compared with the Nishihara model, and a sensitivity analysis of the parameters was performed based on the results of the nonlinear fitting of the fractional derivative. The rationality of the model was verified based on the results, especially for the accelerated creep phase. Moreover, the constitutive relationship of the model was straightforward and easy to apply. The proposed model provides a theoretical basis for future creep laws based on experimental data. The results reflected the creep law of salt rock to a certain extent and are expected to serve as a reference to studies on the long-term stability of deep salt rock.

中文翻译：

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基于分数阶导数理论的盐岩粘弹塑性损伤蠕变模型

摘要 盐岩具有渗透率低、安全性高、力学性能稳定等优点，被广泛用作优良的储能材料。在这项研究中，盐岩通过传统的单轴压缩试验进行了逐渐加载蠕变试验。每个阶段的加载时间约为 14 天，总蠕变时间超过 5 个月。盐岩在不同应力下的稳态蠕变速率和相应的蠕变应变规律与应力和时间的增加呈正相关。此外，通过等时应力-应变曲线拐点法确定的盐岩的长期强度为 12 MPa。此外，基于分数阶导数理论建立了盐岩粘弹塑性损伤蠕变模型。将该模型与 Nishihara 模型进行比较，并根据分数阶导数的非线性拟合结果对参数进行灵敏度分析。根据结果​​验证了模型的合理性，特别是对于加速蠕变阶段。此外，该模型的本构关系简单明了，易于应用。所提出的模型为基于实验数据的未来蠕变规律提供了理论基础。研究结果在一定程度上反映了盐岩蠕变规律，有望为深部盐岩长期稳定性研究提供参考。根据结果​​验证了模型的合理性，特别是对于加速蠕变阶段。此外，该模型的本构关系简单明了，易于应用。所提出的模型为基于实验数据的未来蠕变规律提供了理论基础。研究结果在一定程度上反映了盐岩蠕变规律，有望为深部盐岩长期稳定性研究提供参考。根据结果​​验证了模型的合理性，特别是对于加速蠕变阶段。此外，该模型的本构关系简单明了，易于应用。所提出的模型为基于实验数据的未来蠕变规律提供了理论基础。研究结果在一定程度上反映了盐岩蠕变规律，有望为深部盐岩长期稳定性研究提供参考。