The rheological properties of rock are the main factors affecting the long-term stability of geotechnical engineering. However, the nonlinear rheological behavior in accelerating creep stage is still difficult to explain. In this paper, salt rock was used for triaxial compression experiments through incremental loading with different confining pressure. Determining the instantaneous elastic strain components, visco-elastic and visco-plastic strain components from the total strain by analyzing the experimental data. A damage coefficient was introduced to describe the non-linear strain at the accelerating creep stage considering the influence of damage evolution. Therefore, a new variable-order fractional derivative model with damage is proposed, in which instantaneous elastic response is described by a corresponding Hooke body, the variable-order fractional components are used to present visco-elastic response, and visco-plastic response is described a parallel combination of variable-order fractional components and plastic slide bodies. A sensitivity study for the parameters of accelerating creep is carried out, showing the coefficient of damage plays a more important role than the fractional order in the non-linear rheological behavior of salt rock. Compared with seven different rheological models, the results fitted by the new model proposed in the paper are in better agreement with the experimental data than the results fitted by others. It is shown that the new model gives a precise description of the full stages of creep, especially the accelerating creep stage. This provides a new way to research the nonlinear rheological behavior of salt rocks.

岩石的流变特性是影响岩土工程长期稳定性的主要因素。然而，在加速蠕变阶段的非线性流变行为仍然难以解释。在本文中，盐岩通过在不同围压下的增量载荷被用于三轴压缩实验。通过分析实验数据，从总应变中确定瞬时弹性应变分量，粘弹性和粘塑性应变分量。考虑损伤演化的影响，引入损伤系数来描述加速蠕变阶段的非线性应变。因此，提出了一种新的具有损伤的变分分数阶导数模型，其中瞬时弹性响应由相应的胡克体描述，可变分数组分用于表示粘弹性响应，而粘塑性响应是可变分数组分与塑料滑动体的平行组合。对加速蠕变参数进行了敏感性研究，结果表明，在盐岩非线性流变行为中，损伤系数比分数阶更重要。与七个不同的流变模型相比，本文提出的新模型所拟合的结果与实验数据相比，与其他模型所拟合的结果更加吻合。结果表明，新模型可以精确描述蠕变的整个阶段，尤其是加速蠕变阶段。这为研究盐岩的非线性流变行为提供了一种新途径。