In this study, based on the first application of Caputo fractional derivative with respect to the Mittag–Leffler and power functions, two improved time-varying viscoelastic constitutive models are presented. And the Norton power law and damage factor are applied to build a new damage function. Then the new nonlinear damage creep models 1 and 2 with time-varying viscoelasticity and time-dependent damage are proposed to describe the creep mechanical behavior, which are based on the two improved time-varying viscoelastic constitutive models. Then a series of creep experiments are conducted on the sandstone to obtain the creep experimental data. And based on the creep experimental data of sandstone and creep data of salt rock and mudstone obtained from other papers, the applicability of proposed creep models 1 and 2 is verified. The proposed creep model 2 with power function has a higher accuracy than model 1 with Mittag–Leffler function in describing creep mechanical behavior. And the predicted creep from model 2 is in good agreement with experimental data. Finally, it is shown that compared with creep model 1, model 2 needs fewer parameters to depict the creep mechanical behavior.

在这项研究中，基于Caputo分数导数在Mittag-Leffler和幂函数方面的首次应用，提出了两个改进的时变粘弹性本构模型。并应用诺顿幂定律和损伤因子来建立新的损伤函数。然后，基于两个改进的时变粘弹性本构模型，提出了具有时变粘弹性和时变损伤的新型非线性损伤蠕变模型1和2来描述蠕变力学行为。然后对砂岩进行了一系列蠕变实验，获得了蠕变实验数据。并根据其他文献获得的砂岩蠕变实验数据和盐岩，泥岩蠕变数据，验证了所提出的蠕变模型1和2的适用性。提出的具有幂函数的蠕变模型2在描述蠕变力学行为方面比具有Mittag-Leffler函数的模型1具有更高的精度。模型2的预测蠕变与实验数据非常吻合。最后，表明与蠕变模型1相比，模型2需要较少的参数来描述蠕变力学行为。