基于等效黏弹性的变阶分数阶岩石损伤蠕变模型

基于分数阶Zener模型与时变黏性Zener模型之间的等效黏弹性，突出弛豫时间在岩石流变黏弹性演变过程中的重要性。当弛豫时间趋近于无穷大，蠕变过程中的黏性演变等同于松弛过程中的黏性演变，并且建立了与弛豫时间相关的损伤因子，解释了损伤因子在岩石流变变形过程的物理意义。利用弛豫时间建立分数阶变阶函数，依此构造变阶分数阶损伤蠕变模型，并且将模型推广到三向应力状态，给出三向应力状态下变阶分数阶损伤蠕变模型。最后基于砂岩的三轴蠕变试验数据，验证了三轴状态下变阶分数阶损伤蠕变模型的可应用性和合理性，试验数据与模型拟合曲线吻合度较高，可以较好地描述蠕变全过程力学行为。模型拟合参数的有效性得到分析和验证，增加了模型在其他复杂应力环境下的可应用性。

Variable-order fractional damage creep model based on equivalent viscoelasticity for rock

Based on the equivalent viscoelasticity between the fractional Zener model and the time-varying viscosity Zener model, the significance of the relaxation time in the evolution of rock rheological viscoelasticity is highlighted. As the relaxation time approaches infinity, the evolution of viscosity during creep is equivalent to that during relaxation. Accordingly, the damage factor related to relaxation time is established to explain the physical significance of damage factor in rock rheological deformation. In specific, the function of variable order is constructed by using relaxation time and the variable-order fractional damage creep model is introduced. Furthermore, the variable-order fractional damage creep model is extended to the triaxial status. Based on the triaxial sandstone creep experimental data, the applicability and rationality of the variable-order fractional damage creep model in the triaxial state are verified. The results show that the developed variable-order fractional damage creep model and the creep experimental data are in good agreement, indicating that the damage creep model can be used to describe the nonlinear mechanical behavior of complete creep process. The effectiveness of the model fitting parameters is analyzed and verified, which encourages the applicability of the introduced model in other complex stress issues.