Accurate description of creep behavior is of great significance to the safety evaluation of high-level radioactive waste disposal in granite. In this study, a fractional derivative constitutive model is proposed to depict the creep process of Beishan granite, based on the conformable derivative. A variable-coefficient Abel dashpot considering the effect of damage evolution on creep properties is introduced to describe the nonlinear dilatancy strain in the accelerating stage. A new model is proposed and further generalized to three-dimensional creep equations by adopting Drucker–Prager criterion, and the analytic solutions are given employing the Laplace transform. The parameters of new creep model are determined based on experimental data and fitting results are compared. The fitting curves present a good agreement with experimental data, indicating that the conformable derivative creep model achieves a good performance in describing all three creep stages. The proposed model is validated by the comparison of different experiments and degradation of fractional derivative model. In addition, a sensitivity analysis is carried out to show the effects of stress level, fractional derivative order, damage exponent, and other parameters.

中文翻译：

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用变系数阿贝尔阻尼器表征北山花岗岩三维蠕变

蠕变行为的准确描述对花岗岩高放废物处置的安全性评价具有重要意义。在该研究中，提出了一个分数阶导数本构模型，基于适形导数来描述北山花岗岩的蠕变过程。引入了考虑损伤演化对蠕变特性影响的变系数阿贝尔阻尼器，以描述加速阶段的非线性剪胀应变。提出了一个新的模型，并采用Drucker-Prager准则将其进一步推广到三维蠕变方程，并使用Laplace变换给出了解析解。根据实验数据确定了新蠕变模型的参数，并比较了拟合结果。拟合曲线与实验数据吻合良好，表明在描述所有三个蠕变阶段时，合格的导数蠕变模型均具有良好的性能。通过比较不同实验和分数阶导数模型的退化来验证所提出的模型。另外，进行了敏感性分析以显示应力水平，分数导数阶数，破坏指数和其他参数的影响。