A thorough understanding of the evolution of strain and damage accumulation is a prerequisite for effective control of the surrounding rock to ensure good stability and better maintenance of underground structures. In this work, we have proposed a new way of adjusting the fractional order to obtain a new variable fractional order rheological model to describe the evolution of mechanical properties and to model the stress-strain response of the rock during plastic flow. It is proved that the function law of our variable order fractional model is defined by five parameters , , , , . An analysis of the different parameters of the fractional model confirms that the mechanical behavior of the rock hardens and softens faster when the confining pressure is high. Moreover, the definition of our fractional model by a continuous function of the plastic strain allows us to explore in more detail the hardening/softening duality of the mechanical behavior of the rock. This fractional model not only allows us to model the stress-strain relationship of the rock more accurately and with a relatively short calculation time, it also allows us to model the stress-strain relationship of the rock more accurately and with a relatively short calculation time, but also to accurately capture the contraction-dilation volume transition of quasi-fragile rocks. We believe that the results of this work will help in the decision making process for the construction of underground structures.

中文翻译：

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使用分数阶微积分理论模拟塑性流动过程中岩石的力学行为

透彻了解应变演化和损伤累积是有效控制围岩以确保地下结构良好稳定性和更好维护的先决条件。在这项工作中，我们提出了一种调整分数阶的新方法，以获得新的可变分数阶流变模型来描述力学性能的演变并模拟岩石在塑性流动过程中的应力应变响应。证明了我们的变阶分数模型的函数律由五个参数 , , , , 定义。对分数模型不同参数的分析证实，当围压较高时，岩石的力学行为硬化和软化得更快。此外，通过塑性应变的连续函数定义的分数模型使我们能够更详细地探索岩石机械行为的硬化/软化二元性。这种分数式模型不仅使我们能够以相对较短的计算时间更准确地模拟岩石的应力应变关系，还使我们能够以相对较短的计算时间更准确地模拟岩石的应力应变关系，还能准确捕捉准脆性岩石的收缩-膨胀体积转变。我们相信这项工作的结果将有助于地下结构建设的决策过程。