An accurate characterization of rocks for the modelling of creep is an essential step toward ensuring the safety with respect to reliability of underground rock engineering. In this work, a novel variable fractional order rheological model is established to describe the full-stage creep behavior of rocks. With simpler form and fewer parameters, the proposed model is verified to have the ability for the description of trimodal creep behavior of rocks. The evolution of mechanical properties during creep is quantitatively described by the variable fractional order including the creep hardening, softening and the transition part between them. Moreover, the physical significance of fractional order is further explored by the commonly accepted competition mechanism of creep hardening and softening for brittle creep, which indicates that the mechanical property of rocks during creep is harder with lower water contents but softens faster with larger applied stresses. Furthermore, the linear form of the variable order function is determined by applying the new variable order fractional operator. It is shown that the slope of order function confirms the creep strain rate and the intercept of order function primarily affects the critical time for entering the nonlinear creep phase. Finally, the rising tendency of fractional order reveals that the accelerating creep is a continuous softening process of mechanical properties since the larger values of fractional order exhibits the property of rocks is more viscous.

准确地表征岩石以进行蠕变建模是确保地下岩石工程安全性方面必不可少的一步。在这项工作中，建立了一个新颖的可变分数阶流变模型来描述岩石的全阶段蠕变行为。用简单的形式和较少的参数，验证了所提出的模型具有描述岩石三峰蠕变行为的能力。蠕变过程中机械性能的变化通过可变分数阶来定量描述，包括蠕变硬化，软化和它们之间的过渡部分。此外，对于脆性蠕变，蠕变硬化和软化的普遍公认的竞争机制进一步探索了分数阶的物理意义。这表明岩石在蠕变过程中的机械性能在较低的含水量下较硬，而在较大的施加应力下会较软化。此外，通过应用新的可变阶分数运算符来确定可变阶函数的线性形式。结果表明，阶次函数的斜率确定了蠕变应变率，阶次函数的截距主要影响进入非线性蠕变阶段的临界时间。最后，分数阶的上升趋势表明，加速蠕变是机械性能的连续软化过程，因为分数阶的值越大，表示岩石的性质越粘稠。变量阶函数的线性形式是通过应用新的变量阶分数运算符确定的。结果表明，阶次函数的斜率确定了蠕变应变率，阶次函数的截距主要影响进入非线性蠕变阶段的临界时间。最后，分数阶的上升趋势表明，加速蠕变是机械性能的连续软化过程，因为分数阶的值越大，表示岩石的性质越粘稠。变量阶函数的线性形式是通过应用新的变量阶分数运算符确定的。结果表明，阶次函数的斜率确定了蠕变应变率，阶次函数的截距主要影响进入非线性蠕变阶段的临界时间。最后，分数阶的上升趋势表明，加速蠕变是机械性能的连续软化过程，因为分数阶的值越大，表示岩石的性质越粘稠。