A creep model of rock based on variable order fractional derivative
SU Teng1，ZHOU Hongwei2，3，ZHAO Jiawei1，CHE Jun1，SUN Xiaotong1，WANG Lei1
(1. School of Mechanics and Civil Engineering，China University of Mining and Technology(Beijing)，Beijing 100083，China；
2. School of Energy and Mining Engineering，China University of Mining and Technology(Beijing)，Beijing 100083，China；
3. State Key Laboratory of Coal Resources and Safe Mining，China University of Mining and Technology(Beijing)，
Beijing 100083，China)
Abstract：The creep model is a main form to describe the rheological behavior of rocks. An important focus of research on rock creep is to develop a model with fewer parameters and better simulation performance. From the aspect of the physical meaning of fractional creep element，in this study，the creep process of materials was divided into elastic，viscoelastic and viscoplastic stages，and the variable-order fractional derivative was introduced to describe these three segments. In the case of the loading stress exceeding the yield stress，nevertheless，the creep damage accumulates and the accelerating creep occurs due to that microscopic cracks initiate，expand and evolve. Therefore，a damage coefficient was introduced to describe the non-linear strain at the accelerating creep stage considering the influence of damage evolution. A variable order non-linear visco-elastic-plastic creep model was proposed based on Scott-Blair fractional element and time-dependent fractional element and further generalized to three-dimension situations. A series of three-dimensional creep experiments of deep coal from Pingdingshan were analyzed by segment treatment，showing that the creep model based on the variable order fractional derivative is in good agreement with the experimental data. It is also proved that it is reasonable and reliable to regard the variable order of fractional derivative as a step function. In addition，the parameters of the model were determined on the basis of fitting the existing experimental results. The results show that the theoretical model proposed in this paper can well describe the creep properties of the material.
苏 腾1，周宏伟2，3，赵家巍1，车 俊1，孙晓彤1，王 雷1. 基于变阶分数阶导数的岩石蠕变模型[J]. 岩石力学与工程学报, 2019, 38(7): 1355-1363.
SU Teng1，ZHOU Hongwei2，3，ZHAO Jiawei1，CHE Jun1，SUN Xiaotong1，WANG Lei1. A creep model of rock based on variable order fractional derivative. , 2019, 38(7): 1355-1363.
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2019, Vol. 38 
