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An improved Maxwell creep model for rock based on variable-order fractional derivatives

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Abstract

For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed. The order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. Through the segmentation treatment, according to different creep stages of the experimental results, it is found that the improved creep model based on variable-order fractional derivatives agrees well with the experimental data. In addition, the fact is verified that variable order of fractional derivatives can be regarded as a step function, which is reasonable and reliable. In addition, through further piecewise fitting, the parameters in the model are determined on the basis of existing experimental results. All estimated results show that the theoretical model proposed in the paper properly depicts the creep properties, providing an excellent agreement with the experimental data.

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Acknowledgments

The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 51120145001, 51374148), the National Basic Research Projects of China (Grant No. 2011CB201201), and the Fundamental Research Funds for the Central Universities (Grant No. 2014SCU04A07). The authors wish to offer their gratitude and regards to the colleagues who contributed to this work.

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Authors and Affiliations

  1. Key Laboratory of Energy Engineering Safety and Mechanics on Disaster (Sichuan University), Ministry of Education, Chengdu, 610065, China

    Fei Wu, Jian Feng Liu & Jun Wang

  2. School of Architecture and Environment, Sichuan University, Chengdu, 610065, China

    Fei Wu & Jun Wang

  3. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

    Jian Feng Liu

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  1. Fei Wu
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  3. Jun Wang
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Correspondence to Jian Feng Liu.

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Wu, F., Liu, J.F. & Wang, J. An improved Maxwell creep model for rock based on variable-order fractional derivatives. Environ Earth Sci 73, 6965–6971 (2015). https://doi.org/10.1007/s12665-015-4137-9

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  • DOI: https://doi.org/10.1007/s12665-015-4137-9

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