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A fractional derivative approach to full creep regions in salt rock

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Abstract

Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt rock. Furthermore, a sensitivity study is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient exponent on creep strain of salt rock. It is indicated that the fractional derivative creep model proposed in the paper provides a precise description of full creep regions in salt rock, i.e., the transient creep region (the primary region), the steady-state creep region (the secondary region) and the accelerated creep region (the tertiary region).

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Acknowledgements

The present work is supported by the National Natural Science Foundation of China (11172318, 51120145001), the 973 Program (2009CB724602) and the Program of International S & T Cooperation, MOST (2010DFA64560). The financial supports are gratefully acknowledged. Special thanks are due to Ms. H.Y. Bian for her help in improving the manuscript.

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Authors and Affiliations

  1. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, 100083, China

    H. W. Zhou, C. P. Wang, Z. Q. Duan & J. Y. Ding

  2. Department of Wind Energy, Technical University of Denmark, Risø Campus, 4000, Roskilde, Denmark

    L. Mishnaevsky Jr.

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  1. H. W. Zhou
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  2. C. P. Wang
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  3. L. Mishnaevsky Jr.
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  4. Z. Q. Duan
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  5. J. Y. Ding
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Correspondence to H. W. Zhou.

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Zhou, H.W., Wang, C.P., Mishnaevsky, L. et al. A fractional derivative approach to full creep regions in salt rock. Mech Time-Depend Mater 17, 413–425 (2013). https://doi.org/10.1007/s11043-012-9193-x

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  • DOI: https://doi.org/10.1007/s11043-012-9193-x

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