One-dimensional consolidation with a threshold gradient: a Stefan problem with rate-dependent latent heat

Authors

  • Yang Zhou,

    Corresponding author
    1. School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China
    • State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China
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  • Wan-kui Bu,

    1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China
    2. Department of Mechanical and Electrical Engineering, Heze University, Heze, Shandong, China
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  • Meng-meng Lu

    1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China
    2. School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou, Jiangsu, China
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Correspondence to: Yang Zhou, State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China.

E-mail: tod2006@126.com

SUMMARY

During the process of one-dimensional consolidation with a threshold gradient, the seepage front moves downward gradually, and the problem is indicated as a Stefan problem. The novel feature in this Stefan problem is a latent heat that varies inversely with the rate of the moving boundary. An exact solution for the external load that increases in proportion to the square root of time is constructed using the similarity transformation technique. Computational examples concerning the effect of different parameters on the motion of the seepage front are presented. The exact solution provides a worthwhile benchmark for verifying the accuracy of numerical and approximate methods. Copyright © 2013 John Wiley & Sons, Ltd.

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