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The application of the finite element method to solving Biot's consolidation equation

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Abstract

Biot's theory of consolidation of saturated soil, regards the consolidation process as a coupling problem between stress of elastic body and flow of fluid existing in pores[1]. It can more precisely reflect the mechanism of consolidation than Terzhigi's theory[2]. In this article, we obtain the general Biot's finite element equations of consolidation with classical variational principles. The equations have clear physical meaning and have been applied to analysing the consolidation of Bajiazui earth dam. The computational results are in accord with engineering practice.

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References

  1. Biot, M. A,General theory of three-dimensional consolidation, J. Appl. Phys., Vol. 12, (1941).

  2. Terzhagi, K. and R. B. Peck,Soil mechanics in engineering practice, Wiley, (1948).

  3. Sandhu, R. S. and E. L. wilson,Finite element analysis of seepage in elastic media, J. Engg. Mech. Div. ASCE, Vol. 95, (1969).

  4. Hwang, C.T., N.R. Morgenstern, and D.W. Murray,On solutions of plane strain consolidation problems by finite element methods, Canadian Geotechnical Journal, 8, (1971).

  5. Yin, Z.Z., Xu, H.J. and Zhu, Z.M.,Finite element method on plane consolidation problem, J. of East China College of Hydraulic Engineering, 1978, No. 1.

  6. Washizu, K.,An introduction to variational principle of elasticity, Tokyo, (1972). (in Japanese)

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Authors and Affiliations

  1. Shanghai Institute of Computing Technique, Shanghai

    Zheng Jia-dong & Hu Hui-zhi

  2. Institute of Hydraulic Research, Yellow River Water Conservancy Commission, Zhengzhou

    Xu Hong-jiang & Zhu Ze-min

  3. Eastern China College of Hydraulic Engineering, Nanjing

    Yin Zong-ze

Authors
  1. Zheng Jia-dong
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  2. Hu Hui-zhi
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  3. Xu Hong-jiang
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  4. Zhu Ze-min
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  5. Yin Zong-ze
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Communicated by Chien Wei-zang.

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Jia-dong, Z., Hui-zhi, H., Hong-jiang, X. et al. The application of the finite element method to solving Biot's consolidation equation. Appl Math Mech 3, 857–871 (1982). https://doi.org/10.1007/BF01895341

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  • DOI: https://doi.org/10.1007/BF01895341

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