Advertisement

General axisymmetric active earth pressure obtained by the characteristics method based on circumferential geometric condition

  • GuoJun Xiong
  • JinJian Chen
  • MingGuang LiEmail author
  • YaoLiang Li
Article
  • 2 Downloads

Abstract

Existing solutions for axisymmetric active earth pressure are based on certain hypotheses of the circumferential stress, lacking of strict basis. This article presents a technique for deriving the actual circumferential stress according to the circumferential geometric condition, the Drucker-Prager criterion and incremental theory. Based on the actual circumferential stress, a new characteristics method for determining the axisymmetric active earth pressure in plastic flow is developed in this article. In this new method, the inclined angle of boundaries, interface friction of contact interface, dilatation effect and flow velocity of soil are considered at the same time. The validity of the new method is confirmed using several sets of experimental data from the literature. The pressure coefficients are investigated individually in detail, and some different conclusions are found. Finally, a practical formula for calculating axisymmetric active earth pressure is presented based on the linear superposition principle, and related tables of coefficients are also provided for engineering application.

Keywords

axisymmetric active earth pressure characteristics method practical calculation formula earth pressure coefficients dilatation effect the Drucker-Prager yield criterion 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

This work was supported by the National Natural Science Foundation of China (Grant No. 51678360), the Shanghai Science and Technology Commission Project (Grant No. 19QC1400800), and the National Basic Research Program of China (Grant No. 2014CB046302).

References

  1. 1.
    Qu J T Zhou J. 3-Dimensional numerical analysis in a very deep circle pit. J Kunming Univ Sci Tech (Sci Tech), 2004, 29: 96–99Google Scholar
  2. 2.
    Kumagai T, Ariizumi K, Kashiwagi A. Behaavior large-scale cylindrical earth retaining structure. Stions, 2005, 39: 13–26Google Scholar
  3. 3.
    Zhu S Q. Calculation of ground pressure on shaft due to deep overburden. J China Univ Mining Tech, 1981, 1: 6Google Scholar
  4. 4.
    Zhang M J. Earth pressure on shaft sunk in thick overburden. J China Univ Mining Tech, 1983, 2: 7Google Scholar
  5. 5.
    Ma Y M. Theory and practice of ground pressure on shaft due to thick overburden. J China Univ Mining Tech, 1979, 1: 3Google Scholar
  6. 6.
    Haar A, Kármán T V. Zur Theorie der Spannungszustände in plastischen und sandartigen Medien. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse, 1909, 1909: 204–218zbMATHGoogle Scholar
  7. 7.
    Berezantzev V G. Earth pressure on the cylindrical retaining wall. In: Proceedings of the International Society of Soil Mechanics and foundation Engineering (ISSMFE) Conference on Earth Pressure Problems. London: Butterworths, 1958. 21–27Google Scholar
  8. 8.
    Cox A D, Eason G, Hopkins H G. Axially symmetric plastic deformations in soils. Philos Trans R Soc A-Math Phys Eng Sci, 1961, 254: 1–45MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cox A D. Axially-symmetric plastic deformation in soils-II. Indentation of ponderable soils. Int J Mech Sci, 1962, 4: 371–380CrossRefGoogle Scholar
  10. 10.
    Jenike A W, Yen B C. Slope Stability in Axial Symmetry. In: Proceedings of the 5th Symposium on Rock Mechanics. University of Minnesota, New York, 1962. 689–711Google Scholar
  11. 11.
    Hill J M, Cox G M. Rat-hole stress profiles for shear-index granular materials. Acta Mech, 2002, 155: 157–172CrossRefGoogle Scholar
  12. 12.
    Cox G M, Hill J M. Some exact velocity profiles for granular flow in converging hoppers. Zeitschrift für angewandte Mathematik und Physik (ZAMP), 2005, 56: 92–106MathSciNetCrossRefGoogle Scholar
  13. 13.
    Houlsby G T, Wroth C P. Direct solution of plasticity problems in soils by the method of characteristics. NASA STI/Recon Technical Report. 1982Google Scholar
  14. 14.
    Drescher A. Limit plasticity approach to piping in bins. J Appl Mech, 1983, 50: 549–553CrossRefGoogle Scholar
  15. 15.
    Drescher A. Kinematics of axisymmetric vertical slopes at collapse. Int J Numer Anal Methods Geomech, 1986, 10: 431–441CrossRefGoogle Scholar
  16. 16.
    Cheng Y M, Hu Y Y. Active earth pressure on circular shaft lining obtained by simplified slip line solution with general tangential stress coefficient. Chin J Geotech Eng, 2005, 27: 110–115Google Scholar
  17. 17.
    Prater E G. An examination of some theories of earth pressure on shaft linings. Can Geotech J, 1977, 14: 91–106CrossRefGoogle Scholar
  18. 18.
    Cheng Y M, Hu Y Y, Wei W B. General axisymmetric active earth pressure by method of characteristics-Theory and numerical formulation. Int J Geomech, 2007, 7: 1–15CrossRefGoogle Scholar
  19. 19.
    Cheng Y M, Au S K, Hu Y Y, et al. Active pressure for circular cut with berezantzev’s and prater’s theories, numerical modeling and field measurements. Soils Found, 2008, 48: 621–631CrossRefGoogle Scholar
  20. 20.
    Liu F Q, Wang J H. A generalized slip line solution to the active earth pressure on circular retaining walls. Comput Geotech, 2008, 35: 155–164CrossRefGoogle Scholar
  21. 21.
    Liu F Q, Wang J H, Zhang L L. Discussion of “General axisymmetric active earth pressure by method of characteristics-Theory and numerical formulation” by Y. M. Cheng, Y. Y. Hu, and W. B. Wei. Int J Geomech, 2008, 8: 325–326CrossRefGoogle Scholar
  22. 22.
    Liu F Q, Wang J H, Zhang L L. Axi-symmetric active earth pressure obtained by the slip line method with a general tangential stress coefficient. Comput Geotech, 2009, 36: 352–358CrossRefGoogle Scholar
  23. 23.
    Liu F Q. Lateral earth pressures acting on circular retaining walls. Int J Geomech, 2014, 14: 04014002CrossRefGoogle Scholar
  24. 24.
    Chen J J, Li M G, Wang J H. Active earth pressure against rigid retaining walls subjected to confined cohesionless soil. Int J Geomech, 2017, 17: 06016041CrossRefGoogle Scholar
  25. 25.
    Li M G, Chen J J, Wang J H. Arching effect on lateral pressure of confined granular material: numerical and theoretical analysis. Granular Matter, 2017, 19: 20CrossRefGoogle Scholar
  26. 26.
    Yu M H, Li J H, Zhang Y Q. Unified characteristics line theory of spacial axisymmetric plastic problem. Sci China Series E: Tech Sci, 2001, 44: 207–215CrossRefGoogle Scholar
  27. 27.
    Hu X R. Calculation method of pressures acting on shaft wall based on twin shear unified spatially axisymmetric characteristics line theory. Rock Soil Mech, 2007, 28: 2083–2086Google Scholar
  28. 28.
    Hill R. The Mathematical Theory of Plasticity. Oxford: Oxford University Press, 1950zbMATHGoogle Scholar
  29. 29.
    Chen W F. Limit Analysis and Soil Plasticity. New York: Elsevier, 1975zbMATHGoogle Scholar
  30. 30.
    Xiong G J, Wang J H. A rigorous characteristic line theory for axisymmetric problems and its application in circular excavations. Acta Geotech, 2018, 35: 1–15Google Scholar
  31. 31.
    Xiong G J, Wang J H, Chen J J. Theory and practical calculation method for axisymmetric active earth pressure based on the characteristics method considering the compatibility condition. Appl Math Model, 2019, 68: 563–582MathSciNetCrossRefGoogle Scholar
  32. 32.
    Tobar T, Meguid M A. Experimental study of the earth pressure distribution on cylindrical shafts. J Geotech Geoenviron Eng, 2011, 137: 1121–1125CrossRefGoogle Scholar
  33. 33.
    Terzaghi K. Theoretical Soil Mechanics. New York: Wiley, 1943CrossRefGoogle Scholar
  34. 34.
    Kerisel J, Absi E. Active and Passive Earth Pressure Tables. Rotterdam: Balkema, 1973Google Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • GuoJun Xiong
    • 1
  • JinJian Chen
    • 1
  • MingGuang Li
    • 1
    Email author
  • YaoLiang Li
    • 2
  1. 1.State Key Laboratory of Ocean Engineering, Department of Civil EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Shanghai Foundation Engineering Group Co., LtdShanghaiChina

Personalised recommendations