Geomechanics and Engineering

  • 제10권2호
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  • Pages.189-205
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  • 2016
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  • 2005-307X(pISSN)
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  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
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DOI QR Code

Shear stresses below the rectangular foundations subjected to biaxial bending

  • 투고 : 2015.06.23
  • 심사 : 2015.12.10
  • 발행 : 2016.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

Soils are subjected to additional stresses due to the loads transferred by the foundations of the buildings. The distribution of stress in soil has great importance in geotechnical engineering projects such as stress, settlement and liquefaction analyses. The purpose of this study is to examine the shear stresses on horizontal plane below the rectangular foundations subjected to biaxial bending on an elastic soil. In this study, closed-form analytical solutions for shear stresses in x and y directions were obtained from Boussinesq's stress equations. The expressions of analytical solutions were simplified by defining the shear stress influence values ($I_1$, $I_2$, $I_3$), and solution charts were presented for obtaining these values. For some special loading conditions, the expressions for shear stresses in the soil below the corners of a rectangular foundation were also given. In addition, a computer program was developed to calculate the shear stress increment at any point below the rectangular foundations. A numerical example for illustrating the use of the presented solution charts was given and, finally, shear stress isobars were obtained for the same example by a developed computer program. The shear stress expressions obtained in this work can be used to determine monotonic and cyclic behavior of soils below rectangular foundations subjected to biaxial bending.

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참고문헌

  1. Algin, H.M. (2000), "Stresses from linearly distributed pressures over rectangular areas", Int. J. Numer. Anal. Meth. Geomech., 24(8), 681-692. https://doi.org/10.1002/1096-9853(200007)24:8<681::AID-NAG89>3.0.CO;2-X
  2. Algin, H.M. and Algin, Z. (2009), "Elastic settlements under linear surface pressures on rectangular areas", Int. J. Numer. Anal. Meth. Geomech., 33(8), 1087-1108. https://doi.org/10.1002/nag.757
  3. Arangelovski, G. and Towhata, I. (2004), "Accumulated deformation of sand with initial shear stress and effective stress state lying near failure conditions", Soils Found., 44(6), 1-16. https://doi.org/10.3208/sandf.44.6_1
  4. Boulanger, R.W. (2003), "Relating K${\alpha}$ to relative state parameter index", J. Geotech. Geoenviron. Eng., 129(8), 770-773. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:8(770)
  5. Boussinesq, J. (1885), Application des potentials a l'etude de l'equilibre et du mouvement des solides elastiques, Gauthier-Villars, Paris, France.
  6. Capper, P.L. and Cassie, W.F. (1969), The Mechanics of Engineering Soils, (Fifth Edition), Ceviri: (Kumbasar, V., Kip, F.), "Insaat Muhendisliginde Zemin Mekanigi", Caglayan Kitabevi.
  7. Chiaro, G., Junichi, K. and Sato, T. (2012), "Effects of initial static shear on liquefaction and large deformation properties of loose saturated Toyoura sand in undrained cyclic torsional shear tests", Soils Found., 52(3), 498-510. https://doi.org/10.1016/j.sandf.2012.05.008
  8. Coduto, D.P. (1999), Geotechnical Engineering: Principles and Practices, Prentice Hall, NJ, USA.
  9. Dagdeviren, U. and Gunduz, Z. (2011), "Calculation of shear stresses under uniformly loaded rectangular foundation", Proceedings of the 6th International Advanced Technologies Symposium, Elazig, Turkey, May, pp. 129-134. [In Turkish]
  10. Dagdeviren, U., Gunduz, Z. and Tuncan, M. (2012), "The behavior of clayey soils subjected to initial static shear stress under the monotonic loads", Proceedings of the 14th National Congress on Soil Mechanics and Foundation Engineering, Isparta, Turkey, October, pp. 275-284. [In Turkish]
  11. Das, B.M. (2010), Principles of Geotechnical Engineering, (7th Edition), Cengage Learning.
  12. Fadum, R.E. (1948), "Influence values for estimating stresses in elastic foundations", Proceedings of the 2nd International Conference on Soil Mechanics and Foundation Engineering, Rotterdam, The Netherlands, June, (Volume 3), pp. 77-84.
  13. Gray, H. (1943), "Stresses and displacements from loads over rectangular area", Civil Engineering, ASCE, 13(5), 227-229.
  14. Hyodo, M., Murata, H., Yasufuku, N. and Fujii, T. (1991), "Undrained cyclic shear strength and residual shear strain of saturated sand by cyclic triaxial tests", Soils Found., 31(3), 60-76. https://doi.org/10.3208/sandf1972.31.3_60
  15. Hyodo, M., Yamamoto, Y. and Sugiyama, M. (1994), "Undrained cyclic shear behaviour of normally consolidated clay subjected to initial static shear stress", Soils Found., 34(4), 1-11. https://doi.org/10.3208/sandf1972.34.4_1
  16. Ishibashi, I., Kawamura, M. and Bhatia, S.K. (1985), "Effect of initial shear on cyclic behavior of sand", J. Geotech. Eng., 111(12), 1395-1410. https://doi.org/10.1061/(ASCE)0733-9410(1985)111:12(1395)
  17. Jarquio, R. and Jarquio, V. (1984), "Vertical stress formulas for triangular loading", J. Geotech. Eng., 110(1), 73-78. https://doi.org/10.1061/(ASCE)0733-9410(1984)110:1(73)
  18. Keyhani, R. and Haeri, S.M. (2013), "Evaluation of the effect of anisotropic consolidation and principle stress rotation on undrained behavior of silty sands", Scientia Iranica A, 20(6), 1637-1653.
  19. Newmark, N.M. (1935), "Simplified computation of vertical pressures in elastic foundations", Circular No. 24, University of Illinois Engineering Experiment Station, IL, USA.
  20. Poulos, H.G. and Davis, E.H. (1974), Elastic Solutions for Soil and Rock Mechanics, John Wiley and Sons, Inc.
  21. Rahhal, M.E. and Lefebvre, G. (2000), "Understanding the effect of a static driving shear stress on the liquefaction resistance of medium dense granular soils", Soil Dyn. Earthq. Eng., 20(5-8), 397-404. https://doi.org/10.1016/S0267-7261(00)00089-0
  22. Seed, H.B. (1983), "Earthquake resistant design of earth dams", Proceedings of Symposium on Seismic Design of Embankments and Caverns, ASCE, pp. 41-64.
  23. Sivathayalan, S. and Ha, D. (2011), "Effect of static shear stress on the cyclic resistance of sands in simple shear loading", Can. Geotech. J., 48(10), 1471-1484. https://doi.org/10.1139/t11-056
  24. Song, B.W. (2003), "The influence of initial static shear stress on post-cyclic degradation of non-plastic silt", Lowland Technol. Int., 5(1), 14-24.
  25. Stoll, U.W. (1960), "Computer solution of pressure distribution problem", J. Soil Mech. Found. Div., 86(6), 1-9.
  26. Uchida, K. and Hasegawa, T. (1986), "Strength-deformation characteristics of a soil subjected to initial shear stress", Soils Found., 26(1), 11-24. https://doi.org/10.3208/sandf1972.26.11
  27. Vaid, Y.P. and Chern, J.C. (1983), "Effect of static shear on resistance to liquefaction", Soils Found., 23(1), 47-60. https://doi.org/10.3208/sandf1972.23.47
  28. Vaid Y.P., Stedman, J.D. and Sivathayalan, S. (2001), "Confining stress and static shear effects in cyclic liquefaction", Can. Geotech. J., 38(3), 580-591. https://doi.org/10.1139/t00-120
  29. Vitone, D.M.A. and Valsangkar, A.J. (1986), "Stresses from loads over rectangular areas", J. Geotech. Eng., 112(10), 961-964. https://doi.org/10.1061/(ASCE)0733-9410(1986)112:10(961)
  30. Wang, C.D. and Liao, J.J. (2002), "Elastic solutions for stresses in a transversely isotropic half-space subjected to three-dimensional buried parabolic rectangular loads", Int. J. Numer. Anal. Method. Geomech., 26(14), 1449-1476. https://doi.org/10.1002/nag.253
  31. Yang, J. and Sze, H.Y. (2011), "Cyclic behavior and resistance of saturated sand under non-symmetrical loading conditions", Geotechnique, 61(1), 59-73. https://doi.org/10.1680/geot.9.P.019
  32. Yang, J., Sze, H.Y., Heung, M.K. and Wang, G.H. (2013), "On correction factors for liquefaction analysis of embankments and slopes", Geotechnical Special Publication, 231, 850-853.