Geomechanics and Engineering

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Analysis of circular tank foundation on multi-layered soil subject to combined vertical and lateral loads

  • Hesham F. Elhuni (Department of Civil and Environmental Engineering, Univ. of Waterloo) ;
  • Bipin K. Gupta (Department of Civil Engineering, IIT Kanpur) ;
  • Dipanjan Basu (Department of Civil and Environmental Engineering, Univ. of Waterloo)
  • Received : 2022.06.23
  • Accepted : 2023.01.09
  • Published : 2023.03.25
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Abstract

A circular tank foundation resting on the ground and subjected to axisymmetric horizontal and vertical loads and moments is analyzed using the variational principles of mechanics. The circular foundation is assumed to behave as a Kirchhoff plate with in-plane and transverse displacements. The soil beneath the foundation is assumed to be a multi-layered continuum in which the horizontal and vertical displacements are expressed as products of separable functions. The differential equations of plate and soil displacements are obtained by minimizing the total potential energy of the plate-soil system and are solved using the finite element and finite difference methods following an iterative algorithm. Comparisons with the results of equivalent two-dimensional finite element analysis and other researchers establish the accuracy of the method.

Keywords

References

  1. Ahlvin, R.G. and Ulery, H.H. (1962), "Tabulated values for determining the complete pattern of stresses, strains, and deflections beneath a uniform circular load on a homogeneous half space", Highway Res. Board Bull., 342.
  2. Bell, R.A. and Iwakiri, J. (1980), "Settlement comparison used in tank-failure study", J. Geotech. Eng. Div. - ASCE, 106(2), 153-169. https://doi.org/10.1061/AJGEB6.0000919.
  3. Bowles, L.E. (1996), Foundation analysis and design. McGraw-hill.
  4. Booker, J.R. and Small, J.C. (1983), "The analysis of liquid storage tanks on deep elastic foundations", Int. J. Numer. Anal. Met., 7(2), 187-207. https://doi.org/10.1002/nag.1610070205.
  5. Brown, P.T. (1969), "Numerical analyses of uniformly loaded circular rafts on elastic layers of finite depth", Geotechnique, 19(2), 301-306. https://doi.org/10.1680/geot.1969.19.2.301.
  6. Buczkowski, R. and Torbacki, W. (2001), "Finite element modelling of thick plates on two-parameter elastic foundation", Int. J. Numer. Anal. Met., 25(14), 1409-1427. https://doi.org/10.1002/nag.187.
  7. Chandrasekaran, K. and Kunukkasseril, V.X. (1976), "Forced axisymmetric response of circular plates", J. Sound Vib., 44(3), 407-417. https://doi.org/10.1016/0022-460X(76)90511-3.
  8. D'Orazio, T.B. and Duncan, J.M. (1987), "Differential settlements in steel tanks", J. Geotech. Eng., 113(9), 967-983. https://doi.org/10.1061/(ASCE)0733-9410(1987)113:9(967).
  9. Filonenko-Borodich, M.M. (1945), "A very simple model of an elastic foundation capable of spreading the load", Sb. Tr. Mosk. Elektro. Inst, Inzh. Trans, 53.
  10. Galvis, F.A. and Smith-Pardo, J.P. (2020), "Axial load biaxial moment interaction (PMM) diagrams for shallow foundations: Design aids, experimental verification, and examples", Eng. Struct., 213, 110582. https://doi.org/10.1016/j.engstruct.2020.110582.
  11. Gerrard, C.M. and Harrison, W.J. (1970), Stresses and displacements in a loaded orthorhombic half space.
  12. Ghali, A. (2003), Circular storage tanks and silos, CRC Press.
  13. Girija Vallabhan, C.V. and Das, Y.C. (1991), "Analysis of circular tank foundations", J. Eng. Mech., 117(4), 789-797. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:4(789).
  14. Gunerathne, S., Seo, H., Lawson, W.D. and Jayawickrama, P.W. (2018), "Analysis of edge-to-center settlement ratio for circular storage tank foundation on elastic soil", Comput. Geotech., 102, 136-147. https://doi.org/10.1016/j.compgeo.2018.05.008.
  15. Gunerathne, S., Seo, H., Lawson, W.D. and Jayawickrama, P.W. (2019), "Variational approach for settlement analysis of circular plate on multilayered soil", Appl. Math. Model., 70, 152-170. https://doi.org/10.1016/j.apm.2019.01.009.
  16. Hetenyi, M. (1946), Beams on Elastic Foundation. The University of Michigan Press, Ann Arbor, sect. 56.
  17. Hemsley, J.A. and WINKLER. (1987), "Elastic solutions for axisymmetrically loaded circular raft with free or clamped edges founded on Winkler springs or a half-space", P. I. Civil Eng., 83(1), 61-90. https://doi.org/10.1680/iicep.1987.342.
  18. Jones, G. (1997), Analysis of beams on elastic foundations: using finite difference theory. Thomas Telford.
  19. Komlev, A.A. and Makeev, S.A. (2018), "The calculation of rectangular plates on elastic foundation the finite difference method', J. Physics: Conference Series, 944(1), 012056). https://doi.org/10.1088/1742-6596/944/1/012056.
  20. Kukreti, A.R. and Siddiqi, Z.A. (1997), "Analysis of fluid storage tanks including foundation-superstructure interaction using differential quadrature method", Appl. Math. Model., 21(4), 193-205. https://doi.org/10.1016/S0307-904X(97)00007-3.
  21. Li, R., Zhong, Y. and Li, M. (2013), "Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method", P. Roy. Soc. A: Math. Phy., 469(2153), 20120681. https://doi.org/10.1098/rspa.2012.0681.
  22. Marr, W.A., Ramos, J.A. and Lambe, T.W. (1982), "Criteria for settlement of tanks", J. Geotech. Eng. Div., 108(8), 1017-1039. https://doi.org/10.1061/AJGEB6.0001326.
  23. Mahmood, I.U. (1984), "Finite element analysis of cylindrical tank foundations resting on isotropic soil medium including soil-structure interaction", Doctoral dissertation; University of Oklahoma.
  24. Melerski, E.S. (1991), "Simple elastic analysis of axisymmetric cylindrical storage tanks", J. Structu. Eng., 117(11), 3239-3260. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:11(3239)
  25. Pasternak, P.L. (1954), On a new method of analysis of an elastic foundation by means of two foundation constants, Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow.
  26. Pavlovic, M.N. (2001), "Design analysis of beams, circular plates and cylindrical tanks on elastic foundations-Edmund S. Melerski, AA Balkema, Rotterdam, 1995, xxii+ 284 pp", Eng. Struct., 5(23), 576-577. https://doi.org/10.1016/S0141-0296(00)00102-4
  27. Reddy, J.N. (2006), Theory and analysis of elastic plates and shells, CRC press.
  28. Remadna, M.S., Benmebarek, S. and Benmebarek, N. (2017), "Numerical evaluation of the bearing capacity factor N'c of circular and ring footings", Geomech. Geoeng., 12(1), 1-13. https://doi.org/10.1080/17486025.2016.1153729.
  29. Rosenberg, P. and Journeaux, N.L. (1982), "Settlement limitations for cylindrical steel storage tanks", Can. Geotech. J., 19(3), 232-238. https://doi.org/10.1139/t82-030.
  30. Salgado, R. (2008), The engineering of foundations, (Vol. 888). New York: McGraw-Hill.
  31. Straughan, W.T. (1990), "Analysis of plates on elastic foundations", Doctoral dissertation; Texas Tech University).
  32. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of plates and shells, McGraw-hill.
  33. Turhan, A. (1992), "A consistent Vlasov model for analysis of plates on elastic foundations using the finite element method", Doctoral dissertation; Texas Tech University.
  34. Useche-Infante, D., Aiassa Martinez, G., Arrua, P. and Eberhardt, M. (2022), "Experimental study of behaviour of circular footing on geogrid-reinforced sand", Geomech. Geoeng., 17(1), 45-63. https://doi.org/10.1080/17486025.2019.1683621.
  35. Useche-Infante, D., Aiassa Martinez, G., Arrua, P. and Eberhardt, M. (2021), "Scale effect on the behavior of circular footing on geogrid-reinforced sand using numerical analysis", Geomech. Geoeng., 18(1), 1-14. https://doi.org/10.1080/17486025.2021.2007301.
  36. Utku, M., Citipitioglu, E. and Inceleme, I. (2000), "Circular plates on elastic foundations modelled with annular plates", Comput. Struct., 78(1-3), 365-374. https://doi.org/10.1016/S0045-7949(00)00063-8.
  37. Vallabhan, C.V. and Das, Y.C. (1989), "Beams on elastic foundations: a new approach", In Foundation Engineering: Current Principles and Practices, 613-624.
  38. Vallabhan, C.V. and Das, Y.C. (1991), "Analysis of circular tank foundations", J. Eng. Mech., 117(4), 789-797. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:4(789).
  39. Vlasov, V.Z. and Leontiev, N.N. (1966), "Beams, plates, and shells on elastic foundations", translated from Russian by Israel program for scientific translations, NIST No. N67-14238.
  40. Winkler, E. (1867), Theory of elasticity and strength. Dominicus Prague.
  41. Worku, A. and Habte, B. (2022), "Analytical formulation and finite-element implementation technique of a rigorous two-parameter foundation model to beams on elastic foundations", Geomech. Geoeng., 17(2), 547-560. https://doi.org/10.1080/17486025.2020.1827162.
  42. Yang, T.Y. (1972), "A finite element analysis of plates on a two parameter foundation model", Comput. Struct., 2(4), 593-614. https://doi.org/10.1016/0045-7949(72)90011-9.