Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A two-dimensional hyperbolic spring model for mat foundation in clays subjected to vertical load

  • Der-Wen Chang (Department of Civil Engineering, Tamkang University) ;
  • Tzu-Min Chou (Department of Civil Engineering, Tamkang University) ;
  • Shih-Hao Cheng (Taiwan Building Technology Center, National Taiwan University of Science and Technology) ;
  • Louis Ge (Department of Civil Engineering, National Taiwan University)
  • Received : 2023.10.18
  • Accepted : 2024.05.21
  • Published : 2024.06.10
⟨ Previous Next ⟩

Abstract

This study proposes a two-dimensional hyperbolic soil spring model for mat foundations in clays subjected to vertically uniform loads to simplify the complexity of three-dimensional finite element analysis on mat foundations. The solutions from three-dimensional finite element analysis were examined to determine the hyperbolic model parameters of the soil springs underneath the slab. Utilizing these model parameters, normalized functions across the middle section of the mat were obtained. The solutions from the proposed model, along with the approximate finite difference analysis of the mat in clays under vertical load, were found to be consistent with those from the three-dimensional finite element analysis. The authors conclude that the proposed method can serve as an alternative for the preliminary design of mat foundations.

Keywords

Acknowledgement

This paper presents a partial result of the research project sponsored by the Ministry of Science and Technology (MOST) in Taiwan. Sincere gratitude is expressed towards the financial support through research grant MOST109-2221-E-032-010-MY2.

References

  1. Adeel, M.B., Aaqib, M., Pervaiz, U., Rehman, J.U. and Park, D. (2022), "Numerical response of pile foundations in granular soils subjected to lateral load", Geomech. Eng., 28(1), 11-23. https://doi.org/10.12989/gae.2021.28.1.011.
  2. Anastasopoulos, I., Loli, M., Gelagoti, F., Kourkoulis, R. and Gazetas, G. (2012), "Nonlinear soil-foundation interraction: numerical analysis", Proceedings of the 2nd Int. Conf. on Performance-Based Design in Earthquake Geotechnical Engineering, May 28-30, Taormina, Italy.
  3. Beredugo, Y.O. and Novak, M. (1972), "Coupled horizontal and rocking vibration of embedded footings", Can. Geotech. J., 9(4), 477-497. https://doi.org/10.1139/t72-046.
  4. Bowles, J.E. (1997), Foundation Analysis and Design; McGraw-Hill Pub, 1175.
  5. Chang, D.W., Lien, H.W. and Wang, T. (2018), "Finite difference analysis of vertically loaded raft foundation based on the plate theory with boundary concern", J. GeoEng., 13(3), 135-147.
  6. Chang, D.W., Hung, M.H. and Jeong, S.S. (2021), "Modified Lysmer's analog model for two dimensional mat settlements under vertically uniform load", Int. J. Geomech. Eng., 25(3), 221-231.
  7. Chang, D.W. and Chou, T.M. (2023), "Developing a two-dimensional nonlinear vertical spring model for mat foundation in clays using hyperbolic function", Proceedings of the 17th Asian Regional Conference on Soils Mechanics and Geotechnical Engineering, Astana, Kazakhstan.
  8. Chen, Q., Xu, T. and Tominaga, K. (2002), "Analytical method for nonlinear behaviour of soil under vertically loaded circular plate", J. Asian Architect. Build. Eng., 1(2), 1-7. https://doi.org/10.3130/jaabe.1.2_1.
  9. Chou, T.M. (2022), "Development of nonlinear vertical springs for mat foundations in clays", Master Thesis, Dept. of Civil Engineering, Tamkang University, Taiwan (in Chinese).
  10. Duncan, J.M. and Chang, C.M. (1970), "Nonlinear analysis of stress and strain in soils", J. Soil Mech. Found. Division, 96(5), 1629-1653. https://doi.org/10.1061/JSFEAQ.0001458
  11. Deviprasad, B.S. and Dodagoudar, G.R. (2020), "Seismic response of bridge pier supported on rocking shallow foundation", Geomech. Eng., 21(1), 73-84. https://doi.org/10.12989/gae.2020.21.1.073.
  12. Fellenius, B. (2014), Basics of Foundation Design; electronic edition.
  13. Gajan, S. and Kutter, B.L. (2009), "Contact interface model for shallow foundations subjected to combined cyclic loading", J. Geotech. Geoenviron. Eng., 135(3), 407-419. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:3(407).
  14. Gajan, S., Raychowdhury, P., Hutchinson T.C., Kutter, B.L. and Stewart, J.P. (2010), "Application and validation of practical tools for nonlinear soil-foundation interaction analysis", Earthq. Spectra, 26(1), 111-129. https://doi.org/10.1193/1.32632.
  15. Gazetas, G. (1991), Foundation Vibrations. Foundation Engineering Handbook, 553-593.
  16. Harada, T., Monaka, T., Wang, H., Magoshi, K. and Iwamura, M. (2008), "A nonlinear dynamic soil foundation interaction model using fiber element method and its application to nonlinear earthquake response analysis of cable stayed bridge", Proceedings of the 14th World Conference on Earthquake Engineering, Oct. 12-17, Beijing, China.
  17. Harden, C.W. and Hutchinson, T.C. (2009), "Beam-on-nonlinear-Winkler-foundation modeling of shallow, rocking-dominated footings", Earthq. Spectra, 25(2), 277-300. https://doi.org/10.1193/1.3110482.
  18. Horvilleur, J.F. and Patel, V.B. (1995), "Mat foundation design a soil-structure interaction problem", ACI, 152, 51-94.
  19. Hsieh, P.G., Kung, T.C., Ou, C.Y. and Tang, Y.G. (2003), "Deep excavation analysis with consideration of small strain modulus and its degradation behavior of clay", Proceedings of the 12th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, Singapore.
  20. Jeong, S.S., Park, J.J. and Chang, D.W. (2024), "An approximate numerical analysis of rafts and piled-rafts foundation", Comput. Geotech., 168, 106108. https://doi.org/10.1016/j.compgeo.2024.106108.
  21. Jeong, S.S., Park, J.J., Hong, M.H. and Lee, J.W. (2017), "Variability of subgrade reaction modulus on flexible mat foundation", Geomech. Eng., 13(5), 757-774. https://doi.org/10.12989/gae.2017.13.5.757.
  22. Kondner, R.L. (1963), "Hyperbolic stress-strain response: cohesive soils", J. Soil Mech. Found. Eng., 89(1), 115-143. https://doi.org/10.1061/JSFEAQ.0000479
  23. Leblouba, M., Toubat, S.Al., Rahman, M.E. and Mugheida, O. (2016), "Pratical soil-shallow foundation model for nonlinear structural analysis", Math. Probl. Eng., 4514152. https://doi.org/10.1155/2016/4514152.
  24. Lee, J.W., Jeong, S.S. and Lee, J.K. (2015), "3D analytical method for mat foundations considering coupled soil springs", Geomech. Eng., 8(6), 845-857. https://doi.org/10.12989/gae.2015.8.6.845.
  25. Liou, G.S. and Lai, S.C. (1996), "Structural analysis model for mat foundations", J. Struct. Eng., 122(9), 1114-1117. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:9(1114.
  26. Long, W.S., Limkatanyu S., Hansapinyo, C., Prachasaree, W., Rungamornrat, J. and Kwon, M. (2021), "Nonlinear flexibility based beam element on Winkler Pasternak foundation", Geomech. Eng., 24(4), 371-388. https://doi.org/10.12989/gae.2021.24.4.371.
  27. Lysmer, J. and Richart, F.E. (1966), "Dynamic response of footings to vertical loading", J. Soil Mech. Found. Division, 92(1). https://doi.org/10.1061/JSFEAQ.000084.
  28. Midas (2017), Midas GTS NX User Manual, Midas IT Co.
  29. Novak, M. and Beredugo, Y.O. (1972), "Vertical vibrations of embedded footings", J. Soil Mech. Found. Division, 98(12), 1291-1331. https://doi.org/10.1061/JSFEAQ.00018.
  30. Novak, M. and Sachs, K. (1973), "Torsional and coupled vibrations of embedded footings", Earthq. Eng. Struct. D., 2(1), 11-33. https://doi.org/10.1002/eqe.4290020103.
  31. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvui Arkhitekture, Moscow. (In Russian)
  32. Poulos, H.G. (2018), "Rational assessment of modulus of subgrade reaction", Geotech. Eng. J. SEAGS and AGSSEA, 49(1), 1-7.
  33. Poulos, H. (2001), "Piled raft foundations: design and applications", Geotechnique, 51(2), 95-113. https://doi.org/10.1680/geot.2001.51.2.95.
  34. Schanz, T., Vermeer, P.A. and Bonnier, P.G. (1999), "The hardening soil model: Formulation and verification", Beyond 2000 in Computational Geotechnics - 10 Years of PLAXIS; Balkema, Rotterdam.
  35. Sert, S. and Kilic, A.N. (2016), "Numerical investigation of different superstructure loading type effects in mat foundations", Int. J. Civil Eng., 14, 171-180. https://doi.org/10.1007/s40999-016-0013-6.
  36. Tabsh, S.W., El-Emam, M. and Partazian, P. (2020) , "Numerically based parametric analysis of mat foundations", Practice Periodical on Structural Design and Construction, 25(2), 04020009. https://doi.org/10.1061/(ASCE)SC.1943-5576.000047.
  37. Trombetta, N.W., Mason, B., Hutchinson, T., Zupan, J.D., Bray, J., and Cutter, B.L. (2014), "Nonlinear soil-foundation-structure and structure-soil-structure interaction: centrifuge test observations", J. Geotech. Geoenviron. Eng. ASCE, 140(5), 04013057. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001074.
  38. Ulrich, E. (1991), "Subgrade reaction in mat foundation design", Concrete Int., 13(4), 41-50.
  39. Worku, A. and Seid, T. (2020), "Application of a robust subgrade model in the analysis of plates on an elastic foundation", Int. J. Geomech., 20(10), 0001834. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001834.
  40. Wrench, B.P. (1985), "Plate tests for the measurement of modulus and bearing capacity of gravels", Civil Eng. Siviele Ingenieurswese, 10, 547.
  41. Zhang, W.X., Lv, W.L., Zhang, J.Y., Wang, X., Hwang, H.J. and Yi, W.J. (2021), "Energy-based dynamic parameter identification for Pasternak foundation model", Earthq. Eng. Eng. Vib., 20, 631-643. https://doi.org/10.1007/s11803-021-2043-6.