A Method for Nonlinear Analysis of Raft Resting on Multilayered Heterogeneous Soils
Publication: International Journal of Geomechanics
Volume 22, Issue 6
Abstract
This paper presents a new method for the nonlinear analysis of rafts resting on multilayered heterogeneous soils using the Vlasov model. The finite-element and the finite-difference methods are employed to solve the governing differential equations for the flexure of the raft and the displacement within the supporting soil mass, respectively. The soil heterogeneity in the vertical direction or in the horizontal directions within each soil layer is considered, and the soil nonlinearity is taken into account through the reduction of the soil shear modulus as a function of strains within the supporting soil mass. Through a comprehensive comparative study, it is found that the present method is validated as reasonable by field measurements and is in good agreement with nonlinear three-dimensional finite-element analysis and other existing analysis methods. A study is carried out to investigate the effect of soil layering, soil nonlinearity, and soil heterogeneity in the vertical direction and in horizontal directions on the raft behavior. It is concluded that neglecting the real conditions of the supporting soils (e.g., soil layering, soil nonlinearity, and soil heterogeneities in the vertical or in horizontal directions) in the analysis of the soil–raft interaction leads to an unrealistic prediction of the raft behavior.
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Acknowledgments
The authors would like to acknowledge the support provided by the department of civil engineering at University of Tabuk, Saudi Arabia, for this research work.
References
Ai, Z. Y., Z. Cao, J. J. Mu, and B. K. Shi. 2018. “Elastic thin plate resting on saturated multilayered soils with anisotropic permeability and elastic superstrata.” Int. J. Geomech. 18: 04018137. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001251.
Ai, Z. Y., and Y. D. Hu. 2015. “A coupled BEM-ALEM approach for analysis of elastic thin plates on multilayered soil with anisotropic permeability.” Eng. Anal. Boundary Elem. 53: 40–45. https://doi.org/10.1016/j.enganabound.2014.11.021.
Basu, D. 2006. “Analysis of laterally loaded piles in layered soil.” Ph.D. thesis, Dept. of Civil Engineering, Purdue Univ.
Benz, T. 2007. “Small-strain stiffness of soils and its numerical consequences.” Ph.D. thesis, Institut fur Geotechnik, Univ. Stuttgart.
Boresi, P., K. P. Chong, and J. D. Lee. 2011. Elasticity in engineering mechanics. 3rd ed. Chichester, UK: Wiley.
Breysse, D., H. Niandou, S. Elachachi, and L. Houy. 2005. “A generic approach to soil–structure interaction considering the effects of soil heterogeneity.” Géotechnique 55: 143–150. https://doi.org/10.1680/geot.2005.55.2.143.
Briaud, J., and R. Gibbens. 1999. “Behavior of five large spread footings in sand.” J. Geotech. Geoenviron. Eng. 125: 787–796. https://doi.org/10.1061/(ASCE)1090-0241(1999)125:9(787).
Brown, P. T., and R. E. Gibson. 1972. “Surface settlement of a deep elastic stratum whose modulus increases linearly with depth.” Can. Geotech. J. 9: 467–476. https://doi.org/10.1139/t72-045.
Buczkowski, R., and W. Torbacki. 2001. “Finite element modelling of thick plates on two-parameter elastic foundation.” Int. J. Numer. Anal. Methods Geomech. 25: 1409–1427. https://doi.org/10.1002/nag.187.
Buczkowski, R., and W. Torbacki. 2009. “Finite element analysis of plate on layered tensionless foundation.” Arch. Civ. Eng. 3: 255–274. https://doi.org/10.2478/v.10169-010-0014-9.
Celik, M., and A. Saygun. 1999. “A method for the analysis of plates on a two-parameter foundation.” Int. J. Solids Struct. 36: 2891–2915. https://doi.org/10.1016/S0020-7683(98)00135-8.
Chilton, D. S., and J. W Wekezer. 1990. “Plates on elastic foundation.” J. Struct. Div. ASCE 116 (11): 3236–3241. https://doi.org/10.1061/(ASCE)0733-9445(1990)116:11(3236).
Chow, S. H. W. 2007. “Analysis of piled-raft foundations with piles of different lengths and diameters.” Ph.D. thesis, School of Civil Engineering, Univ. of Sydney.
Colasanti, R., and J. Horvath. 2010. “Practical subgrade model for improved soil-structure interaction analysis: Software implementation.” Pract. Period. Struct. Des. Constr. 15 (4): 278–286. https://doi.org/10.1061/(ASCE)SC.1943-5576.0000060.
Cox, C., and P. Mayne. 2015. “Soil stiffness constitutive model parameters for geotechnical problems: A dilatometer testing approach.” In Proc., 3rd Int. Flat Dilatom, 393–400. Italy: Italian Geotechnical Society (AGI).
Denis, A., S. M. Elachachi, and H. Niandou. 2011. “Effects of longitudinal variability of soil on a continuous spread footing.” Eng. Geol. 122: 179–190. https://doi.org/10.1016/j.enggeo.2011.05.015.
Duncan, J. M., and C. Y. Chang. 1970. “Nonlinear analysis of stress and strain in soils.” J. Soil Mech. Found. Div. 96: 1629–1653. https://doi.org/10.1061/JSFEAQ.0001458.
El-Garhy, B., A. Abdel Galil, and M. Mari. 2018. “Analysis of flexible raft resting on soft soil improved by granular piles considering soil shear interaction.” Comput. Geotech. 94: 169–183. https://doi.org/10.1016/j.compgeo.2017.09.007.
El-Garhy, B., and M. Elsawy. 2017. “Effect of different parameters on the behavior of strip footing resting on weak soil improved by granular piles.” Int. J. Geo-Eng. 8: 1–24. https://doi.org/10.1186/s40703-016-0038-3.
Fahey, M. 1999. “Determining the parameters of a non-linear elastic model for prediction of ground deformation.” Aust. Geomech. 34: 39–59.
Fahey, M., and J. P. Carter. 1993. “A finite element study of the pressuremeter test in sand using a nonlinear elastic plastic model.” Can. Geotech. J. 30: 348–362. https://doi.org/10.1139/t93-029.
Fraser, R. A., and L. J. Wardle. 1976. “Numerical analysis of rectangular rafts on layered foundations.” Géotechnique 26: 613–630. https://doi.org/10.1680/geot.1976.26.4.613.
Gazetas, G. 1980. “Static and dynamic displacements of foundations on heterogeneous multilayered soils.” Géotechnique 30: 159–177. https://doi.org/10.1680/geot.1980.30.2.159.
Gibson, R. E. 1967. “Some results concerning displacements and stresses in a non-homogeneous elastic half-space.” Géotechnique 17: 58–67. https://doi.org/10.1680/geot.1967.17.1.58.
Gunerathne, S., H. Seo, W. D. Lawson, and P. W. Jayawickrama. 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.
Gunerathne, S., H. Seo, W. D. Lawson, and P. W. Jayawickrama. 2019. “Variational approach for settlement analysis of circular plate on multilayered soil.” Appl. Math. Modell. 70: 152–170. https://doi.org/10.1016/j.apm.2019.01.009.
Gupta, B. K., and D. Basu. 2020. “Nonlinear solutions for laterally loaded piles.” Can. Geotech. J. 57: 1566–1580. https://doi.org/10.1139/cgj-2019-0341.
Haldar, S., and D. Basu. 2016. “Analysis of beams on heterogeneous and nonlinear soil.” Int. J. Geomech. 16: 04016004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000599.
Horikoshi, K., and M. F. Randolph. 1997. “On the definition of raft—Soil stiffness ratio for rectangular rafts.” Géotechnique 47: 1055–1061. https://doi.org/10.1680/geot.1997.47.5.1055.
Ishibashi, I., and X. Zhang. 1993. “Unified dynamic shear moduli and damping ratios of sand and clay.” Soils Found. 33: 182–191. https://doi.org/10.3208/sandf1972.33.182.
Jardine, R. J., D. M. Potts, A. B. Fourie, and J. B. Burland. 1986. “Studies of the influence of non-linear stress–strain characteristics in soil–structure interaction.” Géotechnique 36: 377–396. https://doi.org/10.1680/geot.1986.36.3.377.
Kay, J., and L. Cavagnaro. 1983. “Settlement of raft foundations.” J. Geotech. Eng. 109 (11): 1367–1382. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:11(1367).
Kolar, V., and I. Nemec. 1989. Modelling of soil-structure interaction. 1st ed. New York: Transactions of the IMF.
Kristić, I. L., V. Szavits-Nossan, and P. Miščević. 2017. “Direktan postupak za odredivanje slijeganja plitkih temelja.” Gradjevinar 69: 467–477. https://doi.org/10.14256/JCE.1926.2016.
Larsson, R. 1997. Investigations and load tests in silty soils. Rep. No. 54. Linköping, Sweden: Swedish Geotechnical Institute.
Lehane, B., and M. Fahey. 2002. “A simplified nonlinear settlement prediction model for foundations on sand.” Can. Geotech. J. 39: 293–303. https://doi.org/10.1139/t01-091.
Lou, M., H. Wang, X. Chen, and Y. Zhai. 2011. “Structure-soil-structure interaction: Literature review.” Soil Dyn. Earthquake Eng. 31: 1724–1731. https://doi.org/10.1016/j.soildyn.2011.07.008.
Loukidis, D., and G. P. Tamiolakis. 2017. “Spatial distribution of Winkler spring stiffness for rectangular mat foundation analysis.” Eng. Struct. 153: 443–459. https://doi.org/10.1016/j.engstruct.2017.10.001.
Mandal, J. J., and D. P. Ghosh. 1999. “Prediction of elastic settlement of rectangular raft foundation—A coupled FE-BE approach.” Int. J. Numer. Anal. Methods Geomech. 23: 263–273. https://doi.org/10.1002/(SICI)1096-9853(199903)23:3%3C263::AID-NAG965%3E3.0.CO;2-T.
Mittal, R. K., and S. Rawat. 2016. “Effect of soil heterogeneity on soil–structure interaction.” In Indian Geotechnical Conf., 1–4. New Delhi, India: Indian Geotechnical Society.
Ozgan, K., and A. T. Daloglu. 2008. “Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model.” Thin-Walled Struct. 46: 1236–1250. https://doi.org/10.1016/j.tws.2008.02.006.
Ozgan, K., and A. T. Daloglu. 2007. “Alternative plate finite elements for the analysis of thick plates on elastic foundations.” Struct. Eng. Mech. 26: 69–86. https://doi.org/10.12989/sem.2007.26.1.069.
Ozgan, K., A. T. Daloglu, and AIİ Karakaş. 2013. “A parametric study for thick plates resting on elastic foundation with variable soil depth.” Arch. Appl. Mech. 83: 549–558. https://doi.org/10.1007/s00419-012-0703-8.
Ozkeskin, A. 2004. “Settlement reduction and stress concentration factors in rammed aggregate piers determined from full scale load tests.” Ph.D. thesis, Dept. of Civil Engineering, Middle East Technical Univ.
Oztoprak, S., and M. D. Bolton. 2013. “Stiffness of sands through a laboratory test database.” Géotechnique 63: 54–70. https://doi.org/10.1680/geot.10.P.078.
PLAXIS. 2021. CONNECT Edition V21.01 - Material Models Manual 1–274. Accessed March 4, 2021. https://communities.bentley.com/products/geotech-analysis/w/plaxis-soilvision-wiki/46137/manuals---plaxis.
Sall, O. A., M. Fall, Y. Berthaud, M. Ba, and M. Ndiaye. 2014. “Influence of the soil-structure interaction in the behavior of mat foundation.” Open J. Civ. Eng. 4: 71–83. https://doi.org/10.4236/ojce.2014.41007.
Selvadurai, A. 1979. Elastic analysis of soil-foundation interaction. 1st ed. Developments in Geotechnical Engineering. Amsterdam, Netherlands: Elsevier.
Severn, R. T. 1966. “The solution of foundation mat problems by finite-element methods.” Struct. Eng. 44 (6): 223–228.
Small, J. C. 2001. “Practical solutions to soil-structure interaction problems.” Prog. Struct. Eng. Mater. 3: 305–314. https://doi.org/10.1002/pse.87.
Smith, I. M., D. V. Griffiths, and L. Margetts. 2015. Programming the finite element method. 5th ed. New York: Wiley.
Turhan, A. 1992. “A consistent Vlasov model for analysis of plates on elastic foundations using the finite element method.” Ph.D. thesis, Dept. of Civil Engineering, Texas Tech Univ.
Vallabhan, C. V. G., and A. T. Daloglu. 1999. “Consistent FEM-Vlasov model for plates on layered soil.” J. Struct. Eng. 125: 108–113. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:1(108).
Vallabhan, C. V. G., W. T. Straughan, and Y. C. Das. 1991. “Refined model for analysis of plates on elastic foundations.” J. Eng. Mech. 117: 2830–2843. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:12(2830).
Vardanega, P. J., and M. D. Bolton. 2013. “Stiffness of clays and silts: Normalizing shear modulus and shear strain.” J. Geotech. Geoenviron. Eng. 139: 1575–1589. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000887.
Vardanega, P. J., and M. D. Bolton. 2014. “Stiffness of clays and silts: Modeling considerations.” J. Geotech. Geoenviron. Eng. 140: 06014004. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001104.
Vlasov, V. Z., and U. N. Leont’ev. 1966. Vol. 357 of Beams, plates and shells on elastic foundations. Jerusalem, Israel: Israel Program for Scientific Translations.
Wang, Y. H., L. G. Tham, and Y. K. Cheung. 2005. “Beams and plates on elastic foundations: A review.” Prog. Struct. Eng. Mater. 7: 174–182. https://doi.org/10.1002/pse.202.
Yang, T. 1972. “A finite element analysis of plates on a two parameter foundation model.” Comput. Struct. 2: 593–614. https://doi.org/10.1016/0045-7949(72)90011-9.
Zienkiewicz, O. C. 1977. The finite element method. New York: McGraw-Hill.
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Received: Aug 18, 2020
Accepted: Jan 9, 2022
Published online: Apr 6, 2022
Published in print: Jun 1, 2022
Discussion open until: Sep 6, 2022
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