Elastic Thin Plate Resting on Saturated Multilayered Soils with Anisotropic Permeability and Elastic Superstrata
Publication: International Journal of Geomechanics
Volume 18, Issue 10
Abstract
The fundamental solution for saturated multilayered soils with anisotropic permeability and elastic superstrata is deduced by gathering the analytical layer elements of single-phase soil layers and saturated soil layers. According to the displacement coordination along the plate-soil contact surface, the fundamental solution is substituted into the boundary element method (BEM) formula of the elastic thin plate. Some theoretical and experimental results are presented to certify the correctness of the method in this study, and the influences of the elastic superstratum, time factor, plate-soil relative stiffness, and stratification characteristic on the time behavior of elastic thin plates are explored.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study is supported by the National Natural Science Foundation of China (Grants 50578121 and 41672275). The authors would like to thank the editor-in-chief, the processing editor, and the reviewers for their valuable comments, which contributed to improving the quality of this paper.
References
Ai, Z. Y., and J. B. Cai. 2015. “Static analysis of Timoshenko beam on elastic multilayered soils by combination of finite element and analytical layer element.” Appl. Math. Modell. 39 (7): 1875–1888. https://doi.org/10.1016/j.apm.2014.10.008.
Ai, Z. Y., Y. C. Cheng, and W. Z. Zeng. 2011. “Analytical layer-element solution to axisymmetric consolidation of multilayered soils.” Comput. Geotech. 38 (2): 227–232. https://doi.org/10.1016/j.compgeo.2010.11.011.
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 (Apr): 40–45. https://doi.org/10.1016/j.enganabound.2014.11.021.
Ai, Z. Y., Z. Q. Yue, L. G. Tham, and M. Yang. 2002. “Extended Sneddon and Muki solutions for multilayered elastic materials.” Int. J. Eng. Sci. 40 (13): 1453–1483. https://doi.org/10.1016/S0020-7225(02)00022-8.
Banerjee, P. K., and R. Butterfield. 1981. Boundary element methods in engineering science. New York: McGraw-Hill.
Booker, J. R., and J. C. Small. 1982. “Finite layer analysis of consolidation II.” Int. J. Numer. Anal. Methods Geomech. 6 (2): 173–194. https://doi.org/10.1002/nag.1610060205.
Booker, J. R., and J. C. Small. 1984. “The time-deflection behaviour of a circular raft of finite flexibility on a deep clay layer.” Int. J. Numer. Anal. Methods Geomech. 8 (4): 343–357. https://doi.org/10.1002/nag.1610080404.
Booker, J. R., and J. C. Small. 1986. “The behaviour of an impermeable flexible raft on a deep layer of consolidating soil.” Int. J. Numer. Anal. Methods Geomech. 10 (3): 311–327. https://doi.org/10.1002/nag.1610100305.
Butterfield, R., and P. K. Banerjee. 1971. “A rigid disc embedded in an elastic half space.” Geotech. Eng. 2 (1): 35–52.
Cajka, R., V. Křivy, and D. Sekanina. 2011. “Design and development of a testing device for experimental measurements of foundation slabs on the subsoil.” Trans. VŠB 11 (1): 1–5. https://doi.org/10.2478/v10160-011-0002-2.
Cajka, R., and J. Labudkova. 2014. “Dependence of deformation of a plate on the subsoil in relation to the parameters of the 3D model.” Int. J. Mech. 8 (1): 208–215.
Cheung, Y. K., and O. C. Zinkiewicz. 1965. “Plates and tanks on elastic foundation–an application of finite method.” Int. J. Solids Struct. 1 (4): 451–461. https://doi.org/10.1016/0020-7683(65)90008-9.
de Paiva, J. B., and R. Butterfield. 1997. “Boundary element analysis of plate-soil interaction.” Comput. Struct. 64 (1–4): 319–328. https://doi.org/10.1016/S0045-7949(96)00135-6.
Fraser, R. A., and L. J. Wardle. 1976. “Numerical analysis of rectangular rafts on layered foundations.” Géotechnique 26 (4): 613–630. https://doi.org/10.1680/geot.1976.26.4.613.
Gao, S. W., J. H. Wang, and X. L. Zhou. 2005. “Solution of a rigid disk on saturated soil considering consolidation and rheology.” J. Zhejiang Univ. Sci. A 6 (3): 222–228. https://doi.org/10.1631/jzus.2005.A0222.
Melerski, E. S. 1997. “Numerical modelling of elastic interaction between circular rafts and cross-anisotropic media.” Comput. Struct. 64 (1–4): 567–578. https://doi.org/10.1016/S0045-7949(96)00132-0.
Milovic, D. M. 1972. “Stresses and displacements in an anisotropic layer due to a rigid circular foundation.” Géotechnique 22 (1): 169–174. https://doi.org/10.1680/geot.1972.22.1.169.
Milovic, D. M. 1992. Stresses and displacements for shallow foundations. Amsterdam, Netherlands: Elsevier.
Milovic, D. M., and M. Diogo. 1991. “Settlement of circular foundation of any rigidity.” In Proc., 10th European Conf. on Soil Mechanics and Foundation Engineering, 497–500. Rotterdam, Netherlands: Balkema.
Ohga, M., T. Shigematsu, and T. Hara. 1991. “Boundary element-transfer matrix method for plated structures.” J. Eng. Mech. 117 (11): 2509–2526. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:11(2509).
Oskoorouchi, A. M., B. Novrouzian, G. D. Roeck, and J. V. D. Broeck. 1991. “Zoned finite strip method and its applications in geomechanics.” Comput. Geotech. 11 (4): 265–294.
Poulos, H. G. 1968. “The behaviour of a rigid circular plate resting on a finite elastic layer.” Aust. Civ. Eng. Trans. 10: 213–219.
Rashed, Y. F., and M. H. Aliabadi. 2000. “Boundary element analysis of foundation plates in buildings.” Eng. Anal. Boundary Elem. 24 (2): 201–206. https://doi.org/10.1016/S0955-7997(99)00048-X.
Rashed, Y. F., M. H. Aliabadi, and C. A. Brebbia. 1998. “The boundary element method for thick plates on a Winkler foundation.” Int. J. Numer. Methods Eng. 41 (8): 1435–1462. https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8%3C1435::AID-NME345%3E3.0.CO;2-O.
Ribeiro, D. B., and J. B. de Paiva. 2015. “An alternative BE-FE formulation for a raft resting on a finite soil layer.” Eng. Anal. Boundary Elem. 50 (Jan): 352–359. https://doi.org/10.1016/j.enganabound.2014.09.016.
Shaaban, A. M., and Y. F. Rashed. 2013. “A coupled BEM-stiffness matrix approach for analysis of shear deformable plates on elastic half space.” Eng. Anal. Boundary Elem. 37 (4): 699–707. https://doi.org/10.1016/j.enganabound.2012.12.005.
Shukla, S. K., A. Gupta, and N. Sivakugan. 2011. “Analysis of circular elastic plate resting on Pasternak foundation by strain energy approach.” Geotech. Geol. Eng. 29 (4): 613–618. https://doi.org/10.1007/s10706-011-9392-2.
Sinha, A., and A. Hanna. 2017. “3D numerical model for piled raft foundation.” Int. J. Geomech. 17 (2): 04016055. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000674.
Sladek, J., V. Sladek, and H. A. Mang. 2002. “Meshless local boundary integral equation method for simply supported and clamped plates resting on elastic foundation.” Comput. Methods Appl. Mech. Eng. 191 (51–52): 5943–5959. https://doi.org/10.1016/S0045-7825(02)00505-4.
Small, J., and H. Zhang. 2002. “Behavior of piled raft foundations under lateral and vertical loading.” Int. J. Geomech. 2 (1): 29–45. https://doi.org/10.1061/(ASCE)1532-3641(2002)2:1(29).
Small, J. C., and H. L. S. Liu. 2008. “Time-settlement behaviour of piled raft foundations using infinite elements.” Comput. Geotech. 35 (2): 187–195. https://doi.org/10.1016/j.compgeo.2007.04.004.
Talbot, A. 1979. “The accurate numerical inversion of Laplace transforms.” IMA J. Appl. Math. 23 (1): 97–120. https://doi.org/10.1093/imamat/23.1.97.
Vlasov, V. Z., and N. N. Leontiev. 1960. Beams, plates, and shells on an elastic foundation. [In Russian.] Moscow: Fizmatgiz.
Wang, Y. H., and Y. K. Cheung. 2001. “Plate on cross-anisotropic foundation analyzed by the finite element method.” Comput. Geotech. 28 (1): 37–54. https://doi.org/10.1016/S0266-352X(00)00018-5.
Wang, Y. H., L. G. Tham, Y. Thui, and Z. Q. Yue. 2003. “Plate on layered foundation analyzed by a semi-analytical and semi-numerical method.” Comput. Geotech. 30 (5): 409–418. https://doi.org/10.1016/S0266-352X(03)00014-4.
Wang, Y. H., L. G. Tham, and Y. K. Cheung. 2005. “Beams and plates on elastic foundations: A review.” Prog. Struct. Eng. Mater. 7 (4): 174–182. https://doi.org/10.1002/pse.202.
Wardle, L. J., and R. A. Fraser. 1974. “Finite element analysis of a plate on a layered cross-anisotropic foundation.” In Proc., 1st Int. Conf. of Finite Element Methods in Engineering, 565–578. Kensington, NSW, Australia: Unisearch Ltd.
Yue, Z., and A. Selvadurai. 1995. “Contact problem for saturated poroelastic solid.” J. Eng. Mech. 121 (4): 502–512. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:4(502).
Yue, Z. Q., and A. P. S. Selvadurai. 1994. “On the asymmetric indentation of a consolidating poroelastic half space.” Appl. Math. Modell. 18 (4): 170–185. https://doi.org/10.1016/0307-904X(94)90080-9.
Zhong, H., X. Li, and Y. He. 2005. “Static flexural analysis of elliptic Reissner-Mindlin plates on a Pasternak foundation by the triangular differential quadrature method.” Arch. Appl. Mech. 74 (10): 679–691. https://doi.org/10.1007/s00419-005-0377-6.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 10 • October 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jul 24, 2017
Accepted: Apr 11, 2018
Published online: Aug 7, 2018
Published in print: Oct 1, 2018
Discussion open until: Jan 7, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.