Interaction of Beams with Consolidating Nonlinear Poroelastic Layered Soil
Publication: Journal of Engineering Mechanics
Volume 148, Issue 3
Abstract
A computationally efficient semianalytical framework for obtaining the consolidation settlement of flexible foundations such as beams and strip footings resting on nonlinear, saturated, poroelastic, and multilayered continua (soil) is developed. Two-dimensional (2D) plane strain is assumed, and Biot’s consolidation theory is used in the analysis. The differential equations governing the displacements and excess pore pressure dissipation of the beam-soil system are developed using the variational principles of mechanics in which the soil is modeled as a simplified continuum and the foundation is modeled as an Euler-Bernoulli beam. The developed differential equations are coupled and are solved following a unique iterative algorithm using one-dimensional (1D) finite-element analysis. The numerical solution is less expensive than conventional 2D numerical methods. A distinct feature of the developed framework is that the effect of soil stress-strain nonlinearity is considered in the calculation of the consolidation settlement, which is usually not considered in Terzaghi’s and Biot’s consolidation theories. It is observed that soil nonlinearity and foundation flexibility can significantly impact the foundation settlement and consolidation rate. The developed framework provides a fast, easy-to-use, and accurate method for estimating the consolidation settlement of flexible shallow foundations.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request as follows:
•
A version of the code used to generate some of the results in this paper.
References
Ai, Z. Y., and J. B. Cai. 2016. “Static interaction analysis between a Timoshenko beam and layered soils by analytical layer element/boundary element method coupling.” Appl. Math. Modell. 40 (21–22): 9485–9499. https://doi.org/10.1016/j.apm.2016.06.028.
Ai, Z. Y., Z. X. Li, and Y. C. Cheng. 2014. “BEM analysis of elastic foundation beams on multilayered isotropic soils.” Soils Found. 54 (4): 667–674. https://doi.org/10.1016/j.sandf.2014.06.008.
Ai, Z. Y., W. J. Liu, and B. K. Shi. 2018. “Quasi-static interaction between non-uniform beams and anisotropic permeable saturated multilayered soils with elastic superstrata.” Appl. Math. Modell. 53 (Jan): 400–418. https://doi.org/10.1016/j.apm.2017.08.020.
Barden, L., and N. A. Younan. 1969. “Consolidation of layered clays.” Can. Geotech. J. 6 (4): 413–429. https://doi.org/10.1139/t69-042.
Benz, T., P. A. Vermeer, and R. Schwab. 2009. “A small-strain overlay model.” Int. J. Numer. Anal. Methods Geomech. 33 (1): 25–44. https://doi.org/10.1002/nag.701.
Biot, M. A. 1941. “Consolidation settlement under a rectangular load distribution.” J. Appl. Phys. 12 (5): 426–430. https://doi.org/10.1063/1.1712921.
Biot, M. A. 1955. “Theory of elasticity and consolidation for a porous anisotropic solid.” J. Appl. Phys. 26 (2): 182–185. https://doi.org/10.1063/1.1721956.
Biot, M. A. 1956. “General solutions of the equations of elasticity and consolidation for a porous material.” J. Appl. Mech. 23 (1): 91–96. https://doi.org/10.1115/1.4011213.
Biot, M. A. 1962. “Mechanics of deformation and acoustic propagation in porous media.” J. Appl. Phys. 33 (4): 1482–1498. https://doi.org/10.1063/1.1728759.
Booker, J. R. 1974. “The consolidation of a finite layer subject to surface loading.” Int. J. Solids Struct. 10 (9): 1053–1065. https://doi.org/10.1016/0020-7683(74)90011-0.
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.
Bowles, L. E. 1996. Foundation analysis and design. New York: McGraw-Hill.
Chen, Y., N. D. Beskou, and J. Qian. 2018. “Dynamic response of an elastic plate on a cross-anisotropic poroelastic half-plane to a load moving on its surface.” Soil Dyn. Earthquake Eng. 107 (Apr): 292–302. https://doi.org/10.1016/j.soildyn.2018.01.038.
Cheng, A. H. D. 2016. Poroelasticity. Berlin: Springer.
Conte, E., and A. Troncone. 2007. “Nonlinear consolidation of thin layers subjected to time-dependent loading.” Can. Geotech. J. 44 (6): 717–725. https://doi.org/10.1139/t07-015.
Duncan, J. M. 1993. “Limitations of conventional analysis of consolidation settlement.” J. Geotech. Eng. 119 (9): 1333–1359. https://doi.org/10.1061/(ASCE)0733-9410(1993)119:9(1333).
Elhuni, H., and D. Basu. 2019. “Dynamic soil structure interaction model for beams on viscoelastic foundations subjected to oscillatory and moving loads.” Comput. Geotech. 115 (Nov): 103157. https://doi.org/10.1016/j.compgeo.2019.103157.
Elhuni, H., and D. Basu. 2021. “Novel nonlinear dynamic beam–foundation interaction model.” J. Eng. Mech. 147 (4): 04021012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001915.
Haldar, S., and D. Basu. 2016. “Analysis of beams on heterogeneous and nonlinear soil.” Int. J. Geomech. 16 (4): 04016004. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000599.
Idriss, I. M., R. Dobry, and R. D. Singh. 1978. “Nonlinear behavior of soft clays during cyclic loading.” J. Geotech. Eng. Div. 104 (12): 1427–1447. https://doi.org/10.1061/AJGEB6.0000727.
Kim, J., and A. P. S. Selvadurai. 2016. “A note on the consolidation settlement of a rigid circular foundation on a poroelastic half space.” Int. J. Numer. Anal. Methods Geomech. 40 (14): 2003–2016. https://doi.org/10.1002/nag.2519.
Kim, P., Y. G. Kim, C. H. Paek, and J. Ma. 2019. “Lattice Boltzmann method for consolidation analysis of saturated clay.” J. Ocean Eng. Sci. 4 (3): 193–202. https://doi.org/10.1016/j.joes.2019.04.004.
Lin, G., Z. Han, and J. Li. 2013. “An efficient approach for dynamic impedance of surface footing on layered half-space.” Soil Dyn. Earthquake Eng. 49: 39–51.
Osman, A. S., D. J. White, A. M. Britto, and M. D. Bolton. 2007. “Simple prediction of the undrained displacement of a circular surface foundation on non-linear soil.” Géotechnique 57 (9): 729–737. https://doi.org/10.1680/geot.2007.57.9.729.
Pasternak, P. L. 1954. On a new method of analysis of an elastic foundation by means of two foundation constants. Moscow: Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture.
Pe, W. 1995. “Beam on poroelastic foundation.” Accessed June 28, 2020. https://ttu-ir.tdl.org/handle/2346/20781.
Rani, S., R. Kumar, and S. J. Singh. 2011. “Consolidation of an anisotropic compressible poroelastic clay layer by axisymmetric surface loads.” Int. J. Geomech. 11 (1): 65–71. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000073.
Rice, J. R., and R. F. Boisvert. 1996. “From scientific software libraries to problem-solving environments.” IEEE Comput. Sci. Eng. 3 (3): 44–53. https://doi.org/10.1109/99.537091.
Seed, H. B. 1970. Soil moduli and damping factors for dynamic response analysis. Grand Forks, ND: Energy & Environmental Research Center.
Selvadurai, A. P. S., and L. Shi. 2015. “Biot’s problem for a Biot material.” Int. J. Eng. Sci. 97 (Dec): 133–147. https://doi.org/10.1016/j.ijengsci.2015.09.004.
Siddharthan, R., Z. Zafir, and G. M. Norris. 1993. “Moving load response of layered soil.” J. Eng. Mech. 119 (10): 2052–2071.
Srivastava, H. M., and R. G. Buschman. 2013. Theory and applications of convolution integral equations. Berlin: Springer.
Terzaghi, K., R. B. Peck, and G. Mesri. 1996. Soil mechanics in engineering practice. New York: Wiley.
Vallabhan, C. G., and Y. C. Das. 1991. “A refined model for beams on elastic foundations.” Int. J. Solids Struct. 27 (5): 629–637. https://doi.org/10.1016/0020-7683(91)90217-4.
Vallabhan, C. V., and Y. C. Das. 1989. “Beams on elastic foundations: A new approach.” In Foundation engineering: Current principles and practices, 613–624. Reston, VA: ASCE.
Vardanega, P. J., and M. D. Bolton. 2013. “Stiffness of clays and silts: Normalizing shear modulus and shear strain.” J. Geotech. Geoenviron. Eng. 139 (9): 1575–1589. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000887.
Vlasov, V. Z., and N. N. Leontiev. 1966. Beams, plates, and shells on elastic foundations, translated from Russian by Israel program for scientific translations. Gaithersburg, MD: NIST.
Vucetic, M., and R. Dobry. 1991. “Effect of soil plasticity on cyclic response.” J. Geotech. Eng. 117 (1): 89–107. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:1(89).
Wang, L., L. Wang, and C. Liu. 2021. “Analytical model for vertical dynamic interaction between circular raft and saturated soils.” Int. J. Geomech. 21 (4): 06021005. https://doi.org/10.1061/(ASCE)GM.19435622.0001959.
Wilmanski, K. 2006. “A few remarks on Biot’s model and linear acoustics of poroelastic saturated materials.” Soil Dyn. Earthquake Eng. 26 (6–7): 509–536. https://doi.org/10.1016/j.soildyn.2006.01.006.
Winkler, E. 1867. Theory of elasticity and strength. Prague, Czech Republic: Dominicus.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 3 • March 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 11, 2021
Accepted: Oct 28, 2021
Published online: Dec 31, 2021
Published in print: Mar 1, 2022
Discussion open until: May 31, 2022
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