Dynamic Response of Arbitrarily Shaped Foundation Embedded in Multilayered Partially Saturated Half-Space
Publication: International Journal of Geomechanics
Volume 19, Issue 11
Abstract
A novel precise flexibility matrix algorithm is proposed to analyze the dynamic response of a rigid foundation embedded in a multilayered partially saturated half-space (MLPSH) that consists of several dry soil layers and saturated soil layers overlying on a saturated half-space. The wave equations of dry soil layers and saturated soil layers governed by Biot's theory are transformed into a dual vector form. The extended precise integration algorithm is applied to combine microlayers between two interfaces of any two typical layers. Subsequently, the global flexible matrix is assembled based on relative positions of source and receiver points. Finally, the dynamic impedance of the embedded foundation is achieved by using the flexible volume method. The accuracy and effectiveness of the proposed method are validated by comparing them with the results of extended studies. Extensive numerical results are presented to investigate the influence of the foundation shape on the dynamic impedance of the foundation embedded in an MLPSH.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Major Scientific Research Program in the 13th Five Year Plan (2016YFB0201001) and the National Natural Science Foundation of China (Grant No. 51779222). This support is gratefully acknowledged.
References
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 L. H. Wang. 2017. “Influences of Biot's compressible parameters on dynamic response of vertically loaded multilayered poroelastic soils.” Soil Dyn. Earthquake Eng. 94 (Mar): 7–12. https://doi.org/10.1016/j.soildyn.2016.12.010.
Aki, K., and P. G. Richards. 1980. Quantitative seismology. San Francisco: W. H. Freeman and Co.
Apsel, R. J., and J. E. Luco. 1987. “Impedance functions for foundations embedded in a layered medium: An integral equation approach.” Earthquake Eng. Struct. Dyn. 15 (2): 213–231. https://doi.org/10.1002/eqe.4290150205.
Ba, Z., Z. Kang, and V. W. Lee. 2017. “Plane strain dynamic responses of a multi-layered transversely isotropic saturated half-space.” Int. J. Eng. Sci. 119 (Oct): 55–77. https://doi.org/10.1016/j.ijengsci.2017.06.005.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Biot, M. A. 1956a. “Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low-frequency range.” J. Acoust. Soc. Am. 28 (2): 168–178. https://doi.org/10.1121/1.1908239.
Biot, M. A. 1956b. “Theory of propagation of elastic waves in a fluid-saturated porous solid. II. Higher frequency range.” J. Acoust. Soc. Am. 28 (2): 179–191. https://doi.org/10.1121/1.1908241.
Biot, M. A., and D. G. Willis. 1957. “The elastic coefficients of the theory of consolidation.” J. Appl. Mech. 24 (2): 594–601. https://doi.org/10.1190/1.1439709.
Bougacha, S., J. M. Roësset, and J. L. Tassoulas. 1993a. “Dynamic stiffness of foundations on fluid-filled poroelastic stratum.” J. Eng. Mech. 119 (8): 1649–1662. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:8(1649).
Bougacha, S., J. L. Tassoulas, and J. M. Roësset. 1993b. “Analysis of foundations on fluid-filled poroelastic stratum.” J. Eng. Mech. 119 (8): 1632–1648. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:8(1632).
Cai, Y., and X. Hu. 2010. “Vertical vibrations of a rigid foundation embedded in a poroelastic half space.” J. Eng. Mech. 136 (3): 390–398. https://doi.org/10.1061/(ASCE)0733-9399(2010)136:3(390).
Chen, S. L. 2009. “Vertical vibration of a flexible foundation resting on saturated layered soil half-space.” Int. J. Geomech. 9 (3): 113–121. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:3(113).
Dargush, G. F., and M. B. Chopra. 1996. “Dynamic analysis of axisymmetric foundations on poroelastic media.” J. Eng. Mech. 122 (7): 623–632. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:7(623).
Depollier, C., J. F. Allard, and W. Lauriks. 1988. “Biot theory and stress–strain equations in porous sound-absorbing materials.” J. Acoust. Soc. Am. 84 (6): 2277–2279. https://doi.org/10.1121/1.397024.
Dutta, S. C., and R. Roy. 2002. “A critical review on idealization and modeling for interaction among soil–foundation–structure system.” Comput. Struct. 80 (20–21): 1579–1594. https://doi.org/10.1016/S0045-7949(02)00115-3.
Halpern, M. R., and P. Christiano. 1986. “Steady-state harmonic response of a rigid plate bearing on a liquid-saturated poroelastic halfspace.” Earthquake Eng. Struct. Dyn. 14 (3): 439–454. https://doi.org/10.1002/eqe.4290140310.
Han, Z., G. Lin, and J. Li. 2015. “Dynamic impedance functions for arbitrary-shaped rigid foundation embedded in anisotropic multilayered soil.” J. Eng. Mech. 141 (11): 04015045. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000915.
Japón, B. R., R. Gallego, and J. Domínguez. 1997. “Dynamic stiffness of foundations on saturated poroelastic soils.” J. Eng. Mech. 123 (11): 1121–1129. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:11(1121).
Jin, B., and H. Liu. 2000. “Rocking vibrations of rigid disk on saturated poroelastic medium.” Soil Dyn. Earthquake Eng. 19 (7): 469–472. https://doi.org/10.1016/S0267-7261(00)00031-2.
Kassir, M. K., and X. Jimin. 1988. “Interaction functions of a rigid strip bonded to saturated elastic half-space.” Int. J. Solids Struct. 24 (9): 915–936. https://doi.org/10.1016/0020-7683(88)90041-8.
Lamb, H. 1904. “On the propagation of tremors over the surface of an elastic solid.” Philos. Trans. R. Soc. London, Ser. A 72: (477–486): 128-130. https://doi.org/10.1098/rsta.1904.0013.
Lee, J. H., J. K. Kim, and J. L. Tassoulas. 2011. “Implementation of a second-order paraxial boundary condition for a water-saturated layered half-space in plane strain.” Earthquake Eng. Struct. Dyn. 40 (5): 531–550. https://doi.org/10.1002/eqe.1047.
Lee, J. H., J. K. Kim, and J. L. Tassoulas. 2012. “Dynamic analysis of foundations in a layered half-space using a consistent transmitting boundary.” Earthquakes Struct. 3 (3–4): 203–230. https://doi.org/10.12989/eas.2012.3.3_4.203.
Lee, J. H., J. K. Kim, and J. L. Tassoulas. 2013. “Dynamic analysis of a poroelastic layered half-space using continued-fraction absorbing boundary conditions.” Comput. Methods Appl. Mech. Eng. 263: 81–98. https://doi.org/10.1016/j.cma.2013.05.002.
Lin, G., Z. Han, H. Zhong, and J. Li. 2013. “A precise integration approach for dynamic impedance of rigid strip footing on arbitrary anisotropic layered half-space.” Soil Dyn. Earthquake Eng. 49 (Jun): 96–108. https://doi.org/10.1016/j.soildyn.2013.01.009.
Liu, Z., J. Liang, and C. Wu. 2015. “Dynamic Green's function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method.” Eng. Anal. Bound. Elements 60 (Nov): 51–66. https://doi.org/10.1016/j.enganabound.2015.03.011.
Lysmer, J., and R. L. Kuhlemeyer. 1969. “Finite dynamic model for infinite media.” J. Eng. Mech. Div. 95 (4): 859–878.
Novak, M. 1974. “Effect of soil on structural response to wind and earthquake.” Earthquake Eng. Struct. Dyn. 3 (1): 79–96. https://doi.org/10.1002/eqe.4290030107.
Philippacopoulos, A. J. 1989. “Axisymmetric vibration of disk resting on saturated layered half-space.” J. Eng. Mech. 115 (10): 2301–2322. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:10(2301).
Qiang, G., Z. Wanxie, and W. P. Howson. 2004. “A precise method for solving wave propagation problems in layered anisotropic media.” Wave Motion 40 (3): 191–207. https://doi.org/10.1016/j.wavemoti.2003.09.002.
Rajapakse, R. K. N. D., and T. Senjuntichai. 1995. “Dynamic response of a multi-layered poroelastic medium.” Earthquake Eng. Struct. Dyn. 24 (5): 703–722. https://doi.org/10.1002/eqe.4290240507.
Sahebkar, K., and M. Eskandari-Ghadi. 2016. “Time-harmonic response of saturated porous transversely isotropic half-space under surface tractions.” J. Hydrol. 537 (Jun): 61–73. https://doi.org/10.1016/j.jhydrol.2016.02.050.
Senjuntichai, T., S. Mani, and R. K. N. D. Rajapakse. 2006. “Vertical vibration of an embedded rigid foundation in a poroelastic soil.” Soil Dyn. Earthquake Eng. 26 (6–7): 626–636. https://doi.org/10.1016/j.soildyn.2006.01.013.
Senjuntichai, T., and R. K. N. D. Rajapakse. 1994. “Dynamic Green's functions of homogeneous poroelastic half-plane.” J. Eng. Mech. 120 (11): 2381–2404. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:11(2381).
Senjuntichai, T., and R. K. N. D. Rajapakse. 1996. “Dynamics of a rigid strip bonded to a multilayered poroelastic medium.” In Mechanics of poroelastic media, Vol. 35 of Solid mechanics and its applications, 353–369. Dordrecht, Netherlands: Springer. https://doi.org/10.1007/978-94-015-8698-6_20.
Senjuntichai, T., and Y. Sapsathiarn. 2003. “Forced vertical vibration of circular plate in multilayered poroelastic medium.” J. Eng. Mech. 129 (11): 1330–1341. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:11(1330).
Sheng-li, C., and C. Long-zhu. 2002. “The axisymmetric mixed boundary-value problem of the vertical vibration of a rigid foundation on saturated layered soil subgrade.” Appl. Math. Mech. 23 (2): 218–225. https://doi.org/10.1007/BF02436564.
Spyrakos, C. C., and C. Xu. 2004. “Dynamic analysis of flexible massive strip–foundations embedded in layered soils by hybrid BEM–FEM.” Comput. Struct. 82 (29–30): 2541–2550. https://doi.org/10.1016/j.compstruc.2004.05.002.
Todorovska, M. I., and Y. Al Rjoub. 2006. “Plain strain soil–structure interaction model for a building supported by a circular foundation embedded in a poroelastic half-space.” Soil Dyn. Earthquake Eng. 26 (6–7): 694–707. https://doi.org/10.1016/j.soildyn.2006.01.018.
Tsynkov, S. V. 1998. “Numerical solution of problems on unbounded domains. A review.” Appl. Numer. Math. 27 (4): 465–532. https://doi.org/10.1016/S0168-9274(98)00025-7.
Wang, Y., and R. K. N. D. Rajapakse. 1991. “Dynamics of rigid strip foundations embedded in orthotropic elastic soils.” Earthquake Eng. Struct. Dyn. 20 (10): 927–947. https://doi.org/10.1002/eqe.4290201004.
Wong, H. L., and M. D. Trifunac. 1974. “Interaction of a shear wall with the soil for incident plane SH waves: Elliptical rigid foundation.” Bull. Seismol. Soc. Am. 64 (6): 1825–1842.
Wu, D., and L. Yu. 2015. “Torsional vibrations of a cylindrical foundation embedded in a saturated poroelastic half-space.” Front. Struct. Civ. Eng. 9 (2): 194–202. https://doi.org/10.1007/s11709-015-0292-z.
Yang, J., and T. Sato. 1998. “Dynamic response of saturated layered half-space with different hydraulic interface conditions.” Arch. Appl. Mech. 68 (10): 677–688. https://doi.org/10.1007/s004190050196.
Zheng, P., B. Ding, S. X. Zhao, and D. Ding. 2013. “Dynamic response of a multilayered poroelastic half-space to harmonic surface tractions.” Transp. Porous Media 99 (2): 229–249. https://doi.org/10.1007/s11242-013-0182-6.
Zhong, W. X. 2001. “Combined method for the solution of asymmetric Riccati differential equations.” Comput. Methods Appl. Mech. Eng. 191 (1–2): 93–102. https://doi.org/10.1016/S0045-7825(01)00246-8.
Zienkiewicz, O. C., C. T. Chang, and P. Bettess. 1980. “Drained, undrained, consolidating and dynamic behaviour assumptions in soils.” Geotechnique 30 (4): 385–395. https://doi.org/10.1680/geot.1980.30.4.385.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 19 • Issue 11 • November 2019
Copyright
© 2019 American Society of Civil Engineers.
History
Received: Oct 16, 2018
Accepted: Apr 10, 2019
Published online: Sep 11, 2019
Published in print: Nov 1, 2019
Discussion open until: Feb 11, 2020
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.