Vibration response analysis of an unsaturated soil foundation

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (12) : 182-190.

LI Weihua1,WANG Wenqiang2

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Abstract

The development of the wave theory of unsaturated porous media makes the dynamic analysis of unsaturated soil foundation possible.In this paper, an explicit finite element method for the existing dynamic formulation of unsaturated porous media was proposed.The decoupling-technique was used in the explicit finite element method.Based on the method, the computational program was written and verified by comparing with the analytical solution after degeneration.The method was applied to analyze the dynamic responses of a strip rigid and flexible foundation in an unsaturated porous medium separately, and the influence of saturation on the dynamic responses of unsaturated soil foundation was discussed.The computational results indicate that, the dynamic response of the rigid foundation is larger than that of flexible foundation under the same conditions.For both kinds of foundations, the dynamic response for Sr=1 is smaller than that for Sr<1.For the rigid foundation, the vertical displacement of each point decreases and the horizontal displacement increases with saturation level when Sr<1.For the flexible foundation, saturation has limited influence on the dynamic response of unsaturated soil foundations.

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unsaturated porous media / vibration response of foundation / explicit finite element method

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LI Weihua1,WANG Wenqiang2. Vibration response analysis of an unsaturated soil foundation[J]. Journal of Vibration and Shock, 2019, 38(12): 182-190

References

[1] 蔡袁强, 于玉贞, 袁晓铭等. 土动力学与岩土地震工程[J]. 土木工程学报, 2016, 45(9): 9-29.
CAI Yuanqiang, YU Yuzhen, YUAN Xiaoming et al. Soil dynamics and geotechnical earthquake engineering[J]. China Civil Engineering Journal, 2016, 45(9): 9-29.
[2] Biot M A. Theory of propagation of elastic waves in a fluid‐saturated porous solid. I. Low‐frequency range [J]. The Journal of the Acoustical Society of America, 1956, 28(2): 168-178.
[3] PhilippacopoulosA. J. Lamb's problem for fluid-saturated, porous media [J]. Bulletin of the Seismological Society of America, 1988, (2):908-923.
[4] Rajapakse R K N D, Wang Y. Elastodynamic Green's functions of orthotropic half space[J]. Journal of Engineering Mechanics, ASCE, 1991, 117(3): 588-604.
[5] 陈龙珠, 陈胜立. 饱和地基竖向振动的衰减特性[J]. 上海交通大学学报, 2002, 36(3): 376-381.
CHEN Longzhu, CHEN Shengli. Vibration Attenuation of Saturated Strata by Vertical Surface Loads [J]. Journal of Shanghai Jiaotong University , 2002, 36(3): 376-381.
[6] 金波, 徐植信. 多孔饱和半空间上刚体垂直振动的轴对称混合边值问题[J]. 力学学报, 1997, 29(6): 711-719.
JIN Bo, XU Zhixin. The axially symmetric mixed boundary - value problem or the vertical vibration of a rigid body on fluid-saturated porous half space [J]. Acta Mechanica Sinica, 1997, 29(6): 711-719.
[7] 陈胜立. 饱和地基上基础与板的竖向振动特性研究[D]. 杭州: 浙江大学. 2000.
CHEN Shengli. Study on the vibration of foundation and plate on saturated soil [PhD Thesis]. Hangzhou: Zhejiang University. 2000.
[8] 李伟华, 郑洁. 饱和度对平面P波入射下自由场地地震反应的影响分析[J]. 岩土工程学报, 2017, 39 (3): 427 – 435.
LI Weihua, ZHENG Jie. Effects of saturation on free-field responses of site due to plane P-wave incidence. Chinese Journal of Geotechnical Engineering, 2017, 39(3): 427-435.
[9] Berryman J G, Thigpen L, and Chin R C. Y. 1988. Bulk elastic wave propagation in partially saturated porous solids[J]. Journal of the Acoustical Society of America, 84(1), 360–373.
[10] Santos J E, Douglas J, Corbero, J, et al. A model for wave-propagation in a porous-medium saturated by a 2-phase fluid [J]. Journal of the Acoustical Society of America, 1990, 87(4): 1439-1448.
[11] Lo W C, Majer E, Sposito G. Wave propagation through elastic porous media containing two immiscible fluids[J]. Water Resources Research, 2005, 41(2): 1-20.
[12] Tuncay K, Corapcioglu, M Y. Body waves in poroelastic media saturated by two immiscible fluids[J]. Journal of Geophysical Research Atmospheres, 1996, 101(B11): 25149-25159.
[13] Vardoulakis I，Beskos D E. Dynamic behavior of nearly saturated porous media. Mechanics of Materials, 1986, 5(1): 87-108
[14] Wei C, Muraleetharan K K. A continuum theory of porous media saturated by multiple immiscible fluids: I. Linear poroelasticity[J]. International Journal of Engineering Science, 2002, 40(16):1807–1833.
[15] Lu J F, Hanyga A. Linear dynamic model for porous media saturated by two immiscible fluids[J]. International Journal of Solids and Structures, 2005, 42: 2689-2709
[16] Zhao H B, Wang X M. Acoustic wave propagation simulation in a poroelastic medium saturated by two immiscible fluids using a staggered finite-difference with a time partition method [J]. Science in China Series G: Physics, Mechanics & Astronomy, 2008, 51 (7): 723-744.
[17] Wei C F. Static and dynamic behavior of multiphase porous media: governing equations and finite element implementation [D]. Norman: University of Oklahoma. 2001.
[18] Ravichandran N. 2009. Fully coupled finite element model for dynamics of partially saturated soils[J]. Soil Dynamics and Earthquake Engineering, 29(9): 1294-1304.
[19] Gatmiri B, Jabbari E. Time-domain Green_s functions for unsaturated soils. Part I: Two-dimensional solution & Part II: There-dimensional solution[J]. International Journal of Solids and Structures, 2005, 42: 5971–6002.
[20] Maghoul P, Gatmiri B, Duhamel D. Boundary integral formulation and two-dimensional fundamental solutions for dynamic behavior analysis of unsaturated soils[J]. Soil Dynamics and Earthquake Engineering, 2011, 31(11): 1480-1495.
[21] Moldovan I D, Cao T D, Teixeira de Freitas J A. Elastic wave propagation in unsaturated porous media using hybrid-Trefftz stress elements[J]. International Journal for Numerical Methods in Engineering, 2014, 97(1):32-67.
[22] 徐明江. 非饱和土地基与基础的动力响应研究[D]. 华南理工大学, 2010.
XU Mingjiang. Investigation on Dynamic Response of Unsaturated Soils and Foundation [PhD Thesis]. Guangzhou: South China University of Technology. 2010.
[23] 赵成刚, 王进廷, 史培新等. 流体饱和两相多孔介质动力反应分析的显式有限元法[J]. 岩土工程学报. 2001, 23(2): 178-182.
ZHAO Chenggang, WANG Jinting, SHI Peixin et al. Dynamic analysis of fluid-saturated porous media by using explicit finite element method [J]. Journal of Geotechnical Engineering, 2001, 23(2): 178-182.
[24] Wei C, Muraleetharan K. Acoustical waves in unsaturated porous media[C]. in Proceedings 16th ASCE Engineering Mechanics Conference, Seattle, Washington, 2003.
[25] Brooks R H, Corey A T. Hydraulic propertied of porous media[R]. Hydrology Paper No.3, Colorado State Univ., Fort Collins, CO, 1964: 3-27
[26] van Genuchten M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 1980, 44, 892-898.
[27] Liao Z P, Wong H L, Yang B P, et al. A transmitting boundary for transient wave analyses. Scientia Sinica (Series A), 1984, 27(10): 1063-1076.
[28] Simon B R, Zienkiewicz O C, Paul D K. An analytical solution for the transient response of saturated porous elastic solids[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 1984, 8(4):381–398.
[29] 李庆金. 饱和地基上条形基础的竖向振动特性分析[D]. 杭州: 浙江大学. 2005.
LI Qingjin. Vertical Vibration Analysis of Strip Foundation on Saturated Soils [ME Thesis]. Hangzhou: Zhejiang University. 2005.