Solution and analysis for dynamic response of arbitrarily shaped rigid foundation on transversely isotropic layered soil

YANG Lin-qing; HAN Ze-jun; LIN Gao; ZHOU Xiao-wen; PAN Zong-ze

doi:10.11779/CJGE202007009

Volume 42 Issue 7

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Geotechnical Engineering > 2020 > 42(7): 1257-1267. > DOI: 10.11779/CJGE202007009

YANG Lin-qing, HAN Ze-jun, LIN Gao, ZHOU Xiao-wen, PAN Zong-ze. Solution and analysis for dynamic response of arbitrarily shaped rigid foundation on transversely isotropic layered soil[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(7): 1257-1267. DOI: 10.11779/CJGE202007009

Citation:

PDF (787 KB)

Solution and analysis for dynamic response of arbitrarily shaped rigid foundation on transversely isotropic layered soil

1.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, China
2.
Tianhe College of Guangdong Polytechnic Normal University, Guangzhou 510540, China
3.
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

More Information

Received Date: June 02, 2019
Available Online: December 05, 2022

Graphical Abstract

Abstract

Abstract

The solution of dynamic response of foundation is of great significance for a better understanding of the structure-soil interaction. However, the previous studies have mainly solved the frequency-domain solution for the isotropic layered soil, and few reports have been presented on the transverse isotropic layered soil, especially the solution in time domain. In the study, the dynamic response solution for the arbitrarily shaped foundation resting on (or) embedded in transversely isotropic multi-layered soil in time domain is obtained by using the integral transformation method, mixed variable technique and modified subtraction model. Numerical examples verify the accuracy of the proposed algorithm. Then a parameter study is carried out to analyze the influences of the difference between the material parameters in horizontal and vertical directions on the dynamic response of foundation in time domain. The results show that the heterogeneity of the soil has a significant effect on the dynamic response of the foundation, which should be considered in practical projects to obtain more accurate results.

FullText(HTML)

References (36)

References

[1]	LUCO J E. Dynamic interaction of a shear wall with the soil[J]. Journal of the Engineering Mechanics Division, 1969, 95(2): 333-346. doi: 10.1061/JMCEA3.0001101
[2]	TRIFUNAC M D. Interaction of a shear wall with the soil for incident plane SH waves[J]. Bulletin of the Seismological Society of America, 1972, 62(1): 63-83. doi: 10.1785/BSSA0620010063
[3]	WONG H L, TRIFUNAC M D. Interaction of a shear wall with the soil for incident plane SH waves: elliptical rigid foundation[J]. Bulletin of the Seismological Society of America, 1974, 64(6): 1825-1842. doi: 10.1785/BSSA0640061825
[4]	LUCO J E. Torsional response of structures for SH waves: the case of hemispherical foundations[J]. Bulletin of the Seismological Society of America, 1976, 66(1): 109-123. doi: 10.1785/BSSA0660010109
[5]	APSEL R J, LUCO J E. Torsional response of rigid embedded foundation[J]. Journal of the Engineering Mechanics Division, 1976, 102(6): 957-970. doi: 10.1061/JMCEA3.0002193
[6]	LEE V W. Investigation of Three-Dimensional Soil-Structure Interaction[R]. Los Angeles: Department of Civil Engineering, University of Southern California, 1979.
[7]	LYSMER J. Finite dynamic model for infinite media[J]. Journal of the Engineering Mechanics Division, 1969, 95(4): 859-878. doi: 10.1061/JMCEA3.0001144
[8]	TASSOULAS J L, KAUSEL E. On the effect of the rigid sidewall on the dynamic stiffness of embedded circular footings[J]. Earthquake Engineering & Structural Dynamics, 1983, 11(3): 403-414.
[9]	周兴涛, 盛谦, 冷先伦, 等. 颗粒离散单元法地震动力时程计算黏性人工边界及其应用[J]. 岩石力学与工程学报, 2017, 36(4): 928-939. doi: 10.13722/j.cnki.jrme.2016.0426 ZHOU Xing-tao, SHENG Qian, LENG Xian-lun, et al. Viscous artificial boundary for seismic dynamic time-history analysis with granular discrete element method and its application[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(4): 928-939. (in Chinese) doi: 10.13722/j.cnki.jrme.2016.0426
[10]	WAAS G. Earthquake Vibration Effects and Abatement for Military Facilities[R]. Miss: Vicksburg, 1972.
[11]	LIAO Z F, HUANG K, YANG B, et al. A transmitting boundary for transient wave analyses[J]. Science in China (Series A—Mathematics, Physics, Astronomy & Technological Science), 1969, 27(10): 1063-1076.
[12]	SMITH W D. A nonreflecting plane boundary for wave propagation problems[J]. Journal of Computational Physics, 1974, 15(4): 492-503. doi: 10.1016/0021-9991(74)90075-8
[13]	CLAYTON R, ENGQUIST B. Absorbing boundary conditions for acoustic and elastic wave equations[J]. Bulletin of the Seismological Society of America, 1977, 67(6): 1529-1540. doi: 10.1785/BSSA0670061529
[14]	ENGQUIST B, MAJDA A. Absorbing boundary conditions for the numerical simulation of waves[J]. Mathematics of Computation, 1977, 31(139): 629-651. doi: 10.1090/S0025-5718-1977-0436612-4
[15]	HIGDON R L. Absorbing boundary conditions for difference approximations to the multidimensional wave equation[J]. Mathematics of Computation, 1986, 47(176): 437-459.
[16]	WOLF J P, DARBRE G R. Dynamic-stiffness matrix of soil by the boundary-element method: embedded foundation[J]. Earthquake Engineering & Structural Dynamics, 1984, 12(3): 385-400.
[17]	KARABALIS D, BESKOS D. Dynamic response of 3-D rigid surface foundations by time domain boundary element method[J]. Earthquake Engineering & Structural Dynamics, 1984, 12(1): 73-93.
[18]	KARABALIS D, BESKOS D. Dynamic response of 3-D embedded foundations by the boundary element method[J]. Computer Methods in Applied Mechanics and Engineering, 1986, 56(1): 91-119. doi: 10.1016/0045-7825(86)90138-6
[19]	BARROS F, LUCO J E. Dynamic response of a two-dimensional semi-circular foundation embedded in a layered viscoelastic half-space[J]. Soil Dynamics and Earthquake Engineering, 1995, 14(1): 45-57. doi: 10.1016/0267-7261(94)00021-8
[20]	付佳, 梁建文. 场地动力特性对土–基础相互作用的影响[J]. 地震工程与工程振动, 2016, 36(1): 141-147. https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201601018.htm FU Jia, LIANG Jian-wen. Influence of site dynamic characteristics on soil-foundation interaction[J]. Earthquake Engineering Engineering Dynamics, 2016, 36(1): 141-147. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DGGC201601018.htm
[21]	LIANG Jian-wen, FU Jia, TODOROVSKA M I, et al. Effects of the site dynamic characteristics on soil-structure interaction: I incident SH-waves[J]. Soil Dynamics and Earthquake Engineering, 2013, 44: 27-37. doi: 10.1016/j.soildyn.2012.08.013
[22]	LIANG Jian-wen, FU Jia, TODOROVSKA M I, et al. In-plane soil-structure interaction in layered, fluid-saturated, poroelastic half-space: I structural response[J]. Soil Dynamics and Earthquake Engineering, 2016, 81: 84-111. doi: 10.1016/j.soildyn.2015.10.018
[23]	LIANG Jian-wen, FU Jia, TODOROVSKA M I, et al. In-plane soil-structure interaction in layered, fluid-saturated, poroelastic half-space: II pore pressure and volumetric strain[J]. Soil Dynamics and Earthquake Engineering, 2017, 92: 585-595. doi: 10.1016/j.soildyn.2016.10.012
[24]	艾智勇, 曾凯, 曾文泽. 层状地基三维问题的解析层元解[J]. 岩土工程学报, 2012, 34(6): 1154-1158. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201206031.htm AI Zhi-yong, ZENG Kai, ZENG Wen-ze. Analytical layer-element solution for three-dimensional problem of multilayered foundation[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(6): 1154-1158. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201206031.htm
[25]	艾智勇, 胡亚东. 3D横观各向同性地基非耦合解析层元[J]. 岩土工程学报, 2013, 35(2): 717-720. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S2131.htm AI Zhi-yong, HU Ya-dong. Uncoupled analytical layer-element for 3D transversely isotropic multilayered foundation[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(2): 717-720. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S2131.htm
[26]	韩泽军, 林皋, 周小文, 等. 横观各向同性层状地基上埋置刚性条带基础动力刚度矩阵求解[J]. 岩土工程学报, 2016, 38(6): 1117-1124. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201606019.htm HAN Ze-jun, LIN Gao, ZHOU Xiao-wen, et al. Solution of dynamic stiffness matrix for rigid strip foundations embedded in layered transversely isotropic soil[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(6): 1117-1124. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201606019.htm
[27]	韩泽军, 林皋, 周小文. 三维横观各向同性层状地基任意点格林函数求解[J]. 岩土工程学报, 2016, 38(12): 2218-2225. doi: 10.11779/CJGE201612010 HAN Ze-jun, LIN Gao, ZHOU Xiao-wen. Solution to Green's functions for arbitrary points in 3D cross-anisotropic multi-layered soil[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(12): 2218-2225. (in Chinese) doi: 10.11779/CJGE201612010
[28]	王雨, 陈文化, 王凯旋. 地层非均质成层性对地下管道的变形影响[J]. 岩土工程学报, 2018, 40(5): 900-909. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201805018.htm WANG Yu, CHEN Wen-hua, WANG Kai-xuan. Effect of soil stratification on deformation of buried pipelines[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(5): 900-909. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201805018.htm
[29]	LIU W, NOVAK M. Dynamic response of single piles embedded in transversely isotropic layered media[J]. Earthquake Engineering & Structural Dynamics, 1994, 23(11): 1239-1257.
[30]	LU W D, YANG Z W. Finite layer analysis for semi-infinite soils (II): special cases and numerical examples[J]. Applied Mathematics and Mechanics, 1992, 13(11): 987-993.
[31]	李肇胤, 周锋, 陈镕, 等. 横观各向同性层状场地受垂直圆盘状简谐荷载时的响应分析[J]. 岩石力学与工程学报, 2000(5): 608-612. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200005015.htm LI Zhao-yin, ZHOU Feng, CHEN Rong, et al. Respon se analysis on transversely isotropic elastic strata to harmonic disk loads[J]. Chinese Journal of Rock Mechanics and Engineering, 2000(5): 608-612. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX200005015.htm
[32]	GAO Q, ZHONG W X, HOWSON W P. A precise method for solving wave propagation problems in layered anisotropic media[J]. Wave Motion, 2004, 40: 191-207.
[33]	ANDERSEN L, CLAUSEN J. Impedance of surface footings on layered ground[J]. Computers and Structures, 2008, 86: 72-87.
[34]	TABATABAIE, M. The Flexible Volume Method for Dynamic Soil-Structure Interaction Analysis[D]. Berkeley: University of California.
[35]	RUGE P, TRINKS C, WITTE S. Time-domain analysis of unbounded media using mixed-variable formulations[J]. Earthquake Engineering & Structural Dynamics, 2001, 30(6): 899-925.
[36]	钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 34(2): 131-136. https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199402003.htm ZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dlian University of Technology, 1994, 34(2): 131-136. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DLLG199402003.htm