Behaviors of pile-column piers based on modified pasternak foundation model

ZHANG Ling; YUE Shao; ZHAO Ming-hua; PENG Wen-zhe

doi:10.11779/CJGE202210007

Volume 44 Issue 10

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Chinese Journal of Geotechnical Engineering > 2022 > 44(10): 1817-1826. > DOI: 10.11779/CJGE202210007

ZHANG Ling, YUE Shao, ZHAO Ming-hua, PENG Wen-zhe. Behaviors of pile-column piers based on modified pasternak foundation model[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(10): 1817-1826. DOI: 10.11779/CJGE202210007

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Behaviors of pile-column piers based on modified pasternak foundation model

ZHANG Ling^{1, 2, 3,},
YUE Shao^{1, 2, 3},
ZHAO Ming-hua^{1, 2, 3},
PENG Wen-zhe^{1, 2, 3}

1.
College of Civil Engineering, Hunan University, Changsha 410082, China
2.
Key Laboratory of Building Safety and Energy Efficiency of the Ministry of Education, Hunan University, Changsha 410082, China
3.
National International Joint Research Center for Building Safety and Environment, Hunan University, Changsha 410082, China

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Received Date: September 14, 2021
Available Online: December 11, 2022

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Abstract

Abstract

The analysis of behaviors of pile-column piers in layered soils under inclined loads is extremely complicated. An improved Pasternak foundation reaction model considering the plastic yield characteristics of soils is proposed. Considering the influences of 'P-Δ effect', shear deformation and axial force distribution of piles, the governing equations for displacements of free section, elastic section and plastic section of the pile-column pier are respectively established based on the Timoshenko beam theory. Then, the semi-analytical solutions to the internal forces and deformations of the pier in the layered foundation under inclined loads are obtained by using the Laplace transform and the matrix transfer method. On this basis, the influences of shear stiffnesses and foundation stratification are discussed and analyzed in a parametric study. It can be concluded as follows: (1) For the cases with different length-diameter ratios, the horizontal displacement of the piles increases with the increasing shear stiffness of the piles, but the tendency is opposite for the results of bending moment, and the influences of shear stiffness reaches the maximum when the length-diameter ratio reaches approximately 5. (2) Unlike the influences of the 'P – Δ effect', the shear modulus of the soils significantly inhibits the horizontal displacement and the bending moment of the piles. (3) In a multi-layer foundation, the strength of upper soil layers has the greatest influences on the horizontal displacement and the bending moment of the piles, and increasing their strength will significantly reduce the horizontal displacement and bending moment.
- pile-column pier,
- modified Pasternak foundation model,
- Timoshenko beam,
- matrix transfer method

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References

[1]	赵明华. 轴向和橫向荷载同时作用下的桩基计算[J]. 湖南大学学报(自然科学版), 1987, 14(2): 68–81. https://www.cnki.com.cn/Article/CJFDTOTAL-HNDX198702008.htm ZHAO Ming-hua. The calculation of piles under simultaneous axial and lateral loading[J]. Journal of Hunan University (Natural Science), 1987, 14(2): 68–81. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HNDX198702008.htm
[2]	张玲, 赵明华, 赵衡. 倾斜荷载下桩柱式桥墩受力变形分析传递矩阵法[J]. 中国公路学报, 2015, 28(2): 69–76. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201502012.htm ZHANG Ling, ZHAO Ming-hua, ZHAO Heng. Transfer matrix method for deformation of pile type bridge pier under axial transverse load[J]. China Journal of Highway and Transport, 2015, 28(2): 69–76. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201502012.htm
[3]	赵明华, 杨超炜, 杨明辉, 等. 基于有限杆单元法的陡坡段桥梁基桩受力分析[J]. 中国公路学报, 2014, 27(6): 51–58, 108. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201406010.htm ZHAO Ming-hua, YANG Chao-wei, YANG Ming-hui, et al. Mechanical analysis of bridge pile foundation in high and steep slopes based on finite bar element method[J]. China Journal of Highway and Transport, 2014, 27(6): 51–58, 108. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201406010.htm
[4]	赵明华, 彭文哲, 杨超炜, 等. 高陡横坡段桥梁双桩内力计算有限差分解[J]. 中国公路学报, 2019, 32(2): 87–96. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201902010.htm ZHAO Ming-hua, PENG Wen-zhe, YANG Chao-wei, et al. Finite difference solution of bridge double-pile structure on a steep transverse slope[J]. China Journal of Highway and Transport, 2019, 32(2): 87–96. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201902010.htm
[5]	戴国亮, 代浩, 杨炎华, 等. 冲刷作用下水平承载单桩计算方法及承载特性[J]. 中国公路学报, 2018, 31(8): 104–112. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201808012.htm DAI Guo-liang, DAI Hao, YANG Yan-hua, et al. Computation method and bearing characteristics of lateral bearing single pile foundation under scour condition[J]. China Journal of Highway and Transport, 2018, 31(8): 104–112. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201808012.htm
[6]	张小玲, 赵景玖, 杜修力. 基于Vesic圆孔扩张理论的桩周土抗力计算方法研究[J]. 中国公路学报, 2021, 34(6): 19–26. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202106003.htm ZHANG Xiao-ling, ZHAO Jing-jiu, DU Xiu-li. Computation method for soil resistance around pile based on cavity expansion theory[J]. China Journal of Highway and Transport, 2021, 34(6): 19–26. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202106003.htm
[7]	俞剑, 朱俊霖, 黄茂松, 等. 基于虚拟加载上限法和黏土小应变特性的桩基p–y曲线[J]. 岩土工程学报, 2021, 43(11): 2029–2036. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202111011.htm YU Jian, ZHU Jun-lin, HUANG Mao-song, et al. T-EMSD-based p–y curve of laterally loaded piles in clay considering small-strain behavior[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(11): 2029–2036. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202111011.htm
[8]	黄茂松, 俞剑, 张陈蓉. 基于应变路径法的黏土中水平受荷桩p–y曲线[J]. 岩土工程学报, 2015, 37(3): 400–409. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201503003.htm HUANG Mao-song, YU Jian, ZHANG Chen-rong. P–y curves of laterally loaded piles in clay based on strain path approach[J]. Chinese Journal of Geotechnical Engineering, 2015, 37(3): 400–409. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201503003.htm
[9]	GUO W D. Nonlinear response of laterally loaded piles and pile groups[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2009, 33(7): 879–914.
[10]	ZHANG L, ZHAO M, ZOU X. Elastic-plastic solutions for laterally loaded piles in layered soils[J]. Journal of Engineering Mechanics, 2013, 139(11): 1653–1657.
[11]	张磊, 龚晓南, 俞建霖. 水平荷载单桩计算的非线性地基反力法研究[J]. 岩土工程学报, 2011, 33(2): 309–314. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201102027.htm ZHANG Lei, GONG Xiao-nan, YU Jian-lin. Solutions for laterally loaded single pile by nonlinear subgrade reaction method[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(2): 309–314. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201102027.htm
[12]	竺明星, 龚维明, 何小元, 等. 纵横向受荷基桩变形内力的矩阵传递解[J]. 岩土力学, 2014, 35(11): 3281–3288. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201411037.htm ZHU Ming-xing, GONG Wei-ming, HE Xiao-yuan, et al. Matrix transfer solutions to deformation and internal forces of piles under combined vertical and lateral loads[J]. Rock and Soil Mechanics, 2014, 35(11): 3281–3288. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201411037.htm
[13]	GUPTA B K, BASU D. Applicability of Timoshenko, Euler–Bernoulli and rigid beam theories in analysis of laterally loaded monopiles and piles[J]. Géotechnique, 2018, 68(9): 772–785.
[14]	LIU J W, SHI C H, CAO C Y, et al. Improved analytical method for pile response due to foundation pit excavation[J]. Computers and Geotechnics, 2020, 123: 103609.
[15]	赵明华, 彭文哲, 杨超炜, 等. 基于Pasternak双参数地基模型的陡坡段桥梁基桩内力计算方法[J]. 水文地质工程地质, 2018, 45(1): 52–59. https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201801008.htm ZHAO Ming-hua, PENG Wen-zhe, YANG Chao-wei, et al. Inner-force calculation of bridge pile foundation in a high-steep slope based on the Pasternak double-parameter spring model[J]. Hydrogeology & Engineering Geology, 2018, 45(1): 52–59. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SWDG201801008.htm
[16]	梁发云, 李彦初, 黄茂松. 基于Pasternak双参数地基模型水平桩简化分析方法[J]. 岩土工程学报, 2013, 35(增刊1): 300–304. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S1050.htm LIANG Fa-yun, LI Yan-chu, HUANG Mao-song. Simplified method for laterally loaded piles based on Pasternak double-parameter spring model for foundations[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(S1): 300–304. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S1050.htm
[17]	赵明华. 桥梁桩基计算与检测[M]. 北京: 人民交通出版社, 1999. ZHAO Ming-hua. Calculation of Bridge Piles and Their Detection[M]. Beijing: China Communications Press, 1999. (in Chinese)
[18]	TANAHASHI H. Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model[J]. Soils and Foundations, 2004, 44(5): 109–118.
[19]	YAO W J, YIN W X, CHEN J, et al. Numerical simulation of a super-long pile group under both vertical and lateral loads[J]. Advances in Structural Engineering, 2010, 13(6): 1139–1151.
[20]	MATLOCK H. Correlations for design of laterally loaded piles in soft clay[C]// Proceedings of 2nd Offshore Technology Conference. Houston, 1970.
[21]	ZDRAVKOVIĆ L, TABORDA D, POTTS D, et al. Numerical modelling of large diameter piles under lateral loading for offshore wind applications[C]// Third International Symposium on Frontiers in Offshore Geotechnics. Oslo Norway, 2015: 759–764.
[22]	COWPER G R. The shear coefficient in timoshenko's beam theory[J]. Journal of Applied Mechanics, 1966, 33(2): 335–340.
[23]	吴鸣, 赵明华. 大变形条件下桩土共同工作及试验研究[J]. 岩土工程学报, 2001, 23(4): 436–440. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200104011.htm (WU Ming, ZHAO Ming-hua. Study on pile-soil interaction under large deflection and its model test[J]. Chinese Journal of Geotechnical Engineering, 2001, 23(4): 436–440. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC200104011.htm
[24]	朱斌, 熊根, 刘晋超, 等. 砂土中大直径单桩水平受荷离心模型试验[J]. 岩土工程学报, 2013, 35(10): 1807–1815. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201310007.htm ZHU Bin, XIONG Gen, LIU Jin-chao, et al. Centrifuge modelling of a large-diameter single pile under lateral loads in sand[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(10): 1807–1815. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201310007.htm