Elasto-plastic variational solution for vertically loaded noncylindrical piles
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摘要: 现有计算理论无法严格考虑弹塑性土中竖向受荷横截面异形桩的异形效应。针对该问题，基于虚功原理推导出桩-弹塑性土模型的控制方程，采用保角变换技术克服了复杂边界条件控制方程求解问题，结合双曲形D-P本构模型的本构积分算法获得弹塑性土中竖向受荷横截面异形桩的半解析算法，建立了能够考虑横截面异形效应的竖向受荷横截面异形桩荷载传递理论模型。将理论模型的预测结果与有限元计算结果对比，验证了理论模型的可靠性和计算的高效性。最后，通过参数分析探讨了横截面异形效应对荷载沉降曲线的影响，结果表明：在正常工作荷载下，横截面异形效应对桩顶沉降影响不大；横截面异形效应主要对桩的极限承载力大小产生影响。Abstract: The existing analytical or semi-analytical methods cannot rigorously capture the geometrical effects of noncylindrical piles in elasto-plastic soils. To solve this issue, based on the principle of virtual work, the governing equations for the pile-soil system are derived. Solving the governing equation with a complex boundary is overcome by the conformal mapping technique. A semi-analytical algorithm for the vertically loaded noncylindrical piles in elasto-plastic soils is developed by combing the use of integral algorithm for the hyperbolic D-P constitutive model. A general theoretical model for the load transfer of the vertically loaded noncylindrical piles considering the geometrical effects is proposed. The reliability and efficiency of the proposed semi-analytical method is validated by comparing the predicted results with those of FEM. Finally, detailed parametric studies are conducted to investigate the geometrical effects on the influences of load-settlement curve. It is found that the non-circular cross-section has insignificant influences on the settlement of the pile head under working loads, which principally affects the magnitude of the ultimate bearing capacity of the pile.
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图 1 子午面上原D-P与双曲形D-P屈服面
Figure 1. Original D-P and hyperbolic D-P yield surfaces in meridional plane
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图 2 理想弹塑性土中竖向受荷横截面异形桩力学模型
Figure 2. Mechanical model for axially loaded noncylindrical piles embedded in elasto-plastic soils
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图 5 竖向受荷桩-土体系弹塑性分析求解方案
Figure 5. Solution scheme for elasto-plastic analysis of axially loaded pile-soil system
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图 6 对比本文解与有限元法中矩形桩和土的响应
Figure 6. Comparison of responses of rectangular piles and soils from present analysis and FE method
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图 7 矩形桩与等横截面面积圆桩的荷载沉降曲线
Figure 7. Load-settlement curves for rectangular and circular piles with same cross-sectional area
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图 8 对比本文解与有限元法中XCC桩和土的响应
Figure 8. Comparison of responses of XCC piles and soils from present analysis and FE method
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图 9 XCC桩与等横截面面积圆桩的荷载沉降曲线
Figure 9. Load-settlement curves for XCC and circular piles with same cross-sectional area
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图 10 不同参数对归一化的荷载-沉降曲线的影响
Figure 10. Influence of different parameters on normalized load-settlement curves
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[1] LI X C, ZHOU H, LIU H L, et al. Three‐dimensional analytical continuum model for axially loaded noncircular piles in multilayered elastic soil[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2021, 45(18): 2654-2681. doi: 10.1002/nag.3281
[2] SEED H B, REESE L C. The action of soft clay along friction piles[J]. Transactions of the American Society of Civil Engineers, 1957, 122(1): 731-754. doi: 10.1061/TACEAT.0007501
[3] MINDLIN R D. Force at a point in the interior of a semi-infinite solid[J]. Physics, 1936, 7(5): 195-202. doi: 10.1063/1.1745385
[4] POULOS H G, DAVIS E H. The settlement behaviour of single axially loaded incompressible piles and piers[J]. Géotechnique, 1968, 18(3): 351-371. doi: 10.1680/geot.1968.18.3.351
[5] HIRAI H. Settlement analysis of rectangular piles in nonhomogeneous soil using a Winkler model approach[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2014, 38(12): 1298-1320. doi: 10.1002/nag.2270
[6] 雷国辉, 洪鑫, 施建勇. 壁板桩承载特性的近似三维分析[J]. 岩土力学, 2004, 25(4): 590-594, 600. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200404020.htm LEI Guohui, HONG Xin, SHI Jianyong. Approximate three-dimensional analysis of load-carrying behaviour of barrettes[J]. Rock and Soil Mechanics, 2004, 25(4): 590-594, 600. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200404020.htm
[7] VALLABHAN C V G, MUSTAFA G. A new model for the analysis of settlement of drilled piers[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1996, 20(2): 143-152. doi: 10.1002/(SICI)1096-9853(199602)20:2<143::AID-NAG812>3.0.CO;2-U
[8] SHEN W Y, CHOW Y K, YONG K Y. A variational approach for vertical deformation analysis of pile group[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1997, 21(11): 741-752. doi: 10.1002/(SICI)1096-9853(199711)21:11<741::AID-NAG898>3.0.CO;2-D
[9] SHEN W Y, CHOW Y K, YONG K Y. Variational solution for vertically loaded pile groups in an elastic half-space[J]. Géotechnique, 1999, 49(2): 199-213. doi: 10.1680/geot.1999.49.2.199
[10] LEE K M, XIAO Z R. A new analytical model for settlement analysis of a single pile in multi-layered soil[J]. Soils and Foundations, 1999, 39(5): 131-143. doi: 10.3208/sandf.39.5_131
[11] SEO H, PREZZI M. Analytical solutions for a vertically loaded pile in multilayered soil[J]. Geomechanics and Geoengineering, 2007, 2(1): 51-60. doi: 10.1080/17486020601099380
[12] BASU D, PREZZI M, SALGADO R, et al. Settlement analysis of piles with rectangular cross sections in multi-layered soils[J]. Computers and Geotechnics, 2008, 35(4): 563-575. doi: 10.1016/j.compgeo.2007.09.001
[13] TEHRANI F S, SALGADO R, PREZZI M. Analysis of axial loading of pile groups in multilayered elastic soil[J]. International Journal of Geomechanics, 2016, 16(2): 04015063. doi: 10.1061/(ASCE)GM.1943-5622.0000540
[14] 雷国辉, 詹金林, 洪鑫. 壁板桩群桩竖直荷载沉降关系的变分法分析[J]. 岩土力学, 2007, 28(10): 2071-2076. doi: 10.3969/j.issn.1000-7598.2007.10.012 LEI Guohui, ZHAN Jinlin, HONG Xin. Variational analysis of load-settlement relationship of vertically loaded barrette groups[J]. Rock and Soil Mechanics, 2007, 28(10): 2071-2076. (in Chinese) doi: 10.3969/j.issn.1000-7598.2007.10.012
[15] 周航, 李籼橙, 刘汉龙, 等. 均质土中竖向受荷X形混凝土桩的三维弹性变分解[J]. 岩土力学, 2021, 42(4): 1012-1024. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202104014.htm ZHOU Hang, LI Xiancheng, LIU Hanlong, et al. Three-dimensional variational elastic solution for axially loaded X-section cast-in-place concrete pile in homogeneous soil[J]. Rock and Soil Mechanics, 2021, 42(4): 1012-1024. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202104014.htm
[16] JEONG S, LEE J, LEE C J. Slip effect at the pile-soil interface on dragload[J]. Computers and Geotechnics, 2004, 31(2): 115-126. doi: 10.1016/j.compgeo.2004.01.009
[17] 吕亚茹, 丁选明, 刘汉龙, 等. 刚性荷载下现浇X形桩复合地基桩侧摩阻力数值分析[J]. 岩土工程学报, 2012, 34(11): 2134-2140. http://cge.nhri.cn/cn/article/id/14886 LÜ Yaru, DING Xuanming, LIU Hanlong, et al. Numerical analysis of side resistance of composite foundation with X-section cast-in-place concrete piles under rigid load[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(11): 2134-2140. (in Chinese) http://cge.nhri.cn/cn/article/id/14886
[18] ZHANG Q Q, FENG R F, YU Y L, et al. Simplified approach for prediction of nonlinear response of bored pile embedded in sand[J]. Soils and Foundations, 2019, 59(5): 1562-1578. doi: 10.1016/j.sandf.2019.07.011
[19] HAN F, SALGADO R, PREZZI M. Nonlinear analyses of laterally loaded piles-A semi-analytical approach[J]. Computers and Geotechnics, 2015, 70: 116-129. doi: 10.1016/j.compgeo.2015.07.009
[20] GUPTA B K, BASU D. Nonlinear solutions for laterally loaded piles[J]. Canadian Geotechnical Journal, 2020, 57(10): 1566-1580. doi: 10.1139/cgj-2019-0341
[21] 周永强, 盛谦, 刘芳欣, 等. 一种修正的Drucker-Prager屈服准则[J]. 岩土力学, 2016, 37(6): 1657-1664. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201606016.htm ZHOU Yongqiang, SHENG Qian, LIU Fangxin, et al. A study of modified Drucker-Prager yield criterion[J]. Rock and Soil Mechanics, 2016, 37(6): 1657-1664. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201606016.htm
[22] ABBO A J, SLOAN S W. A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion[J]. Computers & Structures, 1995, 54(3): 427-441.
[23] CHEN H H, LI L, LI J P, et al. A rigorous elastoplastic load-transfer model for axially loaded pile installed in saturated modified Cam-clay soils[J]. Acta Geotechnica, 2022, 17(2): 635-651. doi: 10.1007/s11440-021-01248-z
[24] ZHOU H, LIU H L, YUAN J R. A novel analytical approach for predicting the noncylindrical pile penetration-induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2018, 42(11): 1270-1305.
[25] 詹云刚, 袁凡凡, 栾茂田. 纯摩擦型岩土介质本构积分算法及其在ABAQUS中开发应用[J]. 岩土力学, 2007, 28(12): 2619-2623, 2628. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200712029.htm ZHAN Yungang, YUAN Fanfan, LUAN Maotian. Integration algorithm of constitutive equation for cohesionless-frictional geomaterial and its application to ABAQUS[J]. Rock and Soil Mechanics, 2007, 28(12): 2619-2623, 2628. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200712029.htm
[26] RANDOLPH M F. The response of flexible piles to lateral loading[J]. Géotechnique, 1981, 31(2): 247-259. http://www.onacademic.com/detail/journal_1000034855799910_85ab.html
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