Abstract：The load-deformation behavior of pile-supported geosynthetic reinforcements (GRs) is a complicated three-dimensional mechanical problem, and so far the 3-D analytical methods have not been well-established. Therefore the GRs with piles in square-type layout under 3-D conditions are taken as the research objects, which are regarded as the spacial membranes under the combined effect of the upper load and the subsoil reaction among piles. The partial differential equilibrium equations are derived based on the minimum potential energy principle. For the conditions of uniform load and without subsoil reaction, the analog equation method in the membrane analysis is used to solve the equations in view of their complex forms and highly nonlinear characteristics. Then the deformation and tensile force of GRs are accordingly calculated, and the 3-D analytical method for the pile-supported GRs is established. Finally, the rationality of the method is validated primitively by comparing the calculated and observed results of a field test example.
李晓龙, 史宏彦. 基于比拟方程法的桩承式加筋体三维分析方法[J]. 岩土工程学报, 2020, 42(5): 925-933.
LI Xiao-long, SHI Hong-yan. 3-D analysis method for pile-supported geosynthetic reinforcements based on analog equation method. Chinese J. Geot. Eng., 2020, 42(5): 925-933.
 JONES B M, PLAUT R H, FILZ G.M. Analysis of geosynthetic reinforcement in pile-supported embankments. Part I: 3D plate model[J]. Geosynthetics International, 2010, 17(2): 59-67.  HALVORDSON K A, PLAUT R H, FILZ G M.Analysis of geosynthetic reinforcement in pile-supported embankments: Part II 3D cable-net model[J]. Geosynthetics International, 2010, 17(2): 68-76.  PLAUT R H, FILZ G M.Analysis of geosynthetic reinforcement in pile-supported embankments. Part Ⅲ: Axisymmetric model[J]. Geosynthetics International, 2010, 17(2): 77-85.  饶为国, 江辉煌, 侯庆华. 桩-网复合地基工后沉降的薄板理论解[J]. 水利学报, 2002(4): 23-27. (RAO Wei-guo, JIANG Hui-huang, HOU Qing-hua.Deformation of sheet plate due to residual settlement of pile-net composite foundation[J]. Journal of Hydraulic Engineering, 2002(4): 23-27. (in Chinese))  郑俊杰, 张军, 马强, 等. 双向增强体复合地基桩土应力比三维分析[J]. 华中科技大学学报(自然科学版), 2010, 38(2): 83-86. (ZHENG Jun-jie, ZHANG Jun, MA Qiang, et al.Three dimensional analysis of pile-earth stress ratio of biaxial reinforcement composite foundation[J]. Journal of Huazhong University of Science and Technology(Natural Science Edition), 2010, 38(2): 83-86. (in Chinese))  张军, 郑俊杰, 马强. 路堤荷载下双向增强体复合地基受力机理分析[J]. 岩土工程学报, 2010, 32(9): 1392-1398. (ZHANG Jun, ZHENG Jun-jie, MA Qiang.Mechanical performance of biaxial reinforcement composite foundation under embankment loads[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(9): 1392-1398. (in Chinese))  赵明华, 刘猛, 张锐, 等. 路堤荷载下双向增强复合地基荷载分担比及沉降计算[J]. 岩土工程学报, 2014, 36(12): 2161-2169. (ZHAO Ming-hua, LIU Meng, ZHANG Rui, et al.Calculation of load sharing ratio and settlement of bidirectional reinforced composite foundation under embankment loads[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(12): 2161-2169. (in Chinese))  闫澍旺, 郎瑞卿, 孙立强,等. 基于薄板理论的刚性桩网复合地基桩土应力比计算[J]. 岩石力学与工程学报, 2017, 36(8): 2051-2060. (YAN Shu-wang, LANG Rui-qing, SUN Li-qiang, et al.Calculation of pile-soil stress ratio in composite foundation with rigid pile-net based on plate theory[J]. Chinese Journal of Rock Mechanics and Engineering, 2017, 36(8): 2051-2060. (in Chinese))  李波, 黄茂松, 叶观宝. 加筋桩承式路堤的三维土拱效应分析与试验验证[J].中国公路学报, 2012, 25(1): 13-20. (LI Bo, HUANG Mao-song, YE Guan-bao.Analysis of three -dimensional soil arching effect of pile-supported embankment with geosynthetics and its test verification[J]. China Journal of Highway and Transport, 2012, 25(1): 13-20. (in Chinese))  徐超, 林潇, 沈盼盼. 桩承式加筋路堤张力膜效应模型试验研究[J].岩土力学, 2016, 37(7): 1825-1831. (XU Chao, LIN Xiao, SHEN Pan-pan.Model tests of tensile membrane effect of geosynthetic-reinforced piled embankments[J]. Rock and Soil Mechanics, 2016, 37(7): 1825-1831. (in Chinese))  庄妍, 崔晓艳, 王康宇. 考虑加筋体三维变形的桩承式路堤沉降计算方法[J]. 天津大学学报(自然科学与工程技术版), 2019, 52(12): 1227-1234. (ZHUANG Yan, CUI Xiao-yan, WANG Kang-yu.A method to analyze the settlement of reinforced piled embankment considering the three-dimensional deformation of geosynthetic reinforced structure[J]. Journal of Tianjin University(Science and Technology), 2019, 52(12): 1227-1234. (in Chinese))  KANG Fei.A simplified method for analysis of geosynthetic reinforcement used in pile supported embankments[J]. The Scientific World Journal, 2014: 1-9, doi: 10.1155/2014/ 273253.  VAN EEKELEN S J M, BEZUIJEN A, VAN TOL A F. An analytical model for arching in piled embankments[J]. Geotextiles and Geomembranes, 2013, 39: 78-102.  TSIATAS G C, KATSIKADELIS J T.Large deflection analysis of elastic space membranes[J]. International Journal for Numerical Methods in Engineering, 2006, 65: 264-294.  KATSIKADELIS J T.The analog equation method. A powerful BEM-based solution technique for solving linear and non-linear engineering problems[J]. Boundary Element Method Ⅷ, 1994: 167-182.  KATSIKADELIS J T, NERANTZAKI M S, TSIATAS G C.The analog equation method for large deflection analysis of membranes: a boundary-only solution[J]. Computational Mechanics, 2001, 27: 513-523.  KATSIKADELIS J T, TSIATAS G C.The analog equation method for large deflection analysis of heterogeneous orthotropic membranes: a boundary-only solution[J]. Engineering Analysis with Boundary Elements, 2001, 25: 655-667.  GOLDBERG M A, CHEN C S, KAPUR S P.Improved multiquadric approximation for partial differential equations[J]. Engineering Analysis with Boundary elements, 1996, 18: 9-17.  ALMEIDA M S S, EHRLICH M, SPOTTI A P, et al. Embankment supported on piles with biaxial geogrids[C]// Proceedings of the Institution of Civil Engineers, Geotechnical Engineering 160, 2007, Issue GE4: 185-192.  ALMEIDA M S S, MARQUES M ES, ALMEIDA M C F, et al. Performance of two “low” piled embankments with geogrids at rio de janeiro[C]// Proceedings of the First Pan American Geosynthetics Conference and Exhibition, 2008, Cancun: 1285-1295.  VAN EEKELEN S J M, ALMEIDA M S S, BEZUIJEN A. European analytical calculations compared with a full-scale Brazilian piled embankment[C]// Proceedings of IGS10, 2014, Berlin.  VAN EEKELEN S J M, BEZUIJEN A, VAN TOL A F. Validation of analytical models for the design of basal reinforced piled embankments[J]. Geotextiles and Geomembranes, 2015, 43: 56-81.