交通荷载作用下低填方路堤加筋体受力及变形解析方法研究

Research on Analytical Method of Force and Deformation of Reinforcement in Low-Fill Embankment Under Traffic Loading

摘要

在软土地区广泛采用的桩承式加筋路堤中,交通荷载的作用以及下部桩-土的不均匀沉降是导致低填方路堤产生显著变形的主要因素．这类结构中的关键力学现象包括土拱效应和张拉膜效应,使得加筋材料内部的应变分布呈现出从桩间软土上方逐渐向桩顶增加的趋势,并且在桩帽边缘处达到最大值．加筋体内部的最大应变不仅受到上部路堤自重及过往车辆等动态负载的影响,还与桩间距、下层软土的压缩性能密切相关．为深入理解这一复杂问题,本文引入了Kirchhoff薄板理论作为分析框架．基于此假设将加筋体及其垫层视为遵循Kirchhoff条件的理想化薄板模型进行处理．具体而言,在4根支撑桩之间的区域里,设定了1种特定形式的挠度函数,该函数由幂函数与双曲正弦函数组成,用以描述加筋材料在水平方向上的弯曲行为．通过求解满足Kirchhoff薄板平衡微分方程及相应几何约束条件下的未知参数,推导获得加筋体在桩间软土上方区域内沉降分布与应变分布的解析表达式．研究结果表明：当加筋体位于两根相邻桩之间时,其垂直方向上的最大位移通常出现在这两根桩中心连线的中点位置,而最大拉伸或压缩应变则集中在每个桩顶部边缘附近．同时,本文还分析了加筋体刚度和桩净距对加筋体桩间最大应变的影响．本文为优化设计此类特殊地质条件下使用的桩承式加筋路堤提供了重要的理论依据和技术支持．

Abstract

In the pile-supported reinforced embankment widely used in soft soil areas, the effect of traffic load and the uneven settlement of the lower pile-soil are the main factors leading to the significant deformation of low-fill embankment. The key mechanical phenomena in this kind of structure include soil arching effect and tensile membrane effect, which makes the strain distribution inside the reinforced material gradually increase from the top of soft soil between piles to the pile top and reach the maximum at the edge of the pile cap. The maximum strain inside the reinforced body is not only affected by the self-weight of the upper embankment and the dynamic load of passing vehicles, but also closely related to the pile spacing and the compression performance of the lower soft soil. In order to deeply understand this complex problem, the Kirchhoff thin plate theory is introduced as an analytical framework in this paper. Based on this assumption, the stiffened body and its cushion are treated as an idealized thin plate model that follows the Kirchhoff condition. Specifically, in the area between four supporting piles, a specific form of deflection function is set up, which is composed of a power function and a hyperbolic sine function to describe the bending behavior of the reinforced material in the horizontal direction. By solving the Kirchhoff thin plate equilibrium differential equation and the unknown parameters under the corresponding geometric constraints, the analytical expressions of settlement distribution and strain distribution of the reinforced body in the area above the soft soil between piles are derived. Results show that when the reinforced body is located between two adjacent piles, the maximum displacement in the vertical direction usually occurs at the midpoint of the center line of the two piles, while the maximum tensile or compressive strain is concentrated near the top edge of each pile. At the same time, the influence of reinforcement stiffness and pile spacing on the maximum strain between reinforced piles is also analyzed. This study provides an important theoretical basis and technical support for optimizing the design of pile-supported reinforced embankments used under such special geological conditions.

关键词

低填方路堤 / 交通荷载 / 土拱效应 / 加筋体应变 / Kirchhoff 假定

Key words

low-fill embankment / traffic load / soil arching effect / reinforcement strain / Kirchhoff’s assumption

参考文献

[1] Liu S, Yu H Y, Zhao C, et al. Evolution of soil arching in geosynthetic—reinforced pile—supported embankment of a high—speed railway under long—term train traffic loading and excessive subsoil settlement[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2025, 151(5):04025028.

[2] Zhang D, Yang G Q, Li T, et al. Model tests study of multi—layer geosynthetic—reinforced pile—supported embankments and evaluation of analytical design models[J]. Transportation Geotechnics, 2025, 51:101521.

[3] Xiong C X, Guo Z X, Xing Z Q, et al. An analytical solution for settlement of pile—supported reinforced low embankment considering lateral friction along pile shaft[J]. Transportation Geotechnics, 2025, 50:101478.

[4] Agarwal E, Luo N, Liu K W. Probabilistic analyses of geosynthetic—reinforced pile—supported embankments using design methods and 3D finite element models considering soil variability[J]. Geotextiles and Geomembranes, 2025, 53(2):559-576.

[5] Nguyen T C B, Vu D L, Pham M T, et al. 3D numerical investigation of soil arching in deep cement mixing and stiffened deep cement mixing pile—supported embankments[J]. Transportation Infrastructure Geotechnology, 2025, 12(1):13.

[6] Xu C B, Zhang J, Zheng J J, et al. Influence of pile type on the load transfer mechanism in pile—supported low embankments under cyclic loading[C]// 5th International Conference on Transportation Geotechnics. Sydney, Australia, 2024:259-267.

[7] Li G Y, Xu C, Yoo C, et al. Performance of unreinforced and geogrid—reinforced pile—supported embankments under localized surface loading: Analytical investigation[J]. Geotextiles and Geomembranes, 2025, 53(1):260-276.

[8] Sun R, Jiang X, Zhang L, et al. DEM analysis of load transfer in double—layer geosynthetic—reinforced pile—supported embankments[J]. Computational Particle Mechanics, 2025, 12(1):721-735.

[9] 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.

[10] Yan Shuwang, Lang Ruiqing, Sun Liqiang, 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).

[11] 王一楠, 陈梅君. 悬链线法计算桩承式加筋路堤的土拱形态[J]. 岩土工程学报, 2021, 43(增2):276-279.

[12] Wang Yinan, Chen Meijun. Forms of soil arch in GRPS embankment by catenary method[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(Suppl 2):276-279(in Chinese).

[13] 王建军, 陈福全, 李大勇. 低填方加筋路基沉降的Kerr模型解[J]. 岩土力学, 2019, 40(1):250-259.

[14] Wang Jianjun, Chen Fuquan, Li Dayong. A simple solution of settlement for low reinforced embankments on Kerr foundation[J]. Rock and Soil Mechanics, 2019, 40(1):250-259(in Chinese).

[15] 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.

[16] LI Xiaolong, Shi Hongyan. 3—D analysis method for pile—supported geosynthetic reinforcements based on analog equation method[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(5):925-933(in Chinese).

[17] Fang H, Zheng J J, Liu Y, et al. Analytical solutions of the dynamic response of a dual—beam model for a geosynthetic reinforced pile—supported embankment under moving load[J]. Computers and Geotechnics, 2022, 142:104563.

[18] 孙璐, 邓学钧. 运动负荷下黏弹性Kelvin地基上无限大板的稳态响应[J]. 岩土工程学报, 1997, 19(2):14-22.

[19] Sun Lu, Deng Xuejun. Steady response of infinite plate on viscoelastic Kelvin foundation to moving load[J]. Chinese Journal of Geotechnical Engineering, 1997, 19(2):14-22(in Chinese).

[20] 姚海林, 卢正, 罗海宁, 等. 交通荷载作用下Kelvin地基上不平整路面的动力响应分析[J]. 岩土力学, 2009, 30(4):890-896.

[21] Yao Hailin, Lu Zheng, Luo Haining, et al. Dynamic response of rough pavement on Kelvin foundation subjected to traffic loads[J]. Rock and Soil Mechanics, 2009, 30(4):890-896(in Chinese).

[22] BS 8006—1 Code of Practice for Strengthened/Reinforced Soils and Other Fills, Incorporating Corrigendum 1[S]. London: British Standards Institution, 2012.

[23] Kiendl J, Bletzinger K U, Linhard J, et al. Isogeometric shell analysis with Kirchhoff—Love elements[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(49/50/51/52):3902-3914.

[24] 张福范. 以Kirchhoff薄板理论解狭长矩形截面杆的约束扭转[J]. 应用数学和力学, 1982, 3(4):463-476.

[25] Zhang Fufan. On the restrained torsion of narrow rectangular cross section by Kirchhoff’s thin plate theory[J]. Applied Mathematics and Mechanics, 1982, 3(4):463-476(in Chinese).

[26] Bonaldi F, Di Pietro D A, Geymonat G, et al. A hybrid high—order method for Kirchhoff—Love plate bending problems[J]. ESAIM: Mathematical Modelling and Numerical Analysis, 2018, 52(2):393-421.

[27] Ciarlet P G, Mardare C. An intrinsic formulation of the Kirchhoff—Love theory of linearly elastic plates[J]. Analysis and Applications, 2018, 16(4):565-584.

[28] 张玲, 程钦桂, 赵明华. 基于双层Euler梁理论的土工格室加筋体变形计算[J]. 湖南大学学报(自然科学版), 2017, 44(9):114-121.

[29] Zhang Ling, Cheng Qingui, Zhao Minghua. Deformation calculation of geocell reinforcement based on the double Euler beams theory[J]. Journal of Hunan University(Natural Sciences), 2017, 44(9):114-121(in Chinese).

[30] Terzaghi K. Theoretical Soil Mechanics[M]. New York: John Wiley & Sons, Inc., 1943.

[31] Hewlett W J, Randolph M F. Analysis of piled embankment[J]. Ground Engineering, 1988, 21(3):12-18.

[32] 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.

[33] Spangler M G, Handy R L. Soil Engineering[M]. London: Intext Educational Publishers, 1973.

[34] GB 50307—1999 地下铁道、轻轨交通岩土工程勘察规范[S]. 北京: 中国计划出版社, 1999.

[35] GB 50307—1999 Code on Geotechnical Investigations for Metro and Light Rail Transit[S]. Beijing: China Planning Press, 1999(in Chinese).

[36] GB 50307—2012 城市轨道交通岩土工程勘察规范城市轨道交通岩土工程勘察规范[S]. 北京: 中国计划出版社, 2012.

[37] GB 50307—2012 Code for Geotechnical Investigations of Urban Rail Transit[S]. Beijing: China Planning Press, 2012(in Chinese).

[38] 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.

[39] Zheng Junjie, 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 & Technology(Natural Science Edition), 2010, 38(2):83-86(in Chinese).

[40] 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.

[41] Zhang Jun, Zheng Junjie, 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).

[42] JT/T925.1—2014 公路工程土工合成材料 土工格栅 第1部分: 钢塑格栅[S]. 北京: 人民交通出版社股份有限公司, 2014.

[43] JT/T925.1—2014 Geosynthetics in Highway Engineerings—Geogrids—Part 1: Steel—Plastic Compound Geogrid[S]. Beijing: People’s Communications Publishing House Co., Ltd., 2014(in Chinese).

[44] 陆运生. 交通荷载作用下低填方路堤加筋体工作性能研究[D]. 南京: 东南大学土木工程学院, 2024.

[45] Lu Yunsheng. Study on the Working Performance of Reinforced Body of Low Fill Embankment Under Traffic Load[D]. Nanjing: School of Civil Engineering, Southeast University, 2024(in Chinese).

基金资助

国家自然科学基金优秀青年科学基金资助项目(51922029)

国家自然科学基金资助项目(52178316)