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刚性挡墙绕底转动时的非极限主动土压力数值解

马明 李明东 郎钞棚 张京伍 万愉快

马明,李明东,郎钞棚,张京伍,万愉快. 刚性挡墙绕底转动时的非极限主动土压力数值解 [J]. 应用数学和力学,2022,43(3):312-321 doi: 10.21656/1000-0887.420178
引用本文: 马明,李明东,郎钞棚,张京伍,万愉快. 刚性挡墙绕底转动时的非极限主动土压力数值解 [J]. 应用数学和力学,2022,43(3):312-321 doi: 10.21656/1000-0887.420178
MA Ming, LI Mingdong, LANG Chaopeng, ZHANG Jingwu, WAN Yukuai. Numerical Solutions of the Nonlimit-State Active Earth Pressure Under Backfill Wall Rotation Around the Bottom[J]. Applied Mathematics and Mechanics, 2022, 43(3): 312-321. doi: 10.21656/1000-0887.420178
Citation: MA Ming, LI Mingdong, LANG Chaopeng, ZHANG Jingwu, WAN Yukuai. Numerical Solutions of the Nonlimit-State Active Earth Pressure Under Backfill Wall Rotation Around the Bottom[J]. Applied Mathematics and Mechanics, 2022, 43(3): 312-321. doi: 10.21656/1000-0887.420178

刚性挡墙绕底转动时的非极限主动土压力数值解

doi: 10.21656/1000-0887.420178
基金项目: 国家自然科学基金(51869001)
详细信息
    作者简介:

    马明(1997—),男,硕士生 (E-mail:maming@ecut.edu.cn

    李明东(1981—),男,教授,博士(通讯作者. E-mail:lmd@ecit.edu.cn

  • 中图分类号: O39

Numerical Solutions of the Nonlimit-State Active Earth Pressure Under Backfill Wall Rotation Around the Bottom

  • 摘要:

    刚性挡土墙在下部受限时往往呈现绕墙底转动的位移模式,该模式下不同深度土体所处非极限状态不同,给土压力计算带来了困难。在已有研究基础上,推导了适用于绕墙底转动模式下土体强度参数与墙体位移的函数关系;假定墙后土体形成圆弧形土拱,滑裂面为不确定的曲面,将墙后土体按小步长水平分层,构建了绕墙底转动模式下非极限主动土压力的数值迭代格式,给出了该模式下非极限主动土压力的数值计算方法。该数值解既能确定墙后滑裂面的形状,又能计算非极限主动土压力的强度、合力及作用点。将数值解与模型试验结果、现有解析解进行了对比,发现墙后滑裂面为一曲面,该解计算结果与模型试验结果的契合度比现有解析解更高。这提供了刚性挡土墙绕底转动时非极限主动土压力的更精确解答,对这类挡土墙设计具有现实指导价值。

  • 图  1  RB位移模式下土体非极限状态与T模式的不同

    Figure  1.  The difference of soil non-limit state between the RB model and the T model

    图  2  应力Mohr圆

    Figure  2.  Mohr’s circle for states of stress

    图  3  内摩擦角随墙体位移比的变化情况

    Figure  3.  The variation law for the internal friction angle with the wall displacement ratio

    图  4  土拱及土体应力分析

    Figure  4.  The soil arch and its stress analysis

    图  5  土体水平条分及受力分析

    Figure  5.  The division and stress analysis of horizontal slices in this method

    图  7  土压力合力及作用点对比结果

    Figure  7.  The resultant forces of earth pressure and the comparison results of action points

    图  8  滑裂面对比结果

    Figure  8.  Comparison of sliding surfaces

    图  6  土压力分布对比结果:(a) 与模型试验对比结果;(b) 与其他解析解对比结果

    Figure  6.  Comparison results of earth pressure distributions: (a) comparison results with model tests; (b) comparison results with other analytical solutions

  • [1] BANG S. Active earth pressure behind retaining walls[J]. Journal of Geotechnical Engineering, 1985, 111(3): 407-412. doi: 10.1061/(ASCE)0733-9410(1985)111:3(407)
    [2] 张常光, 单冶鹏, 高本贤, 等. 刚性挡墙位移土压力的数学拟合公式研究综述[J]. 土木与环境工程学报(中英文), 2020, 42(6): 19-30. (ZHANG Changguang, SHAN Yepeng, GAO Benxian, et al. State-of-the-art review on displacement-dependent earth pressure formulations of rigidretaining walls via mathematical fitting functions[J]. Journal of Civil and Environmental Engineering, 2020, 42(6): 19-30.(in Chinese)
    [3] 卢坤林, 杨扬. 非极限主动土压力计算方法初探[J]. 岩土力学, 2010, 31(2): 615-619. (LU Kunlin, YANG Yang. Preliminary study of active earth pressure under nonlimit state[J]. Rock and Soil Mechanics, 2010, 31(2): 615-619.(in Chinese) doi: 10.3969/j.issn.1000-7598.2010.02.047
    [4] ZHOU Y T, CHEN Q S, CHEN F Q, et al. Active earth pressure on translating rigid retaining structures considering soil arching effect[J]. European Journal of Environmental and Civil Engineering, 2018, 22(8): 910-926. doi: 10.1080/19648189.2016.1229225
    [5] 王元战, 唐照评, 郑斌. 墙体绕墙顶转动情况下挡土墙主动土压力分布[J]. 应用数学和力学, 2004, 25(7): 695-700. (WANG Yuanzhan, TANG Zhaoping, ZHENG Bin. Distribution of active earth pressure of retaining wall with wall movement of rotation about top[J]. Applied Mathematics and Mechanics, 2004, 25(7): 695-700.(in Chinese) doi: 10.3321/j.issn:1000-0887.2004.07.005
    [6] 刘忠玉, 陈捷. 平动模式下考虑剪应力作用的刚性挡土墙主动土压力计算[J]. 岩土工程学报, 2016, 38(12): 2254-2261. (LIU Zhongyu, CHEN Jie. Active earth pressure against rigid retaining wall considering shear stress under translation mode[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(12): 2254-2261.(in Chinese) doi: 10.11779/CJGE201612014
    [7] XIE Y, LESHCHINSKY B. Active earth pressures from a log-spiral slip surface with arching effects[J]. Géotechnique Letters, 2016, 6(2): 149-155.
    [8] LIU M L, CHEN X S, HU Z Z, et al. Active earth pressure of limited c-ϕ soil based on improved soil arching effect[J]. Applied Sciences, 2020, 2020(10): 3243.
    [9] WANG Z H, WU A X, WANG Y M. Calculation of active earth pressure for narrow backfill with a curved slip surface[J]. Advances in Civil Engineering, 2019, 2019: 3025401.
    [10] XU S Y, KANNANGARA K K P M, TACIROGLU E. Analysis of the stress distribution across a retaining wall backfill[J]. Computers and Geotechnics, 2018, 103: 13-25. doi: 10.1016/j.compgeo.2018.07.001
    [11] 陈建旭, 宋文武. 平动模式下挡土墙非极限主动土压力[J]. 岩土力学, 2019, 40(6): 2284-2292. (CHEN Jianxu, SONG Wenwu. Non-limit active earth pressure for retaining wall under translational motion[J]. Rock and Soil Mechanics, 2019, 40(6): 2284-2292.(in Chinese)
    [12] 陈建旭, 郭宁, 虞佳颖, 等. 刚性挡墙非极限被动土压力计算方法[J]. 长江科学院院报, 2020, 37(11): 107-113, 135. (CHEN Jianxu, GUO Ning, YU Jiaying, et al. Method of calculating non-limit passive earth pressure of rigid retaining wall[J]. Journal of Yangtze River Scientific Research Institute, 2020, 37(11): 107-113, 135.(in Chinese) doi: 10.11988/ckyyb.20190918
    [13] LI D, WANG W, ZHANG Q C. Lateral earth pressure behind walls rotating about base considering arching effects[J]. Mathematical Problems in Engineering, 2014, 2014: 715891.
    [14] 陈建旭, 宋文武, 罗旭, 等. 绕墙底转动挡土墙非极限主动土压力[J]. 中国科技论文, 2018, 13(17): 2045-2049. (CHEN Jianxu, SONG Wenwu, LUO Xu, et al. Non-limit state active earth pressure behind retaining wall rotating about the base[J]. Chinese Science and Technology Paper, 2018, 13(17): 2045-2049.(in Chinese) doi: 10.3969/j.issn.2095-2783.2018.17.017
    [15] 陈奕柏, 柯才桐, 高洪波, 等. 考虑变位影响的刚性挡墙非极限土压力研究[J]. 岩石力学与工程学报, 2015, 34(5): 1060-1070. (CHEN Yibai, KE Caitong, GAO Hongbo, et al. Nonlimit state earth pressure against retaining wall considering influence of deformation[J]. Chinese Journal of Rock Mechanics and Engineering, 2015, 34(5): 1060-1070.(in Chinese)
    [16] 周应英, 任美龙. 刚性挡土墙主动土压力的试验研究[J]. 岩土工程学报, 1990, 12(2): 19-26. (ZHOU Yingying, REN Meilong. An experimental study on active earth pressure behind rigid retaining wall[J]. Chinese Journal of Geotechnical Engineering, 1990, 12(2): 19-26.(in Chinese) doi: 10.3321/j.issn:1000-4548.1990.02.003
    [17] 沈靠山. 覆盖层砂卵石料静止侧压力系数研究[D]. 硕士学位论文. 南京: 河海大学, 2009.

    SHEN Kaoshan. Study of coefficient of earth pressure at rest on gravel soil[D]. Master Thesis. Nanjing: Hohai University, 2009. (in Chinese)
    [18] 蔡正银, 代志宇, 徐光明, 等. 颗粒粒径和密实度对砂土K0值影响的离心模型试验研究[J]. 岩土力学, 2020, 41(12): 3882-3888. (CAI Zhengyin, DAI Zhiyu, XU Guangming, et al. Effect of particle size and compaction on K0 value of sand by centrifugal model test[J]. Rock and Soil Mechanics, 2020, 41(12): 3882-3888.(in Chinese)
    [19] 宋飞, 张建民, 刘超. 各向异性砂土K0试验研究[J]. 岩土力学, 2010, 31(12): 3727-3732, 3740. (SONG Fei, ZHANG Jianmin, LIU Chao. Experimental study of K0 of anisotropic sand[J]. Rock and Soil Mechanics, 2010, 31(12): 3727-3732, 3740.(in Chinese) doi: 10.3969/j.issn.1000-7598.2010.12.006
    [20] 施建勇, 雷国辉, 艾英钵, 等. 土压力变化规律的应力路径三轴试验研究[J]. 岩土力学, 2005, 26(11): 1700-1704. (SHI Jianyong, LEI Guohui, AI Yingbo, et al. Stress path controlled triaxial experimental study of lateral earth pressure behaviour[J]. Rock and Soil Mechanics, 2005, 26(11): 1700-1704.(in Chinese) doi: 10.3969/j.issn.1000-7598.2005.11.002
    [21] HANDY R L. The arch in soil arching[J]. Journal of Geotechnical Engineering, 1985, 111(3).
    [22] 王杰, 夏唐代, 贺鹏飞, 等. 考虑土拱效应的刚性挡墙主动土压力分析[J]. 岩土力学, 2014, 35(7): 1914-1920. (WANG Jie, XIA Tangdai, HE Pengfei, et al. Analysis of active earth pressure on rigid retaining walls considering soil arching[J]. Rock and Soil Mechanics, 2014, 35(7): 1914-1920.(in Chinese)
    [23] 徐日庆, 徐叶斌, 程康, 等. 有限土体下考虑土拱效应的非极限主动土压力解[J]. 岩土工程学报, 2020, 42(2): 362-371. (XU Riqing, XU Yebin, CHENG Kang, et al. Method to calculate active earth pressure considering soil arching effect under nonlimit state of clay[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(2): 362-371.(in Chinese)
    [24] 刘洋, 于鹏强. 刚性挡土墙平移模式的土拱形状与主动土压力分析[J]. 岩土力学, 2019, 40(2): 506-516, 528. (LIU Yang, YU Pengqiang. Analysis of soil arch and active earth pressure on translating rigid retaini-ng walls[J]. Rock and Soil Mechanics, 2019, 40(2): 506-516, 528.(in Chinese)
    [25] 杨明辉, 戴夏斌, 赵明华, 等. 墙后有限宽度无黏性土主动土压力试验研究[J]. 岩土工程学报, 2016, 38(1): 131-137. (YANG Minghui, DAI Xiabin, ZHAO Minghua, et al. Experimental study on active earth pressure of cohesionless soil with limited width behind retaining wall[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(1): 131-137.(in Chinese) doi: 10.11779/CJGE201601014
    [26] IRDMOOSA G, SHAHIR H. Analytical solution for active earth pressure of c-ϕ soil considering arching effect[J]. Geomechanics and Geoengineering, 2019, 14(2): 71-84. doi: 10.1080/17486025.2018.1533649
    [27] HU W, LIU K, ZHU X, et al. Active earth pressure against rigid retaining walls for finite soils in sloping condition considering shear stress and soil arching effect[J]. Advances in Civil Engineering, 2020, 2020: 6791301.
    [28] FANG Y S, ISHIBASHI I. Static earth pressures with various wall movements[J]. Journal of Geotechnical Engineering, 1986, 112(3): 317-333. doi: 10.1061/(ASCE)0733-9410(1986)112:3(317)
    [29] 王海, 周亦涛, 江文放. RB模式下考虑土拱效应的非极限主动土压力[J]. 公路, 2016, 61(10): 29-35. (WANG Hai, ZHOU Yitao, JIANG Wenfang. Non-limit active earth pressure with wall movement of rotation considering soil arching effect[J]. Highway, 2016, 61(10): 29-35.(in Chinese)
    [30] 章瑞文, 徐日庆. 土拱效应原理求解挡土墙土压力方法的改进[J]. 岩土力学, 2008, 29(4): 1057-1060, 1066. (ZHANG Ruiwen, XU Riqing. Solution of problem of earth pressure on retaining wall calculated by method of soil arching effect[J]. Rock and soil Mechanics, 2008, 29(4): 1057-1060, 1066.(in Chinese) doi: 10.3969/j.issn.1000-7598.2008.04.038
    [31] 茅以升. 挡土墙土压力的两个经典理论中的基本问题[J]. 土木工程学报, 1954, 1(3): 249-281. (MAO Yisheng. Some apparent discrepancies in Coulomb’s theory and unjustifiable questions about Rankine’s theory for earth pressure on retaining walls[J]. China Civil Engineering Journal, 1954, 1(3): 249-281.(in Chinese)
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出版历程
  • 收稿日期:  2021-06-29
  • 录用日期:  2021-10-07
  • 修回日期:  2021-10-07
  • 网络出版日期:  2022-02-11
  • 刊出日期:  2022-03-08

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