考虑井阻及涂抹作用的非饱和土竖井地基固结解析解

秦爱芳 许薇芳 李天义

秦爱芳,许薇芳,李天义. 2021. 考虑井阻及涂抹作用的非饱和土竖井地基固结解析解[J]. 工程地质学报,29(1):214-221. doi:10.13544/j.cnki.jeg.2019-572 doi: 10.13544/j.cnki.jeg.2019-572
引用本文: 秦爱芳,许薇芳,李天义. 2021. 考虑井阻及涂抹作用的非饱和土竖井地基固结解析解[J]. 工程地质学报,29(1):214-221. doi:10.13544/j.cnki.jeg.2019-572 doi: 10.13544/j.cnki.jeg.2019-572
Qin Aifang, Xu Weifang, Li Tianyi. 2021. Analytical solution to consolidation of unsaturated soil with vertical drain considering drain resistance and smear effect[J]. Journal of Engineering Geology, 29(1): 214-221. doi: 10.13544/j.cnki.jeg.2019-572
Citation: Qin Aifang, Xu Weifang, Li Tianyi. 2021. Analytical solution to consolidation of unsaturated soil with vertical drain considering drain resistance and smear effect[J]. Journal of Engineering Geology, 29(1): 214-221. doi: 10.13544/j.cnki.jeg.2019-572

考虑井阻及涂抹作用的非饱和土竖井地基固结解析解

doi: 10.13544/j.cnki.jeg.2019-572
基金项目: 

国家自然科学基金面上项目 42072292

详细信息
    作者简介:

    秦爱芳(1966-),女,博士,教授,主要从事非饱和土固结、核废料地质处置研究. E-mail: qinaifang@shu.edu.cn

  • 中图分类号: TU431

ANALYTICAL SOLUTION TO CONSOLIDATION OF UNSATURATED SOIL WITH VERTICAL DRAIN CONSIDERING DRAIN RESISTANCE AND SMEAR EFFECT

Funds: 

the National Natural Science Foundation of China 42072292

  • 摘要: 以往的非饱和土竖井地基研究中未同时考虑竖井的井阻和涂抹作用,大部分按理想竖井进行研究,然而井阻和涂抹作用是影响非饱和土竖井地基固结的重要因素。针对这种情况,本文基于Fredlund非饱和土一维固结理论及等应变假设,引入变量将超孔隙压力耦合控制方程组转化为等价的线性偏微分方程组,考虑涂抹和井阻条件,并采用分离变量法和待定系数法,推导出了瞬时荷载下同时考虑井阻和涂抹作用的非饱和土竖井地基等应变固结解析解。将所得解析解进行退化,与既有的饱和土竖井地基等应变固结解析解对比,验证了本文解析解的正确性,并应用典型算例分析了井阻和涂抹作用对竖井地基固结的影响。结果表明,井阻因子G、井径比N、涂抹系数α及涂抹半径与竖井半径比S这四者任何一个值减小,非饱和土竖井地基的固结速度都将变快;井阻因子G小于0.1时,建议实际工程中不考虑井阻作用的影响;当涂抹半径与竖井半径比S大于5时,涂抹作用对竖井地基固结的影响与S=5时无明显差异。实际工程中建议提高非饱和土竖井地基的透水能力并减少施工扰动,以降低井阻和涂抹作用对非饱和土竖井地基固结影响。
  • 图  1  非饱和土竖井地基固结计算模型

    Figure  1.  Consolidation modeling of vertical drain foundations in unsaturated soils

    图  2  uauw在不同G时的消散曲线

    Figure  2.  Dissipation curves of ua and uwunder different G

    图  3  相对偏差WaWw的变化曲线

    Figure  3.  The change curves of relative deviation WaWw

    图  4  uauw在不同N时的消散曲线

    Figure  4.  Dissipation curves of ua and uwunder different N

    图  5  uauw在不同α时的消散曲线

    Figure  5.  Dissipation curves of ua and uw under different α

    图  6  uauw在不同S时的消散曲线

    Figure  6.  Dissipation curves of ua and uw under different S

  • Barron R A. 1948. Consolidation of fine-grained soils by drain wells[J]. Transactions of the American Society of Civil Engineers, 113(1): 718-742. doi: 10.1061/TACEAT.0006098
    Biot M A. 1941. General theory of three-dimensional consoli dation[J]. Journal of Applied Physics, 12(2): 155-164. doi: 10.1063/1.1712886
    Chen G H, Xie K H, Chen Y F, et al. 2011. Analytical solution for consolidation of sand-drained ground considering variation of permeability coefficient in smeared zone[J]. Journal of Zhejiang University, 45(4): 665-670.
    Fredlund D G, Hasan J U. 1979. One-dimensional consolidate-on theory: unsaturated soils[J]. Canadian Geotechnical Journal, 16(3): 521-531. doi: 10.1139/t79-058
    Gu Y Y. 2017. One-dimensional settlement theory and its influence factors of subgrade of unsaturated and soft soil[D]. Chongqing:: Chongqing University.
    Ho L, Fatahi B. 2018. Analytical solution to axisymmetric consoledation of unsaturated soil stratum under equal strain condition incorporating smear effects[J]. International Journal for Numerical and Analytical Methods in Geomechics, 42(15): 1890-1913. doi: 10.1002/nag.2838
    Li L Z, Wang L, Li P C, et al. 2018. One-dimensional consolidation of fractional derivative viscoelastic saturated soil layer with symmetric semi-permeable boundaries under arbitrary loading[J]. Journal of Engineering Geology, 26(6): 1480-1489.
    Qin A F, Chen G. J, Tan Y W, et al. 2008. Analytical solution to one dimensional consolidation in unsaturated soils[J]. Applied Mathematics and Mechanics, 29(10): 1329-1340. doi: 10.1007/s10483-008-1008-x
    Qin A F, Li T Y, Pei Y C Q, et al. 2019. Consolidation characteristics of drainage well foundation in unsaturated soils with semi permeable boundary[J]. Journal of Engineering Geology, 27(2): 390-397.
    Qin A F, Sun D A, Tan Y W. 2010. Semi-analytical solution for one-dimensional consolidation in unsaturated soils[J]. Applied Mathematics and Mechanics, 31(2): 199-209.
    Qin A F, Yu J F, Ge H. 2017. Analysis of consolidation of free drainage well in unsaturated soil with variable permeability coefficient within smear zone[J]. Journal of Engineering Geology, 25(3): 605-611.
    Tang X W, Onitsuka K. 2001. Consolidation of double layered ground with vertical drain[J]. International Journal for Numerical and Analytical Methods in Geomechics, 25(14): 1449-1465. doi: 10.1002/nag.191
    Terzaghi K. 1943. Theoretical soil mechanics[M]. New York: John Wiley and Sons Inc.
    Wang L, Sun D A, Li L H, et al. 2017a. Semi-analytical solutions to one-dimensional consolidation for unsaturated soils with symmetric semi-permeable drainage boundary[J]. Compu-ters and Geotechnics, 89: 71-80. doi: 10.1016/j.compgeo.2017.04.005
    Wang L, Sun D A, Qin A F. 2017b. General semi-analytical solutions to one-dimensional consolidation for unsaturated soils[J]. Applied Mathematics and Mechanics(English Edition), 38(6): 831-850. doi: 10.1007/s10483-017-2209-8
    Xie K H, Zeng G X. 1989. Consolidation theories for drain wells under equal strain condition[J]. Chinese Journal of Geotechnical Engineering, 11(2): 3-17.
    Yoshikuni H, Nakanodo H. 1974. Consolidation of soils by vertical drain wells with finite permeability[J]. Soils and Foundations, 14(2): 35-46. doi: 10.3208/sandf1972.14.2_35
    Zhou F, Chen Z, Wang X D. 2018. An equal-strain analytical solution for the radial consolidation of unsaturated soils by vertical drains considering drain resistance[J]. Advances in Civil Engineering, 1-9.
    陈国红, 谢康和, 程启峰, 等. 2011. 考虑涂抹区渗透系数变化的砂井地基固结解[J]. 浙江大学学报, 45(4): 665-670. doi: 10.3785/j.issn.1008-973X.2011.04.013
    顾洋洋. 2017. 非饱和软土路基的一维固结沉降及其影响因素的研究[D]. 重庆: 重庆大学.
    李林忠, 汪磊, 李培超, 等. 2018. 任意荷载下双面半透水边界分数阶导数黏弹性饱和土层一维固结[J]. 工程地质学报, 26(6): 1480-1489. doi: 10.13544/j.cnki.jeg.2017-480
    秦爱芳, 李天义, 裴杨丛琪, 等. 2019. 半渗透边界下非饱和土砂井地基固结特性[J]. 工程地质学报, 27(2): 390-397. doi: 10.13544/j.cnki.jeg.2017-534
    秦爱芳, 孙德安, 谈永卫. 2010. 非饱和土一维固结的半解析解[J]. 应用数学和力学, 31(2): 199-209. doi: 10.3879/j.issn.1000-0887.2010.02.009
    秦爱芳, 余继放, 葛航. 2017. 考虑涂抹区渗透系数变化的非饱和土砂井地基固结特性分析[J]. 工程地质学报, 25(3): 605-611. doi: 10.13544/j.cnki.jeg.2017.03.005
    谢康和, 曾国熙. 1989. 等应变条件下的砂井地基固结解析理论[J]. 岩土工程学报, 11(2): 3-17. doi: 10.3321/j.issn:1000-4548.1989.02.002
  • 加载中
图(6)
计量
  • 文章访问数:  289
  • HTML全文浏览量:  66
  • PDF下载量:  20
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-12-31
  • 修回日期:  2020-07-07
  • 刊出日期:  2021-02-01

目录

    /

    返回文章
    返回