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

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

    • 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。

       

      Abstract: Former researches of unsaturated vertical drain foundations mostly treated the foundations with ideal radial boundaries. The drain resistance and smear effect are important factors affecting the consolidation of unsaturated soil with vertical drain. This paper is based on Fredlund's one-dimensional consolidation theory for unsaturated soil mechanics and the equal strain hypothesis. The coupled governing equations of excess pore pressures are transformed into equivalent linear partial differential equations by introducing variables. This paper further takes into account the drain resistance and smear effect conditions in the analytical derivation. Separation of variables and the method of undetermined coefficients are mainly adopted to obtain the analytical solution to consolidation of unsaturated soils with vertical drain under instantaneous load. Moreover, the validity of the solution is verified by degenerating and comparing with the existing solution in saturated soils. A typical example is used to illustrate the influence of drain resistance and smear effect on consolidation of vertical drain foundation. The results show that the decrease of the smear effect-and drain resistance-related coefficients(i.e., drain resistance factor G, ratio of influence radius to vertical drain radius N, smear coefficient α, ratio of smear radius to vertical drain radius S)can lead to an obvious increase in the consolidation speed. When the drain resistance factor G is less than 0.1, the influence of the drain resistance can be neglected in practical engineering; When the ratio of smear radius to vertical drain radius S is bigger than 5, the influence of smear effect cannot cause much more remarkable difference than when S=5. It is expected that the permeability of vertical drain foundation in unsaturated soils should be improved and construction disturbance should be reduced to decrease the influence of drain resistance and smear effect in practical engineering.

       

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