This study proposes a closed‐form solution for axisymmetric electro‐osmotic consolidation of unsaturated soil under semi‐permeable boundary conditions. The governing equations are formulated to allow for vertical and radial flows of liquid and air phases. The techniques of eigenfunction expansion and Laplace transformation are employed to develop the exact solution for excess pore‐air (EPAP) and pore‐water pressures (EPWP). The proposed solution is first validated by comparing it to an existing solution, followed by verification through finite element simulations. Both methods of validation confirm the accuracy of the analytical solution. Then, based on the obtained solution, the effects of vertical flow, semi‐permeable boundary conditions, electrical voltage, electro‐osmosis conductivity and spacing ratio re/rw on the consolidation profile have been further investigated. Parametric studies show that the EPWP at the steady state depends on the electro‐osmosis conductivity and applied electricity gradient. In addition, the dissipation rates of EPWP and EPAP in the axisymmetric electro‐osmotic consolidation would be underestimated if the vertical flows are neglected. The semi‐permeable boundary conditions have great influences on the dissipation rate and the steady‐state solution. The proposed solution could serve as a theoretical basis for axisymmetric electro‐osmotic consolidation of unsaturated soil.

中文翻译：

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半透边界非饱和土轴对称电渗固结通用解析解

本研究提出了半渗透边界条件下非饱和土轴对称电渗固结的封闭式解决方案。制定控制方程以允许液相和空气相的垂直和径向流动。采用本征函数展开和拉普拉斯变换技术来开发过量孔隙空气 (EPAP) 和孔隙水压力 (EPWP) 的精确解。首先通过与现有解决方案进行比较来验证所提出的解决方案，然后通过有限元模拟进行验证。两种验证方法均确认了分析解决方案的准确性。然后，基于所得到的溶液，垂直流、半渗透边界条件、电压、电渗电导率和间距比的影响re/rw对合并概况进行了进一步研究。参数研究表明，稳态下的 EPWP 取决于电渗电导率和施加的电梯度。此外，如果忽略垂直流，则轴对称电渗固结中 EPWP 和 EPAP 的耗散率将被低估。半渗透边界条件对耗散率和稳态解有很大影响。所提出的解决方案可以作为非饱和土轴对称电渗固结的理论基础。