Abstract This paper presents a novel analytical solution for one dimensional consolidation system of unsaturated soil incorporating impeded drainage boundary conditions. Through diagonalizing the coefficient matrix, the consolidation system is firstly transformed into a diagonal one with respect to a new variable vector. Then, using the methods of eigenfunction expansion and undetermined coefficients, the analytical solution is developed through deriving the eigenvalues, corresponding eigenfunctions and undetermined coefficients. Its orthogonality and convergence are proven, and several comparisons against existing solutions and two typical experimental data are performed to verify its validity. Finally, two typical examples are provided to illustrate the consolidation behavior of unsaturated soil with different drainage parameters. The results indicate that the present analytical solution converges rapidly, and it is consistent with existing analytical, semi-analytical and numerical solutions for various drainage boundary conditions. The proposed analytical solution achieves an overall better agreement with experimental data, and the impeded drainage boundary condition is more reasonable to describe the consolidation phenomenon of unsaturated soil. In general, larger drainage parameter accelerates excess pore-pressure dissipation and soil settlement.

中文翻译：

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包含阻碍排水边界的非饱和土一维固结的一般解析解

摘要 本文提出了一种新的非饱和土一维固结系统的解析解，该系统包含不畅排水边界条件。通过对系数矩阵的对角化，首先将固结系统转化为关于新变量向量的对角矩阵。然后，利用特征函数展开和待定系数的方法，通过推导特征值、对应的特征函数和待定系数，得到解析解。证明了其正交性和收敛性，并与现有解决方案和两个典型的实验数据进行了多次比较以验证其有效性。最后，通过两个典型实例来说明不同排水参数下非饱和土的固结行为。结果表明，本文的解析解收敛速度很快，与现有的各种排水边界条件的解析解、半解析解和数值解是一致的。所提出的解析解与实验数据总体上达到了较好的一致性，并且阻碍排水边界条件更能合理地描述非饱和土的固结现象。一般来说，较大的排水参数会加速超孔隙压力消散和土壤沉降。而不畅排水边界条件更能合理地描述非饱和土的固结现象。一般来说，较大的排水参数会加速超孔隙压力消散和土壤沉降。而不通水边界条件更能合理地描述非饱和土的固结现象。一般来说，较大的排水参数会加速超孔隙压力消散和土壤沉降。