A general analytical solution for one dimensional consolidation of unsaturated soil incorporating impeded drainage boundaries

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.