Analytical solution to one-dimensional consolidation in unsaturated soils

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This paper presents an analytical solution of the one-dimensional consolidation in unsaturated soil with a finite thickness under vertical loading and confinements in the lateral directions. The boundary contains the top surface permeable to water and air and the bottom impermeable to water and air. The analytical solution is for Fredlund’s one-dimensional consolidation equation in unsaturated soils. The transfer relationship between the state vectors at top surface and any depth is obtained by using the Laplace transform and Cayley-Hamilton mathematical methods to the governing equations of water and air, Darcy’s law and Fick’s law. Excess pore-air pressure, excess pore-water pressure and settlement in the Laplace-transformed domain are obtained by using the Laplace transform with the initial conditions and boundary conditions. By performing inverse Laplace transforms, the analytical solutions are obtained in the time domain. A typical example illustrates the consolidation characteristics of unsaturated soil from analytical results. Finally, comparisons between the analytical solutions and results of the finite difference method indicate that the analytical solution is correct.


Original languageEnglish
Pages (from-to)1329-1340
JournalApplied Mathematics and Mechanics
Issue number10
Publication statusPublished - Aug 2008


  • Unsaturated soil, one-dimensional consolidation, settlement, analytical solution, excess pore-air pressure, excess pore-water pressure

ID: 93235