Exact analytical solution for one-dimensional consolidation of unsaturated soil stratum subjected to damped sine wave loading

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Conference Proceeding
Proceedings of 12th Australia New Zealand Conference on Geomechanics, 2015, 1 pp. 1 - 8
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A considerable surcharge exerted on an unsaturated soil stratum leads to the emergence of excess pore pressures. During the consolidation process, these pressures tend to dissipate towards permeable boundary surfaces, resulting in a reduction of the soil volume. Such phenomenon can be mathematically described by inhomogeneous governing equations of flow based on Fick’s law (with respect to air phase) and Darcy’s law (with respect to water phase). This paper discusses the dissipation of excess pore-air and pore-water pressures and settlement of an unsaturated soil stratum subjected to an external damped sine wave loading. An analytical solution is derived from the governing equations of flow using eigenfunction expansion and Laplace transformation methods. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on oneway drainage boundary condition. On the other hand, the damped sine wave loading is mathematically simulated and incorporated in the solution. Once the time variable (t) in partial differential equations is transformed into the Laplace complex argument (s), generalised Fourier coefficients can be computed by taking a Laplace inverse, and then the final solution can be obtained. In this study, the air to water permeability ratio (k /k ), influencing changes in dissipation rates of excess pore pressures and settlement are investigated and discussed. It is observed that the increasing permeability ratio has a significant effect on the change in the pore pressures.
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