Exact Solution to Predict Excess Pore Pressures and Settlement of Unsaturated Soil Deposit due to Uniform Loading

Canadian Geotechnical Society
Publication Type:
Conference Proceeding
GEO Montreal 2013, 2013, pp. 1 - 6
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This paper explains a simple yet precise analytical solution for the nonlinear governing equations for one-dimensional (1D) consolidation of an unsaturated soil deposit using eigenfunction expansions and Laplace transform techniques. The mathematical development adopts two-way drainage condition for the unsaturated soil, in which the permeable top and base boundaries allow free dissipation of pore-air and pore-water pressures under uniform loading. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed drainage boundary condition. Furthermore, uniformly distributed initial pore pressures can be used to determine the initial generalised Fourier coefficients. Besides, Laplace transform method is adopted to solve the first-order differential equations. Once the equations with transformed domain are obtained, the final solutions, which are proposed to be functions of time (t) and depth (z), can be achieved by taking an inverse Laplace transform. A worked example is provided to present the consolidation characteristics of unsaturated soils based on the proposed solution. Significance of air permeability to water permeability ratio on the excess pore water and air pressure dissipation rates is investigated and discussed.
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