Catalogue of analytical solutions for consolidation of unsaturated soils subjected to various initial conditions and time-dependent loadings
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Soil consolidation has been a primary geotechnical interest for decades. Such phenomenon involves the gradual dissipation of excess pore pressures from the soil deposit subjected to an external applied load, resulting in a considerable reduction of soil volume. Majority of industrial and residential areas have been vigorously developed in arid and semi-arid climatic regions, where the underground water table is relatively deep. In these regions, construction activities can significantly influence the upper unsaturated zone. In particular, the earthworks, such as excavation and compaction, and changes in the climate and surface vegetation may result in further creation of unsaturated soils, whose properties are much more complicated than those of saturated soils. Past decades have witnessed the significant growth of engineering interests in unsaturated soils and that has motivated researchers to conduct more insightful research. A great attention has been given to the unsaturated consolidation theory due to many foundation-related problems particularly relate to time-dependent soil volume change and settlement. However, a typical unsaturated soil usually has nonlinear properties and intricate phase relationships, which result in theoretical difficulties in formulating a reliable model for the consolidation prediction. This thesis presents a systematic catalogue of analytical solutions for the consolidation of unsaturated soils subjected to various loading and initial conditions. Particularly, eigenfunction expansions and standard Laplace transformation techniques are used to solve the consolidation equations. This research provides rigorous solutions to estimate the rates of excess pore-air and pore-water pressure dissipation and consolidation settlement under the one-dimensional (1D), two-dimensional (2D) plane strain and axisymmetric consolidation conditions. For the mathematical derivation, uniform and linearly depth-dependent initial conditions are adopted along with homogeneous boundary conditions, including one-way and two-way drainage boundary conditions. In addition, effects of time-dependent loadings are also captured in this study. Four primary types of external loads, namely ramping, asymptotic, sinusoid and damped sine wave, are simulated and then incorporated in the proposed solutions. On the other hand, the 1D consolidation of unsaturated soils under non-isothermal conditions is sufficiently discussed. This study also demonstrates that the proposed analytical solutions can change back to the traditional equations for saturated soils. Most results are graphically presented in the semi-logarithmic plots. Changes in excess pore pressures and settlement are investigated against the air to water permeability ratio (Ka/Kw). Moreover, pore pressure isochrones along the flow domains are also highlighted in each consolidation field. Verification exercises are conducted by comparing the predicted results with other solutions obtained from existing literature. The proposed equations can be used by practicing engineers. Programmable methods such as Microsoft Excel or MATLAB can be simply adopted to generate results from proposed equations to predict the time-dependent settlement of unsaturated soils. For all consolidation cases, it is predicted that variations in the permeability ratio Ka/Kw result in double inverse S curves for the excess pore-water pressure and settlement, while forming a single S curve for the excess pore-air pressure. The study shows that the 1D consolidation process in the two-way drainage soil stratum tends to proceed more quickly than that in the one-way drainage system. However, the consolidation rates under these boundary conditions are almost comparable when drain wells (for the 2D plane strain and axisymmetric cases) are installed in the soil profile. In the 2D plane strain consolidation system, if the horizontal permeability is greater than the vertical permeability (i.e. Kx/Kz > 1), the horizontal flow will govern the dissipation rate and the effects of vertical flow is much attenuated. This point is also supported in the axisymmetric analysis. Additionally, the time-dependent loadings and temperature variations have significant impacts on changes in excess pore pressures and settlement. For the loading effects, it can be predicted that excess pore-water pressures and settlement are considerably influenced by the loading patterns irrespective of Ka/Kw values. However, in most loading cases, effects of the applied loads on the excess pore-air pressure are less pronounced as Ka/Kw increases. On the other hand, variations in soil temperature are substantially attributed to the air temperature and the heat from solar radiation. It is predicted that, for time-dependent linear temperature variations, the excess pore-air pressure initially increases dramatically and then attains a constant value, while the excess pore-water pressure diminishes a very long time after the heat begins to increase. Besides, excess pore-air and pore-water pressures near the ground surface increase faster than those at lower depths when the temperature increases exponentially. Both pressures then are fully dissipated as the temperature approaches the maximum value. For the case of diurnal temperature wave, the excess pore pressure curves would oscillate capturing damping and retarding effects. Development of analytical solutions for the unsaturated consolidation incorporating the above influencing factors would provide fundamental understandings of deformation of unsaturated soils.
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