SUMMARYThis paper introduces an exact analytical solution for governing flow equations for one-dimensional consolidation in unsaturated soil stratum using the techniques of eigenfunction expansion and Laplace transformation. The homogeneous boundary conditions adopted in this study are as follows: (i) a one-way drainage system of homogenous soils, in which the top surface is considered as permeable to air and water, whereas the base is an impervious bedrock; and (ii) a two-way drainage system where both soil ends allow free dissipation of pore-air and pore-water pressures. In addition, the analytical development adopts initial conditions capturing both uniform and linear distributions of the initial excess pore pressures within the soil stratum. Eigenfunctions and eigenvalues are parts of the general solution and can be obtained based on the proposed boundary conditions. Besides, the Laplace transform method is adopted to solve the first-order differential equations. Once equations with transformed domain are all obtained, the final solutions, which are proposed to be functions of time and depth, can be achieved by taking an inverse Laplace transform. To verify the proposed solution, two worked examples are provided to present the consolidation characteristics of unsaturated soils based on the proposed method. The validation of the recent results against other existing analytical solutions is graphically demonstrated.
The seismic excitation experienced by structures is a function of the earthquake source, travel path effects, local site effects, and soil-structure interaction (SSI) influences. The result of the first three of these factors is referred to as ''free-field'' ground motion. Structural response to free-field motion is influenced by SSI. In particular, accelerations within structures are affected by the flexibility of foundation support and variations between foundation and free-field motions. Consequently, an accurate assessment of inertial forces and displacements in structures can require a rational treatment of soil-structure interaction effects. In the present study, in order to depict these effects on seismic response of moment resisting building frames, a ten storey moment resisting building frame resting on a shallow foundation is selected in conjunction with three soil types with shear wave velocities less that 600m/s, representing soil classes building frames increase relatively. In brief, the conventional elastic and inelastic design procedure excluding SSI is not adequate to guarantee the structural safety for moment resisting building frames resting on soil classes D e and E e .
The use of native vegetation in the coastal regions of Australia has become increasingly popular for stabilising railway corridors built over expansive clays and compressive soft soils. The tree roots provide three stabilising functions: (a) they reinforce the soil; (b) they dissipate excess pore pressures; and (c) they establish sufficient matric suction to increase the shear strength. The matric suction generated within the tree root zone propagates radially into the soil matrix, as a function of the moisture content change. Considering soil conditions, the type of vegetation and atmospheric conditions, a mathematical model for the rate of root water uptake is developed. A conical shape is considered to represent the geometry of the tree root zone. Based on this model for the rate of root water uptake, the pore water pressure distribution and the movement of the ground adjacent to the tree are numerically analysed. Field measurements taken from the previously published literature are compared with the authors’ numerical predictions. It is found that, given the approximation of the assumed model parameters, the agreement between the predicted results and field data is still promising. The study indicates that native vegetation improves the shear strength of the soil by increasing the matric suction, and also curtails soil movements.
This paper proposes closed-form analytical solutions to the axisymmetric consolidation of an unsaturated soil stratum using the equal strain hypothesis. Following the 1-dimensional (1D) consolidation theory for unsaturated soil mechanics, polar governing equations describing the air and water flows are first presented on the basis of Fick's law and Darcy's law, respectively. The current study takes into account the peripheral smear caused by an installation of vertical drain. Separation of variables and Laplace transformation are mainly adopted in the analytical derivation to obtain final solutions. Then, the hydraulic conductivity ratio, the radius of influence zone and smear parameters influencing time-dependent excess pore pressures, and the average degree of consolidation are graphically interpreted. In this study, a comparison made between the proposed equal strain results and the existing free strain results suggests that both hypotheses would deliver similar predictions. Moreover, it is found that the smear zone resulting from vertical drain installations would hinder the consolidation rate considerably.
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