Summary
Based on the consolidation theory raised by Fredlund, the solutions for the equal‐strain consolidation of unsaturated foundation with the prefabricated vertical drain considering smear effect and drain resistance are analytically formulated in this paper. Firstly, governing equations for excess pore pressures (i.e., excess pore‐air and pore‐water pressures) under the equal‐strain hypothesis are derived with the introduction of radial boundary conditions. Afterwards, the obtained coupled equations are solved by applying general integration, decoupling process, and Fourier sine series expansion. The smear coefficients and factors of drain resistance corresponding to air and water phases are both captured explicitly in the final solutions. Furthermore, the degenerated solutions are employed to verify the reliability of the current solutions. Finally, a parametric study is conducted to study the consolidation characteristics of the proposed foundation model against modeling sizes (S and N), smear coefficients (αa and αw), and drain resistance factors (Ga and Gw).
External disturbances were scarcely considered in the consolidation of unsaturated vertical drain foundation, in which the ideally permeable or impermeable boundary conditions were always adopted to investigated the consolidation patterns. In view of this, by taking the flows along the vertical and radial orientations simultaneously, this study proposes the general analytical solutions for the axisymmetric consolidation of prefabricated vertical drain foundations in unsaturated soils which consider drain resistance, smear effect, and time‐dependent loading under the equal‐strain assumption. Through theories related to consolidation in unsaturated soils, the governing equations of air and water phases in the matrix form are proposed. Subsequently, Fourier series expansion, matrix analysis and decoupling method are used to acquire the analytical solutions. The separate expressions of smear coefficient and drain resistance factors, which can represent the potential influence of the external boundaries more obviously, are included in the solutions. Degradation validity method is used to verify the credibility of the current solutions, and the vertical flow is found to promote the consolidation process under external conditions. Finally, the solutions obtained in this paper can provide guidance for more complicated consolidation problems in unsaturated soils.
Geosynthetic materials are widely adopted as part of barrier liners in landfills, while the existence of defects in geomembrane (GM) will significantly reduce the barrier efficiency and lead to unexpected pollution in the surrounding environment. In this study, a novel semi-analytical model was proposed to investigate the two-dimensional (2D) migration of organic contaminant through the GM with strip defects to the underlying soil liner (SL). This model has the superiority to consider the concentration condition in the defects, and describe more accurate concentration profiles in the SL. The combination of discretization method and integral transforms were applied to obtain semi-analytical solutions, which were then verified by numerical solutions. Results show that the existence of defects can substantially accelerate the migration process of contaminant through flawed GM to the underlying SL. Specifically, the time interval between migration curves in the model with defects can be 2 or 3 orders of magnitude shorter than that without defects under the same condition.
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