Abstract
The consolidation process of soil stratum is a common issue in geotechnical engineering. In this paper, the two-dimensional (2D) plane strain consolidation process of unsaturated soil was studied by incorporating vertical impeded drainage boundaries. The eigenfunction expansion and Laplace transform techniques were adopted to transform the partial differential equations for both the air and water phases into two ordinary equations, which can be easily solved. Then, the semi-analytical solutions for the excess pore-pressures and the soil layer settlement were derived in the Laplace domain. The final results in the time domain could be computed by performing the numerical inversion of Laplace transform. Furthermore, two comparisons were presented to verify the accuracy of the proposed semi-analytical solutions. It was found that the semi-analytical solution agreed well with the finite difference solution and the previous analytical solution from the literature. Finally, the 2D plane strain consolidation process of unsaturated soil under different drainage efficiencies of the vertical boundaries was illustrated, and the influences of the air-water permeability ratio, the anisotropic permeability ratio and the spacing-depth ratio were investigated.
Highlights
The consolidation process of soil stratum is a common issue in geotechnical engineering and it has captured a great deal of attention in the geotechnical community
Where ma1 and mw 1 are the coefficients of air and water volume change with respect to the change of the net normal stress, respectively; ma2 and mw 2 are the coefficients of air and water volume change with respect to the change of suction, respectively; n is the soil porosity; Sr is the degree of saturation; uatm is the atmospheric pressure; Θ is the absolute temperature (K); R is the universal air constant (8.314 J·mol−1 ·K−1 ); g is the gravitational acceleration (9.8 m/s2 ); M is the molecular mass of air phase (0.029 kg/mol); and γw is the unite weight of water (9.8 kN/m3 )
Using Crump’s method [24] to implement the numerical inversion of Laplace transform (NILT) on Equations (17a), (17b) and (20), the semi-analytical solutions for the excess pore-air and -water pressures and the soil layer settlement were obtained in the time domain
Summary
The consolidation process of soil stratum is a common issue in geotechnical engineering and it has captured a great deal of attention in the geotechnical community. In order to ensure that analytical solutions were available, most of the previous studies treated the top and bottom drainage boundaries of the soil layer as fully drained or undrained [16] These boundaries are generally partially drained (i.e., impeded drainage) in most practical consolidation processes. A sand cushion covered on the top surface of the soil layer, which is commonly These boundaries are generally partially drained (i.e., impeded drainage) in most practical. Based on the consolidation equations proposed by Dakshanamurthy and Fredlund [10], this paper paper attempted to derive semi-analytical solutions to the 2D plane strain consolidation process of attempted to derive semi-analytical solutions to the 2D plane strain consolidation process of unsaturated soil by incorporating the vertical impeded drainage boundaries.
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