Abstract
This paper presents the analytical solution of the radial consolidation of a prefabricated vertical drain (PVD) foundation under the unsaturated condition. In the proposed modeling, air and water phases in the foundation are thought to dissipate horizontally toward to the drain, and the smear effect, drain resistance and external time-dependent loading are fully considered. The analytical mathematical tools, namely the general integration method, Fourier series expansion method, decoupling method and the constant variation method, are utilized to solve the partial differential equations. Moreover, the current solutions are verified with existing solutions in the literature. Finally, a case study considering the ramp loading and exponential loading is conducted to investigate the consolidation patterns under various loading parameters. The results show that smear effect and drain resistance can significantly hinder the dissipation process of excess pore pressures, and different external loading types will lead to various dissipation characteristics (i.e., peak values).
Highlights
The shorter drainage paths along the horizontal direction will be produced when a prefabricated vertical drain (PVD) is installed in a soil layer, resulting in the efficient radial dissipation of excess pore pressures
The governing equations of excess pore pressures in the unsaturated PVD foundation following matrix form: under the equal-strain assumption and time-dependent loading are concluded as the fol1
This phenomenon is harmful for real construction, because the sudden variations of excess pore pressures will lead to unpredicted accidents
Summary
Publisherâs Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The soils of foundation are always under the unsaturated state because of the low groundwater levels [15] Under this circumstance, the designs of the foundations based on the consolidation theory in saturated soils may be uneconomical, because the dissipation time of excess pore pressures is misestimated. In 2010, a vertical drain foundation modeling under the partially saturated condition with the radial dissipation of air and water phases was first put forward by Qin et al [33], in which the Laplace transform and the Crump method were applied to obtain the semianalytical solution. The analytical solution is proposed to investigate the consolidation of an unsaturated PVD foundation considering the smear effect, drain resistance and time-dependent loading. It should be emphasized that the current solutions are neat and clear, and can be computed with high efficiency because of the absence of the complicated numerical inversions
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