Analytical Solutions for the Radial Consolidation of Unsaturated Foundation with Prefabricated Vertical Drain Based on Fourier Series Expansion Theory

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).