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Mathematical Problems in Engineering
Volume 2015, Article ID 284181, 9 pages
Research Article

Analytical Study of Unsteady Nested Groundwater Flow Systems

1School of Environmental Studies, China University of Geosciences, Wuhan 430074, China
2Hubei Key Laboratory of Wetland Evolution & Ecological Restoration, School of Environment Studies, China University of Geosciences, Wuhan 430074, China
3Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China

Received 26 June 2015; Accepted 21 September 2015

Academic Editor: Renata Archetti

Copyright © 2015 Hong Niu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Two analytical solutions using segregation variable method to calculate the hydraulic head under steady and unsteady flow conditions based on Tóth’s classical model were developed. The impacts of anisotropy ratio, hydraulic conductivity (K), and specific yield () on the flow patterns were analyzed. It was found that the area of the equal velocity region increases and the penetrating depth of the flow system decreases at steady state with anisotropy ratio increases, which is defined as . In addition, stagnant zones can be found in the flow field where the streamlines have opposite directions. These stagnant zones move toward the surface as the horizontal hydraulic conductivity increases. The results of the study on transient flow indicate that a relative increase in hydraulic conductivity produces a positive impact on hydraulic head and a relative enhancement in specific yield produces a negative effect on hydraulic head at early times.