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Shock and Vibration
Volume 2017, Article ID 4071268, 12 pages
Research Article

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

1School of Environmental Science and Engineering, Chang’an University, Xi’an, China
2Key Laboratory of Subsurface Hydrology and Ecological Effect in Arid Region, Chang’an University, Ministry of Education, China
3School of Civil Engineering and Architecture, Shaanxi Sci-Tech University, Hanzhong, China

Correspondence should be addressed to Dawei Cheng; moc.qq@394891gnehc

Received 23 October 2016; Accepted 2 March 2017; Published 30 March 2017

Academic Editor: Longjun Dong

Copyright © 2017 Dawei Cheng 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.


For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.