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

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.