Rigorous solution for 1-D consolidation of a clay layer under haversine cyclic loading with rest period

Presented in this paper is a rigorous solution of the conventional Terzaghi one-dimensional consolidation under haversine cyclic loading with any rest period. The clay deposit is either permeable at both top and bottom or permeable at the top and impermeable at the bottom. This exact analytical solution was achieved using Fourier harmonic analysis for the periodic function representing the rate of imposition of excess pore water pressure. The double Fourier series in the rigorous solution was found to be rapidly convergent. The analysis of excess pore water pressure and effective stress is done in the Matlab 2010 environment. Both the effects of rest period and frequency of cyclic loading are investigated. The analysis reveals that the excess pore water pressure arrives the steady-state at a time factor T of about 2. Furthermore, finite element method (FEM) is applied to solve numerically the corresponding consolidation problem and the FEM solution is compared to the analytical solution showing a good match.