Abstract
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 v 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.
Highlights
It is well-known that cyclic loading of soils may result from natural phenomena or human activities such as wind and water waves, vehicular traffic, reciprocating machinery and others (Mitchell 1993; Zhang et al 2009)
Due to the fact that many problems of 1-D consolidation of cohesive soils have an equivalent problem in the heat condition in solids, it is necessary to review the wave forms considered by Carslaw and Jaeger (1959) in the field of heat diffusion
Summarizing the results presented it can be concluded that the analytical and numerical solutions coincide perfectly at least for pore water pressure and effective stress evolution at the considered three locations and the fit remains good for different rest periods and load frequencies
Summary
It is well-known that cyclic loading of soils may result from natural phenomena or human activities such as wind and water waves, vehicular traffic, reciprocating machinery and others (Mitchell 1993; Zhang et al 2009). Special structures such as silos and fluid tanks that undergo filling and discharging subject their foundation soils to loading unloading stages that repeat themselves more or less periodically over time (Conte and Troncone 2006). Using either the Fourier series approach or the Laplace transforms approach for solving 1-D heat diffusion problems, Carslaw and Jaeger (1959) considered, among others, periodic boundary conditions in a rectangular wave form or a sine-wave form only. This means that they focused their attention only on the homogeneous 1-D heat equation with periodic boundary conditions
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