Closed-form solutions for one-dimensional consolidation in saturated soils under different waveforms of time-varying external loading

A set of closed-form series solutions that account for the transient and steady-state responses of excess pore water pressure and total settlement to one-dimensional consolidation in saturated soils exposed to various typical types of time-dependent external loading with any desired excitation amplitude and period is symmetrically formulated based on the theory of poroelasticity. The mathematical approach developed in the current study is quite general so that it can be straightforward extended to arbitrary waveform shapes of harmonic loading after they are simply represented in terms of Fourier trigonometric series. These solutions are numerically calculated to evaluate variations in excess pore water pressure and total settlement due to vertical consolidation in saturated soils with two very different magnitudes of intrinsic permeability, Soil A (higher) and Soil B (lower), as representative examples using two illustrative periods per cycle. Our results show that within excitation frequencies we examined, the excess pore water pressure exhibits greater cyclic swings in Soil B than that in Soil A as harmonic stress compression and relaxation are added, but an inverse trend is observed for total settlement. As compared to static external loading, the excess pore water pressure persists longer with periodic fluctuation in the presence of cyclic loading, but less total settlement is induced in Soil B. The discrepancy in the latter (total settlement) between the static and cyclic loading is most significant in Soil B, reflecting a physical implication that low permeability leads to a slower dissipation of excess pore water pressure, thus causing less settlement with time.