Lateral dynamic analysis of single pile in partially saturated soil

A mathematical formulation is presented to investigate the dynamic response of a single pile embedded in a semi-infinite partially saturated soil subjected to lateral dynamic excitations. An approximate scheme is implemented to decompose the pile-soil system into an extended water-air-filled poroelastic half-space and a fictitious pile. The extended porous medium is governed by the three-phase elastodynamic theory, whilst the fictitious pile is treated as a beam and described by the conventional one-dimensional beam vibration theory. By virtue of the Green's function for a set of interior horizontal patch loads in unsaturated soil and the combination with the compatibility condition, the formulation of the interaction problem is reduced to a Fredholm integral equation of the second kind governing the unknown bending moments and displacements along the fictitious pile. The pile head impedance function in the frequency domain is derived and resolved numerically by a discretised method. Its accuracy was validated through a comparison with the existing solutions corresponding to single-phase and fully saturated soils. The numerical results show that the effects of saturation and permeability on the dynamic behaviour of pile are insignificant for the partially saturated cases, whilst remarkable for the nearly saturated case. When the soil approaches the full saturation, the impedance increases rapidly as the degree of saturation increases, but diminishes gradually with increasing permeability.