Oscillations of retaining wall subject to Grob’s swelling pressure

The single-degree-of-freedom nonlinear problem describing the essential dynamics of an oscillating retaining wall based on non-quaking ground and subject to Grob’s swelling pressure is considered. The periodic solutions are derived using harmonic approximation. The amplitude-frequency relation is established by employing Lambert’s special function or alternatively using linearization of the nonlinear force. Analytical results are verified using numerical simulations.