Stochastic stability of pile foundations under multiple parametric excitations

In this paper, the stochastic dynamic stability of pile foundations is investigated under multiple axial loadings along with soil pressures, extending traditional analyses that typically consider only one or two excitations. The system is modelled by a parametrically excited stochastic differential equation incorporating a static load, a harmonic excitation and a stochastic component. The stochastic load is represented by an Ornstein–Uhlenbeck process, offering a rigorous description of wideband engineering randomness. Using stochastic averaging, the system’s response is reduced to diffusive Markov processes governed by averaged equations. Eigenvalue analysis is then applied to derive the moment Lyapunov exponent for a lightly damped, weakly excited system. The effects of key parameters on stochastic stability are systematically examined, with Monte Carlo simulations conducted to validate the theoretical predictions.