This study examines the stochastic stability of a pile foundation subjected to combined axial actions consisting of a constant load, harmonic excitation, and random fluctuations, using moment Lyapunov exponents (MLEs) as the primary metric for assessing stability in stochastic dynamical systems. The pile is idealized as a simply supported column supported by a Pasternak elastic foundation, while the external stochastic excitation is represented by a bounded stochastic process. Employing stochastic averaging, the governing equations are transformed into coupled Ito-type differential equations, enabling direct evaluation of the MLEs, with Monte Carlo simulations used to corroborate the analytical results. The findings demonstrate that increased noise intensity, harmonic and stochastic excitation amplitudes, and static and dynamic load ratios promote parametric instability, whereas higher damping and foundation rigidity improve stability by lowering MLEs and inhibiting higher-order buckling; moreover, longer piles exhibit reduced stability, while greater elastic modulus and cross-sectional dimensions enhance the overall stability of the pile system.
Ajirlou et al. (2026) studied this question.