Stochastic Stability of Pile Foundation Systems Under Combined Static, Harmonic and Gaussian White Noise Excitations
DOI:
https://doi.org/10.65904/Keywords:
Stochastic Stability, Moment Lyapunov Exponent, Pile Foundations, Stochastic Averaging, Monte Carlo SimulationAbstract
This paper examines the stochastic stability of pile foundations under combined static, harmonic, and random loadings using moment Lyapunov exponents (MLEs) as the primary stability metric. The governing stochastic differential equations are first derived and reduced via stochastic averaging, appropriate for lightly damped systems subjected to weak excitations. Based on the reduced system, a new analytical framework is developed to evaluate MLEs for a pile model, allowing closed-form identification of stability boundaries and critical excitation conditions. Monte Carlo simulation is formulated of the original stochastic system, in which numerical results also provide validation for the analytical predictions from stochastic averaging. As an application, a pile subjected to soil pressure, constant axial load, harmonic excitation, and stochastic disturbances is analyzed. The pile is modeled as a simply supported column resting on a Hetényi-type elastic foundation, while the random excitation is represented by Gaussian white noise. The results demonstrate that increases in noise intensity, excitation amplitudes, and load ratios significantly amplify instability, whereas higher damping and foundation stiffness improve stability by reducing MLE values and suppressing higher-mode responses. In addition, longer piles exhibit lower stability, while increased elastic modulus and larger cross-sectional dimensions enhance the overall resistance to instability. The proposed framework provides a rigorous and efficient tool for assessing the stochastic stability of pile systems under complex loading conditions.
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