Dynamic analysis of underground structures with uncertain-but-bounded parameters

The dynamic response of underground structures is significantly influenced by the uncertainties in soil and structural parameters, which cannot be neglected in seismic analysis. This study proposes an improved interval analysis method based on Chebyshev series theory to evaluate the uncertainties in the dynamic response of underground structures. The method predicts the extreme range of system responses by determining the upper and lower bounds of uncertain parameters. Unlike existing interval analysis methods, the proposed approach is specifically extended and applied to the dynamics of underground structures. Additionally, by incorporating the equivalent linearization analysis method, the nonlinear behavior of soil is approximately simulated, and the impact of uncertain soil shear wave velocity on the dynamic response of structures is investigated. Furthermore, numerical studies are conducted, and the results are compared with those from the Monte Carlo Simulation (MCS) method to validate the applicability and effectiveness of the proposed method. The findings indicate that the method accurately captures the upper and lower bounds of the dynamic response of the site and underground structures, with significantly higher computational efficiency than the MCS method, demonstrating its strong engineering practicality. Specifically, when using a third- or fourth-order Chebyshev series expansion, the results align closely with the MCS method. Moreover, the proposed method reduces computational time. It extends the application of the Chebyshev series in uncertainty analysis, providing an efficient and reliable tool for addressing uncertainty problems in underground structures.