The 8th International Conference on Engineering Innovation and Seismic Mitigation of Bridges （ICEISMB 2025） (ICEISMB 2025)

The nonlinear time-history seismic responses of high-pier bridges are performed based on the fiber beam model with complex modeling processes and substantial computational demands. A significant limitation of the fiber beam model is presented for inverse analysis of structural optimization of the seismic responses. Considering ground excitations represent the nature of random processes, a refined hysteretic model is developed to simulate the non-stationary stochastic responses of multi-degree-of-freedom (MDOF) high-pier bridges using the Bouc–Wen hysteresis model. The nonlinear moment-curvature hysteretic behavior, including strength degradation, stiffness degradation, and pinching effects, of reinforced concrete (RC) high-pier bridges under strong earthquakes are investigated using higher-order stochastic equivalent linearization to improve accuracy. By modeling the stochastic excitation as high-pass filtered white noise, the responses of high-pier bridges are solved using the Lyapunov equation, and obtained by considering firm, medium, or soft soil site conditions. Parametric tests are performed to investigate the influence on the stochastic responses. The results show that, considering the stiffness degradation and pinching effect, the peak root mean square (RMS) curvature at the pier bottom significantly increases. Larger peak RMS curvatures are observed under medium and soft soil conditions than under firm soil conditions. The high-order mode contributes to the peak RMS curvature responses of high-pier bridges under firm and medium soft conditions, whereas the fundamental mode mainly contributes to the responses under soft soil conditions. The peak RMS curvature and accumulated hysteretic energy dissipation are sensitive to the plastic parameters of the stiffness degradation constant δ_η, pinching constant ζ₁₀, and post-elastic-to-elastic stiffness ratio α_ϕ of the Bouc–Wen hysteresis model, particularly for soft soil conditions.