Impact of vertical ground motion on the statistical analysis of seismic demand for frictional isolated bridge in near-fault regions

Friction isolation bearings are widely used in engineering structures, which exhibit good seismic isolation effects. Peak displacement of friction isolation bearing is crucial to measure the damage degree of frictional isolated bridge, and excessive displacement of the bearing may lead to serious earthquake damage such as beam-falling. However, the studies conducted for the impact of vertical ground motion on the peak displacement of friction isolation bearings were usually deterministic research, and the probabilistic research is insufficient. Therefore, the statistical method is used to explore the probabilistic distribution of the displacement error which is caused by neglecting the vertical ground motions. The error follows Gaussian distribution, and the relationship between the Gaussian function and the intensity of horizontal and vertical ground motions are quantitatively investigated. The results show that the mean value of the error is approximately equal to zero while the standard deviation is increased significantly with the intensity of the ground motions, which indicates that the vertical ground motion has little impact on the mean of the seismic demand, but strongly influences the dispersion. Finally, to facilitate the seismic design, different quantiles of Gaussian function are defined as the increment coefficient. A set of empirical formulas to predict the value of the increment coefficient are proposed, which provide a convenient method for designers and ensure the safety of bridge structures.