# Stochastic Analysis of a Large-Span Continuous
###### Abstract  
The main objective of the present work is to evaluate the stochastic seismic response of a large-span continuous girder high-speed railway (CGHSR) bridge subjected to fully non-stationary seismic excitation. The stochastic ground motion is determined by a fully non-stationary ground acceleration model with both the time-varying intensity and frequency content. The stochastic seismic analysis of the large-span CGHSR bridge under a tri-directional earthquake, taking into consideration the wave passage effect, is performed using the pseudo excitation method (PEM) in frequency domain and the Monte Carlo sampling (MCS) method in time domain. A framework is proposed to determine the pseudo static displacement for the PEM under fully non-stationary seismic excitation, using the proper orthogonal decomposition (POD). A comparative study on the stochastic seismic response of the bridge is conducted using both the fully and modulated non-stationary ground acceleration. The results show that the structural nodal displacements estimated by the PEM agree well with those obtained by the MCS method. The proposed POD-based method works well in estimating the structural quasi-static displacement. Ignoring the frequency non-stationarity of the earthquake may underestimate the quasi-static displacement caused by the surface waves. high-speed railway bridge; fully non-stationary ground acceleration model; pseudo excitation method (PEM); Monte Carlo sampling method; stochastic analysis +
Footnote †: journal: Applied Sciences  
the stationary and non-stationary seismic response of large-span bridges and proposed a general spatially varying earthquake ground motion model. [PERSON] et al. [12] carried out a study of the simply supported bridges, considering spatially varying earthquake ground motion. [PERSON] et al. [13] investigated non-stationary seismic responses under multiple seismic random excitations. [PERSON] [14] studied the stochastic response of bridges isolated by friction pendulum system and compared the non-stationary response of the bridge with that corresponding to the stationary case. [PERSON] et al. [15] comparatively analyzed a high-pier railway bridge under stationary and non-stationary spatially varying earthquake excitations. [PERSON] et al. [16] studied the non-stationary stochastic seismic response of a large-span bridges with local plastic deformations using an efficient explicit time-domain method. However, most of the non-stationary seismic stochastic analysis focused on the large-span cable supported bridges. In addition, to simplify the stochastic seismic analysis, the time-dependent uniformly modulated function, which can only represent the intensity of non-stationarity, is utilized in most of the research to model the ground motion. Due to the different arrival times of the push, shear and surface waves that vary significantly in frequency content, the frequency non-stationarity should be considered to give a more realistic depiction of the ground motion. Moreover, as the large-span CGHSR bridge is more rigid, to avoid excessive vertical deflection under the rail loads, the seismic performance may be different from other large-span flexible bridges. Therefore, it is of great significance to analyze the stochastic seismic performance of a large-span CGHSR bridge under fully non-stationary seismic excitations. As the ground motion is treated as a stochastic process due to its random characteristics, the random vibration method (RVM) has been widely accepted to analyze the seismic performance of large-scale structures [17; 18]. The Monte Carlo sampling (MCS) method is one of the most commonly used RVMs due to its versatility and simplicity [19; 20]. As for stochastic seismic analysis, the random ground motion can be generated based on the prescribed statistics. Then, the problem becomes deterministic, and an ensemble of solutions can be obtained. Thus, the statistics of the ensemble can be extracted [21].