Running safety assessment of a train traversing a three-tower cable-stayed bridge under spatially varying ground motion

To explore the influence of spatially varying ground motion on the dynamic behavior of a train passing through a three-tower cable-stayed bridge,a 3D train–track–bridge coupled model is established for accurately simulating the train–bridge interaction under earthquake excitation,which is made up of a vehicle model built by multi-body dynamics,a track–bridge finite element model,and a 3D rolling wheel–rail contact model.A conditional simulation method,which takes into consideration the wave passage effect,incoherence effect,and site-response effect,is adopted to simulate the spatially varying ground motion under different soil conditions.The multi-time-step method previously proposed by the authors is also adopted to improve computational efficiency.The dynamic responses of the train running on a three-tower cablestayed bridge are calculated with differing earthquake excitations and train speeds.The results indicate that(1)the earthquake excitation significantly increases the responses of the train–bridge system,but at a design speed,all the running safety indices meet the code requirements;(2)the incoherence and site-response effects should also be considered in the seismic analysis for long-span bridges though there is no fixed pattern for determining their influences;(3)different train speeds that vary the vibration characteristics of the train–bridge system affect the vibration frequencies of the car body and bridge.

On time-step in structural seismic response analysis under ground displacement/acceleration

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

Response of a transmission tower-line system at a canyon site to spatially varying ground motions

Collapses of transmission towers were often observed in previous large earthquakes such as the Chi-Chi earthquake in Taiwan and Wenchuan earthquake in Sichuan,China. These collapses were partially caused by the pulling forces from the transmission lines generated from out-of-phase responses of the adjacent towers owing to spatially varying earthquake ground motions. In this paper,a 3D finite element model of the transmission tower-line system is established considering the geometric nonlinearity of transmission lines. The nonlinear responses of the structural system at a canyon site are analyzed subjected to spatially varying ground motions. The spatial variations of ground motion associated with the wave passage,coherency loss,and local site effects are given. The spatially varying ground motions are simulated stochastically based on an empirical coherency loss function and a filtered Tajimi-Kanai power spectral density function. The site effect is considered by a transfer function derived from 1D wave propagation theory. Compared with structural responses calculated using the uniform ground motion and delayed excitations,numerical results indicate that seismic responses of transmission towers and power lines are amplified when considering spatially varying ground motions including site effects. Each factor of ground motion spatial variations has a significant effect on the seismic response of the structure,especially for the local site effect. Therefore,neglecting the earthquake ground motion spatial variations may lead to a substantial underestimation of the response of transmission tower-line system during strong earthquakes. Each effect of ground motion spatial variations should be incorporated in seismic analysis of the structural system.