Seismic response analysis of an interacting curved bridge–train system under frequent earthquakes

Abstract

Summary This paper establishes a scheme for the seismic analysis of interacting vehicle–bridge systems. The focus is on (horizontally) curved continuous railway bridges and frequent earthquakes. Main features of the proposed scheme are (i) the treatment of the dynamics in all three dimensions (3D), employing an additional rotating system of reference to describe the dynamics of the vehicles and a realistic 3D bridge model; (ii) the simulation of the creep interaction forces generated by the rolling contact between the wheel and the rail; and (iii) the integration of the proposed scheme with powerful commercial finite element software, during the pre‐processing and post‐processing phases of the analysis. The study brings forward the dynamics of a realistic vehicle–bridge (interacting) system during seismic shaking. For the (vehicle–bridge) case examined, the results verify the favorable damping effect the running vehicles have on the vibration of the deck. By contrast, the study stresses the adverse influence of the earthquake‐induced bridge vibration on the riding comfort but, more importantly, on the safety of the running vehicles. In this context, the paper unveils also a vehicle–bridge–earthquake timing problem, behind the most critical vehicle response, and underlines the need for a probabilistic treatment. Among the 20 sets of historic records examined, the most crucial for the safety of the vehicles are near‐fault ground motions. Finally, the study shows that even frequent earthquakes, of moderate intensity, can threaten the safety of vehicles running on bridges during the ground motion excitation, in accordance with recorded accidents. Copyright © 2016 John Wiley & Sons, Ltd.

Vehicle-Bridge Interaction Analysis Using the Localized Lagrange Multipliers Approach

“…This study extends the previous work of the authors on the localized Lagrange multipliers approach [9] by accounting also for rolling contact between the rails and the wheels in the tangential direction [11] and by considering non-linear profiles for the rails and the wheels [12]. Following, it applies the proposed algorithm to a two-vehicle train crossing a HSR bridge consisting of three continuous bridges [13].…”

“…Each vehicle consists of one car body, two bogies and four wheelsets, all connected with linear springs and dashpots ( Figure 1). The car body and the bogies are assigned 5 degrees of freedom (DOFs) each, while each wheelset has 4 DOFs [11]. The equation of motion (EOM) of the vehicle is:…”

“…The simulation of the bridge subsystem employs the Finite Element Method (FEM), in order to export the mass M B and the stiffness K B matrices [11]. Beam elements are used to model the different components of the bridge and rigid contact between the elements is assumed.…”

“…where E V T and E B T are identity matrices pertaining to the vehicle and the bridge, and the vector ξ T V = ξ T B = ξ T g = ξ x ξ y ξ ψ denotes the creepage of the vehicle and the bridge. The calculation of the saturation coefficient ε and the Kalker's creep coefficient matrix f T follows the same procedure as the study of Zeng and Dimitrakopoulos [11]. The creepage vector contains the relative wheel-rail velocity in the tangential direction normalized to the vehicle speed v:…”

Dynamic vehicle–bridge interaction under simultaneous vertical earthquake excitation

“…Further studies have been conducted by Matsumoto et al (2004), Xia et al (2006), Tanabe et al (2008Tanabe et al ( , 2011a, Yau (2010) and Du et al (2012). Recently, the two last authors of the present paper proposed a scheme for the seismic response analysis of interacting (horizontally) curved railway bridges and trains (Zeng and Dimitrakopoulos (2016).…”