Plastic Behavior of Integral Bridge, Consisting of Supporting Steel Beams and Concrete Superstructure, under Spatially Varying Seismic Shock


Article Preview

The paper presents the dynamic response of an integral bridge to an earthquake registered in Central Europe. The acceleration history of the shock was scaled up to peak ground accelerations predicted for this seismic zone (0.4 g). The seismic action was implemented in the form of two models of three dimensional kinematic excitation: uniform and non-uniform (spatially varying). In the uniform model the assumption was made that the motion of all supports of the bridge was identical. In the case of the spatially varying excitation the wave passage effect was taken into consideration, assuming that the seismic wave propagated along the bridge forcing subsequent supports of the bridge to repeat the same motion with a time delay dependent on the wave velocity. The structural system of the integral bridge consisted of steel girders and crossbars whereas the superstructure was made of a concrete material. To represent the inelastic behavior of the integral bridge during the earthquake, plastic models of both the steel and the concrete material were implemented. For the steel material the classical metal plasticity model with the dynamic failure model of progressive damage, provided by the ABAQUS software, was applied. For the concrete material of the superstructure the concrete damaged plasticity constitutive model was taken into consideration. It turned out that when the non-uniform excitation model was imposed, the tensile damage (cracking) and the degradation of the support zones of the concrete deck were more significant than in case of uniform excitation. The non-uniform excitation model also caused considerably higher inelastic strains of the steel girders and crossbars than the uniform model. This resulted from quasi-static effects caused by ground deformations imposed on the bridge supports during the seismic shock.



Edited by:

Yeong-Maw Hwang and Cho-Pei Jiang




J. M. Dulinska and D. Jasinska, "Plastic Behavior of Integral Bridge, Consisting of Supporting Steel Beams and Concrete Superstructure, under Spatially Varying Seismic Shock", Key Engineering Materials, Vol. 626, pp. 438-443, 2015

Online since:

August 2014


* - Corresponding Author

[1] EN 1998-1: 2004 Eurocode 8 - Design of structures for earth-quake resistance. Part 1: General rules, seismic actions and rules for buildings, ENV 1998-1, CEN, Brussels.


[2] A. Zerva, Spatial variation of seismic ground motion. Modeling and engineering applications, CRC Press, Taylor & Francis Group, Boca Raton, FL, (2009).

[3] J.M. Dulinska, Influence of wave velocity in the ground on dynamic response of large dimensional structures, Int. Journal of Earth Sciences and Engineering, 4 (2011) 538-541.

[4] J.M. Dulinska, D. Jasinska, Performance of Steel Pipeline with Concrete Coating (Modeled with Concrete Damage Plasticity) under Seismic Wave Passage, Applied Mechanics and Materials, 459 (2014) 608-613.


[5] ABAQUS, Users Manual V. 6. 13, Dassault Systemes Simulia Corp., Providence, RI (2013).

[6] J. Lubliner, J. Oliver, S. Oller, E. Oñate, A Plastic-Damage Model for Concrete, International Journal of Solids and Structures, 25 (1989) 229-326.


[7] J. Lee, G.L. Fenves, Plastic-Damage Model for Cyclic Loading of Concrete Structures, Journal of Engineering Mechanics, 124 (1998) 892-900.


[8] T. Jankowiak, T. Lodygowski, Identification of parameters of concrete damage plasticity constitutive model. Foundations of Civil and Environmental Engineering, 6 (2005) 53-69.