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Using EDEM to Simulate Collapse of Elevated Expressway Bridges from the Kobe Earthquake

by Kimiro Meguro and Tsuneo Katayama

This article presents research conducted under the auspices of the NCEER-INCEDE (International Center for Disaster-Mitigation Engineering) cooperative project on post-earthquake reconstruction. The article is part of a proceedings from the Center-to-Center Workshop on Earthquake Engineering Frontiers in Transportation Facilities, which will be available later this year as NCEER  Technical Report 97-0005. For more information about INCEDE, visit their home page at http://incede.iis.u-tokyo.ac.jp or contact Kimiro Meguro, INCEDE, University of Tokyo, email: meguro@incede.iis.u-tokyo.ac.jp. u-tokyo.ac.jp.
 

Introduction

The Great Hanshin (Kobe) earthquake of January 17, 1995 caused over 100,000 collapsed houses and buildings, heavy damage to the civil infrastructure, and more than 6,400 deaths. Most of the deaths were due to the collapse of structures.

To assure the safety of the general public in the event of future earthquakes, it is important to study the collapse mechanism of structures. The process used to analyze the behavior of structures in a collapse, addressing problems such as, "Where and how do they undergo collapse?," "Is the time for collapse short or long?," "How far would the segments of structural members move in the process of collapse?," and "Would the collapse of structures be partial or complete?," is expected to greatly reduce the uncertainty of structural collapse behavior and collapse mechanisms.

Figure 1: EDE modeling
The method used to perform the analysis in this study is called the Extended (or Modified) Distinct Element Method (EDEM, MDEM) (Iwashita and Hakuno, 1990, Meguro et al., 1989, 1991) which was developed from the distinct element method (Cundall, 1971). In this study, the collapse mechanism of structures, especially elevated highway bridges during the 1995 Kobe earthquake, is studied using EDEM.

Extended Distinct Element Method

The EDEM was originally developed by researchers at the University of Tokyo. The method can be applied to structural behavior from a continuous state to a perfectly discrete state. This method maintains continuity of the elements because it includes an additional spring, called porespring or jointspring, which represents the effects of the material surrounding the elements (figure 1). The use of DEM was extended to the fracture analysis of structures, usually analyzed only by the methods based on continuum equations such as the FEM (Finite Element Method).

The equations of motion of an element, i, having mass, mi, and moment of inertia, Ii, are

mi d2u/dt2 + Ci du/dt + Fi = 0 (1)

Ii d2f/dt2+ Di df/dt + Mi = 0 (2)

in which Fi is the sum of all the forces acting on the element; Mi is the sum of all the moments acting on it; Ci and Di are the damping coefficients; u is the displacement vector; and f is the rotational displacement. The time histories of u and f are obtained stepbystep in the time domain by the explicit numerical integration of equations (1) and (2).

Numerical Results

Figure 2: Damage to elevated expressway bridges (fallen two adjacent simple-beam decks)

Elevated highway bridges and railway bridges were severely damaged due to the 1995 Kobe earthquake. Since the earthquake occurred in early morning, casualties due to damage to highways and railways were not as great had the earthquake occurred later in the day. Figures 2 and 3 show the collapse of elevated bridges which are part of the Hanshin Expressway. Considering the damage in figure 2, although the piers didn't collapse but suffered some damage at the bottom, two adjacent simple-span decks became unseated at the bearing supports (figure 4). In addition, seventeen piers spanning over 630 m of pilz-type bridges were destroyed and the bridges collapsed (figure 3). To study the collapse mechanism of these elevated bridges, the fracture process of the damage were simulated using EDEM.

Figure 4figure 5 and figure 6 show the damaged elevated bridge models (Models A and B) for EDE simulation. Considering the fracture mode of the damage and computational time, the number of elements used were reduced and the model was simplified. Since the ground motion at these sites was not recorded, numerically integrated displacement motion from the NorthSouth (NS) and EastWest (EW) components of the ground acceleration records at Kobe Marine Meteorological Observatory were used in the simulation.

Simulation Results Using Model A

Effect of time lag of seismic load at the bases:

Effect of differing dynamic properties between decks:

Effect of pounding between decks:

Simulation Results Using Model B

The collapse process of the damage to elevated expressway bridges due to overturning was simulated using Model A-2, which simulated the damage which occurred during the Kobe earthquake as shown in figure 3.

Figure 12 shows the displacement-acceleration relation of the deck. With time, the bridge inclined and finally overturned. Although the exact collapse process is not reported, the final collapse modes obtained in this study agree with those of the real damage.

Conclusions

Using EDEM, the collapse process of structures damaged in the 1995 Kobe earthquake was simulated to study the mechanism of the damage. These simulations were based on the new concept of EDEM, where EDEM was used as an enhanced lumped mass system. Although the phenomena treated in this study were difficult to simulate by conventional methods such as the FEM, the numerical results obtained by EDEM agree well with the real earthquake damage.

Examining the simulation results, a conclusion can be drawn that the macro models of these structures would be capable of demonstrating to some extent how structures would undergo local collapse, whereby the models account for the process or the mechanism of actual earthquake-caused structural collapse with certain accuracy. Although the EDEM can be further refined, the results for fracture as a whole generally replicate observed earthquake damage.

References

Cundall, P. A. (1971), "A Computer Model for Simulating Progressive, Large Scale Movement in Blocky Rock Systems," Proceedings: Symp. ISRM, Nancy, France, Vol. 2, 129-136.

Iwashita, K. and M. Hakuno (1990), "Modified Distinct Element Method Simulation of Dynamic Cliff Collapse," Structural Eng./Earthquake Eng., Japan Society of Civil Engineers (JSCE), Vol. 7, No. 1, 133-142.

Meguro, K. and M. Hakuno (1989), "Fracture Analyses of Concrete Structures by the Modified Distinct Element Method," Structural Eng./Earthquake Eng., JSCE, Vol. 6, No. 2, 283-294.

Meguro, K., K. Iwashita and M. Hakuno (1991), "Fracture Analyses of Media Composed of Irregularly Shaped Regions by the Extended Distinct Element Method," Structural Eng./Earthquake Engineering JSCE, Vol. 8, No.3, 131s-142s.

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