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: firstname.lastname@example.org.
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 equations of motion of an element, i, having mass,
mi, and moment of inertia, Ii, are
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).
|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 4, figure 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.
Effect of time lag of seismic load at the bases:
Using Model A in figure 4, a series of simulations, with and without considering time lag due to wave propagation, were carried out with different apparent wave velocities (Va=500, 1000, 3000, 5000, ?m/s).
Some of the simulation results are shown in figure 7. The figure shows the time history of the forces acting on each fixed bearing. It can be seen that there is pounding between decks and impulsive forces are occurring due to their effects. In this simulation, it is shown that although pounding between decks can occur, the jointsprings between the elements are not destroyed. The maximum forces acting on each of the fixed bearings are compared between the five cases (see figure 8). Among these cases, the case of Va=3,000 m/s was the most severe.
Effect of differing dynamic properties between decks:
Since large differences between dynamic properties among S1, S2 to S5, and S6 are considered one of the main reasons for collapse, a second set of tests were performed to study these effects. A virtual model (Model A2) was made by dividing the continuous longspan S1 deck into three simply supported (S1aS1c) decks and the S6 deck was divided into five simply supported decks (S6aS6e) as shown in figure 4. Using the same conditions as in the previous simulation, dynamic response analysis was performed under the condition of Va=3,000 m/s. Numerical simulation results are shown in figure 9. In this case, severe pounding similar to the previous case does not occur because the dynamic properties of decks S1 and S6 became similar to the S2 to S5 decks when they were divided. By comparing the two results, it can be noted that the effects of the differing dynamic properties due to different structural type had an important role in the collapse mechanism.
Effect of pounding between decks:
Dynamic fracture analyses of the bridges were carried out by using apparent wave velocity, Va=3,000 m/s. Figure 10 shows the simulation results. From this figure, it can be seen that due to pounding between decks propagating from east to west, all the fixed bearings broke at around 8 seconds, which resulted in the collapse of two simply supported decks at piers P2 and P3. The collapse mode obtained here is very similar to that of the actual damage as shown in figures 2 and 4. The difference between the actual case and the simulation is that the S3 and S4 decks collapsed during the earthquake, while the S2 and S3 decks collapsed in the simulation. Considering the uncertainties of input ground motions and boundary conditions, the simulation results satisfactorily explains the mechanism of the damage shown in figure 2. In the next case, a simulation using Model A-2, in which S1 and S6 are divided, was carried out. Figure 11 shows the dynamic displacement response of each deck. From the results of the analysis, the dynamic displacement response was relatively small and the effects of different dynamic properties of bridges played an important role in the collapse mechanism.
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.
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.
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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