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Research Papers

# Blast Responses of Bridge Girders With Consideration of Isolation Effect Induced by Car BombOPEN ACCESS

[+] Author and Article Information
Zhijian Hu

Professor
School of Transportation,
Wuhan University of Technology,
Wuhan 430063, China
e-mail: hzj@whut.edu.cn

Yifeng Zhang, Zhen Zeng

School of Transportation,
Wuhan University of Technology,
Wuhan 430063, China

L. Z. Sun

Department of Civil and
Environmental Engineering,
University of California,
Irvine, CA 92697

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 7, 2016; final manuscript received September 12, 2016; published online February 1, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021003 (Feb 01, 2017) (7 pages) Paper No: MATS-16-1134; doi: 10.1115/1.4035273 History: Received May 07, 2016; Revised September 12, 2016

## Abstract

Car bomb attack exhibits considerable different effects on structures when compared with the bare explosive blast. In this paper, a postdisaster investigation is presented for an existing bridge under accidental car bomb blast loading. Based on the analysis of the explosive properties, the crack distribution and deformation of the blast loaded girders are studied. Numerical analysis is conducted to verify the findings by simulating the truck isolation effect with steel plate. Both field data and numerical results indicate that the isolation effect of the vehicle can significantly affect the blast loading distribution on structures. Specifically, the shock wave propagation is isolated directly under the explosive source with the delayed arriving time. Peak values of overpressure within the steel plate isolating region are diminished while the pressures are magnified outside the isolating region due to reflection and wave merging. The results can be applicable to determine the essential blast-resistant design criteria to reduce the probability of blast induced failures.

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## Introduction

Over the last few decades, the importance of protecting the public transportation infrastructure, especially bridges, has become increasingly significant with the increase in violent events. Recent terrorist attacks in Moscow (2011), Stockholm (2010), London (2005), and Madrid (2004) [13] show that vehicle-delivered bombs or hand-placed explosives on bridges pose increasingly high potential of terrorist attacks on infrastructure systems. Especially, since the highly publicized terrorism bombing attack on Sept. 11, 2001, protecting the public transportation systems has become a top priority for transportation authorities [4] because any major disruption of the transportation flow may yield substantial economic losses in the affected region. Due to its complexity, designing a bridge to withstand blast loads poses considerable challenges to the bridge engineers. These challenges are largely due to lack of necessary training to understand the principles of the blast wave propagation and its potential effect on bridge structures.

Recently, a number of papers have conducted in-depth studies on blast effects on bridges. In light of vulnerability to terrorist attacks, an effective approach to bridge design was first employed to evaluate risk and fragility to a bridge and to determine what was acceptable [56]. Abdollahzadeh and Nemati [5] calculated the annual risk of blast-induced progressive structural collapse with a simulation procedure generating blast configuration and performed kinematic plastic limit analysis to verify the structural stability. Williamson and Winget [6] discussed blast effects on bridge components and outlined a procedure for design and retrofit of bridge for security. Experimental and computational research efforts were carried out to learn the responses of blast-loaded concrete bridge columns [79]. Fujikura et al. [1011] conducted blast testing on the 1/4 scale concrete-filled steel tube columns, ductile reinforced concrete (RC) columns, and nonductile RC columns retrofitted with steel jacketing. A moment-direct shear interaction model was also proposed to account for the reduction of direct shear resistance on cross sections when large moments were simultaneously applied.

A number of tests, in characterizing the dynamic behavior of blast loaded bridge structures, have been carried out by governmental and academic organizations. Wang et al. [19] addressed the scaling of the dynamic response of one-way square RC slabs subjected to close-in blast loadings caused by mass detonation. Two pairs of scaled distances were experimentally compared with the spallation damage. Since blast resistance experiments were performed on relatively small specimens, Foglar et al. [3] presented the results of the field experiments focused on the effect of fibers, concrete compressive strength, and its combination on blast performance of concrete. The tests were performed using real scale precast slabs for better simulation of real in situ conditions and large TNT charges placed in a distance from the slab. Combination of fibers and increased compressive strength proved itself to be very effective for improving the blast performance. Cofer et al. [20] validated a finite element model of a precast, prestressed concrete girder on 6 m long specimens with above or below girder blast loading. The girder model was further expanded to a four-girder, simple-span bridge model. Pan et al. [18] modeled a single-span RC composite steel slab-on-girder bridge system with a multi-Euler domain method to study the blast-resistant capacity.

These experimental and numerical efforts have come up with a number of valuable recommendations in designing and retrofitting blast loaded bridges. Current research investigations, however, mainly focus on single component of structures; few have taken the whole bridge or superstructure into account. The structural behavior and damage of the existing bridge in a blast event are rarely reported due to a lack of full-scale measurement data. In addition, bridges are susceptible to suffer from close-by car bombs whose isolation effect is seldom considered in current researches. The objective of this study is to identify blast responses of bridge girders with consideration of isolation effect induced by above-deck car-bomb detonation. With the postdisaster investigation on an existing bridge damaged by an accidental blast event, blast load distribution on concrete deck is characterized with modified formula. The results can be applicable to determine the essential blast-resistant design criteria to reduce the probability of blast-induced failures.

## Brief Review of Blast Loading Theory

The detonation of a high explosive is a high-rate chemical reaction producing a localized sudden release of energy that dissipates violently through a shock wave, which is a region of highly compressed air radiating spherically away from an explosive source. This region of compressed air creates an overpressure as it passes by a given position in space. The idealized time-history curve of incident and reflected overpressure is shown in Fig. 1. At the arrival of the shock wave front, the overpressure rises nearly instantaneously to its peak before decreasing to zero, during which a small negative overpressure occurs. It is experimentally validated that the pressure of blast wave at a given standoff distance decays quasi-exponentially with time increasing. The negative overpressure (Fig. 1(a)), which is below the ambient atmospheric pressure and creates a vacuumlike effect, is often disregarded in calculation because the influence of the small negative pressure region is negligible compared to the devastation and damage induced by much larger positive overpressure [21].

Furthermore, standoff distance is another key factor to influence a blast wave effect. Fig. 1(b) expresses a decrease in the peak pressure generated at multiple distances along the propagation path of a moving shock front with the distance from the detonation point increasing. In general, often the easiest protection way to decrease the pressure is to increase the distance between a blast and the object of interest.

## Structural Damage Analysis

###### Postdisaster Field Inspection.

The bridge under consideration is an existing bridge called Fengxingpai Bridge, built in 2004. It was designed in accordance with Chinese General Specification for Design of Highway Bridges and Culverts [22]. The designed earthquake intensity was six [23]. The bridge employed a twin bridge system consisting of north and south bridges with a 2 m gap. Both bridges were four-span structures with equal span length of 20 m. The PC/PS void slab girders were simply supported by three-rib abutments at both ends of the bridge and two-column bent at each bent. The elevation view of the bridge is shown in Fig. 2.

Unfortunately, a truck that carried fireworks exploded on the deck of the Fengxingpai Bridge. The truck was destroyed and the south bridge was severely damaged, as shown in Figs. 3 and 4. This incident provides a unique opportunity to evaluate the structural performance of the bridge in car-bomb blast environment. In the postdisaster investigation, the visual inspection and field measurements were conducted, which included photos of damaged components, measurements of the girder deformations and the crack openings, and reproduction of the crack distributions. The explosive properties were also estimated with limited information and interviewing.

###### Damage of Bridge Deck.

The accidental explosion, occurred on the south bridge deck, was roughly located at midspan of the fourth span, and above girders 10 and 11, as shown in Fig. 5. The field inspection indicated that most of the void slab girders in the fourth span of the south bridge were severely damaged, including collapse, extensive cracking, and large permanent deformation. Figure 5 illustrates both the girder layout and re-produced crack distribution on the bridge soffit of the fourth span of the south bridge, where the digitals for each crack represent the crack width with the unit of mm.

It is observed that the exterior girder (girder 1) was collapsed, which caused the failure of the exterior shear keys at the related bent and abutment. As shown in Figs. 4 and 6, the blast loading produces very large permanent deflections, and forms flexural plastic hinges at midspan of girders 2 and 3. The cracks are also roughly distributed in midspan regions of girders 2 and 3, as shown in Fig. 5. The maximum crack width on girders 2 and 3 is 14 mm and 10 mm, respectively. For girders 4–8, the massive cracks were found on the soffits and distributed along the whole length of the girders. The maximum crack opening is 3 mm wide that far exceeds 0.2 mm, the maximum allowed crack width defined by design code [22]. For girders 9 and 10, only several cracks near the supports were found on both the side surfaces and the soffits of the girders, which can be definitely sorted as flexural shear cracks. No evidence shows that the girders 11 and 12 were damaged in the incident, while web-shear cracks were still found on the web of girder 11 near the support when girder 10 was removed in the process of demolishing. It can be concluded that damage or the crack width on concrete girders becomes larger as the standoff distance increases, which is inconsistent with the fact that overpressure decays with the increase of standoff distance, as shown in Fig. 1. This may be explained that the truck body plays a significant role in shock wave propagation. In other words, isolation effect induced by car bomb should be taken into account for above-deck detonation analysis.

###### Girder Deflection.

The blasting induced severe deflection on the girders of the fourth span of the south bridge. All the fourth-span girders of both the north bridge and the south bridge of the Fengxingpai Bridge were measured for the deflections and the final results are shown in Table 1, where minus means the upward camber. It can be seen that little influence has been produced on the girders of the north bridge by the blasting, since all the related deflections of the north bridge in Table 1 are minus. However, for the south bridge, the girders present heavy deformation indicating an increasing tendency from the inner girders to the outer. Beside the fallen girder (girder 1), girder 2 provides the maximum deflection of 756.0 mm. The huge deflections of girders 2 and 3 also indicate that the plastic hinges are formed on these two girders and the integrity of the deck has been destroyed between girders 3 and 4 since the connection between the girders was cast in place concrete which was not strong enough during the accident, as shown in Fig. 6.

From the measured deflection distribution, it can be concluded that more severe damage was found on the girders with larger standoff distance from detonation source. Again isolation effect can be employed to explain this phenomenon which is contradicted with traditional shock wave propagation. To understand isolation effect numerical investigation was performed in Sec. 4.

## Numerical Investigation

###### Numerical Model Description.

The south bridge deck of the fourth span of the Fingxingpai Middle Bridge is modeled with 12 void slab girders. Each girder is 20 m long with 1.0 m and 0.85 m in width and depth, respectively. The girder section has a circular void chamber with a diameter of 0.6 m. Fifteen Φ15.24 mm strands providing prestresses are arranged in the soffit of each girder, while two-leg stirrups are symmetrically placed along the girder span with a 0.1 m interval for the portions near the supports and 0.15 m for the central part. Simplifications were made in the finite element modeling: (1) Both the disturbance effect and energy dissipation of the truck are not modeled independently, because they cannot be identified with current simulation techniques and can only, in this case, be incorporated with the isolation effect by providing the steel plate in the numerical model; (2) It was assumed that the concrete deck is perfectly bonded between void slab girders; and (3) The gravity load is also neglected in the analysis.

According to the truck dimensions, the gross net weight of firework is estimated to be about 1100 kg with a TNT equivalent weight factor of 0.4. Therefore, the charge weight in this event is equivalent to 450 kg TNT, coincident with the explosive weight range of 450 kg to 1800 kg defined for truck bomb [24]. The height of mass center of the firework is estimated at 1.4 m above the deck level (which is 0.2 m higher than the height of 1.2 m proposed as the standard center of mass for most vehicle explosions) with consideration of void ratio of firework. Therefore, an equivalent 450 kg TNT charge is placed at 1.4 m above the bridge deck, and a steel plate with dimensions of 4 m × 4 m × 0.06 m is placed 0.2 m below the charge in the finite element autodyn model to simulate the isolation effect of the truck body in the above-deck car bomb-type explosion event. The ends of the deck model are pin- and roller-supported effectively on a knife edge. This was simpler than modeling the actual bearing of the concrete on a polyurethane pad.

In this study, the bridge deck and the steel plate are modeled as the Lagrange solid elements, while the high-explosive materials and the ambient air are modeled by the Eulerian elements. The reinforcements are modeled as the Lagrange beam elements by conducting a numerical convergence test on various mesh sizes (1 mm, 5 mm, 10 mm, 20 mm, and 25.0 mm); it is found that the 10 mm mesh yields similar results with the smaller meshes tested under close proximity explosion load (450 kg TNT at 1.4 m) but with less simulation time. Figure 7 presents the numerical model employed in this study.

###### Material Properties.

The Riedel-Hiermaier-Thoma (RHT) concrete failure model is employed in this study because the chosen concrete model has been proven to be appropriate in estimating the concrete behavior under rapid dynamic loading conditions [1819]. The RHT model employs a damage factor D to model the progressive crushing and subsequent weakening of concrete. The definition of D is shown as follows: Display Formula

(1)$D=∑Δεplεpfailure$
Display Formula
(2)$εpfailure=D1(P*−Pspall*)D2$

where D1 and D2 are material constants used to describe the effective strain to fracture as a function of pressure, P* is the pressure normalized with respect to fc, $Pspall∗$ is the normalized hydrodynamic tensile limit, and fc is the cylinder strength. The value of D increases from zero to one with damage varying from no damage to complete failure. To track the concrete behavior as the blast event progressed, the material erosion for a solid element was used to eliminate the cells that reach a certain deformation criterion because of both the brisance effect and the fracture induced. A damage-based erosion function was implemented to delete the elements which reached a plastic strain of 0.005.

The steel model used for both the reinforcement and the steel plate is called the Johnson and Cook EOS model [18]. In this analysis, the material parameters are based on the original data for steel 4340. The density, bulk modulus, and shear modulus of steel are 7830 kg/cm3, 159 GPa, and 76.9 GPa, respectively. A yield stress of 792 MPa and a constant strain rate of 0.014 are adopted in this model.

The ambient air is assumed to be an ideal gas with static initial internal energy. To model the infinite space detonation, the boundary condition adopted in the Eulerian domain in this study is the nonreflecting flow-out boundary. The following formula is used to model the ideal gas equation of state: Display Formula

(3)$p=(γ−1)ρe$

where p is the pressure, $γ$ is the constant ratio of specific heats, and e is the specific internal energy. The air density $ρ$ is taken as 1.205 kg/m3 and $γ$ is 1.4. According to the gamma law calculation, its initial internal energy is 2068 kJ/kg under standard atmospheric pressure.

The high explosives (TNT) are modeled with the Jones-Wilkins-Lee (JWL) equation of state, which is described by the following expression: Display Formula

(4)$P=A(1−ωR1V)e−R1V+B(1−ωR2V)e−R2V+ωeV$

where P is the hydrostatic pressure, and e and V are the specific internal energy and volume, respectively. Further, A, B, R1, R2, and $ω$ are constants that are related to the particular explosive material. In this study, A = 3.37377 × 105 MPa; B = 3.7471 × 103 MPa; R1 = 4.15; R2 = 0.9; ω = 0.35; the density of explosive $ρ$= 1630 kg/m3; and detonation velocity is 6930 m/s.

###### Verifications.

Since field investigations were conducted after the accidence, the data from site investigation are limited. Some critical parameters such as charge location and blast reaction period can only be estimated with scenario and experience. Therefore, only measurable damage such as cracking and deformation can be employed as references to numerical results.

Figure 8 illustrates the maximum deflection comparison between the measured values and the numerical results. It is shown that, except for girders 2 and 3, the numerical results are coincident with the measured deflections obtained in the field investigation. The measured midspan deflections of girders 2 and 3 are higher than those of simulation. This can be explained with two aspects: (a) the estimated detonation conditions are not identical to the case in practice, and (b) the deck integrity has been destroyed in practice whereas in numerical simulation, this characteristic has not been modeled effectively since the assumption of perfect connection between void slab girders was applied. In addition, the ruptured girder 1 was also not taken place in numerical simulation. This is again due to the assumption of perfect connection and difference of detonation conditions between on-site and numerical cases. Therefore, with the steel plate to model the truck isolating system, the numerical model has been well matched with the fact that girder deflection is increased as standoff distance increases.

Figure 9 shows the damage occurred on concrete deck in numerical simulation, where dark color represents complete damage while gray region indicates no damage. It is noted that in the region beneath the charge, little damage is observed, although the scale distance in this region is the smallest. In Fig. 5, the same phenomenon is observed that no visible crack can be found in the corresponding region. This can be explained that the overpressure is isolated by the steel plate. For the area away from the detonation center, however, more damage occurs on the deck and extends to a large field longitudinally, which is consistent with the flexural-shear damage observed on girders 4–8 in Fig. 5. Then in the region far from the charge, which is corresponding to the girders 1–3 in Fig. 5, damage is still observed but concentrates on the central portion where flexural cracks were observed in Fig. 5. Therefore, when compared to Fig. 5, a similar damage tendency, which does not follow common knowledge of blast in free air, is observed for both numerical and field investigations, i.e., the numerical failure coincides with the failure identified in the postdisaster investigation. There is, however, still some difference for the damage distribution between numerical modeling and the actual event, as shown in Figs. 5 and 9. From Fig. 9, the symmetry of damage distribution is observed but an asymmetric crack distribution is found in Fig. 5 with respect to crack width. The most severe damage occurs on girders 1–3 where crack widths reached more than 10 mm or rupture happened, while this is not the case in numerical situation, as shown in Fig. 9. These may be again due to the integrity assumption for girder connection and the simplification assumption for the truck isolating system replaced by a steel plate in the numerical simulation. Therefore, from both the damage and the deflection distribution, we can conclude that the presence of a steel plate is effective for modeling the isolation effect on the propagation of overpressure on the deck, and the isolation effect of the truck has a great influence on the amount of damage to the concrete girder.

## Results and Discussion

A total of 273 gauges are set on the deck at longitudinal and transverse intervals of 1 m to obtain the overpressure distribution above deck shown in Fig. 7. Figure 10(a) further illustrates the overpressure distribution above deck without consideration of isolation effect while Fig. 10(b) presents the result with steel plate to simulate the truck isolating system. The numerical comparisons indicate that the peak overpressure directly under the detonation center has been approximately diminished by the presence of the steel plate, and that the peak values are concentrated outside the regions covered by the steel plate. Therefore, when taking isolation effect into account, the field phenomena related to crack and deflection distribution (Figs. 5 and 6) can be explained reasonably. It can be concluded that practically the isolation effect induced by trucks loaded with explosive materials plays significant roles on shock wave propagation and should be taken into account for above-deck blast analysis and design of bridge structures.

Figure 11 displays the peak overpressure distributions along the longitudinal line between girders 7 and 6 for cases with and without consideration of isolation effect. It is observed that, due to isolation effect, peak values of overpressure have been decreased significantly from 4.2 MPa to 0.5 MPa within the region covered by the steel plate. However, outside the covered region, the peak values with isolation effect reach about twice of those without isolation. This may be due to wave reflection and diffraction. When the incident wave, with rapid speed in ambient air, impacts the isolating plate, the blast wave reflects from or diffracts around the barrier. The reflective and diffractive waves join with the initial blast wave at the same location, or named wave mergence. During this process, the blast wave properties, such as the pressure, density, and energy, increase.

To elucidate the isolation effect on above deck car bomb, overpressure-time curves were extracted for four typical positions, as shown in Fig. 12. Point 1 locates in the uncovered region while Points 2–4 are in the covered region, as depicted in Fig. 11. It is clearly observed in Fig. 12(a) that the peak overpressure with the isolating plate (solid red line) has increased to 1.4 MPa from less than 1.0 MPa when compared to the case in free air, i.e., without isolating plate (blue dash line). This is due to wave merging, as mentioned previously. Figure 12(b) presents the overpressure curves at Point 2 which is within the covered region but not directly under the isolating plate, where the peak values linger around 1.0 MPa for both with consideration of isolation effect and without isolation effect. For the points directly under the steel plate, the overpressure curves are demonstrated in Figs. 12(c) and 12(d) where the peak values are reduced to one fifth or one tenth of the initial values in free air. Moreover, in Fig. 12, arriving time for peak pressure is delayed with the presence of the isolating plate. This is due to the blast wave speed decrease during the reflection process [15].

As a result, the isolation effect induced by truck system for above deck car bomb can be described as the following key points: (1) Peak pressure values decrease significantly within the region covered by steel plate; (2) In the uncovered regions, peak values of pressure increase due to wave mergence; and (3) Due to wave speed decreasing, the arriving time for peak pressure is delayed in the case of considering isolation.

## Concluding Remarks

This paper presents the findings in a postdisaster investigation on an existing bridge above-deck blast accident, which includes the explosive properties, blast load distributions on girders, and the damage characteristics of bridge girders. Based on the collected data of bridge damage, the isolation effect induced by truck is analyzed. The numerical method is employed to simulate the above-deck car-bomb explosion event. The numerical results are consistent with those obtained from field investigation. Based on the analysis of distributions of cracks and deflections, the conclusions are made as follows:

For an above-deck blast event, the isolation effect induced by the vehicle can significantly affect the shock wave propagation, and should be considered for analysis of overpressure distributions and structural responses.

With taking isolation effect into account, the overpressure may vanish within the isolated region while in the uncovered regions the intensity of pressure may be magnified due to wave mergence.

Arriving time for peak overpressure in the whole deck region is delayed due to wave reflection and steel plate isolation.

## Acknowledgements

Financial support for this study is provided by the Fundamental Research Funds for Central Universities (Project No. 2013-IV-016). Special thanks are given to Jiangxi Provincial Center for Traffic Engineering Quality Inspection for the field inspection.

## References

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## References

Jenkins, B. M. , 1997, “ Protecting Public Surface Transportation and Patrons From Terrorist Activities: Case Study of Best Security Practices and a Chronology of Attacks,” Moneta Transportation Institute, San Jose, CA, MIT Report No. 97-04.
FHWA, 2003, “ Recommendations for Bridge and Tunnel Security, Prepared by the Blue Ribbon Panel on Bridge and Tunnel Security,” Federal Highway Administration, Washington, DC.
Foglar, M. , and Kovar, M. , 2013, “ Conclusions From Experimental Testing of Blast Resistance of FRC and RC Bridge Decks,” Int. J. Impact Eng., 59(9), pp. 18–28.
Hu, Z. J. , Wu, L. , Zhang, Y. F. , and Sun, L. Z. , 2016, “ Dynamic Responses of Concrete Piers Under Close-in Blast Loading,” Intl. J. Damage Mech., 25(8), pp. 1235–1254.
Abdollahzadeh, G. , and Nemati, M. , 2014, “ Risk Assessment of Structures Subjected to Blast,” Int. J. Damage Mech., 23(1), pp. 3–24.
Williamson, E. B. , and Winget, D. G. , 2005, “ Risk Management and Design of Critical Bridges for Terrorist Attacks,” J. Bridge Eng., 10(1), pp. 96–106.
Williams, G. D. , and Williamson, E. B. , 2011, “ Response of Reinforced Concrete Bridge Columns Subjected to Blast Loads,” J. Struct. Eng., 137(9), pp. 903–913.
Williamson, E. B. , Bayrak, O. , and Davis, C. , 2011, “ Performance of Bridge Columns Subjected to Blast Loads: Experimental Program,” J. Bridge Eng., 16(6), pp. 693–702.
Williamson, E. B. , Bayrak, O. , and Davis, C. , 2011, “ Performance of Bridge Columns Subjected to Blast Loads: Results and Recommendations,” J. Bridge Eng., 16(6), pp. 703–710.
Fujikura, S. , Michel, B. , and Diego, L. , 2008, “ Experimental Investigation of Multihazard Resistant Bridge Piers Having Concrete-Filled Steel Tube Under Blast Loading,” J. Bridge Eng., 13(6), pp. 586–594.
Fujikura, S. , and Bruneau, M. , 2011, “ Experimental Investigation of Seismically Resistant Bridge Piers Under Blast Loading,” J. Bridge Eng., 16(1), pp. 63–71.
Ibrahim, A. , Salim, H. , and Flood, I. , 2011, “ Damage Model of Reinforced Concrete Slabs Under Near-Field Blast,” Int. J. Prot. Struct., 2(3), pp. 315–332.
Ibrahim, A. , and Salim, H. , 2013, “ Finite-Element Analysis of Reinforced-Concrete Box Girder Bridges Under Close-In Detonations,” J. Perform. Constr. Facil., 27(6), pp. 774–784.
Tai, Y. , Chu, T. , and Hu, H. , 2011, “ Dynamic Response of a Reinforced Concrete Slab Subjected to Air Blast Load,” Theor. Appl. Fract. Mech., 56(3), pp. 140–147.
Son, J. , and Astaneh-Asl, A. , 2012, “ Blast Resistance of Steel Orthotropic Bridge Decks,” J. Bridge Eng., 17(4), pp. 589–598.
Tang, E. K. C. , and Hao, H. , 2010, “ Numerical Simulation of a Cable-Stayed Bridge Response to Blast Loads—Part I: Model Development and Response Calculations,” Eng. Struct., 32(10), pp. 3180–3192.
Hao, H. , and Tang, E. K. C. , 2010, “ Numerical Simulation of a Cable-Stayed Bridge Response to Blast Loads—Part II: Damage Prediction and FRP Strengthening,” Eng. Struct., 32(10), pp. 3193–3205.
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## Figures

Fig. 1

Pressure decays for blast waves: (a) idealized overpressure curves and (b) peak pressure decrease at multiple distances

Fig. 2

Existing Fengxingpai Bridge, Jiangxi Province, China (before accident)

Fig. 3

Blast-destroyed truck

Fig. 4

Collapse of exterior girder (girder 1)

Fig. 5

Girder layout and crack distribution on bridge soffit (reproduced from field measurement)

Fig. 6

Permanent deformation of girders 2 and 3

Fig. 7

Numerical model with gauge arrangement

Fig. 8

Comparison of girder deflections

Fig. 9

Above-deck damage zones

Fig. 10

Comparison of overpressure: (a) above-deck overpressure distribution without isolation and (b) above-deck overpressure distribution with isolation

Fig. 11

Damage of the girders

Fig. 12

Comparison of time history curves at typical positions: (a) at point 1, (b) at point 2, (c) at point 3, and (d) at point 4

## Tables

Table 1 Deflections in fourth span of the bridge (unit: mm)

## Discussions

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