2006 MSC.Software

- 1 -

Performance of Bridge Decks Subjected to Blast

Load

Jin Son1 Abolhassan Astaneh-Asl2 Marcus Rutner3

(1. University of California at Berkeley 2. University of California at Berkeley 3.

University of California at Berkeley)

2006 MSC.Software

- 2 -

Performance of Bridge Decks Subjected to Blast

Load

Jin Son1 Abolhassan Astaneh-Asl2 Marcus Rutner3

(1. University of California at Berkeley, USA 2. University of California at Berkeley, USA, 3.

University of California at Berkeley, USA)

Abstract: In the past ten years, the world has seen an alarming increase in the number of terrorist attacks

using explosives on civilian targets. Understanding the performance of structures, including bridges,

subjected to blast loads is of critical importance to prevent progressive collapse of the structure and massive

loss of lives. In this paper, the performance of two types of bridge deck systems, a steel orthotropic box and

a composite steel-concrete plate girder, subjected to simulated blast loads are studied. The car bomb

detonation on the deck is assumed to be the most likely scenario to occur. In these studies, the deck structure

and the air surrounding it that will transfer the explosion effects to the bridge, are modeled as non-linear finite

elements and the MSC Dytran software is used to simulate the explosion and to analyze the effects of the

explosion on the deck structures. The main parameters of the study were types of the deck and material. Two

types of deck systems; steel orthotropic box and traditional steel plate girder- reinforced concrete slab

were considered. For the material, three types of steel and two types of concrete were considered. The

mechanical properties of material used in the analysis were the properties under high strain rates

corresponding to blast loading. By conducting the dynamic analysis the failure modes of these two common

types of bridge deck systems were identified and measures that can enhance blast-resistance behavior and

prevent progressive collapse are developed and proposed.

Keywords: bridge; blast loads; steel bridge deck; progressive collapse; protection against car bombs

1 Introduction

Since 1980’s, a number of structures, particularly military and government buildings, throughout the

world have been subjected to car bomb attacks by terrorists. Although many of these attacks have been on

buildings, in recent years the threat of car bomb attacks on the components of the infra-structure such as

bridges has increased tremendously as terrorists are beginning to show no distinction between military and

civilian targets. As a result, there is a justifiable reason to study response of threatened structures to such

attacks and to increase the resistance of civilian structures against them. Bridges, specially major and

monumental bridges, might be one of the main civilian structure targets since disruption of these main

transportation routes can have high probability of economical disaster in the area. Due to importance of these

structures, as well as number of casualties that can result from such attacks, protection of major

bridge against blast is becoming an important component of homeland security.

One of the major protection measures against car bomb attacks, which are used effectively for buildings,

is to prevent cars from getting too close to the structure. This is done by locating buildings a certain

“stand-off” distance away from the public access streets or by erecting barriers to prevent car bombs from

driving too close to critical buildings. Unfortunately, due to the very nature of the bridges being transportation

structures, none of these access control measures can be used to prevent car bombs from being on the bridge.

Therefore, it is very important that blastresistance of bridges, in particular long span and important bridges,

be studied and if necessary protective and hardening measures be devised and implemented.

2 Response of Bridges to Blast Effects

Due to the unpredictable nature of blast events and security concerns when disclosing blast information,

2006 MSC.Software

- 3 -

it is difficult if not impossible to set quantitative guidelines to prevent bomb damage. Research into the

behavior of materials and structures during these events especially for bridges has only just begun, so

structural response during blast events is largely unknown. As a starting point, the engineering community is

examining parallels between seismic and blast resistant design.

Current building design codes and guidelines, such as U.S. Department of Defense criteria [1, 2], ASCE7

Standard [3] and the European codes [4, 5] contain guidelines and provisions for blast resistant design and

progressive collapse prevention of buildings. However, due to the unpredictable nature of blast events and

security concerns when disclosing blast information, it is difficult if not impossible to set quantitative

guidelines to prevent bomb damage. Research into

the behavior of materials and structures during these events especially for bridges has only just begun, so

structural response during blast events is largely unknown. As a starting point, the engineering community is

examining parallels between seismic and blast resistant design. Like seismic events, blast events are low

probability and high-risk situations and are categorized as “Extreme Event“. Although both events are high

dynamic (transient) and with oscillation ranging

in nature, the distribution of forces imposed on a structure by these respective events is considerably

different. In the case of earthquakes the loadings are ground-generated and the response of the structure

depends heavily on the mass, global damping and global stiffness of the structure. In the case of an explosion

close to a structure, the load effects are primarily very high frequency shockwaves transmitted by the air to

a very localized area of the structure. The response of the structure to such shock waves primarily depends

on relatively local dynamic characteristics of the structure. Even with the above-mentioned differences

between seismic and blast effects on a structure and its response to such effects, the conceptual approach to

seismic and blast design is similar. For example, bridges subjected to either blast or seismic events will both

benefit from redundancy, continuity, and ductility incorporated into the design. However, the

demands placed on the structure under blast loading invoke a much more dramatic response, in a very

localized area, than the relatively subdued response during a major seismic event. Because of this, seismic

design does not provide adequate protection for a blast event.

3 Main Steps in Blast-Resistance Design of Bridges

The main steps in blast-resistance design of major bridges are:

1. Analyzing a realistic model of the bridge subjected to realistic effects of explosions using software that

is capable of simulating explosive effects and transferring such effects to the structure as well as capable of

realistically handling rate-dependent dynamic properties of material and kinematical nonlinearities.

2. Comparing the response of the bridge established in Step 1 above to pre-defined “Performance

Criteria”.

3. Depending on the outcome of Step 2 above, if necessary modifying the structure to ensure that the

response of the structure satisfies the performance criteria.

Performance Criteria, mentioned in the above Step 2, is perhaps the most important item in the

blast-resistance design of any structure and is the driving parameter in the process. Performance criteria are

defined as a series of provisions that define the acceptable level of response of a structure to applied loads.

4 Performance Criteria for Bridges Subjected to Blast

In developing performance criteria, one should consider protection of life and property in an economical

way and without turning the structures into a military bunker. Considering the current prevailing philosophy

of protection of buildings against blast effects, the following “Performance Criteria” for major bridges

subjected to blast loads are suggested.

Bridges considered to be designed for blast-resistance against a car bomb explosion should be designed

such that:

a. The casualties and injuries are limited to the immediate vicinity of the blast and are caused by the

explosion itself and shrapnel from the explosion and not caused by the debris separated from the bridge or by

2006 MSC.Software

- 4 -

the collapsed members of the structure. Unfortunately and tragically preventing all casualties and injuries

due to an explosion on a bridge, or any place for that matter, is almost impossible and some casualties and

injuries in the immediate area around the explosion are unavoidable.

b. The damage to the main gravity load carrying members of the bridge is minimal and such damage

does not compromise the ability of the structure as a whole to remain stable and carry its gravity load after

the blast.

c. Progressive collapse of any span or the bridge as a whole is prevented. It should be emphasized that

such progressive collapse can result in massive and catastrophic number of casualties and injuries and

loss of the transportation link.

5 Objectives of the Study

The main objective of the study reported herein was to investigate expected response of two types of

steel bridge decks namely typical orthotropic deck and typical reinforced concrete slab deck supported on

steel plate girders. Figure 1 shows these two types of bridge decks. This goal covers Criterion “b” in the above

performance criteria. The study reported in this paper is part of a larger project on the investigation of the

performance of long span cable-stayed and suspension bridges subjected to blast loads with the aim of

developing technologies to satisfy above-mentioned performance criteria [16]. The study reported herein

focuses on the car bomb detonation on the deck of a long-span cable-supported bridge. In the following

sections, a brief summary of the general blast theory and material properties used in the analyses are

provided and the models and results of the analyses of the bridge decks with various material strengths and

different size of explosions are presented. The last section includes conclusion and recommendations.

Figure 1 Steel orthotropic box and composite plate girder deck

6 Basic Blast Effects on Structures

When an explosion occurs, two types of waves are generated [6]. One is the incipient pressure wave

which is the pressure wave transferred into the air from a detonation point and another is the reflected

pressure wave which is the pressure wave impacting the solid surface of the exposed object such as a bridge

deck surface. After the shock wave is transferred to the air, an incipient pressure wave is generated. This

wave travels until it strikes objects with larger density than the air or it diminishes. The front of this wave is

called a shock front which can be visualized as a wall of highly compressed air with much higher pressure than

the surrounding air traveling with a very high velocity away from the explosion. This shock front diminishes

rapidly with the distance from the detonation point. After a very short time, the blast wave is propagated far

enough which at that distance the pressure of the shock front drops below the ambient air pressure. Finally,

the pressure of the shock front returns to the ambient air pressure.

When an incipient pressure wave encounters an object which has much larger density than air, a

reflected pressure wave is generated. This wave reflects from or diffract around the object depending on the

geometry, density and other dynamic properties of the object. When a traveling compressed air wave impacts

a relatively dense object such as a wall in a building or a deck surface in a bridge, it is reflected from the dense

surface and moves away from the surface into the compressed air. Then, the reflected pressure wave has

much higher pressure than an incipient wave pressure. The configuration of each wave is shown in Figure 2.

2006 MSC.Software

- 5 -

Figure 2 Pressure-time variation for incipient and reflected waves

7 Material Properties

The types of material used in the studies were steel, concrete, air and explosive (TNT equivalent).

Table 1 shows the range of strain rates for typical static and dynamic loads applied to structures. For

explosions this range is in the order of 101.5~104. Behavior of structural material such as steel and

concrete at such high strain rates is considerably different from the behavior under static or quasi-static

loads. The mechanical properties used in the analyses reported here included high strain rate effects as

discussed below. Although the temperature generated by the explosion can also influence the

properties of steel and concrete, this effect is not taken into consideration in this study due to lack of

precise experimental data.

Table 1 Dynamic modes of loading versus the strain rate [7]

Strain rate: <10-5 10-5 ~ 10-1 10-1 ~ 101.5 101.5 ~104 > 104

Loading: Creep Static or

Quasi-static Dynamic Impact

Hyper velocity

impact

Examples: Constant loading

machine Gravity loads

Impulse pressure

effects on highspeed

craft, wave

breaking loads

Explosion,

vehicle collision

Bombing

7.1 Steel

Under very high strain rates, the elastic modulus and the ultimate strain remain nearly the same as those

of under the static loads. However, under very high strain rates, generally, yield and ultimate strength of

structural steel increases as shown in Figure 3(a) for typical steels. It should be mentioned that the strain

rates in the material exposed to the blast waves decreases as the distance of the object from the blast point

increases. Therefore, the rise in yield stress and ultimate stress of steel will depend on the distance of the

impacted object from the detonation point. The Cowper-Symonds equation, Equation (1) below, is widely

used for describing a dynamic increase factor in material properties of steel [8]. In the equation, fyd is the

dynamic yield stress under high strain rate, fy is the static yield stress, & is the strain rate and C and q are

constants.

1

1.0

q

yd

y

f

f C (1)

Cowper and Symonds [8] have suggested values of C equal to 40.4 and q equal to 5 for low strength steel.

In 1999, Paik and Chung [7] suggested values of C and q equal to 3200 and 5 for high strength steel. In this

study, the stress-strain properties of steel are modeled by the bilinear curves shown in Figure 3(a). The

modulus of elasticity of steel used in the analysis is the same as for static loading and equal to 29000 ksi (200

GPa). The yield strain y varies depending on the dynamic yield strength given by Equation 1. In the analysis,

three different types of steel, common to bridges, namely ASTM-A588, ASTM-A852 and ASTM-A514, were

2006 MSC.Software

- 6 -

used. The static material properties of these steels areshown in Table 2.

Table 2 Material properties of steel used in analysis [9]

Properties

Type of steel

modeled

Density

lbf-sec2/in4

( kg/m3)

Modulus of

elasticity

ksi (Gpa)

Yield stress

ksi ( MPa)

Ultimate

strength

ksi ( MPa)

Maximum

plastic strain

in/in (m/m)

Hardening

modulus

A588 Grade 50 7.347x10-4

(7850) 29000 (200) 50 (345) 70 (485) 0.15 133(9.2)

A852 Grade 70 7.347x10-4

(7850) 29000 (200) 70 (485) 100 (690) 0.15 200 (13.8)

A514 Grade

100

7.347x10-4

(7850) 29000 (200) 100 (690) 120 (830) 0.075 266 (18.4)

(a) (b)

Figure 3 Typical stress-strain curves and bi-linear models of (a) steel and (b) concrete used in the studies

7.2 Concrete

Concrete has significantly different behavior when subjected to tension or compression. In

general, under static loading the tensile strength of concrete is ignored since compared to

compressive strength it is relatively small. However, under very high strain rates, such as those

generated by blasts, the tensile strength of concrete increases significantly and ignoring tensile

strength of concrete cannot be easily justified. The CEB-FIP model code [10] suggests the

following equations for compressive strength of the concrete at high strain rates. 1.026

/c cs

s

f f for 30sec-1 (2)

1/3

s

for 30sec-1

Where

cf = dynamic compressive strength at

csf = static compressive strength at s

/c csf f = compressive strength dynamic increase factor (DIF)

2006 MSC.Software

- 7 -

= strain rate in the range of 30x10-6 to 300 sec-1

s= 30 x 10-6 sec-1 (static strain rate)

log =6.156 -2

=1/5(5+9 /cs cof f )

cof = 10 MPa = 1450 psi

Although CEB-FIP code [10] suggests the dynamic increase factors under tension at high

strain rates, Malvar1 L. J. et al. [11] suggest the modified equations based on the experimental

test data. Their equation is described by Equation 3 below.

/t ts

s

f f for 1 sec-1 (3)

1/3

s

for 1 sec-1

Where

tf = dynamic compressive strength at

tsf = static compressive strength at s

/t tsf f = compressive strength dynamic increase factor (DIF)

= strain rate in the range of 30x10-6 to 300 sec-1

s= 30 x 10-6 sec-1 (static strain rate)

log =6 -2

=1/(1+8 /cs cof f )

cof = 10 MPa = 1450 psi

After reaching maximum strength in tension and compression, concrete shows softening

behavior which means that the stiffness becomes negative, Figure 3(b). Several researchers have

suggested mathematical models to define the negative stiffness of this range. Scott et al [12] and

Soroushian et al [13] suggest the stiffness after the peak point at high strain rates to be the same

as that at the normal (static) strain rates. In this study, the concrete material is modeled by the

bilinear curves with different yield stresses in tension and compression. Due to the difficulty of

modeling, the softening behavior of concrete after reaching maximum strength is ignored. Instead

of softening, it is assumed that concrete after reaching maximum strength maintains that strength

until it reaches ultimate strain. The bilinear model and properties used in analysis is shown in Table

3 and Figure 3(b).

2006 MSC.Software

- 8 -

Table 3 Material properties of concrete used in analysis

Properties

Type of

concrete

modeled

Density

lbf-sec2/in4

( kg/m3)

Modulus of

elasticity

ksi (Gpa)

Compressive

strength

ksi ( MPa)

Tensile

strength

ksi ( Mpa)

Compressive ultimate

Stain

in/in (m/m)

Tensile

ultimate

strain

in/in (m/m)

Normal

Strength

2.249x10-7

(2400) 3600 (25) 4 (28) 0.41(2.8) 0.004 0.0003

High Strength 2.249x10-7

(2400) 5100 (35) 8 (55) 0.58(4.0) 0.004 0.0003

7.3 Air and Explosive (TNT)

Explosive material is assumed to have much higher internal energy and density than the

ambient air around it. After detonation, the energy and density move through ambient air with

high velocity resulting in high pressure. To model explosive and air in the analysis, the same

material is assumed for both except for density and specific internal energy. The properties of air

and explosive used in the analysis are shown in Table 4.

Table 4: Material properties of air and TNT used in analysis [14]

Properties

Type of Material

modeled Density lbf-sec2/in4

( kg/m3)

Reference

temperature (K)

Specific Heat

ratio Internal energy/unit

mass(J/Kg)

Air 1.128x10-7 (1.205) 293 1.4 210x103

Explosive 1.548x10-4 (1654) 293 1.4 4520x103

8 Analysis Models

In these studies, to analyze the transfer of blast wave through the air, pressure from the air to

the structure and the response of the structure to such effects, MSC Dytran software developed

and distributed by the MSC.Software Corporation was used. MSC Dytran and its sister software

MSC Nastran and MSC Marc are highly reliable and powerful tools to simulate highly dynamic and

nonlinear problems such as explosive effects on structures and fluid structure or gas-structure

interaction simulations. The MSC Dytran software, which was used in these studies, has an

element type, the Euler element that can be used to model the explosion in the air and transfer of

blast effects through the air. Another element type, the Lagrangian element of MSC Dytran, was

used to model the structures. The airstructure interaction was calculated using the

“Euler-Lagrange element coupling” of MSC Dytran. The Euler element is constructed using the

Euler equation which is formulated utilizing conservation of mass, linear momentum balance and

energy balance [11]. The Lagrangian element of MSC Dytran is similar to a typical solid element of

other nonlinear dynamic analyses software.

To study responses of common types of bridges subjected to blast loads, two types of bridge

deck segments were modeled. The two deck types are shown in Figure 8. Both deck types had four

lanes and were designed to have the same bending plastic strength capacity. Although, depending

on where the deck segments are located along the length of the bridge the boundary conditions of

the deck segment would be different, in these analyses it is assumed that the two ends of the deck

segment subjected to blast are fixed. This will represent the most severe boundary to result in the

2006 MSC.Software

- 9 -

largest response of deck. Any softening of boundary, due to flexibility of the adjacent segments is

expected to result in reduction of the response relative to the fixed boundary case. The explosive

device was assumed to be a car bomb with several different amount of explosives used in the

analyses. All explosive devices were assumed to be located 60 inch (1.5 m) above the top surface

of bridge deck and over the second lane of the 4-lane decks. Figure 8 shows structural details of

two types of deck used in the analyses.

In dynamic analysis, mass is one of the most important factors. Therefore, the mass of the

wearing surface on the deck (e.g. asphalt) was considered in this study although the wearing

surface has negligible stiffness. The thickness and unit weight of the wearing surface in the

analyses was assumed to be 2 inches (51 mm) and 140 lb/in3 (38,000 kN/m3), respectively.

(a) (b)

Figure 8: (a) Steel orthotropic and composite plate girder deck models and (b) location of explosion

8.1 Models of steel orthotropic decks

To study the effects of strength and ductility of steel on the performance of the orthotropic

decks subjected to blast, three different types of steel material, as was explained earlier in Section

7.1 were used. The thickness of the plates in each of the three decks using three different steel was

selected such that the three decks will have almost the same plastic bending moment capacities.

The thicknesses of the deck for three different types of steel were 5/8 inches (15.9 mm) for A588

Grade 50, 1/2 inches (12.7 mm) for A852 Grade 70 and 5/16 inches (7.9 mm) for A514 Grade 100

steel.

8.2 Models of composite plate girder decks

To study the effects of strength and ductility of steel and concrete on the performance of

composite decks subjected to blast, two different types of concrete material, as was explained

earlier in Section 7.2, were used. A588 Grade 50 steel material was used for steel plate girders and

cross beams. Grade 40 rebars with yield stress of 40 ksi (276 Mpa) were used in the concrete deck.

The area of rebars used in was equal to 2% of the area of the cross section of the slab. The

thickness of the concrete slabs using two different strength of concrete was selected such that the

two decks will have almost the same plastic bending capacities. The thickness of the deck for two

different types of concrete were 12 inches (304.8 mm) for normal strength concrete and 6 inches

(152.4 mm) for high strength concrete. Since strain rate effect is dependent on the compressive

strength of concrete, different strain rate effects for each concrete material were considered.

Further, the strain rate effect of the rebars was taken into account as well.

2006 MSC.Software

- 10 -

9 Results

9.1 Results of steel orthotropic deck

Nine simulation cases that were carried out are described in Table 5. First five cases were

simulated in order to investigate the effect of the explosive size, and the remaining four cases were

done to study the effect of the material properties. The analyses were done using five specific

amounts of TNT explosives. However, since this study is a comparative study of performance of

different bridge decks to the same amount of explosives, mentioning exact amount of explosive is

deemed not to be prudent. Instead throughout the paper the amount of explosives are a given as

a multiplier of “A” amount of explosive where 5A pounds of explosives represents TNT weight of a

compact sedan car bomb.

Figure 9 shows the velocity and displacement time histories at the closest point of the deck

surface to the explosive center for the orthotropic deck using A588 Grade 50 steel for five levels of

explosives. In velocity and displacement responses, the maximum value increases with the

increase in explosive size. The maximum velocity for 20A explosive case is 20 times faster than

that of 1A explosive case. After about 0.016 second, the velocities are nearly zero and the

displacements also bounce to the original point for cases that the deck has not failed.

(a) Velocity (b) Displacement

Figure 9: Velocity and displacement time histories at closest point to explosive center

for A588 Grade 50 steel and two explosive levels

Figure 10 shows the plastic strain, effective stress and strain rate time histories at the closest

point of the deck surface to the explosive center for the orthotropic deck using A588 Grade 50 steel

for five levels of explosives. In the figure of the plastic strains, the values of plastic strain greater

than zero indicates that the element has yielded and plastic strain reaching 0.15 is an indicator of

fracture of the element. Figure 10(a) shows that this element of the deck has yielded when

subjected to 5A, 10A and 20A explosives and the element has fractured at about 0.004 seconds

after detonation when subjected to 20A explosive. The time at which the element yields increases

as the explosive size increases. In Figure 10(b), although the effective stresses are greater than

the static ultimate stress for the case of 10A explosive and they are greater than the static yield

stress for the cases of 1A and 3A explosives, this element has not yielded and fractured as shown

in Figure 10(a). It should be noted that because of strain rate effects failure stress subjected to

20A explosive is 1.5 times higher than the static ultimate stress. As discussed earlier, the high

2006 MSC.Software

- 11 -

strain rate leads to the increase of the dynamic yield and ultimate stresses. Figure 10(c) shows the

time history of strain rates. The strain rate of the element subjected to 20A explosive increases

rapidly as the time approaches to the failure point. This rapid increase of strain rate explains why

the fracture stress of the element subjected to 20A explosive is so high.

Figure 11 shows the velocity and displacement time histories at the closest point of the deck

surface to the explosive center for the orthotropic deck using A588 Grade 50, A852 Grade 70 and

A514 Grade 100 steel. Velocities and displacements for decks made of A588 Grade50 and A852

Grade70 steel are similar, but those of A514 Grade100 are higher. This can be an indication of low

strength steel being better suited to reduce the nodal responses such as displacement and velocity

if a structure is designed to have the same strength.

Figure 12 shows time histories of the plastic strain, effective stress and strain rate at the

closest point of the deck surface to the explosive center for the orthotropic deck using A588 Grade

50, A852 Grade 70 and A514 Grade 100 steels. Similar to displacements and velocities, the plastic

strain response time histories for A588 Grade 50 and A852 Grade 70 are similar and for A514

Grade.100 are different. While the elements with A588 Grade 50 and A852 Grade 70 steels have

not fractured under 10A explosive, the element with A514 Grade100 have fractured under the

same amount explosive. From Figure 12(b) it can be seen that the failure time in A514 Grade.100

steel case is shorter than in the other two cases. This can be interpreted as low strength steels to

have an advantage due to their larger ductility in resisting blast if the structures using high

strength steel is designed to have the same strength as the structure with lower (a) Velocity (b)

Displacement strength steel. Figure 12(c) shows the strain rate time histories again indicating

undesirable and quite large strain rates for A514 high strength steel.

(a) Plastic strain (b) Effective stress

2006 MSC.Software

- 12 -

(c) Strain rate

Figure 10: Plastic strain, effective stress and strain rate time histories at closest element to explosive center for A588 Grade

50 steel and two explosive levels

(a) Velocity (b) Displacement

Figure 11 Time histories of velocity and displacement at closest point to explosive center

for three steel types and two explosive levels

Figure 13 shows the response of three types of steel orthotropic deck using A588 Grade 50, A852

Grade 70 and A514 Grade 100 steels subjected to 20A explosive. The fracture areas of the A588

Grade 50 and A852 Grade 70 decks are similar but that of A514 Grade100 deck is larger. Table 5

summarizes maximum responses of each parameter in all nine study cases.

2006 MSC.Software

- 13 -

(a) Plastic strain (b) Effective stress

(c) Strain rate

Figure 12 Plastic strain, effective stress and strain rate time histories at closest element to explosive center for three steel

types and two explosive levels

Table 5: Maximum responses of three different types of steel orthotropic deck

Explosive

Size

Steel

Material

Type

Maximum

Velocity

in/sec

(m/sec)

Maximum

Accel.

in/sec2

(m/sec2)

Maximum

Displ. in

(mm)

Maximum

Pl. Strain

in/in

(mm/mm)

Maximum

Stress

ksi

(Mpa)

Maximum

Strain rate

in/in/sec

(mm/mm/sec)

Failure

Hole Size

in

(m)

1A A588

Grade 50

511

(13.0)

1.35x106

(3.42x104) 3.68

(93.5) 0

22.4

(154.6) 3.9 No failure

3A A588

Grade 50

1434

(36.4)

4.45x106

(1.13x105)

9.08

(230.6) 0

53.8

(371.2) 7.6

No failure

5A A588

Grade 50

2487

(63.2)7.49x106

(1.90x105)

13.41

(340.6) 0.0081

66.4

(458.2) 13.7 No failure

10A A588

Grade 50

4997

(126.9)

1.60x107

(4.06x105)24.95

(633.7) 0.041

70.4

(458.2) 36.0 No failure

20A A588

Grade 50

9904

(251.6)

3.25x107

(8.26x105)Failure 0.15

102.8

(709.3) 97.4

150

(3.81)

10A A852 5542 1.76x107 24.55 0.040 100.6 45.0 No failure

2006 MSC.Software

- 14 -

Grade 70 (140.8) (4.47x105) (623.6) (694.1)

20A A852

Grade 70

11170

(283.7)

3.56x107

(9.04x105)Failure 0.15

148.4

(1024.0) 135.5

150

(3.81)

10A

A514

Grade

100

7429

(188.7)

2.22x107

(5.64x105)Failure 0.075

172.4

(1189.6) 101.4

100

(2.54)

20A

A514

Grade

100

14913

(378.8) 4.43x107

(1.13x106)Failure 0.075

173.5

(1197.2) 109.7

300

(7.82)

(a) A588 Grade 50 (b) A852 Grade 70 (c) A514 Grade 100

Figure 13: Global responses of steel orthotropic deck using three different materials at 0.02 seconds after detonation (20A

explosive case)

9.2 Results of composite plate girder deck

Four simulation cases that were carried out are described in Table 6. All cases were simulated

in order to evaluate the effect of the explosive size and material properties.

Figure 14 shows the velocity and displacement time histories at the closest point to the

explosive center for two different concrete types and two different explosive levels. The velocity

and displacement responses of composite plate girder deck with normal strength concrete are less

than those with high strength concrete. These results, although limited only to these study cases,

indicate that normal strength concrete decks may have a potential to reduce the nodal responses

such as displacement and velocity if the decks with normal and high strength are designed to have

the same strength.

Figure 15 shows the element responses at the closest element to the explosive center. The

plastic strain time histories are shown in the Figure 15(a). While the element using normal

strength concrete subjected to 10A explosive has not fractured, the composite deck using high

strength concrete has fractured. From the Figure 15(b), the failure time for the deck with normal

strength concrete is shorter than the time to failure for the deck with high strength concrete. This

means that the deck with normal strength concrete has the potential to demonstrate a more

ductile response than the deck with high strength concrete if the two decks are designed to have

the same strength. Figure 15(c) shows the strain rate time histories.

Table 6: Maximum responses of two different types of composite plate girder deck

Explosive

Size

Concrete

Strength

Type

Maximum

Velocity

in/sec

(m/sec)

Maximum

Accel. 106

in/sec

(104m/sec2)

Maximum

Displ. in

(mm)

Maximum

Pl. Strain

in/in

(mm/mm)

Maximum

Stress

ksi

(Mpa)

Maximum

Strain rate

in/in/sec

(mm/mm/sec)

Failure

Size in

(m)

2006 MSC.Software

- 15 -

10A Normal 887 (22.5) 2.66 (6.76) 6.30

(16.0)0

6.86

(47.3) 7.9

No

Failure

20A Normal 1812

(46.0) 5.36 (13.6) Failure 0.0004

11.33

(78.2) 11.8

150

(3.81)

10A High 3296

(89.7) 8.98 (22.8) Failure 0.0004

15.84

(109.3) 28.2

150

(3.81)

20A High 6315

(160.4) 17.9 (45.5) Failure 0.0004

27.46

(189.5) 28.2

300

(7.82)

Figure 14 Time histories of velocity and displacement at closest point to explosive center

for two concrete types and two explosive levels

Figure 16 shows global response of two types of composite plate girder deck subjected 20A

explosive. The fracture area of the deck with normal strength concrete is smaller than that with

high strength concrete. The rebars support the concrete after large failure and leads to the ductile

behavior of the structure shown in Figure 16(b). Table 6 shows maximum responses of each

parameter for four different composite deck case studies.

(a) Plastic strain (b) Effective stress

2006 MSC.Software

- 16 -

(c) Strain rate

Figure 15 Plastic strain, effective stress and strain rate time histories at closest element to explosive center for two

concrete types and two explosive levels

(a) Normal strength concrete (b) High Strength Concrete

Figure 16: Global responses of composite plate girder deck using two different materials at 0.02 seconds after detonation

(20A explosive case)

10 Summary and conclusions

In this paper, objectives of this study and short blast theory are introduced and material

properties of steel, concrete and air used in the analyses are explained. Two types of bridge decks

(steel orthotropic and composite plate girder) were designed using several different materials and

analyzed, and then the results were compared.

From the responses of nine simulations of orthotropic box decks using three different types of

steel subjected to various levels of explosives it was observed that the strength of steel is not the

main parameter in resisting blast but it is the ductility of steel that results in reduced response and

desirable behavior. The responses of A588 Grade 50 and A852 Grade 70, having different strength

but same ductility were similar but the response of A514 Grade 100 with higher strength but lower

ductility was different than the two more ductile steels and in general was more brittle. The

orthotropic decks constructed using steel with higher ductility showed better performance with

respect to nodal and element responses.

Similar to the responses of the steel orthotropic box decks, the importance of ductility was also

demonstrated in the response of composite plate girder decks that were studied. Although two

types of concrete slabs that were used in the studies had the same percentage of steel rebars in

them, the total area of the rebars in the normal strength concrete slab was larger than in the high

strength concrete slab due to the fact to achieve the same strength the thickness (and the area)

of the normal strength concrete slab was larger than the thicknesses of the high strength slab.

2006 MSC.Software

- 17 -

Because of higher reinforcement and relatively higher ductility in the normal concrete slab, the

composite plate girder deck with normal strength concrete showed much better response to the

blasts and sustain much less damage.

In design and construction of decks in order to minimize damage and to prevent progressive

collapse, increase in ductility of both steel and concrete is more important than the increase in

strength. To increase ductility of bridge decks and to obtain better resistance to blast, the use of

low and medium strength steel with larger ultimate strain and normal strength concrete with

larger amount of reinforcements are recommended. The use of very high strength steel and

concrete, which inherently have lower ductility, to resist blast effects appears to be

counter-productive.

11 Acknowledgements

The study reported here is a part of a larger investigation of performance of buildings and

bridge structures currently underway at the University of California Berkeley with the second

author as the Principal Investigator. The information presented in this paper is a part of the

doctoral dissertation of the first author conducting the research on response of long span

cable-supported bridges to blast loads. The third author is a post-doctoral researcher at the

University of California Berkeley and is conducting research with the second author on various

aspects of modeling and response analyses of steel and composite structures subjected to blast

load. His participation in this research is financially supported by the research fellowship of the

German Research Foundation (DFG). The research reported in this paper would not have been

possible without the generous support of the MSC Software Corporation in providing the authors

with the powerful MSC Dytran and Marc software for use in this project. In addition, the technical

input and collaboration of Mr. Casey Heydari, Mr. Vijay Tunga, Mr. Paul Mitigui, Ms. Cassandra

Radigan, and Dr. Reza Sadeghi of the MSC.Software were essential and are sincerely appreciated.

12 References

[1] U.S. Department of the Army Technical Manual: TM5-1300, Structures to resist the effects of accidental

explosions. United States Department of the Army, Navy and Air Force, USA, 1990

[2] U.S. Department of Defense Unified Facilities Criteria, DoD Minimum antiterrorism standards for

buildings, 2002.

[3] American Society of Civil Engineers, Minimum design loads for buildings and other structures, 2002.

[4] EN 1990:2002 Eurocode - Basis of structural design, 2002

[5] prEN 1991-1-7, Eurocode 1 - Action on structures, General actions - Accidental actions European

Standard

[6] Baker W.E., Cox P.A., Westine P.S., Kulesz J.J. and Strehlow R.A.: Explosion hazard and Evaluation.

Elsevier. New York, USA, 1983

[7] Paik J.K. and Thayamballi, A.K.: Ultimate Limit State Design of Steel-Plated Structures. John

Wiley&Sons.LTD. Hoboken, NJ, USA, 2003

[8] Cowper, G.R. and Symonds, P.S.: Strain hardening and strain rate effect in the impact loading of

cantilever beams. Brown University, Division of Applied Mathematics report, 1957; 28

[9] Manual of steel construction: Load & resistance factor design. American Institute Steel Construction,

2001

[10] CEB-FIP model code 1990. Comite´ Euro-international du Be´ton. Trow-bridge. Redwood books.

Wiltshire, UK, 1993

[11] Malvar, L. J. and Crawford, J. E.: Dynamic increase factors for concrete. Twenty-Eighth DDESB