Performance of Bridge Decks Subjected to Blast...
Transcript of Performance of Bridge Decks Subjected to Blast...
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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)
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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,
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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
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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.
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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
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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)
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= 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).
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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
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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.
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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
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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
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(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.
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(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
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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)
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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
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(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.
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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