Behavior of steel box girder bridges under blast loads and the possibility of reopening the bridge immediately following the explosion

Bridges play a vital role in transporting inhabitants and goods both within and outside of cities, making them vulnerable to explosions. Therefore, understanding how bridges perform under blast loads is crucial for the safety of infrastructure and urban societies. This research investigates the dynamic behavior of steel box girder bridges when exposed to blast loads, focusing on factors like explosive weight, blast standoff distance, and blast location. It also explores the possibility of partially reopening the bridge to traffic immediately after an explosion. We used the ABAQUS nonlinear finite element analysis software to model the bridge. The study shows that reinforced concrete slabs and steel girders completely collapse when subjected to an explosive weight of 5000 kilograms (equivalent to a truck filled with explosives). This indicates that these structural elements cannot withstand such a large explosion, leading to their total failure. Reinforced concrete slabs are more likely to collapse when an explosion occurs in the middle of the span, whereas steel box girders tend to collapse at the ends of a span. The detonation's standoff distance correlates with the explosive weight. Explosive weights of 50 kilograms (motorcycle) and 200 kilograms (medium car) damage specific areas of the bridge, allowing for the potential partial reopening of other sections immediately after the explosion. In contrast, explosive weights of 300 kilograms (large car), 1400 kilograms (pickup truck), and 3000 kilograms (van) cause extensive damage, making it impossible to reopen any section partially.


INTRODUCTION
With a rise in terrorist strikes and regional warfare, academics are becoming more concerned about the explosion danger of infrastructure.Bridges are essential for transporting people and goods both within and beyond cities.Because of their importance, they are especially vulnerable to explosions (Amer et al., 2020;Aamir et al., 2023;Lv et al., 2023).Terrorist terrorism has grown fast since the events of September 11, 2001, and its activities are now relatively common.Between 2002 and 2008, there were roughly 190 terrorist strikes on bridges worldwide (Stewart and Mueller, 2014).Explosions can occur because of both terrorist activities and vehicular crashes over bridges, emphasizing the importance of understanding explosion effects to prevent collapses.Many bridges are vital for trade and transportation and often serve as significant landmarks in their communities.Therefore, their destruction could have severe and far-reaching consequences.Therefore, it is critical to protect bridge structures against blast loads.
While significant research has explored the impact of blast loading on building structures and their components, studies on how bridges respond to blast loads remain limited.To safeguard infrastructure and urban environments, it is crucial to deepen our understanding of bridge behavior under such conditions.Researchers used simplified theory methods, such as Timoshenko beam theory and analysis of an equivalent single degree of freedom system, to study how concrete bridge structural components responded to blast loadings (Krauthammer et al., 1993;Low and Hao, 2002;Winget et al., 2005;Fujikura and Bruneau, 2011;Xiao et al., 2017;Anas and Alam, 2022).Although these simplified methods work well overall, they struggle to provide accurate estimates of localized effects.
As computer technology and computational mechanics have advanced, researchers have increasingly used numerical simulations to study blast effects on structures.These simulations have proven effective in producing reliable predictions of structural responses (Zhou and Hao, 2008;Riedel et al., 2010).
In this study, we simulated the bridges using ABAQUS, (2017), a commercial finite element analysis tool.We applied the CONWEP model, available in ABAQUS for shock loading, to simulate the blast effects.This process involved creating an air blast scenario by applying an incident shock wave using the CONWEP model.This model calculates the shock wave's impact based on the explosive's TNT equivalence weight and the explosion's three-dimensional position.We computed the total pressure on the structural surface by considering incident pressure, reflected pressure, and the angle at which the blast wave hit the structure.This analysis is an empirical, uncoupled, dynamic analysis with multiple degrees of freedom.The CONWEP blast-loading model relies on traditional weapon effects calculations, uses several empirical equations, and curves (Hyde, 1988).One major advantage of the CONWEP model is that it calculates actual overpressure amplitudes (both positive and negative phases) and other blast wave properties based on a user-defined amount of TNT at a specific distance from the explosion source.

Figure 1 Blast wave reflection formulation adopted by CONWEP property
Additionally, the CONWEP model simplifies the process by not requiring the modeling of the fluid medium (such as air) to account for reflection effects.Figure 1

Nature of explosion
An explosion happens when energy suddenly releases into the atmosphere, creating a blast wave that expands outward from the source.This wave immediately boosts the ambient pressure to maximum overpressure, and its effect fades with time.Figure 3 depicts changes in overpressure as the distance from the explosion increases.

Figure 3 Overpressure variation with distance from explosion at successive time
There are three explosions: physical, chemical, and nuclear (Grys and Trzciński, 2010).Chemical explosions are the most prevalent kind of explosive that might occur accidentally or because of terrorist activities.The primary cause of a chemical explosion is the rapid oxidation of fuel ingredients, which might be liquids or solidified solids.Table 1 shows the values of explosive weights for various vehicles based on their carrying capacity (Xiao et al., 2017).

Medium Car 200
Large Car 300 Pick-up truck 1400 Van 3000 Truck 5000

Characteristics of blast wave
Blast characteristics create a rapid pressure pulse that spreads from the explosion.When an incident blast wave encounters a structure, it reflects, and the reflected pressure usually exceeds the incident pressure, depending on the angle of incidence.We calculate the reflected pressure value by multiplying the incident wave by the appropriate reflected pressure coefficient, as shown in (Figure 4).The  The researchers pinpointed failure mechanisms and evaluated the residual capacity of the cables after blast exposure.Their findings underscore important considerations for the design and safety assessment of structures using strand cables, especially in contexts involving explosive threats, and highlight the importance of understanding material behavior to enhance structural resilience.
Maiorana et al., (2022) investigated the effect of blast loads on the structural integrity of steel arch bridge slabs using advanced numerical simulations.Their analysis revealed that blast loads significantly compromise the slabs, causing various forms of damage such as cracking, spalling, and deformation.The study emphasized the need for incorporating blast resistance in the design and maintenance of steel arch bridges to ensure resilience against such extreme events.These findings provide critical insights for civil engineers and urban planners in enhancing the safety and durability of essential infrastructure.kg TNT equivalent to simulate the explosion.They found that the bridge undergoes three failure stages: elastoplastic, plastic, and a plastic hinge with a whole section.Failure times and displacements vary depending on whether the explosion occurs above the steel beams or the concrete deck.The study found that explosions occurring from the bearings to one-quarter of the bridge span lead to shear failure in steel beams before bending failure.Both shear and bending failures are important considerations for designing explosion-resistant structures.For explosions between one-quarter and one-half of the bridge length, flexural failure becomes the main factor affecting the damage to the steel-concrete composite bridge, with only localized shear failure occurring.In a multi-beam steelconcrete composite bridge that meets design specifications, any explosion will result in the formation of plastic hinges and a loss of bearing capacity.
Amer et al., (2019) investigated the behavior of a simply supported composite steel I-girder bridge under blast loads.They placed three different explosive sizes at various locations above the deck.The researchers found that steel girder failure primarily causes the bridge collapse, while reinforced concrete slabs do not lead to collapse.They observed a total collapse in the girder directly above the blast when the explosive weight reached 5000 kg.Hashemi et al., (2017) studied the dynamic response of a cable-stayed bridge under blast load.This study develops detailed finite element models of a steel cable-stayed bridge and analyzes them using an explicit solver.
The researchers use three explosive sizes, small, medium, and large, and place them above the deck.The researchers concluded that although they observed extensive damage and steel plate rupture, along with large plastic deformations and strains in the tower and deck in some blast scenarios, the damage did not cause global progressive failure deck or tower in any of the scenarios considered.
The bridge did not collapse gradually under varying blast loads from minor to big explosions; however, major repairs and rehabilitation would be necessary for structural elements like the deck and towers near the explosion.Cofer et al., (2012) studied the effects of blast loading on pre-stressed girder bridges using a finite element model validated by experimental tests.The study expanded the model to a four-girder bridge and examined three scenarios: A blast between girders above the deck, a blast centered on a girder above the deck, and a blast beneath the deck.Blasts from above caused localized damage, making it possible to reopen other sections of the bridge immediately after the event.In contrast, a blast from below severely damaged the slab but left the girders intact.Tokal-Ahmed, (2009) studied the response of concrete I-girder bridges to blast loads, revealing that the standoff distance and charge weight are crucial factors.The distribution of blast pressure along the bridge significantly influences its behavior.
At larger standoff distances, the pressure distribution tends to be uniform, while at smaller distances, it can lead to potential overestimation of the effects.The study also found that when the member's length exceeds the standoff distance, the pressure at the ends increases significantly, approaching incident pressure.The study also examined how the standoff distance affects the reflected pressure on the bridge span.Based on previous studies, there is limited research on the behavior of composite steel box girder bridges under blast effects.The existing research does not sufficiently address the various parameters that might influence this behavior.
Therefore, this research aimed to study the dynamic behavior of steel box girder bridges exposed to blast loads and the parameters that might affect this behavior, such as explosive weight, blast standoff distance, and blast location.Additionally, the research explored the possibility of partially reopening the bridge for traffic after the explosion.

Overview of the Study Building
This study used a composite steel box girder bridge with a 30-meter span and a 10-meter-wide concrete deck, as shown in (Figure 5).
The model restrained the bridge at both ends with hinge and roller supports.The design assumed the bridge would accommodate two traffic lanes.The design followed the Egyptian Code ECP-201, (2012) for live load, dead load, and impact load to determine the steel girder cross-section and concrete slab reinforcement details.The concrete slab reinforcement included Ф25/150 mm for the transversal direction and Ф16/200 mm for the longitudinal direction.Figure 6 shows the dimensions of the steel box girder.
Where σ is the Von Mises stress, A is the yield stress under the static loading condition, B is the hardening constant, C is the strain rate constant, εp is the effective plastic strain, n is the strain hardening coefficient, and εp* is the normalized effective plastic strain rate.

Define loads
Dead load refers to the weight of all the bridge's components, determined by its design and geometry.The typical density for concrete material is 2500 kg/m³, and for steel material, it is 7850 kg/m³.According to the Egyptian Code for Loads, ECP 201, (2012), the design live load consists of concentrated vehicle loads and distributed loads along the span length.The distributed uniform load also varies across the width of the bridge.Figure 8 shows the selected configuration for the traffic load.Since our study focuses on a two-trafficlane bridge, we will adopt two vehicle weights, 60 tons and 40 tons, and the relevant distributed load.The study placed detonation points for explosives at various locations to maximize their impact on bridge elements.Transversally, the study positioned the points between the two girders and directly above one girder.Longitudinally, the blasts occur at the mid-span and at the end-span.The study used standoff distances of 1.0 m, 1.5 m, and 2.0 m.It applied various explosive weights to represent different blast conditions: 50 kilograms (motorcycle), 200 kilograms (medium car), 300 kilograms (large car), 1400 kilograms (pick-up truck), 3000 kilograms (van), and 5000 kilograms (truck), based on the loading capacity of different vehicles.Figure 9 shows the detonation points adopted in the study.

Figure 9
Detonation points along bridge cross-section.

Finite element analyses
This study used ABAQUS nonlinear finite element analysis software to model the bridges.The study modeled concrete slabs with solid elements, steel box girders with mesh elements, and the deck system reinforcement with truss elements.Additionally, the study made the girders composite with the concrete slab during the nonlinear analysis, as shown in (Figure 10).Table 4 lists the different load cases used in the analysis models.Total number of bridges: Ridges

RESULTS AND DISCUSSION
The study used finite element modelling for an extensive parametric analysis to explore how various parameters affect the behavior of composite steel box girder bridges subjected to blast loads.The parameters examined include explosive weight, blast standoff distance, and explosion location.The analysis revealed two primary failure modes.For a blast at mid-span, the bridge experienced bending failure because the bending stress exceeded the bending capacity of the bridge elements.
This failure mode involved initial cracking of the concrete slab, yielding of the tensile reinforcement, compression failure of the concrete slab, and yielding of the steel girders.For a blast at the span end, the bridge suffered shear failure near the supports because the applied shear stress surpassed the shear capacity of the bridge elements.The models showed that part of the reinforced concrete slab and some steel girders reached the failure stage, depending on the loading cases of the bridge.The following section details how each parameter affects the behavior of composite steel box girder bridges under blast loads.

Explosive weight
In this study, we tested various explosive weights to assess the bridge's behavior and examine both minor and severe effects, matching the explosive weights to the loading capacities of different vehicles.Results from ABAQUS software revealed that the blast created a hole in the deck slab as the concrete and reinforcement reached their ultimate capacity.The extent of collapse in the reinforced concrete directly correlated with the explosive weight (W), as shown in (Figure 11 and 12).Similarly, the collapse of the steel box girder also directly correlated with the explosive weight (W), as illustrated in (Figure 13 and Table 5).The bridge collapsed when exposed to an explosive weight of 5000 kilograms (truck).These results align with recent research on the effects of explosive weights on the dynamic behavior of bridges.For example, Aamir et al., (2023) studied the effect of different explosive weights on a steel highway girder bridge and found similar results, confirming the robustness and accuracy of our current models.

Blast Standoff Distance
In this study, we used different standoff distances (R) to predict the bridge's behavior under blast loads and examine both minor and major effects.We tested standoff distances of 1.0 m, 1.5 m, and 2.0 m. Results from ABAQUS software showed that the effect of changing the standoff distance depends on the explosive weight.For smaller weights (50 kg, 200 kg, 300 kg), increasing the standoff distance reduces the blast effect on all bridge elements.For larger weights (1400 kg, 3000 kg, 5000 kg), it causes a more widespread impact on the bridge.For example, with a 300 kilograms charge, increasing the standoff distance from 1 m to 2 m decreased the damaged concrete area from 23% to 18% of the total slab area and eliminated plastic strains in the steel girders, which initially formed only at the top flanges.
Conversely, with a 1400 kilograms charge, increasing the standoff distance from 1 m to 2 m increased the damaged concrete area from 50% to 65% of the total slab area and extended plastic strains in the steel girders from the top flanges and part of the web height to the top flanges and the entire web height.Figures 14,15,16,and 17 show the failure of both concrete and steel at different standoff distances for charge weights of 300 kilograms and 1400 kilograms, respectively.Figure 18 illustrates the concrete damage at different standoff distances, showing how a larger load with a greater standoff distance has a more severe impact on the concrete slab.Table 6 summarizes the blast effect on the steel box girder.These results are consistent with recent research on the effect of standoff distance on the dynamic behavior of bridges subjected to blast loads.A study by Amer et al., (2019) on the effect of standoff distance on a composite steel I-girder bridge found similar results, demonstrating the strength and correctness of our current models.

Location of explosion
In this study, we evaluated the bridge's response to blast loads by testing four different explosion locations: mid-span centered between girders, mid-span centered above girders, end-span centered between girders, and end-span centered above girders.Results from ABAQUS software showed that explosions at mid-span, especially when centered between girders, are more likely to cause failure in reinforced concrete slabs, as seen in (Figure 19 and 20).In contrast, explosions at the span end are more likely to cause failure in steel box girders, as shown in (Figure 21 and Table 7).These results are consistent with current research into the effect of explosion location on bridge dynamics.Aamir et al., (2023) investigated the impact of several explosion locations on steel highway girder bridges and observed the same findings, validating the robustness and correctness of our present models.

Possibility of reopening the bridge partially for traffic after the explosion
This section examines the possibility of reopening other bridge sections after an explosion.The process involves first evaluating bridge's width where deflection remains within the allowable limit after the blast.This width then compared to the standard traffic lane width, which is 3.0 m according to the Egyptian code for design loads on roadway bridges.If the width of the bridge with permissible deflection exceeds the traffic lane width, reopening that section of the bridge is possible.Otherwise, reopening is not feasible.Table 8 shows the potential for reopening the bridge after an explosion.
Table 8 The possibility of reopening the bridge is subject to various explosive weight For example, with a 300-kilogram charge, increasing the standoff distance from 1 m to 2 m decreased the damaged concrete area from 23% to 18% and eliminated plastic strains in the steel girders.Conversely, with a 1400 kilograms charge, increasing the standoff distance from 1 m to 2 m increased the damaged concrete area from 50% to 65% and extended plastic strains in the steel girders from the top flanges to the entire web height.In all cases, a mid-span blast causes more frequent failure of reinforced concrete slabs, especially when the blast occurs between girders, while steel box girders are more likely to fail from a blast at the span ends.Explosive weights of 50 kilograms (motorcycle) and 200 kilograms (medium car) caused localized damage, allowing for the possibility of reopening other sections of the bridge immediately after the explosion.However, explosive weights of 300 kilograms (large car), 1400 kilograms (pick-up truck), and 3000 kilograms (van) severely damaged the bridge, making partial reopening impossible without risking complete collapse.
illustrates the reflection formulation that the CONWEP model uses.Composite steel box girder bridges have recently developed as a potential alternative to classic steel plate and concrete girder bridges.Many studies are investigating ways to enhance bridge design, durability, construction simplicity, and overall cost-effectiveness.Steel box girder bridges have intrinsic advantages over conventional plate girder bridges, including increased efficiency, less steel required for bending and shear due to their torsional rigidity, and improved live load distribution.Additionally, they reduce transverse bending in the deck, resulting in lower differential deflections (Lee et al., 2004; Braxtan et al., 2015; Vinitha et al., 2017).Figure 2 demonstrates how the torsional rigidity of a closed box girder section contributes to superior torsional behavior in bridges.

Figure 2
Figure 2 Live load distribution blast pressure time history divides primarily into positive and negative phases.The positive phase typically causes more damage and can significantly harm the structure.The negative phase, which lasts longer and has a smaller impact, often, gets overlooked (TM 5-1300, 1990; Winget et al., 2005; Pan et al., 2013; Ullah et al., 2017).

Figure 4
Figure 4 Variation of blast pressure over time Anas et al., (2022)  examined the impact response of square reinforced concrete (RC) slabs with normal strength concrete, focusing on different strengthening methods.Their study assesses the performance of slabs reinforced with laminates of mild steel and carbonfiber reinforced polymer (C-FRP), as well as those with C-FRP strips, under falling-weight impact loads.The research, through both numerical simulations and experimental tests, provides insights into how these reinforcement techniques enhance the impact resistance and overall structural performance of the slabs.Tahzeeb et al., (2022) conducted a numerical study comparing the performance of composite and tubular columns under close-in blast loading.Their research found that composite columns offer superior energy absorption and resistance to deformation compared to tubular columns.This study highlights the effectiveness of composite designs in enhancing structural resilience against blast forces, providing valuable insights for optimizing blast-resistant column design.Zhu et al., (2020) studied the damage mechanisms of a multi-beam steel-concrete composite bridge under a car explosion, using a 50

Figure 5 Figure 6
Figure 5 Cross section of the study bridge

Figure 7
Figure 7 Concrete response to a uniaxial loading condition

Figure 8
Figure 8 Loading configuration for a typical bridge width as specified by ECP 201-2012

Figure 10
Figure 10Model for the composite steel box girder bridge using ABAQUS

Figure 11 Figure 12 Figure 13
Figure 11 Area collapsed in concrete slab subject to various explosive weights (mid-span, between girders, R = 1.0m)

Figure 14 Figure 15 Figure 16 Figure 17 Figure 18
Figure 14 Area collapsed in concrete slab subject to various blast standoff distances (mid-span, between girders, W = 300Kg)

Figure 19 Figure 20 Figure 21 Table 7
Figure 19 Area collapsed in concrete slab subject to various locations of explosion (W = 1400Kg, R= 1.0m) This research investigates the dynamic behavior of steel box girder bridges when exposed to blast loads, focusing on factors like explosive weight, blast standoff distance, and blast location.It also explores the possibility of partially reopening the bridge to traffic immediately after an explosion.The study concludes that the collapsed area in reinforced concrete and steel box girders is directly proportional to the explosive weight.Partial collapses occur under explosive weights of 50 kilograms (motorcycle), 200 kilograms (medium car), 300 kilograms (large car), 1400 kilograms (pick-up truck), and 3000 kilograms (van), while an explosive weight of 5000 kilograms (truck) causes complete collapse.The effect of changing the standoff distance depends on the explosive weight.Increasing the standoff distance for smaller weights (50 kg, 200 kg, 300 kg) reduces the blast effect.For larger weights (1400 kg, 3000 kg, 5000 kg), it causes a more widespread impact.

Table 2
(Forni et al., 2016)for concrete with CDP model in class B40 Due to the instantaneous and high-energy nature of the explosion load, the structure's response causes the material to exhibit high strain rate characteristics (Lin et al., 2012; Bobbili and Madhu, 2017; Asala et al., 2019).Many researchers have examined the steel constitutive model under blast loads and found that the Johnson-Cook (JC) model accurately simulates the strain rate sensitivity and thermal softening of steel.Equation (1) provides a detailed description of this model.The study chose Steel S355 for both rafters and reinforcement bars.Table3lists the parameters for S355(Forni et al., 2016).

Table 3
Model parameters for steel.

Table 4
List of multi-case bridge loading

Table 5
State of box girder subject to various explosive weights (mid-span, between girders, R = 1.0m)

Table 6
State of box girder subject to various blast standoff distance (mid-span, between girders)