Nonlinear Finite Element Simulation for the Impact between Overhigh Truck and BridgeSuperstructure Lu Xinzheng^{1}, Zhang Yansheng^{1}, Jiang Jianjing^{1}, Ren Aizhu^{1}, Ning Jing^{2} ^{1}Department of Civil Engineering, Tsinghua University, Beijing, China, 100084 ^{2} Beijing Municipal Computing Center, Beijing, China, 100005 Proc. 7th Int. Conf. Shock & Impact Loads on Structures, Beijing, 2007, 387394. Abstract: According to statistic data supplied by relative departments, about half of the bridgesuperstructures in Beijing have been impacted by overhigh trucks. And over 20% of the bridgesuperstructure failures in Beijing are due to overhigh trucks¡¯ impact. Hence it is an important problem that needs to be studied for the safety of the traffic system. Current researches on the impacts between vehicles and structures are mostly focused on shipbridge pier, carbridge pier and carbarrier impact. The works on the impact between overhigh truck and bridgesuperstructure is lacked. This paper presents the nonlinear finite element (FE) simulation for the impact between overhigh truck and bridgesuperstructure. Besides the nonlinearity of geometry, material and contact, a more accurate reinforced concrete model with FE package of MSC.MARC is adopted in the FE model to give a more realistic simulation for the bridge girders. The whole impact process is simulated and the damages in truck and bridgesuperstructures are discussed. Keywords: Bridge, Overhigh truck, Impact, Simulation, Nonlinear 
1. Introduction More and more bridges are constructed in Chinese cities to relax the traffic load due to rapid increase of economy. But the related driver education and traffic monitoring in China are still far away from the needs of modern transportation, which results in a lot of impact accidents between overhigh trucks and bridges. According to statistic data supplied by relative departments, about half of the bridgesuperstructures in Beijing have been impacted by overhigh trucks. And over 20% of the bridgesuperstructure failures in Beijing are due to overhigh trucks¡¯ impact. So it¡¯s valuable to study damage of bridges due to impact from overhigh trucks for the proper design, management and retrofitting of bridges. But currently studies of impact between overhigh trucks and bridges are still much lacked. Most studies on carbridge impact are focused on carpier impact or carbarrier impact ^{[15]}. Due to the high cost and risk of experimental research by real impact between truck and bridges, in which both truck and bridge will be seriously damaged, the computer simulation has obviously advantages on this problem. In recent years, with the rapid development of car industry, the dynamic analysis for car impact (crash simulation) is developing quickly. Some general purpose finite element (FE) softwares, such as LSDYNA, are widely used in crash simulation. The National Crash Analysis Center (NCAC) of USA, supported by the Federal Highway Administration (FHWA) and National Highway Traffic Safety Administration (NHTA), provides standard car models on the internet which can be freely downloaded by researchers. And with the rapid development of computer technology, large scale computing in engineering fields, such as carbridge impact, becomes more and more feasible. Hence many research institutions now working on the simulation for car impact based on LSDYNA or other softwares ^{[13]}. These works provide important references for this study. However, the existing works for car impact mostly focus on the safety of the cars and the passengers, and the damage to the structures is not analyzed precisely. Very simple models for impacted structures, for example, linear elastic or simple elasticplastic model and even rigid model ^{[4,5]} , are adopted in these simulations. On the contrary, this paper mainly studies on the damage of bridges, such as the yielding of steel reinforcement and the cracking of concrete ^{[6,7]}. So the FE software of LSDYNA, which rises from the fields of car engineering and military research, has difficulties in precisely modeling the structural behaviors of the bridges ^{[8.9]}. Thus this paper¡¯s analysis for impact between over high trucks and bridge is based on the MSC.MARC 2005 software ^{[7]}, which is widely used for nonlinear analysis in civil engineering. And then the damages of impacted bridge are discussed based on the numerical results. 2. Finite element model 2.1. Bridge Model Now, reinforced concrete is the mostly widely used bridge structures Concrete is a very complicated material because of the mechanical behaviors of cracking and crushing. The common FE software in civil engineering fields, such as MSC.MARC, ABAQUS, ANSYS and ADINA, have good material models of concrete. In addition, smeared or discrete models are provided for modeling rebar ^{[6]}. MSC.MARC 2005^{ }software ^{[7]}, which has advantages in analysis for reinforced concrete, is adopted in this research. Concrete is modeled with solid element, while rebar is modeled with rebar element. For concrete material, the compressive behavior is simulated with elasticplastic model, while the tensile behavior is simulated with smearedcrack model basing on maximal tensile stress criterion. The steel material is simulated with ideal elasticplastic model based on von Mises yield criterion, and prestressing is simulated by applying initial stress to rebar elements ^{[6]}. The values of parameters is according to Ref [6,7]. Figure 1 shows the model of the bridge, which is made up of four prestressed T girders, which is 25m in length, 8m in width and 1.6m in height. The high precision of the bridge model conduces to reality of the simulation results. 
Fig.1. FE model of bridge 2.2. Truck model NCAC supplies the finite element model of standard doubleaxle truck based on LSNYNA. This paper transforms the model to MSC.MARC 2005. The steel is modeled with the elasticplastic material basing on Von Mises yield criterion. According to the research of Li et al. ^{[10]}, the mass of the truck is adjusted to agree with that of the common doubleaxle truck in China. The final FE model of truck is shown in Figure 2. The high precision of the truck model ensures reality of the simulation results.
2.3. Analysis load cases The analysis in this paper contains four load cases of impact velocity: (1) Load case 1: V=60km/h (2) Load case 2: V=80km/h (3) Load case 3: V=100km/h (4) Load case 4: V=120km/h 2.4. Verification of meshing convergence for contact analysis It is widely known that the result of finite element analysis is greatly influenced by the element mesh, especially in complicated contact analysis. So it¡¯s important to verify that the meshing is precise enough, and further subdividing is not necessary. In order to avoid the disturbing of nonlinear property of bridge materials, when verifying the meshing convergence, the bridge is simulated with linear elastic model. Figure 3 shows the comparison of results in different meshing conditions. The element size of the fine meshing is half of that of the coarse meshing. The results show that further subdividing has little influence to the deformations of truck and bridge, so the meshing is precise enough for the contact analysis.
3. Computational results 3.1. Damages of truck in different load cases The computed timehistory curve of displacement of the back axle is shown in Figure 4. At the velocity of 60km/h, 80km/h and 120km/h, the deformations of truck are shown in Figure 5.15.3. The lateral beams between girders are not shown in the figures to give a more clear illustration of the damage in girders and trucks. Figure 4 and 5 show that as the impact velocity is increased, the deformation of the truck becomes larger. At the velocity of 60km/h, only the front end of the carriage locally deforms. While at the velocity of 120km/h, both the front 1/4 of the carriage and girder of the truck are badly damaged, and the truck is bended upwards (Fig.5.3c). The impact time is also related to the velocity. As the velocity increases, the impact time rises from 0.04s to 0.065s (Fig.11), and the truck¡¯s moving distance during the impact process rises from 0.51m to 1.32m (see Fig.8).
Fig.4. Displacement of the back axle of truck in the velocity direction

3.2. Damages of bridge in different load cases The computed timehistory curve for the displacement of the impacted point which is located at the bottom of the girder is shown in Figure 6. Taking load cases of 60km/h, 80km/h and 120km/h for examples, the development of cracks in the concrete is shown in Figure 7.17.3. It¡¯s clear that during the impact, the truck gives the girder a punching load, which results in cracking around the impacted area. At the same time, the torsion of the web of the girder results the cracks in the upper flange and the slab of the bridge. From Figure 7, it can be seen that when the velocity of truck is low, the impact impulse is not large, and the damage of the bridge is not serious so that the cracks can close after the impact (see Fig.7.1d). However when the velocity is high (Fig.7.3d), not only during the impact process the web and slab crack seriously, but also after impact there are many cracks left. Figure 6,9 shows that at the velocity of 60km/h and 80km/h, the maximum deformations of the impacted point in the girder are close, which are from 22mm to 24mm. When the velocity rises to 120km/h, the deformation reaches 47mm, which is two times as large as that of 80km/h load case. This is because when velocity is lower than 80km/h, most rebar does not yield and the stiffness of the bridge degenerates slightly. Most impact energy is absorbed by the deformation of the truck. While when the velocity exceeds 80km/h, a lot of rebar yields, and the bridge stiffness degenerates obviously. As both the truck and the bridge absorb the impact energy, the residual deformation of the bridge increases obviously (Fig.10). From the analysis above, it can be seen that impact between trucks and bridges is a nonlinear procedure which is very complex. As the velocity changes, the ratio of absorbing impact energy between truck and bridge varies a lot. Since the modern highperformance computing can satisfy the nonlinear simulation of impact between trucks and bridges, more precise models of truck and bridges can be used to give a deeper understanding of damage mechanism. 
Fig.6. Displacement of the bridge impacted point in the velocity direction
4. Conclusions Impact between overhigh trucks and bridges is an important problem that needs to be studies. And modern highperformance structure computing provides powerful tools for the research. According to the analysis above, the conclusions below are obtained: (1) The finite element software MSC.MARC can well analyze impact between trucks and bridges. The yielding and buckling of materials, and the cracking and residual plastic deformation can all be simulated. (2) Impact between trucks and bridges is a complex nonlinear problem. The damage of bridge is related to the structures of bridge and truck. For the standard doubleaxle truck studied in this paper, when the velocity is lower than 80km/h, the impact energy is mainly absorbed by the truck. But when the velocity exceeds 80km/h, the damage of the bridge is serious. So for the highway bridge, protection measures should be provided to mitigate the damage of possible impact. (3) The impact of truck gives the web of the girder a punching load, which is always not considered in bridge design. As the development of bridge structure, the web of girder becomes thinner and thinner, which is weak to resist the impact load. It¡¯s suggested that the punching load should be considered when designing T girder or thin box beam bridges. Acknowledgement This work is financially supported by Beijing Municipal Science & Technology Commission (Project name: Research on the Realtime assessment system and Computer Simulation for the Safety of Bridge Structures) and the Basic Research Fund of Tsinghua University (No. JC2007003). 