1 Introduction

Accidental collisions between over-height trucks and bridge superstructures occur frequently throughout the world. Approximately 50 % of the overpasses in Beijing, China, have experienced collisions and approximately 20 % of the damages are induced by over-height trucks [1]. In the USA, vehicle collision is also a very serious problem [2]. For example, 61 % of the interchange bridges in USA have been damaged by over-height trucks [3], and such structures constitute about 14 % of total bridge damages [4]. While research has been undertaken on damage evaluation [5] and repair after collision [6, 7], very limited research has been reported on the mechanisms arising from collision forces. The determination of such forces is critical for the establishment of adequate collision-resistance design methods for bridge superstructures.

Vehicular collision is generally classified as an accidental load condition for bridge superstructures in existing design codes [8]. The treatment of collision in design codes, however, varies and such recommendations are not always detailed enough to enable rigorous design. For example, Eurocode-1 [9] suggests equivalent collision forces to be applied for different traffic situations. This document is difficult to apply in individual countries though due to unique traffic conditions such as vehicle speed and weight limitations. Due to such limitations, recourse can be made to more advanced methods of analysis.

Finite element (FE) simulations of truck-bridge collisions have received considerable research attention to date. Thilakarathna et al. [10], for example, conducted numerical simulations of axially loaded concrete columns under transverse impact by utilising the finite element program LS-DYNA. Their simulation results were validated by full scale testing. In addition, the authors of the present paper [11] have conducted numerical simulations which have led to insights in the response of the bridge superstructure subjected to impact, in addition to the failure mechanisms and the collision loads. Simplified models for calculating collision forces have also been proposed [12]. Qiao et al. [13] conducted finite element (FE) analysis using LS-DYNA to predict the response of an I-sandwich protection system for highway bridges under over-height truck impact. Numerical simulation of truck-bridge superstructure collisions is complex due to the geometric nonlinearity, material nonlinearity, and contact nonlinearity, in addition to dynamic effects that are inherent in the problem. Experimental verification is scarce though and is drastically needed to validate the reliability of numerical simulations. On the other hand, considerable research to date has been conducted on ship-bridge pier collisions [14-17]. Both truck-bridge superstructure and ship-bridge pier collisions are an interaction phenomenon between a moving object and a fixed object. In addition, impacts by ships and trucks are always considered as hard impact, with the kinetic energy being dissipated by deformation, so dynamic effects and non-linear behavior should be considered in the analysis. These similarities are viable for knowledge transfer between the two disciplines. Experimental verification is still, however, required on truck-bridge superstructure collisions given the unique geometric and material properties of the system.

In order to address the knowledge gap imposed with limited experimental data available to date in the open literature, this paper reports a series of scaled model tests aimed to simulate collision between over-height trucks and bridge superstructures. More specifically, three different types of bridge models are tested which represent commonly used bridge types (i.e. steel box girder, steel plate girder and reinforced concrete (RC) T-beam girder). In addition, the over-height truck is represented by a metallic barrel which is made to impact the three different bridge girder specimens following a pendulum trajectory. Finite element analysis is finally conducted and the simulation results are shown to compare well with the test results.

2 Experimental details

2.1 Design of girder and tank test specimens

The experimental model comprises of two components, namely (i) a bridge girder component, and (ii) an over-height truck component. According to research presented in References [11, 12], the severity of collisions has been shown to increase for lighter bridges. Therefore, single-span (simply supported) steel box girder, steel plate girder and RC T-beam girder are adopted as the test prototypes as these bridge girders are inherently light-weight and possess low collision resistance. The test prototypes are designed according to the current Chinese bridge design specifications [18, 19] and are then scaled down in accordance with the physical constraints imposed by the test laboratory located at Tsinghua University, China. Existing FE simulation studies conducted by the authors [11] on the relationship between vehicle type and extent of bridge impact damage have concluded that tanker trucks usually cause the most serious damage under similar conditions of self-weight and speed. As a consequence of this finding, a tanker truck is adopted in this experimental testing regime as the over-height truck prototype. The prototype of the tanker truck is a typical Chinese vehicle (i.e. Dongfeng EQ140 cement tanker truck). Considering the most unfavorable condition for a bridge, the truck is loaded to full capacity. In this case, the tank mass is calculated as 25-ton. The truck prototype is then scaled down according to the same similarity ratio as that used for the girder specimens. All model scaling is conducted in accordance with consistent similarity ratios.

2.1.1 Scaling and similarity ratios

In order to correctly scale the test specimens, coefficients accounting for similarity in material properties, geometry, load and dynamic properties are calculated from Buckingham p Theory [20].  According to the physical constraints imposed by the laboratory, the geometric similarity ratio is 0.2. All the material property similarity ratios are set as 1.0. The similarity ratios of load, time and speed are then respectively calculated as 0.04, 0.2, 1.0 by using dimensional analysis. The similarity coefficients are presented in Table 1.

2.1.2 Scaling and design of bridge girder specimens

Actual overpass bridges in cities are typically 20 to 40 meters in length. Due to the physical constraints of the laboratory though, the bridges models considered herein were limited in length to about 4 meters. Utilising a similarity ratio of 0.2 as provided in Table 1 for geometry, the clear span of the test bridge was 3.70 m which represented an actual bridge of 18.5 m in length. Schematic representations of the steel box girder, steel plate girder and RC T-beam girder specimens are provided in Figures 1 to 3, respectively.

The cross-sectional web dimensions for the RC T-beam specimens were uniformly increased at the supporting regions in order to avoid bearing induced damage. Manufacture of the RC T-beam specimen was the more complicated out of the three different types of girders under investigation and Figure 4 shows selected photographs of the manufacture process. The RC T-beam specimen was made in-situ while the steel box girder and steel plate girder specimens were welded together in a factory located off-site.

2.1.3 Scaling and design of tanker truck specimen

The position of collision on a truck is typically on an object mounted onto the chassis (e.g. the barrel mixer of a concrete truck). For this study, the entire truck was conveniently but nonetheless quite realistically represented by a metallic hollow cylinder (herein tank) in which both ends of the tank were sealed and slightly curved outwards in the middle region (Figure 5). The dimensions of the tank, which are shown in Figure 5a, were scaled with the same geometrical similarity ratio as the girder specimens. Other components of the actual tanker truck, for which only the mass effect was considered, were simplified as steel jacketed counterweights. The weight of counterweight was equal to the weight of other parts of the actual tanker truck multiplied by a mass similarity ratio of 0.008. The counterweight was bolted onto the tank as shown in Figure 5b. Finally, the main parameters of the tank for modeling purposes are listed in Table 2.

2.1.4 Material properties

According to current criteria for the design of highway bridges in China [18], Q345 steel plate was used to construct the steel box girder and steel plate girder specimens. For the RC T-beam specimen, 6 mm diameter steel bars (grade HPB235) and 8 mm diameter steel bars (grade HRB335) were used as reinforcement while grade C30 concrete was also utilised. Finally, grade Q235 steel plate was used to construct the tanks.

All material properties were obtained from tests in accordance with the current Chinese testing specifications [21, 22]. Three test samples were prepared for each type of steel plate and reinforcing bar. As for concrete, three samples were prepared for compressive strength testing and three samples were prepared for elastic modulus testing. The properties of all grades of steel plate are shown in Table 3, while the steel reinforcement and concrete properties are shown in Table 4.

2.2 Test configuration and boundary conditions

Details of the experimental layout are provided in Figure 6 and the loading process is shown in Figures 7 and 8. The beam specimens were essentially fixed onto end supports and the motion of the tank followed the path of a single pendulum.

According to numerical simulations of collisions based on various support conditions which were previously conducted by the authors [11, 12], simple supports along the collision direction were found to produce the most serious damage to the bridge models. Simple supports were therefore implemented in this experimental study. The support condition was enforced by the installing 42 mm diameter steel screws at both ends of the girder specimens at the supports (Figure 6). Collisions are typically located at the bottom edge of actual girders. The girder test specimens were therefore placed in an inverted position in order to impact at the base of the girder with the swinging tanker and to also facilitate convenient and easy monitoring of the point of impact with a high speed camera. The girder specimens had a relatively short span and were light-weight. As a result, the influence of self-weight on the inverted orientation of the girder specimens was deemed to not noticeably affect the test results.

As shown in Figure 7, the tank was suspended by four cables which were connected to screw shafts. Prior to application of load, the tank was swung into position to a pre-determined height (Dh is shown in Figure 8) and connected to a rigid wall via a steel cable tie. Upon release of the tie, the tank swung according to the trajectory of a single pendulum upon which it achieved a certain initial impact velocity just prior to impact with the girder specimens. In all cases, the tank impacted with the girder specimens when the tank reached its lowest swing position and in this position its long dimension was parallel to the floor. Based on the principle of energy conservation, the initial impact velocity can be calculated from . Since different bridge models have different self-heights, and the lift height of the tank is manually operated, it is hard to maintain the exact same lift height Dh in different tests. So for each test, the actual lift height Dh was carefully measured. The Dh utilised for the different tests and the initial impact velocities are listed in Table 5. The following discussion and the FE simulation of the collision are based on the actual collision height.

According to Eurocode-1 [9], the height of the collision area between the tank and beam was 50 mm and this length was measured from the bottom of the tank to the top of girder specimens.

2.3 Instrumentation

The purpose of this experimental study was to observe the response and failure modes of the girder specimens during collision. Accelerometers were used to measure the acceleration responses of the girders and were placed at the bottom of the girder at the mid-span (i.e. collision position) as well as both quarter span positions. Two accelerometers were placed at each of these three positions to measure horizontal and vertical motion. Linear variable differential transformers (LVDTs) were placed at the support positions in order to measure support displacement in the collision direction. All of the acceleration and displacement data were collected by a dynamic data acquisition system. Finally, a high-speed digital camera was installed above the mid-span horizontal accelerometer in order to record the horizontal movements of the girder specimens. Figure 9 provides a schematic summary of all instrumentation installed at the mid-span region of each girder specimen. The displacement time-history curves were derived by acceleration integration and digital photogrammetry. Prior to each test, the tank was painted red in order for the collision zone to be precisely identified post test (i.e. red paint transferred to girder specimens at impact location).

3 Experimental results

3.1 Steel box girder specimen

Figure 9a shows the position of impact while Figure 10 also shows the position of impact in addition to the permanent deformation of the tank (about 20 mm in depth and 240 mm in width). In addition, no residual deformation was observed on the girder specimen.

The displacement time-history response for the steel box girder specimen is shown in Figure 11 in which positive displacement indicates initial collision while the negative displacement indicates the spring-back effect. The tank sprang back due to the nature of the cable restraint while the beam sprang back due to the nature of its simple supports. Figure 11 shows consistency in the acceleration integration and digital photogrammetry results which in turn indicates reliability of measurements. The maximum girder bottom displacement (at mid-span) recorded by the high-speed camera was 11.60 mm (i.e. the flange component of the beam), while the top girder displacement (at mid-span) was 8.57 mm. The different displacements indicate the considerable torsion induced at the mid-span as a result of the collision.

The box girder, which consists of a closed section and inner diaphragm, was shown to have strong localized collision and torsional resistance. As a result, the local failure mode is not the dominate failure mode for this case. If the constraints of the superstructures can not resist the lateral collision load, a global failure mode (e.g. girder falling failure) may occur.

3.2 Steel plate girder specimen

The displacement time-history curves for the steel plate girder specimen are shown in Figure 12 while the accelerometers and position of impact are shown in Figure 9b. The maximum displacement of the web on the collision side (i.e. accelerometer A in Figure 9b), which was obtained by acceleration integration, was 40.98 mm. The displacement on the other side of the beam (i.e. accelerometer B location in Figure 9b) was only 6.51 mm. The maximum displacement recorded by the high-speed camera was 63.70 mm. Following impact by the tank and subsequent spring-back of the girder specimen, the tank obstructed the viewing area of the high-speed camera and hence girder displacement results could not be extracted from the camera post-collision.

The reason for the difference of the two curves acquired by accelerometers and the camera in Figure 12 was because the positions they measured did not exactly coincide. As shown in Figure 9b, the collision took place at the bottom plate of the girder specimen. As the stiffness of the bridge web in the collision direction was very small, local deformation occurred in the collision region.

The deformations of both the tank and girder components are shown in Figure 13. Since the stiffness of steel plate girder bridge specimen along the collision direction was quite low (in comparison to say the steel box girder specimen), the damage and the deformation of the tank were much smaller than that of the steel box girder specimen. On the other hand, the local deformation around the collision position of the steel plate girder specimen was very large. In addition, in accordance to Figure 12 the deformation of the non-collided side of the web of the steel box girder specimen was quite small which indicates local damage mainly occurs for this type of girder when collided by an over-height truck.

3.3 RC T-beam specimen

The point of impact is shown in Figure 9c, while the displacement time-history curves obtained by acceleration integration and digital photogrammetry are shown in Figure 14. The maximum displacement was measured to be 39.37 mm which was about 1/94 of the span length. In addition, serious concrete damage was observed post-test.

Upon collision, many concrete fragments from the beam rapidly dispersed adjacent to the collision region. Figures 15 and 16 show the position of the tank just prior to collision, during collision, and after collision. Figure 15 is an overall view of the test specimen and Figure 16 is a close-up view of the impact region.

Numerous cracks appeared on the beam after collision (Figures 17-19). A 148 mm long crack developed at the junction of the impacted web and top flange, with a maximum width of 0.3 mm. Other cracks in the beams had a maximum width of about 0.1 mm. Figure 20 shows damaged concrete in the collision position and the width of damaged region is 214 mm. After the collision at the position of impact, permanent indentation was observed on the tank as shown in Figure 21. The greatest dimensions of the indentation were measured to be 11.48 mm in depth, 203 mm in length and 28 mm in width.

4 Finite element simulation

The general purpose FE software, MSC.MARC [23] was used to undertake numerical simulations of the tests reported in Section 3.

4.1 Material constitutive relationships

The results of Section 3.3 established that upon vehicle-bridge collision in RC bridges, the concrete may experience cracking and crushing at specific locations. In order for numerical simulations to produce reliable and physically representative results, a sound material model capable of representing the essential mechanical processes of the material under varying stress and loading rate conditions is essential [24]. Numerical models should therefore consider these physical realities in addition to the effect of strain. As a result, the elasto-plastic-fracture constitutive law provided by MSC.MARC was adopted to model the concrete [23, 25]. In this model, the concrete compressive behavior was simulated by an elasto-plastic model and the tensile behavior was simulated by a smeared-crack model. The strain rate effect experienced by the concrete was based on the equation proposed by CEB-FIP MC 90 [26] which is provided as follows.

In Equations 1-3, ,  and  are the dynamic compressive strength, tensile strength and elastic modulus, respectively, while  ,  ,  are the corresponding static values. In addition  is the compressive strain rate,  is the tensile strain rate, while ,  are empirical parameters.

The Cowper-Symonds model [27] was adopted to simulate the steel tank as well as the steel reinforcement used in the RC T-beam specimen. It was also used to simulate the plate used in the steel box girder and steel plate girder specimens. This model takes into account steel yielding and strain hardening as well as the strain-rate effect of steel materials. The Cowper-Symonds model is provided in Equation 4

where ¦Ò_y is the yield strength with strain rate effect, ¦Ò₀ is the initial yield strength;  is the strain rate;  is the effective plastic strain; E_p is the plastic hardening modulus; ¦Â is a factor which controls the proportion of isotropic hardening and the kinematic hardening; while C and p are factors which describe the strain rate. According to Jones [27], representative values of C and p are 40.4 and 5, respectively.

4.2 Finite element types, meshes and connectivity

Finite element meshes were constructed for all three test specimens with the girder, tank and cable components being explicitly modeled. Figure 22 is a typical FE mesh (i.e. for a steel plate girder and tank). In all models, the tank was represented by 4-node shell elements while the cables which suspended the tank were represented by 2-node truss elements.

All components of the steel box girder and steel plate girder specimens were modeled with 4-node shell elements. The Cowper Symonds constitutive law with parameters appropriate to the steel girders and tank elements are provided in Table 3. In addition, contact between the tank and the girder models was incorporated by the contact function provided by MSC.MARC. Elements in potential contacting parts of girder and tank were defined as two separate sets of contact bodies. During the iteration process, each potential contact node was repeatedly checked. If a node was within the contact tolerance, it was considered to be in contact with other elements. The contact tolerance was therefore calculated by the MSC.MARC program as the smaller of 5% of the smallest element side or 25% of the smallest (beam or shell) element thickness. In the tangential direction of the contact interface, an approximation of the Coulomb friction model (i.e. arctangent model) was adopted to represent the relationship between the normal stress and tangential stress [23].

For the RC T-beam specimens, the concrete component was modeled with 8-node solid elements while the internal steel reinforcement was modeled with 2-node truss elements. Compatibility of displacement was maintained between the concrete and reinforcement by utilising an ¡ÒInsert¡Â function provided by MSC.MARC [23]. In addition, a contact algorithm was applied to simulate the collision between the tank and bridge specimens, while the appropriate material parameters are provided in Tables 3 and 4.

The results of finite element analysis are greatly affected by the element mesh and level of time step. The finite element mesh (e.g. Figure 22) and the time step that are used in this section are further subdivided to check the convergence. No obvious difference is observed between the proposed meshing and time step and the subdivided ones so the proposed meshing and time step are appropriate for the analysis.

4.3 Finite element results and overall comments

The accuracy of a typical deformed FE mesh following impact is qualified in Figures 23 and 24 with photographs of the tests. More specifically, Figure 23 shows the impacted steel plate girder and tank both numerically (Figure 23a) and experimentally (Figure 23b). In addition, the residual deformation of the tank in isolation is provided for the numerical simulation (Figure 24a) and test results (Figure 24b). In both of these figures, the numerical simulation provides an accurate representation of actual behaviour.

In terms of cracking in the RC T-beam specimen, the cracks patterns observed from the FE simulation compare well with crack patterns extracted from the test specimens on different sides of the T-beam as evident in Figures 17-19.

The displacement time-history responses of all three test girder specimens are provided in Figures 11 and 12, for the steel box girder and steel plate girder specimens, respectively, and in Figure 14 for the RC T-beam specimen. In all cases, the FE results compare well with the test results. In the case of the steel plate girder specimen, the FE results were extracted at the same position as the measurements recorded by the high-speed camera.

On the whole, the numerical simulations compare well with the test results and they can predict the damage caused upon impact of an over-height truck with metallic or concrete bridges in the context of the test parameters reported in this study.

5 Conclusions

The collision phenomenon between over-height trucks and bridge superstructures has been investigated herein via experimental testing and numerical simulation. The following conclusions can be drawn.

1.            For steel superstructures, the steel box girder bridge is a preferable bridge type which shows good anti-impact performance. The steel plate girder bridge was inherently of low lateral stiffness due to its geometric configuration and hence exhibited poor impact resistance. Damage which is locally concentrated in the impact area is preferred and for that reason, a steel box girder superstructure is preferred.

2.            The collision resistance of the concrete T-beam specimen was inferior to that of the steel girder bridges. Not only was there local damage in the collision region, but numerous cracks also formed in the beam along the length of bridge girder, which affected the bridge safety to some extent.

3.            The numerical simulations agree well with experiment results and this indicates that the FE modeling technique can reliably and accurately simulate collision between over-height trucks and bridge superstructures. Such simulation can therefore be used with confidence to study the collision damage mechanism between different vehicles and different bridges.

Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No: 50808106), the Tsinghua University Initiative Scientific Research Program (No. 2010THZ02-1, 2011THZ03), the Major S&T Special Project of Ministry of Transport of PR China (No. 2011-318-223-170) and the Program for New Century Excellent Talents in University (No. NCET-10-0528).

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