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Research Papers

Numerical Simulation on Concrete Median Barrier for Reducing Concrete Fragment Under Harsh Impact Loading of a 25-ton Truck OPEN ACCESS

[+] Author and Article Information
Jaeha Lee

Department of Civil Engineering,
Korea Maritime and Ocean University,
Busan 49112, South Korea
e-mail: jaeha@kmou.ac.kr

Goangseup Zi

Professor
Department of Civil, Environmental and
Architectural Engineering,
Korea University,
Seoul 02841, South Korea
e-mail: g-zi@korea.ac.kr

Ilkeun Lee

Construction and Environment Research Group,
Expressway and Transportation
Research Institute,
Hwaseong-si 20896, Gyeonggi-do, South Korea
e-mail: ilk@ex.co.kr

Yoseok Jeong

Department of Civil Engineering,
Chungnam National University,
Daejeon 34134, South Korea
e-mail: yosoksi@gmail.com

Kyeongjin Kim

Department of Civil and
Environmental Engineering,
Korea Maritime and Ocean University,
Busan 49112, South Korea
e-mail: kkj4159@naver.com

WooSeok Kim

Department of Civil Engineering,
Chungnam National University,
Daejeon 34134, South Korea
e-mail: wooseok@cnu.ac.kr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 31, 2016; final manuscript received January 4, 2017; published online February 9, 2017. Assoc. Editor: Taehyo Park.

J. Eng. Mater. Technol 139(2), 021015 (Feb 09, 2017) (9 pages) Paper No: MATS-16-1161; doi: 10.1115/1.4035766 History: Received May 31, 2016; Revised January 04, 2017

Recently, there was a collision accident involving vehicle–concrete median barrier in South Korea, and unfortunately, passengers on the opposite direction road were killed by the flying broken pieces of concrete generated by the collision. Primarily after this accident, we felt the need for developing an improved concrete median barrier up to level of SB6 impact severity in order to minimize the amount of broken pieces of concrete and any possibility of traffic accident casualty under the impact loading of truck. Accordingly, in this study, several designs of concrete median barriers have been examined, and a preliminary study has been conducted for developing and verifying appropriate collision model. First, type of vehicle was selected based on impact analysis on rigid wall. Then, the effects of element size and other key parameters on the capacity of the concrete median barrier under impact were studied. It was found that the key parameters for controlling behaviors of the median barrier under impact loading were contact option, threshold value, and mesh and boundary conditions. Furthermore, as a parametric study, effect of geometry and amount of wire-mesh or steel rebar in concrete median barrier on impact resistances of median barrier for reducing the collision debris were investigated. The amount of volume loss after the collision of truck was compared for various reinforcement ratios.

In South Korea, the first developed median barrier was the soil median barrier which was located in Gyeongbu highway in 1970. As expected, this type of median barrier did not have the capability to restore a collided vehicle after impact. In order to improve this weakness, in Namhae highway, a permanent concrete median barrier was constructed in 1980. However, the concrete median barrier was also ineffective in reducing traffic casualty since the steel shade net installed and embedded on top of the concrete median barrier was another potential risk under the impact loading of vehicle. During the 5 years from 2001 to 2005, 310 accidents related to the broken pieces from shade net due to the collision occurred and this number accounted for more than 58% of the total accidents related to shade net collisions. Accordingly, new concrete median barriers of 1.27 m height without any shade net were developed to prevent SB5 impact severity and are now in service on Korean highways. Recently, this type of barrier was upgraded up to SB5b impact severity (see Fig. 4(c)) according to the Bridge Design Code (Limit State Design) [1] so that passenger safety can be improved by counteracting the increased number of small and midsized car. However, recently, there was an accident (see Fig. 1) and its impact severity was estimated to be 2300 kJ, which was more than the maximum impact severity SB7 (600 kJ) in Korea. From this collision, flying broken pieces of concrete hit the windshield of a vehicle (sedan) on road in the opposite direction, resulting in two casualties. It was primarily after this accident, the authors felt that developing improved concrete median barrier up to level of SB6 impact severity is absolutely necessary in order to minimize the amount of concrete broken pieces and any possibility of traffic accident casualties under the impact loading of truck. It was also found that the level of impact severity of Korea is comparatively lower than that of other countries, such as the U.S., Europe, and Japan, as shown in Fig. 2. In the present study, a collision model was developed using LS-DYNA [2] and verifications were done in regard to the aforementioned accident. Furthermore, field collision test was run by the Korean Expressway Corporation, and a parametric study depending on geometries and amount of steel ratios of wire-mesh and steel rebar was conducted in order to develop the newly developed concrete median barrier for reducing collision concrete broken pieces under impact loading of truck.

In order to develop the collision model, first a proper truck model was selected and a concrete median barrier model was developed. Next, the parameters related to contact option between a truck and concrete were investigated. The key parameters were selected based on the comparisons with the test data as well as the aforementioned severe accident.

Selection of a Truck Model.

Truck models developed by the National Crash Analysis Center [3] were considered for this study. Two models were selected and suitably modified first. Model I weighed 25 ton without any hinge on the body of the truck. On the other hand, model II weighed 38 ton and there was hinge connection on the body of the truck between trailer and driver's control room. Rigid wall impact simulations were conducted with these two truck models, and model I was found to show a larger impact force (1405 kN) with a smaller impulse (264.64 kN s) than model II, as shown in Fig. 3. For this study, model I was used since flying broken pieces could be generated from large impact force rather than large impulse.

Development of Concrete Median Barrier Model.

To develop the concrete median barrier model, the material models that can be applied in this work were studied first. Material models without parameters related to damage and nonlinear function were excluded. It was found that from LS-DYNA [2], Mat_72R3 (Concrete_damage_rel3), Mat_84/85 (Winfrith), and Mat_159 (CSCM) could be proper models for impact analysis of the concrete body. Mat_72R3 was developed based on pseudotensor model. However, the estimated values of each parameter based on compressive strength were found to be unreliable according to Schwer and Malvar [4]. Mat_84/85 has many key parameters related to plasticity, strain rate effect, and three orthogonal crack planes per element. However, accumulated damages from cyclic loadings were not considered in this model. Mat_159 was originally developed for roadside safety applications and named continuous surface cap model (CSCM). It has several capabilities such as multiaxial strength, strength and stiffness degradation, and dilation (volume expansion under compressive stress) strain rate effects and considered to be an appropriate model for this study. One important feature of this model is continuous intersection between the failure surface and hardening cap [5]. The smooth intersection eliminates the numerical complexity for dealing with compressive region between the failure surface and cap. Shear failure surface of this model has a shape of affine-exponential spine and expressed in Eq. (1). Details regarding this model can be found in FHWA reports [6] Display Formula

(1)Fm(I1)=α1α3exp(α2I1)+α4I1

An important key parameter to determine generation of cracks in concrete body is fracture energy in tension. Fracture energy was estimated based on CEB-FIP [7] equations, as shown in Eqs. (2) and (3)Display Formula

(2)fctm=0.3(fck)2/3
Display Formula
(3)GF=73fcm0.18

For modeling of wire-mesh or steel rebars, material model, Piecewise_Linear_Plasticity, was selected. This model includes strain rate effect and elastoplastic behavior of steel material. For consideration of strain rate effect in rebars or wire-mesh, Cowper–Symonds equation was used. For this study, 1.05 × 107 s−1 and 8.3 were selected as D and q coefficients in Cowper–Symonds equation, respectively, according to Chung et al. [8]. Wire-mesh or steel rebars were embedded within the body of the concrete using constrained Lagrange in solid option. This enabled a coupling behavior between embedded reinforcements and concrete body. For contact option, automatic_single_surface was used. This option found contact condition automatically, so there was no need to define contacted surfaces. Therefore, for interacting bodies of different materials, contact segments were automatically generated. This option is especially helpful if there are a large number of parts in a body and when the position of contact formation is not known in a model. Hourglass control was also considered in order to minimize the hourglass energy. Several options such as Flanagan–Belytschko (stiffness formulation) were considered, and it was found that viscous formulation was deemed suitable for this model. The selected truck model and developed concrete median barrier model are shown in Fig. 4.

Procedure for Model Development.

After considering the material models, a new model was developed and verified with the results obtained from a real truck collision test conducted by Korea Expressway Corporation and the data from the actual collision accident that occurred in 2015 in Korea. A flowchart of this study is shown in Fig. 5.

Effects of several doubtful parameters which control the critical behavior of collision between the barrier and the truck, such as contact option, boundary condition at both end of concrete body, erode value, and mesh sensitivity, were analyzed and compared with the test data for verification of the newly developed model. The impact force generated by collision was plotted in a graph, and the simulated results were also compared with the results using Olson's novel equation [9] as shown in Eq. (4). In Olson's equation, deceleration of the truck due to the collision was assumed to be constant. Due to this assumption, maximum load obtained from Olson's equation could be less than maximum load obtained from actual truck collision Display Formula

(4) Gavg_lat=V0sinθg(tpt0)=V02sin2θ2g[Asin θ0.5B(10.5B(1cosθ)+D]
Display Formula
(5)Gmax_lat=π2(Gavg_lat)

Effect of Contact Option.

As mentioned before, the Automatic_Single_Surface algorithm was used for consideration of the contact among many bodies in the model. In this contact option, there was an optional contact card, such as “Ignore” and “Soft.”

Ignore option considered initial penetration. Since initial penetration did not occur in this model, the ignore option was not considered. In order to confirm any effect that can be generated from ignore option, the effect of the ignore option was studied, as shown in Fig. 6(a). Since difference between the maximum impact forces was less than 2% and time-history graphs showed almost similar behaviors, it was confirmed that the developed model was not sensitive to initial penetration.

Soft option enhances the function of contact for effectiveness between dissimilar materials. If soft option is utilized, contact stiffness can be determined based on time step and nodal mass. The effect of soft option was compared, as shown in Fig. 6(b). The impact force time-history graphs also showed similar behavior in this study. According to LS-DYNA user manual, soft constraint option (SOFT = 1) is recommended for large stiffness difference, such as airbag and other stiff materials. Therefore, in this study, soft constraint option was not used. It was found that contact without soft option was well suited to deal with the range of materials in the model.

Effect of Boundary Condition.

The effect of boundary condition on the behavior of collision between the barrier and truck was studied. The concrete median barrier model had 12 m length, however, the actual median barrier has a continuous length. In this study, fixed and released boundary conditions of concrete median barrier at both ends were considered and these two cases were compared with each other. The actual boundary condition at both ends could be a midlevel between the fixed and released conditions. As shown in Fig. 7, if the boundary condition was considered to be fixed at both ends, mostly, larger impact force was generated during collision, indicating that the larger impulse was obtained from fixed condition. For released case, larger maximum force was generated during a short time duration (0.025 s). For this study, conservatively, fixed boundary condition was used.

Selection of Erode Value.

In this model, the element erosion option was included. In other words, elements would be eroded if the failure criterion is met and exceeded. If all the elements connected to a specific node have been completely damaged, the elements become free particles and they become flying concrete broken pieces during simulation of a collision. An element is eroded if the maximum principal strain exceeds an input value. Therefore, erode values are the most important parameter for this model. For this study, threshold values of 1.1, 1.4, 1.6, and 1.8 were studied, as shown in Fig. 8 and compared with the actual collision test. It was found that the value of 1.4 erode was suitable for the simulation of the collision between concrete barrier and a truck. Other researchers, such as Thai et al. [10] recommended using 1.4 value, while Murray et al. [5] found 1.1 to be the proper value in their study.

Mesh Sensitivity Study.

Softening behavior of concrete material, especially under tension, depends on mesh size. This indicates that different levels of mesh refinements can affect the final analysis results differently. Therefore, it is important to maintain same fracture energy regardless of the size of the elements. In the current study, softening shape parameters, D and B, were investigated using single element analysis. It should be noted that the compressive fracture energy was assumed to be 100 times the tensile fracture energy. The shape parameter B is related to Gfc, and D is related to Gft. It was found that the obtained fracture energy regardless of mesh size was mostly same except the shape of the softening curve. The shape of the softening curve generated fracture energies with negligible margin depending on the size of the element. Therefore, the softening curves that depended on D values were compared, as shown in Fig. 9. It was found that the softening curve followed exponentially and asymptotically when D = 0.1. The fracture energies depending on the size of element, such as 2 mm, 10 mm, and 50 mm, were negligibly small. Therefore, D = 0.1 was selected for regulating the mesh size sensitivity. Likewise, softening curves under uniaxial compressive stress depending on several softening parameter B were also compared, as shown in Fig. 10. It was found that B = 10 was suitable for this study because for this value of B, the minimum fracture energy difference depending on the size of elements (2, 10, and 50 mm) could be observed. After mesh regulation with single element analysis, a push-over analysis was conducted for element size of 22 mm, 36 mm, and 72 mm (see Figs. 11 and 12). It was found that around 36 mm size of the elements, the load–displacement curves started to converge. For computational efficiency, the 36 mm element size, which is two times larger than the maximum aggregate size (19 mm) and will allow capture of cracking processes with a characteristic length [11], was selected in this study. Even though 22 mm mesh size showed convergence, no further mesh refinement was deemed necessary. Figure 12 shows the deformed and damaged bodies before and after the push-over analysis.

Model Verifications.

After developing the models, model verifications were conducted with real truck collision test and the aforementioned collision accident. For the actual accident that occurred in South Korea, the estimated accident conditions were 30 deg impact angle, 80 km/h, and 38 ton truck which exceeded the maximum impact severity (SB7). For model verification, a comparison of damaged shapes between an actual accident and a simulation result using a developed model has been shown in Fig. 13. The developed model predicted the final damaged shape satisfactorily. However, the damaged length and depth of the accident were approximately 6.8 m and 0.5 m, while simulated damaged length and depth was 8.1 m and 0.87 m, respectively. The developed model showed a greater amount of damage than the actual accident, indicating that a relatively conservative design is available using the developed model.

Next, a collision field test was conducted considering SB5b impact severity (270 kJ). The measured parameters obtained from the test were: 15 deg impact angle, 86 km/h, and 14 ton truck impact condition. The actual test results were then compared with the simulation results, as shown in Table 1. Unlike the previous verification, several parameters could be derived from the test and compared with numerical analysis since the data were obtained from a test and not from any accident. Therefore, these results are more reliable for model verification. First, velocity and angle after impact (collision) were compared. The actual test results for those were 73.5 km/h and 7.13 deg, while those obtained through numerical analysis were 73.4 km/h and 6.49 deg, respectively. This indicated that the vehicle behavior during impact and after impact could be well predicted by using the developed model. However, as discussed previously, the damaged length and depth were overestimated by the numerical analysis, since 1.4 m length and 0.25 m depth were obtained from test results, while 2.65 m length and 0.25 m depth were obtained from numerical analysis. When volume loss was compared, numerical analysis showed approximately two times larger value compared to the test results. Therefore, it can be said that a conservative design could be achieved using the developed model with relatively high accuracy. These steps were cycled up until numerical results were comparatively similar to the test results with conservative design view, and finally, these values for the key parameters were selected and utilized for this study, as shown in Table 2.

After model verifications, several modifications in the design of the concrete median barrier were considered. First, steel fiber reinforced concrete (SFRC) could be considered since SFRC has much larger fracture energy in tension. However, since it can raise the cost of construction, SFRC was excluded from the present study. To develop a new concrete median barrier which would form smaller broken pieces of concrete under impact loading, changes in dimension could be considered. However, since the dimensions were already predetermined for not only barrier stiffness under impact but also for driver's safety as well as restoration capability for collided vehicle, such changes in dimensions were disregarded. Therefore, thickness of the top fiber of the concrete median barrier could be only modified (increased). However, such modifications were also ignored since in South Korea, for construction of the highway concrete median barrier, a slip-form method is used, and if the dimension of the slip form is changed, the slip-form modification can increase the cost of construction. Finally, an alternative strengthening method was found which was increasing the steel reinforcement ratio. Single wire-mesh (Ф3.2 × 150 mm × 150 mm) was embedded into the body of the median concrete barrier. It was found that the current design has a relatively smaller reinforcement ratio than other countries, such as the U.S. In the U.S., steel rebar instead of wire-mesh is utilized. For example, the U.S. uses 2.17% steel reinforcement ratio, while the current reinforcement in South Korea is 0.03% [12]. Furthermore, South Korea uses slip-form construction method, while the U.S. uses cast-in-place construction method for construction of concrete permanent median barrier. This indicates that the current Korean concrete median barrier along highway is vulnerable to severe impact loading compared to other countries due to smaller reinforcement ratio. Accordingly, several different reinforcement ratios with some spacing variation between the rebar or wire-mesh were investigated using the developed model. From D3.2 wire-mesh to D25 rebar along with welding effect were considered. For nonwelding condition, at intersected points between vertical and horizontal rebars, nodes were considered separately as two nodes are used for the vertical and horizontal rebars, respectively. However, for welding condition, at intersected points, vertical and horizontal rebars share the nodes. The reinforcement details and results from the numerical analysis are shown in Figs. 14 and 15. The reinforcement details are indicated by the name of each case. For example, reinforcement designs were called “Number of reinforcement layer if it is more than two diameter (mm) of rebar_Weld (W) or No weld (nW) _ Spacing (mm).” Figure 14 shows the damaged shape of the concrete median barrier after impact. The D3.2_W_150 is the current design used in South Korea, and it was found that an increased diameter with welding between the horizontal and vertical rebars is effective under the SB6 impact loading. Figure 15(a) shows that it was observed that if the intersection areas between the rebars are welded together, the average volume loss decreased by 13% compared to nonwelded condition. When the graph was rearranged, as shown in Fig. 15(b), depending on the amount of reinforcement, it was found that two layer (×2) cases (2-D3.2_W_50) showed less volume loss (%) compared to D10_W_150 even though the reinforcement ratio (49 kg/m3) was smaller than D10_W_150 (79.7 kg/m3). This indicated that arrangement of two layers was more effective under an impact loading than that of one layer when the amount of the reinforcement was the same. It was also found that in around 204.1 kg/m3 of reinforcement amount, the volume loss did not decrease further and was considered to be converged. Therefore, 3% volume loss can be considered as an appreciable improvement under the impact loading. It should be noted that 0% volume loss could not be achieved using the developed model. In a model, a crack within a concrete is considered when elements between two separated bodies of concrete are deleted. Since the elements' size is around 36 mm, if there is a crack, the volume loss becomes larger compared to the actual cracked concrete body. However, as mentioned previously, this model and parametric study are based on conservative approaches and can be applied in the design of concrete median barrier.

A numerical study was conducted to evaluate the concrete median barrier. In particular, effects of different reinforcement details based on a developed model under the SB6 impact loading were assessed. The developed model was also verified with one field test and an actual accident. Conclusions derived from this study are as follows:

  1. (1)Development of an improved concrete median barrier up to the level of SB6 impact severity is necessary in South Korea in order to minimize the amount of concrete broken pieces and any possibility of traffic accident casualties under impact loading of truck.
  2. (2)It was found that for developing a collision model between a vehicle and concrete structure, contact option, boundary condition at both sides, erode value, and mesh regulation are the key parameters to be considered. Therefore, careful selection of these parameters is necessary for developing the collision model successfully.
  3. (3)The developed model predicted the collision behavior between the concrete median barrier and a truck satisfactorily. Velocity and angle after impact were accurately predicted with differences less than 0.14% and 8.9% from the actual accident values, respectively. However, the damaged length and depth were overestimated. Therefore, a conservative design was obtained using the developed model with relatively high accuracy.
  4. (4)According to the obtained results from the developed model, the concrete median barrier currently in service in South Korea is deemed to be vulnerable against SB6 (420 kJ) impact loading.
  5. (5)Intersection welding on rebar is required since it was found that the welded reinforcements are more effective compared to the nonwelded cases under impact loading.
  6. (6)The concrete median barrier with D16 or D25 rebar showed a 3% volume loss. Furthermore, it was found that D16 rebar with 150 mm spacing and welding at intersected area could be an alternative design for new concrete median barrier. By using this reinforcement details, the maximum decrease in the volume loss achieved was 81%.
  7. (7)Finally, an increased amount of reinforcement can raise the cost of construction significantly. Therefore, further studies, such as energy absorber to reduce the amount of reinforcement, can be conducted to minimize the raise in the construction cost.

The authors gratefully acknowledge the support of the Korean Expressway Corporation Research Institute (2015-0110-211) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (NRF-2015R1C1A1A02036617).

  • A =

    distance from front bumper to center-of-mass of vehicle

  • a1, a2, a3, a4 =

    coefficients for fitting the model surface to strength measurements from three axial compressive test

  • B =

    overall width of vehicle

  • D =

    dynamic barrier displacement

  • fck =

    characteristic compressive strength

  • fcm =

    a mean value of compressive strength

  • fctm =

    tensile strength

  • Fm(I1) =

    yield surface as a function of I1

  • g =

    gravity acceleration

  • GF =

    the fracture energy of concrete (N/m)

  • Gavg_lat =

    average lateral deceleration of vehicle

  • Gmax_lat =

    maximum lateral deceleration of vehicle

  • I1 =

    the first invariant of the stress tensor

  • θ =

    impact angle

MOLIT, 2012, “ Bridge Design Code (Limit State Design),” Ministry of Land, Infrastructure and Transport, Seoul, South Korea.
LSTC, 2007, “ LS-DYNA Keyword User's Manual,” Livermore Software Technology Corporation, Livermore, CA.
NCAC, 2015, National Crash Analysis Center, George Washington University, Washington, D.C., accessed Jan. 19, 2015, http://www.ncac.gwu.edu
Schwer, L. E. , and Malvar, L. J. , 2005, “ Simplified Concrete Modeling With *MAT_CONCRETE_DAMAGE_REL3,” JRI LS-DYNA User Week, pp. 49–60.
Murray, Y. D. , Abu-Odeh, A. Y. , and Bligh, R. P. , 2007, “ Evaluation of LS-DYNA Concrete Material Model 159,” Report No. FHWA-HRT-05-063.
Murray, Y. D. , 2007, “ Evaluation of LS-DYNA Concrete Material Model 159,” Report No. FHWA-HRT-05-062.
Comite Euro-International Du Beton, 2010, “CEB-FIP Model Code 2010,” International Federation for Structural Concrete, Lausanne, Switzerland.
Chung, C.-H. , Lee, J.-W. , Kim, S.-Y. , and Lee, J.-H. , 2011, “ Influencing Factors on Numerical Simulation of Crash Between RC Slab and Soft Projectile,” J. Comput. Struct. Eng. Inst. Korea, 24(6), pp. 591–599.
Olson, R. M. , Post, E. R. , and Ivey, D. L. , 1971, “ Design Requirements for Safer Highway Bridge Rails,” Transp. Eng. J. ASCE, 97(2), pp. 291–304.
Thai, D.-K. , Kim, S.-E. , and Lee, H.-K. , 2014, “ Effects of Reinforcement Ratio and Arrangement on the Structural Behavior of a Nuclear Building Under Aircraft Impact,” Nucl. Eng. Des., 276(2014), pp. 228–240. [CrossRef]
Coronado, C. , 2006, “ Characterization, Modeling and Size Effect of Concrete-Epoxy Interfaces,” Ph.D. dissertation, The Pennsylvania State University, State College, PA.
D'Angelo, D. , 2007, “ Concrete Barrier (Cast-In-Place),” State of New York Department of Transportation, New York.
Copyright © 2017 by ASME
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References

MOLIT, 2012, “ Bridge Design Code (Limit State Design),” Ministry of Land, Infrastructure and Transport, Seoul, South Korea.
LSTC, 2007, “ LS-DYNA Keyword User's Manual,” Livermore Software Technology Corporation, Livermore, CA.
NCAC, 2015, National Crash Analysis Center, George Washington University, Washington, D.C., accessed Jan. 19, 2015, http://www.ncac.gwu.edu
Schwer, L. E. , and Malvar, L. J. , 2005, “ Simplified Concrete Modeling With *MAT_CONCRETE_DAMAGE_REL3,” JRI LS-DYNA User Week, pp. 49–60.
Murray, Y. D. , Abu-Odeh, A. Y. , and Bligh, R. P. , 2007, “ Evaluation of LS-DYNA Concrete Material Model 159,” Report No. FHWA-HRT-05-063.
Murray, Y. D. , 2007, “ Evaluation of LS-DYNA Concrete Material Model 159,” Report No. FHWA-HRT-05-062.
Comite Euro-International Du Beton, 2010, “CEB-FIP Model Code 2010,” International Federation for Structural Concrete, Lausanne, Switzerland.
Chung, C.-H. , Lee, J.-W. , Kim, S.-Y. , and Lee, J.-H. , 2011, “ Influencing Factors on Numerical Simulation of Crash Between RC Slab and Soft Projectile,” J. Comput. Struct. Eng. Inst. Korea, 24(6), pp. 591–599.
Olson, R. M. , Post, E. R. , and Ivey, D. L. , 1971, “ Design Requirements for Safer Highway Bridge Rails,” Transp. Eng. J. ASCE, 97(2), pp. 291–304.
Thai, D.-K. , Kim, S.-E. , and Lee, H.-K. , 2014, “ Effects of Reinforcement Ratio and Arrangement on the Structural Behavior of a Nuclear Building Under Aircraft Impact,” Nucl. Eng. Des., 276(2014), pp. 228–240. [CrossRef]
Coronado, C. , 2006, “ Characterization, Modeling and Size Effect of Concrete-Epoxy Interfaces,” Ph.D. dissertation, The Pennsylvania State University, State College, PA.
D'Angelo, D. , 2007, “ Concrete Barrier (Cast-In-Place),” State of New York Department of Transportation, New York.

Figures

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Fig. 1

Photos from a severe accident occurred in South Korea

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Fig. 2

Level of impact severity under impact of large vehicle (truck) in the EU, Japan, U.S., and Korea

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Fig. 3

Rigid wall impact analysis with selected two models

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Fig. 4

Selected truck and developed concrete median barrier model

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Fig. 5

Flowchart for developing concrete median barrier model

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Fig. 6

Six sensitivity of contact option and comparison with Olson model

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Fig. 7

Sensitivity of boundary condition at both ends

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Fig. 8

Damaged shapes after impact depending on various erode values: (a) 1.1, (b) 1.4, (c) 1.6, and (d) 1.8

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Fig. 9

Effect of softening function at various D values

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Fig. 10

Effect of softening function at various B values

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Fig. 11

Mesh sensitivity for different element sizes

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Fig. 12

Level of impact severity under impact of large vehicle (truck) in the EU, Japan, U.S., and Korea

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Fig. 13

Comparison of damaged shapes from (a) actual accident and (b) simulated results

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Fig. 14

Comparison of damaged shapes for various reinforcement designs

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Fig. 15

Comparison of volume loss

Tables

Table Grahic Jump Location
Table 1 Comparison of simulation results with test data
Table Grahic Jump Location
Table 2 Selected key parameters for model verification

Errata

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