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Abdelkarim, ElGawady

DESIGN OF SHORT REINFORCED CONCRETE BRIDGE COLUMNS UNDER

VEHICLE COLLISION

Omar I. Abdelkarim

Ph.D. Candidate

Department of Civil, Architectural & Environmental Engineering

Missouri University of Science and Technology

1401 N. Pine Street, 218 Butler-Carlton Hall, Rolla, MO 65401

Tel.: 573-202-1069; Email: oiafgc@mst.edu

Mohamed A. ElGawady, Corresponding Author

Benavides Associate Professor

Department of Civil, Architectural & Environmental Engineering

Missouri University of Science and Technology

1401 N. Pine Street, 324 Butler-Carlton Hall, Rolla, MO 65401

Tel.: 573-341-6947; Fax: 573-341-4729; Email: elgawadym@mst.edu

Word count: 250 words abstract + 4,980 words text + 7 tables/figures x 250 words (each) =

6,980 words

Number of references = 24

TRR Paper number: 16-4436

Submission Date: November 15

th, 2015

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Abdelkarim, ElGawady

ABSTRACT This paper presents the behavior of reinforced concrete bridge columns subjected to vehicle

collision. An extensive parametric study consisting of 13 parameters was conducted, examining

the peak dynamic force (PDF) and the equivalent static force (ESF) of a vehicle collision with

reinforced concrete bridge columns. The ESF was calculated using the Eurocode approach and

the approach of the peak of twenty-five millisecond moving average (PTMSA) of the dynamic

impact force. The ESF from these two approaches were compared to the ESF of the American

Association of State Highway and Transportation Officials- Load and Resistance Factor Design

(AASHTO-LRFD; 2,670 kN [600 kips]). The ESF of the AASHTO-LRFD was found to be

nonconservative for some cases and too conservative for others. The AASHTO-LRFD was

nonconservative when the vehicle’s velocity exceeded 120 kph (75 mph) and when the vehicle’s

mass exceeded 16 tons (30 kips). This paper presents the first equation to calculate a design

impact force, which is a function of the vehicle’s mass and velocity. The equation covered high

range of vehicle velocities ranging from 56 kph (35 mph) to 160 kph (100 mph) and high range

of vehicle masses ranging from 2 tons (4.4 kips) to 40 tons (90 kips). This approach will allow

departments of transportation (DOTs) to design different bridge columns in different highways

depending on the anticipated truck loads and speeds collected from the survey of roadways. A

simplified equation based on the Eurocode equation of the ESF was proposed. These equations

do not require FE analyses.

INTRODUCTION

Vehicle collision with bridges can have serious implications with regard not only to human lives

but also to transportation systems. Harik et al. [1] reported that 17 of the 114 bridge failures in

the United States were the result of truck collisions over the period of 1951-1988. Lee et al. [2]

stated that vehicle collision was the third cause of bridge failures in the United States between

the years of 1980 and 2012 and was the reason for approximately 15% of the failures during this

period. Many vehicle collision events involving bridge piers have been reported throughout the

U.S. In July 1994, a tractor cargo-tank semitrailer hit a road guardrail, and the cargo tank

collided into a column of the Grant Avenue overpass over Interstate 287 in White Plains, New

York [3]. Twenty-three people were injured, the driver was killed, and a fire extended over a

radius of approximately 122 m (400 ft).

According to the American Association of State Highway and Transportation Officials-

Load and Resistance Factor Design (AASHTO-LRFD) Bridge Design Specifications 5th

[4]

abutments and piers located within a distance of 9,140 mm (30 ft.) from the roadway edge should

be designed to allow for a collision load. AASHTO-LRFD Bridge Design Specifications 5th

edition required the collision load to be an equivalent static force (ESF) of 1800 kN (400 kips).

El-Tawil et al. [5] used the commercial software LS-DYNA [6] to numerically examine two

bridge piers impacted by both Chevrolet pickup trucks and Ford single unit trucks (SUTs). The

ESF was calculated to produce the same deflection at the point of interest as that caused by the

impact force. These results suggested that the AASHTO-LRFD could be nonconservative and

the ESF should be higher than 1800 kN (400 kips).

Buth et al. [7, 8] studied the collision of large trucks, SUTs, and tractor-trailers with

bridge piers. This study included experimental work and finite element (FE) analysis conducted

with LS-DYNA software. The design requirements were updated in the 6th

edition of AASHTO-

LRFD Bridge Design Specifications [9] as follows: “the design choice is to provide structural

resistance, the pier or abutment shall be designed for an equivalent static force of 2,670 kN (600

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Abdelkarim, ElGawady

kips), which is assumed to act in a direction of zero to 15 degrees with the edge of the pavement

in a horizontal plane, at a distance of 1.5 m (5.0 ft) above ground.”

Buth et al. [7] defined the ESF of vehicle impact with a bridge column as the peak of the

twenty-five millisecond moving average (PTMSA) of the dynamic force. While the Eurocode

[10] calculates the ESF using equation (1) which takes into consideration the vehicle mass,

velocity, and deformation, and the column deformation, FE analysis is required to determine the

vehicle and column deformations in order to calculate the ESF. Abdelkarim et al. [11] conducted

an extensive study to identify the better approach between ECESF and PTMSA. Their study

revealed that PTMSA is more accurate than the ECESF in determining the static force of vehicle

collision with a bridge column.

𝐸𝐶𝐸𝑆𝐹 = 𝐾𝐸 =

12 𝑚 𝑣𝑟

2

𝛿𝑐 + 𝛿𝑑 (1)

where KE is the vehicle kinetic energy, m = the vehicle mass, 𝑣𝑟 = the vehicle velocity, 𝛿𝑐 = the

vehicle deformation, and 𝛿𝑑 = the column deformation. The δc of each vehicle was calculated as

the maximum change in length between the vehicle nose and its center of mass. The δd of each

column was calculated as the maximum lateral displacement of the column at the point of impact

load.

This paper presented finite element (FE) analyses to investigate the effects of 13 different

parameters on both dynamic and static impact forces. The constant impact load used in the

AASHTO-LRFD did not consider either the vehicle mass or velocity. Hence, the given impact

load may be conservative in some occasions and nonconservative in others. This paper presented

the first equation that can directly calculate the ESF given the vehicle mass and velocity. A

simplified equation had been suggested in this paper for the Eurocode to directly calculate the

ESF without a crash analysis.

PARAMETRIC STUDY

The authors presented the validation of the finite element modeling of vehicle collision with

bridge columns in a previous study [12]. Once the finite element model was validated, a

comprehensive parametric study was conducted to numerically investigate the reinforced

concrete (RC) column’s behavior during a vehicle collision. The LS-DYNA software was used

to examine the effect of 13 different parameters. Table 1 summarizes the columns’ variables.

Thirty-three columns (from C0 to C32) were investigated. Column C0 was used as a reference

column. Figure 1 illustrates the 3D-view model of the reference column C0. A detailed geometry

of the column C0 is also illustrated in this figure. It should be noted that some of the selected

parameters may not be common in practice. They were used, however, to fully understand the

column’s performance under a wide spectrum of parameters.

Columns’ Geometry

The columns investigated in this study were supported on a concrete footing by a fixed condition

at the bottom of the footing. All of the columns except columns C17 and C18 were hinged at the

top ends. Column C17 was free at the top end while the superstructure was attached at the top of

column C18. Most columns had a circular cross-section with a diameter of 1,500 mm (5.0 ft).

Columns C14, C15, and C16, however, had diameters of 1,200 mm (4.0 ft), 1,800 mm (6.0 ft),

and 2,100 mm (7.0 ft), respectively. The reference column’s height (measured from the top of

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Abdelkarim, ElGawady

the footing to the top of the column) was 7,620 mm (25.0 ft) with a span-to-depth ratio of 5.

Columns C12 and C13 were 3,810 mm (12.5 ft), and 15,240 mm (50.0 ft) tall, respectively, with

a span-to-depth ratio of 2.5, and 10, respectively. The span-to-depth ratio of other columns was

5. The soil depth above the top of footing was 1,000 mm (3.3 ft.). The soil depths above the top

of footing of columns C31, and C32, however, were 500 mm (1.7 ft.), and 1,500 mm (4.9 ft.),

respectively.

All of the columns except columns C7 and C8 were reinforced longitudinally by 1% of

the concrete cross-sectional area. Columns C7 and C8 were reinforced by 2% and 3% of the

concrete cross sectional area, respectively. Most columns had hoop reinforcements of D16 (#5)

with 101.6 mm (4 in.) spacing. Columns C9, C10, and C11, however, had hoop reinforcements

of D13 (#4) with 64 mm (2.5 in.) spacing, D19 (#6) with 152.4 mm (6 in.) spacing, and D16 (#5)

with 304.8 mm (12 in.) spacing, respectively. All of the columns except columns C19 and C20 were axially loaded with 5% of Po

where Po was calculated according to AASHTO-LRFD [9] as following:

𝑃𝑜 = 𝐴𝑠𝑓𝑦 + 0.85 𝑓𝑐′𝐴𝑐 (2)

Where 𝐴𝑠 = the cross-sectional area of the longitudinal reinforcement, 𝐴𝑐 = the cross sectional

area of the concrete column, 𝑓𝑦 = the yield strength of the longitudinal reinforcement, 𝑓𝑐′ = the

cylindrical concrete unconfined compressive strength. Column C19 was not axially loaded while

column C20 was axially loaded with 10% of Po.

Material Models

The vehicle collision load is considered to be within the extreme event limit-state according to

AASHTO-LRFD. This limit-state refers to the structural survival of a bridge during the extreme

event. Under these extreme conditions, the structure is expected to undergo considerable inelastic

deformations. Thus, all strength reduction factors (“Φ”) are to be taken as one when designing

concrete bridges for use under extreme events [13]. Therefore, a nonlinear material model was

used for the concrete column and the footing in all of the columns except C1and C2. The impact

force was expected to increase as the linear portion of the stress-strain curve of the column’s

concrete material increased because the energy dissipation would be reduced. Therefore, elastic

(mat. 001) and rigid (mat. 020) material models were used in the columns C1 and C2,

respectively, to identify the impact force’s upper limit. Various material models in LS-DYNA

software can simulate concrete material. The Karagozian and Case Concrete Damage Model

Release 3 (K&C model) was used as a nonlinear material in this study because it exhibited good

agreement with experimental results in previous studies [14, 15]. The material elastic model

mat.001 is an isotropic, hypoelastic material. El-Tawil et al. [5] used this material to study

impact analysis. They suggested that elastic material allowed direct assessment of design

provisions for the ESF. Buth et al. [8] used the rigid material model mat.020 to simulate bridge

piers. This material model does not allow any deformation of the column to calculate the

maximum possible impact force.

With the exception of Columns C3, C4, and C5, each column had an unconfined concrete

compressive strength of 34.5 MPa (5,000 psi). Columns C3, C4, and C5, however had

unconfined concrete compressive strengths of 20.7 MPa (3,000 psi), 48.3 MPa (7,000 psi), and

69.0 MPa (10,000 psi), respectively.

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Abdelkarim, ElGawady

The material model 003-plastic_kinamatic was used to identify the steel reinforcement’s

elasto-plastic stress-strain curve. Five parameters were needed to define this material model

according its properties: the elastic modulus (E), the yield stress (SIGY), Poisson’s ratio (PR),

the tangent modulus, and the ultimate plastic strain. The values used according to Caltrans [16]

were 200.0 GPa (29,000.0 ksi), 420.0 MPa (60,900.0 psi), 0.30, 1102.6 MPa (159.9 ksi), and

0.118, respectively.

Strain Rate Effects

Concrete Material

Previously conducted studies examined concrete’s properties under dynamic loading. The CEB

model [17] code is one of the most comprehensive models used, and introduces the concrete

properties with strain rate effect. Malvar and Ross [18] modified the CEB model through

equations (3-10). Any increase in concrete properties under dynamic loading is typically reported

as a dynamic increase factor (DIF). DIF is the ratio of dynamic concrete strength to static

concrete strength; it is calculated from both the strain rate and the concrete static properties.

𝐷𝐼𝐹𝑐 =𝑓𝑐

𝑓𝑐𝑠= (

휀̇

휀�̇�)

1.026 𝛼𝑠

for 휀̇ ≤ 30 𝑠−1 (3)

𝐷𝐼𝐹𝑐 =𝑓𝑐

𝑓𝑐𝑠= 𝛾𝑠 (

휀̇

휀�̇�)

0.33

for 휀̇ > 30 𝑠−1 (4)

𝛼𝑠 = (5 + 9𝑓𝑐𝑠

𝑓𝑐𝑜)−1 (5)

𝑙𝑜𝑔𝛾𝑠 = 6.156 𝛼𝑠 − 2 (6)

Where

DIFc = compressive strength dynamic increase factor

휀̇ = strain rate in the range of 30 x 10-6

to 300 s-1

휀�̇� = static strain rate of 30 x 10-6

s-1

,

𝑓𝑐 = the dynamic compressive strength at 휀̇ 𝑓𝑐𝑠 = the static compressive strength at 휀�̇�

𝑓𝑐𝑜 = 10 MPa = 1,450 psi

𝐷𝐼𝐹𝑡 =𝑓𝑡

𝑓𝑡𝑠= (

휀̇

휀�̇�)

𝛿

for 휀̇ ≤ 1 𝑠−1 (7)

𝐷𝐼𝐹𝑡 =𝑓𝑡

𝑓𝑡𝑠= 𝛽 (

휀̇

휀�̇�)

0.33

for 휀̇ > 1 𝑠−1 (8)

𝛿 = (1 + 8𝑓𝑐𝑠

𝑓𝑐𝑜)−1 (9)

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Abdelkarim, ElGawady

𝑙𝑜𝑔 𝛽 = 6 𝛿 − 2 (10)

Where

DIFt = tensile strength dynamic increase factor

𝑓𝑡 = the dynamic tensile strength at 휀̇ 𝑓𝑡𝑠 = the static tensile strength at 휀�̇�

휀̇ = strain rate in the range of 10-6

to 160 s-1

휀�̇� = static strain rate of 10-6

s-1

Steel Material

The strain rate affects the stress-strain relation of steel as it affects the speed at which

deformation occurs [19]. Therefore, the strain rate effect on steel was considered when the static

yield stress producing the dynamic yield strength was scaled. Cowper-Symonds [20]

experimentally examined the strain rate effect on steel presenting equation (11) with two

constants (p and c) that can be used to calculate the dynamic yield strength. Several researchers

concluded that p and c constants could be taken as 5 and 40, respectively [21]. The elastic

modulus does not change under impact loading [22].

𝑓𝑦𝑑 = 1 + (휀̇

𝑐)

1𝑝 (11)

where 𝑓𝑦𝑑 = dynamic yield stress and p and c were taken as 5 and 40, respectively.

Vehicles FE Models

Two vehicle models were used in this study: a reduced model of Ford single unit truck (SUT)

(35,353 elements) and a detailed model of Chevrolet C2500 Pickup (58,313 elements). These

models were developed by the National Crash Analysis Center (NCAC) of The George

Washington University under a contract with the FHWA and NHTSA of the U.S. DOT. These

models were posted on the National Crash Analysis Center (NCAC) website in November 2008.

Experimental tests involving head-on collisions were conducted to validate each model [23, 24].

Figure 2 illustrates the FE vehicles’ models.

Maximum speed limits on highways differ from state to state in the U.S. Therefore, a

high range of vehicle velocity was investigated in this study, ranging from 56 kph (35 mph) to

160 kph (100 mph) to cover all of the expected speeds during vehicle collisions. Most vehicles in

this parametric study were traveling with a velocity of 80 kph (50 mph). The Ford SUT of the FE

models C21, C22, and C23, however, was traveling with velocities of 160 kph (100 mph), 120

kph (75 mph), and 56 kph (35 mph), respectively. The mass of the Ford SUT was 8 tons (18

kips) for all of the models except the models C24, C25, and C26. The FE model C24 had the

Chevrolet C2500 Pickup with a mass of 2 tons (4.4 kips) instead of the Ford SUT. The mass of

the Ford SUT of the FE models C25, and C26 was 16 tons (35 kips) and 30 tons (65 kips),

respectively. The increase of the Ford SUT mass was achieved by increasing the mass of the

cargo in the Ford SUT.

The distance between the vehicle and the unprotected column was examined here by the

distance between the vehicle nose and the column face. The distance between the vehicle nose

and the concrete column was 150 mm (0.5 ft.). The vehicles’ noses of the FE models C27, C28,

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Abdelkarim, ElGawady

C29, and C30, however, were 0.0 mm (0.0 ft.), 300 mm (1.0 ft.), 3,000 mm (10.0 ft.), and 9,140

mm (30.0 ft.) apart from the concrete columns, respectively.

RESULTS AND DISCUSSION

Concrete Material Models

This section presented the effects of the selection of concrete material model on the PDF and

ESFs. Three material models mat001, mat020, and mat72RIII representing elastic, rigid, and

nonlinear behavior were used for this investigation. The typical time-impact force relationship is

illustrated in figure 3a. As shown in the figure, the first peak force occurred when the vehicle’s

rail collided with the column. The second peak force on the columns, which was the largest, was

produced by the vehicle’s engine. The third peak occurred when the vehicle’s cargo (in the Ford

SUT only) struck the cabinet and the engine. The fourth peak was produced when the rear

wheels left the ground. Generally, each of the columns reached its PDF nearly at the same time

of 40 millisecond, and had zero impact force beyond 220 millisecond. The PDF of column C2,

which was modeled using a rigid material, was approximately 15% higher than that of column

C0, which was modeled using a nonlinear material. This finding was expected as no

deformations were allowed to take place in the concrete material of column that was modeled

using a rigid material. Hence, no impact energy was dissipated. Column C1, which was modeled

using elastic material, had a slightly lower PDF value than that of column C2.

Figure 3b illustrates the normalized ESFs and PDFs of the columns C0, C1, and C2. The

normalized ESF for columns C0, C1, and C2 ranged from 0.7 to 0.8 of the ESF of AASHTO-

LRFD of 2,670 kN (600 kips). The values of PTMSA and ECESF for all of the columns were

almost constant regardless of the material model. The PTMSA values were higher than the ECESF

values for all of the columns.

The system’s kinetic energy before collision occurred was 18,408 kip.in (2,102 kN.m)

(Figure 3c). The kinetic energy was absorbed entirely during the first 150 milliseconds in the

form of column and vehicle deformations. Converting part of the kinetic energy into thermal

energy (in the form of heat) was excluded from this study.

The vehicle’s deformation of each model was presented in figure 3d. The maximum

deformation of vehicles in FE models C0, C1, and C2 was 1,122 mm (44.2 in.), 1,156 mm (45.5

in.), and 1,127 mm (44.4 in.), respectively.

Unconfined Compressive Strength (𝒇𝒄′ )

Four values of ranging from 20.7 MPa (3,000 psi) to 69.0 MPa (10,000 psi) were investigated

during this section. Changing 𝑓𝑐′ did not significantly affect the values of PDF except when the

𝑓𝑐′ was considerably low for column C3 (Figure 4a). The PDF value of column C3 having 𝑓𝑐

′ of

20.7 MPa (3,000 psi), was 20% lower than that of the other columns. The lower concrete

strength in C3 led to early concrete spalling and bucking of several longitudinal bars, which

dissipated a portion of the impact force. The values of PTMSA and ECESF for all of the columns

were nearly constant regardless of the 𝑓𝑐′. The PTMSA values were higher than the ECESF values

for all of the columns.

Strain Rate Effect

The PDF increased significantly when the strain rate effect was included (Figure 4b). The PDF

of column C0, which was modeled including the strain rate effect, was approximately 27%

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Abdelkarim, ElGawady

higher than that of column C6, which was modeled excluding the strain rate effect. Including the

strain rate effect, the column’s strength and stiffness increased leading to higher dynamic forces.

There is no significant effect of strain rate on ECESF and PTMSA. The PTMSA values were

higher than the ECESF values for all of the columns.

Percentage of Longitudinal Reinforcement

Three values of longitudinal reinforcement ratios ranging from 1% to 3% were investigated

during this section. In general, the PDF increased slightly when the percentage of longitudinal

reinforcement increased (Figure 4c). Tripling the percentage of longitudinal reinforcement

increased the PDF by only 10%. It increased because the column’s flexural strength and stiffness

increased slightly with increasing the flexural steel ratio. When the percentage of longitudinal

reinforcement increased, the ECESF and PTMSA were constant. The PTMSA values were higher

than the ECESF values for all of the columns.

Hoop Reinforcement

Four volumetric hoop reinforcement ratios ranging from 0.17% (D16@305 mm) to 0.54%

(D13@64 mm) were investigated during this section. The PDF decreased when the volume of

hoop reinforcement decreased leading to increased concrete damage which dissipated some of

the impact energy (Figure 4d). The PDF decreased by 12% when the volume of hoop

reinforcement decreased by 67%. When the hoop reinforcement decreased, the ECESF and

PTMSA were constant. The PTMSA values were higher than the ECESF values for all of the

columns.

Column Span-To-Depth Ratio

Three values of column span-to-depth ratio ranging from 2.5 to 10 were investigated during this

section. The relationship between the PDF and the column’s span-to-depth ratio was nonlinear

(Figure 4e). The PDF of column C0, having span-to-depth ratio of 5, was higher than that of

columns C12 and C13, having a span-to-depth ratios of 2.5 and 10, respectively. This was

because the column C12 had high local damaged buckling of several rebars leading to energy

dissipation and the column C13 had the lowest stiffness leading to energy dissipation through

high column’s displacement. The PTMSA and ECESF were approximately constant regardless of

the span-to-depth ratio. The PTMSA values were higher than the ECESF values for all of the

columns.

Column Diameter

Four values of column diameter ranging from 1,200 mm (4.0 ft) to 2,100 mm (7.0 ft) were

investigated during this section. The PDF of all of the columns, except for Column C16,

increased slightly when the column diameter increased (Figure 4f). The PDF of the column C16,

having a diameter of 2,100 mm (7.0 ft), was lower than that of the column C15, having a

diameter of 1,800 mm (6.0 ft) because of the rebars’ buckling. Column C14, with a diameter of

1,200 mm (4.0 ft), subjected to severe rebar buckling. Both the ECESF and the PTMSA for all

columns increased slightly when the column diameter increased. The PTMSA values were

higher than the ECESF values for all of the columns.

Top Boundary Conditions

Three columns top boundary conditions including free, hinged, and superstructure were

investigated during this section. Changing the column’s top boundary condition slightly changed

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Abdelkarim, ElGawady

the PDF values because the PDF was induced in a very short period of time (Figure 5a). The

column’s response was controlled by the amplitude of the imposed kinetic energy as the impact

duration was very small compared to the natural period of the column. However, the maximum

lateral displacement at the point of impact of column C17, having free top boundary condition,

was higher than those of columns C0 and C18, having hinged and superstructure top conditions,

respectively. The existence of the superstructure in column C18 resulted in a top boundary

condition similar to that in column C0 of hinged condition. Changing the top boundary condition

did not change the ECESF and PTMSA. The PTMSA values were higher than the ECESF values

for all of the columns.

Axial Load Level

Three values of axial load level ranging from 0 to 10% of the column’s axial capacity (Po) were

investigated during this section. The PDF typically increased when the axial load level increased

(Figure 5b). Column C19, which sustained zero axial load, had a PDF that was approximately

25% lower than that of column C20, which sustained an axial load that was 10% the Po. The high

axial compressive stresses on the column delayed the tension cracks due to the vehicle impact

and hence increased the column’s cracked stiffness leading to higher dynamic forces. The

PTMSA and ECESF were approximately constant regardless of the axial load level. The PTMSA

values were higher than the ECESF values for all of the columns.

Vehicle Velocity

Four vehicle velocities ranging from 56 kph (35 mph) to 160 kph (100 mph) were investigated

during this section. The PDF tended to increase nonlinearly when the vehicle’s velocity

increased (Figure 5c). It is of interest that the increase in the PDF is not proportional to the

square of the velocity as in the case of elastic impact problems. Damage to the columns reduces

the rate of increase in the PDF. For example, the PDF increased by approximately 507% when

the vehicle’s velocity increased from 56 kph (35 mph) to 160 kph (100 mph). The ECESF and

PTMSA increased approximately linearly with increased vehicle velocity. The PTMSA values

were higher than the ECESF values for all of the columns. The AASHTO-LRFD was found to be

nonconservative when the column was collided by a vehicle travelling with a speed exceeded

120 kph (75 mph) as the ESF of AASHTO-LRFD of 2,670 kN (600 kips) was lower than the

PTMSA values of such cases.

Vehicle Mass

Four vehicle masses ranging from 2 tons (4.4 kips) to 30 tons (65 kips) were investigated during

this section. In general, both the PDF and ESF increased linearly when the vehicle’s mass

increased (Figure 5d). However, the rate of increase is slower than what is anticipated in elastic

impact problems. For example, the PDF increased by approximately 101% when the vehicle’s

mass increased from 2 tons (4.4 kips) to 30 tons (65 kips). The PDF almost did not change when

the vehicle mass increased from 2 tons (4.4 kips) to 8 tons (18 kips) because the energy

dissipation in the form of inelastic deformations whether in the vehicle or in the column did not

significantly change as the kinetic energy was not considerably high. The PTMSA values were

higher than the ECESF values for all of the columns. The AASHTO-LRFD was found to be

nonconservative when the column was collided by heavy vehicles of a mass more than 16 tons

(35 kips) as the ESF of AASHTO-LRFD of 2,670 kN (600 kips) was lower than the PTMSA

values of such cases.

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Abdelkarim, ElGawady

Distance between Vehicle and Column

Five distances between the vehicle and column ranging from zero to 9,140 mm (30 ft) were

investigated during this section. In general, the PDF decreased when the distance between the

vehicle and column increased (Figure 5e). The PTMSA and ECESF are approximately constant

regardless of the distance between the vehicle and the unprotected column. The PTMSA values

were higher than the ECESF values for all of the columns.

Soil Depth above the Top of the Column Footing

Three values of the soil depth above the top of the column footing ranging from 500 mm (1.7 ft)

to 1,500 mm (4.9 ft) were investigated during this section. In general, the change in the soil

depth above the column footing did not significantly affect the PDF (Figure 5f). The PTMSA

and ECESF are approximately constant regardless of the soil depth. The PTMSA values were

higher than the ECESF values for all of the columns.

ESF Equation for Adoption by AASHTO-LRFD and Eurocode

However, the AASHTO-LRFD approach is quite simple as it uses a constant value for ESF,

regardless of the vehicle’s characteristics. The PTMSA and Eurocode approaches presented in

this manuscript use a variable ESF that is dependent on these characteristics. AASHTO-LRFD

was found to be quite conservative in some cases and nonconservative in others in predicting the

ESF of impact loads. The PTMSA and Eurocode approaches, however, require a FE analysis and

iterative design to estimate the ESF of impact loads. Thus, a simple equation considering the

vehicle’s characteristics that can predict the ESF without either a FE or an iterative analysis

would represent a significant improvement over the current AASHTO-LRFD or Eurocode

approaches. Figures 4 and 5 revealed that the most influential parameters on impact problems

were the vehicle’s mass and velocity. However, the other investigated parameters had limited

effects. Therefore, developing a design equation to estimate the ESF as a function of the

vehicle’s mass and velocity seems reasonable. This approach will allow departments of

transportation (DOTs) to design different bridge columns in different highways depending on the

anticipated truck loads and speeds collected from the survey of roadways.

The PTMSA correctly predicted the performance of bridge columns as was proved by

Abdelkarim et al. [11]. Thus, it was selected as the basis for the newly developed equation. The

PTMSAs of the parametric study was studied mathematically using CurveExpert Professional

software, and SAS software to introduce a design equation for estimating kinetic-energy based

ESF (KEBESF) which was presented in equation (14) for international system (SI) units and

equation (15) for English units as below:

𝐾𝐸𝐵𝐸𝑆𝐹 = 33√𝑚 𝑣𝑟2 = 46√𝐾𝐸 (14)

where m = the vehicle mass in tons, vr = the vehicle velocity in m/s, and KE = kinetic energy of

the vehicle in kN.m.

𝐾𝐸𝐵𝐸𝑆𝐹 = 2.1 √𝑚 𝑣𝑟2 = 3 √𝐾𝐸 (15)

where KEBESF = proposed ESF to AASHTO-LRFD (kip), m = the vehicle mass in kip, vr = the

vehicle velocity in mph, and KE = kinetic energy of the vehicle in kip.mph2.

11

Abdelkarim, ElGawady

The proposed equation’s results were compared to the PTMSA’s FE results for a high

range of vehicle masses from 2 tons (4.4 kips) to 40 tons (90 kips) and a high range of vehicle

velocities from 32 kph (20 mph) to 160 kph (100 mph)). The relationship between the vehicle’s

kinetic energy and the normalized PTMSA was presented in figure 6a. Also, the relationship

between the vehicle’s kinetic energy and the normalized KEBESF was presented in the figure. It is

worthy to note that the AASHTO-LRFD was found over predicting to the ESF when the kinetic

energy was lower than 2,500 kN.m (1,844 kip.ft). However, it was found quite nonconservative

beyond that threshold of 2,500 kN.m (1,844 kip.ft). In several instances, the RC columns were

subjected to impact loads that were almost double the ESF of the current AASHTO-LRFD. In

order to illustrate the accuracy of the equation, curves of ± 10% of the KEBESF values were

shown in figure 6a (referred to as upper and lower limits). The figure showed that the proposed

KEBESF equation correlated well with the FE results and predicted most cases with an accuracy

of more than 90% (within the upper and lower limits).

The PTMSA is more accurate than the Eurocode and hence equation (14) or (15) gives a

more reasonable value of ESF. However, this paper simplified the Eurocode equation to avoid

implementing FE models to estimate the ESF. Based on the FE results of ECESF of the parametric

study and using CurveExpert Professional software, and SAS software, a new simplified

equation for estimating momentum-based equivalent static force MBESF was developed and

presented in equation (16) for international system (SI) units and equation (17) for English units

as below:

𝑀𝐵𝐸𝑆𝐹 = 130√𝑚 𝑣𝑟 = 130√𝑃𝑚 (16)

where m = the vehicle mass in tons, vr = the vehicle velocity in m/s, and Pm = the momentum of

the vehicle in tons.m/s.

𝑀𝐵𝐸𝑆𝐹 = 13√𝑚 𝑣𝑟 = 13√𝑃𝑚 (17)

where MBESF= proposed ESF to Eurocode (kip), m = the vehicle mass in kip, vr = the vehicle

velocity in mph, and Pm = the momentum of the vehicle in kip.mph.

The results of the proposed equation were compared to the FE results of ECESF. The

relation between the vehicle’s momentum and the normalized ECESF was presented in figure 6b.

The relation between the vehicle’s momentum and the normalized MBESF was presented in the

figure as well. The proposed MBESF equation correlated well with the FE results and predicted

most cases with an accuracy of more than 90% (within the upper and lower limits).

FINDINGS AND CONCLUSIONS A detailed description of finite element modeling of vehicle collision with reinforced concrete

bridge columns using LS-DYNA software was presented. Evaluation of the peak dynamic force

(PDF) and the equivalent static force (ESF) through a comprehensive parametric study were

conducted. The comprehensive parametric study investigated the effects of concrete material

model, unconfined concrete compressive stress (𝑓𝑐′), material strain rate, percentage of

longitudinal reinforcement, hoop reinforcement, column span-to-depth ratio, column diameter,

the top boundary conditions, axial load level, vehicle velocity, vehicle mass, distance between

12

Abdelkarim, ElGawady

errant vehicle and unprotected column, and soil depth above the top of the column footing on the

behavior of the columns under vehicle collision. This study revealed the following findings:

The AASHTO-LRFD was nonconservative when the vehicle’s velocity exceeded 120

kph (75 mph) and when the vehicle mass exceeded 16 tons (30 kips).

The AASHTO-LRFD was found to be nonconservative when the column was collided

with a vehicle having kinetic energy of 2,500 kN.m (1,800 kip.ft) or more.

Generally, the PDF increases when the longitudinal reinforcement ratio, hoop

reinforcement volumetric ratio, column diameter, axial load level, vehicle velocity, and vehicle

mass increase and when the strain rate effect is considered, while it decreases when the damage

of the column and the clear zone distance increase. However, it is not affected by changing 𝑓𝑐′,

column top boundary condition, and soil depth.

The relation between the PDF and the column’s span-to-depth ratio was nonlinear.

The vehicle’s velocity and mass are the most influential parameters affected the vehicle

collision with a bridge column.

Generally, the PTMSA values were higher than the ECESF values.

A new equation for estimating the ESF based on the vehicle mass and velocity,

(𝐾𝐸𝐵𝐸𝑆𝐹 = 33√𝑚 𝑣𝑟2 ), with an accuracy of more than 90% was developed. This approach will

allow departments of transportation (DOTs) to design different bridge columns to different

impact force demands depending on the anticipated truck loads and velocities.

This paper simplified the Eurocode equation for estimating the ESF based on the

vehicle’s mass and velocity, (𝑀𝐵𝐸𝑆𝐹 = 130√𝑚 𝑣𝑟 ), with an accuracy of more than 90%.

ACKNOWLEDGEMENT

This research was conducted by the Missouri University of Science and Technology and was

supported by the Missouri Department of Transportation (MoDOT) and Mid-American

Transportation Center (MATC). This support is gratefully appreciated. However, any opinions,

findings, conclusions, and recommendations presented in this paper are those of the authors and

do not necessarily reflect the views of sponsors.

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Report 9-4973-1, 2010.

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LRFD Bridge Design Specification. John Wiley and Sons, New York, Third

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14. Abdelkarim, O. and ElGawady, M. Analytical and Finite-Element Modeling of

FRP-Concrete-Steel Double-Skin Tubular Columns. Journal of Bridge

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15. Ryu, D., Wijeyewickrema, A., ElGawady, M., and Madurapperuma, M. Effects of

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LIST OF TABLES

TABLE 1 Summary of the Examined Columns’ Parameters

LIST OF FIGURES

FIGURE 1 Finite element model of the bridge column “C0” for the parametric study; (a)

3D-view, (b) detailed side view of the column components.

FIGURE 2 View of the vehicles FE models: (a) the Ford single unit truck, (b) Chevrolet

pickup detailed model.

FIGURE 3 Effect of various concrete material models: (a) Time versus Impact force for

column C0 with a nonlinear material, (b) PDF and ESFs, (c) Time versus total kinetic

energy, and (d) Time versus vehicle displacement.

FIGURE 4 Effects of: (a) 𝒇𝒄′ , (b) strain rate, (c) longitudinal reinforcements ratio, (d) hoop

reinforcements, (e) span-to-depth ratio, and (f) column diameters on PDF and ESF.

FIGURE 5 Effects of: (a) top boundary conditions, (b) axial load level (c) vehicle velocities,

(d) vehicle masses, (e) distance between vehicle and column, and (f) soil depth above the top

of column footing on PDF and ESF.

FIGURE 6 the ESF proposed equations versus the FE results: (a) Kinetic energy-based

ESF (KEBESF) for AASHTO-LRFD and (b) Momentum-based ESF (MBESF) for Eurocode.

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Abdelkarim, ElGawady

TABLE 1: Summary of the Examined Columns’ Parameters

Col. Conc.

Mat.

𝒇′𝒄,

MPa SR 𝜌s

Hoop

RFT S/D

D,

mm

Top

Bound.

Cond.

P/P0 vr,

kph

m,

ton

LC,

mm

ds,

mm

C0 NL 34.5 C 1%

D16@

102 mm

5 1500 Hinged 5% 80 8 150 1000

C1 EL 34.5 C 1% 5 1500 Hinged 5% 80 8 150 1000

C2 RIG 34.5 C 1% 5 1500 Hinged 5% 80 8 150 1000

C3 NL 20.7 C 1% 5 1500 Hinged 5% 80 8 150 1000

C4 NL 48.3 C 1% 5 1500 Hinged 5% 80 8 150 1000

C5 NL 69.0 C 1% 5 1500 Hinged 5% 80 8 150 1000

C6 NL 34.5 NC 1% 5 1500 Hinged 5% 80 8 150 1000

C7 NL 34.5 C 2% 5 1500 Hinged 5% 80 8 150 1000

C8 NL 34.5 C 3% 5 1500 Hinged 5% 80 8 150 1000

C9 NL 34.5 C 1% D13@

64 mm 5 1500 Hinged 5% 80 8 150 1000

C10 NL 34.5 C 1% D19@

152 mm 5 1500 Hinged 5% 80 8 150 1000

C11 NL 34.5 C 1% D16@

305 mm 5 1500 Hinged 5% 80 8 150 1000

C12 NL 34.5 C 1%

D16@

102 mm

2.5 1500 Hinged 5% 80 8 150 1000

C13 NL 34.5 C 1% 10 1500 Hinged 5% 80 8 150 1000

C14 NL 34.5 C 1% 5 1200 Hinged 5% 80 8 150 1000

C15 NL 34.5 C 1% 5 1800 Hinged 5% 80 8 150 1000

C16 NL 34.5 C 1% 5 2100 Hinged 5% 80 8 150 1000

C17 NL 34.5 C 1% 5 1500 Free 5% 80 8 150 1000

C18 NL 34.5 C 1% 5 1500 Super-

structure 5% 80 8 150 1000

C19 NL 34.5 C 1% 5 1500 Hinged 0% 80 8 150 1000

C20 NL 34.5 C 1% 5 1500 Hinged 10% 80 8 150 1000

C21 NL 34.5 C 1% 5 1500 Hinged 5% 160 8 150 1000

C22 NL 34.5 C 1% 5 1500 Hinged 5% 120 8 150 1000

C23 NL 34.5 C 1% 5 1500 Hinged 5% 56 8 150 1000

C24 NL 34.5 C 1% 5 1500 Hinged 5% 80 2 150 1000

C25 NL 34.5 C 1% 5 1500 Hinged 5% 80 16 150 1000

C26 NL 34.5 C 1% 5 1500 Hinged 5% 80 30 150 1000

C27 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 0 1000

C28 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 300 1000

C29 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 3050 1000

C30 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 9140 1000

C31 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 150 500

C32 NL 34.5 C 1% 5 1500 Hinged 5% 80 8 150 1500

NL = nonlinear material, EL = elastic material, RIG = rigid material, SR = strain rate, NC = Not Considered, C =

Considered, 𝜌s = the percentage of longitudinal reinforcement, S/D = span-to-depth ratio, D = column diameter, P =

applied axial load, P0 = column axial compressive capacity, vr = vehicle velocity, m = vehicle mass, Lc = distance

between vehicle and column, ds = soil depth above the column footing.

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Abdelkarim, ElGawady

(a) (b)

FIGURE 1 Finite element model of the bridge column “C0” for the parametric study; (a)

3D-view, (b) detailed side view of the column components.

Blanked

concrete

elements: only

for showing the

reinforcement

Footing

Concrete

column

36 D25 (36#8)

ρs = 1.0%

H = 7,620 mm

(25.0 ft)

D = 1,500 mm

(5 ft)

D16@127 mm

(#5@5”)

Hinged boundary

condition

Fixed boundary

condition

17

Abdelkarim, ElGawady

(a) (b)

FIGURE 2 View of the vehicles FE models: (a) the Ford single unit truck, (b) Chevrolet

pickup detailed model.

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Abdelkarim, ElGawady

(a) (b)

(c) (d)

Vehicle’s rail impact Vehicle’s Cargo impact

Vehicle’s engine impact Rear wheels left the ground

FIGURE 3 Effect of various concrete material models: (a) Time versus Impact force for

column C0 with a nonlinear material, (b) PDF and ESFs, (c) Time versus total kinetic

energy, and (d) Time versus vehicle displacement.

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Abdelkarim, ElGawady

(a) (b)

(c) (d)

(e) (f)

FIGURE 4 Effects of: (a) 𝒇𝒄′ , (b) strain rate, (c) longitudinal reinforcements ratio, (d) hoop

reinforcements, (e) span-to-depth ratio, and (f) column diameters on PDF and ESF.

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Abdelkarim, ElGawady

(a) (b)

(c) (d)

(e) (f)

FIGURE 5 Effects of: (a) top boundary conditions, (b) axial load level (c) vehicle velocities,

(d) vehicle masses, (e) distance between vehicle and column, and (f) soil depth above the top

of column footing on PDF and ESF.

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Abdelkarim, ElGawady

(a) (b)

FIGURE 6 the ESF proposed equations versus the FE results: (a) Kinetic energy-based

ESF (KEBESF) for AASHTO-LRFD and (b) Momentum-based ESF (MBESF) for Eurocode.