CRASH IMPACT ANALYSIS OF THE G2 GUARDRAIL:

A VALIDATION STUDY

by

O. Sean Martin and Jerry W. Wekezer

FAMU-FSU College of EngineeringComputer Impact Simulation Laboratory (CISL)

TRB National Research Council1998 Annual Meeting

O. Sean Martin, Graduate Research AssistantDavid H. Melvin, Inc., Consulting Engineers, 345 S. Magnolia, Suite C-21,Tallahassee, Florida 32301.Phone: (850) 671-7221 Fax: (850) 671-7223E-mail: omartin@eng.fsu.edu

Jerry W. Wekezer, Ph.D., PE, Professor and ChairmanFAMU-FSU College of Engineering, Department of Civil Engineering, 2525 Pottsdamer Street,Tallahassee, Florida 32310-6046.Phone: (850) 487-6143 Fax: (850) 487-6142E-mail: wekezer@eng.fsu.edu

Text Word Count = 3,433 + 8 (figures and tables) x 250 equivalent words = 5,433 words

Martin/Wekezer 2

ABSTRACT

Prototype guardrails, bridge rails, crash cushions and other roadside safety hardware have been

designed in part by using engineering judgment, experience and intuition. These prototypes have

been later evaluated by performing full-scale crash tests representing expected worst case

scenarios. Since these tests are relatively expensive and because they require specialized

facilities and personnel, the result is that important decisions are quite often based on the results

of a few full-scale crash tests. Many highly effective roadside safety hardware systems have been

developed using this process, but difficult issues remain. Due to the increased complexity of

today’s vehicular fleet and the fact that full-scale crash tests do not provide sufficient information

about loads, accelerations, stresses and strains to develop designs based on the mechanical

behavior of barrier components, analytical methods have become a necessity. This paper reflects

the nationwide research trend to utilize analytical methods for improvement of highway roadside

safety hardware.

A finite element model of the G2 weak-post w-beam guardrail was impacted by a finite element

model of a 1994 Chevrolet pickup truck traveling at 100 km/hr and impacting the barrier at 25

degrees. LS-DYNA3D, a nonlinear, explicit dynamic finite element code, was used to perform

the analysis. Results are discussed and compared to data from a full-scale crash test.

Acceleration time histories are compared using time domain analysis. The average residual,

standard deviation of the residuals and the t-statistic for the simulation and test curves are also

reported.

Keywords: roadside safety hardware, G2 guardrail, nonlinear finite element modeling,

computer impact simulation, validation, LS-DYNA3D.

Martin/Wekezer 3

INTRODUCTION

The weak-post w-beam guardrail, AASHTO designation G2, has come under close

scrutiny after failing to meet Test Level 3 criteria (100 km/hr, 25 degrees) and after performing

marginally at Test Level 2 criteria (70 km/hr, 25 degrees) while being impacted with the 2000P

vehicle specified in NCHRP Report 350 (1).

In the present study, a finite element model of a 1994 Chevrolet pickup truck is used to

impact a finite element model of the G2 weak-post w-beam guardrail at 100 km/hr and 25

degrees. The primary objective of this research is to compare the acceleration histories generated

by a computer analysis using LS-DYNA3D to those of a full-scale crash test using statistical

measures. Ultimately, it is hoped that the G2 finite element model could be used to aid in the

development of design modifications for the G2 guardrail.

G2 FINITE ELEMENT MODEL

Length of Impact Influence

The G2 guardrail redirects impacting vehicles primarily through beam tension, therefore

the length of the barrier modeled is critical in accurately capturing the loading response. The

length of time required to run numerical computations, however, requires that every effort be

made to reduce the number of elements contained within the model. For this reason, springs

were added just outside the contact regions (at each node along the depth of the w-beam) to

simulate the behavior of a longer guardrail as shown in Figure 1. Initially, the beam sections at

one span outside the contact regions were assumed to be in the elastic range during impact and

the axial stiffness was determined using:

Martin/Wekezer 4

Ks = EA

L (elastic spring constant)

A = 1312.6 mm2 (cross-sectional area)

L = 19.05 m (length of five spans of guardrail)

E = 200e+03 MPa, (steel modulus of elasticity).

Impact regionKs Ks

W-beam S 75x143 post

Actual guardrail

Simulation

Figure 1. Application of springs to simulate a long guardrail.

These values lead to a stiffness of Ks = 13.80 N/m. Results of initial simulations revealed,

however, that the assumption of the beam sections at one span outside of the contact region being

in the elastic range were incorrect. For this reason, elastic springs were replaced by elastic-

plastic springs in order to better simulate the behavior of a full length guardrail.

LS-DYNA3D Material Models and Analysis Options

Accurate material models and input parameters are essential for the successful

development of finite element models. Physical material properties can be found in material

handbooks and in specifications, unfortunately this information is usually not sufficient for the

Martin/Wekezer 5

modeling of high energy events due to their conservative nature and their failure to include the

effects of strain hardening, cold-working and residual stresses.

Recently, however, quasi-static and dynamic coupon tests of common guardrail materials

have been conducted and LS-DYNA3D computer simulation of the tests has been used to

develop appropriate material input parameters (2).

Guardrail Steel

Specifications for the manufacturing of guardrails and for the minimum required

mechanical material properties are given in AASHTO M-180 (3,4). These minimum values are

not very useful as a basis for LS-DYNA3D material input parameters for the reasons described

above. Results of experimental tests, however, and subsequent LS-DYNA3D simulations have

shown that LS-DYNA3D Material Type 24 yields a force-elongation response that fall almost

entirely within a 90-percent confidence envelope around the experimental data when the

following input parameters are used:

Table 1 LS-DYNA3D material parameters for modeling AASHTO M-180 Class Type II

steel for material type 24

Density (Mg/mm3) 7.86E-09

Young’s modulus (MPa) 200E+03

Poisson’s ratio 0.33

Yield stress (MPa) 415.0

Strain rate effects none

Plastic strain at failure 0.66

Increments of strain 0.0 0.02 0.08 0.165 0.33 0.49 0.66 1.0

Increments of stress (MPa) 415 415 548 575 585 595 600 0

Martin/Wekezer 6

Steel Guardrail Post

In an impact, S 75x143 (3 x 5.7 inch) steel posts, AASHTO M-183M, generally fail either

by twisting or by bending to the ground (2,4). Steel guardrail posts can also be modeled using

LS-DYNA3D Material Type 24. Properties used for the simulation are as listed in Table 2.

Table 2 LS-DYNA3D material parameters for modeling AASHTO M-183M steel using

material type 24

Density (Mg/mm3) 7.86E-09

Young’s modulus (MPa) 200E+03

Poisson’s ration 0.33

Yield stress (MPa) 315.0

Strain rate effects none

Plastic strain at failure 0.625

Increments of strain 0.0 0.019 0.05 0.165 0.33 0.495 0.625 1.0

Increments of stress (MPa) 315 315 427.8 500.8 504.3 506.5 400 0

Post Embedded in Soil

The G2 guardrail can be supported by several different types of posts, but the most

common is the S 75x143 steel post, AASHTO Standard P-3-7 (5). A soil plate is welded to one

side of the post flange to reduce the dependence of the post performance on soil conditions.

Initially, a post was modeled using the INGRID preprocessor for comparison with full-scale post

tests performed by the California Division of Highways in 1967.

Full-scale post tests consisted of low-velocity impacts using a 5,668 kg truck with a

hollow steel tube mounted on the front bumper. Two load cells between the tube and the bumper

Martin/Wekezer 7

were used to measure the force with which the posts resisted the impact. To simulate this

impact, the post model was impacted with a model of a steel tube and rigid object having the

same mass and velocity as the truck and having contact points in the same location as the load

cells, see Figure 2.

Contact interface(position of load cell)

5,668 kg rigid objectvelocity = 8.94 m/s

Contact interface(position of load cell)

Hollow tubevelocity = 8.94 m/s

S 75x143 steel post

Figure 2. DYNA3D simulation of full-scale post impact test.

The resulting forces between the rigid object and the steel tube were compared with the forces

found in the full-scale tests. This produced a maximum force of 41.0 kN versus 25.8 kN

recorded in the full-scale tests. The finite element model was then calibrated by setting a point of

fixity at 120 mm below the ground surface (6,7).

Martin/Wekezer 8

Post to W-Beam Connection

The primary purpose of the posts in weak-post guardrail is to support the rail at the

correct height, although closer spacing of the posts can increase the rigidity. Decreasing the post

spacing by 50 percent reduces the lateral dynamic deflection by about 20 percent. In the G2

guardrail, the W-beam is connected to the post on one side of the flange with one 8 mm diameter

(5/16 inch) hex bolt through a slotted hole as shown in Figure 3.

S 75x143 post

W-beam shell plate

Post shell plate

Hex bolt head

Figure 3. W-beam to post bolted connection.

The bolt may or may not have a square washer on it, which reduces the ability of the bolt head to

pass through the slotted hole. It has been recommended that the square washer not be used due to

problems with the rail being pulled down under impact on the post. In any case, the method of

connecting the rail to the post must allow failure and separation to occur at a load similar to that

Martin/Wekezer 9

causing the bolt washer combination to fail. Initially, three different methods of modeling this

connection were considered: merging the nodes or using nodal constraints, using tied node sets

with failure, and using elastic-plastic springs.

There are two major problems associated with either constraining or tying the nodes to

simulate the beam to post connection. First, it is difficult to correlate the failure of a bolt to the

effective average strain in the beam and post materials. This greatly hinders the formation of a

well-defined failure criteria. The second problem is that using either of these two methods does

not allow any separation of the nodes until failure has occurred. In the actual connection, the

slotted hole and elongation of the bolt and washer allow movement and separation prior to failure

of the connection.

Elastic-plastic springs were used in initial simulations. To mimic the bolted connection,

the spring is assigned an elastic constant based on the separation of the beam and post just prior

to failure. The plastic spring constant is set to zero, so that the post and beam can continue to

separate with no additional applied force. To establish the necessary spring constants, a detailed

model of the bolted connection was formed. Two plates representing the W-beam and the post

were modeled using shell elements and the bolt and washer were modeled using solid elements.

The edges of the beam plate were fixed and the post plate was given a velocity. The elastic

spring constant determined for the bolted connection was Ks = 1.438 N/m.

Use of elastic-plastic springs yielded good results for initial G2 simulations with an 820C

vehicle where, in general, few of the post to w-beam connections fail. Under large deflections

Martin/Wekezer 10

and where several of the connections fail, as is the case with the 2000P model impact

simulations, the connection with elastic-plastic springs was determined to be unsatisfactory.

First, the wheels of the truck snag on the spring connection when tracking between the post and

w-beam. Second, the elastic stress is constantly maintained even though the plastic spring

constant is set to zero. This results in the guardrail system maintaining an unrealistic stiffness.

For these reasons, connections used for this study consist of constrained spotwelds with failure.

VALIDATION PROCEDURES

Conducting computer simulations using the finite element method for the analysis and

design of roadside safety hardware and for the assessment of vehicle crashworthiness is rapidly

gaining acceptance within the engineering research community. Results of these simulations,

however, have largely been qualitative in nature. This is due, in most cases, to a limited number

of tested roadside hardware and vehicle finite element models and to a limited number of full

scale crash tests. Modeling using the finite element method has now advanced to the point,

however, that validation procedures using standardized procedures are essential.

COMPARISONS TO FULL SCALE CRASH TEST

All data was collected using the nodal time history function in LS-TAURUS.

Unfortunately, this function does not allow the user to control the time interval at which the data

is written to the output files. For this reason, linear regression techniques were used to

interpolate accelerations from the simulated data allowing analysis of both simulation and

experimental data to occur at the same time interval. Next, all raw data, experimental and

Martin/Wekezer 11

simulated, were filtered using the SAE J211 Filter Program. The following validation procedures

were then used:

1) NARD validation procedures,

2) Malcolm Ray’s validation procedure, and

3) Protocol Validation Method.

NARD Validation Procedure

This validation procedure was originally developed approximately a decade ago (9). The

procedure is based on the theory of signal processing and analysis and consists of a time domain

and frequency domain analysis. The present study uses only the time domain portion of the

validation procedure. The following measures are quantified:

1. Relative difference of moments of two signals,

2. Root mean square log measures of two signals, and

3. Correlation measures between two signals.

These results are shown in Table 3 below.

Table 3 Time domain analysis (100 km/hr at 25 degrees)

Relative Moment Difference

Moment 0 = 0.432 Relative moment difference = 0.27Moment 1 = 0.078 Relative moment difference = 0.24Moment 2 = 0.018 Relative moment difference = 0.22Moment 3 = 0.005 Relative moment difference = 0.21Moment 4 = 0.002 Relative moment difference = 0.20Moment 5 = 0.001 Relative moment difference = 0.20

Root Mean Square (RMS) Log Measures

RMS Log Difference (R3) 8.4RMS Log Average (R4) 6.6

Martin/Wekezer 12

RMS Log Form of Signal #1 (R1) 6.9RMS Log Form of Signal #2 (R2) 6.3RMS Log Ratio (R3/R4) 1.3

Correlation Measure

Energy Measure of Correlation 0.49

NARD specifies an absolute difference of moments and RMS log measures of 20% or

less, and a correlation between the fitted test data and the fitted simulation data of 0.99 or more.

Moments 0, 1, 2, and 3 are all greater than 20%. Moments 4 and Moment 5 as well as the RMS

log measures are all 20% or less. The correlation between the fitted test data and the fitted

simulation data is 0.49.

Malcolm Ray’s Method

If two time histories are assumed to represent the same event, the differences between

them (e.g., the residuals) should be attributable to random experimental error. If the residuals are

truly random, then they should be normally distributed around the mean error of zero. Once the

mean and variance of the residual distribution are known, they can be used to plot an envelope

around the average response and a paired t-tail test can be performed with the mean and standard

deviation where the t-statistic is defined as follows:

Te

n=

σ

where e is the average residual between the two curves, σe is the standard deviation of the

residuals and n is the number of paired samples (10). A simulation should be judged an adequate

representation of a full-scale crash test when the following conditions are met:

Martin/Wekezer 13

• The average residual should be less than 5 percent of the peak acceleration

(eRESIDUAL ≤ 0.05 aPEAK)

• The standard deviation of the residuals should be less than 20 percent of the peak

acceleration (σresidual ≤ 0.20 aPEAK)

• A t statistic should be calculated between the test and simulation curve. The

calculated t statistics should be less than 3 (-3 ≤ t0.005,∞ ≤ 3)

The present simulation failed to meet the above criteria. The residual was 1.23 as compared to

0.31 for 5% of the peak acceleration. The standard deviation was 2.63 as compared to 20% of

the peak acceleration and the t-statistic was 9.06.

Protocol Validation Method

The Protocol Validation is another quantitative method, which uses a verbal rating scale

to compare maximum and minimum quantities from crash tests and numerical simulations as

shown in Table 4 (11).

Table 4. Verbal rating scale for comparing differences in full-scale and simulation data.

Agreement ratingDifference in max. quantities Verbal rating

> 50% non-existent40-50% poor30-40% average20-30% good10-20% very good0-10% excellent

Simulation results compare favorably with full-scale crash test data. The maximum

dynamic deflection of the guardrail in the full scale crash test was 1.40 meters. The maximum

Martin/Wekezer 14

dynamic deflection of the guardrail in the simulation was 1.36 meters. The difference in these

two quantities is 3% leading to a rating of excellent. Results of maximum and minimum

accelerations are rated as excellent and average with differences of 4.3% and 36%, respectively.

SUMMARY

Acceleration time histories for the simulated and full-scale crash tests are shown in Figure

4. The Protocol Validation yielded average to excellent results. The NARD Method yielded

mixed results and Malcolm Ray’s Method yielded negative results. The simulation does,

however, predict the general path of the vehicle, the maximum deflection of the guardrail and the

maximum and minimum accelerations. Future simulation efforts will use an upgraded version of

Longitudinal accelerations at C.G. of truck(100 km/hr at 25 degrees)

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

2.00

4.00

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

Time in seconds

Acc

eler

atio

n in

g's

Full-scale crash data

Simulated crash data

Figure 4. Comparison of accelerations at c.g.

Martin/Wekezer 15

the pickup model containing a new suspension model, improved mass distribution, and upgraded

material properties. It is believed that these improvements will enhance simulation efforts.

CONCLUSIONS

Computer impact simulations are frequently recognized as useful analytical tools for

roadside hardware design (12,13). City cars are becoming smaller as an emphasis is placed on

greater gas mileage, pollution and parking problems, while trucks are becoming larger in an

effort to deliver goods with greater economy. Roadside safety hardware must become more

sophisticated in order to accommodate this diversity in design vehicles. The use of computer

simulation codes such as LS-DYNA3D will aid engineers, transportation officials and policy

makers in making these necessary advances.

ACKNOWLEDGEMENT

The research herein is based upon the work supported by the Federal Highway

Administration under Cooperative Agreement No. DTFH61-94-X-00036. Special thanks are

extended to Mr. Martin Hargrave, FHWA’s Contracting Officer for providing continuous support

during the project, to the National Crash Analysis Center for updates on the pickup track model

and other technical assistance, and to Mr. Roger Bligh of the Texas Transportation Institute who

provided electronic data and test reports for the full-scale crash test.

The contents of this paper reflect the views of the authors who are solely

responsible for the facts and accuracy of the data, and the opinions, findings and conclusions

presented herein. The contents do not necessarily reflect the official views or policies of the

Martin/Wekezer 16

Federal Highway Administration or the FAMU-FSU College of Engineering. This paper does

not constitute a standard, specification, or regulation. In addition, the above listed agencies

assume no liability for its content or use thereof. The names of specific products or

manufacturers listed herein does not imply endorsement of those products or manufacturers.

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Results”, Transportation Research Record, Washington, DC: Transportation Research Board,

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Martin/Wekezer 17

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