crashworthiness of guardrail posts embedded in cohesionless soils: a parametric study

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International Journal of Crashworthiness

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Crashworthiness of guardrail posts embedded incohesionless soils: a parametric study

Abdelmonaam Sassi & Faouzi Ghrib

To cite this article:Abdelmonaam Sassi & Faouzi Ghrib (2016): Crashworthiness of

guardrail posts embedded in cohesionless soils: a parametric study, International Journal ofCrashworthiness, DOI: 10.1080/13588265.2016.1167390

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Crashworthiness of guardrail posts embedded in cohesionless soils:a parametric study

Abdelmonaam Sassi and Faouzi Ghrib

Department of Civil and Environmental Engineering, University of Windsor, Windsor, Canada

ARTICLE HISTORY

Received 1 September 2014Accepted 11 March 2016

ABSTRACT

Guardrail systems are designed to provide a safe environment for vehicles and to reduce theseverity of occupants injuries. The performance of this safety system is deemed to be vital tohighway users. Guardrail post is probably the most important component of any guardrail systemdesign. The evaluation of guardrail posts performance usually involves crash tests, which consist ofcolliding the post with a bogie. Crashworthiness tests try to cover a range of design parameterssuch as the soil resistance, impact velocity and blockout crushability. When reviewing the availablevarious dynamic tests conducted to date, it is apparent that the range of the considered designparameters varies widely. Because of the lack of consistency of the diverse test conditions, thestatistical analysis of the test results is not an easy task. In the present paper, the nite element

method has been employed as a tool to conduct a parametric study and generate statistical data.The generated data are used to establish correlations between the post parameters and the systemperformance indicators.

KEYWORDS

Guardrail post; dynamic test;nite element model;cohesionless soil

1. Introduction

Strong post W-beam guardrail systems are widely used

around the world as an essential hardware to ensure the

safety of errant vehicles. It is well established that the

performance of any guardrail system is fundamentally

associated to the interaction of the vehicle with the

embedded post. Since the change of the design cycle of

vehicles is much shorter that of guardrails, it becomes

urgent to review the performance of these systems. For

example, in the context of North America, vehicle eet

has changed signicantly over the last decades. The pri-

vate vehicle automobiles (sedans) market share

decreased while Minivans, SUVs and small trucks made

a signicant increase to reach 25% of the vehicle eet as

of 2002 [22]. This change requires a re-assessment of the

safety hardware designed earlier for different vehicle

eet composition. In fact, statistical data collected from

highway accidents show that SUVs and small trucks

vehicles are more susceptible to roll in case of impactwith the W-beam guardrail [20]. It was argued that the

increase of rollover risk is due the high impact force mag-

nitude between the vehicle and the guardrail system as

well as the higher centre of gravity of SUVs when com-

pared to sedans. The study of vehicles colliding W-beam

guardrail systems has been an active research area [11].

Different procedures exist worldwide to evaluate the

safety performance of highway system. In USA, MASH

which replaced NCHRP 350, are the most used guide-

lines in use, while EN1317 is the procedure used in

Europe to provide criteria and standards for evaluating

new safety hardware devices [8]. Dreznes [6], Hubbel

[12] and Anghileri [2] compared the three testing proce-

dures EN 1317, NCHRP 350 and MASH. Anghileri [2]concluded that many technical aspects of the three pro-

cedures were similar. Dreznes [6] explained that any

design that meet one of these testing requirements could

be used in a country which has no established testing

requirements.

Previous research ndings suggested that the crash-

worthiness of highway guardrail systems is dominated

mainly by the soilpost interaction. Reid and co-authorshave shown that the capacity to contain and redirect

light trucks and SUVs is strongly correlated to the post

stiffness and soil resistance [20]. In fact, the optimum

level of soil reaction is dependent on many parameterssuch as the height of the guardrail mounting, the depth

of the post, the nature of the soil and the design features

of the post. During impact, guardrail systems dissipate

the impact energy mainly through deformations in the

vehicle, the soil and the guardrail. Poor soilpost inter-action may cause the guardrail system to fail performing

CONTACT Faouzi Ghrib [email protected]

2016 Informa UK Limited, trading as Taylor & Francis Group

INTERNATIONAL JOURNAL OF CRASHWORTHINESS, 2016

http://dx.doi.org/10.1080/13588265.2016.1167390
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the intended role and might lead to fatal accidents [32].

For the case of strong posts, the reaction is controlled by

the soil resistance, and it was found that the barrier per-

formance begins to degrade when the reaction force

reaches the level of 50 kN.

The crashworthiness evaluation of guardrail systems

involved experimental tests to assess the performance of

guardrail barriers under various case scenarios. Sultaniet al. [28] presented a performance study of guardrail

systems based on crash test data. The study shows a

wide variability of the responses of the 33 designs con-

sidered. Experimental studies are always expensive and

time consuming; they usually cover only limited case

scenarios. Finite element simulations are an alternative

to testing particularly at the early stages of the design or

when conducting parametric study to cover the design

space. In fact, this technique has become a fundamental

tool in the analysis of vehicle safety [26]. Ideally, combi-

nations ofnite element simulations, carefully designed

tests and the study real crash accidents data lead to a bet-ter insight of the performance of the complex responses

of guardrail systems.

The crash analysis of guardrail systems involves

highly nonlinear material behaviour associated with

large deformations due to the impact load. Thenite ele-

ment analysis method appears to be the preferred tool

that offers full control over the range of the involved

parameters. The different design parameters can be eval-

uated through an optimisation process in order to pro-

pose new guardrail design proposals or improve existing

one that can reduce the risk of truck rollover [29]. Due

to the complexity of the involved mechanical phenom-ena in the impact of a vehicle to a guardrail system, any

nite element model should be confronted with available

experimental results to validate the analysis process.

Consequently, a correlation of any proposed nite ele-

ment model is fundamental to gain condence about its

capability and efciency. Once validated, nite element

models become a reliable design tool and relatively inex-

pensive to evaluate guardrails crashworthiness responses

under a wide range of inputs [29]. The performance of

the whole guardrail system during an impact is closely

dependent on the behaviour of individual pole-soil sub-

system. Therefore, the present work will concentrate on

the analysis of the pole-soil subsystem.

The objective of the present paper is to conduct a

parametric study on the major design parameters on an

isolated postsoil-guardrail in sandy soils. Five parame-ters were selected; they are (i) the impactor speed, (ii)

the impactor mass, (iii) the post embedment depth and

(iv) the blockout crushability. A nite element model of

impactor subjected to an initial velocity colliding a

guardrail post was developed and calibrated to the

impact tests conducted by Coon et al. [3]. The model

was used to investigate the effects of the different test

parameters on the interaction of the post and soil to

compare the loaddeection curves with the baselineresults. A regression analysis of the data generated by

the parametric study allowed the development of series

of correlations between the base design parameters and

the system performances.The paper is organised in two sections: in the rst sec-

tion, the development of the baseline nite element

model and its validation is presented whereas in the sec-

ond section, a parametric study of the effects of the

embedment depth, the soil resistance, the impactor mass

and the blockout compressibility is discussed.

2. Baseline model development and validation

The major issue associated to the development of an ef-

cient nite element model for the simulation of embed-

ded structures is the proper selection of thesoilstructure interaction model. Soilstructure inter-action modelling has been extensively investigated for

structures subjected to quasi-static and dynamic load-

ings, but very few studies dealt with impact loading. The

available models for soil-structure interaction vary in

complexity from continuum to spring-dashpot-mass

(subgrade method or macro-element) elements. Sassi

and Ghrib [24] compared the subgrade and continuum

approach and showed that the subgrade approach could

be used to simulate the interaction between the soil and

the post and represents a good trade-off between sim-

plicity and accuracy. The use of the continuum approachis accurate; however, it is computationally demanding

and the identication of the model parameters of the

constitutive law representing the continuum is very

difcult.

In the present study, we propose to use the horizontal

subgrade method to simulate the soilpole interaction.This method has been extensively used in the area of

geotechnical engineering to simulate the soil lateral resis-

tance against buried structures. It consists of modelling

the soil surrounding the structure by a set of nonlinear

springs attached to the embedded part of the structure.

The horizontal subgrade modulus at a given point is

dened as the ratio of the horizontal subgrade reaction

force and the corresponding average produced displace-

ment at that point. Today, various empirical expressions

are available in the literature for the identication of the

modulus of subgrade reaction. In the specic case of

roadside safety, the method developed by Habibagahi

and Lancer [10], based on the concept of the bearing

capacity, is widely used. The subgrade method is primar-

ily used for its computational efciency. However, the

2 A. SAS SI AND F. GHRIB


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method suffers from many shortcomings where the most

signicant is that it does not account for the inertia effect

as it treats the soils as a massless medium. Previous stud-

ies have shown that the soil inertia plays a major role

especially at the initial contact of the postsoil duringthe impact [14]. Most of the studies conducted in the

area of roadside impact do not consider the effect of the

soil mass neither the energy dissipated through in thesoil mass.

In the present paper, we propose a simple method to

improve the subgrade model by dening a macro-ele-

ment comprising a spring, a mass and a dashpot. The

soil is decomposed into independent layers. The behav-

iour of each layer is simulated by one macro-element as

shown in Figure 1. The overall soil reaction is deter-

mined as the resultant of the all the macro-elements

resultant. The lumped mass represents the mass of the

soil being involved during the impact. The role of the

springs is to store the elastic energy and simulate the

non-linear behaviour of the soil during the impact. The

inclusion of dashpots is a simplistic method to account

for the energy dissipation observed in crash tests. As the

soil is deformed during the impact, many dissipative

phenomena including friction, heat and plastic yielding

occur simultaneously. The process of representing all the

dissipative mechanisms can only be a simplication to

represent the energy loss in the soil. To take into account

the soils parameters variability, the soil mass has been

divided into layers of 100 mm; each layer is assumed to

have independent properties of its adjacent soil. The dis-

cretisation of the postsoil interface is therefore fullymodelled based on the three mechanical parameters: the

nonlinear stiffness, mass and damper coefcient.

To validate the proposed nite element model, the

results of the dynamic tests conducted by Coon et al. [3]

are selected as baseline. These tests will be used to cali-

brate the added masses and dashpots

coef

cients.Coons tests covered various ranges of impactor speeds

with different types of post material and geometry. The

cart impactor consists of a rigid nose bogie vehicle of

946 kg mass, instrumented with an accelerometer to

measure the lateral deceleration during the impact. Four

tests were conducted with W-beam posts, corresponding

to speeds of 4:6 m=s, 5:4 m=s, 5:9 m=s and 8:9 m=s,respectively. The soil density ranged from 1980 kg=m3

to 2240 kg=m3 and the tests were conducted in soilswith no signicant moisture. The length of the post was

1830 mm with an embedment of 1100 mm. The impact

point of the bogie with the post was located at 550 mmabove the ground level. The results of the test showed

that for the impact speeds ranging from 4:6 m=s to5:9 m=s, the impactor rebounds back; however, forhigher speed of 8:9 m=s the impactor slides over thepost. The simulations were conducted using Hyperworks

Finite Element software package, in particular the

impact analysis was conducted using RADIOSS nite

element software.

2.1. Spring stiffness identication

The spring stiffness was calculated by the method ofHabibagahi and Langer [10]. The coefcient of subgrade

reaction was found to increase with the depth and

decrease with the deection. The horizontal stiffness khis dened as follows:

Kh DNqs

0

y (1)

where s0 is the effective overburden stress,yis the lateral

deection and Nq denotes the lateral bearing capacity

and it is dened as function of the deectionyand thedepthz, whereasBis the width of the post.

Nq D A MF

ffiffiffiz

B

r (2)

Ais a dimensionless parameter which depends on the

deection and the internal friction angle and MF is den-

sity-dependent modication factor. Plaxico et al. [17]

proposed a method to extrapolate the value ofA using

Impactor

Post

Lumped soil

mass

Z

Figure 1. Proposed dynamic model for lateral post response.

INTERNATIONAL JOURNAL OF CRASHWORTHINESS 3


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the results of Habibagahi and Langer [10]. The expres-

sion of A as a function of the lateral deection y is

given by:

AD 15; 27614:09 e0:1245y (3)

To calculate the soil equivalent stiffness for different

friction angle, Plaxico et al. [17] dened a density-

dependent modication factor, MF, following a linearrelationship with the friction angle:

MF D2

330 C 1 (4)

Figure 2 shows the distribution of the springs stiff-

ness for the test conditions of Coon et al [3] at different

depths.

2.2. Evaluation of the lumped mass

The lumped mass of the macro-element is dened as the

mass per layer involved during the impact. Numerical sim-

ulations show that only a limited mass surrounding the

post would be activated during the impact. To determine

the size of the block activated during the impact, the

results of a continuum nite element model were used.

The continuum model consists of a post embedded in a

soil block as shown inFigure 3. The soil surrounding the

post is modelled as a cylinder medium in which the post is

embedded at its centre. The soil was divided into three

coaxial cylindrical blocks having different mesh sizes. At

the vicinity of the post, the mesh was ner to capture the

soil deformation and coarser at the outer portion of the

cylindrical block. The size of the soil block used in the

nite element model was 2.7 m whereas the depth of the

block was 2.0 m. The impactor consisted in cylindrical

rigid noose striking the post with an initial velocity. The

soil is modelled using 8-node hexahedron and the parame-

ters of the soil and the guardrail post were determined

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50 60 70 80 90 100

Force(kN)

Deflection (mm)

z = 100 mm

z = 300 mm

z = 500 mm

z = 700 mm

z = 900 mm

z = 1100 mm

Figure 2. Loaddeection curve of the unidirectional spring calculated by Habibagahi and Langer approach for Coon et al. [3] test.

Figure 3.Continuum model for the dynamic loading of the postembedded in cohesionless soil.



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from the literature [25]. The displacement of the post was

measured at the impact point and the force was calculated

at the interface of the post and the impactor. The data col-

lected was ltered using CFC60 lter and the

loaddeection curve is determined.The criterion dening the mass activated during the

impact is based on a displacement thresholddf. The

region with a displacement higher than a given displace-

mentdfwas assumed to be involved in the inertia reac-

tion and it is included in the active mass. The

contribution of the mass exhibiting lower displacement

is neglected. A parametric study was conducted to deter-

mine the threshold df, and from a parametric study it

was found that a displacement 2 mm produces accurate

results. The results from the continuum model showed

that the total volume of the soil mobilised in the front of

the post during the impact dened a volume having the

shape of a cone where the apex is located at the point of

rotation of the post and the base at the ground level as

shown in Figure 4 [25]. The soil block mass dened

within the contour was calculated and lumped to the sys-

tem of macro-element.

2.3. Determination of the damping coefcient

To determine the amount of damping coefcient,Cc, the

damping is assumed viscous and expressed as a percent-

age of the critical value. Since the effect of the soil inertia

occurs at the early loading stage, the stiffness of the

spring is selected from the initial tangent of the nonlin-

ear loaddeection curve as illustrated inFigure 2. Thesprings located close to the ground surface exhibited the

maximum lateral displacement and the lowest spring

stiffness. The spring located close the pole rotation cen-tre exhibited less lateral displacement amount but higher

stiffness.

A parametric study has been conducted to determine

the damping ratio using of Coons et al. [3] experimental

ndings. For each simulation, the average load, the peak

load and the maximum impactor displacement have

been computed and compared to dynamic test results

taken as reference. The damping ratio, j, of 12% gave

the optimum results matching the load defection curve

of the post and the deection of the post with time.

As summarised inTable 1, the numerical simulations

results when compared to the dynamic test results show

Figure 4. Vertical cross-section of the soil mass mobilised during the impact at 20 ms.

Table 1.Comparison of peak load, average force and maximum deection of dynamic test with the nite element simulation.

Maximum deection (mm) Average force (kN) Peak force (kN)

TestImproved

subgrade modelContinuum

method TestImproved


method TestImproved


method

Test #1 (4.6 m/s) 234 233 240 42.8 43.0 41.1 64.0 53.1 50.4Test #2 (5.4 m/s) 314 296 312 43.9 45.9 42.5 66.9 57.8 51.2Test #3 (5.9 m/s) 348 353 338 47.3 47.9 46.3 67.0 64.3 52.3Test #4

(8.9 m/s) Over ride Over ride Over ride NA 56.3 55.3 104.7 97.2 85.2

Note: The post used in test 4 is W150 23.5 instead of W150 13.5.



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a good agreement. These ndings demonstrate that the

proposed subgrade model including an active masses

and dampers predicts accurately the post behaviour dur-

ing the side impact similar to the continuum model

while keeping the computational time reasonable.

3. Evaluation of the impactors speed effect

To study the impact speed effect on the guardrail post

response, a velocity range of 310 m/s was considered.A literature survey of the experimental tests showed that

the impactor speed varies in general from 4.6 m/s [3] to

9.4 m/s [18]. It is to be noted that a speed of 9 m/s repre-

sents approximately the severity of a vehicle impacting a

guardrail at 100 km/h and an angle of 25 when the

vehicle is aligned with the post. The simulations were

conducted over 150 ms time after the impact onset and

the results are summarised inTable 2.

Results of the simulations show that the average load

increases with the speed from 35.4 kN, for the lower

speed of 3 m/s, to 59.6 kN, corresponding to higher

speed of 10 m/s, whereas the peak load increases from

43.3 kN to 106.6 kN, respectively. The load-time history

shows a rst peak for all speeds that occurs between 7

and 9 ms,Figure 5. This initial peak is more pronouncedfor speeds higher than 4 m/s. A linear regression shows

that the relation of the peak and average loads are given:

FpeakD 10:795V

Faverage D 3:439VC 26:863 (5)

The regression curves of the peak and average forces

are plotted as function of the speed in Figure 6 with

comparison of the test results reported by Coon et al.

[3]. These ndings show that the linear regression cap-

tures accurately the variation of the average loads.

Table 2.Summary of the simulation results of impactor hitting the post embedded in the soil with differentimpact speeds.

Speed (m/s) Peak load(kN)

Maximumdisplacement (mm)

Average load(kN)

Observationin the post

3 43.3 130.1 35.4 Stopped4 50.7 191.4 40.4 Stopped4.6 53.8 233.1 42.9 Stopped5.4 58.1 294.6 46.2 Stopped5.9 64.1 336.0 48.1 Stopped7 77.9 435.6 51.9 Stopped

8 88.7 540.1 55.0 Override8.9 97.2 645.5 57.3 Override

10 106.6 795.9 59.6 Override

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140

ImpactorLoad(kN)

Time (ms)

3.0 m/s

4.0 m/s

4.6 m/s

5.4 m/s

5.9 m/s

7.0 m/s

8.0 m/s

8.9 m/s

10.0 m/s

Figure 5. Time histories of the impactor load for different impact speed.



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The maximum displacement increases from 130 mm atan impact speed of 3 m/s to 796 mm at 10.0 m/s, Figure 7.

For a speed higher than 9 m/s, the energy absorbed by the

soilpost system was lower than the initial kinetic energyof the impact. Thus, the post was not able to stop the

impactor which continued its trajectory and overrode the

post. A nonlinear regression of the relationship between

the maximum displacement dened in (m) and the impac-

tor speed in (m/s) is shown inFigure 8and given by:

DmaxD 5:2972 V2C 25:839 V (6)

The variation of the guardrail post response with

the impactor velocity could be attributed to the strainrate effect of the soil and the steel post. Different

studies showed that the shear strength parameters ofcohesionless soil,cand , are not signicantly affected

by the tests speed [19,30]. However, it is well estab-

lished that the steel post behaviour is inuenced by

the strain rate effect. Following Simunovic et al [27],

we propose to include the rate effect by using the

Cowper and Symonds equation [4]:

s0

sD 1C

_e

d

1q

! (7)

where sand s0 are the quasi-static and dynamic stresses,

respectively, _eis the strain rate,qandDdenote the Cow-per and Symonds coefcients. For mild steel, the Cowper

Figure 6. Variation of the maximum and average impactor load as function of the speed.

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80 100 120 140

ImpactorDisp

lacement(mm)

Time (ms)

3.0 m/s

4.0 m/s

4.6 m/s

5.4 m/s

5.9 m/s

7.0 m/s

8.0 m/s

8.9 m/s

10.0 m/s

Figure 7. Variation of the impactor displacement as function of time for different impact speed.



9/18

and Symonds coefcientsq and D are estimated to be 5

and 40, respectively [13].In crash tests, the selection of the appropriate speed to

use in testing guardrails components is very crucial. In

fact, the impact of a single guardrail post by full front

cart should simulate the lateral component of the impact

involving a vehicle with a speed of 100 km/h and an

impact angle of 25o which is theoretically 42 km/h

(11.74 m/s). Experimental tests and nite element simu-

lation shows that the maximum lateral speed of contact

is lower than 11.74 m/s. During the full-scale testing, the

vehicle is positioned at the critical impact point located

between the posts. Because of the energy dissipation dur-

ing the impact and the friction between the guardrail

system and the vehicle, the speed is reduced from

100 km/h to approximately 92 km/h whereas the impact

angle is reduced from 25 to 22 [23]. Moreover, when

testing a single post, the impact energy is localised over a

smaller area of the post which does not reect the full-

scale test condition where the energy is distributed over

a large area. Similar observations have been reported by

Gabauer et al. [9] when evaluating the results of pendu-

lum test conducted to assess the crash performance of

longitudinal barrier with minor damage. These condi-

tions suggest that it is appropriate to use an impactspeed of 7.0 to 9.0 m/s for the component testing instead

of the theoretical value of 11.74 m/s.

4. Effect of the post embedment depth

Simulations of the guardrail post embedded at depth

ranging from 800 to 1300 mm were conducted to assess

the soil reaction. Since the passive reaction applied to

the post increases with the depth, the simulation used a

W152 23.8 post (W6 16) instead of the W152

13.4 (W6 9) post to minimise the post yielding and toprovide better comparison of the post response for the

different embedment depths. The two posts cross sec-

tions, W152 23.8 and W152 13.4, have the same

width of 100 mm. However, the W152 23.8 post has

higher cross section parameters such as web thickness,

section area and moment of inertia compared to

W152 13.4 post. This approach has also been used by

Kuipers and Reid [15] who used a post (W152 23.8)

to determine the dynamic properties of soil-post at vari-

ous embedment depths under impact loading condi-

tions. The authors conducted a series of 10 dynamic

tests on the embedded steel posts at different depths

with a speed xed at 9 m/s, a bumper height of 630 mm

and an embedment varying from 864 to 1092 mm [15].

The impactor displacement time history illustrated in

Figure 9shows that the displacement decreases with the

depth from 400 mm at 1000 mm embedment to

260 mm for 1300 mm embedment. For a post embedded

at 1000 mm or more in the soil, the impactor was

stopped by the post-soil reaction. However, the impactor

overrides the post for the embedment of 800 and

900 mm. The average load increased from 26 kN for a

depth of 800 mm to 60.9 kN for 1300 mm, Table 3.These simulation results are in line with the experiments

conducted by Kuipers and Reid [15]. A nonlinear regres-

sion of the maximum impactor displacement as a func-

tion of the post embedment, Z, shows that the

relationship is given by:

DmaxD 0:4088:Z1:8332 (8)

whereZandDare in metres.

Dmax = 5.2972 V2 + 25.839 V

R = 0.9996

Max.

impactor

displacement(mm)

Impactor Speed (m/s)

CAE simulation

Dynamic test

Figure 8. Variation of the impactor displacement as function of the impact speed.



10/18

Figure 10shows that the peak load increases with the

depth from 64.1 kN to 81.4 kN when the embedment

depth increased from 1100 to 1300 mm. The variations

of the peak and average load as function of the depth fol-low a linear relationship as reported in Figure 11. An

increase of the embedment depth above 1100 mm leads

to higher post-soil interaction and a reaction force that

exceeds the target force of 50 kN. For the case of a

shorter post, where the embedment is less than 900 mm,

the interaction of the post with the soil is low and the

system might lose its efciency and the impactor over-

rides the barrier.

5. Effect of the impactor mass

Crash testing of steel posts embedded in soil was con-

ducted with different impactor mass to evaluate the post

behaviour. The impactor is rigid and consists, in general,

of a thick steel pipe sometimes lled with concrete and

mounted to the front of a bogie vehicle or a pendulum at

a given height above ground level.

To assess the effect of the impactor mass, simulations

of the guardrail post embedded in the soil and impacted

by a cart with different masses were conducted. The

spring stiffness representing the soil reaction, the

damping coefcient of the soil and the calculated con-

centrated masses remain the same for all the simulations.

The impactor mass varies from 500 to 3000 kg to cover

the range of masses used in the literature. Kennedy et al.[14] used a pendulum with a mass of 878 kg whereas

Dewey [5] used a cart of 2324 kg. The soil condition of

the Coon et al. [3] is used for the current study. The

impact speed of 7 m/s remains the same for all masses.

Table 4 summarises the results of the conducted

simulations.

The loaddeection responses of various impactormasses are shown in Figure 12. It can be seen that the

guardrail post displacement increases with the mass.

The curves show that the initial peak load is slightly sen-

sitive to the impactor mass and occurs approximately at

a displacement of 35 mm. The maximum load increases

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140

ImpactorDisp

lacement(mm)

e

Time (ms)

Embedment 800 mm

Embedment 900 mm

Embedment 1000 mm

Embedment 1100 mm

Embedment 1200 mm

Embedment 1300 mm

Figure 9. Variation of the impactor displacement as function time for different depth embedment.

Table 3. Summary of the simulations results of the impactor with the post located at different embedment depths.Depth (mm) Peak load (kN) Maximum displacement (mm) Average load (kN) Observation in the post

800 35.98 636.4 26.4 Not Stopped900 46.01 486.1 33.7 Not Stopped1000 56.17 400.3 40.7 Stopped1100 65.1 329.0 48.3 Stopped1200 70.14 293.1 54.5 Stopped1300 81.41 259.7 60.9 Stopped

Table 4. Results of the energy dissipation for different massimpactor.

Mass (kg) Max energy dissipated (kJ) Peak acceleration (g)

500 8.14 60.7946 15.39 64.11500 23.46 66.42000 29.46 67.22500 34.43 67.73000 37.33 68.0



11/18

slightly with the impactor mass from 60.7 kN for a mass

of 500 kg to 68.0 kN for the heavier impactor (3000 kg).

Figure 13shows that the impactor with a mass between

500 kg to 1500 kg is stopped by the soil post reaction

whereas the impactor overrides the post for a mass

above 2000 kg. Linear regression of the maximum dis-

placement as function of the impactor mass shows that

the relationship is given by DmaxD 0:3494MimpactorwhereDmaxis the maximum displacement of the impac-

tor andMimpactoris the mass of the impactor (units: mm,

kg).Figure 14reports the dissipated energy as function

of the impactor displacement and shows that the dissi-pated energy increases linearly with the mass of the

impactor. The rate of dissipated energy appears to

remain the same for all impactor masses, suggesting that

the post response is independent of the impactor mass.

6. Effect of compressible blockout

To provide the appropriate safety levels for an errant

vehicle impacting the guardrail system, the safety barrier

should be designed to maximise energy absorption

through the soil-guardrail system interaction and main-

tain its integrity [21]. The energy could be dissipated

through the soil deformation and through the post W-beam structure. However, it is easier to control and to

Pavg = 0.0697 Z - 28.953R = 0.9938

Pmax = 0.088 Z - 33.347R = 0.993

0

10

20

30

40

50

60

70

80

90

700 800 900 1000 1100 1200 1300 1400

Impactorload(kN)

Post embedment (mm)

Average load

Max load

Figure 11. Variation of the impactor maximum load as function of the post embedment.

0

10

20

30

40

50

60

70

80

90

0 20 40 60 80 100 120 140

Impactor

Load(kN)

Time (ms)

Embedment 800 mm

Embedment 900 mm

Embedment 1000 mm

Embedment 1100 mm

Embedment 1200 mm

Embedment 1300 mm

Figure 10. Variation of the impactor reaction for different depth embedment.

10 A. SASSI AND F. GHRIB


12/18

maximise the energy dissipation by redesigning the

blockout spacer between the post and the guardrail. For

these reason, collapsible blockout system attached to the

post are proposed and implemented in the baseline

model to replace the traditional wood made blockout.

The current practice uses blockout consisting of a

rectangular wood piece (200 150 360) or steel W-

cross section that serves only as a spacer with no energy

dissipation capacity. In the present work, six blockout

shapes, consisting of a longitudinal box member that

offers higher degree of energy absorption per unit mass

and guarantees a stable folding pattern during theimpact, are proposed. The design was partially inspired

from a concept widely used in automotive crashworthi-

ness where the front rails are designed to absorb the

maximum energy during the frontal impact. Fundamen-

tal theoretical studies in the area of thin-walled struc-

tures have been conducted in the past by Wierzbicki

[31], Jones (1983), Abramowicz and Wierzbicki [1] and

Mahmood and Puluzny [16]. The proposed blockout is

designed to absorb the kinetic energy more efciently

which contributes to reduce the vehicle speed and soften

the impact of an errant vehicle with the guardrail system.

Five proposals with different cross sections and thick-

nesses were considered and integrated in the baselineguardrail post prototype as shown in Figure 15. The

0

10

20

30

40

50

60

70

80

0 100 200 300 400 500 600 700 800

Impactor

load(kN)

Impactor displacement (mm)

Mass 500 kg

Mass 1000 kg

Mass 1500 kg

Mass 2000 kg

Mass 2500 kg

Mass 3000 kg

Figure 12. Effect of the impactor mass on the loaddeection of the guardrail post.

0

100

200

300

400

500

600

700

800

900

0 20 40 60 80 100 120 140 160

Impactordisp

lacement(mm)

Time (ms)

Mass 500 kg

Mass 1000 kg

Mass 1500 kg

Mass 2000 kg

Mass 2500 kg

Mass 3000 kg

Figure 13. Variation of the impactor displacement for different mass impactor.



13/18

dimensions of these models were similar to the original

rectangular wood piece (200 150 360) and made of

HSLA High Strength Low Alloy) having a Youngs mod-

ulus ED205 GPa, a densityD7850 kg/m3 and a yield

stress s0 D 615 MPa. HSLA 340, which is a high-

strength steel commonly used in the automotive area,

has been considered for all the design scenarios to fabri-

cate the blockout system because of its good fatigue

strength, its low price, its ductility and its welding capa-

bility. HSLA 340 was chosen despite the fact that Elmar-

akbi et al. [7] showed that aluminium was better than

steel in terms of energy dissipation for their case. The sixschemes were chosen based either on the simplicity of

the manufacturing process involved, ease of installation

or the expected high energy absorption. The six blockout

components considered in this work consisted of a sim-

plied crash box for frontal impact with a square section.

The considered designs are as follows;

Blockout 1consisted of three square tubes with 80

80 mm cross-section and a wall thickness of 2

mm. The side length of the enclosed square sec-

tion was 150 mm. The three tubes were sand-

wiched between two metal plates of 2 mm

thickness from the same material as the square

tube (Figure 15(a)).

Blockout 2was the same as blockout geometry # 1 with

the exception that the wall box thickness was

reduced to 1.0 mm (Figure 15(b)).

Blockout 3 was similar system as blockout #1 and #2.

To ensure a desirable folding mechanism of the

tubes and reduce the peak load of the impactor,

the design was pre-triggered symmetrically in

both sides of the tube as shown in Figure 15(c).

The triggers consisted of a cut-out material exe-

cuted on all sides of the tube.

Blockout 4The blockout in this case was 100 200

360 mm rectangular tube (Figure 15d) with a wall

thickness of 3.5 mm and made from the same

material as systems 1 and 3. The block was

attached to the post using two bolts simulated as

springs.

Blockout 5 was similar to blockout #4 but the wall

thickness was reduced to be 2.5 mm as shown in

Figure 15e.

To minimise the mesh size effect on the crash simula-

tion results, the same mesh is maintained for the ve

proposed designs. The element size was chosen to be

approximately twice that of the sheet thickness [27],

which offers the best trade-off between accuracy and

computational efciency. The triggers used in the block-

out design were simulated by removing specic elements

from the model.

The results of the analysis are summarised in Table 5

and shows that the performance of the different blockout

systems is quite different. Blockout #3, designed with

three longitudinal tubes and triggered on both sides, dis-

sipated the maximum energy (5.31 kJ) whereas the same

design Blockout 1 with a 2.0 mm thickness reacts as a

rigid block similar to the baseline: a peak load of

66.8 kN, an average load of 48.4 kN and a maximum dis-

placement of 330 mm. The vertical tube with a thickness

of 2.5 mm (blockout 4) absorbs 3.6 kJ within the rst

50 ms as shown inFigure 16, and then collapsed on the

post, the peak load increased to 80 kN as shown in

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800

Energyd

issipated(kJ)

Impactor displacement (mm)

Mass 500 kg

Mass 1000 kg

Mass 1500 kg

Mass 2000 kg

Mass 2500 kg

Mass 3000 kg

Figure 14. Energy dissipation of the guardrail post for different mass impactor.



14/18

Figure 17. The same vertical tube of 3.5 mm thickness

(blockout 5) absorbs even less energy, 0.71 kJ, because

only a localised deformation was created at the lower

part of the blockout as shown inFigure 18. The average

load remained almost the same and the maximumimpactor displacement remains similar to the baseline

model (336 mm).

The triggers used in blockout #3 helped the devel-

opment of a stable asymmetric crushing mode, the

role of the triggers is to force the buckling to be initi-

ated at the specic locations during the crash event

which contributes in attenuation of the

rst peakload from 64.1 to 50.3 kN and reduce the load trans-

ferred to the guardrail structure. It is known that

Figure 15.Different blockout layout to absorb energy during the impact: (a) Blockout 1, (b) Blockout 2, (c) Blockout 3; (d) Blockout 4; (e)Blockout 5; and (f) No blockout.

Table 5. Results of the energy dissipation for different blockout designs.

Design # Energy dissipated (kJ) Maximum load (kN) Average load (kN) Impactor displacement (mm)

Block 1 0.25 66.8 48.4 329.8Block 2 4.44 65.2 48.2 331.6Block 3 5.31 50.3 43.9 378.3Block 4 3.64 80.0 38.9 456.6Block 5 0.71 62.5 47.9 336.3Baseline 0 64.1 48.1 336.0



15/18

triggers reduce the variability of crash mode and

instability due to imperfections associated to material

heterogeneity, geometry or manufacturing processes.

The crushable system also contributes in reducing the

average load to 43.9 kN and absorbing an energy of

5.3 kJ with an impactor displacement of 378.3 mm.

The performance of the crushable blockout #3 sug-

gests that this design capability is superior in trans-

ferring the load to the post during the impact of a

vehicle with a guardrail.

7. Conclusions

A macro-element was used to model the post-soil

interaction to conduct an exhaustive parametric nite

element study and investigate the effects of the differ-

ent design parameters on guardrails post reaction.

The response of the guardrail post was determined

under different loading conditions and the

loaddeection curve for the different parameterswas determined and compared to a baseline test

model. Such parameters include sand density, impac-

tor speed and mass, post depth and the crushable

blockout system.

The study shows that that the peak load and the

impactor displacement increase with the speed following

a linear equation. For high speeds, greater than 9 m/s,

the impactor was not stopped by the post reaction. Forlower speeds, less than 3 m/s, the strain rate effect seems

to be limited.

Figure 16. Internal energy dissipation for the different crushable blockout systems.

Figure 17. Variation of the impactor load for different crushable blockout systems.



16/18

The peak load increases with the depth following a

rst-degree equation whereas the impactor displacement

decreases with depth following a power function. For

embedment depths less 1000 mm, the impactor

overrides the post. For depths higher than 1000 mm, the

post did not show any plastic strain higher than 3%.

The results of the simulation with different densities

of cohesionless soil show that the peak load and the

Figure 18. Behaviour of the crushable system during the impact.



17/18

impactor displacement increase with the sand density.

The impactor overrode the post for the loose sand and

was stopped for medium and dense sand. These results

show that the medium-density sand offers the best soil

interaction as the load level remains around 50 kN.

The post rail undergoes higher displacement with the

heavier weight than with the lighter one. However, the

maximum reaction remains quasi constant with theincrease of the impactor mass. Impactors with masses of

500 to 1500 kg were stopped; however, for impactor

masses above 2000 kg, the impactor overrode the post.

The maximum displacement of the impactor increases

linearly with the mass. The rate of energy dissipation

remains the same for all impactor masses.

The crushable system implemented as a replacement

of the conventional rigid blockout system was able to

reduce the peak load to 50 kN and the average load to

43.9 kN and absorb an energy of 5.3 kJ with an impactor

displacement of 378.3 mm. This performance suggests

that the crushable blockout is able to reduce the impac-tor load transferred to the post during a full crash of a

vehicle impacting the guardrail. The triggered design

crushed better than simple blockout boxes. The triggers

helped initiate a stable asymmetric crushing mode.

Acknowledgments

The work reported in the present paper was supported bygrants from the National Sciences and Engineering Researchof Canada (NSERC) and AUTO21.

Disclosure statement

No potential conict of interest was reported by the authors.

ORCID

Faouzi Ghrib http://orcid.org/0000-0002-0244-0996

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crashworthiness of guardrail posts embedded in cohesionless soils: a parametric study

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