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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
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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.
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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.
4 A. SAS SI AND F. GHRIB
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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
subgrade modelContinuum
method TestImproved
subgrade modelContinuum
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.
6 A. SAS SI AND F. GHRIB
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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.
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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.
8 A. SAS SI AND F. GHRIB
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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
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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.
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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.
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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.
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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
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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.
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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.
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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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