This document presents an improved subgrade model for analyzing guardrail posts during crash testing. The model combines continuum and subgrade methods to account for inertia effects. It models the soil-post interaction using spring stiffness calculated from bearing capacity, lumped soil masses, and viscous dampers. Simulation results matched well with four dynamic tests, improving accuracy over traditional subgrade models while maintaining computational efficiency compared to full continuum modeling. The proposed method can better simulate guardrail crash tests in cohesionless soils.

1. An Improved Subgrade
Model for the Crash
Analysis of Guardrail Posts
Abdelmonaam SASSI, Ph.D.
May 17, 2012
Dept. of Civil and Environmental Engineering, University of Windsor

2. Introduction: Regulations
NCHRP 350 (1993) MASH (2009)
Recommended Procedures
Manual for Assessing
for the Safety Performance
Evaluation of Highway
Safety Hardware
Features
TL3-11 TL3-10 TL3-11 TL3-10
2000 kg light 820 kg Sedan 2270 kg light 1100 kg Sedan
truck truck V = 100kph
V = 100kph
V = 100 kph V = 100 kph Angle : 250
Angle : 200
Angle : 250 Angle : 250
Pickup truck impacting the guardrail, with 100 km/h
speed at 25 deg impact angle, should not penetrate,
under-ride or override the installation.

3. I- Full scale guardrail model
L= 53.3 m
D = 1950 mm
N = 30 posts
V = 100 km/h
Angle = 25 deg
Depth = 1100 mm

4. TYPICAL FULL SCALE
GUARDRAIL TEST

5. II- Component testing of the guardrail
post
Post
Impactor
550 mm
1830 mm
1100 mm
Dynamic testing Set-up
Dynamic testing Set-up used by Coon et al (1999)
Soil Density Moisture Impact Speed Max Deflection Soil Density 2011 Slide #5
Sassi Moisture
Test
Kg/m3 Content m/s3 mm Kg/m3 Content
Test #1 1980 Dry 4.6 234 42.8 42.8
Test #2 2110 Dry 5.4 314 43.9 43.9
Test #3 2240 Dry 5.9 348 47.3 47.3
Test #4 --- Dry 8.9 Override NA NA

6. III-1 Soil Modeling
Subgrade Method Continuum Method
-Fast -Accurate
-Widely used -Does account for
-Accurate after the peak the inertial effect
-Does not account for -Computationally very costly
the inertial effect -Soil parameters not available

7. III-2 Soil simulation with combining the twIo
methods
Kennedy et al. (2004)
Continuum Method
Subgrade Method
Combined of two methods:
-Subgrade method in all the
guardrail post
-Add continuum method in
-Does account for the inertial the impact zone with no little
effect or no stiffness and right
-Computationally relatively density.
costly

8. III-3 Typical Results of the FE Study of the
dynamic testing of the guardrail post
Plaxico (2002)
Traditional subgrade
modeling only with
springs missed the
inertia effect.

9. IV Proposed model
Impactor
Post
Lumped
soil mass
Soil modeled as:
Spring stiffness ( k )
Damper (c )
Lumped mass (m)
C, k & m are not
constant
along the pile
embedment

10. III-1 Stiffness Calculation (k)
Method of Habibaghi and Langer (1984).
(Based on the bearing capacity approach)
'
kh Nq Nq is the bearing capacity factor
y
z
Nq A
B
0.1245y
A 15.276 14.09 e
Z is the depth
B is the width of the post
y is post deflection
σ’ overburden pressure

11. III-2 Lumped Mass calculation
Iso-displacement contour from Continuum model
Iso-displacement defined cone
centered around the rotation
centre of the guardrail post .
Lumped soil mass
function of z
M1
M2
M3
Parametric Study to determine
the damping factor ξ

12. III-3 Damper calculation
Parametric Study Results
mx cx kx f Z Mass K Cc 5% Cc 20% Cc 12%
Mm kg kN/mm N/s
cc 2 mk 100 34.08 1.49 18.05 1.81 2.71 2.26
c 200 25.61 2.39 15.65 1.56 2.35 1.96
300 18.35 4.95 19.06 1.91 2.86 2.38
cc
400 12.30 7.62 19.36 1.94 2.90 2.42
500 7.46 10.37 17.59 1.76 2.64 2.20
600 3.83 13.13 14.19 1.42 2.13 1.77
700 1.41 16.09 9.53 0.95 1.43 1.19
800 0.20 19.04 3.92 0.39 0.59 0.49
Parametric Study to determine
the damping factor ξ 900 0.65 22.12 9.38 0.76 1.13 0.95

13. IV Results of the simulation
Maximum Deflection Average Force Peak Force
(mm) (kN) (kN)
Test Model Test Model Test Model
Test #1 234 233 42.8 43.0 64.0 53.1
Test #2 314 296 43.9 45.9 66.9 57.8
Test #3 348 338 47.3 47.9 67.0 64.3
Test #4* Override Override NA 56.3 104.7 97.2
Good correlation between the 4 dynamic tests
and the model results

14. V- Results of the simulation
Modeled improved by defining space between the
post and the lumped mass
Model Continuum Method Spring model Spring/Damper
Simulation time (S) 0.180 0.180 0.180
Run time 8.49T T 1.06T
T = 40 minutes

15. CAE Results

16. IV-3-1 Full Scale guardrail test simulation

17. IV-3-2 Vehicle response
Roll Angle
Vehicle Speed

18. IV-3-2 Sequential of impact event of dynamic test
Frontal View Overhead View

19. V- Conclusions
Method developed for cohesionless and could
be extended to cohesive soil
Method accounts for the inertia effect
Method accounts for the damping effect
Method accurate and tunable
Method computer time consumption efficient