Calibration of MechanisticEmpirical Models Using the
California Heavy Vehicle
Simulators
P. Ullidtz
Dynatest International, Denmark
J. Harvey & V. Kanekanti
University of California, Davis, California, USA
B.W Tsai & C. Monismith
University of California, Berkeley, California, USA
Mechanistic-Empirical methods are
simplifications of reality
• Response models are based on solid
mechanics and must be validated for
pavement materials
• Performance prediction models derived
from laboratory tests must be
validated/calibrated to in situ pavements
HVS: a ”large scale” laboratory test
Advantages of HVS testing
• Short test section, carefully constructed
• Intensive materials characterization
• Instrumented to measure response and
performance
• Climatic conditions controlled or closely
monitored
• All load applications are known exactly
• Testing can be carried out to failure
MDD
Multi Depth Deflectometer
Road Surface Deflectometer (RSD)
27 HVS tests on flexible pavements
were used to calibrate the damage
models in CalME
• Caltrans current methods, the R-value method,
deflection reduction method for rehabilitation
design
• “Classical” ME design (Asphalt Institute method)
• Incremental-recursive method
Models calibrated in CalME
• Asphalt stiffness as a function of reduced
time (temperature and loading time)
log(E ) = δ +
AC modulus
α
γ
⎞
⎛
1+ ⎜ t
⎟
t
/
2
α
⎠
⎝
Modulus, MPa
100000
10000
1000
100
0.00001 0.0001
0.001
0.01
0.1
1
Reduced time, sec
10
100
1000
10000
Models calibrated in CalME
• Asphalt stiffness as a function of reduced
time (temperature and loading time)
• Stiffness of unbound materials as a
function of confinement and of stress
condition
Unbound layer moduli
Confinement
( (
)
)
E = Eo × 1 − 1 − S / S ref × Stiffness factor , with
⎛ n −1
S = ⎜ ∑ hi × 3 Ei
⎜
⎝ 1
⎞
⎟
⎟
⎠
3
Stress condition
⎛ stress ⎞
⎟⎟
E = k1 × ⎜⎜
⎝ pa ⎠
k2
Models calibrated in CalME
• Asphalt stiffness as a function of reduced
time (temperature and loading time)
• Stiffness of unbound materials as a
function of confinement and of stress
condition
• Reduction in asphalt stiffness caused by
damage
log (E ) = δ +
α × (1 − ω
)
⎞
1 + ⎛⎜ t
⎟
t
α /2 ⎠
⎝
γ
β
γ
⎞
⎛
⎞
⎛
με
E
⎟⎟ × exp(δ × t )
⎟⎟ × ⎜⎜
ω = A × MN α × ⎜⎜
⎝ 3000 MPa ⎠
⎝ 200 μstrain ⎠
7000
6000
5000
4000
3000
2000
1000
0
0
50000
100000
150000
200000
250000
300000
Models calibrated in CalME
• Asphalt stiffness as a function of reduced
time (temperature and loading time)
• Stiffness of unbound materials as a
function of confinement and of stress
condition
• Reduction in asphalt stiffness caused by
damage
• Permanent deformation of asphalt layers
Permanent deformation of AC
⎞
⎛
γ p = exp⎜ A + α × ⎡⎢1 − exp⎛⎜ − ln ( N )γ ⎞⎟ × ⎛⎜1 + ln (N )γ ⎞⎟⎤⎥ ⎟ × exp⎛⎜ β × τ 0.1 MPa ⎞⎟ × γ e
⎣
⎝
⎝
⎠ ⎝
⎠⎦ ⎠
⎝
⎠
Goal 3 DGAC FMFC AV5.5
4
Gamma fit
ln(Normalized Strain)
3
2
1
0
RSST-CH
-1
-2
0
2
4
6
ln(Number of loads)
8
10
12
Models calibrated in CalME
• Asphalt stiffness as a function of reduced
time (temperature and loading time)
• Stiffness of unbound materials as a
function of confinement and of stress
condition
• Reduction in asphalt stiffness caused by
damage
• Permanent deformation of asphalt layers
• Permanent deformation of unbound layers
Permanent deformation of unbound layers
β
γ
⎛
⎞
⎛
⎞
E
με
α
⎟⎟ × ⎜⎜
⎟⎟
dp mm = A × MN × ⎜⎜
⎝ 1000 μstrain ⎠
⎝ 40 MPa ⎠
Step 1: Pavement response
Change in response during testing
Final/initial deflection
5.00
4.50
4.00
Calculated
3.50
3.00
RSD
MDD
Equality
2.50
2.00
1.50
1.00
0.50
0.00
0.00
1.00
2.00
3.00
Measured
4.00
5.00
Permanent deformation of AC
Permanent deformation in AC (pro rated)
20
18
Calculated, mm
16
14
12
10
8
6
4
Equality
20 ºC at surface
45 or 50 ºC at surface
2
0
0
2
4
6
8
10
12
Measured, mm
14
16
18
20
Permanent deformation at pavement surface
20.0
Calculated, mm
15.0
10.0
5.0
0.0
0.0
5.0
10.0
Measured, mm
Goal 1
Goal 3 45/55°C
Goal 3 20°C
Goal 5
Goal 9
Equality
15.0
20.0
WesTrack: FWD deflections
Average FWD centre deflection Fine mix
1.200
Calculated deflection, mm
1.000
y = 0.9861x
R2 = 0.8436
0.800
0.600
0.400
0.200
0.000
0.000
0.200
0.400
0.600
0.800
Measured deflection, mm
26 original test sections
1.000
1.200
WesTrack: Cracking
Cracking % versus CalME damage
100
Cracking %
80
Fine Right
Fine Left
Coarse Right
Coarse Left
Fine Plus Right
Fine Plus Left
Model
60
40
20
0
0.00
0.10
0.20
0.30
0.40
0.50
Damage
0.60
0.70
0.80
0.90
1.00
WesTrack: Permanent deformation
CalME deformation and maximum rutting
60
50
CalME
Max Right
Max Left
30
20
10
CHL
CML
PLM
PMH
PMM1
FHL
FMH
FLH2
FMM2
FHM
PML
PMM2
PLH
CLM
CHM
CMH
CMM1
FML
FLH1
FLM
0
FMM1
mm
40
Conclusion
• A large change in pavement response was
observed during the HVS tests
• Most of the large increase in deflection
happened before any cracking was observed
• The increase in deflection was due to a
decrease in the moduli of all layers
• Both response and performance were
reasonably well predicted by CalME
• The next step is calibration against in situ
pavement sections
Thank you