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Permanent Deformation Prediction in Asphalt Mixes and Pavements: A Current Approach
and a Look Ahead
Carl L. Monismith and Lorina PopescuPavement Research Center, UC Berkeley
NVF 34 and NordFoU
Project-Pavement Performance Models Joint Seminar on Pavement Design Systems
and Pavement Performance Models
March 22,23, 2007, Reykjavic, Iceland
Acknowledgement
The authors would like to thank the California Department of Transportation, which sponsored this work.
The conclusions are those of the authors and not necessarily those of the sponsor.
Some Considerations For Mix Evaluation – Permanent
Deformation
•
Volume change vs. shape distortion•
Representative volume element
•
Specimen preparation
Mechanics of Permanent Deformation
•
Volume change versus shape distortion
0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.020
0 20 40 60 80 100 120 140 160 180 200 220 240 260
Time (seconds)
Stra
in Volume changeShape distortionLoad
Mechanics of Permanent Deformation
K = 0.1 Kref
K = Kref
Vertical deformation
G = 0.1 Gref
G = Gref
K = 10 KrefG = 10 Gref
Mechanics of Permanent Deformation
•
Pavement simulation
0
1
2
3
4
0.1 1 10Normalized modulus value
Vert
ical
def
orm
atio
n
KG
Mechanics of Permanent Deformation
•
Conclusion–
Shape distortion dominant contributor to rutting
Test Selection Factors
•
RVE dimensions function of–
Aggregate •
size
•
shape •
orientation
–
Temperature–
Rate of loading
•
Specimen size < RVE ?
Test Selection Factors •
Non-linear response characteristics
( )E*G*
2 1=
+ υ
E* Complex Young's ModulusG* Complex Shear Modulus
Poisson's Ratio
==
υ =
Test Selection Factors
•
Constant height shear test (RSST- CH)
–
Specimen sizee.g., 19 mm aggregate L/H ≥
3
75 x 225 mm ⇒
100 x 300 mm
Test Selection Factors
•
Specimen compaction–
In-situ (field)
–
Gyratory–
Rolling wheel
•
Creep vs
repeated loading–
Non-conventional binders
Test Selection Factors (cont.)•
Specimen compaction, results at 50°C
1.E+02
1.E+03
1.E+04
1.E+05
0 2 4 6 8 10 12 14 16
Air Voids (%)
RSS
T R
epet
ition
s to
5%
Def
orm
atio
n
Field CoresGyratoryRolling wheel
Rut Depth Estimation
•
Use of Shear Stress and Strain•
Compound Loading: Time hardening
Pavement Representation
Pavement Representation
Inelastic strains in asphalt concrete
•
Under simple loading (effect of shearing stress, elastic shearing strain and load repetitions)
•
γ i = a exp(b τ) γ en c
•
Under compound loading•
aj
= a exp(b τj
) γ ej
•
γ i1
= a1
[Δn1
]c
•
γ ij
= aj
[(γ ij-1
/aj
)(1/c)
+ Δnj
]c
Compound Loading -
Time Hardening
Number of Load Applications
Inel
astic
Str
ain
1st
2nd 3rd
4th 5th
6th 7th
8th 9th
10th
Inelastic strain -n relationship for
smaller load
Inelastic strain -n relationship for
larger load
Surface rutting due to shear within asphalt concrete
•
rd = K·γ ij
, where K = shift factor
•
K = f (HMA layer thickness)
Surface rutting due to deformation of unbound materials
•
The Asphalt Institute subgrade strain criterion for 0.5-inch surface
rutting•
N = 1.05 ·10-9
·ε-4.484
•
With time hardening, rd = dne
•
d = f /[1.05 ·10-9
·ε-4.484]e
•
rd1
= d [Δn1
]e
•
rdj
= dj
[(rdj-1
/dj
)(1/e)
+ Δnj
]e
•
(for Asphalt Institute criterion, f = 0.5 inches)
Applications of RSST-CH
•
Mix design•
Performance analysis/evaluation–
WesTrack
•
Rut Depth analysis
Simple Shear Test
0.0001
0.001
0.01
0.1
1 10 100 1000 10000 100000RSST Repetitions
Perm
anen
t She
ar S
trai
n 5 %
Simple Shear Test
Mix Evaluation
•
WesTrack–
Original Sections: coarse, fine, fine + mixes
–
Replacement Sections, coarse
WesTrack, Section 4 Fine grading
0
2
4
6
8
10
12
14
16
18
10/28/19955/15/1996 12/1/1996 6/19/1997 1/5/1998 7/24/1998 2/9/1999
Year
Max
imum
rut d
epth
, mm
Total rut - base
Total predicted rut
Total measured rut
WesTrack, Section 7 Coarse grading
0
3
6
9
12
15
18
21
24
27
30
2/5/1996 3/26/1996 5/15/1996 7/4/1996 8/23/1996 10/12/1996 12/1/1996
Year
Max
imum
rut d
epth
, mm
Total rut - base
Total predicted rut
Total measured rut
WesTrack, Section 19 Fine plus grading
0
3
6
9
12
15
18
10/28/19955/15/1996 12/1/1996 6/19/1997 1/5/1998 7/24/1998 2/9/1999Year
Max
imum
rut d
epth
, mm
Total rut - base
Total predicted rut
Total measured rut
WesTrack, Section 38 Replacement Section, coarse grading
0
3
6
9
12
15
18
6/19/1997 9/27/19971/5/19984/15/19987/24/199811/1/19982/9/19995/20/1999Year
Max
imum
rut d
epth
, mm
Total rut - base
Total predicted rut
Total measured rut
New Pavement Design: Rut Depth Estimation
•
Three sections designed according to Caltrans
procedure
•
Traffic, ESALS: 1.3x105, 5.5x106, 74.5x106
•
Three environments–
Los Angeles (coastal)
–
Daggett (high desert)–
Reno (cold winter)
Total Rut Depth Estimation ~5.5x106
ESALs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06
Cumulative ESALs
Rut
Dep
th (in)
LA-PBA-6a LA-AR8000 Reno-AR8000
Reno-AR4000 Daggett-PBA-6a Daggett-AR8000
HMA Rut Depth Estimation ~5.5x106
ESALs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.00E+00 1.00E+06 2.00E+06 3.00E+06 4.00E+06 5.00E+06 6.00E+06
Cumulative ESALs
Rut
Dep
th (in)
LA-PBA-6a LA-AR8000 Reno-AR8000 Reno-AR4000
Daggett-PBA-6a Daggett-AR8000 Reno-PBA-6a
Total Rut Depth Estimation, `~75x106 ESALs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07 6.00E+07 7.00E+07 8.00E+07
Cumulative ESALs
Rut
Dep
th (in)
LA-PBA-6a LA-AR8000 Reno-PBA-6a Daggett-PBA-6a
HMA Rut Depth Estimation, `~75x106 ESALs
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07 6.00E+07 7.00E+07 8.00E+07
Cumulative ESALs
Rut
Dep
th (in)
LA-PBA-6a LA-AR8000 Reno-PBA-6a Daggett-PBA-6a
•
A Look Ahead
•
Large Rotations.•
Use finite deformation theory.
An Example Model
•
Model developed for Caltrans.•
Model consists of 2 components acting in parallel:–
An elastoplastic
solid
–
A viscoelastic
fluid
Elastoplastic Component
•
Multiplicative decomposition: F=FeFp. •
Stressed intermediate configuration (Bauschinger
effect).
•
Yield surface: a sphere in stress space.
•
Hardening: isotropic and kinematic.•
Yield also depends on the hydrostatic component of the back stress.
Viscoelastic Component
•
Maxwell elements in parallel.•
Multiplicative decomposition: F=FeFv.
Some Uses
•
Sensitivity analyses to identify critical properties
•
Use of the constitutive relationship to identify to tests to defin
critical
properties•
Develop tests to predict field peformance
Shear Stress Distribution, RSST-CH
Vertical Stress Distribution, RSST-CH
Concluding Remarks
•
The methodology presented provides a procedure to estimate the contribution of the proposed asphalt bound layer to permanent deformation in the pavement structure. It is based on shear test data as compared to axial load test data included in the New Design Guide.
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