field validation and parametric study of a thermal crack spacing model
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Field Validation and Parametric Study of a Thermal Crack Spacing
Model
David H. Timm - Auburn UniversityVaughan R. Voller - University of Minnesota
Presented at the Annual Meeting of the Association of Asphalt Paving Technologists
Lexington, KentuckyMarch 10 – 12, 2003
Cracking Characteristics• Thermal cracking common in cold
climates• Features
– Transverse cracks– Regular spacing
0
0.25
0.5
0.75
1
0 50 100 150 200 250 300 350 400 450 500
Location, ft
Dis
tanc
e A
cros
s La
nes
Crack Spacing
Focus of thisStudy is the question
What features control the spaces betweenCracks?
Model Stress Profile in Thermally Cooled Asphalt Layer on Granular
Base
E, , , H,
E, , , c,
Modeled in Two ways
Finite Difference Code--FLAC
x
50x250 mm
Grid Element Sizes
63x315 mm
313x1563 mm
Asphalt Concrete (Elastic Model)
z
Granular Base (Mohr Coulomb Model)
1-D Semi-Analytical ModelElastic Layer with Elastic-Plastic
Restraint
catan q=kux
Timm, Guzina and VollerInt J Solids and Structures, 2002
xt
2/xxwHku
xxtanHc
dxd
tx
tx
Form of Stress Profile
Curling Stress
Rate of StreesIncrease T
1E
Distance fromfree end
Comparison of Models
Crack Spacing from Stress Curve
St
xc
1
xCracking
may occurCrackingwill notoccur
SlidingOn Rigid Base
xtanHc
Hx
1
St
x
Crack Spacing from Stress Curve
xcxc
Average Spacing = 1.5·Xc
• Validate thermal crack spacing model with field data
• Perform sensitivity analysis on length scale– Help guide future laboratory work– Develop more complete understanding– Identify how material selection will
affect spacing
Objectives
• Field Validation– 4 similar sections at Mn/ROAD
• Parametric Study– 10 input variables
• Layer 1– Stiffness, Poisson, Density, Thickness, Thermal
Coef.• Layer 2
– Stiffness, Poisson, Density, Cohesion, Friction Angle
Scope
E, , , H,
E, , , c,
1. Select MnROAD sections2. Analyze thermal crack spacing by
section3. Analyze in situ thermal conditions4. Gather material property data for
model5. Simulate pavement, determine
spacing6. Compare predictions to measured7. Assess validity
Field Validation Methodology
• Similar thickness designs• Identical binders• Common subgrade• Different base layers
MnROAD Sections
150 155 160231
838
102 102
711838
0
200
400
600
800
1000
1200
Cell 1 Cell 2 Cell 3 Cell 4
Dep
th B
elow
Pav
emen
t Sur
face
, mm
HMAC
Class 4 G.B.
Class 6 G.B.
Class 5 G.B.
Class 3 G.B.
LEGEND
Average Crack Spacing
0
0.25
0.5
0.75
1
0 100 200 300 400 500
Location, ft
0
0.25
0.5
0.75
1
0 100 200 300 400 500
Location, ft
0
0.25
0.5
0.75
1
0 100 200 300 400 500
Location, ft
Avg Spacing
Cell 1: 12 m
Cell 2: 8 m
Cell 3: 13 m
Cell 4: 9 m0
0.25
0.5
0.75
1
0 100 200 300 400 500
Location, ft
-35
-30
-25
-20
-15
-10
-5
0
5
10
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72
Time, hr
Tem
pera
ture
, C
D = 0.03048D = 0.054864D = 0.158496D = 0.192024D = 0.292608D = 0.445008D = 0.597408D = 0.902208D = 1.207008D = 1.511808D = 2.426208
Depth, m
Top of pavement
Bottom of pavement
Feb 1 Feb 2 Feb 3
Temperature Cycling
• Backcalculation• Laboratory testing as part of
Mn/ROAD project• Derived values
– Thermal coefficient = fn (Volumetrics)• Model ‘tuned’ with friction and
cohesion
Material Property Data
E, , , H,
E, , , c,
Resulting Friction and Cohesion
Cell Friction Angle, o Cohesion, kPa1 30 102 50 153 35 104 25 10
Mohr-Coulomb Properties of Material DirectlyBeneath HMA
Model Comparison
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12 14 16
Measured Average Spacing, m
Pred
icte
d Sp
acin
g, m
Line of Equality
Cell 1
Cell 2
Cell 3
Cell 4
• Crack spacings pass reasonableness check
• Recently, model has been used to predict other crack spacing phenomenon
Model Assessment
0
1
2
3
4
5
6
7
0 20 40 60 80 100 120 140Location, m
Dis
tanc
e Acr
oss
Pave
men
t, m
Average Spacing = 12 mStandard Deviation = 4.88 m
TiN Coating
Curling Stress
Rate of StressIncrease
Max stress
Factors that Influence Stress Profile
• Uniform temperature change• 2-layer structure• 10 input parameters varied from low,
medium, and high• Maximum tensile stress curves
plotted and evaluated– Maximum Stress– Rate of Stress Increase– Curling Stress
Parametric Investigation Methodology
Input ParametersLayer Input Units Low Medium
(Baseline)High
1 E1 Pa 5*109 1.4*1010 3*1010
unitless
0.15 0.20 0.25
kg/m3 2,200 2,300 2,400H1 cm 7.6 15 30 /C 1.33*10-5 2.15*10-5 2.97*10-5
2 E2 Pa 5.5*107 5.5*108 5.5*109
unitless
0.35 0.4 0.45
kg/m3 1,800 2,000 2,200c2 kPa 0, 0.1, 1, 10, 70, 140 2 20 40 60
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
E1 = 3*1010 Pa
E1 = 1.4*1010 Pa
E1 = 5.0*109 Pa
Distance From Free End, m
Maximum Tensile Stress, PaFLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
E1 = 3*1010 Pa
E1 = 1.4*1010 Pa
E1 = 5.0*109 Pa
Distance From Free End, m
Maximum Tensile Stress, Pa
HMAC Stiffness (E1)
1
TEx
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
1=0.15
1 =0.20
1 =0.25
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
1=0.15
1 =0.20
1 =0.25
HMAC Poisson Ratio (1)
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
H1 = 0.076 mH1 = 0.152 m
H1 = 0.305 m
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
H1 = 0.076 mH1 = 0.152 m
H1 = 0.305 m
HMAC Thickness (H1)
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
1=2.97*10-5
1=2.15*10-5
1=1.33*10-5
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
Distance From Free End, m
Maximum Tensile Stress, Pa
1=2.97*10-5
1=2.15*10-5
1=1.33*10-5
HMAC Thermal Coeff. (1)
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
E2=5.5*107 Pa
E2=5.5*109 Pa
E2=5.5*108 Pa
Distance From Free End, m
Maximum Tensile Stress, PaFLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
E2=5.5*107 Pa
E2=5.5*109 Pa
E2=5.5*108 Pa
Distance From Free End, m
Maximum Tensile Stress, Pa
Base Stiffness (E2)
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
c2=140 kPac2=70 kPa
c2=10 kPa
c2=1 kPac2=.1 kPac2=0 kPa
Distance From Free End, m
Maximum Tensile Stress, PaFLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
c2=140 kPac2=70 kPa
c2=10 kPa
c2=1 kPac2=.1 kPac2=0 kPa
Distance From Free End, m
Maximum Tensile Stress, Pa
Base Cohesion (c2)
As c getsLargeOnly elasticresistance
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
2 = 60o
2 = 40o
2 = 20o
Distance From Free End, m
Maximum Tensile Stress, PaFLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
2 = 60o
2 = 40o
2 = 20o
FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06FLAC (Version 3.30)
10 20 30 40 50 60 70
.500
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
(10 )+06
2 = 60o
2 = 40o
2 = 20o
Distance From Free End, m
Maximum Tensile Stress, Pa
Base Friction Angle (2)
Note: c = 10 kPa
Curling Stress
Rate of StressIncrease
Max stress
Factors that Influence Stress Profile
Relative Influence on Each CriteriaInput
ParameterMaximum
StressRate of Stress
IncreaseCurlingStress
E1 3 1 --
2 -- --
1 -- -- --
H1 -- -- 3
1 3 1 --
E2 -- 3 --
-- -- --
2 -- -- --
c2 -- 3 3
2 -- 2 --
• Model compared favorably to field data• Model is sensitive to base material
properties• Model is simple, yet provides length
scale to thermal cracking problem• Key input parameters are…
– Stiffnesses of HMAC and Base– Thermal coefficient– Frictional properties of Base material
Conclusions
• Further validation with field sections– Model has compared favorable to other
types of cracking• Incorporate a fracture mechanics
model to simulate crack propagation• Examine viscoelastic constitutive
models
Recommendations
• Plan mitigation strategies– Saw and seal– Material selection
• Assess probability and expectation of cracking
Potential Uses of Model
• Dr. Bojan Guzina
• Minnesota Department of Transportation– Minnesota Road
Research Project
Acknowledgements
Thank You!
Questions?
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