www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 1
Thermal Cracking Analysis Model AND
Pavement Temperature Profile Prediction Model
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 2
THERMAL CRACKING ANALYSIS PACKAGE (TCAP)
Comprehensive Evaluation of Thermal Cracking in Asphalt Pavements
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 3
Thermal Cracking Analysis Influential Factors • Pavement Structure
Asphalt layer thickness. Interface condition.
• Environmental Conditions Pavement temperatures. Cooling/warming rates.
• Asphalt mixture properties Viscoelastic properties Thermal Volumetric properties Fracture and Crack Initiation Properties
• Asphalt mixture aging Property change with oxidative aging
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 4
Thermal Cracking Analysis Existing Models • Aging of asphalt binder over time is not considered
“viscoelastic, fracture, and volumetric properties of asphalt material constant over time.”
• Thermal coefficient of contraction (CTC) is considered constant with temperature and usually estimated.
• Tensile strength is considered constant with temperature.
• Pavement temperature model (currently EICM) can be improved.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 5
Thermal Cracking Analysis Supportive Experimental Plan (Morian, N. 2014)
Asphalt Binder Testing
• 15 asphalt binder types Unmodified, polymer modified, lime modified
• Testing
Carbonyl Area (FT-IR) Binder Master Curves and LSV
1 mm film asphalt binder pan aging over different times and durations
(50, 60, 85 and 100°C up to 320 days)
Asphalt Mixture Testing (partial factorial) • 5 Agg. Sources (Abs. from 0.9 to 5.97%) • 3 Gradations (coarse, interm. & fine) • 2 Binders (PG64-22, PG64-28 SBS mod.) • Binder Contents (3.62 to 9.14% TWM) • 3 Air Void levels (4, 7, 11%) • Testing
Dynamic modulus (E*) Uniaxial Thermal Stress & Strain
Test (UTSST)
Asphalt Mixture aging: 4 Levels (0, 3, 6, and 9 months at 60°C)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 6
Thermal Cracking Analysis Proposed Model
Step 1 Pavement Temperature Profile
and History Prediction
Step 2 Oxidative Aging Prediction
Step 3 Thermal Stress Calculation
Step 4 Thermal Cracking Event
Probability
Pavement temperature at depth z (Step 1) Asphalt binder aging properties • Kinetics (Ea, and APα) • Hardening parameters (HS, m) Asphalt mixture properties • Air void size • Effective aging zone
Predict Carbonyl (CA) as a function of time and depth
Climatic and meteorological data: • air temperature • solar radiation and • Wind speed Layer properties: • Pavement layers’ thicknesses • Thermal diffusivity Surface radiation properties • Albedo, emissivity, absorption coefficients
1-D Heat Diffusion Equation TEMPS Software
Predicted hourly thermal stress • Considering aging effect • temperature dependent CTC Predicted carbonyl (CA) (Step 2) Asphalt mixture crack initiation stress (CIS) • Measured using UTSST (i.e., thermal loading) • Age-dependent Coefficient of thermal contraction • Temperature dependent CTC • Obtained from the thermal strain curve
Compare 𝝈 𝒕,𝑪𝑪 to % of CIS Numbers of events over design life
Predicted pavement temperature (Step 1) (over time and at depth z) Predicted carbonyl (CA) (Step 2) (over time and at depth z) Asphalt mixture Relaxation modulus • Directly from the E* complex modulus • based on continuous relaxation spectrum • Age dependent Coefficient of thermal contraction (CTC) • Temperature dependent CTC • Obtained from the thermal strain curve • Age dependent
1-D Linear viscoelastic model
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 7
Thermal Cracking Analysis Prediction of Field Aging (Numerical solution using FCVM)
Pavement location: Reno, NV Aggregate: Northern Nevada Binder type: PG64-28 (SBS mod.) Binder content: 5.22% Air voids: 7%
Ea= 72.53 kJol/mol APα = 4.08 E+8 ln(CA/day) HS = 2.7 (1/CA) m = 9.24 (poise) Air void diameter = 0.5 mm Eff. aging zone = 1.0 mm (film thickness)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 8
Thermal Cracking Analysis Lab Simulation of Field Aging
NV_PG64-28(SBS)_5.22%AC_7.0%Va long-term lab aging
Field aging (Reno, NV)
3 months at 60°C 5.9 years 6 months at 60°C ~ 10.9 years 9 months at 60°C ~16.7 years
0.5 months at 85°C Over 20 years Modeling of fast-rate aging is needed
X
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 9
Thermal Cracking Analysis Thermal Stress Calculation
• 1D linear viscoelastic constitutive equation with oxidative aging effect.
𝜎𝑇𝑇 𝑡,𝐶𝐶 = � 𝐸(𝜉 𝑡 − 𝜉′ 𝑡 ,𝐶𝐶)𝜕𝜀𝑇𝑇(𝑡,𝐶𝐶)
𝜕𝑡′𝑑𝑡𝑑
𝑡
0
Relaxation Modulus Function of time,
temperature, and aging
Thermal strain rate Function of temperature and
age-dependent CTC
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 10
Thermal Cracking Analysis Age-Dependent Relaxation Modulus • Relaxation modulus determined from dynamic complex modulus.
– Continuous relaxation spectrum directly obtained by inverse Laplace Fourier Transform of complex E* (2S2P1D, Olard & Di Benedetto, 2003).
Ideal viscoelastic model
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 11
Thermal Cracking Analysis Evolution of 2S2P1D Coefficient with Aging
Consistent trends were found for the evaluated mixtures!
1
10
100
1,000
0.00 0.20 0.40 0.60
E0 (M
Pa)
CA-CA0
1,000
10,000
100,000
0.00 0.20 0.40 0.60
E∞ (M
Pa)
CA-CA0
0.10
1.00
10.00
0.00 0.20 0.40 0.60
δ
CA-CA0
0.30
0.40
0.50
0.00 0.20 0.40 0.60
k
CA-CA0
0.01
0.10
1.00
0.00 0.20 0.40 0.60
h
CA-CA0
1.0E-04
1.0E-03
1.0E-02
1.0E-01
0.00 0.20 0.40 0.60
T0
CA-CA0
0.005.00
0.00 0.20 0.40 0.60CTCL
(E
05/
°C)
CA CA0 NV19I28_5.22_4%_60°C NV19I28_5.22_7%_60°C NV19I28_5.22_11%_60°C
(𝟐𝟐𝟐𝟐𝟐𝟐 𝒄𝒄𝒄𝒄𝒄)𝒋 = 𝑪𝒋 × 𝒄𝑩𝒋(𝑪𝑪−𝑪𝑪𝟎)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 12
Thermal Cracking Analysis Evolution of 2S2P1D Coefficient with Aging
2S2P1D coeff. CA Va (%) Abs. (%) LSVTank
(poise)B.C. (%) Retained # 8 Passing # 200
E0 √ √ √ √ √
E∞ √ √ √ √ √ √ √
δ √ √ √ √ √ √
k √ √ √ √
h √ √ √
T0 √ √ √
Mixture variable
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 13
Thermal Cracking Analysis Evolution of 2S2P1D Coefficient with Aging
y = 0.569x + 20.553 R² = 0.770
0
100
200
300
0 100 200 300
Pred
icted
E0 (
MPa)
Measured E0 (MPa)
E0 (MPa) Line of Eguality
y = 0.822x + 3,334.734 R² = 0.849
0
10,000
20,000
30,000
40,000
0 10,000 20,000 30,000 40,000Pr
edict
ed E
∞ (M
Pa)
Measured E∞ (MPa) E∞ Line of Eguality
y = 0.851x + 0.163 R² = 0.884
0.0
1.0
2.0
3.0
4.0
0.0 1.0 2.0 3.0 4.0
Pred
icted
δ
Measured δ
δ Line of Eguality
y = 0.761x + 0.098 R² = 0.775
0.0
0.2
0.4
0.6
0.0 0.2 0.4 0.6
Pred
icted
k
Measured k k Line of Eguality
y = 0.525x + 0.074 R² = 0.545
0.0
0.1
0.2
0.3
0.0 0.1 0.2 0.3
Pred
icted
h
Measured h h Line of Eguality
y = 0.553x + 0.002 R² = 0.689
0.E+00
5.E-03
1.E-02
2.E-02
2.E-02
0.E+00 5.E-03 1.E-02 2.E-02 2.E-02
Pred
icted
T0
Measured T0
T0 Line of Eguality
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 14
Thermal Cracking Analysis Temperature and Age-Dependent CTC •
-0.0015
-0.001
-0.0005
0
-50 -40 -30 -20 -10 0 10 20
Ther
mal S
train
(mm/
mm)
Temperature (°C)
CTCl
CTCg
Tg
Unrestrained Specimen
Restrained Specimen
Dummy Specimen
Uniaxial Thermal Stress & Strain Test (UTSST)
𝜀𝑡𝑇 =∆𝑙𝑙0
= 𝐶 + 𝐶𝐶𝐶𝑔 𝐶 − 𝐶𝑔 + 𝑙𝑙 1 + 𝑒(𝑇−𝑇𝑔)
𝑅
𝑅(𝐶𝑇𝐶𝑙−𝐶𝑇𝐶𝑔)
𝜀 𝐶(𝑡) = � 𝐶𝐶𝐶(𝐶(𝑡)) × 𝑑𝐶𝑑𝑇(𝑡)
𝑇0
𝐶𝐶𝐶 𝐶 = 𝐶𝐶𝐶𝑔 + (𝐶𝐶𝐶𝐿 − 𝐶𝐶𝐶𝑔) × 𝑒(
𝑇−𝑇𝑔𝑅 )
(1 + 𝑒𝑇−𝑇𝑔𝑅 )
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 15
Thermal Cracking Analysis Age-Dependent Crack Initiation Stress (CIS)
0
2000
4000
6000
8000
10000
-30 -20 -10 0 10 20
Stiffn
ess (
MPa)
Temperature (°C)
Crack Initiation (CI)
Glassy Hardening
Viscous-Glassy Transition
Viscous Softening Fracture
Crack Initiation Temp. (CIT)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 16
Thermal Cracking Analysis Age-Dependent Crack Initiation Stress (CIS)
• Validation of CIS with VECD. – Elastic-Viscoelastic Correspondence Principle
𝜎𝑇𝑇 𝑡 = 𝐸𝑅 × I × 𝜀𝑇𝑇𝑅 (𝑡) 𝜀𝑇𝑇𝑅 𝑡 =
1𝐸𝑅
� −𝐸𝑟(𝜉(𝑡) − 𝜉(𝑡′))𝜕𝜀𝑇𝑇(𝑡′)𝜕𝑡𝑑 𝑑𝑡𝑑
𝑡
0
0
0.5
1
1.5
2
2.5
3
-40 -30 -20 -10 0 10 20
The
rmal
Stre
ss (M
Pa)
Temperature (°C)
Mesured thermal stress from UTSSTPredicted stress without continuum damageing
Damage Initiation Temperature (DIT)
0
0.5
1
1.5
2
2.5
3
0 1 2 3
Ther
mal S
tress
(MPa
)
Thermal Pseudo-Strain * Ι
Start of nonlinearity due to damage
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 17
Thermal Cracking Analysis Age-Dependent Crack Initiation Stress (CIS)
• Validation of CIS with VECD.
y = 1.24x + 4.54 R² = 0.93
-40
-30
-20
-10
0
10
-40 -30 -20 -10 0 10
Dama
ge In
itiatio
n Tem
pera
ture
(°C)
Crack Initiation Temperature (°C)
Various mixtures with different binder grades, aggregates, and mix designs.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 18
Thermal Cracking Analysis Age-Dependent Crack Initiation Stress (CIS)
Similar trends were observed for all evaluated mixtures!
𝑪𝑪𝟐 = 𝑬 × 𝒄𝑭(𝑪𝑪−𝑪𝑪𝟎)
0.1
1.0
10.0
0.00 0.20 0.40 0.60
Crac
k init
iation
stre
ss (M
Pa)
CA-CA0
-40
-30
-20
-10
0
0.00 0.20 0.40 0.60Crac
k init
iation
temp
eratu
re (°
C)
CA-CA0
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 19
Thermal Cracking Analysis Age-Dependent Crack Initiation Stress (CIS)
CA Va (%) Abs. (%)
LSVTank (poise)
B.C. (%)
Retained # 8
Passing # 200
CIS √ √ √ √ √
CIT √ √ √ √ √ √
Mixture variable
y = 0.98x R² = 0.89
-40
-30
-20
-10
0
10
-40 -30 -20 -10 0 10
Pred
icted
Cra
ck in
i. Tem
p (°C
)
Measured Crack ini. Temp (°C) Crack initiation temperature Line of equality
y = 0.97x R² = 0.72
0
1
2
3
4
5
0 1 2 3 4 5
Pred
icted
Cra
ck in
i stre
ss (M
Pa)
Measured Crack ini stress (MPa)
Crack initiation stress Line of equality
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 20
Thermal Cracking Analysis Thermal Cracking Event Probability
• The accumulative events during which thermal stress reaches a defined percentage of the asphalt mixture Crack Initiation Stress (CIS) over the analysis period! Possible Cracking events
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 21
MATLAB Graphical User Interface (GUI) Thermal Cracking Analysis Package (TCAP)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 22
Examples: TCAP Analysis
• Pavement Location – Reno, Nevada
• Asphalt Mixtures: – Polymer-modified PG64-28; 3 air void levels: NV_5.22PG64-28_4%; NV_5.22PG64-28_7%; NV_5.22PG64-28_11%
• Design Period
– 20 years
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 23
Examples: TCAP analysis Effect of Oxidative Aging on Thermal Stresses
Difference in predicted thermal stresses between aging and no-aging effect analyses.
4% Air Voids
7% Air Voids
11% Air Voids
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 24
Examples: TCAP analysis Thermal Stress vs. Crack Initiation Stress (CIS)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 25
Examples: TCAP analysis
Effect of Mixtures Air Voids
Cracking likelihoods increase for mixture with higher air voids level….
∼11 yrs
Acc. CI = Weighted average of number of events at which thermal stresses reach different % of CIS.
𝐶𝐶𝐶𝐶𝐶𝐶𝑙𝐶 𝐼𝑙𝑑𝑒𝐼 =∑𝐶𝐶𝐶𝐶𝐶𝐶𝑙𝐶 𝑒𝑒𝑒𝑙𝑡𝑖 %𝐶𝐶𝐶 × 𝐶%
∑ 𝐶 % ,
𝐶 = 100, 80, 70, 60, 50
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 26
Examples: TCAP analysis Effect of Modification (Two field projects from Reno, NV)
Un-modified PG64-22 (Moana, 2006)
SBS polymer-modified PG64-28 (Sparks, 2008)
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 27
TCAP Implementation
Asphalt Mixture(s) (Agg., Binder, Mix Design)
Pavement Structure & Location
Pavement Temperature Prediction
Oxidative Aging Prediction
Materials Input Complex modulus (E*), CTC, CIS
Thermal Cracking Analysis ✔ Pass ✖ Fail
• Level 1: Measured kinetics (Mix-aged) • Level 2: Accelerated Aging • Level 3: Database
• Level 1: Measured (Full Testing) • Level 2: Measured (Reduced Testing) • Level 3: Predictive Equations
• Climatic/meteorological data • Material thermal prop. • Surface radiation prop.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 28
Future Research and Improvements
• Field validation of TCAP model.
• Sensitivity analysis of TCAP model.
• Level 3 material input: – Regression models for materials oxidative aging, viscoelastic,
and crack initiation properties.
• Development of a stand-alone TCAP software.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 29
TEMPERATURE ESTIMATE MODEL FOR PAVEMENT STRUCTURES (TEMPS)
Pavement Temperature Profile History
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 30
Pavement Temperature Profile Prediction
Improvement of the Heat Transfer model [Han et al., 2011 (TAMU)]
Enhanced boundary conditions. Variable pavement surface radiation properties.
Application of Finite Control Volume method (FCV) with
Implicit Scheme [Zia et al., 2014 (UNR)] Considering discontinuity in pavement layers’ material. Improving the time efficiency of calculation.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 31
Pavement Temperature Profile Prediction Heat Transfer Model Concept
Heat Transfer Balance Between Pavement Structure & Surrounding Environment
Solar Radiation (Albedo)
Incoming (Absorption) and Outgoing (Emissivity) Radiation Heat Convection
(Wind speed)
Heat Diffusion
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 32
Pavement Temperature Profile Prediction Numerical Computation: Finite Control Volume Method (FCVM)
Energy Balance in Each of Control Elements
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 33
Pavement Temperature Profile Prediction Standalone Software: TEMPS (Alpha Version) Temperature Estimate Model for Pavement Structures (TEMPS)
• Materials • Climatic Data • Surface Characteristics • Pavement Structure • Mesh Generator
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 34
Pavement Temperature Profile Prediction TEMPS – Materials Input
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 35
Pavement Temperature Profile Prediction TEMPS – Climatic Data Input
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 36
Pavement Temperature Profile Prediction TEMPS – Surface Characteristics Input
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 37
Pavement Temperature Profile Prediction TEMPS – Pavement Structure
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 38
Pavement Temperature Profile Prediction TEMPS – Mesh Generator
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 39
Pavement Temperature Profile Prediction TEMPS – Run Analysis
Time Efficiency of Computation: Implicit Scheme Run time for 1 years analysis period (3.10 GHz proc. and 4.00 GB RAM) < 10 seconds using 1 hour time step* * Note: 1 hour time step was chosen without jeopardizing the model accuracy for prediction.
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 40
Pavement Temperature Profile Prediction TEMPS – Output Results
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 41
Pavement Temperature Profile Prediction TEMPS – Output Results
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 42
Pavement Temperature Profile Prediction TEMPS – Output Summary
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 43
Pavement Temperature Profile Prediction TEMPS – Output Summary
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 44
Pavement Temperature Profile Prediction TEMPS – Predicted versus Measured Great Falls, MT at depth of 0.09 m (3.5 inch)
-20-10
01020304050
11/5/2001 12/25/2001 2/13/2002 4/4/2002 5/24/2002 7/13/2002 9/1/2002 10/21/2002 12/10/2002 1/29/2003
Temp
eratu
re (°
C)
Predicted TemperatureMeasured Temperature (LTPP)
-20-10
01020304050
11/5/2001 12/25/2001 2/13/2002 4/4/2002 5/24/2002 7/13/2002 9/1/2002 10/21/2002 12/10/2002 1/29/2003
Temp
eratu
re (°
C)
Calibrated TemperatureMeasured Temperature (LTPP)
Particle Swarm Optimization (PSO) Algorithm: Single yearly surface characteristics
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 45
Pavement Temperature Profile Prediction TEMPS – Predicted versus Measured Great Falls, MT at depth of 0.09 m (3.5 inch)
-20
-10
0
10
20
30
40
50
-20 -10 0 10 20 30 40 50
Max D
aily C
alibr
ated T
empe
ratur
e (De
gree
s C)
Max Daily Measured Temperature (Degrees C)
-20
-10
0
10
20
30
40
50
-20 -10 0 10 20 30 40 50
Max D
aily P
redic
ted Te
mper
ature
(Deg
rees
C)
Max Daily Measured Temperature (Degrees C)
Particle Swarm Optimization (PSO) Algorithm: Single yearly surface characteristics
Optimization need to be refined to include monthly surface characteristics
www.wrsc.unr.edu ; www.arc.unr.edu Slide No. 46
Pavement Temperature Profile Prediction TEMPS – Additional Improvements
• Optimize the surface characteristics for the US (Albedo, Emissivity, Absorption) using Particle Swarm Optimization (PSO) Algorithm – Monthly or seasonal values.
• Create/Include input files for LTPP SMP sections. • Provide a summary of the average 7-day pavement
temperature at various depths. • Provide a summary of pavement cooling/warming rates