CONCEPTUAL PHENOMENOLOGICAL
MODEL FOR INTERACTION OF ASPHALT
BINDERS WITH MINERAL FILLERS
By:
Ahmed F. Faheem,
Hussain U Bahia
University of Wisconsin- Madison
Outline
• Background
• Introduction
• Conceptual Model
• Test for Free Asphalt Volume
• Experimental Plan
• Summary of Results
• Factors Affecting Filler Stiffening
• Summary of Findings and Conclusions
Background
• Einstein Model for Diluted
Composites (1911)
ηr = 1 + KEø
ηr= Viscosity of composite/
viscosity of matrix
KE= Einstein Constant =2.5
Ø: Filler volume fraction
Fillers
• Many modification to this
equation have followed.
Einstein Model
After Shenoy 1999
Background
• The Marion–Pierce model
2
*
Gmastic
*
Gbinder
1
m
• Nelsen Model
Gc
Gm
1 ABV P
1 B VP
GP
B
GP
Gm
Gm
1
A
Where A= KE-1, and
1
1
m
2
m
Filler Maximum Packing
Fraction.
VP
• BRRC Model
R&B
1021.2 K
(100 V F (1 K ))
K = f/b, f = filler volume fraction (%), b = bitumen volume fraction (%) and Vf = % voids
(Rigden)
Evaluation of Models
Evaluation
of Prediction
Models for
Binder A
Evaluation
of Prediction
models
1.00E+08
9.00E+07
8.00E+07
Marion-Pierce
y = 10.108x - 1E+08
Marion-Peirce Model
Nelsen
y = 8.3524x - 1E+08
BRRC Model
Nelsen Model
Line of Equality
Actual G*
BRRC
7.00E+07 y = 3.3432x - 4E+07
Linear (Nelsen
Model)
Linear (BRRC
Model)
Linear (MarionPeirce Model)
6.00E+07
Filler volume
concentration of
0.4 of total mix
5.00E+07
4.00E+07
3.00E+07
2.00E+07
1.00E+07
0.00E+00
0.00E+00
1.00E+07
Filler volume
concentration of
0.2 of total mix
2.00E+07
3.00E+07
4.00E+07
5.00E+07
6.00E+07
Predicted G*
7.00E+07
8.00E+07
9.00E+07
1.00E+08
After Faheem et al 2008
Problem Statement
• Currently the filler influence on asphalt mastic is
estimated using the Fractional voids method.
– Measures filler volume fraction at maximum mastic stiffness.
– Does not elaborate the trend of increase in stiffness as the
filler concentration increases.
– Does not help identify the mechanism by which filler particles
interact with the asphalt matrix.
Hypothesis
• The filler influence in the mastic follows two
regions:
a.
b.
DILUTED, where the increase in the stiffness takes a
linear trend as a function of volume of filler, where the
rate of increase is named: “Initial Stiffening Rate”
CONCENTRATED, where the increase in stiffness
transitions to a higher rate of stiffness called:
“Terminal Stiffening Rate”.
Conceptual Model
G* Ratio vs. Filler Volume Fraction
Diluted Region
G* ratio
40
30
In the diluted region,
the filler particles are separated
enough by the free asphalt volume
20
Terminal Stiffening Rate
Concentrated Region
50
10
0
0
20
40
Filler Volume Fraction (%)
At this filler concentration, all
the asphalt is influenced
by the filler
60
Initial Stiffening Rate
= Einstein Coefficient
80
Test for the Presence of Free Asphalt
– Free Asphalt
– Influenced Asphalt

• Asphalt in the mastic is
divided into 2 fractions
Filler
Particle
Influenced
Asphalt

Free
Asphalt
• The free asphalt is
holding the mastic
system together
(After Kanitpong 2004)
Experimental Variables
Filler Properties
Binder Properties
Mastic Properties
1- Filler source
- Limestone
- Dolomite
Controlled
Variable
- Granite
- Fly Ash
- Carbon Black
1- PG grad
- PG64-22
1- Filler Volume
Fraction
- 5 concentrations
1- Fractional Voids
Dependent 2- Size distribution
Variables
1- Complex Shear
Modulus
2- Tack Factor
1- Relative
Complex Shear
Modulus
2- Tack Factor
Summary of Results
Physical Properties of Fillers
Filler Type
Granite
Type C Fly Ash
Dolomite
Limestone
Carbon Black
Rigden Voids
(%)
38%
26%
43%
35%
11%
D10
(μm)
2.07
0.97
4.03
2.54
0.08
D50
(μm)
17.97
9.77
31.44
26.37
0.08
D90
(μm)
149.15
49.22
81.62
67.21
0.08
SG
2.62
2.53
2.59
2.65
0.23
Effect of Filler on Mastic Stiffness
Relative G*
35
Dolomite
Carbon Black
Fly Ash
Limestone
Granite
30
G* Ratio
25
20
15
10
5
0
0
10
20
30
40
50
Filler Volume Fraction (%)
60
70
80
Mastic Stiffness and Tackiness
Fly Ash
35
500
G*r
Tackiness
400
G* Ratio
25
350
300
20
250
15
200
150
10
100
5
50
0
0
0
10
20
30
40
50
Filler Volume Fraction (%)
60
70
Tack Factor (s.N)
30
450
Mastic Stiffness and Tackiness
Granite
35
G*r
Tackiness
30
500
450
G* Ratio
25
350
300
20
250
15
200
150
10
100
5
50
0
0
0
10
20
30
40
50
Filler Volume Fraction (%)
60
70
Tack Factor (s.N)
400
Mastic Stiffness and Tackiness
Carbon Black
35
500
G*r
Tack Factor
30
450
G* Ratio
25
350
300
20
250
15
200
150
10
100
5
50
0
0
0
10
20
30
40
50
Filler Volume Fraction (%)
60
70
80
Tack Factor (s.N)
400
Factors Affecting Initial and Terminal
Stiffening Rates
Effect of Filler Size on Initial Stiffening Rate
160
140
Size (microns)
120
100
D90
D50
D10
Linear (D10)
Linear (D50)
Linear (D90)
y = 1458.5x - 10.76
R2 = 0.983
80
60
y = 225.86x + 4.7035
R2 = 0.4348
40
20
0
0.00
y = 26.842x + 0.4617
R2 = 0.4269
0.02
0.04
0.06
0.08
Initial Rate
0.10
0.12
0.14
Factors Affecting Initial and Terminal
Stiffening Rates (Cont’d)
Effect of Filler Size on Terminal Stiffening Rate
160
D90
D50
D10
Linear (D90)
Linear (D50)
Linear (D10)
140
Size (microns)
120
y = 46.176x + 7.6888
R2 = 0.6805
100
80
60
y = 1.3307x + 15.346
R2 = 0.0104
40
20
y = 0.0845x + 1.825
R2 = 0.0029
0
0
0.5
1
1.5
2
Terminal Rate
2.5
3
3.5
Factors Affecting Initial and Terminal
Stiffening Rates (Cont’d)
Initial and Terminal Stiffening Rates Against Rigden Voids
0.10
Initial Stiffening Rate
3
Initial Rate
Terminal Rate
Linear (Terminal Rate)
Linear (Initial Rate)
2.5
0.08
2
0.06
1.5
Terminal Rate
y = 3.2437x + 0.3451
R2 = 0.178
0.04
1
Initial Rate
y = 0.2421x - 0.0204
R2 = 0.7058
0.02
0.5
0.00
5%
10%
15%
20%
25%
30%
Rigden Voids (%)
35%
40%
0
45%
Terminal Stiffening Rate
0.12
How to Measure the Influenced Asphalt
Volume Fraction
Determination of Influenced Asphalt Volume
Fraction
450
Tack Factor (s.N)
400
350
300
y = -1.4069x2 + 101.86x - 1462
R2 = 1
Estimated Influenncing Filler
Concentration = 36.2%
250
200
150
100
50 Using the fitted parabola, the estimated
"Influenced Asphalt Volume Fraction" = 63.8%
0
20
25
30
35
40
45
Filler Volume Concentration (%)
50
55
Fractional Voids vs. Influenced Asphalt
Volume
Influenced Asphalt (%)
80%
70%
60%
50%
y = 0.0302x + 0.6517
R2 = 0.0008
40%
25%
30%
35%
Rigden Voids (%)
40%
(Fixed Asphalt)
45%
Factors Affecting Initial and Terminal
Stiffening Rates (Cont’d)
Influenced Asphalt Against Initial and Terminal Stiffening
Rates
Initial Stiffening Rate
0.35
0.30
3
Initial Rate
Terminal Rate
Linear (Terminal Rate)
Linear (Initial Rate)
2.5
y = 0.1101x - 5.6606
R2 = 0.9593
0.25
0.20
2
1.5
0.15
1
0.10
y = 0.0025x - 0.0993 0.5
R2 = 0.5869
0.05
0.00
55.0
60.0
65.0
70.0
Influenced Asphalt (%)
75.0
0
80.0
Terminal Stiffening Rate
0.40
Summary of Findings
• The tackiness test allows calculating the volume of the
“influenced asphalt” directly
• The tackiness test helped validate the Two-Regions
hypothesis of this study
• The stiffening rate within the Diluted Region is highly
dependent on the Rigden voids of the filler and the
Nominal Maximum Particle Size.
• The stiffening rate within the Concentrated Region,
which is assumed to be an indication of filler-bitumen
interaction, is highly dependent on the Influenced
Asphalt Volume fraction.
Update and Acknowledgment
• Update on Recent Testing
– Recent testing matched the results of this study.
– New testing included measuring physical and
chemical properties of filler.
• Thanks to MTE for their help in filler procurment
and testing.
Conceptual Model Parameters
50
G* ratio
40
30
In the diluted region,
the filler particles are separated
enough by the free asphalt volume
20
10
Concentrated Region
Diluted Region
G* Ratio vs. Filler Volume Fraction
2
1
0
0
20
40
3
60
80
Filler Volume Fraction (%)
1. Initial Stiffening Rate
2. Terminal Stiffening Rate
3. Critical Filler Concentration
At this concentration the transition
is due to the consumption of “Free
Asphalt”
Thank You!