Prediction of Fatigue Life of Rubberized Asphalt Concrete Mixtures Containing Reclaimed Asphalt Pavement Using Artificial Neural Networks (MT/2007/023481) ASCE Journal of Materials in Civil Engineering Feipeng Xiao 1 , Serji Amirkhanian 2 , M., ASCE, and C. Hsein Juang 3 , M., ASCE Abstract: Accurate prediction of the fatigue life of asphalt mixtures is a difficult task due to the complex nature of materials behavior under various loading and environmental conditions. This study explores the utilization of artificial neural network (ANN) in predicting the fatigue life of rubberized asphalt concrete (RAC) mixtures containing reclaimed asphalt pavement (RAP). Over 190 fatigue beams were made with two different rubber types (ambient and cryogenic), two different RAP sources, four rubber contents (0%, 5%, 10%, and 15%), and tested at two different testing temperatures of 5ºC and 20ºC. The data were organized into 9 or 10 independent variables covering the material engineering properties of the fatigue beams and one dependent variable, the ultimate fatigue life of the modified mixtures. The traditional statistical method was also used to predict the fatigue life of these mixtures. The results of this study showed that the ANN techniques are more effective in predicting the fatigue life of the modified mixtures tested in this study than the traditional regression-based prediction models. CE Database subject headings: Rubberized Asphalt Concrete, Reclaimed Asphalt Pavements, Artificial Neural Network, Crumb Rubber, Fatigue Life. ____________________ 1 Research Associate, Department of Civil Engineering, Clemson University, Clemson, SC ail: [email protected]29634-0911. E-m 2 Professor, Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911. E- mail: [email protected]3 Professor, Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911. E- mail: [email protected]
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Prediction of Fatigue Life of Rubberized Asphalt Concrete Mixtures Containing Reclaimed Asphalt Pavement Using Artificial Neural Networks
(MT/2007/023481) ASCE Journal of Materials in Civil Engineering
Feipeng Xiao1, Serji Amirkhanian2, M., ASCE, and C. Hsein Juang3, M., ASCE
Abstract: Accurate prediction of the fatigue life of asphalt mixtures is a difficult task due to the
complex nature of materials behavior under various loading and environmental conditions. This
study explores the utilization of artificial neural network (ANN) in predicting the fatigue life of
Proceedings of Association of Asphalt Paving Technologists, Vol. 54. 347-406
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Xiao et al. (2007)
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22
Xiao et al. (2007)
LIST OF TABLES
TABLE 1 Average values of independent and dependent variables of modified mixtures tested at 5ºC
TABLE 2 Average values of independent and dependent variables of modified mixtures tested at
20ºC TABLE 3 Strain dependent fatigue prediction models of the mixtures
TABLE 4 Energy dependent fatigue prediction models of the mixtures
TABLE 5 Coefficient of determination (R2) and coefficient of variation (COV) of the specific regression models
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Xiao et al. (2007)
LIST OF FIGURES
FIG. 1 Example of a three-layer feedforward neural network architecture
FIG. 2 Flowchart illustrating backpropagation training algorithm
FIG. 3 Comparison of fatigue lives between predicted and measured results using regression-based strain-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC
FIG. 4 Comparison of fatigue lives between predicted and measured results using regression-
based strain-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 5 Sample spreadsheet of ANN model based strain-dependent for ambient rubberized
mixtures at 5ºC FIG. 6 Comparison of fatigue lives between predicted and measured results using ANN-based
strain-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 7 Comparison of fatigue lives between predicted and measured results using ANN-based
strain-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 8 Sensitivity analysis of rubber and RAP percentages in ANN fatigue models (a) RAP
analysis; (b) Rubber analysis FIG. 9 Important indexed of input variables in the developed ANN FIG. 10 Comparison of fatigue lives between predicted and measured results using regression-
based energy-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 11 Comparison of fatigue lives between predicted and measured results using regression-
based energy-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 12 Comparison of fatigue lives between predicted and measured results using ANN-based
energy-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC FIG. 13 Comparison of fatigue lives between predicted and measured results using ANN-based
energy-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC
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Xiao et al. (2007)
TABLE 1 Average value of each of the variables of modified mixtures tested at 5ºC
Dependent5ºC R b (%) R P (%) Ln(ε 0 ) VFA V 0 Ln(w 0 ) Ln(S 0 ) Ln(N f )
Note: Rb = the percentage of rubber in the binder; Rp = the percentage of RAP in the mixture; 0ε = initial flexural strain; VFA = volume of voids filled with asphalt binder; V0 = initial air-void content in percentage; w0 = initial dissipated energy; S0 = initial mix stiffness; = fatigue life. fN
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Xiao et al. (2007)
TABLE 2 Average value of each of the variables of modified mixtures tested at 20ºC
Dependent20ºC R b (%) R P (%) Ln(ε 0 ) VFA V 0 Ln(w 0 ) Ln(S 0 ) Ln(N f )
Note: Rb = the percentage of rubber in the binder; Rp = the percentage of RAP in the mixture; 0ε = initial flexural strain; VFA = volume of voids filled with asphalt binder; V0 = initial air-void content in percentage; w0 = initial dissipated energy; S0 = initial mix stiffness; = fatigue life. fN
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Xiao et al. (2007)
TABLE 3 Strain dependent fatigue prediction models of the mixtures
Ambient Traditional Predicting Model R2 COV
VFA (5oC) 2.2
0*2.206.1
0 ***)13(0.1 SeEN VFAf ε−= 0.37 66%
A.V. (5oC) 7.0
0*1.02.0
0 ***)2(8.4 0 SeEN Vf
−−−= ε 0.09 28%
VFA (20oC) 9.1
0*9.205.6
0 ***)5(3.3 SeEN VFAf ε= 0.36 82%
A.V. (20oC) 2.0
0*4.08.6
0 ***)26(9.1 0 SeEN Vf
−= ε 0.53 106% Cryogenic
VFA (5oC) 9.2
0*1.07.6
0 ***)5(3.1 SeEN VFAf
−= ε 0.13 47%
A.V. (5oC) 3.2
0*2.02.7
0 ***)11(6.3 0 SeEN Vf
−= ε 0.32 78%
VFA (20oC) 02.0
0*5.01.9
0 ***)34(7.1 SeEN VFAf
−= ε 0.27 51%
A.V. (20oC) 6.0
0*2.04.3
0 ***)20(9.3 0 SeEN Vf
−= ε 0.36 61% Note: = fatigue life fN 0ε = initial flexural strain; VFA = volume of voids filled with asphalt binder; V0 = initial air-void content in percentage; S0 = initial mix stiffness; A.V. = air voids
27
Xiao et al. (2007)
TABLE 4 Energy dependent fatigue prediction models of the mixtures
Ambient Traditional Predicting Model R2 COV
VFA (5oC) 01.0
0*8.13 **74.0 εVFA
f eN = 0.22 57%
A.V. (5oC) 2.0
0*1.0 **)4(9.4 0 −−= εV
f eEN 0.09 37%
VFA (20oC) 6.2
0*6.21 **)4(1.4 εVFA
f eEN −= 0.49 135%
A.V. (20oC) 0.1
0*3.0 **)5(1.1 0 εV
f eEN −= 0.42 121% Cryogenic
VFA (5oC) 5.0
0*2.0 **)4(1.1 εVFA
f eEN −= 0.04 31%
A.V. (5oC) 4.0
0*2.0 **)4(4.2 0 εV
f eEN = 0.21 78%
VFA (20oC) 9.0
0*2.0 **)4(0.4 εVFA
f eEN −= 0.40 84%
A.V. (20oC) 0.1
0*5.2 **)4(1.8 0 εV
f eEN −= 0.27 66% Note: = fatigue life fN 0ε = initial flexural strain; VFA = volume of voids filled with asphalt binder; V0 = initial air-void content in percentage; S0 = initial mix stiffness; A.V. = air voids
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Xiao et al. (2007)
TABLE 5 Coefficient of determination (R2) and coefficient of variation (COV) of the specific regression models
Note: VFA = volume of voids filled with asphalt; A.V. = air voids
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Xiao et al. (2007)
Nf
VFA
ε
S
Rb
Rp
Input layer Hidden Output
Rb = the percentage of rubber in the binder; Rp = the percentage of RAP in the mixture; ε = initial flexural strain; VFA= Volume of Voids filled with asphalt binder; S = initial mix stiffness; Nf= fatigue life.
FIG. 1 Example of a three-layer feedforward neural network architecture
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Xiao et al. (2007)
Scaling Input/Output Vectors
Assigning Initial Weights
Calculating Output
Out_err = Target- Prediction
Update Weights for Output-Layer Neurons
Update Weights for Hidden-Layer Neurons
Backpropagation Training Completed
Out_err < Goal_err (?) YES
NO
FIG. 2 Flowchart illustrating backpropagation training algorithm (Juang and Chen 1999)
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Xiao et al. (2007)
0
1
2
3
4
5
0 1 2 3 4 5Measured Fatigue Life (104Cycles)
Pred
icte
d Fa
tigue
Life
(104 C
ycle
s) VFA PredictedAir Voids Predicted
R2=0.95 (VFA)R2=0.77 (A.V)
0123456789
10
0 1 2 3 4 5 6 7 8 9 10
Measured Fatigue Life (104Cycles)
Pred
icte
d Fa
tigue
Life
(104 C
ycle
s) VFA PredictedAir Voids Predicted
R2=0.84 (VFA)R2=0.91 (A.V)
(a) (b)
FIG. 3 Comparison of fatigue lives between predicted and measured results using regression-based strain-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC
32
Xiao et al. (2007)
0
1
2
3
4
0 1 2 3 4
Measured Fatigue Life (104Cycles)
Pred
icte
d Fa
tigue
Life
(104 C
ycle
s) VFA PredictedAir Voids Predicted
R2=0.65 (VFA)R2=0.65 (A.V)
0
1
2
3
4
5
6
0 1 2 3 4 5 6
Measured Fatigue Life (104Cycles)
Pred
icte
d Fa
tigue
Life
(104 C
ycle
s) VFA PredictedAir Voids Predicted
R2=0.73 (VFA)R2=0.73 (A.V)
(a) (b)
FIG. 4 Comparison of fatigue lives between predicted and measured results using regression-based strain-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC
33
Xiao et al. (2007)
1 A B C D E F G2 COMMANDS OF EXECUTING EQ.8 Hidden Layer3 ARGUMENT("R b ", "R p ", "P 1 ", "P 2 ", "P 3 ","Ln(ε 0 ) ") Weight matrix Hidden 1 Hidden 2 Hidden 3 Hidden 44 ARGUMENT("VFA ", "P 4 ", "P 5 ", "Ln(S 0 ) ") Bias 8.50785 -9.71422 -2.95993 -1.944225 R b =(R b +0.019)/0.19; R p =(R p +0.038)/0.38 Input 1 -2.92512 3.77847 0.21774 -2.584166 P 1 =(P 1 +0.0056)/0.056; P 2 =(P 2 +0.003)/0.03 Input 2 -5.43439 2.23798 1.56790 -4.475967 P 3 =(P 3 +0.0004)/0.004; Ln(ε 0 ) =(Ln(ε0 )+7.91)/0.37 Input 3 -2.05854 3.93442 3.62199 0.229308 VFA=(VFA -0.725)/0.053; P 4 =(P 4 +0.015)/0.15 Input 4 2.04824 3.40047 -0.12879 2.489739 P 5 =(P 5 +0.028)/0.28; Ln(S 0 ) =(Ln(S 0 ) -16.64)/0.333 Input 5 2.17721 3.49616 -5.61273 4.0260510 pi1=1/(1+EXP(-(R b *D$5+R p *D$6+P 1 *D$7+P 2 *D$8+ Input 6 -1.07765 3.16621 1.70724 -1.5014611 P 3 *D$9+Ln(ε 0 ) *D$10+VFA *D$11+P 4 *D$12+ Input 7 -7.00788 -0.51641 2.25666 -1.6631312 P 5 *D$13+Ln(S 0 ) *D$14+D$4))) Input 8 0.78339 -1.49672 2.87061 2.3366013 pi2=1/(1+EXP(-(R b *E$5+R p *E$6+P 1 *E$7+P 2 *E$8+ Input 9 0.25014 2.09887 3.63714 -3.4439614 P 3 *E$9+Ln(ε 0 ) *E$10+VFA*E$11+P 4 *E$12+ Input 10 0.34972 3.67111 -3.83600 -0.3682815 P 5 *E$13+Ln(S 0 ) *E$14+E$4)))16 pi3=1/(1+EXP(-(R b *F$5+R p *F$6+P 1 *F$7+P 2 *F$8+ Output Layer17 P 3 *F$9+Ln(ε0) *F$10+VFA *F$11+P 4 *F$12+ Bias 4.0670818 P 5 *F$13+Ln(S 0 ) *F$14+F$4))) Hidden 1 -3.8366419 pi4=1/(1+EXP(-(R b *G$5+R p *G$6+P 1 *G$7+P 2 *G$8+ Hidden 2 2.8123020 P 3 *G$9+Ln(ε 0 ) *G$10+VFA *G$11+P 4 *G$12+ Hidden 3 -4.3789921 P 5 *G$13+Ln(S 0 ) *G$14+G$4))) Hidden4 -4.1719522 Z=pi1*D18+pi2*D19+pi3*D20+pi4*D21+D1723 Z=1/(1+EXP(-Z))24 Ln(F)=2.041*Z+9.00725 RETURN (F)
Cells B3:B25 are macro commands to execute Eq.8
Weight matrix:Cells D4: G4 are BHK
Cells D5: G14 are Wik
Weight matrix:Cell D17 is Bo
Cells D18: D21 are Wik
FIG. 5 Sample spreadsheet of ANN model based strain-dependent for ambient rubberized mixtures at 5ºC
FIG. 6 Comparison of fatigue lives between predicted and measured results using ANN-based strain-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC
FIG. 7 Comparison of fatigue lives between predicted and measured results using ANN-based strain-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC
36
Xiao et al. (2007)
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 5 10 15 20 25 30 35
RAP Percentage (%)
Fatig
ue L
ife (x
104 cy
cles
)
8%Rubber 10%Rubber12%Rubber
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 5 10 15 20
Rubber Percentage (%)
Fatig
ue L
ife (x
104c
ycle
s)
10%RAP 15%RAP20%RAP
(a) (b)
FIG. 8 Sensitivity analysis of rubber and RAP percentages in ANN fatigue models
(a) RAP analysis; (b) Rubber analysis
37
Xiao et al. (2007)
0
1
2
3
4
5
0 1 2 3 4 5Measured Fatigue Life (x104cycles)
Pred
icte
d Fa
tigue
Life
(x10
4 cycl
es) VFA Predicted
Air Voids PredictedR2=0.79 (VFA)R2=0.66 (A.V)
0123456789
10
0 1 2 3 4 5 6 7 8 9 10
Measured Fatigue Life (x104cycles)
Pred
icte
d Fa
tigue
Life
(x10
4 cycl
es)
VFA PredictedAir Voids Predicted
R2=0.81 (VFA)R2=0.78 (A.V)
(a) (b)
FIG. 9 Comparison of fatigue lives between predicted and measured results regression-based energy-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC
FIG. 11 Comparison of fatigue lives between predicted and measured results using ANN-based energy-dependent models for ambient rubberized mixtures (a) 5ºC; (b) 20ºC
FIG. 12 Comparison of fatigue lives between predicted and measured results using ANN-based energy-dependent models for cryogenic rubberized mixtures (a) 5ºC; (b) 20ºC