Model developments of long-term aged asphalt binders

Construction and Building Materials 37 (2012) 248–256

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Model developments of long-term aged asphalt binders Feipeng Xiao a,b,⇑, Serji N. Amirkhanian c, C. Hsein Juang b, Shaowei Hu d, Junan Shen a a

Road Engineering Laboratory, Suzhou University of Science and Technology, Suzhou, China Department of Civil Engineering, Clemson University, 2002 Hugo Drive, Clemson, SC 29634, USA c State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Wuhan 430070, China d Nanjing Hydraulic Research Institute, Nanjing 210029, China b

h i g h l i g h t s " This study developed a series of models to simulate long-term aged asphalt binders. " ANN models are more effective than regression models. " And these ANN models were easily implemented in a spreadsheet. " Aging temperature, duration and molecular sizes are the most important factors.

a r t i c l e

i n f o

Article history: Received 8 September 2011 Received in revised form 26 June 2012 Accepted 22 July 2012 Available online 31 August 2012 Keywords: Artificial neural network Regression analysis Pressurized aging vessel Penetration index Mass loss Stiffness m-Value HP-GPC Important Index

a b s t r a c t Artificial neural networks (ANNs) are useful in place of conventional physical models for analyzing complex relationship involving multiple variables and have been successfully used in civil engineering applications. The objective of this study was to develop a series of ANN models to simulate the long-term aging of three asphalt binders (PG 64-22, crumb rubberized asphalt modifier, PG 76-22) regarding seven aging variables such as aging temperature and duration, m-value, mass loss of pressurized aging vessel (PAV) samples, percentages of large and small molecular sizes of high pressure-gel permeation chromatographic (GPC) testing, and binder stiffness. The results indicated that ANN-based models are more effective than the regression models and can easily be implemented in a spreadsheet, thus making it easy to apply. The results also show that the aging temperature, aging duration, percentage of large and small molecular sizes, and binder stiffness are the most important factors in the developed ANN models for prediction of penetration index after a long-term aging process. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Pavement researchers and engineers often encounter and have to solve some complex problems involving a number of interacting factors or engineering parameters (variables) for asphalt or concrete pavements. However, in some problems, the underlying first principles are not well defined and it is not possible to define a concise relationship between the factors (variables), or the problem is too complicated to be described mathematically. For example, the long-term aging of asphalt binder is involved a number of factors such as construction process, traffic loading, pavement structure or materials, weather conditions and so on. One common ⇑ Corresponding author at: Department of Civil Engineering, Clemson University, 2002 Hugo Drive, Clemson, SC 29634, USA. Tel.: +1 864 6566799; fax: +1 864 6566186. E-mail address: [email protected] (F. Xiao). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.07.047

approach to solve these problems is to utilize experimental (measured) data to build empirical or semi-empirical models that relate the variables (input–output relationship) in the system. This extraction of knowledge from the data is a formidable task requiring sophisticated modeling techniques as well as human intuition and experience. Increasingly, modern pattern recognition techniques such as neural network and fuzzy systems are being considered to develop models from data to their ability to learn and recognize trends in the data pattern. Artificial neural networks (ANNs) are useful in place of conventional physical models for analyzing complex relationships involving multiple variables and have been successfully used in civil engineering applications such as process optimization, slope stability analysis, and deep excavation forecast models [1–8]. Asphalt binder long-term aging is a complicated process which might involve irreversible chemical changes and reversible physical hardening. The former mechanism derives from the oxidation,

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loss of volatile components, and exudation [9–14]. As aging progresses, more of the asphaltene fractions are formed, the saturate fractions remain unchanged while both the polar and naphthenearomatics decrease [13,14]. The advantage of the saturate is that increasing their amount of reactive components and, therefore, probably imparts to the asphalt an ability to resist chemical change and the effects of aging [13,14]. The latter physical hardening process may be attributed to reorganization of asphalt molecules to approach an optimum thermodynamic state under a specific set of conditions, such as repeated traffic loading [15–17]. The factors affecting asphalt aging include characteristics of the asphalt binder (e.g. source and grade) and its content in the mixture, nature of aggregate and particle size distributions, air void contents of the mixture; production related factors, service temperature and duration as well as the repeated traffic loading [13–17]. Previous researchers found that the aging mechanisms of asphalt at the high-temperature levels employed in accelerated conditions did not differ significantly from those occurring under the relatively mild conditions in the field [10,13,18]. The study by Chari et al. [19] on age hardening of asphalt binder indicated that a high temperature thin film oven test (TFOT) or rolling thin film oven test (RTFOT) procedures and pressurized aging vessel (PAV) could be used to simulate long-term field aging. Penetration index (PI) values can be used to determine the stiffness (modulus) of an asphalt binder at any temperature, aging state, and loading time. It can also, to a limited extent, be used to identify a particular type of bituminous material. One drawback of the PI is that it relies on the change in asphalt binder properties over a relatively small range of temperatures to characterize asphalt binder. Penetration is related to viscosity and empirical relationships have been developed for Newtonian materials. If the penetration is measured over a range of temperatures, the temperature susceptibility of the bitumen can be established. Mirza and Witczak [20] developed a series of sequential analytical models to predict the aging characteristics of conventional type asphalt cements due to both short and long term effects. These models were developed from a statistical analysis of results in a Master Data Base comprised of asphalt consistency results. The approved models were effective in predicting the aging behavior of asphalt binder. Asphalt binders were separated into four main fractional groups according to its origin, namely: saturates, aromatics, resins and asphaltenes [14]. However, some researchers found that the definition of three classified groups in the bitumen, namely large molecular size (LMS), medium molecular size (MMS), and small molecular size (SMS), is helpful in analyzing the aging process in high pressure-gel permeation chromatographic (HP-GPC) analysis method [21,22]. Kim et al. [21] discussed the influence of aging on chromatographic profiles and the relationship between selected properties of the binders and the HP-GPC parameters. The objective of this study was to develop a series of ANN models to simulate the long-term aging behavior of three asphalt binders under various aging temperatures and durations using PAV. Here, the penetration index values were predicted from ANN models regarding aging variables such as aging temperatures and durations, binder stiffness, m-value, mass loss of PAV specimen, percentages of large molecular sizes (LMS) and small molecular sizes (SMS) of high pressure-gel permeation chromatographic (HP-GPC) testing. 2. Experimental materials and test procedures 2.1. Materials Three types of asphalt binder sources, referred to as sources 1, 2 and 3 in this paper, were used in this study (Table 1). Each of the sources included virgin PG 64-22, crumb rubberized modifier (CRM) binders, which were produced in the

Table 1 Rheological properties of asphalt binders. Rheological properties

G/sin d (kPa)

G/sin d (MPa)

64 °C Control

64 °C CRM

76 °C CRM

76 °C SBS

25 °C Control

25 °C CRM

25 °C SBS

Source 1 Source 2 Source 3

1.29 1.71 1.46

2.96 2.60 3.34

1.01 1.87 1.01

1.98 1.36 1.66

3.02 2.37 3.66

1.94 1.63 2.04

3.78 2.63 3.32

Note: Control: PG 64-22 binder; CRM: PG 64-22 + 10% crumb rubber by weight of binder; SBS: 3% Styrene–butadiene-styrene PG 76-22.

laboratory using 10% (by weight of the base binder) 40 mesh (0.425 mm) ambient rubber with PG 64-22 binder, and PG 76-22 (3% Styrene–butadiene–styrene (SBS)). In this paper, they are defined as control (A), CRM (B), and SBS (C) binders, respectively. Each CRM binder was produced with a blade mixer at 177 °C for 30 min in a can filled with 600 g of binder [23]. The artificially accelerated aging processes of RTFO (163 °C for 85 min) and PAV aging were used to generate aged binders (Table 2).

2.2. Penetration index The penetration index, as a quantitative measure of the temperature sensitivity of bituminous materials, can determine the aging behavior of an asphalt binder. In this study, a penetration test was employed to measure the penetration index values at various aging statuses according to AASHTO T59. The penetration index results were measured using a penetration temperature of 25 °C between the range of 5 and 300, under a load of 100 g applied for 5 s. The test results of the four types of aging temperatures (60, 85, 100, and 110 °C) in various aged durations for each binder were analyzed.

2.3. BBR testing The bending beam rheometer (BBR) testing was used to evaluate the properties of the aged binder at a low temperature of 12 °C according to AASHTO T313. The measured creep stiffness and m-values were utilized to describe the aged levels of the various aged binders in this study.

2.4. Mass loss In the Superpave design, one purpose of the RTFO is to determine the mass quantity of volatiles lost from the asphalt during the rolling process. Volatile mass loss is an indication of the aging that may occur in the asphalt during mixing and construction operations. However, the change of mass quantity of asphalt binder in PAV aging is not designed to be a sign of the field aging, due to the long-term traffic loading and weather conditions. Similar to the mass loss in RTFO, the study of mass change in PAV was completed in this project, in which mass change is defined as the average percentage increase of the samples after PAV aging. The weighted 50 g PAV sample, prepared from the RTFO-aged binder, was aged using the various aging conditions and then degassed. The aged sample was then measured for further mass loss study after reaching the room temperature. This PAV aging process was performed in accordance with AASHTO PP1-98. The following equation is used to calculate the mass change.

Mass change; % ¼

PAV aged mass  RTFO aged mass  100 RTFO aged mass

ð1Þ

These mass changes, derived from the various aging temperatures and durations, were used to describe the aging levels of the asphalt binders during a longterm aging.

2.5. HP-GPC HP-GPC was adopted from the polymer industry to determine the molecular size distribution (MSD) of asphalt binders. A Waters 1515 Isocratic high performance liquid chromatography (HPLC) Pump was used in conjunction with a Waters 2414 Refractive Index Detector. The solvent used was tetrahydrafuran (THF), the dilution ratio was 400:1 (solvent: binder), the injection volume was 50 lL, and the elution time was 30 min. Three samples were tested for each vial [23]. As shown in Fig. 1, the chromatographic profile of each asphalt binder sample was divided into 13 slices based on the equal elution time at the midpoint of the beginning and ending periods [23]. The first 5 slices and the next 6–9 slices were defined as LMS and medium molecular sizes (MMSs), respectively. The rest of the area under the curve was referred to as SMS. All of the areas under the curve were expressed as a percentage.

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20

Table 2 Test temperature and aging duration of asphalt binders.

Response (MV)

16 12 8

Test temperature (°C)

Aging duration (hours): 2070 kPa

60 85 100 110

15 15 15 15

20 20 20 20

40 40 40 –

80 80 – –

144 – – –

4 LMS LMS

0 10

11

12

13

5th 14 15

MMS MMS

16

SMS SMS

9th 17 18

19

20

13 equal elution time

Elution Time (minutes) Fig. 1. Methodology of calculation of LMS, MMS and SMS.

PI ¼ f ðT C ; T H ; Mv ; ML ; PLMS ; P SMS ; SÞ

3. Experimental model development 3.1. Statistical regression model Previous research by Heukelon [24] presented relationships between penetration and viscosity of asphalt binders, and established the rational explanation of bitumen viscosity behavior based upon the equiviscous TRB (ring and ball softening point) temperature and penetration by:

log



g

13; 000



 pen  8:5 log 800  pen  ¼ 5:42 þ log 800

ð2Þ

pen where g is the viscosity in poise, and 800 is the value of penetration at TRB. Furthermore, Mirza and Witczak [20] successfully developed a series of statistical penetration models to predict the long-term aging characteristics.

log g ¼ 10:5012  2:2601 logðpenÞ þ 0:00389 logðpenÞ2

ð3Þ

log log gt¼1 ¼ 10:752  3:577 log T R

ð4Þ

where g is the viscosity in poise, gt=1 the ultimate viscosity, and TR is the temperature in degrees Rankine. The developed penetration models are quite easy to use because no more tests are necessary. Although the development of models requires detailed parameters and input variables that respond to

Input layer

Hidden layer

Output layer

TC TH MV ML

PI

PLMS PSMS S Error Propagation

Fig. 2. A schematic diagram of three-layer artificial neural network.

the varieties of penetration, the penetration index is easy to obtain through standard tests specified by ASTM or AASHTO. For example, the aging behavior of asphalt binder can be characterized by the penetration index and viscosity. In this study, the aging factors such as aging temperature and duration, m-value, mass loss, percentages of LMS and SMS, and binder stiffness can be expressed as independent variables to yield the penetration index (PI) values.

ð5Þ

where PI is the penetration index (mm), TC, TH the aging temperature (°C) and duration (hours), respectively, MV, ML the m-value and mass loss (%), respectively, PLMS ; P SMS the percentages of LMS and SMS, respectively, and S is the binder stiffness (MPa). Statistical regression line model can be developed from these aging variables. The linear equation is expressed as follows.

PI ¼ a þ b  T C þ c  T H þ d  M v þ e  M L þ f  PLMS þ g  P SMS þhS

ð6Þ

where a, b, c, d, e, f, g, h is the regression constant 3.2. ANN model Past several decades, the neural networks approach has been broadly employed to develop the predictions in civil engineering. It may be used to develop the predictive models of the penetration index values of asphalt binders considering the interaction of complicated variables. A three-layer feedforward neural network,

Table 3 Pearson correlation matrix for the variables (a) Control binder; (b) CRM binder; (c) SBS binder. TC

TH

MV

ML

PLMS

PSMS

S

PI

(a) TC TH MV ML PLMS PSMS S PI

1.00 0.45 0.38 0.70 0.09 0.42 0.11 0.63

1.00 0.21 0.15 0.21 0.03 0.21 0.23

1.00 0.61 0.34 0.28 0.46 0.51

1.00 0.19 0.33 0.27 0.87

1.00 0.71 0.11 0.26

1.00 0.10 0.44

1.00 0.23

1.00

(b) TC TH MV ML PLMS PSMS S PI

1.00 0.45 0.39 0.65 0.22 0.05 0.29 0.52

1.00 0.18 0.21 0.28 0.21 0.32 0.11

1.00 0.46 0.11 0.16 0.41 0.21

1.00 0.08 0.02 0.58 0.58

1.00 0.80 0.19 0.08

1.00 0.12 0.02

1.00 0.30

1.00

(c) TC TH MV ML PLMS PSMS S PI

1.00 0.45 0.39 0.67 0.09 0.16 0.09 0.64

1.00 0.28 0.22 0.11 0.27 0.40 0.02

1.00 0.58 0.02 0.20 0.42 0.31

1.00 0.09 0.07 0.48 0.78

1.00 0.60 0.01 0.17

1.00 0.02 0.15

1.00 0.39

1.00

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F. Xiao et al. / Construction and Building Materials 37 (2012) 248–256

35

35 2

R = 0.81;

Training: R2= 0.99;

30

RMSE = 2.14

Predicted PI value (mm)

Predicted PI value (mm)

30 25 20 15 10

Testing: R2= 0.84; 25

RMSE = 1.25

20 15 10

5

5

0

0

Training data 0

5

10

15

20

25

30

35

0

5

10

Testing data

15

20

25

Measured PI value (mm)

Measured PI value (mm)

(a)

(b)

30

35

Fig. 3. Penetration index values of control (PG 64-22) asphalt binder, (a) Regression analysis; (b) ANN analysis.

35

35

R2= 0.40;

Training: R 2= 0.97;

30

RMSE = 2.67

Testing: R 2= 0.50;

Predicted PI value (mm)

Predicted PI value (mm)

30 25 20 15 10

25

RMSE = 1.63

20 15 10

5

5

0

0

Training data 0

5

10

15

20

25

30

0

35

5

10

15

20

Testing data 25

Measured PI value (mm)

Measured PI value (mm)

(a)

(b)

30

35

Fig. 4. Penetration index values of CRM (PG 64-22 + 10% crumb rubber) asphalt binder, (a) Regression analysis; (b) ANN analysis.

35

35 2

R = 0.70;

Training: R2= 0.98;

30

RMSE = 2.23

Predicted PI value (mm)

Predicted PI value (mm)

30 25 20 15 10

Testing: R 2= 0.72; 25

RMSE = 1.60

20 15 10

5

5

0

0

Training data 0

5

10

15

20

25

30

35

0

5

10

15

Testing data 20

25

Measured PI value (mm)

Measured PI value (mm)

(a)

(b)

30

Fig. 5. Penetration index values of SBS (PG 76-22) asphalt binder, (a) Regression analysis; (b) ANN analysis.

35

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F. Xiao et al. / Construction and Building Materials 37 (2012) 248–256

Table 4 Coefficient values of regression models.

Control CRM SBS

a

b

c

d

e

/

g

h

35.8597 24.6176 32.4147

0.0635 0.0037 0.0368

0.0338 0.0251 0.0122

9.9455 1.4231 14.3939

37.1945 26.7560 33.4041

0.0131 0.0146 0.1547

0.0977 0.0224 0.0393

0.0001 0.0020 0.0165

Note: Control: PG 64-22 binder; CRM: PG 64-22 + 10% crumb rubber by weight of binder; SBS: 3% Styrene–butadiene–styrene PG 76-22.

shown in Fig. 2, was trained with the experimental data. This architecture consists of an input layer (seven variables), a hidden layer (five neurons), and an output layer (one variable). Each of the neurons in the hidden and output layers consists of two parts, one dealing with aggregation of weights and the other providing a transfer function to process the output. Unlike the traditional multiple stepwise regression models, the ANN is a model free estimator. It does not require the knowledge of the form of functions (i.e., models) to begin with the analysis. The overall ANN models used a goal error of 0.00001 and an epoch (An epoch is the presentation of the entire training set to the neural network) of 1000 in this study. The sampling process is largely random, since no effort was made to keep track of the characteristics of input and output variable. While randomness in the data selection was largely maintained, the training data set is believed to be representative (4). For the three-layer network shown in Fig. 2, the output of the network, the penetration index value (PI), is calculated as follows [4]:

( PI ¼ fT Bo þ

" n X

W k  fT BHK þ

m X W ik Pi

!#) ð7Þ

i¼1

k¼1

Table 5 Sample training and testing data of independent and dependent variables of control Binders.

where Bo is the bias at the output layer, Wk is the weight of the connection between neuron k of the hidden layer and the single output layer neuron, BHK the bias at neuron k of the hidden layer, Wik the weight of the connection between input variable i and neuron k of the hidden layer, Pi the input ith parameter, and fT is the transfer function, defined as:

f ðtÞ ¼

1 1 þ et

ð8Þ

In Eq. (7), the number of input variables (m) is 7; the input variables (defined previously) are P1 = TC, P2 = TH, P3 = MV, P4 = ML, P5 = PLMS, P6 = PSMS, and P7 = S. The number of hidden neuron (n = 5) is determined through a trial and error procedure; normally, the smallest number of neurons that yields satisfactory results should be used. In this study, the backpropagation algorithm was used to train this neural network. The objective of the network training using the backpropagation algorithm was to minimize the network output error through determination and updating of the connection weights and biases. Backpropagation is a supervised learning algorithm where the network is trained and adjusted by reducing the error between the network and the targeted outputs. The neural

Table 6 Sample training and testing values of independent and dependent variables of CRM Binders.

N

TC (°C)

TH (h)

MV

ML (%)

PLMS (%)

PSMS (%)

S (MPa)

PI (mm)

N

TC (°C)

TH (h)

Mv

ML (%)

PLMS (%)

PSMS (%)

S (MPa)

PI (mm)

1

60 60 60 60 60 60 60 60 60 60 85 85 85 85 85 85 85 85 100 100 100 100 100 100 110 110 110 110 110

15

0.394

0.038

13.42

44.33

200

32

1

15

0.866

0.039

12.32

46.33

90.8

24

20

0.383

0.040

14.56

43.65

127

31

7

20

0.362

0.054

12.56

45.65

93.6

27

40

0.329

0.125

13.65

43.36

200

31

13

40

0.357

0.086

12.65

44.36

95.7

26

80

0.318

0.096

14.2

40.33

225

26

19

80

0.344

0.107

13.2

41.33

109

24

144

0.339

0.175

16.65

36.23

174

21

25

144

0.32

0.178

14.65

38.23

135

23

15

0.311

0.119

18.52

35.62

206

25

31

15

0.339

0.112

17.95

36.55

106

25

20

0.371

0.117

23.58

21

142

24

37

20

0.342

0.127

18.58

29

103

21

40

0.242

0.206

17.6

28.91

236

22

43

40

0.35

0.198

15.4

29.45

116

21

80

0.212

0.286

20.35

30.65

240

18

49

80

0.369

0.283

19.54

32.56

174

18

15

0.315

0.145

10.99

44.35

216

25

55

15

0.31

0.131

13.6

31.96

132

23

20

0.351

0.220

12.52

34.68

147

21

61

20

0.324

0.202

10.07

52.6

116

19

40

0.304

0.313

15.64

31.1

259

15

67

40

0.295

0.303

10.4

46.54

135

17

15

0.345

0.224

14.32

33.72

157

20

73

15

0.311

0.190

8.79

48.17

110

21

20

0.316

0.282

14.41

30.12

183

17

79

20

0.305

0.245

10

45.78

114

17

20

0.293

0.223

15.63

28.03

289

17

84

60 60 60 60 60 60 60 60 60 60 85 85 85 85 85 85 85 85 100 100 100 100 100 100 110 110 110 110 110

20

0.326

0.231

11.21

35.75

153

25

7 13 19 25 31 37 43 49 55 61 67 73 79 84

Note: TC: aging temperature; TH: duration time; MV: m-value; ML: mass loss; PLMs: and PSMS: percentage of LMS and SMS; S: stiffness; and PI: penetration index.

Note: TC: aging temperature; TH: duration time; MV: m-value; ML: mass loss; PLMs: and PSMS: percentage of LMS and SMS; S: stiffness; and PI: penetration index.

F. Xiao et al. / Construction and Building Materials 37 (2012) 248–256 Table 7 Sample training and testing values of independent and dependent variables of SBS binders.

253

outputs represents the error. The error is then propagated backward through the network, and the weights and biases are adjusted to minimize the error in the next round of prediction. The iteration continues until the error goal (tolerable error) is reached. It should be noted that a properly trained backpropagation network would produce reasonable predictions when it is presented with input not used in the training. This generalization property makes it possible to train a network on a representative set of input/output pairs, instead of all possible input/output pairs [25]. Many implementations of the backpropagation algorithm are possible. In the present study, the Levenberg–Marquart algorithm [26] is adopted for its efficiency in training networks. This implementation is readily available in popular software Matlab and its neural network toolbox [26]. In the present study, ANN is treated as an analysis tool, just like statistical regression method.

N

TC (°C)

TH (h)

Mv

ML (%)

PLMS (%)

PSMS (%)

S (MPa)

PI (mm)

1

60 60 60 60 60 60 60 60 60 60 85 85 85 85 85 85 85 85 100 100 100 100 100 100 110 110 110 110 110

15

0.59

0.053

15.35

45.86

132

21

20

0.384

0.066

13.52

38.56

140

24

40

0.333

0.096

14.56

32.88

169

22

80

0.34

0.137

14.25

31.22

198

24

144

0.32

0.174

14.56

30.22

222

18

15

0.31

0.115

14.23

31.56

121

24

20

0.344

0.108

25.58

18

155

23

40

0.31

0.195

10.39

34.07

221

17

4. Experimental results and discussions

80

0.28

0.294

16.88

27.55

251

15

4.1. Standard rheological properties

15

0.365

0.193

15.74

24.94

151

21

20

0.322

0.191

9.63

53.31

162

21

40

0.304

0.298

11.64

44.76

183

15

15

0.39

0.224

13.79

27.82

165

17

20

0.311

0.282

11.8

33.18

182

15

20

0.306

0.223

14.27

40.06

168

8

The performance of an asphalt binder at high service temperatures can be determined using a DSR testing and the complex shear modulus (G) and phase angle (d) of an asphalt binder. The G/sin d values, a parameter addressed the rutting related issues, obtained for the binders used in this research project is shown in Table 1. These values of control (A) and SBS (C) binders were tested at 64 °C and 76 °C, respectively, while those values of CRM (B) binders were measured at 64 °C and 76 °C. As shown in Table 1, the G/sin d values of CRM binder are significantly higher than those values of the control binder at 64 °C regardless of binder source. Moreover, at 76 °C these values are still slightly greater than 1.00 kPa, a minimum G/sin d value, clearly indicating the importance of crumb rubber in improving PG grade of asphalt binder. The loss modulus (Gsin d) value of the aged binder is strongly associated with the fatigue life of the mixture and is a basic parameter for describing the fatigue characteristics of an asphalt binder. The loss stiffness values, as shown in Table 1, were measured at a temperature of 25 °C after a standard PAV aging testing procedures (2070 kPa, 100 oC, and 20 h). The statistical analysis indicated that the Gsin d values of the CRM binders were significantly less than the control and SBS binders, regardless of binder source. Consequently, it was concluded that the crumb rubber is much beneficial in improving the fatigue resistance of the asphalt binder tested in this research project (see Table 2).

7 13 19 25 31 37 43 49 55 61 67 73 79 84

Note: Tc: Aging temperature; TH: duration time; MV: m-value; ML: mass loss; PLMs: and PSMS: percentage of LMS and SMS; S: stiffness; and PI: penetration index.

network training starts with the initiation of all of the weights and biases with random numbers. The input vector is presented to the network and intermediate results propagate forward to yield the output vector. The difference between the target and the network

Fig. 6. ANN calculation spreadsheet for control (PG 64-22) asphalt binder.

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1

Important Index

0.8 0.6 0.4 0.2 0 TC

TH

MV

ML

PLMS

PSMS

S

Input Variables

the dependent variable exhibits the different correlation values with the each of the independent variables (i.e. between PI and TC or other variables). In many cases, the Pearson correlation matrix analysis indicated the poorly correlated values can been found between the independent variables. Multiple linear regression analyses of these data were performed using Statistical Analysis System (SAS) with the Eq. (6). The coefficient value of each variable, as shown in Table 4, is noticeably different for three binders due to the different asphalt binder materials. The predicted and measured values of regression models for three binders are shown in Figs. 3a, 4a, and 5a. The coefficient of determination (R2) is 0.81 and the root mean squared error (RMSE) is 2.14 for control binder regression model (Fig. 3a). In this case, the predicted and measured penetration index values are close to 1:1 line (perfect match line). Fig. 4a presents that regression model of CRM binder has a low R2 of 0.40 and a RMSE value of 2.67. It can be noted that the predicted and measured values are not close to 1:1 line due to the poor model forecasting. The regression model of SBS binder shows that a good R2 value is 0.70 and a RMSE value is 2.23, respectively. The results indicated that the CRM model shows the poorest penetration index prediction amongst three binder models.

(a) 4.3. ANN model

1

Important Index

0.8 0.6 0.4 0.2 0 TC

TH

MV

ML

PLMS

PSMS

S

Input Variables

(b) 1

Important Index

0.8 0.6 0.4 0.2

The same data were used to develop the ANN models. The original dependent and independent data of control, CRM, and SBS binders are shown in Tables 5–7, respectively. In this study, the independent input variables included aging temperature (Tc), durations (TH), m-value (MV), mass loss (ML), the percentages of LMS (PLMS) and SMS (PSMS), and binder stiffness (S). The dependent output variable was selected to be the penetration index (PI). Among 84 data sets (containing three binder sources), 63 of them were selected as the training data set, and the other 21 were used as the testing data set. The sampling process is considered largely random, since no effort was made to keep track of the characteristics of input and output variable. While randomness in the data selection was largely maintained, the training data set is believed to be representative [28]. The completed ANN model, expressed in terms of the connection weights and biases in the three-layer topology (Table 8), can then be used to predict penetration index for any given set of data (Tc, TH, MV, ML, PLMS, PSMS, and S) using Eq. (7). Note that Eq. (7) can easily be implemented in a spreadsheet for routine applications. Although it takes time to develop the ANN model, use of the ANN-based spreadsheet model for calculating penetration index is simple and the execution is very fast. Fig. 6 shows an example ANN-based spreadsheet for control asphalt binder (PG 64-22). Similar spreadsheets for CRM and SBS are available but not present to save space. Figs. 3b, 4b, and 5b show the results obtained with the ANN models (in the form of Eq. (7)) for control, CRM, and SBS binders, respectively. Although different materials and testing conditions were used in the project, the predicting performance of the trained neural network, as shown in Figs. 3b, 4b, and 5b, is considered satisfactory and a significant improvement is achieved (in terms of R2 and RMSE) over those obtained by regression analyses as presented in Figs. 3a, 4a, and 5a. Yang and Zhang [29] suggested that the relative strength of the effect of an input variable on the output can be derived based on the weights stored in the trained neural network. They define the relative strength of effect (RSE) for each input variable on each output variable as follows:

RSE ¼ c

XX in in1



X W in k Gðkk ÞW in1 in Gðkin Þ    W i1 i2 Gðki1 Þ

ð9Þ

i1

0

TC

TH

MV

ML

P

LMS

PSMS

S

Input Variables

(c) Fig. 7. Important indexes of the variables in neural network analysis, (a) Control binder; (b) CRM binder; (c) SBS binder.

4.2. Regression model For a reliable regression model, the independent variables should be such that there should not be a strong correlation amongst them. Independent variables, if they were highly correlated, would weaken the prediction capability of the model, a problem referred to as multicollinearity [27]. However, for simple linear regression model, the dependent variables shall have the strong correlations with independent variables and thus yield stable regression coefficients and can efficiently improve the use of models for inference and forecasting. Pearson correlation analysis for three binders, as shown in Table 3, presents that the dependent variable (PI) generally has the strong correlation with other independent variables regardless of binder types. In Table 3, it can be noted that the correlation values between each of the independent variables are generally different for three binders; furthermore,

where c is the a normalized constant; Gðkk Þ ¼ expðkk Þ=ð1 þ expðkk ÞÞ2 ; Wik the weight of the connection between input variable i and neuron k of the hidden layer; P kk ¼ i fT W ik þ Bk ; BK bias at neuron k of the hidden layer; and fT the transfer function. The important indices for the seven input variables for three binders, Tc, TH, MV, ML, PLMS, PSMS, and S, was obtained and are shown in Fig. 7. However, these weights should be viewed only as a rough estimate, as they are determined based on the assumption that only one input variable at a time is allowed to vary although the developed ANN is highly nonlinear. The independent variables exhibit a noticeably different important index for three binders due to the difference in the base binders. It can be noted that aging temperature (Tc), duration time (TH), percentage of LMS (PLMS) and SMS (PSMS), and stiffness (S) are relatively more important, as shown in Fig. 7. The values of LMS and SMS are completely based on the asphalt binder sources, which is playing an important role in determining the light oil and asphaltene fractions. Consequently, asphalt binder is relatively important for this ANN model. Compared with other independent variables, m-value (MV) is relatively unimportant and reflected in the behavior of the developed ANN since MV only represents the rate of change in the creep stiffness versus loading time. Similarly, the result also indicates that mass loss (ML) is relatively unimportant in the developed ANN. One might consider that the ML only exhibits a very small percentage change during aging process, thus its effect on penetration index value is relatively low. As a result, in long-term aging, the penetration index is strongly correlated with those relatively important indexes and their test results can be used for predicting the aged level of asphalt binder.

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F. Xiao et al. / Construction and Building Materials 37 (2012) 248–256 Table 8 Weights and biases of the neural network defined in Eq. (7) for three binders. Weight

Bias

Wik (i = 7; k = 5) Input 1

Input 2

Input 3

Input 4

Input 5

Input 6

Input 7

Tc

TH

Mv

ML

PLMS

PSMS

S

wk

Bk

Bo

Onput neuron

Hidden layer

Output layer

Control

Hidden Hidden Hidden Hidden Hidden

neuron neuron neuron neuron neuron

1 2 3 4 5

21.929 1.780 60.213 12.794 0.847

22.605 3.530 2.242 13.330 0.147

6.558 97.389 1.189 4.468 0.122

8.047 33.002 2.570 6.655 0.004

28.984 18.803 6.574 7.559 0.844

14.160 33.150 11.233 9.923 0.001

2.818 77.218 3.025 3.851 0.139

2.661 1.130 4.020 3.774 69.080

13.539 52.130 19.805 8.909 1.855

7.899

CRM

Hidden Hidden Hidden Hidden Hidden

neuron neuron neuron neuron neuron

1 2 3 4 5

3.458 3.566 7.309 7.509 3.145

51.436 51.936 10.760 10.955 0.810

8.664 8.662 20.634 21.746 3.595

23.756 24.019 19.532 19.735 2.369

10.948 11.057 18.715 18.912 0.889

5.337 5.287 17.547 17.688 0.572

6.807 6.959 26.337 26.603 0.810

319.101 315.400 417.257 417.888 11.799

9.159 9.255 16.678 16.679 1.020

736.966

SBS

Hidden Hidden Hidden Hidden Hidden

neuron neuron neuron neuron neuron

1 2 3 4 5

4.149 229.027 93.830 0.460 3.683

7.425 216.547 37.289 5.128 17.482

1.017 58.937 186.369 1.337 14.228

3.859 9.725 49.010 1.533 8.048

3.295 13.272 19.348 3.331 10.573

0.158 11.965 209.657 0.526 0.686

1.718 12.545 171.109 1.238 6.585

40.567 39.308 1.025 63.046 1.561

7.340 235.495 126.650 6.098 2.069

78.377

Note: Tc: Aging temperature; TH: duration time; MV: m-value; ML: mass loss; PLMS: and PSMS: percentage of LMS and SMS; and S: stiffness.

5. Conclusions Artificial neural network is increasingly becoming an engineering tool for deriving data-driven predictive models. The developed ANN can easily be implemented in spreadsheet module for practical applications. Regardless of whether a straightforward neural network or a more sophisticated ANN is employed, the developed ANN must conform to the physical principles and/or behavior of a system it is intended to emulate. Based on the analysis of the experimental testing data of three asphalt binders after a long-term aging process, the following conclusions are reached: 1. Experimental data on the penetration index of three binders obtained in this study were used for model development. The results showed that the regression-based models were unable to predict the penetration index values of three binders accurately. 2. ANN approach, as a new modeling method used in this study, was developed for estimating the penetration index values of asphalt binder after a long-term aging process, and has been shown to be effective in creating a feasible predictive model. The established ANN-based models were able to predict the penetration index accurately, as evidenced by high R2 values and low RMSE regardless of the types of asphalt binders and test conditions. The results indicated that ANN-based models are more effective than the regression models. The ANN models can easily be implemented in a spreadsheet, thus making it easy to apply. 3. The analysis of the ‘‘importance’’ of variables show that the aging temperature, aging duration, percentage of LMS and SMS, and binder stiffness are the most important factors in the developed ANN model for prediction of penetration index. The m-value and mass loss of asphalt binders were found to be relatively unimportant compared to the other five independent variables.

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