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Viscosity prediction of CRM binders using artificialneural network approachFeipeng Xiao a , Bradley J. Putman a & Serji N. Amirkhanian aa Department of Civil Engineering , Clemson University , Clemson, SC, 29634, USAPublished online: 25 Jan 2010.

To cite this article: Feipeng Xiao , Bradley J. Putman & Serji N. Amirkhanian (2011) Viscosity prediction of CRMbinders using artificial neural network approach, International Journal of Pavement Engineering, 12:5, 485-495, DOI:10.1080/10298430903578903

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Viscosity prediction of CRM binders using artificial neural network approach

Feipeng Xiao*, Bradley J. Putman and Serji N. Amirkhanian

Department of Civil Engineering, Clemson University, Clemson, SC 29634, USA

(Received 12 May 2008; final version received 30 November 2009)

The primary objective of this study was to develop a series of artificial neural network (ANN) models to predict the viscosityvalues of crumb rubber-modified (CRM) binders using four input variables: asphalt binder source, rubber size, mixingduration and rubber content. The results indicated that ANN-based models are effective in predicting the viscosity values ofCRM binders regardless of rubber type and can easily be implemented in a spreadsheet. In addition, the developed ANNmodel can be used to predict viscosity values of other types of CRM binders. Furthermore, the results also show that asphaltbinder source, rubber size and rubber content are the most important factors in the developed ANNmodels while the mixingduration is relatively unimportant. The sensitivity analysis of input variables indicated that the viscosity changessignificantly with changes in asphalt binder source, rubber size and rubber content.

Keywords: artificial neural network; viscosity; rubber size; rubber content; mixing duration

1. Introduction

The recycling of scrap tyres has been of interest in the

asphalt industry throughout the world for over 40 years.

Currently, approximately 82% of the 299,000,000 scrap

tyres generated in the USA each year are utilised for

applications such as tyre-derived fuel, moulded products,

crumb rubber and other applications (RMA 2006). There

are many problems associated with the disposal of these

tyres including the banning of tyres from landfills in many

states. In addition, tyre piles create breeding grounds for

disease vectors such as mosquitoes. One solution to

alleviate the scrap tyre problem is to use them as crumb

rubber modifier (CRM) in asphalt binders (Bahia and Davis

1994; Raad and Saboundjian 1998; Airey et al. 2003;

Huang et al. 2004). The use of scrap tyres as CRM in asphalt

mixtures has been investigated since the early 1960s.

However, there has been some speculation between

researchers and engineers as to the optimum physical

characteristics that crumb rubber should exhibit for the

best performance as an asphalt binder modifier. This has

raised the need for more research in the specific area of

CRM binder specifications. When selecting crumb rubber

for the modification of asphalt, some of the factors that the

researcher/engineer must first consider include the type of

binder and crumb rubber to be used in the modification and

the percentage and size of rubber to be used in the mix. In

addition, the reaction time is an important factor that might

potentially affect the properties of the modified binder.

There are many factors that need to be considered

when determining the optimum combination of materials

for CRM binders. For example, each crude source is

different in chemical composition; therefore, each source

could exhibit different mechanical properties. In addition,

crumb rubber can be produced in almost any size from

large aggregate-sized particles to fine powder by employ-

ing different production methods (i.e. ambient shredding

or cryogenic grinding). With all of these factors

contributing to the performance of the CRM binder,

there is a need to develop CRM binder performance

models. It was the focus of a previous study to examine the

effects of these factors on the performance of CRM

binders produced by the wet process (Putman et al. 2005).

Previous researchers indicated that the mixing of crumb

rubber with conventional binders results in an improve-

ment in the resistance to rutting, fatigue cracking and

thermal cracking (McDonald 1966; Little 1986; Way

2003). Many researchers have found that utilising crumb

rubber in pavement construction is effective and

economical (Bahia and Davis 1994; Raad and Saboundjian

1998; Airey et al. 2003; Huang et al. 2004; Shen et al.

2006; Xiao et al. 2007; Thodeson et al. 2009).

The viscosity values of CRM binders involving a

number of interacting factors or engineering parameters

(variables) are not well predicted, and it is difficult to

define a concise relationship between the factors

(variables), or the problem is too complicated to be

described mathematically. Increasingly, modern pattern

recognition techniques such as neural network and fuzzy

systems are being considered to develop models from

data due to their ability to learn and recognise trends in

the data pattern. Artificial neural networks (ANNs) are

useful in place of conventional physical models for

ISSN 1029-8436 print/ISSN 1477-268X online

q 2011 Taylor & Francis

http://dx.doi.org/10.1080/10298430903578903

http://www.tandfonline.com

*Corresponding author. Email: feipenx@clemson.edu

International Journal of Pavement Engineering

Vol. 12, No. 5, October 2011, 485–495

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analysing complex relationships involving multiple

variables and have been successfully used in civil

engineering applications such as process optimisation,

slope stability analysis and deep excavation forecast

models (Goh 1994; Agrawal et al. 1995; Goh et al. 1995;

Juang and Chen 1999; Jen et al. 2002; Kim et al. 2004,

2005; Tarefder et al. 2005).

The objective of this study was to develop a series of

ANN models to predict the viscosity values of various

CRM binders at three mixing durations. The important and

sensitivity analyses of input variables were performed to

evaluate the influence of each independent variable on the

viscosity of CRM binders. The additional viscosity values

from other projects were used to validate the developed

ANN model in this study.

2. Experimental materials and test procedures

2.1 Materials

Two types of crumb rubber (i.e. ambient and cryogenic)

were included in this research, and they were shipped from

the crumb rubber manufacturer. In the factory, the ambient

crumb rubber was produced by first shredding tyres into

approximately 38–50mm chips, which were then passed

through cracker mills and shredded into smaller particles

at ambient temperature. The steel and fibre were separated

from the crumb rubber using magnets and blowers,

respectively. The crumb rubber was sized using screens.

The cryogenic production of crumb rubber began in a

similar manner as the ambient process, but then the tyre

chips were frozen with liquid nitrogen and ground to size

in a hammer mill. As with the ambient process, the steel

and fibre were removed and the crumb rubber was sized

using screens.

Three sizes of crumb rubber were evaluated for each

type of rubber [ 21.410mm (14 mesh), 20.595mm (30

mesh) and 20.425mm (40mesh)]. The gradation of each

crumb rubber is included in Table 1. It is important to note

that the only requirement regarding crumb rubber sizing

set by ASTM D5603 is that no more than 10% can be

retained on the designated sieve for crumb rubber

designated as 0.595mm and smaller. For example, a

20.595mm rubber shall have no more than 10% material

retained on the 0.595mm sieve. For sizes larger than

0.595mm, the requirement is that no more than 5% can be

retained on the designated sieve.

Three different asphalt binders were used in this study.

A PG 64-22 binder was obtained from two different

sources (referred to binders 1 and 2) and a PG 58-22 binder

was obtained from one source (referred to binder 3). The

properties of these binders are shown in Table 2.

Two crumb rubber contents were evaluated for each

type and size of crumb rubber (10 and 15% by weight of

the binder). This was an important factor to investigate as

the addition of crumb rubber has limits. To produce an

effective CRM binder, there is a minimum amount of

crumb rubber that must be added. On the other hand, there

is a maximum amount of crumb rubber that can be added

before the CRM binder becomes too viscous to apply and

use in the field.

Preliminary testing indicated that the most effective

method of mixing the crumb rubber with the asphalt binder

was to use a high-shear radial flow impeller at a speed of

700 rpm and a temperature of 1778C in the laboratory.

Each 600 g container of the binder was placed on a hot

plate and heated to 1858C. The binder was heated above a

blending temperature of 1778C to compensate for the heat

loss that resulted when adding the crumb rubber to the

binder. After the crumb rubber was added, the temperature

was stabilised at 1778C for the mixing duration. Three

mixing durations (15, 30 and 45min) were evaluated in

this study.

2.2 Viscosity testing

A Brookfield rotational viscometer was used to test the

viscosity of the CRM binders at 1358C in accordance with

AASHTO T316. A number 27 spindle and a specimen size

of 10.5 g were used for this study. However, there was one

modification made to this procedure. Instead of pouring all

Table 1. Gradation of crumb rubber.

Percentage passing (% by weight)

Ambient Cryogenic

Sieve size 1.410mm 0.595mm 0.425mm 1.410mm 0.595mm 0.425mm

No. 16 (1.180mm) 97.1 100.0 100.0 100.0 100.0 100.0No. 20 (0.850mm) 70.3 100.0 100.0 63.8 100.0 100.0No. 30 (0.595mm) 44.1 100.0 100.0 26.9 99.5 99.3No. 40 (0.425mm) 27.0 60.8 91.0 4.0 34.2 91.7No. 50 (0.300mm) 16.7 19.3 59.1 3.3 3.6 45.9No. 80 (0.180mm) 9.0 13.1 26.2 3.3 3.6 11.5No. 100 (0.150mm) 7.6 11.1 18.6 3.3 3.6 7.4

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four viscosity samples at the same time, one sample was

poured at a time to minimise settlement of the crumb

rubber in the specimen that could produce inaccurate

results. Prior to pouring each sample, the container of the

CRM binder was gently stirred for 1min to disperse the

crumb rubber throughout the binder.

3. Experimental model development

3.1 Statistical regression model

The viscosity–temperature susceptibility (VTS) method

of binder temperature susceptibility classification has been

used for a number of years (Griffith and Puzinauskas 1963;

Puzinauskas 1967). Although it has not been a popular

index value used for this purpose, it does inherently

possess a simple formulation (Rasmussen et al. 2002). One

basic definition of the VTS is

VTS ¼log½log ðhT2Þ�2 log½log ðhT1Þ�

log½T2�2 log½T1�; ð1Þ

where T1 and T2 are temperatures (degree Rankine) of the

binder at two known points and hT1 and hT2 are viscosities

(cP) of the binder at the same two points.

Fonseca and Witczak (1996) developed a new model

for the prediction of the dynamic modulus of HMA that

included the binder viscosity as an input variable. The

model included a calculation method for the binder

viscosity as a function of temperature and age. These

formulations were based on the VTS formula, as well as on

a second parameter, A. The A parameter is the y-axis

intercept of the log–log-viscosity and log-temperature

curves. The basic formulation for VTS and A is

log½logðhÞ� ¼, 1:0945 2 log½logðhÞ� ¼ Aþ VTS £ logðTÞ

$ 1:0945 2 log½logðhÞ� ¼ 1:0945

(;

ð2Þ

where h is the viscosity (cP); T, the temperature (8R) of the

binder; A, the intercept parameter and VTS, the slope

parameter.

In addition, previous research by Heukelon (1973)

presented relationships between penetration and viscosity

of asphalt binders, and established the rational explanation

of bitumen viscosity behaviour based upon the equiviscous

TRB (ring and ball softening point) temperature and

penetration by

logh

13; 000

� �¼

28:5 logðpen=800Þ

5:42 þ logðpen=800Þ; ð3Þ

where h is the viscosity (poise) and pen/800 is the value of

penetration (TRB).

However, these models are generally used for the

prediction of the virgin binder and cannot be used for

predicting the viscosity values of CRM binders as the

previous research.

3.2 ANN model

The neural network approach may be used to develop the

predictive models of the viscosity values of CRM binders

considering the interaction of complicated variables. In

this study, a three-layer feedforward neural network,

shown in Figure 1, was trained with the experimental data.

This architecture consists of an input layer (four

variables), a hidden layer (three 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

AT

RP

RS

T

Input layer Hidden layer Output layer

V

Error propagation

Figure 1. A schematic diagram of a three-layer ANN.

Table 2. Properties of three original binders.

Ageing states

Unaged RTFO PAV

Binder type SourceViscosity

(cP)G*/sin d, kPa

(648C)G*/sin d, kPa

(648C)G*/sin d, kPa

(258C)Stiffness, MPa

(2128C)m-Values(2128C)

PG 64-22 (1) Inman 395 1.28 2.87 3229 257 0.312PG 64-22 (2) Venezuela 585 2.03 4.94 1429 103 0.376PG 58-22 (3) Venezuela 330 1.66a 2.43a 1248 88 0.352

Notes: RTFO, rolling thin film oven; PAV, pressurised ageing vessel.a Tested at 588C.

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function to process the output. In this study, the

independent variables included asphalt binder types (AT),

rubber size (RS), mixing durations (T) and rubber

percentage (RP). The dependent variable was selected to

be the viscosity values of ambient and cryogenic CRM

binders (Va) and (Vc), respectively.

For the three-layer network shown in Figure 1, the

output of the network, the viscosity value (Va and Vc), is

calculated as follows (Juang and Chen 1999):

V ¼ f T B0 þXnk¼1

Wk · f T BHK þXmi¼1

WikPi

!" #( ); ð4Þ

where B0 is the bias at the output layer; Wk, 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, the transfer function,

defined as

f ðTÞ ¼1

1 þ e2t: ð5Þ

In Equation (4), the number of input variables (m) is 4; the

input variables (defined previously) areP1 ¼ AT,P2 ¼ RS,

P3 ¼ T and P4 ¼ RP. The number of hidden neurons

(n ¼ 3) 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

minimise 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

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 outputs

represents the error. The error is then propagated backward

through the network, and the weights and biases are

adjusted to minimise 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 generalisation property makes it

possible to train a network on a representative set of

input/output pairs, instead of all possible input/output pairs

(Chen 1999; Xiao et al. 2009; Gandhi et al. 2009).

Many implementations of the backpropagation algor-

ithm are possible. In the present study, the Levenberg–

Marquardt algorithm is adopted for its efficiency in

training networks (Demuth and Beale 2003). This

implementation is readily available in the popular software

Matlab and its neural network toolbox (Demuth and Beale

2003). In the present study, ANN is treated as an analysis

tool, just like statistical regression methods.

4. Experimental results and discussions

4.1 Viscosity properties of CRM binders

The results of the viscosity testing are illustrated in

Figures 2 and 3. It is evident from these results that the

addition of crumb rubber to an asphalt binder has a

significant impact on the binder’s viscosity, as expected.

In general, each of the variables (i.e. crumb rubber content,

type, size and binder source) had an effect on the viscosity

of the CRM binders. Crumb rubber content was deemed as

having the most influence on the viscosity. For each binder

source, the CRM binders containing 15% crumb rubber

(Figures 2(b) and 3(b)) had significantly higher viscosities

than those modified with 10% crumb rubber (Figures 2(a)

and 3(a)), as expected.

Figure 2. Viscosity analyses of ambient rubber regardingmixing duration: (a) 10% rubber and (b) 15% rubber.

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Figures 2 and 3 indicate that the type of crumb rubber

also has a significant effect on the viscosity of the CRM

binders. In all cases, the ambient crumb rubber produced

higher viscosities than the cryogenic crumb rubber of

the same size and content. This has been attributed to the

increased surface area of crumb rubber produced by the

ambient method as compared to the cryogenic method.

Crumb rubber size had an effect on the viscosity, but

the trends were not as expected. It was expected that the

finer crumb rubber would produce higher viscosities due to

the increased surface area. This was not necessarily the

case. However, for the ambient crumb rubber, the 20.425

and 21.410mm crumb rubber resulted in the higher

viscosity than the 20.595mm crumb rubber for all of the

binders. For the cryogenic crumb rubber, at the 10% crumb

rubber content, there was no significant difference among

the three sizes of the crumb rubber; however, there was not

a repeating trend at the 15% crumb rubber content. This

might be the effect of cryogenic rubber gradation on the

surface area of the experimental samples.

The source of the asphalt binder also had an effect on

the CRM binder. This is evident as the CRM binder made

with binder 2 (PG 64-22) showed a higher increase in

viscosity over the control than the CRM binder made with

binder 1 (PG 64-22). In addition, in some cases, binder 3

(PG 58-22) produced CRM binders with viscosities higher

than binder 1. This demonstrates that the crude source does

affect the performance of CRM binders. Figures 2 and 3

show that, in most cases, the viscosity values at various

mixing durations (15, 30 and 45min) do not exhibit

significant differences for each type of crumb rubber.

These relationships are considered likely due to the

physical and chemical properties of different binder

sources at the various mixing conditions. Previous

research projects also indicted that, in general, the

viscosity values do not have an obvious change as the

reaction time increases from 15 to 45min (Putman 2005;

Putman et al. 2005; Xiao 2006).

4.2 ANN model

The viscosity values were used to develop the ANN

models. The original dependent and independent data of

CRM binders are shown in Table 3. In this study, the

independent variables included AT, RS, T and RP, and the

dependent variable was selected to be the Va and Vc.

Among 216 data-sets (containing three binder sources),

162 of them were selected as the training data-set and the

other 54 were used as the testing data-set. The whole ANN

model used a goal error of 0.00001 and an epoch of 1000 in

this study. The sampling process is considered largely

random, because no effort was made to keep track of the

characteristics of input and output variables. While

randomness in the data selection was largely maintained,

the training data-set is believed to be representative

(Kuang et al. 2007; Xiao and Amirkhanian 2009).

The developed ANN model, expressed in terms of the

connection weights and biases in the three-layer topology,

can then be used to predict viscosity values for any given

set of data (AT, RS, T and RP) using Equation (4). Note that

Equation (4) can easily be implemented in a spreadsheet

for routine applications. The spreadsheets for ambient and

cryogenic CRM binders are shown in Tables 4 and 5,

respectively. Although it takes time to develop the ANN

model, use of the ANN-based spreadsheet model for

calculating the penetration index is simple and the

execution is very fast. Figure 4 shows the results obtained

with the ANN models (in the form of Equation (4)) for

ambient and cryogenic binders. The coefficient of

determination (R 2) values of the ANN viscosity model

using ambient rubber are 0.97 and 0.96 for training and

testing data-sets, respectively. The root mean squared

errors (RMSE) value of this model is 149.3. For cryogenic

rubber, the ANN model has a R 2 value of 0.97 for both the

training and testing data-sets while the RMSE value is

339.1. Although different materials and testing conditions

were used in this work, the predicting performance of the

trained neural network, as shown in Figure 4, is considered

satisfactory.

Figure 3. Viscosity analyses of cryogenic rubber regardingmixing duration: (a) 10% rubber and (b) 15% rubber.

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4.3 Sensitivity analysis of the ANN model

Due to the highly complex and non-linear form of analysis

of ANN, additional sensitivity analysis was conducted to

estimate the impact of input variables on the output, Va and

Vc. During the sensitivity analysis process, one input

parameter was changed slightly (approximately ^ 5 to

10%) from the initial condition, while the remaining

parameters were kept constant, and then the predicted

viscosity value was determined. Further modification of

Table 3. Sample training and testing data of rubberised asphaltbinders.

No. AT typeRS

(mm)T

(min)RP

(%)Va

(cP)Vc

(cP)

1 1 0.42 15 10 1300 945. . . 1 . . . . . . . . . . . . . . .5 1 0.42 30 10 1270 1145. . . 1 . . . . . . . . . . . . . . .9 1 0.42 45 10 1265 1120. . . 1 . . . . . . . . . . . . . . .13 1 0.595 15 10 1530 1085. . . 1 . . . . . . . . . . . . . . .17 1 0.595 30 10 1930 1080. . . 1 . . . . . . . . . . . . . . .21 1 0.595 45 10 1900 1015. . . 1 . . . . . . . . . . . . . . .25 1 1.41 15 10 1705 1315. . . 1 . . . . . . . . . . . . . . .29 1 1.41 30 10 1470 1190. . . 1 . . . . . . . . . . . . . . .33 1 1.41 45 10 1525 1205. . . 1 . . . . . . . . . . . . . . .37 1 0.42 15 15 2580 2040. . . 1 . . . . . . . . . . . . . . .41 1 0.42 30 15 2625 1900. . . 1 . . . . . . . . . . . . . . .45 1 0.42 45 15 3355 2005. . . 1 . . . . . . . . . . . . . . .49 1 0.595 15 15 3395 1470. . . 1 . . . . . . . . . . . . . . .53 1 0.595 30 15 4295 1735. . . 1 . . . . . . . . . . . . . . .57 1 0.595 45 15 3505 1740. . . 1 . . . . . . . . . . . . . . .61 1 1.41 15 15 3075 1555. . . 1 . . . . . . . . . . . . . . .65 1 1.41 30 15 3255 1675. . . 1 . . . . . . . . . . . . . . .69 1 1.41 45 15 3040 1745. . . 1 . . . . . . . . . . . . . . .72 1 1.41 45 15 3490 204073 2 0.42 15 10 2425 1755. . . 2 . . . . . . . . . . . . . . .144 2 1.41 45 15 8210 3580145 3 0.42 15 10 2425 1320. . . 3 . . . . . . . . . . . . . . .216 3 1.41 45 15 4570 2610

Notes: AT, asphalt type; RS, rubber size; T, mixing duration; RP, rubber percentage;Va, viscosity of the ambient rubberised binder; Vc, viscosity of the cryogenicrubberised binder.

Table

4.

SpreadsheetoftheANN

model

foram

bientrubberised

binders.

AB

CD

EF

G

2CommandsofexecutingEquation(4)

Hidden

layer

3Argument(“A

T”,

“RS”,

“T”,

“RP”)

Weightmatrix

Hidden

1Hidden

2Hidden

34

Bias

213.94510

23.19001

4.40104

5A

T¼

ðAT2

0:7

5Þ=

2:5

;RS¼

ðRS2

0:2

96Þ=

1:2

38

Input1

251.90254

21.57437

29.71416

6T¼

ðT2

11:2

5Þ=

37:5

;RP¼

ðRP2

0:5

91Þ=

6:2

39

Input2

62.75759

26.97809

23.22539

7Input3

220.95531

0.78062

20.16226

8p

i1¼

1=ð1

þE

XPð2

ðAT*

D$5þR

S*

D$6þ

T*

D$7þR

P*

D$8þ

D$4)))

Input4

45.78655

20.41937

6.63828

9 10

pi2

¼1=ð1

þE

XPð2

ðAT*

E$5þ

RS*

E$6þ

T*

E$7þ

RP*

E$8þ

E$4)))

Outputlayer

11

Bias

23.89830

Weightmatrix:

CellsD4:F4areBHK

CellsD5:F8areW

ik

12

pi3

¼1=ð1

þE

XPð2

ðAT*

F$5þ

RS*

F$6þ

T*

F$7þR

P*

F$8þ

F$4)))

Hidden

11.23473

13

Hidden

22.37434

14

Hidden

31.87631

15

Z¼

pi1*

D1

2þ

pi2*

D1

3þ

pi3*

D1

4þ

D1

1Weightmatrix:

CellsD11isBo

CellsD12:D14areW

ik

16

Z¼

1=ð1

þE

XPð2

ZÞÞ

CellsB3:B18are

macro

commandsto

execute

Equation(4)

17

LnðFÞ¼

40

87:5*

Zþ

36

1:2

518

Return

(F)

Notes:A

T,

asphal

tty

pe;

RS,

rubber

size

;T,

mix

ing

dura

tion;R

P,

rubber

per

centa

ge.

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the parameter consequently yielded an increase or

decrease in the predicted viscosity value. This process

was repeated for all input variables or modification

thereof, as well as each case. The input variables (AT, RS, T

and RP) were considered in the sensitivity analysis of the

viscosity model for ambient and cryogenic rubber.

Figures 5 and 6 show the relative changes in both input

and output parameters. The output variable data-set (Va

and Vc) was segregated into several groups in terms of

predicted and measured results while plotting the trend

curves. This segregation of expected ranges of viscosity

values illustrates the non-linearity of the proposed models

and the performance of the output at various viscosity

values. For example, the viscosity values were grouped

into 0–2000, 2000–4000, 4000–6000 and .6000 cP

categories based on the range of viscosity values for

ambient rubber. The change in the input variable values

was dependent on the category. This method will facilitate

visualisation of the relationship between input and

corresponding output (i.e. a relative change in an input

parameter will yield a relative change in the viscosity

value; Danzer 1999).

As shown in Figure 5, changes in input variables (AT,

RS, T and RP) result in changes in output values for the

CRM binders containing ambient rubber. Figure 5(a)

indicates that changes in some of the binders yield

noticeable changes in viscosity value. The viscosity values

also change significantly as the binder source changes for

cryogenic rubber (Figure 6(a)). As described previously

(Figures 2 and 3), the same conclusions that binder source

significantly affects the viscosity values are obtained using

the ANN model sensitivity analysis.

As shown in Figure 5(b), the change in rubber size

generally results in a slight change in the viscosity values

for ambient CRM binders. There is not a significant trend

obtained in all of the four categories. However, for

cryogenic rubber, the percentage change in viscosity value

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000

Measured viscosity (cP)

Pred

icte

d vi

scos

ity (

cP)

Training data Testing data

Training: R2 = 0.97

Testing: R2 = 0.97

RMSE = 339.1

0

1000

2000

3000

4000

5000

0 1000 2000 3000 4000 5000

Measured viscosity (cP)

Pred

icte

d vi

scos

ity (

cP)

Training data Testing data

Training: R2 = 0.97

Testing: R2 = 0.96

RMSE = 149.3

(a) (b)

Figure 4. Comparison of measured and predicted viscosity values of ANN models: (a) ambient rubber and (b) cryogenic rubber.

Table 5. Spreadsheet of the ANN model for cryogenic rubberised binders.

A B C D E F G

2 Commands of executing Equation (4) Hidden layer3 Argument(“AT”, “RS”, “T”, “RP”) Weight matrix Hidden 1 Hidden 2 Hidden 34 Bias 6.263 0.100 21.2685 AT ¼ ðAT 2 0:75Þ=2:5;RS ¼ ðRS 2 0:296Þ=1:238 Input 1 2.958 56.574 242.7966 T ¼ ðT 2 11:25Þ=37:5;RP ¼ ðRP 2 0:591Þ=6:239 Input 2 20.515 22.178 2116.2097 Input 3 0.023 0.120 22.0988 pi1 ¼ 1=ð1 þ EXPð2ðAT*D$5 þ RS*D$6 þ T*D$7 þ RP*D$8þ

D$4)))Input 4 22.136 26.130 2119.710

910 pi2 ¼ 1=ð1 þ EXPð2ðAT*E$5 þ RS*E$6 þ T*E$7 þ RP*E$8þ

E$4)))Output layer

11 Bias 1311.526 Weight matrix:

12 pi3 ¼ 1=ð1 þ EXPð2ðAT*F$5 þ RS*F$6 þ T*F$7 þ RP*F$8þF$4)))

Hidden 1 21335.369 Cells D4: F4 are BHK

13 Hidden 2 19.080 Cells D5: F8 are Wik

14 Hidden 3 2.66415 Z ¼ pi1*D12 þ pi2*D13 þ pi3*D14 þ D1116 Z ¼ 1=ð1 þ EXPð2ZÞÞ Cells B3:B18 are

macro commands to

execute Equation (4)

Weight matrix:

Cells D11 is Bo

Cells D12: D14 are Wik17 LnðFÞ ¼ 9668:75*Z þ 288:125

18 Return (F)

Notes: AT, asphalt type; RS, rubber size; T, mixing duration; RP, rubber percentage.

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increases as the percentage change in the rubber size

increases (Figure 6(b)).

Results of the sensitivity analysis on the mixing

duration of CRM binders performed in this study are

presented in Figures 5(c) and 6(c) for the ambient and

cryogenic crumb rubbers, respectively. The results

indicate that the increase in the mixing duration generally

does not result in a remarkable change in the magnitude of

the viscosity value for the two types of crumb rubber. The

previous statistical analyses showed similar results. The

reason is that the absorption and the swelling of crumb

rubber in the CRM binder occur quickly at a high

temperature, and thus its viscosity value does not have a

significant change (Airey et al. 2003; Putman et al. 2005;

Xiao et al. 2007).

Similar sensitivity analyses were performed for the

rubber content of the two crumb rubbers. As shown in

Figures 5(d) and 6(d), it can be noted that, as expected, the

–80

–40

0

40

80

–80–40

04080

120160200

0

200100

–100

400300

600500

(a)

–100 –50 0 50 100

Per cent change in AT

–60 –30 0 30 60

Per cent change in RS

–60 –30 0 30 60

Per cent change in T

–60 –30 0 30 60

Per cent change in RP

Per

cent

cha

nge

invi

scos

ity

(b)

Per

cent

cha

nge

invi

scos

ity

–80

–40

0

40

80(c)

Per

cent

cha

nge

invi

scos

ity

(d)

Per

cent

cha

nge

invi

scos

ity

0–1500 cP; 1500–3000 cP; 3000–4500 cP

Figure 6. Sensitivity analyses of input variables for the cryogenic rubberised binder. AT, asphalt type; RS, rubber size; T, mixingduration; RP, rubber percentage.

–80

–40

0

40

80(a) (b)

(d)(c)

–80

–40

0

40

80

–100 –50 0 50 100 –60 –30 0 30 60Per cent change in AT

–60 –30 0 30 60

Per cent change in T

Per cent change in RS

–60 –30 0 30 60

Per cent change in RP

Per

cent

cha

nge

invi

scos

ity

–80

–40

0

40

80

Per

cent

cha

nge

invi

scos

ity

Per

cent

cha

nge

invi

scos

ityPe

r ce

nt c

hang

e in

visc

osity

–80–40

04080

120160200

0–2000 cP; 2000–4000 cP; 4000–6000 cP; >6000 cP

Figure 5. Sensitivity analyses of input variables for the ambient rubberised binder. AT, asphalt type; RS, rubber size; T, mixing duration;RP, rubber percentage.

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increase in rubber percentage generally results in the

increase in viscosity values for each rubber.

4.4 Important index analysis of the ANN model

Yang and Zhang (1997) 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 network.

They defined an important index to express the degree of

sensitivity for each input variable on the output. Following

the procedures described by Yang and Zhang (1997), the

important indices for the four input variables, AT, RS, T and

RP, were obtained and are shown in Figure 7. However,

these weights should be viewed only as a rough estimate,

as they are determined based on the same assumption that

only one input variable at a time is allowed to vary

although the developed ANN is highly non-linear.

The independent variables exhibit a noticeably

different important index for the two crumb rubber types

due to the difference in the base binders. It can be noted

that asphalt binder source (AT), rubber size (RS) and

percentage of rubber (RP) are relatively more important, as

shown in Figure 7. Compared with other independent

variables, mixing duration (T) is relatively unimportant

and reflected in the behaviour of the developed ANN since

the mixing duration (15, 30 and 45 min) does not

noticeably affect the viscosity values of the two CRM

binders. One might consider that the T only exhibits a very

small percentage change during the mixing process, thus

its effect on the viscosity value is relatively low. As a

result, the viscosity value is strongly correlated with those

relatively important indices and their test results can be

used for predicting the viscosity values of the CRM binder.

4.5 Validation of the ANN model

The viscosity values from a previously conducted study

were used to validate the developed ANN model (Putman

2005). Those validation data came from the various

research projects (i.e. various materials and mixing

procedures; Table 6). Three input variables, AT, RS and

RP, were determined based on the given information. The

input variable, T, used 30 min as the input value. Using the

developed model, viscosity values were then calculated and

compared with the measured data. Figure 8 shows the

measured values from Putman (2005) and those predicted

values by the developed ANN model. The results show that,

in general, the viscosity values for ambient and cryogenic

rubber binders can be predicted by the developed ANN

since the measured and predicted values have the R 2 values

of 0.67 and 0.46 and the RMSE values are 883 and 902,

respectively.

5. Conclusions

Based on the ANN analysis of the experimental testing

data in this study, the following conclusions were reached:

(1) The conventional statistical analysis indicates that the

asphalt binder source, rubber size and rubber content

have an effect on the viscosity values of CRM binders

while the mixing duration does not exhibit a

significant effect.

(2) An ANN approach, as a new modelling method used

in this study, was developed for estimating the

0

0.2

0.4

0.6

0.8

1

1.2

Input variable

Impo

rtan

t ind

ex

AT TRS RP

Input variable

AT TRS RP

0

0.2

0.4

0.6

0.8

1

1.2

Impo

rtan

t ind

ex

(a) (b)

Figure 7. Important index of input variables: (a) ambient rubber and (b) cryogenic rubber.

Table 6. Validation viscosity data-sets of binders.

AT type RS (mm) T (min) RP (%) Va (cP) Vc (cP)

1 0.85 30 10 2330 18601 0.425 30 10 2560 17301 0.18 30 10 2710 –1 0.85 30 15 – 32301 0.425 30 15 – 29602 0.85 30 10 1550 14702 0.425 30 10 1410 11302 0.18 30 10 1450 10802 0.85 30 15 2830 –2 0.425 30 15 3520 –2 0.18 30 15 3890 –3 0.85 30 10 1470 12503 0.425 30 10 1360 17303 0.18 30 10 1460 10703 0.85 30 15 3050 21703 0.425 30 15 3510 20003 0.18 30 15 3800 1970

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viscosity values of CRM binders, and has been shown

to be effective in creating a feasible predictive model.

The established ANN-based models were able to

predict the viscosity accurately, as evidenced by high

R 2 values and low RMSE regardless of the types of

asphalt binders and test conditions. The ANN models

can easily be implemented in a spreadsheet, thus

making it simple to apply.

(3) The important indices of the four input variables were

calculated using the method developed by Yang and

Zhang. The results show that the asphalt binder

sources, rubber size and rubber percentage are the

most important factors in the developed ANN model

for the prediction of viscosity values regardless of

crumb rubber types. The mixing duration was found

to be relatively unimportant compared to the other

three independent variables.

(4) The developed ANN is shown to be able to

satisfactorily predict the viscosity values as evi-

denced by the results of validation using the viscosity

values from other research projects.

Acknowledgement

The financial support of the South Carolina Department of Healthand Environmental Control (SC DHEC) is greatly appreciated.However, the results and opinions presented in this paper do notnecessarily reflect the view and policy of the SC DHEC.

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(a) (b)

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