Modeling Viscosity Behavior of CRM Binders.pdf

8/14/2019 Modeling Viscosity Behavior of CRM Binders.pdf

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Modeling Viscosity Behavior of Crumb Rubber Modified Binders

Carl Thodesen1, Feipeng Xiao

2*, and Serji N. Amirkhanian

3

1

Senior Civil Engineer, ECOPATH Industries, 14821 N. 43rd Street, Scottsdale, AZ, 85260,Tel.:+001 480 990 7623, Fax: +001 480 991 0314, E-mail: [email protected]

2*Research Assistant Professor, Asphalt Rubber Technology Service (ARTS), Department of

Civil Engineering, Clemson University, Clemson, SC 29634-0911, Tel.: +001 864 656 6799;

Fax: +001 864 656 6186; E-mail: [email protected]

3Professor, Department of Civil Engineering, Clemson University, Clemson, SC 29634-0911,

Tel.: +001 864 656 6799; Fax: +001 864 656 6186; E-mail: [email protected]

Abstract

Accurately predicting the viscous properties of crumb rubber modified (CRM) binders has

proven difficult, especially as these properties tend to vary with changing crumb rubberconcentrations and temperatures. This study explores the utilization of the statistical regression

and neural network (NN) approaches in predicting the viscosity values of CRM binder at various

temperatures (135oC and greater). A total of 53 CRM binder combinations were prepared from

two different rubber types (ambient and cryogenic), three different binder sources, four rubber

concentrations (0%, 5%, 10%, and 15%), and five crumb rubber gradations (ADOT, SCDOT,

0.18mm, 0.425mm, and 0.85 mm). The results indicated that the regression model is easy to use

and can be used for viscosity prediction, similarly NN-based models also provided accurate for

predictions for the viscosity values of CRM binders regardless of rubber type and can easily beimplemented in a spreadsheet. In addition, the developed NN model can be used to predict

viscosity values of other types of CRM binders efficiently. Furthermore, the sensitivity analysisof input variables indicated that the changes of viscosity are significant as the changes of asphalt

binder grade, test temperature, and rubber content. The results also show that these three

independent variables are the most important factors in the developed NN models in comparison

with other variables.

Keywords:Crumb rubber, Viscosity, Regression, Artificial neural network, Important index

*: Corresponding Author


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Introduction

The ability to predict a materialsbehavior provides the materials designer with an important tool

in developing future products. Moreover, this capacity also provides information with regards to

the relative importance of each variable with respect to the overall material performance. Crumb

rubber modified (CRM) binder is one such material whose properties are dependent on variables

such as crumb rubber concentration and temperature. This modification of asphalt has been

found effectively in improving the flexible pavements resistance to permanent deformation.

Many studies indicate that adding crumb rubber to asphalt binder increases its viscosity and

resistance to high temperatures [1-3].

The effects of crumb rubber grinding method are also relevant with respect to CRM

binder properties. The principal difference between rubber particles produced using the

cryogenic and ambient procedures lies in the shape of the resulting particle. Crumb rubber

produced using cryogenic means tends to exhibit a smooth surface, comparable to shattered

glass. Ambient grinding tends to yield particles with a rougher surface, thus producing greater

surface area than cryogenic particles. Studies have shown that ambient ground crumb rubber

typically produces greater effects on the CRM binder properties [3-6].

AASHTO T 316 is the commonly used the Strategic Highway Research Program (SHRP)

procedure for evaluating asphalt binder viscosity. Achieving asphalt viscosity requirements is of

utmost importance for ease of pumping as asphalt is generally stored in asphalt plants at

temperatures between 149oC and 177

oC depending on the grade or viscosity [7]. However,

fulfilling these requirements becomes more difficult with the increasing viscosity due to

modification of the binder by crumb rubber [8] as well as the specifications established by SHRP

indicating that asphalt viscosity should not exceed 3.0 Pa.s at 135oC [9].


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Research has shown that CRM asphalt binder viscosity increases as crumb rubber

concentration is increased, regardless of crumb rubber type. Non-Newtonian behavior of the

CRM binders was also shown to be more pronounced with increasing amounts of rubber. The

same study also concluded that lower viscosity asphalt increases the rate of the modified binder

reaction when compared to higher viscosity binders from the same source [10].

All combinations of crumb rubber and binder produce a uniquely modified binder. The

resulting viscosity increases due to absorption of the aromatic oil causing the swelling of the

rubber particles. It has been shown that the increase in rubber concentration yielded significant

increase in viscosity [10]. Viscosity of CRM binder is known to be dependent on crumb rubber

content [8], particle size and processing method [11], mixing temperature and duration [12], and

rubber type (passenger tire or truck tire) [13].

Due to these complicated parameters, the viscosity values of CRM binders 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 are being considered to develop models from data

to their ability to learn and recognize trends in the data pattern. Statistical viscosity prediction

regression model developed by Thodesen [14] was proved effective. Recently, Neural Networks

(NN) 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 [15-

20].

The objective of this study was to develop the regression and a series of NN models to

predict the viscosity values of various CRM binders. The important and sensitivity analyses of


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input variables were performed in NN to evaluate the influences of each independent variable on

the viscosity of CRM binders. Additional viscosity values from previously untested materials

were used to validate the developed regression and NN models in this study.

Materials and Data Collection

The first study used two binder sources (A and B) which were blended with 4 different CRM

sources. Both binder sources were PG 64-22, and were each reacted for 30 minutes at 177oC at

5, 10, 15, and 20 % CRM by weight of binder. All crumb rubber used in this study fell within

consistent specifications for crumb rubber (Table 1), two crumb rubber sources utilized

cryogenic grinding while the other two were obtained through ambient grinding.

The second study was performed using all three binder sources (Table 2); all three binder

sources were PG 64-22, and were each reacted for 30 minutes at 177oC at 10 and 15 % CRM by

weight of binder. In this case two crumb rubber sources were tested; one cryogenic and one

ambient ground. However, in this study the crumb rubber was separated into different sizes and

the effects of particle size studied, the sizes studied were 0.18, 0.425, and 0.85 mm. All testing

was performed on a Brookfield viscometer between the temperatures of 135-180oC.

During the model development stage a total of twelve (Binder code: A-L) base asphalt

binders were evaluated. In addition, during verification five other asphalt binders (Binder code:

M-Q) were evaluated. The binders were selected from many sources to determine the effects of

geographic locations of the binders. On some occasions, the same binder source was evaluated

over several months to determine if the binder properties were maintained over time. Table 3

provides a description of the binders used in this study. The test dates and test locations are also


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given in order to provide a description of the various dates and locations the binders were

evaluated.

The gradation of the crumb rubber sources was highly varied and therefore, five different

gradations were evaluated. The gradations were: Arizona Department of Transportation (ADOT)

and South Carolina Department of Transportations (SCDOT) specifications, 0.850 mm, 0.425

mm, and 0.180 mm. This range of gradations provides both coarse and fine gradations, as well as

individual coarse and fine crumb rubber particles. The SCDOT and ADOT gradations are given

in Table 4.

Crumb rubber data was available for twelve different types of crumb rubber (Table 5).

The variables that were varied for the crumb rubbers included: production location, grinding

procedure, gradation, and tire type. As described in later chapters, many of the crumb rubber

sources were added to various asphalt binders at concentrations ranging between 5 and 20% by

weight of binder.

The 600 g samples were stored in sealed individual quart cans at room temperature until

they were blended with the crumb rubber. Prior to blending, the specified binder cans were

placed in a 163oC oven for approximately 75 minutes. The wet process was used when reacting

the crumb rubber with the binders. The mechanical mixer used was a high shear 50.8 mm

diameter radial flow impellor; appropriate crumb rubber concentrations were used to react the

materials using a reaction time of 30 minutes while maintaining a constant binder temperature of

177oC and speed of 700 rpm. This temperature was selected as it is a common temperature used

to produce CRM binders in the field in South Carolina. Upon completion of blending the crumb

rubber with the binder, the can of CRM binder was sealed and allowed to cool for 24 hours at

room temperature prior to testing.


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AASHTO T316 was used when determining the viscosity at 135oC. During this

procedure 8.5 grams of asphalt binder is poured into a standard Brookfield Viscometer test tube,

the test tube and asphalt were then placed in temperature control device and the desired

temperature selected. The appropriate spindle was selected (#21 for virgin binder), attached to

the viscometer, and then submerged in the test tube to the specified depth. The sample was then

allowed to heat up for 20 minutes, followed by 10 minutes of the spindle rotating at 20 RPM.

Finally, three viscosity measurements are recorded at one minute intervals (AASHTO, 2006).

It should be noted that when CRM binder samples were used 10.5 gram samples were

used instead of 8.5 grams samples, subsequently a smaller spindle size (#27) was also selected.

Careful attention was placed on ensuring that the CRM binder samples were well mixed prior to

pouring into the test tube tested at various temperatures (135, 150, 170, and 190C).

Viscosity Model Development

Regression Model

The regression model was developed in two parts; first, the effects of the addition of

crumb rubber to the virgin binders were studied. Once a working model was developed for the

addition of the crumb rubber to the virgin binders, the model for temperature variation was

developed. Such a division assumes that once the binder viscosity is set at 135oC, binder

viscosities will vary with temperatures greater than 135oC in the same fashion. Therefore, the

starting point for the model is described by Equation (1), given by:

, 0,135( )( )x t Rubber Factor Temperature Factor (1)

Where,x,t is the viscosity with rubber contentx at temperature t, and 0,135is the neat binderviscosity at 135

oC.


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The rubber factor was considered first because preliminary experimental results indicated

that when crumb rubber was added to the binder, the asphalt viscosity consistently increased. It

was seen that viscosity ratio change with respect to crumb rubber percent followed an

exponential trend [14]. The Rubber Factor in the model has the form given in Equation (2):

CVR x

x e (2)

Where,Rcvis the rubber coefficient for viscosity andxis the rubber content.

The effect of temperature on binders was also studied; here too the asphalt binder

viscosity was normalized. However, in this case the viscosity at 135oC was used as the reference.

A temperature of 135oC is commonly used by many testing agencies as the reference for

Brookfield viscometer viscosity measurements.

The Arrhenius equation was used as the starting point of establishing the temperature

factor component of the model. The Arrhenius equation is used for modeling viscous behavior

of thermo-rheologically simple materials; thermo-rheologically simple materials are those

materials whose chemical structure is stable at the testing temperatures (135-210oC). The form of

the Arrhenius equation is given in Equation (3):

aE

Rt

t Ae (3)

Where, t: Viscosity of the asphalt binder at temperature t; A:Constant;Ea: Activation energy;R: Universal gas constant (8.314 J.mol

-1.K

-1).

The model was normalized by allowing the viscosity to be predicted at a desired

temperature (Equation (4)):

t

t Ae

(4)


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Where,Aand:Constants; t:Temperature in degrees Celsius

The rubber and temperature factors (Equations (2) and (4)) were combined to produce

Equation (5):

, 0,135( )( )CVR x t

x t e Ae

(5)

Since the values for 0,135andRcvare known constants which have been previously derived, only

the values for parametersAandneed to be estimated. The method of nonlinear least squares

was used to estimate the parameters A and . All calculations were performed using the

Statistical Analysis System (SAS) procedure, whereby a nonlinear regression model was fitted to

the data.

NN models

The neural networks approach was used to develop the predictive models of the viscosity

values of asphalt mixtures considering the interaction of complicated variables. In this study, six

parameters from asphalt binder, crumb rubber, and test conditions (e.g. asphalt binder source

(Bs), binder grade (G), rubber source (Rs), test temperature (T), rubber gradation (RG), and

rubber content (RC)) were expressed as independent variables to yield the viscosity values. In

addition, a three-layer feedforward neural network was trained with the experimental data. This

architecture consists of an input layer, a hidden layer, and an output layer. 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.

For the three-layer network, the output of the network, the viscosity value , is calculated

as follows [17]:


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0

1 1

n m

T k T HK ik i

k i

f B W f B W P

(6)

Where

Bo= bias at the output layer; Wk= weight of the connection between neuron kofthe hidden layer and the single output layer neuron;BHK= bias at neuron k of the hidden

layer; Wik= weight of the connection between input variable i and neuron kof the hidden

layer;Pi= input ith

parameter; andfT= transfer function, defined as:

1( )

1 kk

fe

(7)

In Equation (6), the number of input variables (m) is 6; the input variables (defined

previously) areP1=Bs, P2=G, P3=Rs, P4=T, P5 = RG, andP6 = RC,The number of hidden neuron

(n=3 for two types of crumb rubber) 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 backpropagationalgorithm 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 in which the network is trained and adjusted

by reducing the error between the network output and the targeted output. 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 output and the network output 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.


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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 [21].

Experimental Results and Discussion

Regression model

Equation (8) describes the resulting estimated equation using SAS:

0.040

, 0,135( )(211.8 )CVR x t

x t e e (8)

With the standard errors ofAandfound to be 28.4084 and 0.00096, respectively. Equation (8)

was used to predict values of viscosity for an array of binder and temperature combinations. The

coefficient of determination (R2) was used to provide a measure of the goodness of fit of the

model Additionally, the root mean squared error (RMSE), a frequently-used measure of the

differences between values predicted by a model and the values actually observed from the thing,

was employed in determining the viscosity prediction accuracy in this study.

The predicted and measured values of regression models for the mixtures containing

ambient and cryogenic rubbers at two testing temperatures are shown in Figure 1. It can be noted

that the R2value of regression model for specimens containing ambient rubber is 0.816 and its

RMSE value is 1.51 Pa.s. These values indicate that the regression is obviously effective to

predict the viscosity values of various CRM binders.

Values for theRcvwere calculated and are summarized in Tables 6 (a) and 6 (b). As seen

in these tables, statistically significant differences are present depending on the binder source and

grinding procedure. The highestRcvwas exhibited by the Russian binder source; it is thought that

this elevatedRcvis due to the high shear mixing procedure and higher temperature used during

reaction, rather than unique crumb rubber and binder properties. This is likely the case as the


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Russian binder, whose viscosity was similar to the other binders tested, was modified with

ambient crumb rubber. For the remaining binders, the Rcv values tended to decrease with

decreasing virgin viscosity, thus suggesting that as the virgin binder viscosity decreases so too

does the corresponding CRM binder viscosity [14, 22].

Tables 6 (a) and 6 (b) used the Fisher least significant difference (LSD) procedure to

distinguish statistically significant differences amongst the Rcv values. This procedure is a

commonly used statistical analysis method to determine the difference between two sample

estimates necessary to declare the corresponding differences between population means. Rcv

values having at least one LSD letter in common produced statistically similar values.

The influence of the Rcv on CRM binder viscosity is quite profound, for example if a

binder of 0.5 Pa.s was reacted with a crumb rubber yielding an Rcvof 0.1 and another of 0.12 the

two binder viscosities produced would be of approximately 3.7 and 5.5 Poise, respectively. This

difference in predicted viscosity is dependent on the Rcv, as seen in Table 6 (b) ambient ground

particles typically tend to produce higher Rcv values than cryogenically ground particles. The

difference in grinding procedures was seen to produce statistically different Rcv values, by

definition the Rcv of a binder containing no crumb rubber is zero. Preliminary results also

indicate that the Rcvtends to increase for ambient ground particles with increasing fineness, no

such increase was found for cryogenic particles of differing fineness.

NN models

The measured viscosity values of the testing specimens were used to develop the NN

models. The original dependent and independent data of the viscosity values were categorized in

accordance with the ambient and cryogenic rubbers due to the various material components and

temperature sensitivity of the asphalt mixtures. In this study, unlike the regression models using


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2 variables, the independent variables of NN models included the only 6 basic input variables

described earlier. The dependent variable was selected to be the viscosity value (). Ambient

rubber modified binder included 276 viscosity value data sets and 187 of them were selected as

the training data set, and the other 89 were used as the testing data sets. At the same time,

cryogenic rubber modified binder included 222 viscosity value data sets and 152 of them were

selected as the training data set, and the other 70 were used as the testing data sets (Table 7).

The overall NN models used a goal error of 0.00001 and an epoch 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 [23, 24].

The developed NN 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 (Bs, G,

Rs, T, RG, and RC) using Equation 6. Note that Equation 6 can easily be implemented in a

spreadsheet for routine applications. The spreadsheets for ambient rubberized modifiers are

shown in Table 8. While time consuming to develop the NN model, use of the NN-based

spreadsheet model to calculate performance temperature is simple and the execution rapid.

Figure 2 shows the results obtained from the NN models (in the form of Equation 6) for the

specimens containing ambient rubber. As shown in Figure 2, the R2 values of NN viscosity

model using ambient rubber are 0.9951 and 0.9942 for training and testing data sets,

respectively. Their RMSE values are 0.294 and 0.325. Figure 2 indicates that the NN exhibits an

accuracy prediction based on a high R2value and a low RMSE value. As a result, the developed

NN viscosity model effectively improves the prediction possibility of viscosity value of ambient

rubber at various conditions.


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Similarly, the NN viscosity models of the specimens containing cryogenic rubber were

implemented in accordance with Equation (6) and expressed in terms of the connection weights

and biases shown in Table 9. The comparisons of the measured and predicted viscosity values

are shown in Figure 3. It can be noted that the NN model has the R2values of 0.9832 and 0.9773

for training and testing data sets while their RMSE values are 0.154 and 0.181.

Obviously, Figures 2 and 3 present that the viscosity prediction of NN model is more

effective than the regression model regardless of the rubber types (ambient or cryogenic).

Although different materials and testing conditions were used in the project, the predicting

performance of the trained neural network, as shown in Figures 2 and 3, is considered

satisfactory.

Sensitivity analysis of NN model

Due to highly complex and non-linear form of analysis of NN, additional sensitivity

analysis was conducted to estimate the impact of input variables on the output. During sensitivity

analysis process, one input parameter was changed slightly (approximately 5 to 10%) from the

initial condition, while the remaining parameters were kept constant. The predicted performance

temperature was then determined. Further modification of the parameter consequently yielded

increases/decreases in the predicted performance temperature. This process was repeated for all

input variables or modifications. The six input variables (Bs, G, Rs, T, RG, and RC) were

considered in the sensitivity analysis of the performance model for rubberized binders. The

figures (Figures 4 and 5) are plotted on axes depicting relative changes in both input and output

parameters. The output variable data set was segregated into several groups regarding predicted

and measured results during plotting the trend curves. This segregation of expected ranges


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illustrates the non-linearity of the proposed models and the performance of the output at various

viscosity values. For example, the viscosity values were categorized to < 1.0 Pa.s, = 1.0-5.0

Pa.s and > 5.0 Pa.s based on the scope of the measured values. The changes of the input

variable values were dependent on their category. This method facilitates visualization of the

relationship between input and corresponding output (i.e. a relative change in an input parameter

yields a relative change in the performance temperature value) [25-27].

As shown in Figure 4, the input variables show that the changes of input variables result

in the changes of output values for the specimens containing ambient rubber. Figure 4(a)

indicates that, as expected, the change of asphalt binder source results in the noticeable percent

change of the viscosity values for three categories. Obviously, it seems that the binder source

affects the viscosity value of ambient rubber modifier. As shown in Figure 4(b), as the increase

of the performance grade, the viscosity of asphalt binder increases remarkably. This is consistent

with the fact that the asphalt binder with a higher performance grade often has a greater viscosity

values and is often employed in a high temperature area. The analysis result in Figure 4(c)

illustrates that rubber source does not have a significant impact on the viscosity of binder for

overall categories since the viscosity almost kept constant as the change of rubber source. The

sensitivity analysis of test temperature in NN model indicates that the increase of test

temperature results in a rapid decrease in binder viscosity (Figure 4(d)). The effect of rubber

gradation is shown in Figure 4(e), it can be noted that the increase of rubber gradation slightly

reduces the viscosity value. However, in Figure 4(f), as the rubber content increases, the

viscosity value increases significantly. As a result, generally, these model analysis results are

consistent with the experimental test results.


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Similar sensitivity analyses were performed for the viscosity values of the specimens

made with cryogenic rubber. The results indicate that the sensitivities of input variables from the

mixtures made with cryogenic rubber are approximately the same with those of the ambient

ground CRM binder mixtures. The charts of these analyses are presented in Figure 5.

Important index analysis of NN model

Yang and Zhang [28] suggest 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 define the relative

strength of effect (RSE) for each input variable on each output variable. The equation is

expressed as follows.

1 1 2 1

1 1

... ( ) ( )... ( )n n ni k k i i in i i i

in in i

RSE c W G W G W G

(9)

Where

c = a normalized constant; 2( ) exp( ) /(1 exp( ))k k kG ; Wik= weight of the

connection between input variable i and neuron kof the hidden layer; k T ik k i

f W B ;

BK= bias at neuron k of the hidden layer; andfT= transfer function,

The important indices for the six input variables, Bs, G, Rs, T, RG, andRCof the binders made

with ambient rubber, were obtained from Equation (9) and are shown in Figure 6. 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 NN is highly nonlinear [.

It can be noted that asphalt binder grade ( G ), test temperature (T), and rubber content

(CR ) are relativelymore important, as shown in Figures 6(a). Compared with other independent

variables, binder source (SB ), rubber source ( sR ), and rubber gradation ( GR ) is relatively


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unimportant as reflected in the behavior of the developed NN. However, the input variables of

the binders containing cryogenic rubber exhibit that rubber source (sR ) are also relatively

important (Figures 6(b)). This may be that the absorption and swelling properties of crumb

rubber differ due to the product process. As a result, the viscosity values strongly correlate with

those relatively important indices and their test results can be used to predict the viscosity values

of the asphalt binders.

Validation of models

The viscosity values (104 data sets) from other binder sources (e.g. Middle East, Texas,

Canada) were employed to validate the statistical regression and the developed NN models. The

designed two variables (using known values) were input into the statistical regression models to

calculate the viscosity values. The comparison of the predicted and measured viscosity values is

shown in Figure 7. It can be seen that the R2 and RMSE values of this regression model are

0.901 and 0.65.

The given six input variable values were used with the developed NN models to calculate

predicted viscosity values and compared with the measured data. Figure 8 shows the measured

values from other projects and those predicted values by the developed NN models. The results

generally show small differences between the predicted and measured viscosity values of the

mixtures made with both rubber types (i.e., the RMSE values of these models are low), which

can be considered satisfactorily from the developed NN. Generally, the developed NN models

have a better prediction rate than the statistical regression models since the NN models have a

higher R2value and lower RMSE value in comparison with the statistical regression model.


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CONCLUSIONS

Based on the analysis of the experimental testing data of the viscosity values for two

crumb rubber, this study determined that:

1. The analysis showed the regression-based models with two variables of the asphaltbinders could effectively predict the viscosity values of binders at various testing

temperatures and mixing types.

2. The NN approach, as a new modeling method used in this study, can effectively create afeasible predictive model using six variables from the binders and mixtures. The

established NN-based models could effectively and accurately predict the viscosity

values, as evidenced by higher R2and lower RMSE values than regression-based models

regardless of either rubber types or test conditions. These NN models can easily be

implemented in a spreadsheet, thus making it easy to apply.

3. The sensitivity analyses of six input variables indicated that, in most cases, the percentchanges in input variables (e.g. binder source, rubber gradation and source)

insignificantly affect the percent changes of the viscosity values regardless of the testing

temperatures and crumb rubber types.

4. The important indices of six input variables show that the asphalt binder grade, testingtemperature, and crumb rubber content are the most important factors in the developed

NN models to predict viscosity values for the binder containing ambient rubber, while

rubber source is also an important factor for cryogenic rubberized binder. However,

binder source, and rubber gradation are relatively unimportant as compared to the other

independent variables.


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5. The regression and developed NN models could satisfactorily predict the viscosity valuesas shown by validation results using the viscosity values from the other research projects.

ACKNOWLEDGMENTS

The financial support of the South Carolina Department of Health and Environmental

Control (SC DHEC) is greatly appreciated. The results and opinions presented in this paper do

not necessarily reflect the views and policies of the SC DHEC.


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16.Goh ATC, Wong KS, and Broms BB, Estimation of lateral wall movements in bracedexcavations using neural networks, Canadian Journal of Geotechnique, Vol. 32, 1059-

1064, 199517.Juang CH and Chen CJ, CPT-based liquefaction evaluation using artificial neural

networks,Journal of Computer-Aided Civil and Infrastructure EngineeringVol. 14, 221-

229, 1999


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18.Jen JC, Hung SL, Chi SY, and Chen JC, Neural network forecast model in deepexcavation,Journal of Computing in Civil Engineering, Vol. 16, 59-65, 2002

19.Tarefder FA, White L, and Zaman M, Neural network model for asphalt concretepermeability,Journal of Materials in Civil Engineering, Vol. 17, 19-27, 2005

20.Xiao F and Amirkhanian SN, Asphalt Binder Rheology Sensitivity Investigation onResilient Modulus of Rubberized Mixtures Using Artificial Neural Network ApproachJournal of Testing and Evaluation(ASTM) Vol. 37, 2, 129-138, 2009

21.Chen CJ, Risk-based liquefaction potential evaluation using cone penetration tests andshear wave velocity measurements. Ph.D dissertation, 1999, Clemson University

22.Xiao F, Amirkhanian SN, Shen J, and Putman BJ, Influences of Crumb Rubber Size andType on Reclaimed Asphalt Pavement (RAP) Mixtures, Construction and Building

Materials,Vol. 23(2), pp.1028-1034, 2009

23. Kuang TC, Hsiao CL, Schuster M, and Juang HC, A neural network approach toestimating deflection of diaphragm walls caused by excavation in clays, Computers andGeotechnics, Vol. 34, 385-396, 2007

24.Xiao F and Amirkhanian SN, An Artificial Neural Network Approach to EstimatingPavement Stiffness Behavior, Journal of Transportation Engineering(ASCE) (in press,2009)

25.Danzer MC, Estimation of liquefaction-induced vertical and horizontal displacementsusing artificial neural networks and regression analysis, Ph. D dissertation, Clemson

University, South Carolina, USA, 199926.Xiao F, Amirkhanian SN, and Juang CH, Prediction of Fatigue Life of Rubberized

Asphalt Concrete Mixtures Containing Reclaimed Asphalt Pavement Using Artificial

Neural Networks,Journal of Materials in Civil Engineering (ASCE) (in press, 2009)27.Gandhi T, Xiao F, and Amirkhanian SN, Estimating Indirect Tensile Strength of

Mixtures Containing Anti-Stripping Agents Using An Artificial Neural Network

Approach,International Journal of Pavement Research and Technology, Vol.2 (1), pp.1-

12, 200928.Yang Y, and Zhang Q, A hierarchical analysis for rock engineering using artificial neural

networks,Rock Mechanics Rock Engineering, Vol.30, 207-222, 1997


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Table 1 Crumb Rubber Gradation used from Thodesen study

Sieve Number No. 8 No. 10 No. 16 No. 30 No. 50 No. 200

Opening size (mm) 2.38 2 1.19 0.6 0.3 0.074

Upper Specification

(% passing)100% 100% 100% 100% 45% 5%

Lower Specification

(% passing)100% 100% 65% 20% 0% 0%


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Table 2 Virgin binder properties

Aging State ParameterBinder

A B C

Unaged

Binder

Rotational Viscosity @ 135oC (Pa.s) 0.703 0.43 0.472

G*/sin@ 64o

C (kPa) 2.413 1.279 1.468

RTFO aged

ResidueG*/sin @ 64oC (kPa) 6.075 2.81 2.579

RTFO + PAV

aged residue

G*/sin@ 25oC (kPa) 3352.1 4074 3573.5

Stiffness @ -12oC (MPa) 141.3 217 232.3

m-value @ -12oC 0.359 0.307 0.321


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Table 3 Description of binder used in this research study

Binder

Code Source Description Superpave PG

Test

Date Test Location

A Venezuela - PG 70-22 2006-7

ARTS Lab,

Clemson, SC

B South Carolina Blend PG 64-22 2006-7ARTS Lab,Clemson, SC

C Russia - PG 64-22 2005

Pannonia Lab,

Veszprem, Hungary

D Venezuela - PG 70-22 2004-5

ARTS Lab,

Clemson, SC

E Middle East - PG 64-22 2004-5

ARTS Lab,

Clemson, SC

F South Carolina Blend PG 64-22 2004-5

ARTS Lab,

Clemson, SC

G South Carolina Blend PG 64-22 2005

ARTS Lab,

Clemson, SC

H South Carolina SBS PG 76-22 2005

ARTS Lab,

Clemson, SC

I Unknown - PG 58-28 1999

FHWA Lab,

McLean, VA

J Unknown - PG 64-22 1999

FHWA Lab,

McLean, VA

K Unknown NOVOPHALT PG 76-22 1999

FHWA Lab,

McLean, VA

L Unknown STYRELF PG 82-22 1999

FHWA Lab,

McLean, VA

M Middle East - PG 64-22 2007

ARTS Lab,

Clemson, SC

N Texas - PG 70-22 2007

ARTS Lab,

Clemson, SC

O Canada 2 - PG 64-22 2007 ARTS Lab,Clemson, SC

P West Texas - PG 64-22 2007

ARTS Lab,

Clemson, SC

Q Canada 1 - PG 64-22 2007

ARTS Lab,

Clemson, SC

Note: ARTS-asphalt rubber technology service


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Table 4 (a) ADOT and (b) SCDOT gradations

(a)

Sieve Number No. 10 No. 16 No. 30 No. 50 No. 200

Opening size (mm) 2.000 1.190 0.600 0.300 0.075

Upper Specification

(% passing)

100 100 100 45 5

Lower Specification

(% passing)100 65 20 0 0

(b)

Sieve Number No. 20 No. 40 No. 80 No. 100

Opening size (mm) 0.850 0.425 0.180 0.150

Upper Specification

(% passing)100 100 50 30

Lower Specification

(% passing)100 85 10 5


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Table 5 Description of crumb rubber used in this research study

CRM

Designation

Production

Location Grinding Gradation Tire Type

Test

Date Test Location

Source 1

South

Carolina Cryogenic ADOT Passenger 2006-7

ARTS Lab,

Clemson, SC

Source 2 Arizona Cryogenic ADOT Passenger 2006-7 ARTS Lab,Clemson, SC

Source 3 California Ambient ADOT Unknown 2006-7

ARTS Lab,

Clemson, SC

Source 4 Florida Ambient ADOT Truck 2006-7

ARTS Lab,

Clemson, SC

Source 5 Hungary Ambient ADOT Unknown 2005

Pannonia Lab,

Veszprem,

Hungary

Source 6

South

Carolina Ambient SCDOT Passenger 2005

ARTS Lab,

Clemson, SC

Source 7

South

Carolina Cryogenic 0.850 mm Passenger 2004-5

ARTS Lab,

Clemson, SC

Source 8

South


ARTS Lab,

Clemson, SC

Source 9

South


ARTS Lab,

Clemson, SC

Source 10

South

Carolina Ambient 0.850 mm Passenger 2004-5

ARTS Lab,

Clemson, SC

Source 11

South


ARTS Lab,

Clemson, SC

Source 12

South


ARTS Lab,

Clemson, SC

Source 13

South

Carolina Cryogenic SCDOT Passenger 2007

ARTS Lab,

Clemson, SC

Source 14

South

Carolina Ambient SCDOT Passenger 2007

ARTS Lab,

Clemson, SC

Source 15South

Carolina Cryogenic 0.850 mm Passenger 2007ARTS Lab,Clemson, SC

Source 16

South

Carolina Cryogenic 0.425 mm Passenger 2007

ARTS Lab,

Clemson, SC

Source 17

South

Carolina Cryogenic 0.180 mm Passenger 2007

ARTS Lab,

Clemson, SC

Source 18

South

Carolina Ambient 0.850 mm Passenger 2007

ARTS Lab,

Clemson, SC

Source 19

South


ARTS Lab,

Clemson, SC

Source 20

South


ARTS Lab,

Clemson, SC


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Table 6 (a) MeanRcvby Binder Source; (b) MeanRcvby Binder Source

(a)

Source Binder MeanRcv Observations LSD

Russia C 0.187 1 aBlend B 0.120 6 b

Venezuela A,D 0.120 17 bMiddle Eastern E 0.110 6 b cBlend F 0.094 4 c

(b)

Grinding

Mean

Rcv Observations LSD

Ambient 0.133 17 a

Cryogenic 0.100 17 b


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Table 7 Sample training and testing data for ambient rubberized binder

No. BS G RS T RG RC

C C mm % Pa.s

1 1 70 3 135 1.19 0 0.65

2 2 64 3 135 1.19 0 0.51

3 5 64 10 135 0.85 10 2.354 6 64 10 135 0.85 10 1.63

5 7 64 10 135 0.85 10 1.49

6 3 64 5 135 1.19 2 0.96

187 2 64 6 154 1.19 15 1.35

1* 1 70 3 135 1.19 0 0.64

2* 2 64 3 135 1.19 0 0.46

3* 5 64 10 135 0.85 10 2.28

4* 6 64 10 135 0.85 10 1.59

5* 7 64 10 135 0.85 10 1.50

6* 3 64 5 135 1.19 2 0.96

89* 2 64 6 154 1.19 15 1.31

1 1 70 1 135 1.19 0 0.65

2 2 64 1 135 1.19 0 0.44

3 5 64 7 135 0.85 10 1.85

4 6 64 7 135 0.85 10 1.60

5 7 64 7 135 0.85 10 1.29

152 7 64 9 135 0.18 15 1.99

1* 1 70 1 135 1.19 0 0.64

2* 2 64 1 135 1.19 0 0.51

3* 5 64 7 135 0.85 10 1.86

4* 6 64 8 135 0.425 10 1.15

5* 7 64 7 135 0.85 10 1.24

70* 7 64 9 135 0.18 15 1.98

Ambientrubber

Cry

ogenicrubber

Note: BS-binder source; G-binder grade; RS-rubber source; T-temperature; RG-rubber gradation; RC-rubber

content; - viscosity; *: testing data


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Table 8 NN calculation spreadsheet for ambient rubberized binder

1 A B C D E F G

2 COMMANDS OF EXECUTING EQ.6 Hidden Layer

3 ARGUMENT("B S", "G ", "R S", "T", "R G ", "R C") Weight matrix Hidden 1 Hidden 2 Hidden 3

4 Bias 189.6071 16.2315 4.1297

5 B S=(B S- 0.25)/7.5; G =(G -63.25)/7.5 Input 1 -41.4578 -100.8770 1.6279

6 R S=(R S-0)/10.0; T=(T-128.125)/68.75 Input 2 -20.9794 -15.9820 -0.3671

7 R G =(R G -0.0538)/1.263; R C=(R C+ 2.5)/25 Input 3 -57.9890 0.1109 0.4455

8 Input 4 181.5715 -2.5521 2.0455

9 Input 5 -181.2738 4.6543 0.4966

10 pi1=1/(1+EXP(-(R b *D$5+R p *D$6+V*D$7+F*D$8+ Input 6 -6.2513 4.2590 -3.5647

11 S* D$9+MV*D$10+D$4)))

12 pi1=1/(1+EXP(-(R b *E$5+Rp *E$6+V*E$7+F*E$8+

13 S* E$9+MV*E$10+E$4)))

14 pi1=1/(1+EXP(-(R b *F$5+R p *F$6+V*F$7+F*F$8+

15 S* F$9+MV*F$10+F$4)))

16 Output Layer

17 Bias 272.290518 Hidden 1 -236.5587

19 Hidden 2 -13.1849

20 Hidden 3 -37.9789

21 Z=pi1*D18+pi2*D19+pi3*D20+D17

22 Z=1/(1+EXP(-Z))

23 Ln(F)=30312.5*Z-2976.25

24 RETURN (F)

Weight matrix:

Cells D4: F4 are BHKCells D5: F11 are Wik

Weight matrix:Cell D17 is BoCells D18: D20 are

Cells B3:B24 are

macro commands toexecute Eq.6


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Table 9 NN calculation spreadsheet for cryogenic rubberized binder

1 A B C D E F G

2 COMMANDS OF EXECUTING EQ.6 Hidden Layer

3 ARGUMENT("B S", "G ", "R S", "T", "R G ", "R C") Weight matrix Hidden 1 Hidden 2 Hidden 3

4 Bias 11.2452 -10.5683 5.1785

5 B S=(B S- 0.25)/7.5; G =(G -63.25)/7.5 Input 1 5.7205 -6.0537 -3.7724

6 R S=(R S-0)/10.0; T=(T-128.125)/68.75 Input 2 -1.4293 1.4990 1.6328

7 R G =(R G -0.0538)/1.263; R C=(R C+ 2.5)/25 Input 3 -7.5077 7.9615 4.2961

8 Input 4 0.8820 -0.9110 0.1770

9 Input 5 -4.1376 4.4992 1.8188

10 pi1=1/(1+EXP(-(R b *D$5+R p *D$6+V*D$7+F*D$8+ Input 6 -2.0487 2.1218 -0.1942

11 S* D$9+MV*D$10+D$4)))

12 pi1=1/(1+EXP(-(R b *E$5+R p *E$6+V*E$7+F*E$8+

13 S* E$9+MV*E$10+E$4)))

14 pi1=1/(1+EXP(-(R b *F$5+Rp *F$6+V*F$7+F*F$8+

15 S* F$9+MV*F$10+F$4)))

16 Output Layer

17 Bias 7722.19018 Hidden 1 -7151.494

19 Hidden 2 -2263.327

20 Hidden 3 -573.893

21 Z=pi1*D18+pi2*D19+pi3*D20+D17

22 Z=1/(1+EXP(-Z))

23 Ln(F)=8973.9583*Z-851.5625

24 RETURN (F)

Weight matrix:Cells D4: F4 are BHKCells D5: F11 are Wik

Weight matrix:Cell D17 is BoCells D18: D20 are

Cells B3:B24 aremacro commands toexecute Eq.6


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30

0

5

10

15

20

25

0 5 10 15 20 25Predictedviscosityvalues(Pa.s

)

Measured viscosity values (Pa.s)

R2 = 0.8160

RMSE = 1.51

498 data sets

Figure 1 Measured and predicted viscosity values of CRM binder from regression model


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31

0

5

10

15

20

25

0 5 10 15 20 25Predictedviscosity

values(Pa.s

)


Training data

Training R2 = 0.9951

RMSE = 0.294

184 data sets

0

5

10

15

20

25


values(Pa.s

)


Testing data

Testing R2 = 0.9942

RMSE = 0.32589 data sets

(a) (b)

Figure 2 Measured and predicted viscosity values of ambient rubberized binder from NN models,

(a) Training data results; (b) Testing data results


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0

2

4

6

8

10


values(Pa.s

)


Training data

Training R2 = 0.9832

RMSE = 0.154

149 data sets

0

2

4

6

8

10

0 2 4 6 8 10Predictedviscosityvalues(Pa.s

)


Testing data

Testing R2 = 0.9773


(a) (b)

Figure 3 Measured and predicted viscosity values of cryogenic rubberized binder from NN

models, (a) Training data results; (b) Testing data results


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-400

-200

0

200

400

-200 -100 0 100 200Percentchangeinviscosity(%)

Percent change in binder source (%)

-400

-200

0

200

400

-60 -30 0 30 60

Percent change in binder grade (%)

-400

-200

0

200

400

-200 -100 0 100 200

Percent change in rubber source (%) (a) (b) (c)

-400

-200

0

200

400

-60 -40 -20 0 20 40 60Percentcha

ngeinviscosity(%)

Percent change in temperature (%)

-400

-200

0

200

400

-60 -40 -20 0 20 40 60

Percent change in rubber gradation (%)

-400

-200

0

200

400

-60 -30 0 30 60

Percent change in rubber content (%) (d) (e) (f)

1.5 Pa.s

Figure 4 Sensitivity analysis of input variables for ambient rubberized binders (a) binder source;

(b) binder performance grade; (c) rubber source; (d) temperature; (e) rubber gradation; (f) rubber

content


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-400

-200

0

200

400

-200 -100 0 100 200Percentcha

ngeinviscosity(%)

Percent change in binder source (%)

-400

-200

0

200

400

-60 -30 0 30 60

Percent change in binder grade (%)

-400

-200

0

200

400

-200 -100 0 100 200

Percent change in rubber source (%) (a) (b) (c)

-400

-200

0

200

400

-60 -40 -20 0 20 40 60

Percentcha

ngeinviscosity(%)

Percent change in temperature (%)

-400

-200

0

200

400

-60 -40 -20 0 20 40 60

Percent change in rubber gradation (%)

-400

-200

0

200

400

-60 -30 0 30 60

Percent change in rubber content (%)(d) (e) (f)

1.5 Pa.s

Figure 5 Sensitivity analysis of input variables for cryogenic rubberized binders (a) binder

source; (b) binder performance grade; (c) rubber source; (d) temperature; (e) rubber gradation;

(f) rubber content


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0.0

0.2

0.4

0.6

0.8

1.0

Importa

ntIndex

Input variables

BS RCTRSG RG

0.0

0.2

0.4

0.6

0.8

1.0

ImportantIndex

Input variables

BS RCTRSG RG

(a) (b)

Figure 6 Important indices of NN model, (a) ambient rubberized binder;

(b) cryogenic rubberized binder


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0.0

2.0

4.0

6.0

0.0 2.0 4.0 6.0Predictedviscosityvalues(Pa.s

)


R2 = 0.9010


Figure 7 Validation of regression model


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0.0

2.0

4.0

6.0

0.0 2.0 4.0 6.0Predictedviscosit

yvalues(Pa.s

)

Measured viscosit values Pa.s

R2=0.9897


0.0

1.0

2.0

3.0

0.0 1.0 2.0 3.0Predictedviscosityvalues(Pa.s

)


R2=0.9306


(a) (b)

Figure 8 Validation of NN model, (a) ambient rubberized binder;

(b) cryogenic rubberized binder

Documents

Modeling Viscosity Behavior of CRM Binders.pdf