stiffness modulus of polyethylene terephthalate modified asphalt mixture: a statistical analysis of...

Accepted Manuscript

Stiffness modulus of Polyethylene Terephthalate modified asphalt mixture: A

statistical analysis of the laboratory testing results

Taher Baghaee Moghaddam, Mehrtash Soltani, Mohamed Rehan Karim

PII: S0261-3069(14)00965-0

DOI: http://dx.doi.org/10.1016/j.matdes.2014.11.044

Reference: JMAD 6995

To appear in: Materials and Design

Received Date: 14 September 2014

Accepted Date: 25 November 2014

Please cite this article as: Baghaee Moghaddam, T., Soltani, M., Karim, M.R., Stiffness modulus of Polyethylene

Terephthalate modified asphalt mixture: A statistical analysis of the laboratory testing results, Materials and

Design (2014), doi: http://dx.doi.org/10.1016/j.matdes.2014.11.044

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http://dx.doi.org/10.1016/j.matdes.2014.11.044

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1

Title: Stiffness modulus of Polyethylene Terephthalate modified asphalt mixture: A statistical

analysis of the laboratory testing results.

Authors’ names:

Taher Baghaee Moghaddam a,* (First name: Taher, Last name: Baghaee Moghaddam),

Mehrtash Soltani a, Mohamed Rehan Karim

a (First name: Mohamed Rehan, Last name: Karim)

Authors’ affiliation addresses:

a Center for Transportation Research, Department of Civil Engineering, Faculty of Engineering,

University of Malaya, 50603 Kuala Lumpur, Malaysia.

*Corresponding author:

Taher Baghaee Moghaddam

Tel.:+60108927064; Fax: +60379552182

Corresponding author E-mail address:

[email protected]; [email protected]

Corresponding author postal address:

Center for Transportation Research, Department of Civil Engineering, Faculty of Engineering,

University of Malaya, 50603 Kuala Lumpur, Malaysia.

mailto:[email protected]

https://profiles.google.com/?hl=en&tab=mX

2

Stiffness modulus of Polyethylene Terephthalate modified asphalt

mixture: A statistical analysis of the laboratory testing results

Taher Baghaee Moghaddam

a,*, Mehrtash Soltani

a, Mohamed Rehan Karim

a

aCenter for Transportation Research, Department of Civil Engineering, Faculty of Engineering,

University of Malaya, 50603 Kuala Lumpur, Malaysia

Abstract

Stiffness of asphalt mixture is a fundamental design parameter of flexible pavement. According

to literature, stiffness value is very susceptible to environmental and loading conditions. In this

paper, effects of applied stress and temperature on the stiffness modulus of unmodified and

Polyethylene Terephthalate (PET) modified asphalt mixtures were evaluated using Response

Surface Methodology (RSM). A quadratic model was successfully fitted to the experimental

data. Based on the results achieved in this study, the temperature variation had the highest impact

on the mixture’s stiffness. Besides, PET content and amount of stress showed to have almost the

same effect on the stiffness of mixtures. The optimal amount of PET was found to be 0.41% by

weight of aggregate particles to reach the highest stiffness value.

Keywords: Asphalt mixture; Mixture stiffness; Waste polyethylene terephthalate;

Environmental temperature; Applied stress; Response surface methodology.

*Corresponding author: [email protected]; [email protected]

mailto:[email protected]

https://profiles.google.com/?hl=en&tab=mX

3

1. Introduction

Stiffness of asphalt mixture is a fundamental design parameter of flexible pavement. It was

found that there is a correlation between stiffness and other mixture properties such as rutting

and fatigue, and thus it can be used as a criterion to evaluate Asphalt Concrete (AC) mixture

performance [1]. As it is mentioned by Strategic Highway Research Program (SHRP) the

stiffness value of AC mixture is very susceptible to environmental temperature and loading

conditions [2].

Stone Mastic Asphalt (SMA) is gap-graded AC mixture which has been developed in Germany

in 1916s. SMA consists of more course aggregate particles, mineral filler and asphalt binder.

Due to inherited structure of SMA, it provides better permanent deformation (rutting)

performance and durability compared to conventional dense-graded mixture [3, 4]. Draindown is

a common problem in SMA mixture because it contains higher amount of asphalt binder. Hence,

to prevent from draindown in SMA mixture stabilizer additives, fibers and polymers are used.

Using polymer in SMA mixture is very common. Utilizing polymer in SMA mixture prevents

not only from the binder draindown but also it can enhance mixture performance [5, 6]. In many

cases, using polymers causes higher construction cost due to high cost of polymers. To overcome

this disadvantage, many studies investigated using waste polymers in asphalt mixtures [6-8].

One of the important industrial plastic materials is Polyethylene Terephthalate (PET). PET is a

semi-crystalline thermo plastic polymer material which is used in beverage and food industries

for years. Nowadays, a large amount of waste PET is produced in the world and it is going to

cause a serious environmental challenge due to non-biodegradability of PET [9]. Hence, some

studies have been previously performed to evaluate the effects of using post-consumer PET as

secondary materials in road pavement in order to find solutions to tackle with this potential

4

environmental hazard and, moreover, to decrease construction cost imposed by application of

polymers in asphalt mixture [6, 10-12].

Statistical analysis is a precise and popular way to explore and present interactions between

parameters affecting one phenomenon. Statistical analysis in pavement engineering has

prominent utilization because it helps road engineers and designers to have better perspective

about the pavement performance parameters. In this case, factorial Design of Experiments

(DOE) which through the use of techniques such as Response Surface Methodology (RSM) -

simultaneously consider several factors at different levels, and give a suitable model for the

relationship between the various factors and the response came into popularity [13-15].

Aim of this study was examining the AC mixture stiffness at elevated temperatures and stress

levels for the unmodified and PET modified mixtures following by finding interactions between

these fundamental factors using RSM based on Central Composite Design (CCD).

2. Materials and methods

Asphalt mixtures were fabricated using 80-100 asphalt penetration grade. Granite-rich aggregate

particles were used for this investigation. 9% of filler was utilized. The aggregate particle size

distribution is shown in Fig. 1. In order to have better understanding about the materials

characteristics several tests were performed on asphalt cement and aggregate particles and the

results are listed in Table 1.

PET flakes have been used for this study which were obtained from waste PET bottles. For using

PET flakes in asphalt mixture, the PET bottles were cut to small parts and by using crushing

5

machine these small parts were crushed. Thereafter, the crushed PET particles were sieved and

the particles which were smaller than 2.36 mm in size were used for this investigation.

Fig. 1. Aggregate particle size distribution for stone mastic asphalt

Table 1: Properties of materials

2.1 Mixture fabrication

In order to fabricate SMA mixture, 1100 g of mixed aggregate and filler were heated inside oven

with temperature of 160˚C for 3 hours. Asphalt cement was also heated at 130˚C to be suitable

for mixing with aggregate particles. All the materials were mixed at the temperature of 160˚C.

PET particles with different percentages (0%, 0.5 and 1% by weight of aggregate particles) were

added directly to the mixture as the method of dry process. The loose mixture was compacted

using Marshall compactor and 50 blows of compaction efforts were applied on each side of the

mixture. It is worth mentioning that all the mixtures were fabricated at their optimum asphalt

contents (OAC). The optimum asphalt content for SMA mixtures is usually selected to produce

3–5% air voids [4, 5]. In this study, the OAC was selected to produce 4% air voids. The

summary of the mix design is reported in Table 2.

Table 2: Summary of mix design

2.2 Indirect tensile stiffness modulus test

Indirect tensile stiffness modulus (ITSM) test gives the relationship between stress and strain of

asphalt mixture and used to evaluate the stiffness of asphalt mixture at specific environmental

6

conditions. ITSM test was performed in accordance with AASHTO TP31. ITSM test can be

performed by using Universal Testing Machine (UTM) which is one of the important testing

equipment in pavement laboratory. UTM is a computer controlled system which operates

automatically. During the test, compressive haversine waveform loads were applied across the

thickness of specimen, and by utilizing Linear Variable Differential Transducers (LVDTs) which

were installed along diametrical section of specimen displacement of asphalt mixture was

measured. Horizontal tensile stress and stiffness modulus of asphalt mixtures was calculated

using the following equations [10, 16]:

Where is the maximum horizontal tensile stress in middle of specimen (kPa); is the

stiffness modulus (MPa); P, applied vertical peak load (N), H; amplitude of horizontal

deformation (mm), t; average thickness of specimen (mm); d, average diameter of specimen

(mm) and ν, Poisson’s ratio.

In order to characterize effects of applied stress and temperatures on the mixture’s stiffness,

ITSM test was conducted at stress levels of 200, 300 and 400 kPa for each percentage of PET

which are the stress amounts mostly used at pavement laboratories. Additionally, testing

temperatures of 10˚C, 25˚C and 40˚C were designated which can be referred to relatively low,

medium and high environmental temperatures respectively.

7

2.3 Method of analysis

One factor at a time (OFAT) methodology is a conventional approach to optimize multifactor

experiments. OFAT includes a changeable single factor for a specific experiments design while

other factors are kept constant. OFAT is unable to provide appropriate output because the effect

of interactions amongst all involved factors in the designs is not examined truly, and it is not

capable of reaching the true optimum value [17, 18]. Hence, RSM methodology was introduced

for parameter optimization in a way that number of experiments and interaction among the

parameters are reduced to minimal value [19-21]. Consequently, the Design Expert 8.0.5 was

designated for this study to generate statistical analysis, experimental designs, and to calculate

the sorbent adaption conditions.

For this study, a developed quadratic model and a=0.5 were utilized using RSM method for

design and data analyzing. In this investigation, the effects of three independent numerical

variables including PET modifier (A) from zero to 1%, stress levels (B) from 200 kPa to 400 kPa

and temperatures (C) between 10 and 40 ºC, all at three levels, were studied through the central

composite design (CCD). Related literature and preliminary studies were used to choose these

variables and the irrespective regions of interest [5-8, 10-12].

Table 3 shows the levels and range of the actual values of independent numerical variables. By

using Eq. (3) all defined numerical variables transformed to the coded form.

(3)

xi describes the coded value of the ith independent factor which is dimensionless. Actual value

is defined as Xi, X0 is the center point actual value and ΔX refers to the step change of the ith

variable.

8

Totally 34 experiments in randomized order were performed, together with five replications at

center points to provide accurate assessment of errors (Table 3). The stiffness was defined as the

response to develop design of experiment modeling. Eq. (4) was introduced to calculate the

dependent variables [22, 23]:

(4)

In the Eq. (4), Y is the calculated response, β0 is the constant. Independent variables in coded

forms are described as xi, and xj. The coefficients of βi and βii are the linear and quadratic terms.

βij is the interaction term coefficient, ε is the random error, and the studied number of factors is

described as n.

Besides, in order to assess appropriateness of the proposed model, analysis of variance

(ANOVA) was performed. The coefficients of determination (R2 and R

2adj) express the wellness

of the fit to suggested model. These values can be determined using the following equations [24,

25]:

(5)

(6)

In this equation, SS is the sum of squares and DF is degrees of freedom.

Eq. (7), Eq. (8) and an F-test in the program were used to check the model’s adequate precision

ratio (AP) to determine the statistical importance of the model [24- 26]:

9

(7)

(8)

Where Y is the predicted response, p represents the number of model parameters, residual mean

square is described as σ2, and n is the number of experiments.

After the F-test had been performed, the insignificant terms were found and eliminated from the

model. Thereafter, the finalized model was introduced based on the significant variables.

Eventually, the optimum condition was determined to give the highest stiffness response, along

with better mixture performance.

Table 3: Layout of experimental results and DOE design

Table 4: Anova analysis for stiffness

3. Results and discussion

Indirect tensile stiffness modulus test was conducted on the PET modified SMA mixtures at

elevated temperatures and stress levels. Table 3 represents the layout for experimental design and

the amounts of stiffness responses. Having these values, RSM was utilized to find interactions

between the outputs and variables which are independent. Eventually, a fitted quadratic

polynomial equation was produced after a regression analysis had been applied to all responses

described in the design matrix. The highest order polynomials with significant model

10

performance are suggested by the software. This model was utilized to find the optimum

condition. The numerical parameters (A, B and C) were used to generate the predictive model

according to Eq. 9:

Final Equation for Stiffness = 4051.55-325.25A-171.5B-4776.15C+256.75AC-157.96A2+

1602.54C2 (9)

Checking the adequacy of the model is an important part of the data analysis, as the model

functions would give improper responses in case the fit is not adequate [20, 27]. Hence, in this

study in order to assess the significance and adequacy of the model ANOVA analysis was

performed and the results are reported in Table 4. In addition, this table shows the quadratic

models for coded factors, and represents the other statistical parameters for stiffness response. In

this table, p-values which are less than 0.0001 imply that the model and parameter are significant

(model and term p-value <0.05 indicate the model and the term are significant for 95%

confidence intervals) for assessing the value of responses [28].

In this study, the effect of PET (A), on stiffness property of SMA mixtures at different stress

levels (B) and temperatures (C) is modeled. Besides, in order to improve the model performance,

insignificant terms (with p-value >0.100) are eliminated from the model [29].

In order to check the fitness of the model, regression coefficients, R2 and R

2adj were calculated.

Values of 0.9990 and 0.9986 were obtained for the R2

and R2

adj, respectively. This shows that

99.8 % of the total variation in the stiffness response could be explained by the quadratic model.

The high R2 and adjusted R

2 values indicate that there is a good agreement between predicted

and actual values [21, 22, 30]. Ratio of signal-to-noise is measured by adequate precision to

compare the variety of the estimated amounts at the design points to the average prediction error.

Adequate model discrimination was found in this study when the adequate precision ratio of

11

136.602 was calculated for the stiffness which is much higher than the value of 4 [31]. The lack

of fit (LOF) F-test was also used to evaluate the adequacy of the model. LOF depicts the

variation of the data around the fitted model, and the amount of LOF would be significant if the

model does not fit the data well. It is worth noting that despite the lack-of-fit was significant, the

reasonable agreement between the predicted and adjusted R2 were found for all responses which

can be concluded the suggested model for all responses can be used to navigate into design

space to find an optimum condition [32,33].

3.1 Statistical analysis

In order to have better understating about model satisfactoriness, diagnostic plots such as the

predicted versus actual values are worthwhile. Fig. 2 shows the actual versus predicted values

plots of parameters removal for stiffness modeling. As it is depicted in this figure there is an

adequate agreement between the actual data amounts and the predicted ones. The same thing can

be achieved from AP value (AP>4) for the stiffness responses (see Table 4). This verifies that

predicted model can be used to navigate the design space defined by the CCD.

Fig. 2. Design-expert plot; predicted vs. actual values plot for stiffness

3.2 One factor analysis

One factor analysis is “changing one factor at a time” method. That is to say, in this method a

single factor is varied while all other factors are kept constant for a particular set of experiments.

And this process exists for optimizing other variables which would be time consuming. In this

method, trial and error are commonly existed for the optimization of variables, and, moreover,

12

there is always a lack to reach a true optimum amount which should be obtained by considering

the interaction among all the variables [32, 34].

Each factor in this analysis is evaluated separately. Fig. 3 reveals the effect of PET on the

stiffness properties of SMA mixtures. As it can be seen in this figure the amount of stiffness is

decreased at higher PET contents. The possible reason for this result might be due to the

mechanical properties of PET particles in the mix. In fact, because the melting point of PET is a

high (over 250˚C) and is higher than the mixture’s fabrication temperature, the PET particles do

not melt during mixing. The solid PET particles can make mixture more flexible and cause

higher deformation under loading application. The same pattern is found between stress level and

stiffness value as it is depicted in Fig. 4. That is to say, by increasing the stress level, the amount

of deformation in the mixture is increased and according to Eq. 2 the stiffness is reduced

mutually. Moreover, in Fig. 5, the higher decreasing slope line may imply that the temperature

variation has dominating influence on the stiffness property of SMA mixtures, and this

represents the importance of ambient temperature on the stiffness property of asphalt mixture.

Fig. 3. Effect of PET percentage on the stiffness

Fig. 4. Effect of different stress levels on the stiffness

Fig. 5. Effect of different temperatures on the stiffness

3.3 Effects of temperature and stress levels on the stiffness

The quadratic model for the effect of stress level and temperature on stiffness is presented in Fig.

6. The response was generated using the Eq. (9). The Fig. 6 shows that by variation of

temperature from 10˚C to 40˚C the amount of stiffness is decreased, however, the effect of stress

seems to be negligible compared to the temperature variation.

13

Fig. 6. Effects of stress level and temperature on the stiffness, 0.5% PET

3.4 Effects of temperature and PET content on the stiffness

Effects of two parameters including PET and temperature are evaluated on stiffness as shown in

Fig. 7. The Fig. 7 depicts the mixture stiffness is more susceptible against variation of

temperature. The stiffness amounts decrease from over 10000 MPa to under 1000 MPa when the

temperature increases from 10˚C to 40˚C. Additionally, it is shown at lower temperatures the

PET amounts have more influence on the mixture stiffness. This can be referred to susceptibility

of asphalt binder against temperature variation which plays an important role on the mixture

properties. In other words, when the ambient temperature increases, the asphalt binder becomes

soft which can eventually results in lower mixture stiffness. Besides, the influence of PET on

mixture’s stiffness is overshadowed by the temperature.

Fig. 7. Effects of PET percentage and temperature on the stiffness, stress level 300 kPa

3.5 Effects of PET and stress level on the stiffness

Fig. 8 shows the effects of stress level and PET on the stiffness of asphalt mixture. It might be

realized that both level of stress and PET content have nearly the same effect on stiffness

property of asphalt mixture though the variation of PET might be more influential, for instance at

400 kPa by increasing the PET amount from 0 to 1% the stiffness value decreases by 378 MPa.

Fig. 8. Effects of PET percentage and stress level on stiffness, 25˚C

14

3.6 Finding the optimum condition

In the construction of asphalt mixture, relatively high stiffness is demanded to resists against

traffic loading and consequently permanent deformation. Optimum PET content for maximizing

the stiffness within the considered experimental range was accomplished using the Design-

Expert software. An overlay plot is used to view constraints on process or formulation. The

optimum conditions could be graphically visualized by super imposing the contours of the

response surfaces in an overlay plot. As depicted by Fig. 9, 0.41 percent of PET is suggested by

the software to provide the highest stiffness value.

Fig. 9. Design-expert plot; overlay plot for optimal amount of PET

4. Conclusions

This paper aimed to evaluate the effects of applied load and temperature on the stiffness property

of unmodified and PET modified asphalt mixtures. Statistical analysis was used in this

investigation to find interactions between selected variables. A good agreement was found

between predicted and actual values. A quadratic model was successfully fitted to the

experimental data. Based on the results achieved in this study the following conclusions can be

derived:

(1) Stiffness of asphalt mixture was affected by amounts of applied stress and PET content.

However, Mixture stiffness was more susceptible against temperature variations.

(2) The results showed that the PET modification had more influence on the asphalt

mixture’s stiffness at lower temperatures.

15

(3) The findings of this study revealed that the variation of PET was more influential on the

stiffness of mixtures compared to the stress levels.

(4) 0.41 % of PET content was selected as the optimal PET value to reach the highest

stiffness for the SMA mixtures which have been designated for this study.

Acknowledgements

The authors express their sincere thanks for the funding support they received from the Ministry

of Higher Education Malaysia, grant no: FP021-2011A and University of Malaya grant no:

RP010A-13SUS.

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Figure captions:




Fig.4. Effect of different stress levels on the stiffness




Fig. 8. Effects of PET percentage and stress level on the stiffness, 25˚C


Table titles:


Table 2: Summary of mix design


Table 4: Anova analysis for stiffness

19


0

20

40

60

80

100

120

0.075 0.3 0.6 2.36 4.75 9.5 12.5

Pass

ing (

%)

Sieve size (mm)

Lower limit

Upper limit

Design limit

20



21

Fig. 4. Effect of different stress levels on the stiffness


22


23


Fig. 8. Effects of PET percentage and stress level on the stiffness, 25˚C

24


25


Property Unit Used specification Value Requirements

Asphalt

Penetration at 25°C 0.1mm ASTM: D5 87.5 -

Softening point °C ASTM: D36 46.6 -

Flash point °C ASTM: D92 300 -

Fire point °C ASTM: D92 320 -

Specific gravity (g/cm3) ASTM: D70 1.03 -

Coarse aggregate

L.A. Abrasion % ASTM: C131 19.45 <30

Flakiness index % BS 812 Part 105.1 2.72 <20

Elongation index % BS 812 Part 105.2 11.26 <20

Aggregate crushing value % BS 812 Part 3 19.10 <30

Bulk specific gravity (g/cm3) ASTM: C127 2.60 -

Absorption % ASTM: C127 0.72 <2

Fine aggregate

Bulk specific gravity (g/cm3) ASTM: C128 2.63 -

Absorption % ASTM: C128 0.4 <2

Soundness loss % ASTM: C88 4.1 <15

http://www.astm.org/Standards/D5.htm





http://www.astm.org/Standards/C131.htm






26

Table 2:Summary of mix design

PET(%) BSGa

VMAb(%) VFA

c(%) OAC

d (%)

0 2.294 18.12 77.92 6.77

0.5 2.296 17.34 76.90 6.36

1 2.283 17.55 77.20 6.51

abulk specific gravity of compacted mixture

b void in mineral aggregate

cvoid filled with asphalt

doptimum asphalt content

27


Run Factor 1:

PET (%)

Factor 2: stress

level (kPa)

Factor 3:

Temperature ( °C)

Stiffness

(MPa)

1 0 200 10 10801

2 1 400 40 452

3 0.5 300 10 10608

4 0 200 40 1011

5 1 300 25 3689

6 0.5 300 25 4088

7 0.5 200 25 4310

8 0.5 400 25 3758

9 0 300 25 4041

10 0.5 300 25 4083

11 1 400 10 9391

12 0 300 25 4083

13 1 200 10 9710

14 0 400 10 10762

15 0 200 40 1071

16 0.5 300 25 4025

17 0.5 300 25 4081

18 1 400 40 431

19 0.5 300 25 4022

20 0 400 40 632

21 1 200 10 9712

22 1 300 25 3722

23 0.5 300 40 645

24 0.5 300 40 623

25 0 400 40 664

26 0.5 300 10 10701

27 1 400 10 9410

28 0.5 400 25 3671

29 1 200 40 832

30 0 400 10 10769

31 0.5 200 25 4261

32 1 200 40 821

33 0.5 300 25 4089

34 0 200 10 10841

28

Table 4:Anova analysis for stiffness

Source Sum of

Squares

Degree of

Freedom Mean

Square F Value Prob > F

Model

performance

Model 478763078.9 9 53195897.65 2625.158 < 0.0001 Significant

A 2115751.25 1 2115751.25 104.4099 < 0.0001 Significant

B 588245 1 588245 29.02923 < 0.0001 Significant

C 456232176.5 1 456232176.5 22514.55 < 0.0001 Significant

A2 133703.7816 1 133703.7816 6.598131 0.0169 Significant

B2 9322.861812 1 9322.861812 0.460073 0.5041 Insignificant

C2 13761302.46 1 13761302.46 679.1048 < 0.0001 Significant

AB 15252.25 1 15252.25 0.752681 0.3942 Insignificant

AC 1054729 1 1054729 52.04969 < 0.0001 Significant

BC 42436 1 42436 2.094169 0.1608 Insignificant

Residual 486333.2542 24 20263.88559

Lack of Fit

(LOF) 466621.9209 5 93324.38418 89.95654 < 0.0001 Significant

Pure Error 19711.33333 19 1037.438596

Cor Total 479249412.1 33

Adequate

precision (AP) 136.602

29

Highlights

> Effect of PET modification on stiffness property of asphalt mixture was examined.

> Different temperatures and loading amounts were designated.

> Statistical analysis was used to find interactions between selected variables.

> A good agreement between experimental results and predicted values was obtained.

> Optimal amount of PET was calculated to achieve the highest mixture performance.

stiffness modulus of polyethylene terephthalate modified asphalt mixture: a statistical analysis of...

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