# Characterization of Various Plant-Produced Asphalt Concrete Mixtures Using Dynamic Modulus Test

Authors: Muhammad Irfan; Asad S. Waraich; Sarfraz Ahmed; Yasir Ali
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

This research characterizes the performance of various plant-produced asphalt concrete mixtures by dynamic modulus|
E
∗
| test using asphalt mixture performance tester (AMPT). Marshall designed specimens of seven different mixtures were prepared using the Superpave gyratory compactor and subjected to sinusoidal compressive loading at various temperatures (4.4 to 54.4°C) and loading frequencies (0.1 to 25 Hz). A catalog of default dynamic modulus values for typical asphalt concrete mixtures of Pakistan was established by developing stress-dependent master curves separately, for wearing and base course mixtures. The sensitivity of temperature and loading frequency on determination of dynamic modulus value was observed by typical isothermal and isochronal curves, respectively. Also, the effects of various variables on dynamic modulus were investigated using statistical technique of two-level factorial design of experiment. Furthermore, two dynamic modulus prediction models, namely, Witczak and Hirsch, were evaluated for their regional applicability. Results indicated that both the Witczak and Hirsch models mostly underpredict the value of dynamic modulus for the selected conditions/mixtures. The findings of this study are envisaged to facilitate the implementation of relatively new performance based mechanistic-empirical structural design and analysis approach.


---

## Body

## 1. Introduction

Hot-mix asphalt (HMA) consists of the optimum combination of two basic ingredients: aggregate and asphalt binder. In order to meet the diverse and often conflicting performance parameters, for example, resistance to fatigue, deformation, cracking, and moisture damage; durability; skid resistance; and workability and economy, the mix designer generally manipulates three variables, namely, aggregates, asphalt binder, and the ratio of asphalt binder to aggregates, and thus seeks to achieve the aforementioned performance requirements. In Pakistan, the past few years have seen an increase in the premature failure due to fatigue cracking and rutting in both newly constructed and rehabilitated asphalt concrete pavements. The phenomenon of premature failure of pavement structures is attributed to the current design procedures based on 1993 AASHTO design guide which are inherently empirical and incapable of providing adequate and reliable designs for heavy axle loads and tyre pressures in diversity of climatic regions and necessitates a more comprehensive design approach which incorporates both mechanistic and empirical aspects of design. Mechanistic-empirical pavement design guide (AASHTO Pavement ME) encompasses two parts: mechanistic (determine pavement responses) and empirical (distress prediction models/transfer functions). The success of the mechanistic-empirical structural design approach or framework lies in the accurate material characterization for predicting realistic pavement responses and ultimate performance. However, the viscoelastic nature of HMA is a challenge to be considered for its accurate characterization by the material properties. Dynamic modulusE
∗ of HMA is one such material property which reflects the loading time and temperature dependency of HMA. Dynamic modulus is considered as the stiffness property of HMA which can partially characterize its viscoelastic nature. It is the measure of the HMA’s resistance to deformation under sinusoidal loading and is given by the absolute value of the complex modulus [1, 2]. Dynamic modulus of HMA has gained attention of the researchers during the past decade especially after its selection as a design input parameter for material characterization of asphalt concrete in the AASHTO Pavement ME pavement design guide and a candidate for a simple performance test to complement Superpave mix design methodology.Several studies have been conducted in order to gain an insight into the factors affectingE
∗. Bonnaure et al. [3] determined the modulus of asphalt mixtures by the application of a sinusoidal load to trapezoidal specimens and reported that the amount of aggregate and percent of air voids had a significant effect on the stiffness of the mix. Another study reported that the mixtures containing stiffer binders resulted in higher values of E
∗. Furthermore, sample preparation techniques did not affect the dynamic modulus test results [4]. Kim et al. [5] reported that aggregate sources and gradation, within the North Carolina Department of Transportation, Superpave classification, did not seem to have a significant effect on dynamic modulus. This study also determined that the binder source, binder performance grade (PG), and asphalt content seemed to affect the dynamic modulus of asphalt mixtures. Flintsch et al. [6] concluded that mixes of the same type resulted in different measured E
∗ values because of different constituents, that is, aggregate type, asphalt content, and percentage RAP which showed that E
∗ was sensitive to mix constituents and properties. Cross et al. [7] evaluated the factors affecting E
∗ and observed that the testing on lowest temperature of −10°C caused significant frost buildup on the test frame, samples, and LVDTs making it a difficult and time consuming task to determine E
∗ below 0°C. Further, it was reported that the gyratory sample should be compacted to 6.0 ± 1.0% air voids in order to obtain a cored test specimen of required dimensions at 4.5 ± 1.0% air voids. PG grade in addition to test temperature and frequency was reported to have a significant effect on E
∗. However, no significant effect of nominal maximum aggregate size (NMAS) or mix designation was observed. Tashman and Elangovan [8] developed a database of E
∗ values of seven different job mix formulae (JMF) mixes with aggregates of different types and sources typically used in Washington state. Statistical analysis of the results revealed that use of different JMF mixes affected the dynamic modulus. However, it was also observed that the difference in E
∗ due to different JMF was more significant at high temperatures and low frequencies. It was also observed that variation in the aggregate percent passing number 200 sieve did not have any effect on the dynamic modulus. Mohammad et al. [9] documented the effect of aggregate size on E
∗ as a result of the study conducted for characterization of Louisiana asphalt mixtures. It was observed that NMAS had a significant effect on E
∗, as the larger aggregate size combined with recycled asphalt (RAP) yielded higher values of E
∗ at high temperatures. Another study developed a dynamic modulus catalog for NJDOT for implementation of AASHTO Pavement ME structural design approach which was achieved by characterizing twenty-one different typical plant-produced HMA mixes [10]. Bonaquist [11] conducted dynamic modulus testing and reported that, for the same aggregate source mixes, dynamic modulus values were not much different from one another. Further, the aggregate sources with higher dynamic modulus values had the higher limiting minimum modulus values also when compared to other aggregate sources. Limiting minimum modulus values represents the stiffness of aggregate. A study compared the dynamic modulus of field extracted core with laboratory fabricated specimens and concluded that at 4°C dynamic modulus can be compared [12]. Laboratory evaluated dynamic modulus was related to field response and results indicated that laboratory obtained dynamic modulus was inversely proportional to the field measured pavement response of the asphalt longitudinal strains [13]. A number of recent comparative research studies characterized different HMA mixes based upon dynamic modulus test and constructed master curves in order to meet the practitioner needs [14–16].Kim et al. [16] investigated the effect of additive (LEADCAP) on warm-mix asphalt using dynamic modulus, resilient modulus, and in-door accelerated pavement test (APT). The results suggested that additive is capable of producing mixture at relatively low temperature up to 30°C in comparison to conventional mixture and can be compared reasonably well with controlled hot-mix asphalt. Various researches determined the dynamic modulus of plant-produced or laboratory prepared mixes and validated the predictive ability of Witczak 1-37A model to a reasonable conformity [17–19]. El-Badawy et al. [20] in ensuing research study also calibrated the predictive equations for Idaho state mixtures. Cho et al. [21] evaluated the dynamic modulus of mixtures used in Korea and developed the E
∗ predictive equation for Korean AASHTO Pavement ME and concluded that developed predictive equations were well correlated with measured values. A study was carried out in Saudi Arabia for implementation of AASHTOWare Pavement design and evaluated two models, namely, NCHRP 1-37A and 1-40D, and concluded that NCHRP 1-37A E
∗ model showed accurate and unbiased results [22]. A recent study evaluated the viscoelastic properties of a performance grade binder modified with different percentages of a wax-based warm-mix asphalt (WMA) using dynamic modulus test. This study concluded that the Hirsch model (2003) [23] provided better approximations of the E
∗ values than the Witczak model [24]. In consequence of requisition of skilled personnel, time, and cost effect associated with the dynamic modulus test, researchers have been attempting for several years by using various modeling techniques to develop the prediction equations which can predict the E
∗ values directly from the mix properties. The last few decades have seen the development of these predictive equations as listed in Table 1.Table 1
List of dynamic modulus|
E
∗
| predictive models [25].
Model number
E
∗ predictive model
Year (published)
1
Van der Poel model
1954
2
Bonnaure model
1977
3
Shook and Kallas model
1969
4
Witczak’s early model
1972
5
Witczak and Shook’s model
1978
6
Witczak’s model
1981
7
Witczak, Miller, and Uzan’s model
1983
8
Witczak and Akhter’s model
1984
9
Witczak, Leahy, Caves, and Uzan’s model
1989
10
Witczak and Fonseca’s model
1996
11
Andrei, Witczak, and Mirza’s revised model
1999
12
Hirsch model of Christensen, Pellinen, and Bonaquist
2003The most recent models listed in Table1, that is, Andrei, Witczak, and Mirza’s revised model (hereafter referred to as Witczak model) and Hirsch model of Christensen, Pellinen, and Bonaquist (hereafter referred to as Hirsch model), have been reported to be reasonably accurate and were used to evaluate understudy HMA mixtures in this research.The findings of studies mentioned in Table1 indicate dynamic modulus, a key material property of HMA that better reflects the viscoelastic nature of asphalt concrete. Its significance has further been increased as a result of its selection as a material characterization design input parameter in the AASHTO Pavement ME and thus asphalt concrete mixtures need to be characterized in terms of E
∗ at regional levels [20–22]. However, to the knowledge of authors, no such research study characterized locally used mixtures in Pakistan. Hence, this research study aimed to determine the dynamic modulus of plant-produced asphalt mixtures in laboratory and results obtained were employed to two-level factorial design for determination of factor affecting E
∗. This research study characterizes and develops the master curves for different asphalt concrete mixes (for wearing and base course mixes), investigates the factors affecting dynamic modulus (stiffness parameter) in order to compare and rank selected asphalt concrete mixes, and validates the laboratory observed dynamic modulus values with the two dynamic modulus prediction models, namely, Witczak and Hirsch models.


## 2. Methodology

### 2.1. Objective and Scope

The objective of this study is to develop master curves for various plant-produced asphalt concrete mixtures and rank them based on dynamic modulus. The study incorporates four wearing mixes of nominal maximum aggregate size (NMAS) of 19 mm and three base mixes of NMAS of 37.5 mm procured from different highway construction sites of Pakistan. The binder and aggregate type used for testing were penetration grade 60/70 and limestone aggregate, each from two different sources. The study variables for different selected mixtures are presented in Table2.Table 2
Project and mixtures designation—wearing and base course mixtures.
Mix course
Abbreviated name
Project name
Aggregate source
NMAS (mm)
Mix type
Bitumen source and pen. grade
Wearing course mixtures
LNLP
Lakhi-Naudero-Larkana Road
Quetta
19
Marshall
NRL 60/70
HMW-W
Head Muhammad Wala Bridge (N-70)
Sargodha
19
Marshall
NRL 60/70
WUP-W
Wah Underpass(N-5)
Margalla
19
Marshall
ARL 60/70
SWB-TP
Swabi-Topi Road
Margalla
19
Marshall
ARL 60/70
Base course mixtures
JPU
Jalalpur-Pirwala-Uch Sharif  Road (N-115)
Sargodha
37.5
Marshall
NRL 60/70
HMW-B
Head Muhammad Wala Bridge (N-70)
Sargodha
37.5
Marshall
NRL 60/70
WUP -B
Wah Underpass(N-5)
Margalla
37.5
Marshall
ARL 60/70
Note. NRL: National Refinery Limited; ARL: Attock Refinery Limited.


### 2.2. Selection of Material

Seven plant-produced asphalt concrete mixtures were procured from different highway construction projects keeping in view the desired variability and availability of the plant-produced HMA in Pakistan. Representative samples of all seven mixes were collected from dump trucks at plant site, following the proper sampling techniques [26]. The mixtures used in the study were designed using Marshall method (optimum bitumen content determination) by the contractors of the selected projects pursuant to specifications of National Highway Authority (NHA) [27]. Job mix formulae and gradations of the selected asphalt mixtures are presented in Table 3.Table 3
Job mix formulae for selected asphalt mixtures.
Mix type/
Wearing course mixtures
Base course mixtures
name
LNLP
HMW-W
WUP-W
SWB-TP
JPU
HMW-B
WUP-B
Binder type
NRL 60/70
NRL 60/70
ARL 60/70
ARL 60/70
NRL 60/70
NRL 60/70
ARL 60/70
Binder content (%)
4.0
4.4
4.2
4.2
3.3
3.4
3.5
Air void (%)
4.0
4.0
4.0
4.0
4.0
4.0
4.0
VMA (%)
14.8
15.3
14.2
13.4
13.7
13.2
12.8
VFA (%)
66.9
63.5
66.5
59.5
58.1
59.2
58.0
Metric (US) sieve
Gradation (% passing)
37.5 mm (1
1
/
2 in.)
100
100
100
100
100
100
98.8
25 mm (1 in.)
100
100
100
100
82.6
85.4
82.7
19 mm (3
/
4 in.)
100
99.9
99.7
100
69.7
71.0
67.4
12.5 mm (1
/
2 in.)
82.5
79.5
84.5
80
59.2
59.9
56.2
9.5 mm (3
/
8 in.)
68.7
69.4
63.4
67
52.2
53.4
43.5
4.75 mm (number 4)
49.3
48.7
46
48
41.6
35.5
35.0
2.36 mm (number 8)
30.8
35.3
30.5
33
24.5
26.4
25.1
0.3 mm (number 50)
10.5
11.8
10.3
11
9.4
10.8
7.6
0.075 mm (number 200)
5.2
5.2
5.0
4.7
5.0
4.7
4.2


### 2.3. Specimens Preparation

Representative plant-produced asphalt mix samples were subjected to testing for maximum theoretical specific gravity, asphalt content, and gradation of the aggregate. Then these samples were reheated to compaction temperature of 135°C in the laboratory and triplicate specimens for each test temperature were fabricated in accordance with ASTM 3496-99 [28] using Superpave gyratory compactor with target voids in total mix (VTM) of 4
%
±
1
% (after coring and/or cutting). The binders on these plant-produced mixes underwent short-term aging during their production stage; however, these binders were extracted/tested. The variation among triplicates specimens was in specified range as specified in AASHTO TP62-07 [1]. Each gyratory compacted specimen was carefully sawed up to required dimension of 100 mm diameter and 150 mm height to comply with the dynamic modulus test specimen requirements as per AASHTO TP 62-07 [1].


### 2.4. Laboratory Testing

TheE
∗ test yields phase angle and E
∗ value. The phase angle (φ) is the angle by which induced axial strain lags behind the applied compressive stress. Figure 1 illustrates the sinusoidal stress and the resulting strain defined by the angular velocity which in turn are related to the loading frequency and time which implies that the phase lag represents the time dependency of HMA. AASHTO Pavement ME has three levels of input: level 1 includes determination of E
∗ in laboratory (material input), whereas levels 2 and 3 encompass determination of E
∗ by the use of predictive equations. Dynamic modulus has also been adopted by AASHTO as a provisional standard in AASHTO designation TP62-07 [1]. The dynamic modulus test method is a widely used laboratory test that requires application of a compressive axial stress to a cylindrical specimen of HMA and the recoverable strain is calculated from axial deformations measured at two, three, or four locations (as required) by using linear variable differential transformers (LVDTs). Dynamic modulus is then calculated as the ratio of stress magnitude to average strain magnitude.Figure 1
Phase lag between sinusoidal stress and recoverable strain [2].The dynamic modulus test was conducted at four temperatures and six frequencies for each mixture using asphalt mixture performance tester (AMPT). Specimens were conditioned for the required equilibrium in order to achieve the desired test temperatures before conducting the test. The test equipment consists of environmental chamber, which controls temperature ranging from 4 to 60°C, and confined pressure system which provides pressure up to 210 kPa. Three replicate specimens were tested at each test temperature with COV ranging from 4% to 21%. The tests were performed at the loading frequencies of 25, 10, 5, 1, 0.5, and 0.1 Hz and the temperatures used for the testing were 4.4°C, 21.1°C, 37.8°C, and 54.4°C. The laboratory results were further cast off to develop master curves and statistical analysis.


## 2.1. Objective and Scope

The objective of this study is to develop master curves for various plant-produced asphalt concrete mixtures and rank them based on dynamic modulus. The study incorporates four wearing mixes of nominal maximum aggregate size (NMAS) of 19 mm and three base mixes of NMAS of 37.5 mm procured from different highway construction sites of Pakistan. The binder and aggregate type used for testing were penetration grade 60/70 and limestone aggregate, each from two different sources. The study variables for different selected mixtures are presented in Table2.Table 2
Project and mixtures designation—wearing and base course mixtures.
Mix course
Abbreviated name
Project name
Aggregate source
NMAS (mm)
Mix type
Bitumen source and pen. grade
Wearing course mixtures
LNLP
Lakhi-Naudero-Larkana Road
Quetta
19
Marshall
NRL 60/70
HMW-W
Head Muhammad Wala Bridge (N-70)
Sargodha
19
Marshall
NRL 60/70
WUP-W
Wah Underpass(N-5)
Margalla
19
Marshall
ARL 60/70
SWB-TP
Swabi-Topi Road
Margalla
19
Marshall
ARL 60/70
Base course mixtures
JPU
Jalalpur-Pirwala-Uch Sharif  Road (N-115)
Sargodha
37.5
Marshall
NRL 60/70
HMW-B
Head Muhammad Wala Bridge (N-70)
Sargodha
37.5
Marshall
NRL 60/70
WUP -B
Wah Underpass(N-5)
Margalla
37.5
Marshall
ARL 60/70
Note. NRL: National Refinery Limited; ARL: Attock Refinery Limited.


## 2.2. Selection of Material

Seven plant-produced asphalt concrete mixtures were procured from different highway construction projects keeping in view the desired variability and availability of the plant-produced HMA in Pakistan. Representative samples of all seven mixes were collected from dump trucks at plant site, following the proper sampling techniques [26]. The mixtures used in the study were designed using Marshall method (optimum bitumen content determination) by the contractors of the selected projects pursuant to specifications of National Highway Authority (NHA) [27]. Job mix formulae and gradations of the selected asphalt mixtures are presented in Table 3.Table 3
Job mix formulae for selected asphalt mixtures.
Mix type/
Wearing course mixtures
Base course mixtures
name
LNLP
HMW-W
WUP-W
SWB-TP
JPU
HMW-B
WUP-B
Binder type
NRL 60/70
NRL 60/70
ARL 60/70
ARL 60/70
NRL 60/70
NRL 60/70
ARL 60/70
Binder content (%)
4.0
4.4
4.2
4.2
3.3
3.4
3.5
Air void (%)
4.0
4.0
4.0
4.0
4.0
4.0
4.0
VMA (%)
14.8
15.3
14.2
13.4
13.7
13.2
12.8
VFA (%)
66.9
63.5
66.5
59.5
58.1
59.2
58.0
Metric (US) sieve
Gradation (% passing)
37.5 mm (1
1
/
2 in.)
100
100
100
100
100
100
98.8
25 mm (1 in.)
100
100
100
100
82.6
85.4
82.7
19 mm (3
/
4 in.)
100
99.9
99.7
100
69.7
71.0
67.4
12.5 mm (1
/
2 in.)
82.5
79.5
84.5
80
59.2
59.9
56.2
9.5 mm (3
/
8 in.)
68.7
69.4
63.4
67
52.2
53.4
43.5
4.75 mm (number 4)
49.3
48.7
46
48
41.6
35.5
35.0
2.36 mm (number 8)
30.8
35.3
30.5
33
24.5
26.4
25.1
0.3 mm (number 50)
10.5
11.8
10.3
11
9.4
10.8
7.6
0.075 mm (number 200)
5.2
5.2
5.0
4.7
5.0
4.7
4.2


## 2.3. Specimens Preparation

Representative plant-produced asphalt mix samples were subjected to testing for maximum theoretical specific gravity, asphalt content, and gradation of the aggregate. Then these samples were reheated to compaction temperature of 135°C in the laboratory and triplicate specimens for each test temperature were fabricated in accordance with ASTM 3496-99 [28] using Superpave gyratory compactor with target voids in total mix (VTM) of 4
%
±
1
% (after coring and/or cutting). The binders on these plant-produced mixes underwent short-term aging during their production stage; however, these binders were extracted/tested. The variation among triplicates specimens was in specified range as specified in AASHTO TP62-07 [1]. Each gyratory compacted specimen was carefully sawed up to required dimension of 100 mm diameter and 150 mm height to comply with the dynamic modulus test specimen requirements as per AASHTO TP 62-07 [1].


## 2.4. Laboratory Testing

TheE
∗ test yields phase angle and E
∗ value. The phase angle (φ) is the angle by which induced axial strain lags behind the applied compressive stress. Figure 1 illustrates the sinusoidal stress and the resulting strain defined by the angular velocity which in turn are related to the loading frequency and time which implies that the phase lag represents the time dependency of HMA. AASHTO Pavement ME has three levels of input: level 1 includes determination of E
∗ in laboratory (material input), whereas levels 2 and 3 encompass determination of E
∗ by the use of predictive equations. Dynamic modulus has also been adopted by AASHTO as a provisional standard in AASHTO designation TP62-07 [1]. The dynamic modulus test method is a widely used laboratory test that requires application of a compressive axial stress to a cylindrical specimen of HMA and the recoverable strain is calculated from axial deformations measured at two, three, or four locations (as required) by using linear variable differential transformers (LVDTs). Dynamic modulus is then calculated as the ratio of stress magnitude to average strain magnitude.Figure 1
Phase lag between sinusoidal stress and recoverable strain [2].The dynamic modulus test was conducted at four temperatures and six frequencies for each mixture using asphalt mixture performance tester (AMPT). Specimens were conditioned for the required equilibrium in order to achieve the desired test temperatures before conducting the test. The test equipment consists of environmental chamber, which controls temperature ranging from 4 to 60°C, and confined pressure system which provides pressure up to 210 kPa. Three replicate specimens were tested at each test temperature with COV ranging from 4% to 21%. The tests were performed at the loading frequencies of 25, 10, 5, 1, 0.5, and 0.1 Hz and the temperatures used for the testing were 4.4°C, 21.1°C, 37.8°C, and 54.4°C. The laboratory results were further cast off to develop master curves and statistical analysis.


## 3. Results and Discussion

The dynamic modulus exhibits stress-strain relationship under compressive sinusoidal loading. As expected, for all the tested asphalt concrete mixtures, the dynamic modulus values decreased with an increase in temperature and decrease in the loading frequency. It was observed that LNLP and WUP wearing course mixtures have relatively higher dynamic modulus values at low and high temperature variations, respectively, whereas JPU base course mix has relatively highest dynamic modulus values at both low and high temperatures for the range of loading frequencies (Table4).Table 4
Measured dynamic modulus,|
E
∗
| (MPa), and phase angle, φ.
(a)
Wearing course mixes
Temperature
Freq.
HMW-W
WUP-W
SWB-TP
LNLP
(°Celsius)
(Hz)
|
E
∗
|
φ
|
E
∗
|
φ
|
E
∗
|
φ
|
E
∗
|
φ
4.4
25
23077
7.90
17395
7.85
23821
5.93
29820
6.89
10
21360
8.15
16258
8.21
22305
6.52
27572
7.62
5
20346
9.12
15368
8.95
21229
6.91
26028
8.29
1
16947
9.92
13293
11.27
18712
8.82
22829
10.56
0.5
15865
11.58
12376
12.26
17382
9.58
20815
11.49
0.1
13279
14.21
10259
14.87
14555
11.83
16623
14.66
21.1
25
17099
12.20
14141
11.12
17306
10.61
17547
13.91
10
14769
13.36
12679
12.41
15610
11.51
15320
15.73
5
13348
13.87
11811
13.10
14720
12.81
13803
16.80
1
10639
16.65
9384
16.65
11342
16.52
10108
20.25
0.5
9315
17.90
8246
17.81
9935
17.70
8770
21.75
0.1
6750
22.07
5819
21.41
7281
21.52
5833
26.39
37.8
25
9942
17.09
8908
19.52
11238
16.86
6322
27.98
10
7998
19.77
9754
21.17
9494
19.38
4695
29.91
5
7040
21.35
8580
22.23
8370
20.65
3716
30.40
1
5047
23.83
3284
24.62
5964
23.77
2075
31.24
0.5
4337
24.61
2732
25.17
5033
24.69
1586
30.95
0.1
2744
26.76
1575
27.16
3054
27.23
869
29.32
54.4
25
5268
25.62
6750
22.07
5619
27.50
3323
32.50
10
4158
26.55
5502
24.11
4413
28.50
2351
32.60
5
3475
26.05
4675
24.78
3372
28.45
1772
32.37
1
2158
28.46
3103
27.18
1917
28.63
917
30.97
0.5
1717
28.58
2517
27.52
1462
28.21
676
30.29
0.1
889
26.56
1289
29.39
731
27.42
359
27.75
(b)
Base course mixes
Temperature
Freq.
JPU
HMW-B
WUP-B
(°Celsius)
(Hz)
|
E
∗
|
φ
|
E
∗
|
φ
|
E
∗
|
φ
4.4
25
31626
6.60
29068
6.72
23228
6.77
10
30199
7.65
27379
7.71
21801
7.92
5
28448
8.24
25973
8.62
20650
9.02
1
24387
10.97
22229
11.79
17609
12.61
0.5
22477
12.34
20415
13.22
16154
14.30
0.1
17837
16.30
16092
17.67
12569
19.19
21.1
25
21167
11.68
19105
14.29
18699
12.41
10
18940
14.37
16534
16.98
16603
14.76
5
17037
16.15
14734
19.14
15141
16.62
1
12886
21.30
10432
25.55
11307
22.40
0.5
11156
23.33
8708
28.14
9694
24.66
0.1
7212
29.02
4950
34.93
5909
30.80
37.8
25
11783
22.81
19580
22.68
12349
21.02
10
9336
26.83
15789
26.57
9956
24.94
5
7770
28.89
13190
29.11
8205
27.22
1
4245
33.34
7663
35.27
4744
32.26
0.5
2982
34.04
5669
36.78
3475
33.09
0.1
1299
34.33
2243
38.53
1448
32.70
54.4
25
7757
28.73
3399
42.17
5392
33.94
10
5557
32.31
2082
43.91
3544
36.05
5
4226
33.75
1351
44.68
2434
36.59
1
1958
35.89
462
44.44
1069
35.77
0.5
1317
35.33
276
44.40
689
34.92
0.1
524
31.44
110
38.61
331
30.55The average test results/typical isothermal and isochronal curves for dynamic modulus at four different temperatures and six different loading frequencies for wearing and base mixtures tested in the study have been presented in Figures2(a) and 2(b), respectively. It is evident from these plots that dynamic modulus decreases with increase in temperature and increases with increase in frequency. Also, sensitivity analysis reveals that, for a given loading frequency, an increase in temperature (from 21.1 to 37.8°C) translated into 57% and 55% drop in E
∗ values on average for wearing and base course mixes, respectively, whereas, for a given temperature, an increase in loading frequency (from 0.1 to 25 Hz), 68% and 79% of variation in E
∗ values on average, was attributed to wearing and base course mixes, respectively.Figure 2
Dynamic modulus test results.
(a)
Isothermal curves
(b)
Isochronal curves


### 3.1. Master Curves for Dynamic Modulus

The test results obtained were used for development of master curve for subsequent use in pavement structural response and design process. The test results for the replicate specimens were averaged for each test temperature and master curves for the average values ofE
∗ at a reference temperature of 21°C for each mix were constructed using the time-temperature superposition principle using Microsoft® solver sheet. Also, keeping in view the testing limitation and inability of the asphalt mixture performance tester (AMPT) to conduct test at −10°C, an abbreviated approach developed in NCHRP Project 9-29 was used for construction of the stress-dependent master curves [29].The general form of sigmoidal function used to develop a master curve is given as follows [30]:(1)
log
⁡
E
∗
=
δ
+
α
1
+
e
β
+
γ
log
⁡
f
r
,where  log
⁡
(
E
∗
) is log of dynamic modulus. δ is minimum modulus value. f
r is reduced frequency, that is, f
/
a
(
T
), where f is actual frequency and a
(
T
) is the required shift factor at reference temperature. α is span of modulus value (range of lowest and highest dynamic modulus values). β, γ are shape parameters of sigmoidal function.The master curves wearing and base mixes are presented in Figure3 which illustrates that they tend to converge at higher frequencies; however they have considerable degree of separation at lower frequencies. Higher frequency is analogous to lower temperature and vice versa in terms of temperature. It can be inferred that E
∗ of LNLP wearing mix (Figure 3(a)) and JPU base mix (Figure 3(b)) are relatively better performing for given tested mixtures which is attributed to the mixtures packing arrangement with the relatively lower design asphalt content than other mixtures, thus exhibiting higher stiffness values (see Table 3).Figure 3
Dynamic modulus master curves for plant-produced mixtures.
(a)
Log-log plot (wearing course mixes)
(b)
Semilog plot (wearing course mixes)
(c)
Log-log plot (base course mixes)
(d)
Semilog plot (base course mixes)


### 3.2. Evaluation of Dynamic Modulus Prediction Equations

As part of this study two prediction equations were evaluated for regional applicability in Pakistan. As there was no information available with reference to the default dynamic modulus values for commonly used mixtures in Pakistan, it was necessary to characterize the commonly used mixtures accordingly. The inputs parameters for both the equations were primarily obtained from the JMF of the mixtures. However, certain other information like viscosity and shear modulus of binder were obtained by conducting laboratory tests on the extracted binders.


#### 3.2.1. Witczak Model

The current Witczak model used in AASHTO Pavement ME is improved version of the previous Witczak and Fonseca model in order to use a wide range of AC mixtures. The Witczak model used 205 mixtures prepared with both modified and unmodified binders having a temperature range from 0 to 54.4°C and the loading frequency ranging from 0.1 to 25 Hz. A total of 39 different aggregate types were made part of this database and the mixtures tested included both kneading and gyratory compacted specimens [31]. Input parameters of Witczak 1-37A viscosity based model (2) include bitumen viscosity, effective asphalt content, aggregate gradations, air voids, and loading frequency: (2)
Log
⁡
E
∗
=
-
1.249337
+
0.029232
p
200
-
0.001767
p
200
2
-
0.00284
p
4
-
0.05809
V
a
-
0.802208
V
b
e
f
f
V
b
e
f
f
+
V
a
+
3.871977
-
0.0021
p
4
+
0.003958
p
38
-
0.000017
p
38
2
+
0.00547
p
34
1
+
e
-
0.603313
-
0.313351
log
⁡
f
-
0.393532
log
⁡
η
,where E
∗ is dynamic modulus of mix, 105 psi (1 psi = 0.00689 MPa). η
´ is viscosity of binder, 106 Poise. f is loading frequency, Hz. p
200 is % passing number 200 sieve. p
4 is cumulative % retained on number 4 sieve. p
38 is cumulative % retained on 3/8 in. sieve. p
34 is cumulative % retained on 3/4 in. sieve. V
a is air voids, % by volume. V
b
e
f
f is effective binder content, % by volume.For evaluation purposes, values of dynamic modulus were predicted using the Witczak model at the conditions corresponding to each measured value ofE
∗. E
∗ values were predicted using the volumetric details and aggregate gradations obtained from the JMF of the mixtures tested: loading frequency (0.1 to 25 Hz); % passing number 200 sieve (4.2 to 5.2%); cumulative % retained on number 4 sieve (35 to 49%); cumulative % retained on 3/8 in. sieve (43 to 69%); cumulative % retained on 3/4 in. sieve (67 to 100%); and air voids % by volume (3.5 to 4.5%). Results indicated that the Witczak model mostly underpredicts the values for dynamic modulus for HMA mixes of Pakistan. Figure 4(a) illustrates the comparison of measured and predicted dynamic modulus values grouped on the basis of temperature. It can be inferred from the figure that the values are distributed along the line of equality for lower temperatures. However, with an increase in temperature, the model tends to underpredict the values for dynamic modulus of the mixtures selected for the study. This implies that the said model is more relevant and significant at lower test temperatures as compared to higher temperature conditions for the tested mixtures in the study.Figure 4
Measured versus predicted plot of dynamic modulus.
(a)
Witczak model
(b)
Hirsch model


#### 3.2.2. Hirsch Model

Christensen et al. [23] developed Hirsch dynamic modulus prediction equation based on law of composite mixtures. The model was developed using database of various mixtures to determine dynamic modulus using binder shear modulus, that is, G
∗, and the volumetric properties of the mix, that is, voids in mineral aggregate (VMA) and voids filled with asphalt (VFA). The Hirsch model used 18 different mixtures and five different binder types to fabricate both Marshall and Superpave designed specimens. The tests were conducted at temperature ranging from 4 to 38°C and loading frequencies of 0.1 and 5 Hz. The database used for the development of model had air voids ranging from 5.6 to 11.2%; VMA ranging from 13.7 to 21.65%; and VFA of 38.7 to 68%. However, the input parameters range used for validation purpose in this study is given in parentheses against each parameter below. Hirsch model is presented as follows:(3)
E
∗
=
P
c
4200000
1
-
V
M
A
100
+
3
G
∗
b
V
F
A
×
V
M
A
10000
+
1
-
P
c
1
-
V
M
A
/
100
/
4200000
+
V
M
A
/
3
×
V
F
A
G
∗
b
,where (4)
P
c
=
20
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
650
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
.
E
∗ is dynamic modulus, psi (1 psi = 0.00689 MPa). VMA is voids in mineral aggregate, % (12.8 to 15.3%). VFA is voids in aggregate filled with asphalt, % (58 to 67%). G
∗
b is dynamic shear modulus of binder, psi (0.12 to 0.55 psi) or (0.83 to 3.79 kPa).The test results obtained from laboratory testing were also used for evaluation of the Hirsch model by comparison of the measuredE
∗ and the predicted E
∗ values. Hirsch model predictions were made using the input data, that is, VMA and VFA obtained from the JMF of each selected mix. Comparison of the results indicated that Hirsch model consistently underpredicts the dynamic modulus values for HMA mixes of Pakistan regardless of the test temperature, the frequency, or the mix selected as shown in Figure 4(b).The underprediction of dynamic modulus values is attributed to the variation in binder and volumetric (JMF) properties used for preparation of plant-produced mixtures compared to that used for the development of Witczak and Hirsch models. The parameter values obtained from the density-void analysis on the test sample could be more accurate than JMF parameters. Also, these models were calibrated using datasets of conditions quite different from Pakistan which are quarry dependent: variation in aggregate mineralogical composition (limestone, etc.) and gradation (percent passing different sieves) and variation in binder properties and its manufacturing process and industry. Also, the underprediction of dynamic modulus values is in agreement with similar past studies conducted on the local material for calibration of these models [32, 33].


## 3.1. Master Curves for Dynamic Modulus

The test results obtained were used for development of master curve for subsequent use in pavement structural response and design process. The test results for the replicate specimens were averaged for each test temperature and master curves for the average values ofE
∗ at a reference temperature of 21°C for each mix were constructed using the time-temperature superposition principle using Microsoft® solver sheet. Also, keeping in view the testing limitation and inability of the asphalt mixture performance tester (AMPT) to conduct test at −10°C, an abbreviated approach developed in NCHRP Project 9-29 was used for construction of the stress-dependent master curves [29].The general form of sigmoidal function used to develop a master curve is given as follows [30]:(1)
log
⁡
E
∗
=
δ
+
α
1
+
e
β
+
γ
log
⁡
f
r
,where  log
⁡
(
E
∗
) is log of dynamic modulus. δ is minimum modulus value. f
r is reduced frequency, that is, f
/
a
(
T
), where f is actual frequency and a
(
T
) is the required shift factor at reference temperature. α is span of modulus value (range of lowest and highest dynamic modulus values). β, γ are shape parameters of sigmoidal function.The master curves wearing and base mixes are presented in Figure3 which illustrates that they tend to converge at higher frequencies; however they have considerable degree of separation at lower frequencies. Higher frequency is analogous to lower temperature and vice versa in terms of temperature. It can be inferred that E
∗ of LNLP wearing mix (Figure 3(a)) and JPU base mix (Figure 3(b)) are relatively better performing for given tested mixtures which is attributed to the mixtures packing arrangement with the relatively lower design asphalt content than other mixtures, thus exhibiting higher stiffness values (see Table 3).Figure 3
Dynamic modulus master curves for plant-produced mixtures.
(a)
Log-log plot (wearing course mixes)
(b)
Semilog plot (wearing course mixes)
(c)
Log-log plot (base course mixes)
(d)
Semilog plot (base course mixes)


## 3.2. Evaluation of Dynamic Modulus Prediction Equations

As part of this study two prediction equations were evaluated for regional applicability in Pakistan. As there was no information available with reference to the default dynamic modulus values for commonly used mixtures in Pakistan, it was necessary to characterize the commonly used mixtures accordingly. The inputs parameters for both the equations were primarily obtained from the JMF of the mixtures. However, certain other information like viscosity and shear modulus of binder were obtained by conducting laboratory tests on the extracted binders.


### 3.2.1. Witczak Model

The current Witczak model used in AASHTO Pavement ME is improved version of the previous Witczak and Fonseca model in order to use a wide range of AC mixtures. The Witczak model used 205 mixtures prepared with both modified and unmodified binders having a temperature range from 0 to 54.4°C and the loading frequency ranging from 0.1 to 25 Hz. A total of 39 different aggregate types were made part of this database and the mixtures tested included both kneading and gyratory compacted specimens [31]. Input parameters of Witczak 1-37A viscosity based model (2) include bitumen viscosity, effective asphalt content, aggregate gradations, air voids, and loading frequency: (2)
Log
⁡
E
∗
=
-
1.249337
+
0.029232
p
200
-
0.001767
p
200
2
-
0.00284
p
4
-
0.05809
V
a
-
0.802208
V
b
e
f
f
V
b
e
f
f
+
V
a
+
3.871977
-
0.0021
p
4
+
0.003958
p
38
-
0.000017
p
38
2
+
0.00547
p
34
1
+
e
-
0.603313
-
0.313351
log
⁡
f
-
0.393532
log
⁡
η
,where E
∗ is dynamic modulus of mix, 105 psi (1 psi = 0.00689 MPa). η
´ is viscosity of binder, 106 Poise. f is loading frequency, Hz. p
200 is % passing number 200 sieve. p
4 is cumulative % retained on number 4 sieve. p
38 is cumulative % retained on 3/8 in. sieve. p
34 is cumulative % retained on 3/4 in. sieve. V
a is air voids, % by volume. V
b
e
f
f is effective binder content, % by volume.For evaluation purposes, values of dynamic modulus were predicted using the Witczak model at the conditions corresponding to each measured value ofE
∗. E
∗ values were predicted using the volumetric details and aggregate gradations obtained from the JMF of the mixtures tested: loading frequency (0.1 to 25 Hz); % passing number 200 sieve (4.2 to 5.2%); cumulative % retained on number 4 sieve (35 to 49%); cumulative % retained on 3/8 in. sieve (43 to 69%); cumulative % retained on 3/4 in. sieve (67 to 100%); and air voids % by volume (3.5 to 4.5%). Results indicated that the Witczak model mostly underpredicts the values for dynamic modulus for HMA mixes of Pakistan. Figure 4(a) illustrates the comparison of measured and predicted dynamic modulus values grouped on the basis of temperature. It can be inferred from the figure that the values are distributed along the line of equality for lower temperatures. However, with an increase in temperature, the model tends to underpredict the values for dynamic modulus of the mixtures selected for the study. This implies that the said model is more relevant and significant at lower test temperatures as compared to higher temperature conditions for the tested mixtures in the study.Figure 4
Measured versus predicted plot of dynamic modulus.
(a)
Witczak model
(b)
Hirsch model


### 3.2.2. Hirsch Model

Christensen et al. [23] developed Hirsch dynamic modulus prediction equation based on law of composite mixtures. The model was developed using database of various mixtures to determine dynamic modulus using binder shear modulus, that is, G
∗, and the volumetric properties of the mix, that is, voids in mineral aggregate (VMA) and voids filled with asphalt (VFA). The Hirsch model used 18 different mixtures and five different binder types to fabricate both Marshall and Superpave designed specimens. The tests were conducted at temperature ranging from 4 to 38°C and loading frequencies of 0.1 and 5 Hz. The database used for the development of model had air voids ranging from 5.6 to 11.2%; VMA ranging from 13.7 to 21.65%; and VFA of 38.7 to 68%. However, the input parameters range used for validation purpose in this study is given in parentheses against each parameter below. Hirsch model is presented as follows:(3)
E
∗
=
P
c
4200000
1
-
V
M
A
100
+
3
G
∗
b
V
F
A
×
V
M
A
10000
+
1
-
P
c
1
-
V
M
A
/
100
/
4200000
+
V
M
A
/
3
×
V
F
A
G
∗
b
,where (4)
P
c
=
20
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
650
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
.
E
∗ is dynamic modulus, psi (1 psi = 0.00689 MPa). VMA is voids in mineral aggregate, % (12.8 to 15.3%). VFA is voids in aggregate filled with asphalt, % (58 to 67%). G
∗
b is dynamic shear modulus of binder, psi (0.12 to 0.55 psi) or (0.83 to 3.79 kPa).The test results obtained from laboratory testing were also used for evaluation of the Hirsch model by comparison of the measuredE
∗ and the predicted E
∗ values. Hirsch model predictions were made using the input data, that is, VMA and VFA obtained from the JMF of each selected mix. Comparison of the results indicated that Hirsch model consistently underpredicts the dynamic modulus values for HMA mixes of Pakistan regardless of the test temperature, the frequency, or the mix selected as shown in Figure 4(b).The underprediction of dynamic modulus values is attributed to the variation in binder and volumetric (JMF) properties used for preparation of plant-produced mixtures compared to that used for the development of Witczak and Hirsch models. The parameter values obtained from the density-void analysis on the test sample could be more accurate than JMF parameters. Also, these models were calibrated using datasets of conditions quite different from Pakistan which are quarry dependent: variation in aggregate mineralogical composition (limestone, etc.) and gradation (percent passing different sieves) and variation in binder properties and its manufacturing process and industry. Also, the underprediction of dynamic modulus values is in agreement with similar past studies conducted on the local material for calibration of these models [32, 33].


## 3.2.1. Witczak Model

The current Witczak model used in AASHTO Pavement ME is improved version of the previous Witczak and Fonseca model in order to use a wide range of AC mixtures. The Witczak model used 205 mixtures prepared with both modified and unmodified binders having a temperature range from 0 to 54.4°C and the loading frequency ranging from 0.1 to 25 Hz. A total of 39 different aggregate types were made part of this database and the mixtures tested included both kneading and gyratory compacted specimens [31]. Input parameters of Witczak 1-37A viscosity based model (2) include bitumen viscosity, effective asphalt content, aggregate gradations, air voids, and loading frequency: (2)
Log
⁡
E
∗
=
-
1.249337
+
0.029232
p
200
-
0.001767
p
200
2
-
0.00284
p
4
-
0.05809
V
a
-
0.802208
V
b
e
f
f
V
b
e
f
f
+
V
a
+
3.871977
-
0.0021
p
4
+
0.003958
p
38
-
0.000017
p
38
2
+
0.00547
p
34
1
+
e
-
0.603313
-
0.313351
log
⁡
f
-
0.393532
log
⁡
η
,where E
∗ is dynamic modulus of mix, 105 psi (1 psi = 0.00689 MPa). η
´ is viscosity of binder, 106 Poise. f is loading frequency, Hz. p
200 is % passing number 200 sieve. p
4 is cumulative % retained on number 4 sieve. p
38 is cumulative % retained on 3/8 in. sieve. p
34 is cumulative % retained on 3/4 in. sieve. V
a is air voids, % by volume. V
b
e
f
f is effective binder content, % by volume.For evaluation purposes, values of dynamic modulus were predicted using the Witczak model at the conditions corresponding to each measured value ofE
∗. E
∗ values were predicted using the volumetric details and aggregate gradations obtained from the JMF of the mixtures tested: loading frequency (0.1 to 25 Hz); % passing number 200 sieve (4.2 to 5.2%); cumulative % retained on number 4 sieve (35 to 49%); cumulative % retained on 3/8 in. sieve (43 to 69%); cumulative % retained on 3/4 in. sieve (67 to 100%); and air voids % by volume (3.5 to 4.5%). Results indicated that the Witczak model mostly underpredicts the values for dynamic modulus for HMA mixes of Pakistan. Figure 4(a) illustrates the comparison of measured and predicted dynamic modulus values grouped on the basis of temperature. It can be inferred from the figure that the values are distributed along the line of equality for lower temperatures. However, with an increase in temperature, the model tends to underpredict the values for dynamic modulus of the mixtures selected for the study. This implies that the said model is more relevant and significant at lower test temperatures as compared to higher temperature conditions for the tested mixtures in the study.Figure 4
Measured versus predicted plot of dynamic modulus.
(a)
Witczak model
(b)
Hirsch model


## 3.2.2. Hirsch Model

Christensen et al. [23] developed Hirsch dynamic modulus prediction equation based on law of composite mixtures. The model was developed using database of various mixtures to determine dynamic modulus using binder shear modulus, that is, G
∗, and the volumetric properties of the mix, that is, voids in mineral aggregate (VMA) and voids filled with asphalt (VFA). The Hirsch model used 18 different mixtures and five different binder types to fabricate both Marshall and Superpave designed specimens. The tests were conducted at temperature ranging from 4 to 38°C and loading frequencies of 0.1 and 5 Hz. The database used for the development of model had air voids ranging from 5.6 to 11.2%; VMA ranging from 13.7 to 21.65%; and VFA of 38.7 to 68%. However, the input parameters range used for validation purpose in this study is given in parentheses against each parameter below. Hirsch model is presented as follows:(3)
E
∗
=
P
c
4200000
1
-
V
M
A
100
+
3
G
∗
b
V
F
A
×
V
M
A
10000
+
1
-
P
c
1
-
V
M
A
/
100
/
4200000
+
V
M
A
/
3
×
V
F
A
G
∗
b
,where (4)
P
c
=
20
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
650
+
V
F
A
×
3
G
∗
b
/
V
M
A
0.58
.
E
∗ is dynamic modulus, psi (1 psi = 0.00689 MPa). VMA is voids in mineral aggregate, % (12.8 to 15.3%). VFA is voids in aggregate filled with asphalt, % (58 to 67%). G
∗
b is dynamic shear modulus of binder, psi (0.12 to 0.55 psi) or (0.83 to 3.79 kPa).The test results obtained from laboratory testing were also used for evaluation of the Hirsch model by comparison of the measuredE
∗ and the predicted E
∗ values. Hirsch model predictions were made using the input data, that is, VMA and VFA obtained from the JMF of each selected mix. Comparison of the results indicated that Hirsch model consistently underpredicts the dynamic modulus values for HMA mixes of Pakistan regardless of the test temperature, the frequency, or the mix selected as shown in Figure 4(b).The underprediction of dynamic modulus values is attributed to the variation in binder and volumetric (JMF) properties used for preparation of plant-produced mixtures compared to that used for the development of Witczak and Hirsch models. The parameter values obtained from the density-void analysis on the test sample could be more accurate than JMF parameters. Also, these models were calibrated using datasets of conditions quite different from Pakistan which are quarry dependent: variation in aggregate mineralogical composition (limestone, etc.) and gradation (percent passing different sieves) and variation in binder properties and its manufacturing process and industry. Also, the underprediction of dynamic modulus values is in agreement with similar past studies conducted on the local material for calibration of these models [32, 33].


## 4. Conclusions

Performance evaluation of seven plant-produced HMA mixtures was carried out using dynamic modulus testing and factors influencing the dynamic modulus of HMA were evaluated. It was observed that the test temperature and loading frequency are significant factors affecting dynamic modulus for both wearing and base course mixtures; however, VMA is marginally significant in case of base course mixtures, only. Furthermore, there was significant difference between the dynamic modulus of different mixtures based on different aggregate size, gradation, and aggregate source. At low (cold) temperatures, the parameter of viscous (or elastic) properties of the mixtures (phase angle) decreases which indicates more elastic behavior of material with high modulus values and is attributed to the dependency of binder on asphalt concrete response at lower temperatures. However, at high (warm) temperatures, the effect of aggregate skeleton/interlock starts to overpower the viscous binder effect causing the phase angle to decline. As part of this study the dynamic modulus prediction models, namely, Witczak and Hirsch, were also evaluated for their potential regional applicability. Results indicated that both models mostly underpredict the value of dynamic modulus for the selected conditions/mixtures. Nevertheless, these models could be used for evaluation purposes and for the design of low and medium traffic volumes pending future investigation of the revised prediction equation incorporated in the new AASHTO Pavement ME software/guide. The established default dynamic modulus values catalog for typical asphalt concrete mixtures of Pakistan at various temperatures and frequencies by developing the master curves ofE
∗ is the foremost effort in the country, thus facilitating the future implementation of performance based mechanistic-empirical structural design and analysis approach.



---

*Source: 5618427-2016-03-24.xml*