Materials and Structures DOI 10.1617/s11527-015-0689-0

ORIGINAL ARTICLE

Evaluation of resilient behavior of flexible pavement asphalt layers Gholamali Shafabakhsh . Amin Tanakizadeh

Received: 28 April 2015 / Accepted: 8 August 2015 Ó RILEM 2015

Abstract Asphalt concrete is a viscoelastic material that has a resilient behavior during cyclic loads. One of the important features for defining this behavior is resilient modulus (MR). Usually, asphalt mixture is laid down in two layers known as binder and surface layers at different depth beneath the road surface. The current test methods use only one loading pulse shape, namely, haversine that represents the shape of loading exerted to the binder layer. Thus, this paper investigates resilient behavior of asphalt material in different depths. Indirect tensile test was employed for determination of MR using universal testing machine. The modulus of asphalt mixture was measured by applying the two pulse shapes in a range of temperatures and pulse widths. The pulse shapes were haversine and square, describing the behavior of mixture in binder and surface layers, respectively. The test results showed that difference between resilient behavior of binder and surface layers is more apparent at high temperatures and under fast traffic loadings. In addition, using the best-fitted functions to MR results and mathematical calculations, haversine pulse widths for surface layer were specified. The MR testing under haversine pulse should be performed with longer pulse G. Shafabakhsh  A. Tanakizadeh (&) Faculty of Civil Engineering, Semnan University, Semnan 35131-19111, Iran e-mail: [email protected] G. Shafabakhsh e-mail: [email protected]

widths compared to square loading to fulfill resilient behavior of surface layer accurately. The MR test under haversine pulse was more accurate and beneficial than square one. Keywords Asphalt concrete  Resilient modulus  Pavement depth  Loading pulse shape  Pulse width

1 Introduction In recent mechanistic-empirical pavement design method, the flexible pavements are designed based on their response under different temperature and loading conditions. One of the most important characteristics in design procedure of asphalt pavements is modulus of asphalt layers. This parameter represents resilient behavior of asphalt materials under various thermal and traffic loading conditions. In addition, multilayer elastic theory and finite element models use it for determination of asphalt pavement thickness and analysis of pavement structure. The dynamic modulus (|E*|) is a key design parameter in mechanistic-empirical pavement design guide. The standard dynamic modulus test procedure does not consider the rest period between loading pulses. On the other hand, traffic loading in the field is not continue and has a gap between applied loads due to different traffic densities and axle spaces. Therefore, the standard |E*| test characterizes

Materials and Structures

stiffness modulus of asphalt mixtures with some inaccuracies. Add to this issue, the effects of healing phenomena during rest times cannot be taken into account using standard |E*| test. In addition, previous studies have showed that determination of asphalt layers modulus using dynamic modulus instead of resilient modulus (MR) makes some underestimated pavement responses, which can be effective on pavement performance prediction [3, 36]. Based on the above reasons, the authors, and some researchers [36] recommended using MR in analysis and design of flexible pavements. This study has focused on MR to analyze resilient behavior of asphalt layers. Applying the small cyclic loads, the deformations under each load cycle are recovered approximately. As the number of cycles increases, the plastic strain caused by each load cycle decreases. After 100–200 cycles, the strain is nearly recoverable, as indicated by (er). With application of deviator stress (rd), which is the axial stress in an unconfined compression test, the MR defined as Eq. (1) [22]: rd MR ¼ : ð1Þ er As mentioned previously, the MR is used in thickness design of flexible pavements. With application of two pulse shapes and various pulse widths, it can be possible to consider the resilient behavior of asphalt layers (binder and surface layers) separately. The presented paper aims to explore correctness of this claim through an experimental study. In addition, the resilient behavior of both layers can be studied using typical haversine shape and different loading times, as an alternative procedure. Using this method, we can prevent from uncommon square shape tests that caused damage to specimens and resulted in possibly inaccurate MR values.

2 Literature review Behavioral analysis of pavement asphalt layers is an important part of studies has been done in recent years. The followings are some of research studies about behavior of asphalt pavements under different loading conditions through experimental and computational techniques focusing on stiffness modulus.

Reference [17] introduced indirect tensile stiffness modulus as a main property of asphalt mix closely related to permanent deformation. In a summary of findings by the RILEM Technical Committee 206 on Advanced Testing and Characterization of Bituminous Materials, interlayer bond between pavement layers was considered. The effects of specimen diameter, test temperature, test speed, applied stress, and aging on shear bond strength were evaluated through shear tests [31]. Reference [19] investigated 3D strains near the surface of asphalt concrete layers using optic fiber sensors and compared the shape and magnitude of strain pulse with theoretical viscoelastic model results. Reference [32] evaluated response of cracked asphalt concrete pavement under a half-sinusoidal impact load. The effects of different vehicle speeds, crack locations and depths, and damping ratios on dynamic response of pavement were explored using dynamics and fracture mechanics and finite element method. Zhao et al. [35] determined the linear viscoelastic properties of asphalt concrete under confining pressure applying two models for master curve of triaxial storage modulus and continuous relaxation spectrum. The models describe time-, temperature-, and pressure-dependent behavior of asphalt mixture well. Ameri et al. [4] analyzed viscoelastic multilayered structures using a quasi-static finite element formulation. The influence of load rate and time on the quasistatic response of asphalt concrete pavement was investigated. Graziani et al. [18] determined bulk and shear moduli of bituminous mixtures with application of the elastic–viscoelastic correspondence principle and uniaxial tension–compression tests at selected frequencies and temperatures. The uniaxial tests induced variations in volume and shape of specimens. Reference [15] explored flexural-tension properties and uniaxial compressive strength of microsurfacing mixture under different loading rate. To this aim, the three point bending test and uniaxial compressive test were used. In addition, a logarithmic relationship between the strength and loading rate was established. Zhang et al. [34] studied the effects of various temperatures, vehicle loads, and speeds on dynamic properties of asphalt mixtures. The stress and displacement of asphalt mixtures and vehicle were not

Materials and Structures

related to each other linearly. The effect of temperature on dynamic properties was more significant. Reference [20] modeled mechanistic responses of asphalt concrete layers by simulation of acceleration and deceleration modes of vehicle motions using a finite element program. The program measured 3D vertical tire-pavement contact pressure accurately. Reference [27] evaluated dynamic displacement response of axially loaded pavements under two-axle moving high frequency harmonic loads, thoroughly. The effects of load distance and phase, axial compression, load velocity and frequency, and foundation damping on the displacement were explored. Chailleux et al. [13, 14] investigated secant modulus of high modulus bituminous mixture using indirect tensile test and compared it with complex modulus. In addition, the impact of loading waveform on the test results was explored. The indirect tensile tests were performed according to EN 12697-26 standard procedure. The authors evaluated the loading law presented in this test method and found that the correction factor used in the standard method cannot be applied at all temperatures and is dependent to material type. In another study, the experimental conditions of indirect tensile test to reach the design reference modulus were considered using Maxwell and Huet viscoelastic linear models. The difference between reference complex modulus and indirect tensile stiffness modulus was dependent on loading waveform [13, 14]. Reference [16] determined the viscoelastic properties of asphalt mixtures using indirect tensile stiffness modulus test performed by Nottingham asphalt tester machine. The model including a Maxwell element in series with one Voigt element had a good correlation with test results. The viscoelastic parameters of fitted model were dependent on the rise time of modulus test. Khavassefat et al. [26] investigated stresses and strains in viscoelastic flexible pavement due to moving traffic implementing a general quasi-static computational procedure. The serious effect of traffic speed and density on viscoelastic stress redistribution in asphalt concrete layer was evaluated based on numerical simulations. The effect of truck axle configuration was not significant compared to the effect of traffic. Nguyen et al. [30] investigated linear and nonlinear behavior of asphalt materials using complex modulus tests at different temperatures and loading frequencies. The complex modulus and Poisson’s ratio were

measured under sinusoidal cyclic loading with three strain amplitudes lower than 125 lm/m. The equivalent temperature–frequency pair affected nonlinear behavior of asphalt concrete. Carbonneau et al. [12] evaluated application of indirect tensile stiffness modulus test as an alternative to direct tension modulus test. The results showed a good correlation between two test methods. Based on limits of measuring devices, reaching target strain was difficult especially for high modulus mixtures. The alternative test was applied for cold mixes with some damage to samples during the test. In another study, [11] compared indirect tension modulus tests carried on two different mixtures using six machines with direct tensile test. The MR, measured according to EN 12697-26 annex C (IT-CY) standard procedure, was compared with estimated complex modulus and direct tensile modulus. The indirect tensile test was a reliable, quick, and low cost method and recommended for mix design of semi-coarse asphalt mix. However, for high modulus mixtures, the test procedure needs some adjustments. Many factors affect MR of asphalt concrete subjected to indirect tensile test. These include the geometric features of the test specimens, temperature, loading pulse duration, loading pulse shape, and allowed time for recovery between loading times (rest periods) [24]. The resilient characteristic of asphalt materials is highly dependent on test temperatures. Boudreau et al. [9] show that MR of various mixes decreased at different rates. As the temperature increases, so does the ductility of asphalt binder, decreasing the strength of the asphalt mixture. In addition, their studies have shown a high degree of material sensitivity at 5 °C and a low degree at 25 °C. Tabatabaie et al. [33] investigated the impact of temperature on resilient moduli of asphalt mixes for tropical zones of Iran. The MR test conducted at three temperatures (5, 25, 40 °C), with AC 40–50 and AC 60–70 binders, compacted in medium and high levels. The changes in MR values at 5 °C were far more than 25 and 40 °C. Some studies have indicated that the pulse shapes and pulse widths in an asphalt layer varies regarding asphalt layer thickness, vehicle speed, and depth from top of the road surface [21]. Reference [8] have found that a greater loading duration reduces the MR and produces more damage comparison with a shorter loading time at the 25 and 40 °C test temperature. The

Materials and Structures

3 Materials and experiments 3.1 Aggregates The aggregates employed in preparation of the test samples were crushed siliceous aggregates (granite). The nominal maximum aggregate size of mixture was 19 mm, according to Iran highway asphalt paving code [23]. This grading can be used for constructing the surface and binder layers. Figure 1 shows the aggregates gradation curve. Tables 1 and 2 summarized the physical and engineering properties of the aggregates, respectively.

Lower Limit

Results

Upper Limit

1

10

100

Passing from sieve (%)

longer loading duration will cause larger deformations and with a shorter rest period, the sample will have less time to recover from the deformation experienced. Kamal et al. [25] considered resilient behavior of asphalt concrete at several temperatures and time of loadings. MR reduced to about 85 % with just an increase of 15 °C (from 25 to 40 °C). At each temperature, asphalt specimens were tested for three pulse widths of 150, 300 and 450 ms. The MR values at same temperature decreased from about 20 to 45 %, with an increase in pulse width from 150 to 450 ms. The other studies have found that the ratio of rest time–pulse width does not make a significant change in the MR [8, 29]. The pulse shape as well as pulse width can be related to loading specification, depth, and properties of pavement structure [21]. By now, some pulse shapes or pulse widths of stress that distributed at different depths of pavement were determined [5, 10, 21, 28]. Some researchers claimed vertical stress pulse near the road surface can be represented by square function, while at higher depths (usually more than 5 cm), shape of stress pulse approaches to haversine or triangle functions [21]. Reference [8] compared MR of asphalt mixtures under 100 ms square and haversine pulses. They concluded that moduli under square shape is less than that under haversine one. It observed that the MR under haversine pulse was about two–three times of that under square pulse. According to the literatures, the resilient behavior of the flexible pavements in different depths can be explored using several pulse widths and shapes.

80 60 40 20 0 0.01

0.1

100

Particle size (mm) Fig. 1 Gradation curve of aggregates

3.2 Bitumen Asphalt mixture samples were prepared by using a widespread 60/70 bitumen from Tehran refinery. The specification of the bitumen is given in Table 3. 3.3 Mixture design The mixture design of asphalt concrete was accomplished according to the Marshall method specified in [1] standard method. The optimum bitumen content was 5.5 % by weight of mixture resulted in 4 % air void approximately. This content of bitumen satisfies all the other requirements such as air void and specific gravity. Maximum stability and maximum unit weight were 10.25 kN and 2269 kg/m3, respectively. 3.4 Resilient modulus test The magnitude of applied load in MR test should be selected as a portion of indirect tensile strength (ITS) of asphalt mix [2, 7]. The static ITS of a given specimen was determined using the procedure outlined in [6] at temperature of 25 °C and loading rate of 50 mm/min. The ITS value of asphalt mixture was 792.5 kPa. In this study, the MR of asphalt concrete samples was determined using the indirect tension method in accordance with [2] standard using UTM-14P device. The MR test was conducted at three temperatures of 5, 25, and 40 °C. The minimum allowable loading time, which could be applied by universal testing machine (UTM) device, was 50 ms. The assumed loading

Materials and Structures Table 1 Physical properties of aggregates

Aggregate properties

Standards

Fractions Coarse

Fine

Filler

LA abrasion loss (%)

ASTM-C131

18

–

–

Sodium sulphate soundness (%)

ASTM-C88

1.3

7.1

–

Sand equivalent (%) Flakiness (%)

ASTM-D2419 ASTM-D4791

– 12

72 –

– –

Crushed in one face (%)

ASTM-D5821

96

–

–

Plastic index (PI)

ASTM-D4318

–

NP

8

Plastic limit (PL)

ASTM-D4318

–

–

18

Liquid limit (LL)

ASTM-D4318

–

–

26

Table 2 Engineering properties of aggregates Fractions

Standards

Specific gravity

Water absorption (%)

Apparent

Bulk

Coarse aggregate ([2.36 mm)

ASTM-C127

2.67

2.53

Coarse aggregate (0.075–2.36 mm)

ASTM-C128

2.67

2.50

2.6

Filler (\0.075 mm)

ASTM-D854

–

2.68

–

Bulk specific gravity of blended aggregate

–

–

2.53

2.6

Table 3 Properties of the bitumen

Bitumen properties

Value standards

2.0

Standards

Penetration (25 °C, 0.1 mm)

69

ASTM-D5

Softening point (°C)

50

ASTM-D36

Ductility at 25 °C (cm)

[100

ASTM-D113

Solubility in C2HCl3 (%)

99.8

ASTM-D2042

Flash point (°C)

313

ASTM-D92

Viscosity at 135 °C (cSt)

380

ASTM-D2170

Thin film oven test, TFOT (163 °C, 5 h)

ASTM-D1754

Change of mass (%) Retained penetration

0.01 86

Ductility after TFOT at 25 °C (cm)

[100

pulses in the MR test were haversine and square functions with five pulse widths of 50, 100, 300, 600, and 1000 ms for simulation of actual traffic loading. Because the ratio of rest period–loading time has no significant effect on MR values [8, 29], the standard value of 9 was selected. In other words, the rest periods after 50, 100, 300, 600 and 1000 pulse widths were 450, 900, 2700, 5400 and 9000 ms, sequentially. In the MR test based on [2] standard, the maximum applied load at temperature of 5, 25, and 40 °C assumed as 30, 15, and 5 % of ITS of asphalt mix at temperature of 25 °C, respectively.

ASTM-D113

Resilient modulus in indirect tension method can be computed using Eq. (2): MR ¼

P  ðm þ 0:27Þ ; t  DH

ð2Þ

where MR is resilient modulus (MPa), P is repeated load (N), m is Poisson’s ratio, t is thickness of specimen (mm) and DH is recoverable horizontal deformation (mm) [6]. The Poisson’s ratio in Eq. (2) was selected based on test temperature. The Poisson’s ratio at three temperatures of 5, 25, and 40 °C was determined as 0.2, 0.35, and 0.4, respectively [5].

Materials and Structures Table 4 Experiment design and MR test results statistics for haversine loading Temperature (°C)

5

Loading time (ms)

Individual MR (MPa)

Mean MR (MPa)

Standard deviation (MPa)

Relative difference (%)

COV (%)

50

11,407

11,842

435

7.63

3.67

100

10,552

10,828.5

276.5

5.24

2.55

9654

483

10.53

5.00

8473

339

8.34

4.00

7166

287

8.34

4.01

3953.5

110.5

5.75

2.79

3209

107

6.90

3.33

10.86

5.15

12,277 11,105 300

9171 10,137

600

8134 8812

1000

6879 7453

25

50

3843

100

3102

4064 3316 300

1704 1889

1796.5

92.5

600

1582

1636

54

6.83

3.30

1434

49

7.08

3.42

963

26

5.55

2.70

536.5

20.5

7.95

3.82

228.5

9.5

8.68

4.16

183.5

6.5

7.34

3.54

141.5

6.5

9.63

4.59

1690 1000

1385 1483

40

50

937 989

100

516 557

300

219 238

600

177 190

1000

135 148

Two specimens were prepared for MR test in any combination of temperatures, loading times, and waveforms. According to AASHTO and ASTM standard procedures for determination of MR of asphalt mixtures, any specimen is tested in two different orientation along diametrical plane perpendicular to each other. First, the average of the measured values in two directions was calculated. Then, the mean of these values for two specimens is obtained. This mean value diminishes undesirable effects of difference aggregate orientations and sample heterogeneity on MR to an acceptable level. Tables 4 and 5 illustrate experimental design and test

results statistics under haversine and square loading, respectively.

4 Results and discussion The results of indirect tensile tests on Marshall specimens at different temperatures and loading times for haversine and square pulses have been illustrated in Figs. 2 and 3, respectively. The various pulse widths simulate the diverse vehicle speeds and the square and haversine pulse forms represent stress pulse in surface and binder layers, successively.

Materials and Structures Table 5 Experiment design and MR test results statistics for square loading Temperature (°C)

5

Loading time (ms) 50

Individual MR (MPa)

Mean MR (MPa)

Standard deviation (MPa)

Relative difference (%)

COV (%)

10,912

10,776

136

-2.49

1.26

8927.5

67.5

-1.50

0.76

8031

293

-7.04

3.65

7245

366

-9.62

5.05

6346

94

-2.92

1.48

2874

127

-8.46

4.42

2058

56

-5.30

2.72

10,640 100

8995 8860

300

8324 7738

600

7611 6879

1000

6440 6252

25

50

3001

100

2114

2747 2002 300

1284 1182

1233

51

-7.05

3.65

600

1222

1167.5

54.5

-8.92

4.67

1108.5

40.5

-7.05

3.65

342

11

-6.23

3.22

252.5

14.5

-10.86

5.74

168.5

11.5

-12.78

6.82

146.5

7.5

-9.74

5.12

132.5

5.5

-7.97

4.15

1113 1000

1149 1068

40

50

353 331

100

267 238

300

180 157

600

154 139

1000

138 127

For investigation of resilient behavior of asphalt mixtures in different depths, the MR ratios are obtained by dividing the MR under square loading to MR in typical haversine loading at the same temperatures and pulse widths. The MR ratio for binder layer will be equal to one. The results have given in Figs. 4, 5 and 6 for temperatures of 5, 25, and 40 °C, sequentially. As demonstrated in Fig. 4, the mean MR of surface layer at 5 °C is about 86 % of binder layer. The differences of MR values in this temperature are not

significant in the range of loading times. As depicted in Fig. 5, the mean MR of surface layer at 25 °C is about 71 % of binder layer. In this temperature, the differences are more significant than ones at 5 °C. The MR ratios have a similar trend as seen in the prior case. Based on Fig. 6, the mean MR of surface layer at 40 °C is about 65 % of binder layer. The MR ratios follow a trend that differ from other cases and the differences are the most significant due to more viscous nature of asphalt concrete at this temperature. The most gap between the MR of surface and binder

Materials and Structures MR at 5

MR at 25

MR at 40

Binder layer

Surface MR / Binder MR

Resilient Modulus (MPa)

12000 10000 8000 6000 4000

Surface layer

1 0.9 0.77

0.8 0.73

0.71

0.69

0.7

0.64

0.6 0.5

2000

50

100

300

600

1000

Loading Time (milliseconds)

0 50

100

300

600

1000

Loading Time (milliseconds)

Fig. 5 Comparison of MR of asphalt mixtures in binder and surface layers at 25 °C

Fig. 2 MR values of asphalt mixtures in binder layer of asphalt pavement (haversine) MR at 25

Surface MR / Binder MR

Binder layer

MR at 5

MR at 40

Resilient Modlus (MPa)

12000 10000 8000 6000 4000

Surface layer

1 0.87 0.80

0.8

0.74

0.6 0.47 0.36

0.4

0.2 50

2000

100

300

600

1000

Loading Time (milliseconds) 0 50

100

300

600

1000

Loading Time (milliseconds)

Fig. 6 Comparison of MR of asphalt mixtures in binder and surface layers at 40 °C

Fig. 3 MR values of asphalt mixtures in surface layer of asphalt pavement (square) Surface Layer

0.91

0.89

0.9 0.82

0.83

0.86

0.8 0.7 0.6 0.5

50

100

300

600

1000

Horizontal Deformation (µm)

Surface MR / Binder MR

Binder Layer 1

haver5 square25

square5 haver40

haver25 square40

18 15 12 9 6 3 0 5

5.1

5.2

5.3

5.4

5.5

Time (s)

Loading Time (milliseconds) Fig. 4 Comparison of MR of asphalt mixtures in binder and surface layers at 5 °C

layers was occurred at 40 °C and in loading time of 50 ms in which MR ratio was 36 %. The least difference was at 5 °C and in loading time of 50 ms with MR ratio of 91 %.

Fig. 7 Comparison of horizontal deformation for 100 ms haversine and square loadings

As mentioned previously, the maximum applied load at every temperature for haversine and square loading is same and particular (30, 15 and 5 % of ITS). Then based on Eq. (2), the horizontal deformation has

Materials and Structures square50 haver1000

Haversine pulse

haver100 square1000

30

1200 25 20 15

900 600

10

300 5 0

0 0

0.2

0.4

0.6

0.8

1

1.2

Fig. 8 Comparison of horizontal deformation for haversine and square loadings at 40 °C

Haversine Test Results

Square Test Results

5000 4000 3000 y = 15575x -0.354 R² = 0.9671

2000 1000 0

y = 9446.7x -0.326 R² = 0.9278

0

200

400

600

0

2

4

6

8

Horizontal deformation (µm)

Time (s)

Resilient Modulus (MPa)

Square pulse

1500

Load (N)

Horizontal Deformation (µm)

haver50 square100

800

1000

1200

Loading Time (milliseconds) Fig. 9 MR values under haversine and square loadings at 25 °C with the best-fitted functions

an important role for computation of MR. As shown in Fig. 7, the horizontal deformations under square loading are greater than the haversine one at all temperatures. However, the differences between square and haversine deformations are more obvious as the test temperature increases. The higher temperature results the more changes in MR ratios. Asphalt concrete is more viscous and time dependent at high temperatures. In the other words, the deformations need shorter time to recover during rest periods. Therefore, with change in loading time, the mixture experiences more recoverable deformation resulted in more changes in MR. Because of this property of asphalt mixture, the MR ratios at 5 and 25 °C slightly depend on loading times. On the other hand, the differences between MR of binder and surface layers are time dependent at 40 °C and decreased as pulse width increased. Figure 8 shows

Fig. 10 Load–deformation diagram in IDT test at 25 °C with 100 ms loading

the comparison of horizontal deformations under haversine and square loading with default pulse width of 100 ms and short and long pulse widths of 50 and 1000 ms at 40 °C. The deformation curves became closer together since loading time increased. Therefore, the differences decreased between MR of surface and binder layers. The results show that difference between resilient behavior of binder and surface layers is more apparent at high temperatures and in fast–medium vehicle speeds. The standard test method for determination of MR of asphalt mixtures utilizes haversine pulse as typical pulse form. The tests under square pulse cause damage to specimen and yield values with some inaccuracies. Therefore, to prevent from extra tests using uncommon square loading (for surface layer) and for prevention from such inaccuracies, it is worthwhile that haversine pulse widths equivalent to square loading times are specified. To this end, using Excel spreadsheets, the MR values of asphalt mixtures were plotted against loading times and trend lines that were well fitted to the experiment results were determined. For instance, Fig. 9 shows this matter at 25 °C. The best-fitted function for MR test results was power function at all temperatures. The substitution of MR values of square pulse in haversine pulse equation resulted in the equivalent widths of haversine pulse for square loading (for surface layer). Table 6 illustrates the estimated equivalent loading times in a range of temperatures used in this study. Application of these equivalent loading times can prevent from additional expensive MR tests under square loading.

Materials and Structures Table 6 Equivalent haversine loading times for square loading

Square loading time (ms)

Equivalent haversine loading time (ms) 5 °C

25 °C

40 °C

50

120

150

240

100

250

290

340

300 600

760 1550

780 1490

600 860

1000

2600

2380

1110

Table 7 The results of additional MR tests for validation Temperature (°C)

Square loading time (ms)

Equivalent haversine loading time (ms)

MR under square pulsea (MPa)

MR under equivalent haversine pulsea (MPa)

Relative difference (%)

5

50

100

11,131

10,786

-3.1

25

100

300

2234.5

2214

-0.9

40

300

600

182.5

177

-3.0

a

MR values are mean of test results for two specimens

As mentioned in Table 6, equivalent haversine loading times for surface layer are longer than square loading times. Because of the larger area under load– deformation diagram of square loading pulse (Fig. 10), damage to asphalt concrete sample can be more significant and resulted in fewer MR values. Therefore, the testing under haversine loading should be performed with longer pulse widths to give the results just as square loading. Due to less damage to specimens, this procedure can be more practical and beneficial than the testing under square pulse. The suggested equivalent haversine loading times are for a widely used mixture in Iran. Additional tests should be performed on different mixtures to verify these suggestions. It exacts more costs that exceed available funds for this academic research study. But, the authors had done some extra tests in three loading times of 50, 100, and 300 ms under square loading and in three loading times of 100, 300, and 600 ms under haversine loading at 5, 25, and 40 °C, respectively, except those performed for development of equivalent loading times. These tests can be used for validation purposes. According to Table 6, the equivalent haversine loading times for 50, 100, and 300 ms square loadings are 120, 290, and 600 ms, respectively, which are nearly close to 100, 300, and 600 ms. Therefore, the authors used these extra test results as

validation data. The additional test results have shown in Table 7 (revised manuscript). The MR values were approximately same so as the relative differences were less than 5 % that is a desirable level of equality.

5 Conclusion This study intended to find out the resilient behavior of asphalt concrete in different depths using MR property with indirect tensile test. The MR of asphalt mixtures was determined under haversine and square pulse shapes in various temperatures and loading times (or pulse widths). Based on the results of this study the following conclusions can be drawn: (1)

(2)

The MR parameter represents the resilient behavior of asphalt concrete in binder and surface layers, especially at high temperatures. In the scope of this study, ratio of surface layer MR–binder layer MR was from 36 to 91 %. The mean MR of surface layer at 5 and 25 °C were about 86 and 71 % of binder layer, respectively. At these temperatures, differences were not very obvious. This value was about 65 % at 40 °C and the differences were more significant than two other temperatures.

Materials and Structures

(3)

(4)

(5)

The horizontal deformations under square loading were greater than the haversine one at all temperatures. However, the differences between square and haversine deformations were more obvious as the test temperature increases. The higher temperature results the more changes in MR ratios. Because of viscous and time dependent behavior of asphalt concrete at high temperatures, the MR ratios at 5 and 25 °C slightly depended on loading times. At 40 °C, the differences between MR of binder and surface layers were time dependent and decreased as loading times increased. Since the area under load–deformation diagram of square loading pulse was larger than haversine one, damage to asphalt concrete sample was more significant. Therefore, it is recommended that the tests performed under haversine loading with longer pulse widths. This recommendation can be more practical and useful than the testing under square loading.

In this study, to explore the impressions of loading characteristics on asphalt concrete, only a specific type of aggregate and bitumen was used for preparation of asphalt mixture. The effects of various aggregates and bitumen including modified bitumen may be evaluated in the future works.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

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