Rutting performance of rubberized porous asphalt using Finite Element Method (FEM)

Construction and Building Materials 106 (2016) 382–391

Contents lists available at ScienceDirect

Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Rutting performance of rubberized porous asphalt using Finite Element Method (FEM) Reaz Imaninasab a,⇑, Behazad Bakhshi b, Bahram Shirini a a b

Department of Civil Engineering, Iran University of Science and Technology, Tehran, Iran Department of Civil Engineering, Zanjan University, Zanjan, Iran

h i g h l i g h t s
Finite Element Method was employed to estimate rut depth of rubberized porous asphalt using static and repeated loading.
Parameters of creep power law were determined using dynamic creep test.
From 10% to 20%, crumb rubber reduced the rut depth regarding both loading simulation.
Static loading resulted in slightly greater rut depth.

a r t i c l e

i n f o

Article history: Received 30 June 2015 Received in revised form 16 December 2015 Accepted 17 December 2015

Keywords: Porous asphalt Rut depth Finite Element Method (FEM) Dynamic creep test Static loading

a b s t r a c t The aim of this study is to investigate impact of crumb rubber on rut depth reduction. Dynamic creep and indirect resilient modulus tests were performed on control porous mix as well as rubberized mixtures containing modified binder content at concentrations of 10%, 15%, and 20%. Results of dynamic creep test were used to calibrate parameters of creep power law and resilient modulus (MR) was assigned to pavement layers. By conducting static and repeated loading in ABAQUS, it is found that static loading results in slightly greater rut depth than repeated one. Moreover, results show that 10%, 15%, and 20% rubber content causes rut depth reduction of 41%, 56%, and 61% with regard to static loading and 40%, 55%, and 60% regarding repeated loading, respectively. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Rutting is one of main distresses of pavements [2]. It is defined as the permanent deformation of pavement along the wheel path caused by load repetition. Rutting may be observed deep in the subgrade or be limited to surface [8,2]. Among the different layers contribution to rutting, cumulative permanent deformation in surface is known to be responsible for major rut depth of pavement surface [2]. Porous asphalt is a gap-graded asphalt mixture that is not rut resistant compared to conventional dense-graded asphalt mix [23]. Nevertheless, it is mainly used for water drainage purposes. This type of asphalt mix also has other advantages including friction increase, vision sight improvement while raining, and noise reduction [19]. Using rubberized asphalt cement not only does ⇑ Corresponding author at: Asphalt Mixtures and Bitumen Research Center, Iran University of Science and Technology, Narmak, Tehran Postal code: 1684613114, Iran. E-mail address: [email protected] (R. Imaninasab). http://dx.doi.org/10.1016/j.conbuildmat.2015.12.134 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.

improve rutting properties of porous asphalt, but also is it environmentally friendly because of recycling used tire and service life increase [17,21]. There are many experimental studies that evaluate impact of crumb rubber on rutting resistance improvement [27,24]. In laboratory, different tests such as dynamic creep, static creep, wheel tracking and indirect tensile tests can be used to evaluate rut resistance of asphaltic materials. Among these tests, NCHRP reported that dynamic creep test is better correlated with measured rut depth and had high capability to estimate rutting potential of asphalt layer [26]. Choosing a suitable constitutive equation to model creep behavior of asphalt mixtures and calibration its parameters using results of dynamic creep and resilient modulus tests, Finite Element Method (FEM) can be used to simulate rutting process of pavement structure under external load repetition and determine each layer contribution to rut depth [25]. This way, an empirical– mechanistic solution is employed to evaluate rutting resistance of asphalt mixes which is definitely more sophisticated.

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

Asphalt mixtures are composed of elastic, plastic, visco-elastic and visco-plastic deformations under repeated loading [20]. To estimate rut depth of asphalt layer, nonlinear visco-plastic Finite Element Analysis (FEA) is commonly performed using ABAQUS or ANSYS programs. Moreover, because of large longitudinal dimension, 2D models are often adopted for modeling purposes [8,2]. In this research, rut depth of rubberized porous asphalt at different concentrations of 10%, 15%, and 20% were predicted using Finite Element Method and compared with unmodified one. In addition, rut depth obtained from repeated loading were compared with that obtained from static loading simulation. Finally, the sensitivity of creep power law’s parameters and resilient modulus with regard to rutting potential were investigated.

383

(1) Minimum air void of 18%. (2) Maximum CL of 20% for unaged specimens. In addition, there are maximum amount of draindown according to AASHTO T305-97 and minimum coefficient of permeability according to ASTM D3637 that must be satisfied. Table 5 presents optimal binder content as well as amount of draindown and coefficient of permeability for different types of mixtures. Although 15% and 20% rubberized asphalt do not satisfy minimum permeability requirement, they effectively contribute to rutting resistance. 5. Rutting of pavement system There are three types of rutting mechanism that occur in pavement system [8]:

2. Methodology Within this research, used materials and their preparation, mix design procedure and sample fabrication were first carried out. After determining optimal binder content for each concentration, dynamic creep and indirect resilient modulus tests were performed on control and modified samples to calibrate parameters of creep power law and determine resilient modulus, respectively. A 3D model is then developed in ABAQUS in order to be assigned with different required properties. Finally, loading specifications were determined with accordance to 80 kN dual axle load assembly and single direction traffic with velocity of 20 km/h. 3. Used materials Physical properties of used Lime aggregates are presented in Table 1 and, as shown in Fig. 1, used gradation falls within the upper and lower limits of the proposed gradations of Iran Highway asphalt paving code [6]. Properties of used 60/70 bitumen by penetration are also presented in Table 2. Furthermore, the used rubber was produced from car tires by ambient shredding. The particle size distribution of rubber content is given in Table 3. In order to blend rubber with virgin binder, highspeed stirrer apparatus was used at reaction temperature of 180 °C and a reaction speed of 3500 rpm for 30 min [18].

4. Sample preparation and mix design Cylindrical specimens weighting 1000 g with a diameter 100 mm and approximate height 67 mm were compacted by Suprepave Gyratory Compactor (SGC). Compaction parameters of SGC, presented in Table 4, were set to be equivalent to 50 blows of Marshall hammer. For mix design and all performed tests in this research, average of three identical samples, which were fabricated as described, were used as the result for each mixture type. Optimal binder content of porous asphalt is determined according to Cantabro test (ASTM C131) results and air void content. It is the average of binder contents that are related to 18% air void content and 20% Cantabro Loss. However, any binder content that falls within these two binder contents is an acceptable optimal binder content. Overall, mixtures at selected optimal binder content must satisfy following criteria:

Table 1 Aggregate physical properties. Measured properties

Standard (ASTM)

Value

Bulk specific gravity of coarse aggregate (g/cm3) Bulk specific gravity of fine aggregate (g/cm3) Water absorption of coarse aggregate (%) Water absorption of fine aggregate (%) Los Angeles abrasion value (%) Percentage of Fractured Particles in one side Percentage of Fractured Particles in two sides

C127 C127 C127 C127 C131 D5821 D5821

2.59 2.52 2.2 2.4 22.3 97 94

(1) Rut depth is limited to the asphaltic layers (Fig. 2). (2) Rut depth is due to densification of all layers of pavement system (Fig. 3). (3) Rut depth is due to subgrade settlement (Fig. 4). The first mechanism is common where layers beneath the asphaltic layers are sufficiently stabilized. It involves no volume change and gives rise to shear displacements in which both depression and heave are usually manifested along wheel path. The second mechanism is combination of plastic flow of asphaltic layer and the whole layers densification. It is mainly because of lack of compaction within construction. The third mechanism is observed in pavements constructed over weak subgrade. As shown in Fig. 4, pavement layers’ thicknesses do not decrease in this type of rutting. In this study, by assuming stabilized base, subbase, and subgrade, the first mechanism is investigated for rubberized porous asphalt mixtures. Dynamic creep test is employed to determine parameters of creep power law. Moreover, resilient modulus values of asphalt mixtures under study were determined by performing indirect resilient modulus test and resilient modulus values of other layers were selected based on realistic values. Creep power law and resilient modulus are determinant for rut depth prediction of pavements. 5.1. Dynamic creep test Three kinds of curves are obtained from dynamic creep test that represent resilient modulus, creep modulus, and permanent deformation [20]. Eq. (1) shows different types of deformations occurs in visco-elastoplastic materials under load applications. Furthermore, Fig. 5 shows the deformation elements of square loading pulse of dynamic creep test.

eðtÞ ¼ ee þ ep þ ev e ðtÞ þ ev p ðtÞ

ð1Þ

where e(t) is total deformation after elapses of time (t), ee is the elastic deformation, ep is the plastic deformation, eve is the visco-elastic deformation, evp is the visco-plastic deformation. Resilient (sum of elastic and visco-elastic) and permanent (sum of plastic and visco-plastic) deformations versus cycles can be identified in using resilient modulus and permanent deformation curves [12]. For modeling purposes, the plastic component of permanent deformation is not considered separately, instead it is assumed to be a part of visco-plastic deformation which is commonly counted as permanent deformation [15]. Cumulative visco-plastic deformation versus number of cycles curve is the most important outcome of the dynamic creep test [12]. It consists of three zones that is illustrated in Fig. 6. The primary

384

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

100 90

past percent

80

Upper Limit

70 60

Used Gradaon

50 40

Lower Limit

30 20 10 0 0.01

0.1

1

10

100

sieve size (mm) Fig. 1. Particle size distribution.

Table 2 Binder properties. Measured properties

Standard (ASTM)

Value

Penetration at 25 °C (0.1 mm) Softening point (R &B °C) Ductility at 25 °C (cm) Density at 25 °C (g/cm3) Flash point (°C)

D5-73 C36-76 D113-79 D70-76 D92-78

64 53 >100 cm 1.05 308

Table 3 Crumb rubber particle size distribution.

load pulse can be imposed by this apparatus but its software was developed in accordance with Australian Code [16]. Therefore, square pulse wave with frequency of 0.5 Hz (allocating 0.5 s for loading and 1.5 s for rest) was chosen according to AS 2891.12.1. Before carrying out the test, specimens were kept at least 5 h at 40 °C temperature. Setup parameters of dynamic creep test are presented in Table 6. Notice that mean slope of three identical specimens for each mix type was used to define slope of secondary zone.

5.2. Resilient modulus

Sieve size (mm)

Past percent

0.6 0.425 0.3 0.18 0.15 0.075

100 91 78 43 8 0

Table 4 Setup parameters of Suprepave Gyratory Compactor. Setup parameters

Value

Stress level (kPa) Number of gyration Angle (°) Rotational speed (rpm)

600 50 1.25 30

Table 5 Optimal binder content at different crumb rubber contents. Crumb rubber content (%)

Optimal binder content (%)

Draindown (maximum amount 0.3%)

Coefficient of permeability (minimum 100 m/day)

0 10 15 20

5.3 5.3 5.9 5.8

0.19 0.16 0.12 0.11

122.85 113.9 85.91 54.41

zone is identified as initial rutting within which densification of asphalt mixtures happens. In the secondary zone, shear rutting occurs and the slope of cumulative deformation versus cycle is approximately constant [5]. The slope of this zone is used to determine one of the parameters related to time-hardening creep power law. Moreover, number of load cycle repetition for initiation of tertiary stage is called Flow Number. It is the minimum slope occurrence of in Fig. 6. In this research, UTM-5 at Iran University of Science and Technology was used for carrying out dynamic creep test. Any type of

Resilient modulus (MR) is of fundamental materials property that is required for all used materials in any Finite Element Analysis. It represents the ratio of an applied stress to the recoverable strain that takes place after the applied stress has been removed. The MR was determined from tests on cylindrical specimens for each mixture at designed asphalt contents in the indirect tension mode. Approximately 15% of the indirect tensile strength of each mixture was applied on the vertical diameter for conventional and rubberized specimens. The frequency of load application was 1 Hz with load duration of 0.1 s to represent field conditions and a resting period of 0.9 s [3].

6. Creep power law The constitutive model of time-hardening version of creep power law is presented by Eq. (2) as it is defined in ABAQUS Finite Element program. It is simple, however, practical for problems related to rutting of flexible pavements [25].

e ¼ Arn tm

ð2Þ

where e is creep strain rate, r is uniaxial equivalent deviatoric stress, and t is loading time. A, n, and m are constant related to the material properties. According to the creep test carried out in previous researches [13,20], A, m, and n range from 0.47  105 to 1.03  105, from 0.78 to 0.75, and from 0.82 to 0.85, respectively. These parameters depend on aggregate size, aggregate angularity, and asphalt viscosity [8]. In this research, parameters’ value of control and rubberized asphalt mixes at concentrations of 10%, 15%, and 20% are computed according to repeated loading results obtained from dynamic creep test. It should be noted that if creep power law is used to model time-related behavior of materials, repeated and continuous loading have the same estimation of creep strain on condition that the total loading periods are the same [14].

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

385

Fig. 2. Rut depth limited to the asphaltic layers.

Fig. 3. Rut depth due to densification of all layers of pavement system.

Fig. 4. Rut depth due to subgrade settlement.

7. Finite Element Method

e ¼ Bu

Finite Element Method involves dividing a complex domain into triangles and quadrilaterals subdomains called finite elements [10]. The displacements within each finite element are interpolated using the nodal displacements. On the other hand, the strain vector is obtained from the nodal displacements using appropriate cinematic relations that depend on the problem (e.g., plane stress, plane strain, solid). In a matricial form, these relations are:

where B is the strain–displacement matrix. In 1968, Duncan [7] first used FEM to analyze flexible pavement which then leads to development of ILLI-PAVE by Raad and Figueroa in 1980. This program never caught on as the result of high memory usage requirement. Later in 1989, Harichnran developed nonlinear Finite Element computer program ‘‘MICH-PAVE” in Michigan State University for pavement analysis purposes. Nowadays, Finite Element programs such as ABAQUS, LS-DINA, DSC-

ð3Þ

386

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

Fig. 5. Deformations of visco-elastoplastic materials.

Fig. 6. Creep curve of dynamic creep test.

Table 6 Dynamic creep test parameters. Parameter

Value

Loading pattern Loading period Rest period Contact stress Applied repeated stress Termination criteria

Rectangular 500 ms 1500 ms 10 kPa 200 kPa and 300 kPa 400,000 cycles of load repetition or 300,000 ls

SST20, and CAPA-3D are commonly used in Netherlands to investigate nonlinear dynamic response of pavements. ABAQUS, which is used in this research, is a powerful FEM program that can solve complex problems easily using nonlinear analysis. The software has a library with large number of finite element and with various materials’ behavior models. ABAQUS is also able to choose reasonable increments and logical standard deviations automatically. To establish correlation between the specification of transverse section and rutting distribution of hot mix asphalt, modeling can be performed by ABAQUS effectively [1]. In recent years, using Finite Element Method (FEM) to analyze pavement structure has been growing because nonlinear correlation between stress and different types of strains can be easily established [4].

Although, because of large longitudinal dimension, 2D models are acceptable for estimating rut depth of pavements, here 3D models are used to compute more accurate and realistic responses [11]. The analytic model is an asphaltic layer with 1.3 m length and 0.1 m thickness. The dimensions are selected to meet minimum number of elements required in order to avoid solution time extension. The thickness of other pavement layers is shown in Fig. 7 and its properties are presented in Table 7. Moreover, subgrade is a semi-finite layer and it must be modeled with springs having stiffness modulus of K. However, since determining the stiffness modulus of spring is complicated, assuming 2 (m) thickness for subgrade that causes negligible stress in such depth is logical. Therefore, considering the surface at depth of 2 (m) of subgrade as rigid bearing is an acceptable assumption. As the selected element is C3D8R, the elemental rotation is constraint, three degree of freedom are defined for boundary conditions. Moreover, the contact conditions between layers are tie. In this research, pavement layers under both static and cyclic loading of 80 kN exerted by a dual wheel axle assembly are evaluated. In repeated loading, loading period is 5 s that is followed by 1 s rest period. Loading pattern is shown in Fig. 8. It simulate ALF machine loading pattern which represents single direction traffic with velocity of 20 km/h. In addition, it is assumed that 40 kN wheel load is equally distributed over the contact surface with tire pressure of 700 kPa. According to Huang recommendation, a rectangle plus two semi-circle, which is shown in Fig. 9 and is commonly used as the contact section between tire and asphalt surface, is equivalent to a rectangle with area of 0.5227 L2 and width of 0.6 L. As shown in Fig. 10, the length of 0.33 m is calculated for the equivalent rectangle [9]. Due to symmetry, the pavement under half wheel load is considered. A pavement block under half wheel load, having a length of 1.3 m, a width of 1.5 m and a depth of 3.02 m, is considered for the analysis. This pavement structure was loaded in an area of 0.144 m  0.198 m which represents the half wheel load of the area shown in Fig. 10. Loading and boundary condition that is in ABAQUS analysis are shown in Fig. 11. Furthermore, mesh of the used model is shown in Fig. 12. Although, for comparison purposes in this research, a specific loading condition is used, the condition can be varied to simulate other type of loading conditions. For repeated loading, load repetition can be selected with accordance to predicted number of cycles that each axle type is expected to pass over pavement during its design life. Then rut depth that axles may cause, accumulates to calculate overall rut depth and it can be compared with rut depth threshold. This way, different pavement configuration can also be investigated regarding rutting which may lead to a new M-E approach development. It can estimate rut depth directly instead of determining critical compressive stress and strain to find the

Fig. 7. Pavement configuration.

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

387

Table 7 Properties of pavement layers. Layer type

Elastic modulus (MPa)

Poison ratio

AC 60/70 CR-10% CR-15% CR-20% Base Subbase Fill Rockfill Subgrade

1455.67 2044.33 1933.33 754.33 138 72.45 62.1 96.6 52.2

0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35

Stress (KPa)

800 600 400 200 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

Time (sec) Fig. 8. Loading pattern.

Fig. 11. Loading and boundary condition of the model in ABAQUS.

Fig. 9. Contact surface of tire.

Fig. 10. Equivalent contact surface.

number of allowable load repetition and calculating incremental damage factor. 8. Results and discussion Slope of the secondary territory of dynamic creep test is used to compute the creep power law parameters. As the temperature in

Fig. 12. Mesh of the model in ABAQUS.

the analysis is fixed at 40 °C, the derived parameters of creep power law are just applicable for the same temperature. The relationship between viscoplastic axial strain of second stage versus time at stress levels of 200 kPa and 300 kPa for control mixture and rubberized mixtures at concentrations of 10%, 15%, and 20%

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

10000

Visco Plasc strain (10-3)

y = 0.516x + 1273. R² = 0.969 y = 0.395x + 521.8 R² = 0.975

1000

AC-200KPa AC-300KPa

100 100

1000

10000

y = 0.315x + 857.1 R² = 0.988 y = 0.148x + 854.8 R² = 0.976

1000 CR15%-200KPa CR15%-300KPa

100 100

10000

1000

Time (sec)

Time (sec)

(a) AC 60/70

(c) CR-15%

10000

10000

10000

y = 0.404x + 1660. R² = 0.983 y = 0.2791x + 1031. R² = 0.971

Visco Plasc strain (10-3)

Visco Plasc strain (10-3)

Visco Plasc strain (10-3)

388

1000 CR10%-200KPa CR10%-300KPa

100 100

1000

10000

y = 0.298x + 1534. R² = 0.972 y = 0.132x + 1042. R² = 0.977

1000

CR20%-200KPa CR20%-300KPa

100 100

1000

10000

Time (sec)

Time (sec)

(b) CR-10%

(d) CR-20% Fig. 13. Visco plastic strain rate.

are shown in Fig. 13, respectively. Parameter (b) of creep power law is estimated as the average tangent of slopes for each mixture. Having parameter (b), at least two stress levels are required to be performed on each type of mixture at 40 °C in order to be able to form quadratic regression equation. At this stage, only viscoplas-

tic strain at Flow Number (FN) is used. Eq. (4) gives a creep model in which the left side of the equation is known for three stress levels of 0 KPa, 200 KPa, and 300 KPa. In addition, parameter b relates with parameter (m) of creep power law as defined in Eq. (5) [22].

β

1.4 y = 2E-06x2 + 0.00001x R² = 0.99

0.4

Visco Plasc Strain/t

Visco Plasc Strain/tβ

0.5

0.3 0.2 0.1 0

100

200

0.4 0.2 100

200

Stress (KPa)

(a) AC 60/70

(c) CR-15%

β

y = 3E-06x2 + 0.00001x R² = 1

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

0

Stress (KPa)

Visco Plasc Strain/t

Visco Plasc Strain/tβ

0.6

300

0.8

0

1 0.8

0 0

y = 4E-06x2 + 0.003x R² = 0.99

1.2

100

200

300

Stress (KPa)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

y = 3E-06x2 + 0.0018x + 3E-15 R² = 1

0

(b) CR-10%

100

Stress (KPa)

200

(d) CR-20% Fig. 14.

evp tm

300

versus stress level at FN.

300

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391 Table 8 Parameters of creep power law. Type of mixture

A (105)

n

m

AC 60/70 CR-10% CR-15% CR-20%

1.15 1.15 1.15 1.15

1.6 1.6 1.6 1.6

0.5445 0.6585 0.7685 0.785

evp ðr; t; NÞ tb

¼ BðrÞ

ð4Þ

m¼b1

ð5Þ evp

Fig. 14 shows tb (viscoplastic strain at Flow Number (FN) over tb) versus stress level for mixtures at different rubber content. They are second order polynomial, so B(r) is described as Eq. (6):

BðrÞ ¼ b1 r þ b2 r2

ð6Þ

389

By determining coefficients (b1 and b2) of second order equation B(r), creep model is presented as Eq. (7). Using regression analysis, b1 and b2 are determined and creep power law’s parameters can be obtained from it.

evp ðr; t; NÞ ¼ ðb1 r þ b2 r2 Þ  t b

ð7Þ

Parameters of creep power format that are obtained from Eq. (7) are shown in Table 8. Among them, just parameter (m), which is directly derived from curves of dynamic creep test, is not constant for different dosage of crumb rubber. Parameters (n) and (A) are independent form rubber content of porous asphalt at 40 °C. Deriving the creep power law’s parameters, creep behavior of pavement layer system block, as previously described, can be modeled. Two conventional types of loading including static and cyclic were used to simulate in situ loading condition. It should be noted that creep behavior is just defined for the asphalt layer and rest of the layers are assumed to be enough stabilized with a modulus of elasticity defined at Table 7. Permanent deformations of the

(a) AC60/70

(c) CR-15%

(b) CR-10%

(d) CR-20% Fig. 15. Permanent deformation for cyclic loading.

390

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

(a) AC60/70

(c) CR-15%

(b) CR-10%

(d) CR-20% Fig. 16. Permanent deformation for static loading.

pavement system block for different mixtures after 332 cycles are depicted through Fig. 15. Results of equivalent static loading (2000 s loading) on the same model are also shown through Fig. 16. Although both loading types suggest the same order of rut resistance ranking; 20% crumb rubber content has the least rut

Table 9 Rut depth summary. Loading type

Control (mm)

CR-10% (mm)

CR-15% (mm)

CR-20% (mm)

Static loading Repeated loading

8.8 8.3

5.2 5

3.9 3.7

3.4 3.3

depth followed by concentrations of 15%, 10%, and control mixture, maximum permanent deformations of static loading are greater than those of cyclic for each type of mixture. It is due to no rest interval to let mixtures recover in static loading during the period. Although elastic modulus of CR-20% is far less than CR-15%, its rut depth is even a bit greater than the later. By comparing Tables 7 and 8 with Table 9, it can be inferred that resilient modulus has no effect on rut depth and it has direct relation with absolute value of parameter (m), i.e., the greater (m) value results in more rut resistance mixture. Parameter (m) increases with average slope of permanent deformation curve in secondary zone at performed stress levels decrease. Therefore, it is concluded that less rut resistant asphalt mixes have greater average visco-plastic slope.

R. Imaninasab et al. / Construction and Building Materials 106 (2016) 382–391

9. Conclusion This study focuses on impact of crumb rubber on improvement of porous asphalt mixes. Mixtures containing modified binder content at concentration of 10%, 15%, and 20% were compared with control mixture using Finite Element Method. The results obtained from performing static and cyclic loading show following conclusion:
Greater rut depth is computed by static loading than repeated loading as the former has no rest period to recover.
Regarding static loading results, using 10%, 15%, and 20% crumb rubber content reduce rut depth by 41%, 56%, and 61% compared to control mixture.
Regarding repeated loading results, using 10%, 15%, and 20% crumb rubber content reduce rut depth by 40%, 55%, and 60% compared to control mixture.
Parameter (m) of creep power law is indicator of rutting potential of asphaltic mixtures. The greater its absolute value is, the more rut resistant the mixture will be.
Resilient modulus relates to recoverable deformation and has no direct effect on rut depth prediction model used in this study. However, correlations have been established between resilient modulus and asphalt mixes’ creep properties.

References [1] ABAQUS Inc., ABAQUS version 6.5, Analysis User’s Manual, Providence, RI, 2004. [2] A.H. Abed, A.A. AL-Azzawi, Evaluation of rutting depth in flexible pavements by using finite element analysis and local empirical model, Am. J. Eng. Appl. Sci. 5 (2) (2012) 163–169. [3] ASTM 4123-82, Standard Test Method for Indirect Tension Test for Resilient Modulus of Bituminous Mixtures, American Society for Testing and Materials, 1996. [4] J.W. Button, D. Perdomo, R.L. Lytton, Influence of aggregate on rutting in asphalt concrete pavements, Transp. Res. Rec. (1259) (1990). [5] F. Cardarelli, Materials Handbook: A Concise Desktop Reference, Springer Science & Business Media, 2008. [6] Iran Highway Asphalt Paving Code, Publication No. 234 Ministry of Road and Transportation Research and Education Center, Iran, 2003. [7] J.M. Duncan, C.L. Monismith, E.L. Wilson, Finite element analyses of pavements, Highw. Res. Rec. (228) (1968).

391

[8] H. Fang, J.E. Haddock, T.D. White, A.J. Hand, On the characterization of flexible pavement rutting using creep model-based finite element analysis, Finite Elem. Anal. Des. 41 (1) (2004) 49–73. [9] M.N. Hadi, B.C. Bodhinayake, Non-linear finite element analysis of flexible pavements, Adv. Eng. Softw. 34 (11) (2003) 657–662. [10] A.S.D. Holanda, E. Parente Junior, T.D.P.D. Arajujo, L.T.B.D. Melo, F. Evangelista Junior, and J.B. Soares, Finite element modeling of flexible pavements, in: Ibreian Latin American Congress on Computational Methods in Engineering, 2006. [11] R. Imaninasab, B. Bakhshi, Rutting analysis of modified asphalt concrete pavements, Proc. Inst. Civ. Eng.-Constr. Mater. (2015) 1–12. [12] A. Khodaii, A. Mehrara, Evaluation of permanent deformation of unmodified and SBS modified asphalt mixtures using dynamic creep test, Constr. Build. Mater. 23 (7) (2009) 2586–2592. [13] J.S. Lai, D. Anderson, Irrecoverable and recoverable nonlinear viscoelastic properties of asphalt concrete, Highw. Res. Rec. (468) (1973). [14] L.F.M. Leite, B.G. Soares, Interaction of asphalt with ground tire rubber, Pet. Sci. Technol. 17 (9–10) (1999) 1071–1088. [15] Y. Lu, P.J. Wright, Numerical approach of visco-elastoplastic analysis for asphalt mixtures, Comput. Struct. 69 (2) (1998) 139–147. [16] M.R. Mirzahosseini, A. Aghaeifar, A.H. Alavi, A.H. Gandomi, R. Seyednour, Permanent deformation analysis of asphalt mixtures using soft computing techniques, Expert Syst. Appl. 38 (5) (2011) 6081–6100. [17] J.R. Oliveira, H.M. Silva, L.P. Abreu, S.R. Fernandes, Use of a warm mix asphalt additive to reduce the production temperatures and to improve the performance of asphalt rubber mixtures, J. Clean. Prod. 41 (2013) 15–22. [18] M. Panda, M. Mazumdar, Utilization of reclaimed polyethylene in bituminous paving mixes, J. Mater. Civ. Eng. 14 (6) (2002) 527–530. [19] Permanent International Association of Road Congresses, Porous Asphalt World Road Association, PIARC Report of the Committee TC4-3, 1993. [20] M. Perl, J. Uzan, A. Sides, Visco-elasto-plastic constitutive law for a bituminous mixture under repeated loading, Transp. Res. Rec. (911) (1983). [21] H.B. Takallou, A. Sainton, Advances in technology of asphalt paving materials containing used tire rubber, Transp. Res. Rec. (1339) (1992). [22] L. Uzarowski, The Development of Asphalt Mix Creep Parameters and Finite Element Modeling of Asphalt Rutting (Doctoral dissertation), University of Waterloo, 2006. [23] Y. Wang, G. Wang, Improvement of porous pavement, Final Report to US Green Building Council, East Carolina University, Greenville, NC, 2011. [24] H. Wang, Z. You, J. Mills-Beale, P. Hao, Laboratory evaluation on high temperature viscosity and low temperature stiffness of asphalt binder with high percent scrap tire rubber, Constr. Build. Mater. 26 (1) (2012) 583–590. [25] T.D. White, Contributions of Pavement Structural Layers to Rutting of Hot Mix Asphalt Pavements (No. 468), Transportation Research Board, 2002. [26] M.W. Witzcak, Simple Performance Test for Superpave Mix Design, vol. 465, Transportation Research Board, 2002. [27] F. Xiao, S. Amirkhanian, C.H. Juang, Rutting resistance of rubberized asphalt concrete pavements containing reclaimed asphalt pavement mixtures, J. Mater. Civ. Eng. 19 (6) (2007) 475–483.