- Email: [email protected]
Development of mechanistic–empirical design method for an asphalt pavement rutting model using APT
Construction and Building Materials 25 (2011) 1685–1690
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of mechanistic–empirical design method for an asphalt pavement rutting model using APT Young-Chan Suh a, Nam-Hyun Cho a, Sungho Mun b,⇑ a b
Department of Transportation Engineering, Hanyang University, Ansan, Gyeonggi-do, South Korea School of Civil Engineering, Seoul National University of Science and Technology, 172 Gongreung-2 Dong, Nowon-Gu, Seoul 139-743, South Korea
a r t i c l e
i n f o
Article history: Received 21 June 2010 Received in revised form 7 September 2010 Accepted 27 October 2010 Available online 20 November 2010 Keywords: Accelerated pavement testing Rut model Plastic strain Resilient strain Multi-depth deflectometer
a b s t r a c t This paper describes the study of accelerated pavement testing (APT) with test variables of temperature and air void ratio, which are important factors that influence rutting. The purpose of the study was to use the APT results to calibrate a laboratory rutting model for asphalt concrete (AC) mixtures and to develop an appropriate rutting model for AC pavements. The test specimen for the APT was prepared as a pavement system with an AC layer of 30 cm, subbase of 30 cm, and subgrade of 180 cm. The experimental variables were chosen to be the important factors that influence the rutting of AC pavement: temperature (50 °C) and air void ratios (7.31% and 10.57%). A multi-depth deflectometer was installed at depths of 12 and 30 cm from the AC pavement surface to measure the plastic and resilient strains, which are necessary for the development of the rutting model. The result was used to examine the rutting models of AC pavement layers suggested by the AASHTO 2002 model as well to calibrate a laboratory rutting model. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The current domestic Korean asphalt concrete (AC) pavement design, which relies on the experimental method of regression analysis of laboratory test data, is limited due to boundary conditions as well as environmental and material characteristics. This has led to interest in the development of a mechanistic–empirical pavement design method [1,2]. Korean pavement design techniques are also changing to incorporate mechanistic–empirical pavement design methods. This study included conduct of accelerated pavement testing (APT) using temperature and air void ratio, important factors that influence rutting, as test variables. The purpose of this study was to use the APT results to calibrate a laboratory rutting model of asphalt mixtures and to develop an appropriate rutting model for AC pavement. The APT was first used in 2006 to develop a fatigue crack model for asphalt pavement and to estimate its remaining service life [3]. APT has been extended to the development of a rutting model in this study. The test specimen for the APT was prepared as a typical crosssection of AC pavement with an AC layer of 30 cm, subbase of 30 cm, and subgrade of 180 cm. The experimental variables were chosen to be the most important factors influencing AC pavement rutting: temperature (50 °C) and air void ratios (7.31% and 10.57%). A multi-depth deflectometer (MDD) was installed at depths of 12 ⇑ Corresponding author. Tel.: +82 2 970 9014; fax: +82 2 948 0043. E-mail address: [email protected] (S. Mun). 0950-0618/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2010.10.014
and 30 cm from the asphalt pavement surface to measure plastic and resilient strains, which are necessary for the development of the rutting model. The permanent and resilient deformations were calculated through MDD measurements, as shown in Fig. 1, to determine the plastic and resilient strains. The resilient deflection at the pavement surface, which cannot be measured by MDD, was calculated by a multilayered elastic analysis for comparison with the MDD data. The modulus of elasticity at 50 °C was computed both by a falling-weight deflectometer (FWD) test and by temperature calibration. These data were used to verify the rutting model suggested by the AASHTO 2002 Design Guide [4] and a domestic laboratory rutting model that uses the air void ratio as an experimental variable. The experimental tests conducted in this study are the APT prepared with controlling temperature (50 °C) and air void ratios (7.31% and 10.57%) as well as the FWD used to evaluate the elastic modulus of asphalt concrete layer in pavement structure. 2. Rutting model Rutting is a typical deterioration of AC pavement that is used to determine the service life of the pavement. In the past, rutting was considered to be closely related to vertical strain on the top of the subgrade layer, and the procedure for determining the thickness of its structure was based on reducing the compressive stress of the subgrade. However, as shown in Eq. (1), the plastic strain of the surface of AC pavement is now computed by the sum of the rutting at each layer of the pavement system [4]
1686
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
Resilient Permanent Deformation Deformation
Deflection (mm)
1.2 1 0.8 0.6 0.4 0.2 0 0
150
300
450
600
750
900 1,050 1,200 1,350
Time (sec) Fig. 1. Resilient and permanent deformations obtained from MDD measurement.
RD ¼
nsublayers X
epi hi ;
ð1Þ
i¼0
where RD is the rut depth of AC pavement, nsublayer is the number of sub-layers, and epi and hi are the total plastic strain and thickness, respectively, in sub-layer i. The AASHTO 2002 design method [4] suggests equations for the prediction of the permanent deformation for the AC layer, the coarse aggregate subbase, and the subgrade. Eqs. (2)–(5) predict the permanent deformation of the AC layer, and they are computed from laboratory experimental values and field-measured values
ep ¼ k1 103:35412 T 1:5606 N0:4792 ; er
ð2Þ
k1 ¼ ðC 1 þ C 2 depthÞ 0:328196depth ;
ð3Þ
C1 ¼ C2 ¼
2 0:1039 hac þ 2:4868 hac 17:342; 2 0:0172 hac 1:7331 hac þ 27:428;
ð4Þ
Table 1 HAPT characteristics. Classification
Specification
Loading system Test section Wheel type Wheel loading Test speed
Length: 20 m; width: 2 m; height: 3.4 m Length: 12.5 m; width: 9.3 m; depth: 3.2 m Dual tire 3.2–12 tons Operation speed: 8–15 km/h Maximum speed: 17 km/h Heating system and water table
Environment control
3. APT setup The APT was performed using the Hanyang Accelerated Pavement Tester (HAPT), which is shown in Fig. 2. Table 1 shows the characteristics of the HAPT. 3.1. Experimental conditions
ð5Þ
where ep is the accumulated plastic strain at N load repetitions; er is the resilient strain of the asphalt material as a function of mixture properties; N is the number of load repetitions; T is the temperature (°F); k1 is a function of the total asphalt layer thickness and depth to the point of computation, which is revised for the confining pressure at different depths; depth is the depth from asphalt surface; and hac (in.) is the total thickness of the AC layer. Based on the rutting models for AC mixtures obtained from the laboratory test results, Eq. (6) is a prediction model for a surface course mixture of 19-mm aggregate to which AP-5 binder (the material most similar to the APT material) is applied. Eq. (7) is a model for a base course mixture of 25-mm aggregate to which AP-5 binder is applied [5]. These models predict the ratio of plastic strain to resilient strain as a function of the AC layer temperature, the number of load repetitions, and the air void ratio, which is not considered in the ASSHTO model [4]
ep ¼ br1 100:044 N0:185br2 T 0:708br3 AV 0:688br4 ; er ep ¼ br1 100:171 N0:159br2 T 0:603br3 AV 0:116br4 ; er
Fig. 2. Hanyang Accelerated Pavement Tester (HAPT).
The APT test specimen had the same dimensions as a typical cross-section of domestic highways, using an aggregate and binder typically used in highways. As shown in Fig. 3, the AC pavement was structured so that the air void ratio of the 12-cm-thick surface layer made up of AP-5 binder and 19-mm aggregate varied from 7.31% to 10.57%. The air void ratio of the base course with AP-5 binder and 25-mm aggregate was set to 7.42% for the construction of the test specimen. The temperature of the test specimen at a depth of 5 cm from the surface was maintained at 50 °C. Moreover, wandering was applied to simulate an actual vehicular load on the AC pavement of 9.0 ton (e.g., single axle, dual tire) in a pattern of ±0.35-m standard deviation. The permanent deformation in the surface course was measured with a transverse laser profilometer to determine the permanent deformation of the surface layer, and an MDD linear variable differential transformer (LVDT) sensor was embedded at depths of 12 and 30 cm from the surface to measure permanent deformation and resilient deflection inside the asphalt layer [5]. 3.2. Modulus of computation and temperature calibration
ð6Þ ð7Þ
where N is the number of load repetitions; T is the temperature (°C); AV is the air void (%); and br1, br2, br3, and br4 are the calibration factors. The constant values in Eqs. (6) and (7) were determined through laboratory testing. The objectives of this study are to examine the rutting model of Eqs. (2), (6), and (7) and to develop a rutting model appropriate to the Korean environment using the calibration suggested in Eqs. (6) and (7) as well as APT.
The resilient deflection and permanent deformation of the AC were measured with the MDD LVDT sensor, and the plastic strain at the surface was measured with a transverse laser profilometer. However, because the measurement of resilient deflection at the surface was rather difficult, it was computed by comparing the surface resilient deflection, measured through multilayered elastic analysis, with the resilient deflection values at depths of 12 and 30 cm. The FWD test was used at the average temperature of the AC layer (20 °C) to determine the values of elastic modulus necessary for multilayer elastic analysis: 4897 MPa for the air void ratio of 7.31% and 3215 MPa for the air void ratio of 10.57%. The elastic
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
1687
Fig. 3. Cross-section of the pavement test specimen showing location of the MDD installation.
3.3. Multilayer elastic analysis using KENLAYER software
Temperature ( C) 0.0 0
10.0
20.0
30.0
40.0
50.0
60.0
Multilayer elastic analysis was conducted using the KENLAYER software package with the elastic modulus in Table 3, the pavement thickness, and the loading condition as the input variables to predict resilient deflection of the asphalt surface [6]. The results of KENLAYER program analysis were then compared with the results measured using the MDD to obtain the resilient deflection value at the surface, and this was calibrated by comparison with the actual measured value at a depth of 12 cm. The measured resilient deflection value was the average of the measured data, and Table 4 shows the standard deviation of each average value.
5
Depth (cm)
Pavement Temperature
10 15 20 25 30 35 Fig. 4. Temperature as a function of asphalt layer depth.
4. Results and discussions
Table 2 Elastic modulus calibrated by asphalt temperature. Depth (cm)
Air void (%)
Temp. (°C)
kE
AC layer modulus (MPa)
0–12 0–12 12–30
7.31 10.57 7.42
50.07 50.07 38.88
16.58 16.58 4.77
289.30 193.93 1004.85
The APT was terminated when the permanent deformation exceeded 1.27 cm at the section of the asphalt surface layer with the 7.31% air void ratio. Rutting as a function of air void ratios of 7.31% and 10.57% as well as data on the permanent deformation and resilient deflection at depths of 12 and 30 cm from the surface were acquired through this test. 4.1. Permanent deformation
modulus as a function of pavement depth was calibrated to the elastic modulus at the experiment temperature, as shown in Fig. 4, to use it as an input variable for KENLAYER [6], a multilayer elastic analysis program. The temperature calibration was conducted according to Eq. (8) [7]. Table 2 shows the elastic modulus calibrated by temperature and air void ratio 1:886
kE ¼ 100:0002175ð70
T 1:886 Þ
;
ð8Þ
where kE is the correction factor for converting the reference modulus at 68°F (20 °C) to the modulus at the temperature of interest, and T is the temperature (°F). The modulus at a specific temperature can be obtained by
ET ¼ Ereference =kE ;
ð9Þ
where ET is the modulus at a specific temperature and Ereference is the reference modulus at 68°F.
Figs. 5 and 6 show the permanent deformations due to the vehicular load at the test temperature of 50 °C in the test sections with air void ratios of 7.31% and 10.57%, respectively, at depths of 12 and 30 cm. These figures show a definite difference in permanent deformation according to the air void ratio. The permanent deformation, which was measured by MDD at 12 and 30 cm from the surface, shows a similar pattern and magnitude. The measured permanent deformations at the surface were 15.07 and 12.40 mm for the specimens with air void ratios of 10.57% and 7.31%, respectively. The permanent deformations at 12 cm for air void ratios of 10.57% and 7.31% were not significantly different: 5.3 and 5.2 mm, respectively. Similarly, the permanent deformations at 30 cm for air void ratios of 10.57% and 7.31% were 2.0 and 1.9 mm, respectively. The difference in permanent deformation according to the air void ratio at the surface is thus attributed to the control of the air void ratio within 12 mm of the surface layer. Table 5 lists the permanent deformation by each layer in the asphalt pavement specimen. The permanent deformation by layer was about 65% and
1688
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
Table 3 KENLAYER input variable. LAYER
Thicknesses (cm)
Asphalt layer (0–12 cm)
12
Asphalt layer (12–30 cm) Aggregate subbase Subgrade
18 30 Infinite
Load (9 ton) on surface – Contact pressure: 815 kPa – Contract radius: 14.1 cm – Wheel spacing: 34.2 cm
Modulus (MPa)
Air void (%)
Poisson’s ratio
289.30 193.93 1004.85 282.00 91.70
7.31 10.57 7.48 –
0.4 0.35 0.35 0.4
Table 4 Measured and predicted resilient deflection. Depth (cm)
Air void: 7.31%
0 12 30
Air void: 10.57%
MDD measured (mm)
KENLAYER (mm)
MDD measured (mm)
KENLAYER (mm)
1.1199 0.9779 ± 0.061 0.8799 ± 0.032
1.0819 0.9447 –
1.4081 1.1236 ± 0.074 1.0268 ± 0.043
1.2087 0.9645 –
18.0 Surface
16.0
12cm
Permanent Deformation (mm)
Permanent Deformation (mm)
18.0 30cm
14.0 12.0 10.0 8.0 6.0 4.0 2.0
Surface
16.0
12cm
30cm
14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0
0.0 0
9,170
19,685
0
33,180
9,170
19,685
33,180
Number of Loadings
Number of Loadings Fig. 5. Permanent deformation as a function of depth for the specimen with an air void ratio of 7.31%.
Fig. 6. Permanent deformation as a function of depth for the specimen with an air void ratio of 10.57%.
57% of the total permanent deformation for specimens with air void ratios of 10.57% and 7.31%, respectively, in the surface layer. Both sections exhibited greater than 84% of total permanent deformation in the asphalt layer including the base layer. The permanent deformation in the subbase and subgrade layer accounted for about 12–16% of the total permanent deformation. These permanent deformation values by layer due to vehicular loading were divided by the thickness of each layer to compute the plastic strain value (ep) due to vehicular loading.
difference in the resilient deflection at the top and bottom of each layer was divided by the thickness of the layer to compute the resilient strains at 12 cm from the surface layer and 18 cm from the base layer. Table 6 shows the resilient strain for each layer and value of air void ratio.
4.2. Resilient strain
The measured values of resilient strain er and plastic strain ep based on the APT condition of this study were applied to Eq. (2) of the AASHTO 2002 model. Figs. 7 and 8 show the result of comparing the model equation value with the actual and measured
The resilient strain er was computed using the difference in the resilient deflection as a function of depth, as shown in Table 4. The
5. Verification and development of rutting model 5.1. Comparison with AASHTO 2002 model
Table 5 Permanent deformation of each asphalt layer. Classification
10.75% air void section rutting of each layer (mm)
7.31% air void section rutting of each layer (mm)
Load repetitions (9 ton)
Total
9170
10.32
19,685
12.33
33,180
15.07
Surface
Base
Subbase + subgrade
Total
2.05 (19.9%)
1.18 (11.43%)
7.24
2.74 (22.3%)
1.57 (12.7%)
10.19
3.34 (22.2%)
1.92 (12.7%)
12.40
Asphalt layer 7.09 (68.8%) 9.15 (88.9%) 8.02 (65.0%) 10.76 (87.3%) 9.81 (65.1%) 13.15 (87.3%)
Surface
Base
Subbase + subgrade
1.78 (24.5%)
1.10 (15.2%)
2.50 (24.5%)
1.59 (15.6%)
3.40 (27.4%)
1.60 (15.8%)
Asphalt layer 4.36 (60.3%) 6.14 (84.8%) 6.10 (59.9%) 8.60 (84.4%) 7.04 (56.8%) 10.44 (84.2%)
1689
Table 6 Resilient strain by each asphalt layer. Layer
Air void (%)
Resilient strain
Surface layer (0–12 cm)
10.57 7.31 7.48
2.371E03 1.184E03 5.377E04
20.0 15.0 10.0 APT
5.0
Calibration Model
0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings
60.0 Measure (APT)
50.0
Fig. 9. Permanent deformation of the entire asphalt layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
AASHTO Model
40.0 30.0 20.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Fig. 7. Permanent deformation of the entire asphalt layer predicted by the AASHTO model for the specimen with an air void ratio of 7.31% in the surface layer.
70.0 60.0
Measure (APT)
50.0
Permanent Deformation (mm)
10.0
Number of Loadings
25.0 20.0 15.0 10.0 APT
5.0
Calibration Model
0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings
AASTHO Model
40.0
Fig. 10. Permanent deformation of the entire asphalt layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
30.0 20.0 10.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 8. Permanent deformation of the entire asphalt layer predicted by the AASHTO model for the specimen with an air void ratio of 10.57% in the surface layer.
permanent deformations of the entire asphalt layer for specimens with air void ratios of 7.31% and 10.57%. These figures show that the results predicted by the AASHTO model equation were significantly greater than the measured results for the plastic and resilient strains due to APT loading. In particular, the plastic strain in the surface layer was measured to be 57–65% using the APT, whereas the AASHTO model predicted a plastic strain of greater than 99% in the surface layer. The depth coefficient of the AASHTO model in the base layer (k1 = 0.00569 in Eq. (3)) was so small that it predicted almost no permanent deformation when compared with the depth coefficient (Eq. (3)) of the surface layer of 1.1717. As the resilient strain increased, the AASHTO model predicted a permanent deformation about three times the measured permanent deformation for the specimen with the larger air void ratio (10.57%). 5.2. Calibration of laboratory test model The laboratory test models shown in Eqs. (6) and (7), which were developed in Korea, model domestic AC mixtures using the air void percentage as a variable instead of the depth coefficient (k1 in Eq. (3)) of AASHTO model. This is in line with the APT variables used in this study. Thus, rather than determining the previously mentioned calibration factor and suggesting individual rutting models based on aggregate size, this study presents a
Permanent Deformation (mm)
Permanent Deformation (mm)
25.0
70.0
25.0 APT (0~12cm)
20.0
Calibration Model (0~12cm)
15.0 10.0 5.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 11. Permanent deformation of the surface layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
Permanent Deformation (mm)
Permanent Deformation (mm)
Base layer (12–30 cm)
Permanent Deformation (mm)
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
25.0 APT (0~12cm)
20.0
Calibration Model (0~12cm)
15.0 10.0 5.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 12. Permanent deformation of the surface layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
Permanent Deformation (mm)
1690
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690 Table 7 Calibration factor.
10.0 APT (12~30cm)
8.0
Calibration Model (12~30cm)
6.0
br1
br2
br3
br4
AP-5, 19 mm AP-5, 25 mm
1.106624 1.482518
2.02973 2.361636
2.19322 2.57512
1.30235 7.72431
4.0 2.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 13. Permanent deformation of the base layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
Permanent Deformation (mm)
Classification
10.0 APT (12~30cm)
8.0
Calibration Model (12~30cm)
6.0 4.0 2.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 14. Permanent the deformation of the base layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
unified rutting prediction model suitable for Korea that is independent of the aggregate size. Figs. 9 and 10 compare the results of the rutting model prediction based on regression analysis of the APT results and actual measurement of the rutting of the complete asphalt sample using APT. In addition, Figs. 11–14 compare measured plastic strain with the plastic strain predicted by the rutting model proposed in this study. Figs. 11–14 show the permanent deformation as a function of the number of vehicular loadings and demonstrate that the predictions of the proposed rutting model are very similar to the actual measured results. The APT conditions and the measured resilient and plastic strains were applied to a domestic laboratory test model, and the actual measured values were subjected to regression analysis to obtain the following revised equation. Table 7 shows the calibration factor (bri, where i = 1, 2, 3, and 4) for domestic laboratory test model Eqs. (6) and (7).
ep ¼ 101:85927 N0:3755 T 1:5528 AV 0:89602 ; er
ð10Þ
where ep is the plastic strain, er is the recoverable strain, N is the number of load repetitions, T is the temperature (°C), and AV is the air void (%). 6. Conclusions This study included APT with experimental variables of temperature and air void percentage, which are important factors in rutting. The study also used the acquired plastic strain and resilient strain data acquired using an MDD; the parameters are fundamental for rutting modeling. The result was used to examine the rutting model of asphalt layers suggested by the AASHTO 2002 model, and a rutting model suitable for Korea was suggested by calibrating a laboratory rutting model. The measured resilient strain er and plastic strain ep values based on the APT conditions of this study were applied to the AASHTO 2002 model. The results predicted by the AASHTO model equation were significantly higher than the measured results obtained in this study based on vehicular loading and APT. Permanent deformation in the surface layer was measured at 57–65% based on APT, whereas the AASHTO model predicted a plastic strain greater than 99% in the surface layer. The depth coefficient k1 of the AASHTO model was so small that it predicted almost no plastic strain occurring in the base layer. References [1] Harichandran RS, Buch N, Baladi GY. Flexible pavement design in Michigan: transition from empirical to mechanistic methods. Transpor Res Record 2001;1778:100–6. [2] El-Basyouny M, Jeong MG. Effective temperature for analysis of permanent deformation and fatigue distress on asphalt mixtures. Transpor Res Record 2009;2127:155–63. [3] Yeo I, Suh Y, Mun S. Development of a remaining life model for asphalt black base through accelerated pavement testing. Constr Build Mater 2008;22(6):1881–6. [4] NCHRP 2002 Design Guide. Guide for mechanistic–empirical design of new and rehabilitated pavement structures. National Cooperative Highway Research Program, 2004. [5] Ministry of Land, Transport and Maritime Affairs. Korea pavement research program: asphalt pavement research report, 2008. [6] Jonson AM, Baus RL. Alternative method for temperature correction of backcalculated equivalent pavement moduli. Trans Res Record 1992;1355:75–81. [7] Huang YH. Pavement analysis and design. 2nd ed. Prentice Hall Inc.; 2004.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Development of mechanistic–empirical design method for an asphalt pavement rutting model using APT Young-Chan Suh a, Nam-Hyun Cho a, Sungho Mun b,⇑ a b
Department of Transportation Engineering, Hanyang University, Ansan, Gyeonggi-do, South Korea School of Civil Engineering, Seoul National University of Science and Technology, 172 Gongreung-2 Dong, Nowon-Gu, Seoul 139-743, South Korea
a r t i c l e
i n f o
Article history: Received 21 June 2010 Received in revised form 7 September 2010 Accepted 27 October 2010 Available online 20 November 2010 Keywords: Accelerated pavement testing Rut model Plastic strain Resilient strain Multi-depth deflectometer
a b s t r a c t This paper describes the study of accelerated pavement testing (APT) with test variables of temperature and air void ratio, which are important factors that influence rutting. The purpose of the study was to use the APT results to calibrate a laboratory rutting model for asphalt concrete (AC) mixtures and to develop an appropriate rutting model for AC pavements. The test specimen for the APT was prepared as a pavement system with an AC layer of 30 cm, subbase of 30 cm, and subgrade of 180 cm. The experimental variables were chosen to be the important factors that influence the rutting of AC pavement: temperature (50 °C) and air void ratios (7.31% and 10.57%). A multi-depth deflectometer was installed at depths of 12 and 30 cm from the AC pavement surface to measure the plastic and resilient strains, which are necessary for the development of the rutting model. The result was used to examine the rutting models of AC pavement layers suggested by the AASHTO 2002 model as well to calibrate a laboratory rutting model. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The current domestic Korean asphalt concrete (AC) pavement design, which relies on the experimental method of regression analysis of laboratory test data, is limited due to boundary conditions as well as environmental and material characteristics. This has led to interest in the development of a mechanistic–empirical pavement design method [1,2]. Korean pavement design techniques are also changing to incorporate mechanistic–empirical pavement design methods. This study included conduct of accelerated pavement testing (APT) using temperature and air void ratio, important factors that influence rutting, as test variables. The purpose of this study was to use the APT results to calibrate a laboratory rutting model of asphalt mixtures and to develop an appropriate rutting model for AC pavement. The APT was first used in 2006 to develop a fatigue crack model for asphalt pavement and to estimate its remaining service life [3]. APT has been extended to the development of a rutting model in this study. The test specimen for the APT was prepared as a typical crosssection of AC pavement with an AC layer of 30 cm, subbase of 30 cm, and subgrade of 180 cm. The experimental variables were chosen to be the most important factors influencing AC pavement rutting: temperature (50 °C) and air void ratios (7.31% and 10.57%). A multi-depth deflectometer (MDD) was installed at depths of 12 ⇑ Corresponding author. Tel.: +82 2 970 9014; fax: +82 2 948 0043. E-mail address: [email protected] (S. Mun). 0950-0618/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2010.10.014
and 30 cm from the asphalt pavement surface to measure plastic and resilient strains, which are necessary for the development of the rutting model. The permanent and resilient deformations were calculated through MDD measurements, as shown in Fig. 1, to determine the plastic and resilient strains. The resilient deflection at the pavement surface, which cannot be measured by MDD, was calculated by a multilayered elastic analysis for comparison with the MDD data. The modulus of elasticity at 50 °C was computed both by a falling-weight deflectometer (FWD) test and by temperature calibration. These data were used to verify the rutting model suggested by the AASHTO 2002 Design Guide [4] and a domestic laboratory rutting model that uses the air void ratio as an experimental variable. The experimental tests conducted in this study are the APT prepared with controlling temperature (50 °C) and air void ratios (7.31% and 10.57%) as well as the FWD used to evaluate the elastic modulus of asphalt concrete layer in pavement structure. 2. Rutting model Rutting is a typical deterioration of AC pavement that is used to determine the service life of the pavement. In the past, rutting was considered to be closely related to vertical strain on the top of the subgrade layer, and the procedure for determining the thickness of its structure was based on reducing the compressive stress of the subgrade. However, as shown in Eq. (1), the plastic strain of the surface of AC pavement is now computed by the sum of the rutting at each layer of the pavement system [4]
1686
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
Resilient Permanent Deformation Deformation
Deflection (mm)
1.2 1 0.8 0.6 0.4 0.2 0 0
150
300
450
600
750
900 1,050 1,200 1,350
Time (sec) Fig. 1. Resilient and permanent deformations obtained from MDD measurement.
RD ¼
nsublayers X
epi hi ;
ð1Þ
i¼0
where RD is the rut depth of AC pavement, nsublayer is the number of sub-layers, and epi and hi are the total plastic strain and thickness, respectively, in sub-layer i. The AASHTO 2002 design method [4] suggests equations for the prediction of the permanent deformation for the AC layer, the coarse aggregate subbase, and the subgrade. Eqs. (2)–(5) predict the permanent deformation of the AC layer, and they are computed from laboratory experimental values and field-measured values
ep ¼ k1 103:35412 T 1:5606 N0:4792 ; er
ð2Þ
k1 ¼ ðC 1 þ C 2 depthÞ 0:328196depth ;
ð3Þ
C1 ¼ C2 ¼
2 0:1039 hac þ 2:4868 hac 17:342; 2 0:0172 hac 1:7331 hac þ 27:428;
ð4Þ
Table 1 HAPT characteristics. Classification
Specification
Loading system Test section Wheel type Wheel loading Test speed
Length: 20 m; width: 2 m; height: 3.4 m Length: 12.5 m; width: 9.3 m; depth: 3.2 m Dual tire 3.2–12 tons Operation speed: 8–15 km/h Maximum speed: 17 km/h Heating system and water table
Environment control
3. APT setup The APT was performed using the Hanyang Accelerated Pavement Tester (HAPT), which is shown in Fig. 2. Table 1 shows the characteristics of the HAPT. 3.1. Experimental conditions
ð5Þ
where ep is the accumulated plastic strain at N load repetitions; er is the resilient strain of the asphalt material as a function of mixture properties; N is the number of load repetitions; T is the temperature (°F); k1 is a function of the total asphalt layer thickness and depth to the point of computation, which is revised for the confining pressure at different depths; depth is the depth from asphalt surface; and hac (in.) is the total thickness of the AC layer. Based on the rutting models for AC mixtures obtained from the laboratory test results, Eq. (6) is a prediction model for a surface course mixture of 19-mm aggregate to which AP-5 binder (the material most similar to the APT material) is applied. Eq. (7) is a model for a base course mixture of 25-mm aggregate to which AP-5 binder is applied [5]. These models predict the ratio of plastic strain to resilient strain as a function of the AC layer temperature, the number of load repetitions, and the air void ratio, which is not considered in the ASSHTO model [4]
ep ¼ br1 100:044 N0:185br2 T 0:708br3 AV 0:688br4 ; er ep ¼ br1 100:171 N0:159br2 T 0:603br3 AV 0:116br4 ; er
Fig. 2. Hanyang Accelerated Pavement Tester (HAPT).
The APT test specimen had the same dimensions as a typical cross-section of domestic highways, using an aggregate and binder typically used in highways. As shown in Fig. 3, the AC pavement was structured so that the air void ratio of the 12-cm-thick surface layer made up of AP-5 binder and 19-mm aggregate varied from 7.31% to 10.57%. The air void ratio of the base course with AP-5 binder and 25-mm aggregate was set to 7.42% for the construction of the test specimen. The temperature of the test specimen at a depth of 5 cm from the surface was maintained at 50 °C. Moreover, wandering was applied to simulate an actual vehicular load on the AC pavement of 9.0 ton (e.g., single axle, dual tire) in a pattern of ±0.35-m standard deviation. The permanent deformation in the surface course was measured with a transverse laser profilometer to determine the permanent deformation of the surface layer, and an MDD linear variable differential transformer (LVDT) sensor was embedded at depths of 12 and 30 cm from the surface to measure permanent deformation and resilient deflection inside the asphalt layer [5]. 3.2. Modulus of computation and temperature calibration
ð6Þ ð7Þ
where N is the number of load repetitions; T is the temperature (°C); AV is the air void (%); and br1, br2, br3, and br4 are the calibration factors. The constant values in Eqs. (6) and (7) were determined through laboratory testing. The objectives of this study are to examine the rutting model of Eqs. (2), (6), and (7) and to develop a rutting model appropriate to the Korean environment using the calibration suggested in Eqs. (6) and (7) as well as APT.
The resilient deflection and permanent deformation of the AC were measured with the MDD LVDT sensor, and the plastic strain at the surface was measured with a transverse laser profilometer. However, because the measurement of resilient deflection at the surface was rather difficult, it was computed by comparing the surface resilient deflection, measured through multilayered elastic analysis, with the resilient deflection values at depths of 12 and 30 cm. The FWD test was used at the average temperature of the AC layer (20 °C) to determine the values of elastic modulus necessary for multilayer elastic analysis: 4897 MPa for the air void ratio of 7.31% and 3215 MPa for the air void ratio of 10.57%. The elastic
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
1687
Fig. 3. Cross-section of the pavement test specimen showing location of the MDD installation.
3.3. Multilayer elastic analysis using KENLAYER software
Temperature ( C) 0.0 0
10.0
20.0
30.0
40.0
50.0
60.0
Multilayer elastic analysis was conducted using the KENLAYER software package with the elastic modulus in Table 3, the pavement thickness, and the loading condition as the input variables to predict resilient deflection of the asphalt surface [6]. The results of KENLAYER program analysis were then compared with the results measured using the MDD to obtain the resilient deflection value at the surface, and this was calibrated by comparison with the actual measured value at a depth of 12 cm. The measured resilient deflection value was the average of the measured data, and Table 4 shows the standard deviation of each average value.
5
Depth (cm)
Pavement Temperature
10 15 20 25 30 35 Fig. 4. Temperature as a function of asphalt layer depth.
4. Results and discussions
Table 2 Elastic modulus calibrated by asphalt temperature. Depth (cm)
Air void (%)
Temp. (°C)
kE
AC layer modulus (MPa)
0–12 0–12 12–30
7.31 10.57 7.42
50.07 50.07 38.88
16.58 16.58 4.77
289.30 193.93 1004.85
The APT was terminated when the permanent deformation exceeded 1.27 cm at the section of the asphalt surface layer with the 7.31% air void ratio. Rutting as a function of air void ratios of 7.31% and 10.57% as well as data on the permanent deformation and resilient deflection at depths of 12 and 30 cm from the surface were acquired through this test. 4.1. Permanent deformation
modulus as a function of pavement depth was calibrated to the elastic modulus at the experiment temperature, as shown in Fig. 4, to use it as an input variable for KENLAYER [6], a multilayer elastic analysis program. The temperature calibration was conducted according to Eq. (8) [7]. Table 2 shows the elastic modulus calibrated by temperature and air void ratio 1:886
kE ¼ 100:0002175ð70
T 1:886 Þ
;
ð8Þ
where kE is the correction factor for converting the reference modulus at 68°F (20 °C) to the modulus at the temperature of interest, and T is the temperature (°F). The modulus at a specific temperature can be obtained by
ET ¼ Ereference =kE ;
ð9Þ
where ET is the modulus at a specific temperature and Ereference is the reference modulus at 68°F.
Figs. 5 and 6 show the permanent deformations due to the vehicular load at the test temperature of 50 °C in the test sections with air void ratios of 7.31% and 10.57%, respectively, at depths of 12 and 30 cm. These figures show a definite difference in permanent deformation according to the air void ratio. The permanent deformation, which was measured by MDD at 12 and 30 cm from the surface, shows a similar pattern and magnitude. The measured permanent deformations at the surface were 15.07 and 12.40 mm for the specimens with air void ratios of 10.57% and 7.31%, respectively. The permanent deformations at 12 cm for air void ratios of 10.57% and 7.31% were not significantly different: 5.3 and 5.2 mm, respectively. Similarly, the permanent deformations at 30 cm for air void ratios of 10.57% and 7.31% were 2.0 and 1.9 mm, respectively. The difference in permanent deformation according to the air void ratio at the surface is thus attributed to the control of the air void ratio within 12 mm of the surface layer. Table 5 lists the permanent deformation by each layer in the asphalt pavement specimen. The permanent deformation by layer was about 65% and
1688
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
Table 3 KENLAYER input variable. LAYER
Thicknesses (cm)
Asphalt layer (0–12 cm)
12
Asphalt layer (12–30 cm) Aggregate subbase Subgrade
18 30 Infinite
Load (9 ton) on surface – Contact pressure: 815 kPa – Contract radius: 14.1 cm – Wheel spacing: 34.2 cm
Modulus (MPa)
Air void (%)
Poisson’s ratio
289.30 193.93 1004.85 282.00 91.70
7.31 10.57 7.48 –
0.4 0.35 0.35 0.4
Table 4 Measured and predicted resilient deflection. Depth (cm)
Air void: 7.31%
0 12 30
Air void: 10.57%
MDD measured (mm)
KENLAYER (mm)
MDD measured (mm)
KENLAYER (mm)
1.1199 0.9779 ± 0.061 0.8799 ± 0.032
1.0819 0.9447 –
1.4081 1.1236 ± 0.074 1.0268 ± 0.043
1.2087 0.9645 –
18.0 Surface
16.0
12cm
Permanent Deformation (mm)
Permanent Deformation (mm)
18.0 30cm
14.0 12.0 10.0 8.0 6.0 4.0 2.0
Surface
16.0
12cm
30cm
14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0
0.0 0
9,170
19,685
0
33,180
9,170
19,685
33,180
Number of Loadings
Number of Loadings Fig. 5. Permanent deformation as a function of depth for the specimen with an air void ratio of 7.31%.
Fig. 6. Permanent deformation as a function of depth for the specimen with an air void ratio of 10.57%.
57% of the total permanent deformation for specimens with air void ratios of 10.57% and 7.31%, respectively, in the surface layer. Both sections exhibited greater than 84% of total permanent deformation in the asphalt layer including the base layer. The permanent deformation in the subbase and subgrade layer accounted for about 12–16% of the total permanent deformation. These permanent deformation values by layer due to vehicular loading were divided by the thickness of each layer to compute the plastic strain value (ep) due to vehicular loading.
difference in the resilient deflection at the top and bottom of each layer was divided by the thickness of the layer to compute the resilient strains at 12 cm from the surface layer and 18 cm from the base layer. Table 6 shows the resilient strain for each layer and value of air void ratio.
4.2. Resilient strain
The measured values of resilient strain er and plastic strain ep based on the APT condition of this study were applied to Eq. (2) of the AASHTO 2002 model. Figs. 7 and 8 show the result of comparing the model equation value with the actual and measured
The resilient strain er was computed using the difference in the resilient deflection as a function of depth, as shown in Table 4. The
5. Verification and development of rutting model 5.1. Comparison with AASHTO 2002 model
Table 5 Permanent deformation of each asphalt layer. Classification
10.75% air void section rutting of each layer (mm)
7.31% air void section rutting of each layer (mm)
Load repetitions (9 ton)
Total
9170
10.32
19,685
12.33
33,180
15.07
Surface
Base
Subbase + subgrade
Total
2.05 (19.9%)
1.18 (11.43%)
7.24
2.74 (22.3%)
1.57 (12.7%)
10.19
3.34 (22.2%)
1.92 (12.7%)
12.40
Asphalt layer 7.09 (68.8%) 9.15 (88.9%) 8.02 (65.0%) 10.76 (87.3%) 9.81 (65.1%) 13.15 (87.3%)
Surface
Base
Subbase + subgrade
1.78 (24.5%)
1.10 (15.2%)
2.50 (24.5%)
1.59 (15.6%)
3.40 (27.4%)
1.60 (15.8%)
Asphalt layer 4.36 (60.3%) 6.14 (84.8%) 6.10 (59.9%) 8.60 (84.4%) 7.04 (56.8%) 10.44 (84.2%)
1689
Table 6 Resilient strain by each asphalt layer. Layer
Air void (%)
Resilient strain
Surface layer (0–12 cm)
10.57 7.31 7.48
2.371E03 1.184E03 5.377E04
20.0 15.0 10.0 APT
5.0
Calibration Model
0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings
60.0 Measure (APT)
50.0
Fig. 9. Permanent deformation of the entire asphalt layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
AASHTO Model
40.0 30.0 20.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Fig. 7. Permanent deformation of the entire asphalt layer predicted by the AASHTO model for the specimen with an air void ratio of 7.31% in the surface layer.
70.0 60.0
Measure (APT)
50.0
Permanent Deformation (mm)
10.0
Number of Loadings
25.0 20.0 15.0 10.0 APT
5.0
Calibration Model
0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings
AASTHO Model
40.0
Fig. 10. Permanent deformation of the entire asphalt layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
30.0 20.0 10.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 8. Permanent deformation of the entire asphalt layer predicted by the AASHTO model for the specimen with an air void ratio of 10.57% in the surface layer.
permanent deformations of the entire asphalt layer for specimens with air void ratios of 7.31% and 10.57%. These figures show that the results predicted by the AASHTO model equation were significantly greater than the measured results for the plastic and resilient strains due to APT loading. In particular, the plastic strain in the surface layer was measured to be 57–65% using the APT, whereas the AASHTO model predicted a plastic strain of greater than 99% in the surface layer. The depth coefficient of the AASHTO model in the base layer (k1 = 0.00569 in Eq. (3)) was so small that it predicted almost no permanent deformation when compared with the depth coefficient (Eq. (3)) of the surface layer of 1.1717. As the resilient strain increased, the AASHTO model predicted a permanent deformation about three times the measured permanent deformation for the specimen with the larger air void ratio (10.57%). 5.2. Calibration of laboratory test model The laboratory test models shown in Eqs. (6) and (7), which were developed in Korea, model domestic AC mixtures using the air void percentage as a variable instead of the depth coefficient (k1 in Eq. (3)) of AASHTO model. This is in line with the APT variables used in this study. Thus, rather than determining the previously mentioned calibration factor and suggesting individual rutting models based on aggregate size, this study presents a
Permanent Deformation (mm)
Permanent Deformation (mm)
25.0
70.0
25.0 APT (0~12cm)
20.0
Calibration Model (0~12cm)
15.0 10.0 5.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 11. Permanent deformation of the surface layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
Permanent Deformation (mm)
Permanent Deformation (mm)
Base layer (12–30 cm)
Permanent Deformation (mm)
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690
25.0 APT (0~12cm)
20.0
Calibration Model (0~12cm)
15.0 10.0 5.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 12. Permanent deformation of the surface layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
Permanent Deformation (mm)
1690
Y.-C. Suh et al. / Construction and Building Materials 25 (2011) 1685–1690 Table 7 Calibration factor.
10.0 APT (12~30cm)
8.0
Calibration Model (12~30cm)
6.0
br1
br2
br3
br4
AP-5, 19 mm AP-5, 25 mm
1.106624 1.482518
2.02973 2.361636
2.19322 2.57512
1.30235 7.72431
4.0 2.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 13. Permanent deformation of the base layer predicted by the calibration model for the specimen with an air void ratio of 7.31% in the surface layer.
Permanent Deformation (mm)
Classification
10.0 APT (12~30cm)
8.0
Calibration Model (12~30cm)
6.0 4.0 2.0 0.0 0
20,000
40,000
60,000
80,000
100,000
Number of Loadings Fig. 14. Permanent the deformation of the base layer predicted by the calibration model for the specimen with an air void ratio of 10.57% in the surface layer.
unified rutting prediction model suitable for Korea that is independent of the aggregate size. Figs. 9 and 10 compare the results of the rutting model prediction based on regression analysis of the APT results and actual measurement of the rutting of the complete asphalt sample using APT. In addition, Figs. 11–14 compare measured plastic strain with the plastic strain predicted by the rutting model proposed in this study. Figs. 11–14 show the permanent deformation as a function of the number of vehicular loadings and demonstrate that the predictions of the proposed rutting model are very similar to the actual measured results. The APT conditions and the measured resilient and plastic strains were applied to a domestic laboratory test model, and the actual measured values were subjected to regression analysis to obtain the following revised equation. Table 7 shows the calibration factor (bri, where i = 1, 2, 3, and 4) for domestic laboratory test model Eqs. (6) and (7).
ep ¼ 101:85927 N0:3755 T 1:5528 AV 0:89602 ; er
ð10Þ
where ep is the plastic strain, er is the recoverable strain, N is the number of load repetitions, T is the temperature (°C), and AV is the air void (%). 6. Conclusions This study included APT with experimental variables of temperature and air void percentage, which are important factors in rutting. The study also used the acquired plastic strain and resilient strain data acquired using an MDD; the parameters are fundamental for rutting modeling. The result was used to examine the rutting model of asphalt layers suggested by the AASHTO 2002 model, and a rutting model suitable for Korea was suggested by calibrating a laboratory rutting model. The measured resilient strain er and plastic strain ep values based on the APT conditions of this study were applied to the AASHTO 2002 model. The results predicted by the AASHTO model equation were significantly higher than the measured results obtained in this study based on vehicular loading and APT. Permanent deformation in the surface layer was measured at 57–65% based on APT, whereas the AASHTO model predicted a plastic strain greater than 99% in the surface layer. The depth coefficient k1 of the AASHTO model was so small that it predicted almost no plastic strain occurring in the base layer. References [1] Harichandran RS, Buch N, Baladi GY. Flexible pavement design in Michigan: transition from empirical to mechanistic methods. Transpor Res Record 2001;1778:100–6. [2] El-Basyouny M, Jeong MG. Effective temperature for analysis of permanent deformation and fatigue distress on asphalt mixtures. Transpor Res Record 2009;2127:155–63. [3] Yeo I, Suh Y, Mun S. Development of a remaining life model for asphalt black base through accelerated pavement testing. Constr Build Mater 2008;22(6):1881–6. [4] NCHRP 2002 Design Guide. Guide for mechanistic–empirical design of new and rehabilitated pavement structures. National Cooperative Highway Research Program, 2004. [5] Ministry of Land, Transport and Maritime Affairs. Korea pavement research program: asphalt pavement research report, 2008. [6] Jonson AM, Baus RL. Alternative method for temperature correction of backcalculated equivalent pavement moduli. Trans Res Record 1992;1355:75–81. [7] Huang YH. Pavement analysis and design. 2nd ed. Prentice Hall Inc.; 2004.