Materials and Structures (2014) 47:1339–1358 DOI 10.1617/s11527-014-0307-6
ORIGINAL ARTICLE
Mechanistic evaluation of cracking in in-service asphalt pavements Hong Joon Park • Mehran Eslaminia Y. Richard Kim
•
Received: 22 December 2013 / Accepted: 8 April 2014 / Published online: 24 April 2014 RILEM 2014
Abstract Cracking in asphalt pavements is a complex problem that is affected by pavement structural design, material properties, and environmental conditions. It is now well accepted that load-related topdown fatigue cracking (i.e., cracking that initiates at the surface of the pavement and propagates downward) commonly occurs in asphalt pavements. Conventional fracture mechanics-based finite element analysis must assume the location of macrocrack initiation a priori and, therefore, is not appropriate for general-purpose cracking simulation. This paper presents the use of the layered viscoelastic pavement analysis for critical distresses (LVECD) program to evaluate 18 pavements in local condition regions of 9 in-service pavement sites in North Carolina. In order to obtain the material properties of the individual layers from the field-extracted cores, dynamic modulus tests and simplified viscoelastic continuum damage tests are performed using small geometry specimens obtained from 150 mm diameter cores. This study verifies the capability of the LVECD model to capture crack initiation locations, propagation propensity, and cracking severity by comparing the simulation results with the observations of field cores and the field condition survey of in-service pavements in North Carolina. Overall, the agreement rate between the field core observations and field condition H. J. Park M. Eslaminia Y. R. Kim (&) North Carolina State University, Raleigh, NC, USA e-mail:
[email protected]
survey and the predicted LVECD simulation results is about 78 % in terms of cracking direction and severity. Keywords Asphalt pavement Top-down cracking Bottom-up cracking Layered viscoelastic pavement analysis for critical distresses (LVECD) program
1 Introduction The description of bottom-up cracking (BUC) mechanisms is based on the assumption that cracks initiate at the bottom of the asphalt layer due to excessive tensile strain and then propagate upward. In the case of top-down cracking (TDC), cracks initiate at the surface of the asphalt pavement and then propagate downward. Thus, pavement analysis models that consider bending stress at the bottom of the asphalt layer cannot effectively capture the pavement responses that result in the stress–strain conditions of TDC. TDC is caused by the combination of many factors, such as the contact stress between the tire and the pavement, traffic loading at low temperatures, aged and stripped asphalt binder, segregation during construction, and layer thickness [1]. Some researchers tried to develop tire-pavement interaction model in order to investigate TDC mechanisms [3, 12, 15]. To determine optimal pavement management strategies, the origin of the cracks that appear on the
1340
pavement surface needs to be identified, because identification of the crack origin will help to determine the most structurally effective and cost-effective maintenance plans. However, without full-depth trench cuts or coring near and in the cracked areas, it is not possible to identify the origin with visual observations, because TDC and full-depth cracking caused by BUC look identical on the pavement surface. The location of crack initiation must be assumed a priori for conventional fracture mechanics-based finite element analysis; therefore, such analysis is not an appropriate tool for identifying crack initiation locations for general purposes [13]. Also commonly used multi-layered elastic pavement analysis cannot model the time dependent nature of asphalt concrete appropriately. In order to calculate the stress and strain in pavements to identify the crack initiation and propagation, the completed NCHRP 1-42A project uses the viscoelastic continuum damage finite element program (VECDFEP??) that does not require the assumption of crack initiation a priori. The flexibility of the VECDFEP?? model allows cracks to initiate and propagate wherever the fundamental material law suggests, so that a realistic and accurate TDC simulation can be conducted [13]. Then, the VECD-FEP?? program evolved into the VECD-Fourier finite element (FFE) program by Eslaminia et al. [4, 5]. The major difference between these two tools in terms of pavement response analysis is that the VECD-FEP?? program uses stationary circular loading combined with axisymmetrical finite element time stepping, whereas the VECD-FFE is a threedimensional analysis tool that is based on Fourier transform-based finite element analysis and moving loads. However, the shortcoming of the FFE method is its required simulation time. Depending on the number of layers and mesh size, the FFE program requires up to 12 h or more of computational time, even with a quality personal computer. A complete review of the FFE program concept is beyond the scope of this paper, so interested readers are directed to the paper of Eslaminia et al. [5] for details. Thus, researchers at North Carolina State University (NCSU) developed the layered viscoelastic pavement analysis for critical distresses (LVECD) program [5]. This program enables the characterization of longterm pavement performance within just an hour.
Materials and Structures (2014) 47:1339–1358
In this paper, the data obtained from field tests and laboratory experiments with field cores are used in the simplified viscoelastic continuum damage (S-VECD) model along with the LVECD program to identify crack initiation, propagation, and severity of the pavements in 18 condition regions from 9 pavement sites in North Carolina. These simulation results are verified using observations from field cores and a field condition survey.
2 Field test sites, cores, and condition survey As part of a fatigue forensic research project for the North Carolina Department of Transportation (NCDOT), field sections were selected and field cores were extracted from selected field sites for laboratory testing. The test sites were selected on the basis of the 2010 NCDOT condition survey, which is the construction history and profile database of the NCDOT. Once the project was underway, it was found that some of the actual sites did not match the records in this NCDOT construction history and profile database. Therefore, the list of scheduled resurfacing sites was used to select additional field sites later on in the project. Table 1 presents detailed information for the sites selected for this study. It is noted that the US 17 and NC 209 sections were selected because these pavements are relatively old, but are performing quite well. Other pavement sections were selected because they had extensive cracking problems. In order to investigate the different cracking performance characteristics of different areas within the same site, the field sites were selected to avoid major intersections, which resulted in the lengths of most of the selected field sites being shorter than the length of the site reported in the pavement condition rating (PCR) index of the NCDOT condition survey database. In spite of identical external pavement conditions, some regions of a site were observed to exhibit different levels of crack severity. Accordingly, each site was divided into different cracking severity regions in order to verify differences in the material properties. Each test site presented in this paper has an A condition region and a B condition region, and generally the B condition region has relatively more severe cracking than the A condition region. In order to secure the safety of the field workers on the roads during a partial lane closure on field testing
US-17 (Brunswick Co.)
US-70 (Johnston Co.)
NC-24 (Mecklenburg Co.)
A1
I-540 (Wake Co.)
A2
B2
A2
B2
A1
B1
B2
Loc ID
County
51.3 115.4 29.1 40.7 66.7 106.9
3 4 1 2 3 4
38.6
93.7
4 2
73.8
3 28.0
61.2
1
74.2
92.6
4 2
76.2
1
63.5
3
112.2
3 2
32.3
2 40.2
93.7 42.3
3 1
1
46.6 34.9
123.5
4 1
82.4
3
2
53.3
2
4 38.5
83.2 119.4
3 1
36.8 59.1
1
12.5
25.0
19.0
9.5
25.0 9.5
19.0
9.5
9.5
25.0
9.5
9.5
9.5
25.0
9.5
9.5
9.5
19.0
9.5
19.0 9.5
9.5
9.5
25.0
19.0
9.5
12.5
25.0
19.0
12.5
0.001
0.001
0.001
0.001
0.000 0.001
0.001
0.001
0.000
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001
0.001 0.002
0.001
0.002
0.001
0.001
0.001
0.001
0.001
0.001
0.001
-0.177
-0.140
-0.145
-0.143 -0.189
-0.141
-0.162
-0.170
-0.152
-0.140
-0.162
-0.164
-0.159
-0.166
-0.164
-0.171
-0.148
-0.172
-0.159 -0.270
-0.159
-0.222
-0.147
-0.144
-0.176
-0.158
-0.147
-0.150
-0.168
-0.162
3.119
2.584
2.617
2.661 3.486
2.601
2.933
3.215
2.784
2.587
2.916
3.011
2.851
2.990
3.053
3.109
2.726
3.053
2.874 4.671
2.898
3.833
2.692
2.687
3.114
2.843
2.693
2.758
2.993
2.993
1.357
1.792
1.968
1.755 0.007
1.940
0.835
-63.228
1.696
1.882
0.972
0.804
1.696
1.882
0.972
0.804
2.161
2.125
1.956 -76.481
1.122
1.291
1.792
1.883
1.644
1.719
1.733
1.695
1.818
0.412
3.401
2.903
2.472
2.374
2.656
2.726
2.536
2.600
2.320
3.968
3.052
2.597
2.420
2.664 4.393
2.415
3.544
67.594
2.704
2.513
3.241
3.625
2.704
2.513
3.241
3.625
2.212
2.191
2.450 80.513
b
a
a3
a1
a2
Sigmoidal Coefficient
Shift factor
Thick (mm)
NMSA (mm)
Dynamic modulus
Asphalt layer
2
Layer
Table 1 Summary of Pavement Information for Selected Sites
1.150
0.775
0.516
1.058 2.892
0.913
1.250
5.254
0.868
0.470
1.741
1.933
0.868
0.470
1.741
1.933
0.007
0.216
0.350 5.178
0.949
1.602
0.489
0.320
0.882
0.324
0.319
0.412
0.712
1.803
d
0.608
0.796
0.721
0.687 0.430
0.807
0.490
0.294
0.684
0.582
0.450
0.517
0.684
0.582
0.450
0.517
0.803
0.603
0.690 0.268
0.470
0.407
0.835
0.753
0.608
0.349
0.776
0.710
0.651
0.450
g
3.23
3.03
3.42
3.28 3.16
3.16
3.36
2.69
3.46
3.21
4.39
3.57
3.26
3.87
3.8
3.2
3.34
4.13
3.44 2.14
3.56
4.23
2.95
3.21
3.46
4.80
3.01
3.18
3.61
3.82
Alpha
Materials and Structures (2014) 47:1339–1358 1341
US-74 (Swain Co.)
NC-87 (Cumberland Co.)
US-76 (New Hanover Co.)
A1
US-601 (Union Co.)
A1
B1
A2
B1
A1
B1
B2
Loc ID
County
Table 1 continued
40.8 93.2 46.3
2 3
44.1
3 1
39.7
73.0
5 88.1
48.9
4 1
83.8
3
2
35.4
100.8
5 2
38.1 60.3
90.5
3 4 1
27.8
76.2
3 2
58.2
2 65.1
59.7 81.5
3 1
1
29.5 25.4
1
49.5 46.4
3 4 2
36.8
43.3
4 2
44.1
3 34.3
49.2
1
39.3
2
19.0
19.0
9.5
19.0
19.0
9.5
19.0
12.5
9.5
9.5
9.5
19.0
9.5
9.5
9.5
9.5
19.0
9.5
9.5 9.5
9.5
9.5
19.0
9.5
12.5
9.5
19.0
9.5
12.5
12.5
0.001
0.000
0.000
0.001
0.000
0.001
0.001
0.001
0.001
0.001
0.000
0.001
0.000
0.001
0.001
0.001
0.000
0.001
0.001 0.001
0.001
0.001
0.001
0.000
0.001
0.001
0.001
0.001
0.001
0.000
-0.150
-0.170
-0.138
-0.154
-0.145 -0.169
-0.165
-0.189
-0.236
-0.210
-0.165
-0.143
-0.181
-0.167
-0.164
-0.180
-0.215
-0.163
-0.156
-0.194 -0.164
-0.163
-0.160
-0.193
-0.162
-0.170
-0.155
-0.206
-0.175
-0.171
2.841
3.097
2.651
2.877
2.727 3.109
2.985
3.546
4.207
3.671
3.077
2.720
3.212
3.137
3.057
3.197
3.735
3.119
2.837
3.348 2.976
3.003
2.978
3.570
3.080
3.093
2.855
3.640
3.285
3.193
0.867
1.474
1.819
2.056
1.912 2.026
1.513
-14.9 K
0.499
-2.833
0.312
2.084
-22.708
0.996
1.907
1.697
-5.986
-5.971
1.628
-2.065 1.017
0.505
1.511
-8.455
0.988
1.370
0.878
-2.557
-3.067
-1.924
3.336
3.158
3.607
7.166
7.462
6.360
3.542
2.956
2.699
2.286
2.503 2.334
2.733
14.9 K
3.866
7.309
4.187
2.387
27.195
3.457
2.477
2.736
10.374
10.305
2.550
6.184 3.178
3.779
2.913
13.103
b
a
a3
a1
a2
Sigmoidal Coefficient
Shift factor
Thick (mm)
NMSA (mm)
Dynamic modulus
Asphalt layer
1
Layer
1.072
0.985
1.027
0.986 0.731
1.279
10.344
1.576
2.286
1.595
0.885
3.146
1.410
1.057
1.165
3.154
3.089
0.513
2.629 1.525
1.859
1.113
3.004
1.736
1.129
1.254
2.442
2.294
2.406
1.113
d
0.486
0.625
0.664
0.659 0.542
0.767
0.262
0.317
0.273
0.416
0.647
0.196
0.369
0.487
0.508
0.371
0.336
0.624
0.453 0.483
0.458
0.495
0.231
0.364
0.527
0.556
0.336
0.297
0.419
0.549
g
3.85
3.44
3.84
3.51 4.23
3.09
1.62
3.95
2.95
3.34
3.69
5.19
4.21
4.39
3.95
1.94
2.65
3.61
2.18 3.63
3.95
3.85
2.59
4.27
3.05
3.04
2.53
2.98
2.57
3.1
Alpha
1342 Materials and Structures (2014) 47:1339–1358
A1
NC-209 (Haywood Co.)
NC-24 (Mecklenburg Co.)
A1
I-540 (Wake Co.)
A1
B1
B2
Loc ID
County
B1
Loc ID
County
Table 1 continued
-0.0007 -0.0033
2 3
-0.0011
3 -0.0053
-0.0004
2 1
-0.0138
-0.0026 -0.0172
1
-0.0022
3 4
-0.0011
4 2
-0.0004
3 0.0000
-0.0002
2
1
-0.0001
1
a
0.5136
0.6455
0.5612
0.6023
0.6789
0.4173
0.5624 0.3886
0.5247
1.1638
0.6426
0.7141
0.7819
0.8180
b
STB ABC
Cement Treated ABC
-0.148
380
230
200
2.823
406.0
376.7
10.3 K
88.6
112.0
98.3
Es (MPa)
3.049
2.935
2.973
2.936
2.845
Eb (MPa)
-0.166
-0.157
-0.158
-0.153
-0.157
Base thick (mm)
DCP
Base type
0.001
0.001
0.000
0.000
Exp. coefficient
19.0
9.5
9.5
19.0
0.000 0.001
Base and subgrade layer
45.5
3
9.5 9.5
S-VECD
29.2
2
Layer
46.2
49.8
3 1
46.0 31.0
1
0.715
3.651
4.113
3.441
3.350
3.958
2.553
88.5
104.6
Speed limit (km/hr)
Traffic
0.323
0.936
1.041
0.444
1.722
b
1.630
1.240
1.412
1.605
0.760
1.552
d
523 K
1,146 K
20 year ESAL
a
a3
a1
a2
Sigmoidal Coefficient
Shift factor
Thick (mm)
NMSA (mm)
Dynamic modulus
Asphalt layer
2
Layer
3.62
3.53
3.66
3.58
3.62
3.71
35130 38.11780360 38.9500
3520 59.6800 -783500 26.4400
Lattitude/ longitude
Location
0.391
0.457
0.475
0.391
0.594
0.467
g
Alpha
Materials and Structures (2014) 47:1339–1358 1343
US-601 (Union Co.)
US-17 (Brunswick Co.)
B2
US-70 (Johnston Co.)
B2
A1
A2
B2
A2
Loc ID
County
Table 1 continued
-0.0014 -0.0002 -0.0137 -0.0053
2 3 4
-0.0053
4 1
-0.0001 -0.0137
2 3
-0.0004
4 -0.0005
-0.0021
1
-0.0023
3
0.0000
4 2
-0.0020
3 -0.0025
-0.0008
2
1
-0.0006
0.0000
4 1
-0.0013 -0.0030
-0.0023
4 2 3
-0.0019
3 -0.0005
-0.0005
2
1
-0.0005
a
0.4821
0.3759
0.7077
0.5424
0.4643
0.7249 0.3759
0.6487
0.6811
0.5304
0.5252
0.4899
0.8927
0.5459
0.6098
0.6044
0.9324
0.5987 0.5219
0.6316
0.5317
0.5509
0.6756
0.6236
b
ABC
ABC
ABC
Base type
Exp. coefficient
244
289
203
203
239
238
Base thick (mm)
DCP
Base and subgrade layer
S-VECD
1
Layer
607.3
411.3
118.4
164.4
511.5
374.3
Eb (MPa)
94.2
120.8
150.7
158.0
184.7
150.5
Es (MPa)
88.5
88.5
88.5
Speed limit (km/hr)
Traffic
424 K
343 K
736 K
20 year ESAL
3510 12.147 80320 29.9600
3410 13.8500 78150 56.3900
35330 5.4500 78180 57.880800
Lattitude/ longitude
Location
1344 Materials and Structures (2014) 47:1339–1358
US-74 (Swain Co.)
NC-87 (Cumberland Co.)
B1
US-76 (New Hanover Co.)
A1
B1
A2
B1
A1
Loc ID
County
Table 1 continued
-0.0005 -0.0001 -0.0006
2 3
-0.0017
3 1
-0.0005
2
-0.0157
5 -0.0013
-0.0043
1
-0.0033
4
-0.0005
5
3
-0.0002
4
-0.0005
-0.0016
3
2
-0.0011
2
-0.0216
-0.0014 -0.0197
3 1
1
-0.0038
2
-0.0114
3 -0.0067
-0.0001
2 1
-0.0014
a
0.8025 0.6415
0.6275
0.5670
0.6302
0.5550
0.3771
0.4687
0.5138
0.6325
0.2971
0.6720
0.7177
0.5388
0.5603
0.5766 0.4000
0.5169
0.4735
0.5243
0.7469
0.5165
b
Coarse ABC
Soil
ABC
Base type
Exp. coefficient
300
260
288
228
290
240
Base thick (mm)
DCP
Base and subgrade layer
S-VECD
1
Layer
617.7
609.0
205.4
178.2
226.8
508.4
Eb (MPa)
174.2
142.3
119.7
43.1
195.6
197.7
Es (MPa)
88.5
88.5
72.4
Speed limit (km/hr)
Traffic
271 K
K
399
164 K
20 year ESAL
35240 46.6700 83270 3.5600
34550 30.3000 78510 26.9700
34130 19.0400 77490 11.4700
Lattitude/ longitude
Location
Materials and Structures (2014) 47:1339–1358 1345
15 K 88.5
346.1 280 0.5670 -0.0017 3
0.6302 -0.0005
0.5550 -0.0013 1
2
B1
-0.0001 -0.0006 2 3
0.8025 0.6415
ABC 0.6275 -0.0005 1 A1 NC-209 (Haywood Co.)
NMAS nominal maximum aggregate size, Eb resilient modulus of base layer, Es resilient modulus of subgrade
112.1
137.9 363.4
Es (MPa) Eb (MPa) Base thick (mm) b a
DCP Base type Exp. coefficient
260
Speed limit (km/hr)
20 year ESAL
Location Traffic Base and subgrade layer S-VECD Layer Loc ID County
Table 1 continued
35360 32.6200 82560 16.2100
Materials and Structures (2014) 47:1339–1358
Lattitude/ longitude
1346
dates, a straight section of the field site was selected for field investigation and material extraction. For these reasons, the ‘short’ condition regions necessitated a detailed PCR for the numerical comparison of pavement conditions in a site or other condition regions in other sites. Therefore, in order to define the surface pavement condition of each condition region, the authors adopted the long-term pavement performance (LTPP) program’s computational method, which is the so-called alligator cracking index (ACI). Since the researchers for LTPP program developed deduction values from the percentage of three different distress level and subtracted deduction values from 100 that was assumed as the pavement condition without distress, higher ACI value indicates better condition than lower ACI values. In Table 2, the ACI values for each condition region are presented based on the field condition survey. Detailed information about determining the ACI values from the field condition survey is presented elsewhere [8]. The extracted field cores and a field condition survey were used to evaluate the severity and types of cracking in terms of propagation direction (i.e., TDC, BUC, and/ or bi-directional cracking). Cores were taken from both highly distressed areas and from parts of the wheel path that did not show any surface cracks. If a core from a highly distressed area had a vertical crack that was continuous from the top to the middle of the core, the condition region was identified as a TDC-observed region. If cores from a highly distressed area had a fulldepth crack, and cores with no visible crack on the surface had cracks at the bottom of the cores that did not propagate all the way to the pavement surface, then the condition region was identified as a BUC-observed region. The cores to be subjected to mechanical testing were obtained from the center of the lane where no visible crack was present on the surface and next to the cored area where the TDC or BUC was observed. The base layer modulus values, thicknesses, and subgrade modulus values shown in Table 1 were determined from dynamic cone penetrometer (DCP) test results.
3 Asphalt material properties As described in Sect. 2, all the cores used for material characterization were extracted from the lane center where damage due to traffic loading is minor.
Materials and Structures (2014) 47:1339–1358
1347
Table 2 Cracking Severity and Propagation Direction Observed from Field Cores and Their Agreement with LVECD Prediction Results Route
Field observations Condition region
Field cores TDC?
US-17 US-70
BUC?
Condition survey
NCDOT database
Local ACI
Oxidization?
B2
Yes
No
91.7
Yes
A2
No
No
90.5
Yes
B2
Yes
No
90.9
No
A2
No
No
100
No
I-540
B2
Yes
No
32.6
No
NC-24
A1 B1
No Yes
No No
91.4 62.9
No No
A1
Yes
No
71.6
No
B1
No
Yes
68.7
No
A1
No
Yes
81.1
No
B1
No
No
95.9
No
A1
No
No
100
No
B1
Yes
No
75.2
Yes
A1
Yes
Yes
96.7
Yes
B1
Yes
No
88.6
No
A1
No
Yes
95.5
No
B2
No
Yes
84.1
No
A1
Yes
Yes
91.4
No
US-74 NC-209 US-76 NC-87 US-601
Accordingly, the cores were appropriate for mechanical experiments even if the cores were taken from relatively bad condition regions. For the linear viscoelastic characterization of the material taken from the individual layers of the field cores, uniaxial tension– compression dynamic modulus tests were conducted at 5, 20, and 40 C and frequencies of 25, 10, 5, 1, 0.5, and 0.1 Hz. The dynamic modulus mastercurve and time–temperature shift factor is represented by a sigmoidal functional form in Eq. (1) and quadratic function in Eq. (3), respectively. logjE j ¼ a þ
b 1 1 þ =edþglog10 ðfR Þ
ð1Þ
f R ¼ aT f
ð2Þ
logðaT Þ ¼ a1 T 2 þ a2 T þ a3
ð3Þ
where |E*| is the dynamic modulus (MPa), fR is the reduced frequency (Hz), a, b, d, g is the regression constants, aT is the time–temperature shift factor, f is the loading frequency (Hz), T is the temperature (C), and a1, a2, a3 is the regression constants.
Also, controlled crosshead cyclic direct tension tests were conducted at 19 C and 10 Hz for damage characterization. The test results were analyzed to develop the S-VECD model. The S-VECD model represents the unique damage characteristic of the material by expressing the pseudo stiffness (C) as a function of the damage parameter (S), as shown in Eq. (4). b
C ¼ eaS
ð4Þ
where C is the normalized pseudo stiffness, e is the exponential function, S is the damage parameter, and a, b is the regression constants. The pseudo stiffness represents the integrity of material, and the damage parameter is the internal state variable that represents the amount of damage in the material. The S-VECD model is the simplified form of the viscoelastic continuum damage (VECD) model [9] that can be used in analyzing cyclic test data. The S-VECD model overcomes the lengthy computing time of the VECD model by employing a piecewise
1348
approach. That is, the S-VECD model separates the analysis of the first loading cycle from the analysis of the entire loading history, because 15–25 % reduction in pseudo stiffness occurs during the first loading cycle in a controlled crosshead cyclic test. After full analysis of the data points obtained from the first loading cycle, the successive peak data points from the subsequent load cycles are used to calculate the pseudo stiffness and damage parameter using the load shape function obtained from the first load cycle analysis. Detailed information about the S-VECD model is available from Underwood et al. [17] and [18]. All of the coefficients for Eqs. (1), (3), and (4) that were obtained from the mechanical experiments of the field materials are presented in Table 1.
4 Small specimen geometries and evaluation of anisotropy effects Because it is difficult, if not impossible, to perform laboratory fatigue tests on field cores using standard cylindrical specimens, small cylindrical specimens, as proposed by Kutay et al. [10], and prismatic specimens, proposed by Park [14], are used in this study. The key advantage of these small geometries is that samples can be obtained from a pavement layer as thin as 44.5 mm for the small cylindrical specimen and 25 mm for the prismatic specimen. The dimensions of the small cylindrical specimens are 38 mm in diameter and 100 mm in height, and the dimensions of the prismatic specimens are 25 mm 9 50 mm 9 100 mm. In a previous study [13], the material properties derived using these two different geometries obtained from gyratory specimens by vertical coring and cutting are compared against the material properties derived from the full specimen geometry (i.e., 100 mm diameter and 130 mm height) obtained from gyratory-compacted specimens. However, the aggregate orientation that results from vertical coring and cutting can be different from that of side (horizontal) coring and cutting. Therefore, the effect of anisotropic aggregate orientation needed to be verified for the small geometry specimens. Underwood [16] already have presented experimental results of the effect of the anisotropy of aggregate orientation on the mechanical responses of asphalt concrete specimens compacted by the
Materials and Structures (2014) 47:1339–1358
Servopac Superpave gyratory compactor. These researchers concluded that the inherent anisotropy does not affect the dynamic modulus results and the mechanical responses of asphalt concrete in tensile mode [16]. Despite this detailed research into the effects of aggregate orientation, another verification process was conducted for this research because the specimen geometry used in the Underwood study was 75 mm in diameter and 90 mm in height, whereas the small specimen geometries used in this study are much smaller. Therefore, an additional verification study was performed using a 9.5-mm asphalt mixture comprised of 50 % #78 stone, 14.5 % screenings, 33 % sand, and 2.5 % bag-house fines. The blended gradation is shown in Fig. 1. The asphalt used in this mixture was a PG 58–28 unmodified binder with the optimum asphalt content of 6.2 % by total mix mass. In the verification study, the gyratory specimens were cored in both the vertical (Fig. 2a, b) and horizontal (Fig. 2c, d) directions, and the mechanical responses were compared. This same directional coring approach was applied to the prismatic specimens. Note that in order to obtain consistent air void distributions in the test specimens, 100-mm diameter specimens were obtained by vertically coring the middle of the gyratory-compacted specimens. Then, the test specimens were cored or cut vertically as shown in Fig. 2a, b or horizontally as shown in Fig. 2c, d. The tops and bottoms of the specimens were removed evenly from the cored and cut specimens to keep the height of the specimens at 100 mm. Dynamic modulus and S-VECD tests were performed for the small geometry specimens obtained from the different coring and cutting directions, and the results are summarized in Fig. 3a–d. The data presented in Fig. 3a–c provide the dynamic modulus values measured at -10 to 40 C and at frequencies from 25 to 0.1 Hz for these two geometries from two fabrication directions. Figure 3a–c show that, except for the results for the prismatic specimens that were cut from the side (perpendicular to the compaction direction), all of the dynamic modulus test results obtained from the different geometries and coring directions fall within reasonable sample-to-sample variation. For the case of the side coring of the prismatic specimens, it is believed that the sample came from the center of the specimen where the air void distribution is low. Figure 3d shows the damage characteristic curves
Materials and Structures (2014) 47:1339–1358
1349
100
% Passing
80 60 40 Control Points Restricted Zone
20
Mixture Gradation
0
0
1
2
3
4
as those obtained from standard-sized specimens. It is noted that the largest NMAS used in Li and Gibson’s study is 19 mm. The findings from Li and Gibson’s study and the work conducted by the NCSU research team provide sufficient evidence that the small geometry specimens obtained by horizontally coring 150-mm diameter field cores can yield reliable modulus and fatigue characteristics for asphalt layers.
Sieve Size 0.45 Power
Fig. 1 Aggregate gradation
obtained from the different coring directions and geometries. Although the curves for the vertical cutting of the prismatic specimens are located slightly lower than those for the other conditions, all the test results show similar trends. In a recent publication by Li and Gibson [11], the authors showed in an extensive laboratory study that the dynamic modulus and fatigue characteristics of 38-mm diameter specimens are statistically the same
Fig. 2 Schematic of specimen extraction from gyratory specimens: a vertical cutting for prismatic specimen, b vertical coring for small cylindrical specimen, c side cutting for prismatic specimen, and d side coring for small cylindrical specimen
5 Layered viscoelastic continuum damage program A layered viscoelastic structural model and fastFourier transform-based finite element analysis program were used in this study to predict LTPP under moving traffic loads. The simulation software, the LVECD program, was developed by Eslaminia et al. [5] at NCSU. It can perform three-dimensional analysis of pavements under moving loads in a computationally efficient manner and can capture the
1350
30000 25000
|E*| (MPa)
(b) 100000
35000 P-Side Cutting P-Veritcal Cutting 38-Side Coring 38-Vertical Coring
|E*| (MPa)
(a)
Materials and Structures (2014) 47:1339–1358
20000 15000 10000
10000
P-Side Cutting P-Veritcal Cutting 38-Side Coring 38-Vertical Coring
1000
5000 0 1E-07
1E-05
1E-03
1E-01
1E+01
1E+03
100 1E-07
1E+05
(c)
(d)
45 P-Side Cutting P-Verical Cutting 38-Side Coring 38-Vertical Coring
35 30
1E-03
1E-01
1E+01
1E+03
1E+05
25
1.0 P-Side Coring P-Vertical Coring 38-Side Coring 38-Vertical Coring
0.8 0.6
C
Phase Angle (deg)
40
1E-05
Reduced Frequency (Hz)
Reduced Frequency (Hz)
20
0.4
15 10
0.2
5 0 1E-06
1E-04
1E-02
1E+00
1E+02
0.0 0.E+00
1E+04
2.E+05
4.E+05
6.E+05
S
Reduced Frequency (Hz)
Fig. 3 Comparison of material properties measured from vertical and side coring of 38 mm and prismatic geometry specimens: a dynamic modulus in semi-log space, b dynamic modulus in log–log space, c phase angle, and d damage characteristic curves
effects of the viscoelasticity of asphalt concrete, thermal stress, and viscoelastic property changes caused by temperature and traffic loading conditions. The framework of the LVECD program was developed based on a combination of the following ideas [5]: •
•
•
The pavement structure is assumed to be an infinite layered system where the material properties vary only along the depth of the pavement. This assumption is based on the fact that the pavement length and width dimensions are very large compared to the tire size and thickness of the pavement layers. In addition, the effects of fatigue/ rutting on the material properties/structure are ignored in the program. The temperature variation along the length of a pavement is not significant. Therefore, the temperature is constant for all points at a given depth, and the temperature varies only as a function of the pavement depth. Although the yearly variation in temperature can be captured by spending significantly more time in
•
•
•
computational efforts, the temperature profile can be modeled as a cyclic function for a one-year period. Therefore, the stress and strain calculations can be reduced to a representative year. Note that the performance calculations, however, must be done for the entire life of the pavement and cannot be limited to the representative year. Despite the complicated nature of traffic loading, it can be modeled as a periodic load with a constant tire shape moving at a constant speed. Although this design is a significant simplification, it is nonetheless an acceptable approximation due to the random nature of the traffic. Because a single cycle of the traffic load induces small deformations in the pavement structure, the asphalt concrete is modeled as linear viscoelastic material, and the base and subgrade layers are assumed to be linear elastic. Temperature changes gradually as a function of time, whereas traffic loading varies within just a few seconds (i.e., time-scale separation). Thus, the analysis of the pavement responses under traffic
Materials and Structures (2014) 47:1339–1358
loading can be performed assuming a fixed temperature profile. Utilizing these assumptions and simplifications, a segmented analysis framework [1, 4, 5] can be proposed to reduce the cost of the pavement response and performance analysis without losing accuracy. The proposed framework, which is the basis of the LVECD program, can be summarized in the following steps: Step 1: The temperature is a cyclic function with a one-year time period. Thus, the pavement response analysis must be performed for a representative year for which the profile temperature is available by averaging the enhanced integrated climate model (EICM) temperature data over the life of the pavement Step 2: The representative year is divided into shorter periods called stages. The length of each stage is dependent on the seasonal variation of both temperature and traffic. The representative year is divided naturally into 12 months (i.e., each stage is a month). This assumption is well suited for traffic and temperature data. However, more accurate analysis can be conducted by assuming shorter stage lengths (e.g., 2 weeks). Step 3: Each stage, whether it is a month or 2 weeks, is divided further into smaller periods called segments. Each segment represents a short period of the day. The length and number of the segments are determined based on the hourly variations of traffic and temperature. For example, three segments could represent morning, afternoon, and evening. The temperature profile is assumed to be fixed during each segment. The temperature profile is the averaged value over the length of the stage; daily changes of temperature are not significant within a month or 2 weeks. Step 4: For each segment, e.g., morning, afternoon, and evening, the pavement responses are computed under a single cycle of traffic load using threedimensional layered viscoelastic analysis. The details of this Step 4 are discussed in the next section (Sect. 5.1). Step 5: Given the response analysis results for each segment, the fatigue cracking analysis can be carried out using the VECD model [9] combined with an efficient nonlinear extrapolation scheme. The procedure for the damage calculation is
1351
discussed below. Note that the damage calculation is performed for the entire life of the pavement 5.1 LVECD pavement response analysis Using the segmented analysis framework discussed in the previous section, the pavement response analysis can be reduced to a few dozen analyses of a layered pavement system under a moving load with a fixed temperature profile. Despite the significant simplification of this design, using conventional three-dimensional finite element methods for this response analysis is impractical due to the extremely high computational costs. The layered viscoelastic analysis method has been proposed to perform response analysis under moving loads. This method is an extension of the layered elastic method that has been widely used for pavement analysis [7]. The idea of a layered viscoelastic analysis with a moving load has been used already in several programs, such as 3D-Move [19], Viscoroute [2], and VEROAD [6], with slight changes and modifications. In all of these software programs, including the LVECD program, Fourier transform in space and time is used to reduce an infinite layered system to a small one-dimensional problem along the pavement depth. The LVECD program solves the reduced problem using an accurate and efficient one-dimensional finite element method, whereas the other programs use an analytical solution based on layer interface conditions. The ideas behind layered viscoelastic analysis are summarized below. Assume an infinite layered pavement where x (-? \ x \ ??) is the transverse direction, y (-? \ y \ ??) is the traffic direction, and z is the pavement depth (z = 0 is pavement surface). Assuming that the traffic load has a constant shape and pressure and is moving at a constant speed V, the spatial distribution and history of the traffic load can be combined as p ¼ pðx; y VtÞ;
ð5Þ
where the traffic load, p, is a vector that includes vertical tire pressure and horizontal shear traction. Thus, the mathematical statement for layered viscoelastic analysis can be summarized in the following formulation. Strain–displacement relationship:
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Materials and Structures (2014) 47:1339–1358
3 0 7 0 78 9 7 o= 7< ux = 0 oz 7 u o= o 7: y ; ¼ Lu: oz =oy 7 7 uz o= 7 0 ox 5 o= 0 ox ð6Þ
2
o= ox 6 6 0 6 6 0 6 zz ¼6 e¼ c > > 6 0 yz > > > > 6 > > c > > 6 zx > ; 4 o=oz : > cxy o= oy 8 9 exx > > > > >e > > > > yy > > =
0 o= oy
szx
LT r ¼ f : ð7Þ
0
ð8Þ
Bottom boundary condition: ux ¼ uy ¼ uz ¼ 0at z ¼ zmax :
ð9Þ
Top boundary condition: rzz
szy gT ¼ pðx; t y=V Þ:
ð10Þ
In the above formulation, u is the displacement vector; e is the strain vector; L is the strain displacement operator; r is the stress vector; C is the stress– strain matrix; and f is the body force vector. As mentioned earlier, the central idea behind the layered viscoelastic analysis is using Fourier transform in time and space to simplify the problem, because the material properties vary only along the depth of the pavement. The Fourier transform of a function is defined as: f^ kx ; ky ; z; x ¼
Zþ1 Zþ1 Zþ1 1
1
ð14Þ
Bottom boundary condition: u^x ¼ u^y ¼ u^z ¼ 0
Equilibrium equations:
tr ¼ f sxz
ð13Þ
Equilibrium equations:
sxy gT
LT r ¼ f:
at z ¼ zmax :
Top boundary condition: ^tr ¼ p^ kx ; ky ; z; x :
ð15Þ
ð16Þ
The LVECD program uses an efficient finite element method to solve this one-dimensional problem for a given set of x, kx, and ky. Apply this Fourier transform to the load function in Eq. (5): p^ kx ; ky ; z; x Zþ1 Zþ1 Zþ1 ¼ pðx; y VtÞeikx x eiky y eixt dxdydt: 1
1
1
ð17Þ Assume t ¼ t y=V: Pp^ kx ; ky ; z; x Zþ1 Zþ1 Zþ1 x pðx; tÞeikx x eiðky þV Þy eixtdxdyd:t ¼ 1
1
1
ð18Þ
1
f ðx; y; z; tÞeikx x eiky y eixt dxdydt;
ð12Þ
Stress–strain relationship: ^ðz; xÞ^ r^ ¼ ixC e:
Stress–strain relationship: r ¼ f rxx ryy rzz syz Zt de ¼ Cðt sÞ ds: ds
3 0 0 ikx 6 0 iky 0 7 78 9 6 7< u^x = 6 0 o 0 = 6 oz 7 ^u: ^ e^ ¼ 6 7 u^y ¼ L o= 6 0 iky 7: ; oz 7 u^z 6 4 o= 0 ikx 5 oz iky ikx 0 2
ð11Þ
where f^ is the Fourier transform of a function, f; x is the (temporal) frequency; and kx and ky are the wave numbers (spatial frequencies) along the x and y axes, respectively. Using this Fourier transform for the problem set defined in Eqs. (6) through (10), the reduced one-dimensional problem set becomes the following formulation. Strain–displacement relationship:
It can be shown easily that Eq. (18) is non-zero if and only if ky ¼ xV . This result implies that the solution of the one-dimensional problem in Eqs. (12) through (16) is not required for all sets of x and ky. In other words, the reduced problem must be solved only for all values of x with ky ¼ xV . Therefore, the computational cost of the analysis of moving loads can be reduced significantly. When the one-dimensional problem is solved for all sets in kx and x, the inverse Fourier transform can be used to determine the temporal and spatial distributions of the pavement responses.
Materials and Structures (2014) 47:1339–1358
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5.2 LVECD thermal stress analysis
and
The next step is to obtain the pavement responses due to temperature variation. LVECD thermal stress analysis is based on two assumptions. First, the pavement temperature varies only as a function of the pavement depth and is constant in the traffic or transverse directions. Second, the thermal displacement is zero in the traffic direction because the pavement is infinite. Therefore, the thermal stresses can be determined using the following plane strain problem with the pavement cross-section. 3 8 9 2o =ox < exx = 6 7 ux o e ¼ ezz ¼ 4 ¼ Lu: ð19Þ =oz 5 uz : ; czx o= o= oz ox
f^ ¼
Stress–strain relationship: sigma ¼ f rxx
rzz
szx gT ¼
Zt
C ð t sÞ
de ds: ds
0
f^x
f^z
T
" # E^ðxÞ ikx DT^ðxÞ a ¼ : dDT^ 1 2m dz
ð26Þ
The rest of the formulation is similar to that for traffic loading, as discussed in Sect. 5.1. The above problem set can be solved using an efficient onedimensional finite element method within the pavement depth for given wave number kx and frequency x. The thermal stress in the traffic direction is later determined by postprocessing the in-plane thermal strain components. The LVECD program uses temperature profiles generated by the EICM to compute thermal stress. For a given month, hourly variations of the temperature profile are extracted from the EICM data for different depths, and the thermal stresses are determined using the formulation discussed in this section. The thermal stresses are later averaged and added to the traffic loading data to compute the fatigue cracking for a given analysis segment.
ð20Þ 5.3 LVECD fatigue cracking analysis
Equilibrium equations: LT r ¼ f:
ð21Þ
Bottom boundary condition: ux ¼ uy ¼ uz ¼ 0
at z ¼ zmax :
ð22Þ
Top boundary condition: tr ¼ f sxz
rzz gT ¼ 0:
ð23Þ
Body force f in Equation (21) is determined using the thermal expansion coefficient a and temperature increment DT as follows: " dðDT Þ # Zt E ðt s Þ T f ¼ f fx fz g ¼ a dðdDTx Þ ds; ð24Þ 1 2m d z 0 where E is the relaxation modulus and m is Poisson’s ratio. Similar to traffic loading, the Fourier transform is used with respect to the time and x (transverse direction), which yields: 8 9 2 3 ikx < e^xx = o= 5 u^x ^u; ^ e^ ¼ e^zz ¼ 4 ¼L ð25Þ oz u^z : ; o= c^zx oz ikx
The LVECD framework that can be used to calculate fatigue cracking is described in this section. Specifically, this framework is based on the VECD model where asphalt concrete is modeled as a viscoelastic material with microcrack-induced damage [9]. The 3D-move program is also capable of fatigue performance analysis, but its framework is based on the conventional tensile strain-based fatigue model. 5.3.1 Uniaxial viscoelastic continuum damage model The VECD model presented in Kim et al. [9] is used to represent the damage evolution in the asphalt concrete layer. Starting with the uniaxial setting, the stress– strain relationship of the damaged viscoelastic material is given by: r ¼ CðSÞER eR ;
ð27Þ
where C is the normalized stiffness (pseudo stiffness) that represents the effect of damage on the material stiffness; S is the damage parameter; and eR is pseudo strain, which is defined as:
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Materials and Structures (2014) 47:1339–1358
1 e ¼ ER R
Zt
de Eðt sÞ ds; ds
ð28Þ
0
where ER is an arbitrary reference modulus, often assumed to be equal to one. Based on the available experimental data [9] for viscoelastic materials, the damage characteristic curve (i.e., pseudo stiffness, C, as a function of damage parameter, S) can be assumed in the following form: b
C ðSÞ ¼ eaS ;
ð29Þ
where a and b are the material model parameters. The damage evolution law is given by: a oS oW R ¼ ; ð30Þ ot oS where WR is the pseudo strain energy density: 2 1 W R ¼ C ðSÞER eR ; 2
ð31Þ
A11 23 A12 þ 19 A22 þ A66 6 A11 2 A12 þ 1 A22 A66 6 3 9 6 A11 þ 1 A12 2 A22 R 6 3 9 CL ¼ 6 0 6 4 0 0
The stress-pseudo strain relationship for damaged material is given by: r ¼ CRL eR ;
A11 23 A12 þ 19 A22 A66 A11 23 A12 þ 19 A22 þ A66 A11 þ 13 A12 29 A22 0 0 0
5.3.2 One-parameter multiaxial viscoelastic continuum damage model The current model can be extended to the multiaxial case using the definition for pseudo strain energy density function: 1
A11 e2 þ A22 e2d þ 2A12 ed eV 2 V R2 R2 2 þ A44 cR2 13 þ c23 þ A66 c12 þ eS ;
ð34Þ
where
and a is a material model parameter.
2
about the axis in the direction of the maximum experienced principal pseudo strain within the first analysis segment. Thus, the damaged material is transversely isotropic, with the local axis of symmetry coinciding with the maximum experienced pseudo strain. Essentially, A11, A22, A44, A66, and A12 in Eq. (32) take the following form:
1 2ð1 þ mÞ A11 ¼ CðSÞ þ ; 9 ð1 2mÞ ð1 2mÞ ; A22 ¼ CðSÞ þ 2ð1 þ mÞ ð33Þ 1 A12 ¼ ½CðSÞ 1; 3 1 A44 ¼ A66 ¼ : 2ð1 þ mÞ
WR ¼
ð32Þ
where ev = eR11 ? eR22 ? eR33; ed = eR33 - ev/3; R R R R R R eS = e11 - e22; and e11, e22, e33, c12, cR12, and cR23 are the pseudo strains along the local axes. Currently, it is assumed that an undamaged material is isotropic and that damage grows symmetrically
A11 þ 13 A12 29 A22 A11 þ 13 A12 29 A22 A11 þ 43 A12 þ 49 A22 0 0 0
0 0 0 A44 0 0
0 0 0 0 A44 0
3 0 0 7 7 0 7 7: 0 7 7 0 5 A66
ð35Þ
Note that all the stresses and pseudo strains in Eq. (35) are in the direction of the material axes, i.e., the local axes about the direction of the maximum pseudo strain. The LVECD program uses a standard transformation to determine the local stresses from the stress vector in the x–y–z coordinate system. The local pseudo strains can be determined by solving Eq. (35). Substituting Eq. (32) into Eq. (30) and using Eq. (33), the damage evolution function becomes: 2a a oS oW R 1 oC a 1 R ¼ eV þ eRd ¼ a : ot 2 oS 3 oS ð36Þ
Materials and Structures (2014) 47:1339–1358
1355
This damage calculation and extrapolation must be repeated for entire stages within the pavement life.
5.3.3 LVECD nonlinear extrapolation Using the chain rule and integrating in time, the change in the normalized stiffness in a single cycle can be obtained easily:
DC ¼
1 oC oC a 2a oS oS
Tcycle Z
2a 1 R eV þ eRd dt; 3
ð37Þ
0
where Tcycle is the time period of the cyclic moving load. The damage increment in Eq. (37) is computed for each segment (morning, afternoon, or evening) independently, assuming the pseudo stiffness value, C0, at the beginning of each stage (e.g., a month). In order to accumulate damage over thousands of cycles under the same loading condition, it appears straightforward to multiply DC by the number of cycles for the segment. However, such straightforward extrapolation leads to significant error, and thus, a more accurate nonlinear extrapolation method is required. First, the equivalent damage increment must be determined for a given stage (e.g., a month) by combining the damage increments of all the segments, which can be accomplished by finding the weighted averages of the damage increments of all the segments. Therefore, the combined damage increment is Pnum of segements DCComb ¼
i
Ni DCi ðC0 Þ ; Pnum of segements Ni i
ð38Þ
where Ni is the number of load cycles in each segment. Next, nonlinear extrapolation can be conducted by solving the following ordinary differential equation: oCa oC oC ¼ DCComb oS oS a ; ð39Þ oC0 on oC0 oS0
oS0
where C0 and S0 are the pseudo stiffness and damage parameters at the beginning of the month (or stage), respectively. Assuming the damage characteristic curve as Eq. (29), the above formulation can be simplified to: 1 1þa oC C logðCÞ ð1þaÞð1bÞ ¼ DCComb : on C0 logðC0 Þ
ð40Þ
5.4 LVECD program inputs The material properties and thicknesses obtained from the cores, and the base layer modulus values, thicknesses, and subgrade modulus values converted from the DCP results were all used as inputs for the pavement simulations. These values are summarized in Table 1. The simulations were performed for the equivalent single axle loads (ESALs) of actual field traffic as obtained from the NCDOT Traffic Survey Unit. The design load was based on actual field conditions as follows: rectangular with a width of 17.78 cm (7 in.), length of 27.94 cm (11 in.), load of 40 kN (9,000 lb), constant contact pressure of 805.9 kPa (116.9 psi), and constant velocity based on the speed limit at each site. All of the simulations were conducted using temperature variables obtained from the EICM. 5.5 LVECD simulation results The damage contours presented in Fig. 4 are the contours of normalized pseudo stiffness (C), which starts from 1.0 in an intact condition and decreases as the level of damage increases, at the end of 20 year simulations. Normalized pseudo stiffness is a structural integrity parameter that is calculated by the ratio of the pseudo stiffness in the damaged condition of the material to the pseudo stiffness in the undamaged condition of the material. The same grayscale (i.e., between 0.25 and 0.8) is used in presenting all the damage contours shown in Fig. 4. A small value of normalized stiffness, which is represented by the white color in the subfigures in Fig. 4, corresponds to areas with high levels of damage and, consequently, areas where cracking is more severe. Note that all of the subfigures on the left-hand sides of Fig. 4 are from relatively bad condition regions (B condition regions) at the site, and all of the subfigures on the right-hand sides of these figures are from relatively good condition regions (A condition regions), as indicated at the top of Fig. 4. The crack propagation propensity of each region selected for LVECD simulations and the corresponding ACI values are presented in Table 2. The shaded
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Materials and Structures (2014) 47:1339–1358
B Condition Region
A Condition Region
0
Depth (in)
6 0.4
8 -1
-0.5
0 Width (ft)
0.5
1
0.5
1
0.6 0.4 0.5
1
-1
-0.5
0 Width (ft)
0.5
1
4 0.4
6
Depth (in)
-0.5
0 Width (ft)
0.5
1
2
0.6
4
0.4
-1.5
-1
-0.5
0 Width (ft)
0.5
1
1.5
Depth (in)
0.6 0.4
4
Depth (in)
-1
-0.5
0 Width (ft)
0.5
1
0.6
10
0.4 -1
-0.5
0 Width (ft)
0.5
1
1.5
0.6
4 0.4 6 -1.5
-1
-0.5
0 Width (ft)
0.6 0.4 -1
-0.5
0.5
1
1.5
0.5
1
1.5
0.8 0.6
4 0.4
6 -1
-0.5
0 Width (ft)
0.5
1
1.5
0
0.8
2
0.6
4
0.4 -1
-0.5
0 Width (ft)
0.5
1
1.5
0.8
2 0.6
4 6
0.4 -1
-0.5
0 Width (ft)
0.5
1
1.5
0
0.8
5
0.6 0.4
10 -1
-0.5
0 Width (ft)
0.5
1
1.5
0
0.8
2
0.6
4 0.4
6 -1.5
(i)
0 Width (ft)
2
-1.5
0.8
2
1.5
6
(h)
0
1
0.8
(g) 0.8
0.5
4
8 -1.5
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Fig. 4 20-year simulation results from the LVECD program: a US 17, b US 70, c I 540, d NC 24, e US 74, f NC 209, g US 76, h NC 87, and i US 601
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cell with italic-bold font under the Field Cores column in Table 2 indicates the cases where the simulation results do not match the field core and field condition observations. Because a damage contour is not a numerical value, the rank of the predicted damage severity from the damage contours is used for comparison with the different condition regions’ ACI ranking for the same site. That is, the ranking of the ACI values from different condition regions in a single site is compared to that for the area or severity of normalized stiffness, which is represented by the white color in the damage contour plots, as described earlier, in order to verify the sensitivity of the LVECD program under the same environmental and traffic conditions. Several important observations can be made from the damage contours presented in Fig. 4 and the cracking conditions summarized in Table 2, as follows. In general, the predicted simulation results presented in Fig. 4 indicate better conditions in the A condition regions than in the B condition regions (except NC 24), which is supported by the field condition survey and the visual observation of the cores. The old and good pavements, i.e., US 17 and NC 209, show relatively minor damage from the 20-year pavement simulations. The predicted simulation results presented in Fig. 4b, c indicate that the TDC simulation results for US-70 and I-540 are in agreement with the field core observations. A noteworthy finding from NC-24 and US-74 is presented in Fig. 4d, e. The thicknesses of the asphalt layers in these two sections are similar (about 7 in.), and higher base and subgrade modulus values were measured from US-74 than from NC24. If the asphalt layer properties were the same, these conditions would give the NC-24 section a greater potential for BUC. However, TDC was observed from NC-24 and BUC was observed from US-74 due to the different asphalt mixtures used in these two sections. The predicted simulation results shown in Fig. 4d, e match these field core observations. The predicted results from the A condition region of US-76 presented in Fig. 4g match the field core observations, but none of the field core observations
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are captured by the simulations of the B condition region. According to the 2010 NCDOT condition survey, as shown in the far right column in Table 2, this site contains oxidized pavement. Accordingly, it appears that the TDC observed from the field cores is caused by excessive oxidization. This oxidization is not captured by the LVECD program because an aging model has not been implemented in the LVECD model yet. The A condition region of NC 87 has a thicker base layer and stiffer substructure than the B condition region. However, BUC is observed from the A condition region, whereas TDC is observed from the B condition region. These field observations indicate that the BUC and TDC propensity is governed not only by the pavement structure, but also by the material properties, which are shown to affect such propensity significantly. The predicted simulation results match the field core observations. The TDC that is observed in the field cores from the A condition region of US-601 is not observed in the predicted simulations presented in Fig. 4i. Overall, the expected crack directions of 26 out of 36 (72 %) condition regions match the field core observations. This agreement rate increases to 78 % once the severity rankings of the different condition regions in a single site are included.
6 Summary Cost-effective and structurally effective pavement maintenance strategies begin from the identification of the different causes of cracking. Accordingly, maintenance engineers should design different rehabilitation plans according to the crack initiation locations and the propensity of the asphalt pavements. This study verifies the capability of the LVECD model to capture crack initiation locations and propagation propensity compared to the observations of field cores and the field condition survey of in-service pavements in North Carolina. Overall, the agreement rate between the field core observations and field condition survey and the predicted LVECD simulation results is about 78 % in terms of crack propensity and damage severity. The LVECD-based mechanistic approach can be used as a performance prediction model for pavement design and maintenance and can help
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maintenance engineers to create cost-effective rehabilitation strategies for project-level pavement management systems.
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10.
Acknowledgments The authors would like to acknowledge the financial support from the North Carolina Department of Transportation under project NCDOT HWY-2010-01. 11.
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