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Using overlay test to evaluate fracture properties of field-aged asphalt concrete
Construction and Building Materials 101 (2015) 1059–1068
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Using overlay test to evaluate fracture properties of field-aged asphalt concrete Fan Gu a,⇑, Xue Luo b, Yuqing Zhang c, Robert L. Lytton d a
Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508K, College Station, TX 77843, United States Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508B, College Station, TX 77843, United States c Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508E, College Station, TX 77843, United States d Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, CE/TTI Bldg. 503A, College Station, TX 77843, United States b
h i g h l i g h t s Fracture properties of field-aged asphalt concrete are determined using overlay test. A two-step overlay test protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. Theoretical equations are formulated to calculate fracture properties, A and n. Summer climatic condition clearly accelerates the rate of aging. Impact of warm mix asphalt technology is investigated by comparing the determined fracture properties.
a r t i c l e
i n f o
Article history: Received 26 November 2014 Received in revised form 15 July 2015 Accepted 24 October 2015
Keywords: Field-aged asphalt concrete Warm mix asphalt Overlay test Crack propagation Paris’ law
a b s t r a c t Field material testing provides firsthand information on pavement conditions which are most helpful in evaluating performance and identifying preventive maintenance or overlay strategies. High variability of field asphalt concrete due to construction raises the demand for accuracy of the test. Accordingly, the objective of this study is to propose a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the overlay test (OT). The OT is selected because of its efficiency and feasibility for asphalt field cores with diverse dimensions. The fracture properties refer to the Paris’ law parameters based on the pseudo J-integral (A and n) because of the sound physical significance of the pseudo J-integral with respect to characterizing the cracking process. In order to determine A and n, a two-step OT protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. To ensure the accuracy of determined undamaged and fracture properties, a new analysis method is then developed for data processing, which combines the finite element simulations and mechanical analysis of viscoelastic force equilibrium and evolution of pseudo displacement work in the OT specimen. Finally, theoretical equations are derived to calculate A and n directly from the OT test data. The accuracy of the determined fracture properties is verified. The proposed methodology is applied to a total of 27 asphalt field cores obtained from a field project in Texas, including the control Hot Mix Asphalt (HMA) and two types of warm mix asphalt (WMA). The results demonstrate a high linear correlation between n and log A for all the tested field cores. Investigations of the effect of field aging on the fracture properties confirm that n is a good indicator to quantify the cracking resistance of asphalt concrete. It is also indicated that summer climatic condition clearly accelerates the rate of aging. The impact of the WMA technologies on fracture properties of asphalt concrete is visualized by comparing the n-values. It shows that the Evotherm WMA technology slightly improves the cracking resistance, while the foaming WMA technology provides the comparable fracture properties with the HMA. After 15 months aging in the field, the cracking resistance does not exhibit significant difference between HMA and WMAs, which is confirmed by the observations of field distresses. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction ⇑ Corresponding author. E-mail addresses: [email protected] (F. Gu), [email protected] (X. Luo), [email protected] (Y. Zhang), [email protected] (R.L. Lytton). http://dx.doi.org/10.1016/j.conbuildmat.2015.10.159 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
Field material sampling and testing have played an important role in pavement forensic investigations, such as determining
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reasons for poor pavement performance or premature failure, validating pavement performance prediction, identifying preventive maintenance or overlay strategies, etc. [1]. Effective assessment of fracture of field-aged asphalt concrete can provide best guidelines to these questions in terms of cracking distresses in an inservice flexible pavement. More specifically, it is necessary to obtain the fracture properties that accurately predict the crack propagation behavior of an asphalt concrete; meanwhile, to quantify the influence of field aging on its fracture properties. A number of studies have been reported to design laboratory tests to measure fracture properties/parameters and predict crack propagation in asphalt concrete. For example, Wen and Kim [2] modified the traditional indirect tensile (IDT) test to determine the viscoelastic properties by a creep test protocol and fracture properties/parameters by an indirect tensile strength test protocol. Li and Marasteanu [3] used the semi-circular bending (SCB) test apparatus and applied a monotonic loading to evaluate the fracture resistance of asphalt concrete at low temperatures. Wagoner et al. [4] designed a disk-shaped compact tension (DSCT) test to characterize the crack propagation behavior of asphalt concrete under the monotonic loading condition. In these studies, the fracture energy, which is the energy required for crack growth, is regarded as a good indicator of the cracking resistance of asphalt concrete. The fracture energies of laboratory-mixed-laboratory-compacted (LMLC) specimens were found to be higher than that of fieldmixed-field-compacted (FMFC) specimens [5]. A satisfactory correlation existed between the measured fracture energy of a limited number of FMFC specimens and the amount of fatigue cracking observed in a chosen pavement test track [6]. With the increasing application of fracture mechanics in pavement materials, the prevailing fracture properties, the coefficients of A and n in Paris’ law [7], are measured from a repeated loading test on asphalt concrete. The Paris’ law relates the crack growth function (the increment of crack length per load cycle) to the stress intensity factor by A and n. For instance, Jacobs [8] used the repeated tensile test to determine the Paris’ law parameters for a variety of LMLC specimens. In order to obtain A and n, the crack length was measured by a crack foil on the asphalt specimen and the crack opening displacement was measured by the clipgauges. Zhou [9] utilized the overlay tester (OT) to evaluate the fracture properties of LMLC asphalt specimens based on the Paris’ law. The shape of the crack growth function was approximated by the load history, and the magnitude was calibrated to monitoring by a digital camera. The stress intensity factor for a recorded crack length was computed by finite element modeling. With the crack growth function and stress intensity factor being known, the fracture properties were finally determined from regression analysis. During the analysis, the asphalt concrete was assumed to be elastic, which ignored its viscoelastic nature. In order to apply to the viscoelastic media, the Paris’ law was modified by replacing the stress intensity factor by the pseudo J-integral [10,11]. The pseudo J-integral is equivalent to the pseudo strain energy release rate, namely the dissipated pseudo strain energy created per unit of crack surface area. The dissipated pseudo strain energy is the energy responsible for the crack growth after removing the viscoelastic effects. Luo et al. [12] and Tong et al. [13] developed an energy-based mechanistic (EBM) approach to analyze the data of LMLC asphalt specimens from the repeated direct tension (RDT) test. The crack growth function and the pseudo J-integral were solved analytically by the EBM approach so no additional crack length measurements were required. The results proved that n can be used alone to compare the resistance to cracking of different materials and a smaller n-value was preferable. Normally the laboratory-aged LMLC specimens had larger n values than those unaged. Gu et al. [11] proposed a new OT protocol to determine the viscoelastic fracture properties of LMLC
asphalt specimens. This viscoelastic fracture approach involved a two-step procedure: (1) the nondestructive step, which controlled the movement of the specimen in a small range; and (2) the crack growth step, which set the controlled displacement as a relatively large value. The nondestructive step was designed to obtain the undamaged relaxation modulus of the asphalt specimen being tested. In the destructive step, the crack growth function and the incremental pseudo J-integral with each load cycle were determined based on finite element simulation techniques and the mechanical analysis of the OT data. After a review of the aforementioned studies, it is found that most of the cracking tests are mainly used to characterize the fracture resistance of LMLC asphalt concrete, while just a few studies focus on field materials. These cracking tests are performed on LMLC specimens, either unaged or laboratory aged, to estimate the fatigue performance of asphalt concrete in the field. However, the fracture properties/parameters of field-aged asphalt concrete are almost impossible to be accurately estimated by performing the cracking tests on the lab-aged specimens. This is because the asphalt concrete in the field has a unique air voids distribution and a complex aging condition, which leads to the variant fracture properties from those of lab-aged specimens. Therefore, it is highly desired to directly evaluate the fracture properties of field-aged specimens from an appropriate cracking test. More importantly, considerations must be given to the selected fracture properties/parameters regarding reliability and repeatability in characterizing the cracking behavior of asphalt concrete. Among the various cracking tests, the OT is the candidate for this study because of its efficiency and feasibility for field cores with diverse dimensions. Among the different fracture properties/parameters discussed above, the Paris’ law parameters based on the pseudo J-integral are preferred in this paper because of the sound physical significance of the pseudo J-integral and the successful applications mentioned above. As a result, the primary objectives of this paper are to propose a reliable and repeatable methodology to evaluate the fracture properties (A and n) of field-aged asphalt concrete by the OT, and to quantify the influence of the field aging condition on the fracture properties that were determined. The field-aged asphalt concrete includes the control Hot Mix Asphalt (HMA) and warm mix asphalt (WMA) to investigate whether the determined fracture properties can discern different materials. As a side product, the impact of different WMA technologies can be visualized through the measured fracture properties by the OT. The paper is organized as follows. The following section describes the proposed OT protocol to characterize the crack propagation behavior of asphalt field cores. The subsequent section presents the methodology to determine the fracture properties A and n using the OT data. The proposed methodology is employed to quantify the influence of the field-aging condition on both the HMA and WMA field core specimens. The impact of WMA technologies on the fracture behavior of asphalt mixtures is also investigated. The final section summarizes the contributions of this paper. 2. Overlay test protocol for field cores This section first presents the information on materials used in this study as well as how to prepare field core specimens for OT testing. Then the test setup and procedure of the proposed OT test are elaborated for field core specimens. 2.1. Asphalt field cores The asphalt field cores used in this study were obtained from an experimental overlay project set up by the Texas Department of
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Transportation (TxDOT) to conduct testing and long-term performance monitoring for HMA and WMA mixes. The overlay construction started in December 2011 and ended in January 2012. A TxDOT type C mix with PG 70–22 grade binder and Texas limestone aggregates was used in the field project. The control air voids for construction range from 7% to 10%. The binder content of the mix was 5.2%. Two warm mix technologies were used, including Evotherm DAT and water-based foaming. The WMA with Evotherm DAT is termed EWMA herein and the other FWMA. The dosage of the Evotherm DAT was 5% by weight of the binder, and the water content used in the foaming process was 5% by weight of the binder. The WMA mixes were mixed at 275 °F and compacted at 240 °F, and the control HMA mixes were mixed at 320 °F and compacted at 275 °F. Three sets of field cores were collected in the first, ninth, and fifteenth month after construction, respectively. The field cores were drilled as cylinders at the center of the travel lane (between the wheelpaths). These specimens were not subjected to traffic, but had been aged in the field. The dimensions of the cylindrical field core are 152 mm (6 inches) in diameter and 25 mm (1 inch) or 38 mm (1.5 inches) in thickness, as shown in Fig. 1a. Each cylindrical field core was trimmed in the laboratory into a prismatic specimen with a dimension of 102 mm (4 inches) high, 75 mm (3 inches) wide and 25 (1 inch) or 38 mm (1.5 inches) thick, as shown in Fig. 1b. The thickness of the specimen depends on the original thickness of the field core. Table 1 shows the detailed information of the drilled field cores and produced specimens for this study.
Table 1 Field core specimens tested in the OT. Mixture type
Field aging month
Numbering of specimens
Specimen thickness (mm)
Air voids (%)
HMA
1
H1 H2 H3 H4 H5 H6 H7 H8 H9
38 25 25 38 25 38 38 38 38
7.41 8.63 8.44 6.64 10.12 11.09 6.03 10.14 8.89
E1 E2 E3 E4 E5 E6 E7 E8 E9
38 38 38 38 38 38 38 38 25
7.10 5.01 5.65 7.33 7.00 10.82 9.84 10.99 7.23
F1 F2 F3 F4 F5 F6 F7 F8 F9
38 38 38 25 38 38 38 25 25
10.10 9.59 8.20 9.22 7.74 8.33 6.98 7.51 9.22
9
15
EWMA
1
9
15
FWMA
1
9
15
2.2. OT test protocol The setup of the OT machine is presented in Fig. 2. It has two aluminum plates: one is fixed and the other slides back and forth horizontally with controlled displacements. The field core specimen is glued on top of the center of the plates. Through an electro-hydraulic system, a repeated direct tension load is applied to the specimen. The data acquisition system records the loading time, loading magnitude, plate displacement and test temperature during the test. The temperature is controlled at 25 °C during the test. The Texas Standard overlay test protocol is shown in Fig. 3a, which is a destructive test [14]. The test stops when a 93% reduction of the maximum load occurs, which is assumed to be the failure of the specimen [15]. The number of failure cycles is recorded for evaluating the fracture characteristics of asphalt concrete. In this study, the standard overlay test is modified as a two-step test protocol, including a non-destructive step and a destructive step. The non-destructive and destructive load patterns are shown in Fig. 3b. In each load cycle, the specimen is subjected to a triangular
a. Before trimming
b. After trimming
Fig. 1. Preparation of field core specimen for OT testing.
Fig. 2. Setup of OT test for field core specimen.
shaped displacement load with a 5-s loading and 5-s unloading process. The non-destructive step includes 10 load cycles with an opening displacement of 0.05 mm, which is the minimum moving displacement allowed by the OT machine. Using the minimum of allowed displacement load is to ensure that no damage is induced into the specimen during this step [11]. The test rests for 15 min after the non-destructive step ends. The destructive step includes 200 load cycles with a maximum opening displacement of 0.32 mm. The destructive test is designed to stop if the measured maximum load reduces by 93%. Note that the proposed maximum opening displacement for the destructive step is only half of the opening displacement used in the standard test. The reason for this modification is to ensure that the specimen with 1 inch thickness goes through a relatively large number of load cycles. In this step, the crack initiates from the bottom of the specimen, and then propagates to the top of the specimen.
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Displacement (mm)
1.28
force equilibrium in the OT specimen and finite element (FE) modeling simulations. The finite element models are firstly developed to simulate the non-destructive test and destructive test in order to provide a horizontal strain profile input for the derived force equilibrium equations. Based on the undamaged force equilibrium equation and the FE strain profile input, the undamaged properties (relaxation modulus coefficients E1 and m) are calculated using the OT data. The determined undamaged properties are then input into the damaged force equilibrium equation to estimate the crack dc growth function dN in the destructive step. According to Schapery’s viscoelastic fracture theory, the evolution of the dissipated pseudo displacement work with load cycles is also determined to characterize the cracking damage of field cores during the displacement-controlled test. By means of the estimated crack growth function and dissipated pseudo displacement work growth function, the fracture properties A and n are finally determined using the theoretical equations derived from Eq. (1). The details of the approach are explained as follows.
Standard Test Till the Failure of Specimen 0.64
...... 0
0
10
20
30
40 Time (sec)
50
60
70
80
a. Standard OT Protocol Destructive step 200 load cycles
Displacement (mm)
0.32
Non-destructive step
Test rests 15 minutes
10 load cycles
3.1. Finite element model of the OT
0.05
0
10
20
30
100
1000 1010 1020 1030
Load Time (s)
b. Proposed Two-Step OT Protocol Fig. 3. Displacement load patterns used in OT.
3. Methodology to determine fracture properties of field cores
A two-dimensional (2D) finite element model is constructed to simulate the OT in the computer software ABAQUS [16]. Fig. 5 shows the boundary conditions used in this study. The bottom left portion of the specimen is fully fixed and the bottom right portion can only move in the horizontal direction. A vertical seam is assigned along the center of the specimen to determine the horizontal strain profile at various crack lengths. The determined horizontal strain profile is then integrated with respect the depth of the specimen to obtain the integration area of the horizontal strain, as shown in Eq. (2).
Z This section comprehensively presents the methodology to determine the fracture properties A and n for field cores using the Paris’ law based on the pseudo J-integral, which is shown as follows:
dc ¼ AðDJ R Þn dN
ð1Þ
where c is the crack length; n is the number of load cycles; DJ R is the increment of the pseudo J-integral within one load cycle; and A and n are the Paris’ law parameters, or fracture properties. Fig. 4 presents a flowchart to illustrate the proposed methodology. The proposed approach combines the mechanical analysis of viscoelastic
FE simulation of nondestructive test
FE simulation of destructive test
Horizontal strain profiles
Force equilibrium analysis of undamaged specimen
Horizontal strain profiles Undamaged properties E1 and m
Force equilibrium analysis of damaged specimen
Computed integration area of horizontal strain Estimation of crack growth function
h
Sðci Þ ¼ 0
eðzÞdz
where ci is the crack length; Sðci Þ is the integration area of the horizontal strain in terms of the depth of specimen; eðzÞ is the horizontal strain at the depth z; and h is the intact thickness of the specimen. If a bottom crack exists in the specimen in the destructive step and its length is ci mm, the corresponding h is equal to H ci mm, H is the thickness of the field core. Since the OT is a displacement controlled test, the strain profiles are not affected by the viscoelastic behavior of the material or the magnitude of the elastic modulus. Note that the stress profiles are dependent of the viscoelastic material properties. The Poisson’s ratio of the field core is assumed to be 0.35 in this study. The computed horizontal strain distribution of the 38 mm thick specimen corresponding to the maximum opening displacement in the non-destructive step is shown in Fig. 6. The horizontal strains along the center of the simulated specimen are extracted from the FE calculations and plotted in Fig. 7. The shaded area is used to represent the integration area of the horizontal strain Sðu0 ; c ¼ 0Þ, where u0 is the controlled displacement in undamaged tests (i.e., 0.05 mm). Fig. 7 also presents the extracted horizontal strain for the simulated specimen with various crack lengths. The corresponding integration areas Sðud ; ci Þ are calculated and plotted against the crack lengths in Fig. 8. It is shown that the curve of Sðud ; ci Þ versus crack length is fitted well by an exponential equation, which is presented in Eq. (3).
Sðud ; ci Þ ¼ 0:1026e0:06ci Evolution of dissipated pseudo displacement work
Determination of fracture properties A and n
Fig. 4. Flowchart of proposed methodology to determine fracture properties of field cores.
ð2Þ
ð3Þ
where Sðud ; ci Þ is the integration area of the horizontal strain profile at the crack length ci . As mentioned before, the integration area of the horizontal strain profile in the non-destructive step Sðu0 ; c ¼ 0Þ is used to compute the undamaged tensile properties
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102 mm Assigned Seam Direction (z-direction)
Field Core Specimen
25 or 38 mm
Controlled Displacement
Move Horizontally
Fixed
(u0 or ud )
2mm Fig. 5. Simulation of the OT using finite element model.
Field Core Specimen
Magnified View
38 mm in Thicknes
102 mm in Length Fig. 6. Horizontal strain (E11) distribution at maximum opening displacement in non-destructive step.
0.025
Integrated Area (Strain*mm)
0.10
Horizontal Strain
0.02 Crack Length=2.375mm 0.015
Crack Length=7.125mm Crack Length=11.875mm Crack Length=16.625mm
0.01
Crack Length=21.375mm Crack Length=26.125mm
0.005
Crack Length=30.875mm
0.08 0.06
y = 0.1026e-0.06x R² = 0.9962
0.04 0.02 0.00 0
0
5
10
15
20
25
30
35
Crack Length (mm) 0
10
20
30
40
Fig. 8. Plot of covered area under horizontal strain profiles vs. crack length.
Specimen Depth (mm)
Fig. 7. Horizontal strain profiles along the center of field core specimen at different crack lengths.
of the asphalt mixtures. Eq. (3) will be used to estimate the crack growth function in the destructive step. 3.2. Determination of the undamaged tensile properties Fig. 9 presents the free-body diagram of a specimen in the OT. The force equilibrium equation is expressed as,
Z 0
h
rðt; zÞbdz ¼ PVE
ð4Þ
where rðt; zÞ is the viscoelastic stress within the specimen as a function of time t at depth z; b is the width of the specimen; and PVE ðtÞ is the measured viscoelastic force as a function of time t. Since there is no crack initiating in the non-destructive step, the corresponding h is the thickness of the entire specimen.
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Setting that
51 mm
Z sðu0 ; c ¼ 0Þ ¼ 0
Field Core Specimen
(t,z)
eðu0 ; zÞdz
ð11Þ
where sðu0 ; c ¼ 0Þ is the integration area of the horizontal strain profile over the depth at the maximum opening displacement in the non-destructive step, which is represented by the shaded area in Fig. 7. Eq. (10) is then simplified as
H mm
PVE(t)
z-direcon
h
PVE ðtÞ ¼
Fig. 9. Free-Body Diagram of Field Core Specimen.
bE1 t 1m sðu0 ; c ¼ 0Þ ð1 mÞt1
ð12Þ
Taking the natural logarithm on both sides, Eq. (12) can be transformed as The viscoelastic stress rðt; zÞ is further calculated using the constitutive model for the one-dimensional viscoelastic response [17], which is expressed as,
rðt; zÞ ¼
Z 0
t
Eðt sÞ
deðs; zÞ ds ds
ð5Þ
where eðs; zÞ is the linear viscoelastic strain at depth z; s is a timeintegration variable; and Eðt sÞ is the relaxation modulus, which is approximately represented using a power law model, which is shown in Eq. (6) [18].
Eðt sÞ ¼ E1 ðt sÞ
m
ð6Þ
in which E1 and m are the undamaged tensile properties of the asphalt mixture, which will be determined in this section. The reason for using the power law model is to simplify the derivation of the analytical methodology in this study. According to the displacement loading patterns in Fig. 3, Eq. (5) is expanded as a piecewise function separated at each inflection point, which is shown in Eq. (7) [19].
8R t > Eðt sÞ dedðss;zÞ ds ð0 < t < t1 Þ > 0 > > > > R R > > > 0t1 Eðt sÞ dedðss;zÞ ds þ tt Eðt sÞ dedðss;zÞ ds ðt1 < t < 2t 1 Þ > 1 > > < rðt; zÞ ¼ R0t1 Eðt sÞ dedðss;zÞ ds þ Rt2t1 Eðt sÞ dedðss;zÞ ds > 1 > > > > R > t d e ð s ;zÞ > > ð2t1 < t < 3t1 Þ > þ 2t1 Eðt sÞ ds ds > > > : :::
ð7Þ where t 1 is the loading and unloading interval, i.e., 5-s; 0 < t < t1 is the first loading period; t 1 < t < 2t 1 is the first unloading period and 2t 1 < t < 3t 1 is the second loading period. The opening displacement at time t is calculated using Eq. (8).
uðtÞ t ¼ u0 t1
ð8Þ
where uðtÞ is the opening displacement at time t and u0 is the maximum opening displacement in the non-destructive step, i.e., 0.05 mm. Accordingly, the strain at time t is calculated using Eq. (9).
eðuðtÞ; zÞ t ¼ eðu0 ; zÞ t1
ð9Þ
where eðuðtÞ; zÞ is the horizontal strain at time t and depth z and eðu0 ; zÞ is the horizontal strain at time t1 and depth z.
Take the data from the first loading period 0 < t < t 1 as an example to calculate the undamaged properties of asphalt mixture. Substituting the first equation in Eq. (7), and Eq. (9) into Eq. (4) yields Eq. (10).
bE1 t 1m PVE ðtÞ ¼ ð1 mÞt 1
Z 0
h
eðu0 ; zÞdz
ð10Þ
ln
PVE ðtÞt1 E1 ¼ ln þ ð1 mÞ ln t bsðu0 ; c ¼ 0Þ 1m
ð13Þ
Since PVE ðtÞ is the recorded load as a function of time t, the only unknown parameters E1 and m can be calculated from the OT data using a linear regression method. 3.3. Estimation of the crack growth function dc , Two steps are involved to estimate the crack growth function dN including:
I. Calculating the integration area of the horizontal strain profile at each loading interval; and II. Back-calculating the crack length corresponding to each obtained area of the horizontal strain profile using Eq. (3). In the destructive step, the crack propagates with increasing load cycles. The horizontal strain at time t, depth z and crack length c is represented by eðuðtÞ; z; cÞ, which is calculated using Eq. (14).
eðuðtÞ; z; cÞ t ¼ eðud ; z; cÞ t1
ð14Þ
where eðud ; z; cÞ is the horizontal strain corresponding to the maximum opening displacement ud in the destructive step at time t and depth z. Similar to the analysis in the non-destructive step, the measured force can be represented in terms of the undamaged tensile properties E1 and m, loading time interval t 1 , specimen width b and the integration area of the horizontal strain profile of the specimen Sðud ; ci Þ. The only difference is that the intact thickness h reduces with the increasing number of load cycles. Take the first loading period 0 < t < t 1 as an example. Substituting the first equation in Eq. (7), and Eqs. (6) and (14) into Eq. (4) yields Eq. (15), which is used to calculate the integration area of the horizontal strain profile at the first maximum opening displacement Sðud ; c1 Þ.
Pðt 1 Þ ¼
bE1 t 11m Sðud ; c1 Þ ð1 mÞt 1
ð15Þ
where Pðt 1 Þ is the measured force at time t1 . Likewise, the integration area of the horizontal strain profile at the ith maximum opening displacement Sðud ; ci Þ is calculated using Eq. (16).
P½ð2i 1Þt 1 ¼
n o X bE1 Sðud ; ci Þ 2i1 ð1Þn1 ½ðn 1Þt 1 1m þ ðnt 1 Þ1m t 1 ð1 mÞ n¼1 ð16Þ
where P½ð2i 1Þt 1 is the measured force at the ith loading peak. Eq. (16) and the measured E1 and m from the nondestructive characterization are used to determine the integration area of the horizontal strain profile Sðud ; ci Þ at each loading interval. According to Eq. (3),
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the crack length for each load cycle is then back-calculated and presented in Fig. 10. In the destructive step, the crack propagates fast during the first few cycles and the rate of crack growth reduces with the increasing load cycles. A power function is employed to fit the curve of the accumulated crack length against the number of the load cycles. An R-squared value of 0.977 obtained from the curve fitting indicates that the crack growth function can be properly expressed as a power function shown in Eq. (17).
cðNÞ ¼ 6:6233 N 0:2339 R2 ¼ 0:977
2500 2000 1500
Load (N)
1000 500 0 -0.2
-0.1
0
0.1
0.2
0.3
0.4
-500
ð17Þ
-1000
where n is the number of the load cycles; and cðNÞ is the crack length at the Nth cycle.
-1500 -2000
Displacement/Pseudo Displacement (mm)
3.4. Analysis of change of the dissipated pseudo displacement work According to Schapery’s viscoelastic fracture theory [20], dissipated pseudo strain energy or dissipated pseudo displacement work was found to be efficient in characterizing the cracking damage of viscoelastic medium during a strain-controlled or displacement-controlled test [21]. In this study, the dissipated pseudo displacement work is used to quantify the crack propagation in the specimen during the destructive test. The pseudo displacement is calculated using Eq. (18) [22].
uR ðtÞ ¼
1 ER
Z 0
t
Eðt sÞ
duðsÞ ds ds
ð18Þ
where ER is the reference modulus that is assigned as the undamaged modulus E1 in this study; Eðt sÞ is the relaxation modulus; uðsÞ is the displacement as a function of time; and s is a timeintegrated variable. Similar to Eq. (7), Eq. (18) is also expanded as a piecewise function separated by each loading and unloading period, which is shown in Eq. (19).
8 Rt 1 > Eðt sÞads ð0 < t < t1 Þ > > E R R0 > Rt > t1 > 1 1 > Eðt s Þ a d s þ Eðt s Þð a Þd s ðt1 < t < 2t 1 Þ > ER 0 ER t 1 < R R R t 2t 1 u ¼ 1 1 Eðt sÞads þ 1 Eðt sÞðaÞds > ER t 1 > ER 0 R > > t > 1 > þ Eðt s Þ a d s ð2t 1 < t < 3t 1 Þ > ER 2t 1 > : ::: ð19Þ where a is the slope of the displacement curve versus loading time. An example of the load-pseudo displacement hysteresis loop is shown in Fig. 11. The enclosed area of the load-pseudo displacement hysteresis loop represents the dissipated pseudo displacement work, which is used to drive the propagation of the crack within the specimen. Eq. (20) is used to calculate the dissipated pseudo displacement work by integrating the load and pseudo displacement.
Load vs. Displacement at 1st Loading Cycle Load vs. Pseudo Displacement at 1st Loading Cycle Fig. 11. Example of load-pseudo displacement hysteresis loop of a field core specimen.
Z WR ¼
R
tb
PðtÞ ta
du ðtÞ dt dt
ð20Þ
where W R is the dissipated pseudo displacement work in a load cycle ½t a ; t b . As can be seen from Fig. 11, the load-pseudo displacement loop enclosed area is much smaller than the load–displacement loop enclosed area, which indicates that only a small portion of the total work is dissipated for the propagation of the crack, and the remaining work is actually dissipated due to the viscoelastic stress relaxation of the asphalt concrete. Fig. 12 shows the evolution of the cumulative dissipated pseudo displacement work with the increasing number of load cycles. It suggests that the power function is also able to capture the trend of the cumulative dissipated pseudo displacement work with the increasing number of load cycles. Eq. (21) is the fitted power function for the example in Fig. 12.
W RC ðNÞ ¼ 424:88 N0:1193
R2 ¼ 0:9729
ð21Þ
where W RC ðNÞ is the cumulative dissipated pseudo displacement work. 3.5. Determination of the fracture properties of asphalt field cores As mentioned previously, the fracture properties of an asphalt mixture are determined based on the modified Paris’ law, as shown in Eq. (1). Because DJ R represents the work dissipated to propagate cracks in the material, it can be represented by Eq. (22).
DJ R ¼
@W RC @ðc:s:aÞ
ð22Þ
Cumulative Dissipated Pseudo Displacement Work (N*mm)
900
35
Crack Length (mm)
30 25
6.6233x0.2339
y= R² = 0.9772
20 15 10 5
800 700 y = 424.88x0.1193 R² = 0.9729
600 500 400 300 200 100 0 0
0 0
100
200
300
400
500
600
700
50
100
150
200
250
Number of Load Cycles
Number of Load Cycles Fig. 10. Estimation of crack growth function in destructive step.
Fig. 12. Example of evolution of cumulative dissipated pseudo displacement work with increasing number of load cycles.
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where c:s:a is the total crack surface area. Taking the partial derivatives of W RC and c:s:a with respect to the number of the load cycles n, Eq. (22) is expressed as @W RC
@N DJR ¼ @ðc:s:aÞ
ð23Þ
@N
As shown in Fig. 12, the evolution of the pseudo displacement work with the increasing number of the load cycles can be represented as a power function, which is shown in Eq. (24).
W RC ðNÞ ¼ a Nb
cðNÞ ¼ d Ne
ð25Þ
where c and d are regression parameters. Therefore, the crack surface area c:s:a is calculated using Eq. (26).
c:s:aðNÞ ¼ d N e w 2
ð26Þ
where w is the width of the specimen, i.e. 0.076 m. Substituting Eqs. (23)–(26) into Eq. (1) yields:
n ab ðdeÞ N e1 ¼ A NnðbeÞ 2wde
ð27Þ
Comparing both sides of Eq. (27) gives the following: nþ1
ðdeÞ A ¼ ab n
ð28Þ
2w
e1 be
ð29Þ
Based on Eqs. (28) and (29), the fracture properties A and n can be determined from the OT. Table 2 presents the results of A and n calculated by the inputs of the presented example. In order to verify the values of A and n calculated by the proposed approach, Schapery’s estimation method [20] and Luo’s regression equation which relates A0 and n0 [10] are used to calculate the values of A0 and n0 , as shown in Eqs. (30) and (31).
n0 ¼
4. Results and discussions
ð24Þ
where A and b are regression parameters. Likewise, the crack growth function can also be represented by a power function, which is expressed as
n¼
cores have relatively higher air voids than the LMLC asphalt mixtures, which results in a smaller A values [10]. Therefore, the comparison of fracture properties in Table 2 demonstrates that the proposed approach can provide rational results of the fracture properties. After verifying the rationality and comparability of A and n values, the proposed methodology will be applied to evaluate the fracture properties of field-aged asphalt concrete in the next section.
Based on the OT test protocol and methodology introduced in the previous two sections, the test and analysis results are presented in this section as well as the discussions. 4.1. Determination of fracture properties of field cores Based on the methodology elaborated above, the fracture properties of all of the specimens are calculated to investigate the cracking resistance of field-aged asphalt concrete. Fig. 13 presents the relationship between A and n for the tested cores. A linear regression model is used to fit the scattered points, which are shown in Eq. (32).
log A ¼ 2:2045n þ 1:3133;
R2 ¼ 0:9348
ð32Þ
An R-squared value of 0.93 is obtained from the regression model, which indicates a highly linear correlation between n and log A. According to the Paris’ law with the pseudo J-integral, the crack propagation speed is proportional to both A and n. In other words, an asphalt mixture has a lower cracking resistance when A increases or n increases. However, the established relationship between A and n indicates they cannot increase at the same time. In order to quantify the cracking resistance of asphalt concrete by comparing A and n, Luo et al. [10] conducted a sensitivity analysis on the damage density of asphalt mixtures with various groups of A and n. It was found that the change of n is predominant to the resulting damage density, and suggested that n can be used alone to evaluate the cracking resistance of different asphalt mixtures.
30
2 m
ð30Þ
where m is the undamaged tensile property. 0
20
2
log A ¼ 0:93 n þ 5:30 R ¼ 0:91
ð31Þ
-log (A)
0
y = 2.2045x + 1.3133 R² = 0.9348
25
0
The estimation of A and n0 using Eqs. (30) and (31) is also presented in Table 2. It is seen that the values of n calculated by the proposed approach are comparable to the values of n0 estimated by the Schapery’s method. However, the calculated A values using the proposed method is smaller than the estimated A0 values using Luo’s regression equation. The reason is that Luo’s regression equation is based on the statistical analysis of LMLC asphalt mixtures, while the field
15 10 5 0 0
2
4
6
8
10
12
14
n
Fig. 13. Relationship between A and of tested field cores.
Table 2 Examples of comparison of calculated fracture properties using proposed approach and estimation approach. Mixture type
Estimation approach based on Schapery’s method and regression equation Inputs m
H3 E3 F3
0.32 0.35 0.32
Outputs
Proposed approach obtained by OT results Inputs
0
n0
A (mm) 12
7.7 10 2.5 1011 7.7 1012
6.25 5.71 6.25
a 424.9 413.2 364.9
Outputs b 0.12 0.11 0.10
d 6.62 5.65 5.82
e 0.234 0.245 0.221
A (mm)
n 16
3.2 10 2.4 1014 3.1 1015
6.72 5.59 6.44
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4.2. Effect of field aging on fracture properties
35.0
4.3. Impact of WMA technologies on fracture properties In order to clearly investigate the impact of WMA technologies on cracking resistance of asphalt concrete, Fig. 14 is converted to Fig. 16 by changing the legend from aging time to types of asphalt mixture. The n values of the first set of cores demonstrate that the EWMA technology slightly improves the initial cracking resistance, while the FWMA technology provides comparable fracture properties to the HMA field cores. This is because the WMA technology has lower production and paving temperatures, which reduces the oxidation of the asphalt binder and potentially improves the cracking resistance of WMA [28–29]. The reason why the FWMA performed similarly to the HMA is that the injected water inside of asphalt binder also reduces the cracking resistance of WMA at the same time, which may counteract the improvement of cracking resistance due to the decreased mixing and paving temperatures. After 15 months aging, it is found that both EWMA and FWMA have comparable or even higher n values than the HMA. This indicates that the 15 month aged EWMA and FWMA field cores have
12.00 10.00
n
8.00 6.00 4.00 2.00 0.00 HMA
1 Month
FWMA
9 Months
EWMA
15 Months
Fig. 14. Influence of aging time on n value for three types of asphalt field cores.
Air Temperature (°C)
30.0
Paving in December 2011
25.0 20.0
Second set of field cores
15.0
First set of field cores
10.0
Third set of field cores
5.0 0.0 0
1
2
3
4
5
6 7 8 9 Aging Month
10 11 12 13 14 15
Fig. 15. Change of average monthly air temperature in aging period.
12.00 10.00 8.00 n
Fig. 14 compares the cracking resistance of the three types of asphalt field cores with different aging times. The level of test accuracy is shown by the error bar with one standard deviation. As shown in Fig. 14, the average n value increases with the aging time for all the three types of field cores. This indicates that the cracking resistance of asphalt concrete decreases with the aging time, which is consistent with the fact that the aged material is prone to be more brittle and easier to crack. A further observation reveals that the n value increases significantly from the first aging month to the ninth aging month, and then slightly increases from the ninth aging month to the fifteenth aging month. This nonlinear impact demonstrates that there should be other factors influencing the change of cracking resistance of asphalt field cores besides the aging time. Fig. 15 shows the change of average monthly air temperature in the entire aging period. A significant difference among the three set of field cores is that the first set of field cores only experienced the winter climatic condition, while the second and third sets of field cores both experienced the entire summer climatic condition (i.e., 6th month-9th month aging period). Generally, the aging factors on the fracture properties of field cores include geographical location, aging time, air temperature, wind speed, solar radiation etc. [23–26]. Compared to the winter climate, the summer normally has a higher air temperature and solar radiation, which can accelerate the aging of asphalt concrete. Yin et al. [27] concluded that the subjected summer climatic condition is a more important factor than aging time that embrittles the asphalt concrete in the field. In this study, the summer climatic condition is also believed to be the major cause of an accelerated reduction of cracking resistance of field cores.
6.00 4.00 2.00 0.00 1-Month
9-Month
HMA
FWMA
15-Month
EWMA
Fig. 16. Influence of WMA technologies on n value at different aging times.
Table 3 Summary of pavement performance distress in the field sections (After Glover et al. 2013). Mixture type
Observed distresses Longitudinal cracks under wheel-path (%)
Longitudinal cracks under non wheelpath (%)
Fatigue cracks (%)
Transverse cracks (%)
HMA FWMA EWMA
0.8 1.2 1.5
1.2 1.0 1.2
0 0 0
0 0 0
the same or even lower cracking resistance compared to the HMA. Table 3 summarizes the distresses of three types of flexible pavement sections observed in the field after 15 months of service [30]. There is no significant difference between the HMA and WMA sections at this time. This field distress observation is consistent with the trend of the fracture properties of field cores determined using the OT shown in Fig. 16.
5. Summary and conclusions This paper proposes a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the OT. A two-step OT method is devised to determine the fracture properties A and n for asphalt field cores. A total of 27 field cores are investigated in this study in order to quantify the effect of field aging on their fracture properties and develop a better understanding of the impact of WMA technologies on their fracture properties. The major contributions of this paper are summarized as follows: Starting from the mechanical analysis of force equilibrium in the OT specimen, the developed approach combines analytical and numerical analyses to determine the undamaged properties in the nondestructive step, and estimate the crack growth function
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in the destructive step. The trend of crack propagation in the destructive step is found to follow the power function. Based on Schapery’s fracture theory, the dissipated pseudo displacement work is determined to characterize the cracking damage of asphalt field cores in the OT. The power function fits well the evolution of the cumulative dissipated pseudo displacement work with the number of load cycles. Theoretical equations are formulated to calculate the fracture properties A and n. The rationality of the proposed methodology is verified by comparing the results of A and n calculated in this study to those using Schapery’s estimation method. Investigation of the effect of field aging on fracture properties of field cores agree with the results in the published literature [10] that n is a good indicator to evaluate the cracking resistance of asphalt materials. The cracking resistance of field cores significantly reduces from the 1st month to the 9th month, and then slightly decreases from the 9th month to the 15th month. This suggests that the subjected summer climatic condition is a more important factor than the aging time that affects the fracture properties of the material. Comparison of n values of the field cores indicates that the EWMA technology slightly improves the cracking resistance, while the FWMA technology provides comparable fracture properties to the HMA. After 15 months aging, the n value does not exhibit a significant difference between HMA and WMA field cores, which is confirmed by the observations of field distresses where the field cores are taken. Acknowledgement The authors acknowledge the TxDOT for the financial support. Special thanks are to Yasser Koohi from Fugro Consultants, Jeff Perry and Lubinda Walubita from Texas A&M Transportation Institute for their help in this study. References [1] G.R. Rada, D.J. Jones, J.T. Harvey, K.A. Senn, M. Thomas, Guide for conducting forensic investigations of highway pavements. Research Report No. 747, National Cooperative Highway Research Program, Washington, D.C., 2013. [2] H. Wen, Y.R. Kim, Simple performance test for fatigue cracking and validation with WesTrack mixtures, Transp. Res. Rec. 1789 (2002) 66–72. [3] X. Li, M.O. Marasteanu, Using semi circular bending test to evaluate low temperature fracture resistance for asphalt concrete, Exp. Mech. 50 (7) (2010) 867–876. [4] M.P. Wagoner, W.G. Buttlar, G.H. Paulino, Disk-shaped compact tension test for asphalt concrete fracture, Exp. Mech. 45 (3) (2005) 270–277. [5] H. Wen, Characterization of fatigue performance of WesTrack pavement using work potential theory, Road Mater. Pavement 4 (1) (2003) 109–121. [6] Y.R. Kim, J.S. Daniel, H. Wen, Fatigue performance evaluation of WesTrack asphalt mixtures using viscoelastic continuum damage approach. Research Report No. FHWA/NC/2002-004, 2002.
[7] P.C. Paris, F. Erdogan, A critical analysis of crack propagation laws, J. Basic Eng. T ASME 85 (1963) 528–534. [8] M.J. Jacobs. Crack growth in asphaltic mixes (Ph.D. dissertation), Delft University of Technology, Delft, The Netherlands, 1995. [9] F. Zhou, S. Hu, X. Hu, T. Scullion, M. Mikhail, L.F. Walubita, Development, calibration, and verification of a new mechanistic-empirical reflective cracking model for HMA overlay thickness design and analysis, J. Transp. Eng. 136 (4) (2010) 353–369. [10] X. Luo, R. Luo, R.L. Lytton, Modified Paris’s law to predict entire crack growth in asphalt mixtures, Transp. Res. Rec. 2373 (2013) 54–62. [11] F. Gu, Y. Zhang, X. Luo, R. Luo, R.L. Lytton, Improved methodology to evaluate fracture properties of warm mix asphalt using overlay test, Transp. Res. Rec. 2506 (2015) 8–18. [12] X. Luo, R. Luo, R.L. Lytton, Energy-based mechanistic approach to characterize crack growth of asphalt mixtures, J. Mater. Civ. Eng. 25 (9) (2013) 1198–1208. [13] Y. Tong, R. Luo, R.L. Lytton, Moisture and aging evaluation of asphalt mixtures using the repeated direct tensional test method, Int. J. Pavement Eng. 16 (5) (2015) 397–410. [14] Texas Department of Transportation (TxDOT), Tex-248-F: overlay test. Austin, TX: Texas Department of Transportation, 2009. [15] F. Zhou, S. Hu, D. Chen, T. Scullion, Overlay tester: simple performance test for fatigue cracking, Transp. Res. Rec. 2001 (2007) 1–8. [16] ABAQUS. ABAQUS user’s manual, version 6.12. Pawtucket, R I: Hibbit, Karlsson and Sorensen Inc., 2012. [17] A.S. Wineman, K.R. Rajagopal, Mechanical Response of Polymers, Cambridge University Press, New York, 2000. [18] S.W. Park, Y.R. Kim, Interconversion between relation modulus and creep compliance for viscoelastic solids, J. Mater. Civ. Eng. 11 (1) (1999) 76–82. [19] J.S. Daniel, Y.R. Kim, Development of a simplified fatigue test and analysis procedure using a viscoelastic continuum damage model, J. Assoc. Asphalt Pav. 71 (2002) 619–650. [20] R.A. Schapery, A theory of crack growth in viscoelastic media. Research Report No. MM 2764-73-1. Mechanics and Materials Research Center, Texas A&M University, College Station, 1973. [21] Z. Si, D.N. Little, R.L. Lytton, Characterization of microdamage and healing of asphalt concrete, J. Mater. Civ. Eng. 14 (6) (2002) 461–470. [22] R.A. Schapery, Correspondence principles and a generalized J integral for large deformation and fracture analysis of viscoelastic media, Int. J. Fract. 25 (3) (1984) 195–223. [23] G.D. Airey, State of the art report on ageing test methods for bituminous pavement materials, Int. J. Pavement Eng. 4 (3) (2003) 165–176. [24] R.L. Lytton, J. Uzan, E.G. Fernando, R. Roque, D. Hiltunen, S.M. Stoffels. Development and validation of performance prediction models and specifications for asphalt binders and paving mixtures. Research Report No. SHRP-A-357, Strategic Highway Research Program, National Research Council, Washington, D.C, 1993. [25] M.W. Mirza, M.W. Witczak, Development of a global aging system for short and long term aging of asphalt cements, J. Assoc. Asphalt Pav. 64 (1995) 393– 430. [26] X. Luo, F. Gu, R.L. Lytton, Prediction of field aging gradient in asphalt pavements, Transp. Res. Rec. 2507 (2015). in press. [27] F. Yin, L.C. Cucalon, A. Martin, E. Arambula, E.S. Park, Performance evolution of hot-mix and warm-mix asphalt with field and laboratory aging, J. Assoc. Asphalt Pav. 83 (2014) 109–142. [28] G. Hurley, B. Prowell, Evaluation of potential processes for use in warm mix asphalt, J. Assoc. Asphalt Pav. 75 (2006) 41–90. [29] C. Estakhri, J. Button, A. Alvarez. Field and laboratory investigation of warm mix asphalt in Texas. Research Report No. FHWA/TX-10/0-5597-2, 2010. [30] C.J. Glover, G. Liu, A.A. Rose, Y. Tong, F. Gu, M. Ling, E. Arambula, C. Estakhri, R. L. Lytton. Evaluation of binder aging and its influence in aging of hot mix asphalt concrete. Research Report No. FHWA/TX-14/0-6613-1, Texas A&M Transportation Institute, College Station, Texas, 2014.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Using overlay test to evaluate fracture properties of field-aged asphalt concrete Fan Gu a,⇑, Xue Luo b, Yuqing Zhang c, Robert L. Lytton d a
Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508K, College Station, TX 77843, United States Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508B, College Station, TX 77843, United States c Texas A&M Transportation Institute, Texas A&M University System, 3135 TAMU, CE/TTI Bldg. 508E, College Station, TX 77843, United States d Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, CE/TTI Bldg. 503A, College Station, TX 77843, United States b
h i g h l i g h t s Fracture properties of field-aged asphalt concrete are determined using overlay test. A two-step overlay test protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. Theoretical equations are formulated to calculate fracture properties, A and n. Summer climatic condition clearly accelerates the rate of aging. Impact of warm mix asphalt technology is investigated by comparing the determined fracture properties.
a r t i c l e
i n f o
Article history: Received 26 November 2014 Received in revised form 15 July 2015 Accepted 24 October 2015
Keywords: Field-aged asphalt concrete Warm mix asphalt Overlay test Crack propagation Paris’ law
a b s t r a c t Field material testing provides firsthand information on pavement conditions which are most helpful in evaluating performance and identifying preventive maintenance or overlay strategies. High variability of field asphalt concrete due to construction raises the demand for accuracy of the test. Accordingly, the objective of this study is to propose a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the overlay test (OT). The OT is selected because of its efficiency and feasibility for asphalt field cores with diverse dimensions. The fracture properties refer to the Paris’ law parameters based on the pseudo J-integral (A and n) because of the sound physical significance of the pseudo J-integral with respect to characterizing the cracking process. In order to determine A and n, a two-step OT protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. To ensure the accuracy of determined undamaged and fracture properties, a new analysis method is then developed for data processing, which combines the finite element simulations and mechanical analysis of viscoelastic force equilibrium and evolution of pseudo displacement work in the OT specimen. Finally, theoretical equations are derived to calculate A and n directly from the OT test data. The accuracy of the determined fracture properties is verified. The proposed methodology is applied to a total of 27 asphalt field cores obtained from a field project in Texas, including the control Hot Mix Asphalt (HMA) and two types of warm mix asphalt (WMA). The results demonstrate a high linear correlation between n and log A for all the tested field cores. Investigations of the effect of field aging on the fracture properties confirm that n is a good indicator to quantify the cracking resistance of asphalt concrete. It is also indicated that summer climatic condition clearly accelerates the rate of aging. The impact of the WMA technologies on fracture properties of asphalt concrete is visualized by comparing the n-values. It shows that the Evotherm WMA technology slightly improves the cracking resistance, while the foaming WMA technology provides the comparable fracture properties with the HMA. After 15 months aging in the field, the cracking resistance does not exhibit significant difference between HMA and WMAs, which is confirmed by the observations of field distresses. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction ⇑ Corresponding author. E-mail addresses: [email protected] (F. Gu), [email protected] (X. Luo), [email protected] (Y. Zhang), [email protected] (R.L. Lytton). http://dx.doi.org/10.1016/j.conbuildmat.2015.10.159 0950-0618/Ó 2015 Elsevier Ltd. All rights reserved.
Field material sampling and testing have played an important role in pavement forensic investigations, such as determining
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reasons for poor pavement performance or premature failure, validating pavement performance prediction, identifying preventive maintenance or overlay strategies, etc. [1]. Effective assessment of fracture of field-aged asphalt concrete can provide best guidelines to these questions in terms of cracking distresses in an inservice flexible pavement. More specifically, it is necessary to obtain the fracture properties that accurately predict the crack propagation behavior of an asphalt concrete; meanwhile, to quantify the influence of field aging on its fracture properties. A number of studies have been reported to design laboratory tests to measure fracture properties/parameters and predict crack propagation in asphalt concrete. For example, Wen and Kim [2] modified the traditional indirect tensile (IDT) test to determine the viscoelastic properties by a creep test protocol and fracture properties/parameters by an indirect tensile strength test protocol. Li and Marasteanu [3] used the semi-circular bending (SCB) test apparatus and applied a monotonic loading to evaluate the fracture resistance of asphalt concrete at low temperatures. Wagoner et al. [4] designed a disk-shaped compact tension (DSCT) test to characterize the crack propagation behavior of asphalt concrete under the monotonic loading condition. In these studies, the fracture energy, which is the energy required for crack growth, is regarded as a good indicator of the cracking resistance of asphalt concrete. The fracture energies of laboratory-mixed-laboratory-compacted (LMLC) specimens were found to be higher than that of fieldmixed-field-compacted (FMFC) specimens [5]. A satisfactory correlation existed between the measured fracture energy of a limited number of FMFC specimens and the amount of fatigue cracking observed in a chosen pavement test track [6]. With the increasing application of fracture mechanics in pavement materials, the prevailing fracture properties, the coefficients of A and n in Paris’ law [7], are measured from a repeated loading test on asphalt concrete. The Paris’ law relates the crack growth function (the increment of crack length per load cycle) to the stress intensity factor by A and n. For instance, Jacobs [8] used the repeated tensile test to determine the Paris’ law parameters for a variety of LMLC specimens. In order to obtain A and n, the crack length was measured by a crack foil on the asphalt specimen and the crack opening displacement was measured by the clipgauges. Zhou [9] utilized the overlay tester (OT) to evaluate the fracture properties of LMLC asphalt specimens based on the Paris’ law. The shape of the crack growth function was approximated by the load history, and the magnitude was calibrated to monitoring by a digital camera. The stress intensity factor for a recorded crack length was computed by finite element modeling. With the crack growth function and stress intensity factor being known, the fracture properties were finally determined from regression analysis. During the analysis, the asphalt concrete was assumed to be elastic, which ignored its viscoelastic nature. In order to apply to the viscoelastic media, the Paris’ law was modified by replacing the stress intensity factor by the pseudo J-integral [10,11]. The pseudo J-integral is equivalent to the pseudo strain energy release rate, namely the dissipated pseudo strain energy created per unit of crack surface area. The dissipated pseudo strain energy is the energy responsible for the crack growth after removing the viscoelastic effects. Luo et al. [12] and Tong et al. [13] developed an energy-based mechanistic (EBM) approach to analyze the data of LMLC asphalt specimens from the repeated direct tension (RDT) test. The crack growth function and the pseudo J-integral were solved analytically by the EBM approach so no additional crack length measurements were required. The results proved that n can be used alone to compare the resistance to cracking of different materials and a smaller n-value was preferable. Normally the laboratory-aged LMLC specimens had larger n values than those unaged. Gu et al. [11] proposed a new OT protocol to determine the viscoelastic fracture properties of LMLC
asphalt specimens. This viscoelastic fracture approach involved a two-step procedure: (1) the nondestructive step, which controlled the movement of the specimen in a small range; and (2) the crack growth step, which set the controlled displacement as a relatively large value. The nondestructive step was designed to obtain the undamaged relaxation modulus of the asphalt specimen being tested. In the destructive step, the crack growth function and the incremental pseudo J-integral with each load cycle were determined based on finite element simulation techniques and the mechanical analysis of the OT data. After a review of the aforementioned studies, it is found that most of the cracking tests are mainly used to characterize the fracture resistance of LMLC asphalt concrete, while just a few studies focus on field materials. These cracking tests are performed on LMLC specimens, either unaged or laboratory aged, to estimate the fatigue performance of asphalt concrete in the field. However, the fracture properties/parameters of field-aged asphalt concrete are almost impossible to be accurately estimated by performing the cracking tests on the lab-aged specimens. This is because the asphalt concrete in the field has a unique air voids distribution and a complex aging condition, which leads to the variant fracture properties from those of lab-aged specimens. Therefore, it is highly desired to directly evaluate the fracture properties of field-aged specimens from an appropriate cracking test. More importantly, considerations must be given to the selected fracture properties/parameters regarding reliability and repeatability in characterizing the cracking behavior of asphalt concrete. Among the various cracking tests, the OT is the candidate for this study because of its efficiency and feasibility for field cores with diverse dimensions. Among the different fracture properties/parameters discussed above, the Paris’ law parameters based on the pseudo J-integral are preferred in this paper because of the sound physical significance of the pseudo J-integral and the successful applications mentioned above. As a result, the primary objectives of this paper are to propose a reliable and repeatable methodology to evaluate the fracture properties (A and n) of field-aged asphalt concrete by the OT, and to quantify the influence of the field aging condition on the fracture properties that were determined. The field-aged asphalt concrete includes the control Hot Mix Asphalt (HMA) and warm mix asphalt (WMA) to investigate whether the determined fracture properties can discern different materials. As a side product, the impact of different WMA technologies can be visualized through the measured fracture properties by the OT. The paper is organized as follows. The following section describes the proposed OT protocol to characterize the crack propagation behavior of asphalt field cores. The subsequent section presents the methodology to determine the fracture properties A and n using the OT data. The proposed methodology is employed to quantify the influence of the field-aging condition on both the HMA and WMA field core specimens. The impact of WMA technologies on the fracture behavior of asphalt mixtures is also investigated. The final section summarizes the contributions of this paper. 2. Overlay test protocol for field cores This section first presents the information on materials used in this study as well as how to prepare field core specimens for OT testing. Then the test setup and procedure of the proposed OT test are elaborated for field core specimens. 2.1. Asphalt field cores The asphalt field cores used in this study were obtained from an experimental overlay project set up by the Texas Department of
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Transportation (TxDOT) to conduct testing and long-term performance monitoring for HMA and WMA mixes. The overlay construction started in December 2011 and ended in January 2012. A TxDOT type C mix with PG 70–22 grade binder and Texas limestone aggregates was used in the field project. The control air voids for construction range from 7% to 10%. The binder content of the mix was 5.2%. Two warm mix technologies were used, including Evotherm DAT and water-based foaming. The WMA with Evotherm DAT is termed EWMA herein and the other FWMA. The dosage of the Evotherm DAT was 5% by weight of the binder, and the water content used in the foaming process was 5% by weight of the binder. The WMA mixes were mixed at 275 °F and compacted at 240 °F, and the control HMA mixes were mixed at 320 °F and compacted at 275 °F. Three sets of field cores were collected in the first, ninth, and fifteenth month after construction, respectively. The field cores were drilled as cylinders at the center of the travel lane (between the wheelpaths). These specimens were not subjected to traffic, but had been aged in the field. The dimensions of the cylindrical field core are 152 mm (6 inches) in diameter and 25 mm (1 inch) or 38 mm (1.5 inches) in thickness, as shown in Fig. 1a. Each cylindrical field core was trimmed in the laboratory into a prismatic specimen with a dimension of 102 mm (4 inches) high, 75 mm (3 inches) wide and 25 (1 inch) or 38 mm (1.5 inches) thick, as shown in Fig. 1b. The thickness of the specimen depends on the original thickness of the field core. Table 1 shows the detailed information of the drilled field cores and produced specimens for this study.
Table 1 Field core specimens tested in the OT. Mixture type
Field aging month
Numbering of specimens
Specimen thickness (mm)
Air voids (%)
HMA
1
H1 H2 H3 H4 H5 H6 H7 H8 H9
38 25 25 38 25 38 38 38 38
7.41 8.63 8.44 6.64 10.12 11.09 6.03 10.14 8.89
E1 E2 E3 E4 E5 E6 E7 E8 E9
38 38 38 38 38 38 38 38 25
7.10 5.01 5.65 7.33 7.00 10.82 9.84 10.99 7.23
F1 F2 F3 F4 F5 F6 F7 F8 F9
38 38 38 25 38 38 38 25 25
10.10 9.59 8.20 9.22 7.74 8.33 6.98 7.51 9.22
9
15
EWMA
1
9
15
FWMA
1
9
15
2.2. OT test protocol The setup of the OT machine is presented in Fig. 2. It has two aluminum plates: one is fixed and the other slides back and forth horizontally with controlled displacements. The field core specimen is glued on top of the center of the plates. Through an electro-hydraulic system, a repeated direct tension load is applied to the specimen. The data acquisition system records the loading time, loading magnitude, plate displacement and test temperature during the test. The temperature is controlled at 25 °C during the test. The Texas Standard overlay test protocol is shown in Fig. 3a, which is a destructive test [14]. The test stops when a 93% reduction of the maximum load occurs, which is assumed to be the failure of the specimen [15]. The number of failure cycles is recorded for evaluating the fracture characteristics of asphalt concrete. In this study, the standard overlay test is modified as a two-step test protocol, including a non-destructive step and a destructive step. The non-destructive and destructive load patterns are shown in Fig. 3b. In each load cycle, the specimen is subjected to a triangular
a. Before trimming
b. After trimming
Fig. 1. Preparation of field core specimen for OT testing.
Fig. 2. Setup of OT test for field core specimen.
shaped displacement load with a 5-s loading and 5-s unloading process. The non-destructive step includes 10 load cycles with an opening displacement of 0.05 mm, which is the minimum moving displacement allowed by the OT machine. Using the minimum of allowed displacement load is to ensure that no damage is induced into the specimen during this step [11]. The test rests for 15 min after the non-destructive step ends. The destructive step includes 200 load cycles with a maximum opening displacement of 0.32 mm. The destructive test is designed to stop if the measured maximum load reduces by 93%. Note that the proposed maximum opening displacement for the destructive step is only half of the opening displacement used in the standard test. The reason for this modification is to ensure that the specimen with 1 inch thickness goes through a relatively large number of load cycles. In this step, the crack initiates from the bottom of the specimen, and then propagates to the top of the specimen.
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Displacement (mm)
1.28
force equilibrium in the OT specimen and finite element (FE) modeling simulations. The finite element models are firstly developed to simulate the non-destructive test and destructive test in order to provide a horizontal strain profile input for the derived force equilibrium equations. Based on the undamaged force equilibrium equation and the FE strain profile input, the undamaged properties (relaxation modulus coefficients E1 and m) are calculated using the OT data. The determined undamaged properties are then input into the damaged force equilibrium equation to estimate the crack dc growth function dN in the destructive step. According to Schapery’s viscoelastic fracture theory, the evolution of the dissipated pseudo displacement work with load cycles is also determined to characterize the cracking damage of field cores during the displacement-controlled test. By means of the estimated crack growth function and dissipated pseudo displacement work growth function, the fracture properties A and n are finally determined using the theoretical equations derived from Eq. (1). The details of the approach are explained as follows.
Standard Test Till the Failure of Specimen 0.64
...... 0
0
10
20
30
40 Time (sec)
50
60
70
80
a. Standard OT Protocol Destructive step 200 load cycles
Displacement (mm)
0.32
Non-destructive step
Test rests 15 minutes
10 load cycles
3.1. Finite element model of the OT
0.05
0
10
20
30
100
1000 1010 1020 1030
Load Time (s)
b. Proposed Two-Step OT Protocol Fig. 3. Displacement load patterns used in OT.
3. Methodology to determine fracture properties of field cores
A two-dimensional (2D) finite element model is constructed to simulate the OT in the computer software ABAQUS [16]. Fig. 5 shows the boundary conditions used in this study. The bottom left portion of the specimen is fully fixed and the bottom right portion can only move in the horizontal direction. A vertical seam is assigned along the center of the specimen to determine the horizontal strain profile at various crack lengths. The determined horizontal strain profile is then integrated with respect the depth of the specimen to obtain the integration area of the horizontal strain, as shown in Eq. (2).
Z This section comprehensively presents the methodology to determine the fracture properties A and n for field cores using the Paris’ law based on the pseudo J-integral, which is shown as follows:
dc ¼ AðDJ R Þn dN
ð1Þ
where c is the crack length; n is the number of load cycles; DJ R is the increment of the pseudo J-integral within one load cycle; and A and n are the Paris’ law parameters, or fracture properties. Fig. 4 presents a flowchart to illustrate the proposed methodology. The proposed approach combines the mechanical analysis of viscoelastic
FE simulation of nondestructive test
FE simulation of destructive test
Horizontal strain profiles
Force equilibrium analysis of undamaged specimen
Horizontal strain profiles Undamaged properties E1 and m
Force equilibrium analysis of damaged specimen
Computed integration area of horizontal strain Estimation of crack growth function
h
Sðci Þ ¼ 0
eðzÞdz
where ci is the crack length; Sðci Þ is the integration area of the horizontal strain in terms of the depth of specimen; eðzÞ is the horizontal strain at the depth z; and h is the intact thickness of the specimen. If a bottom crack exists in the specimen in the destructive step and its length is ci mm, the corresponding h is equal to H ci mm, H is the thickness of the field core. Since the OT is a displacement controlled test, the strain profiles are not affected by the viscoelastic behavior of the material or the magnitude of the elastic modulus. Note that the stress profiles are dependent of the viscoelastic material properties. The Poisson’s ratio of the field core is assumed to be 0.35 in this study. The computed horizontal strain distribution of the 38 mm thick specimen corresponding to the maximum opening displacement in the non-destructive step is shown in Fig. 6. The horizontal strains along the center of the simulated specimen are extracted from the FE calculations and plotted in Fig. 7. The shaded area is used to represent the integration area of the horizontal strain Sðu0 ; c ¼ 0Þ, where u0 is the controlled displacement in undamaged tests (i.e., 0.05 mm). Fig. 7 also presents the extracted horizontal strain for the simulated specimen with various crack lengths. The corresponding integration areas Sðud ; ci Þ are calculated and plotted against the crack lengths in Fig. 8. It is shown that the curve of Sðud ; ci Þ versus crack length is fitted well by an exponential equation, which is presented in Eq. (3).
Sðud ; ci Þ ¼ 0:1026e0:06ci Evolution of dissipated pseudo displacement work
Determination of fracture properties A and n
Fig. 4. Flowchart of proposed methodology to determine fracture properties of field cores.
ð2Þ
ð3Þ
where Sðud ; ci Þ is the integration area of the horizontal strain profile at the crack length ci . As mentioned before, the integration area of the horizontal strain profile in the non-destructive step Sðu0 ; c ¼ 0Þ is used to compute the undamaged tensile properties
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102 mm Assigned Seam Direction (z-direction)
Field Core Specimen
25 or 38 mm
Controlled Displacement
Move Horizontally
Fixed
(u0 or ud )
2mm Fig. 5. Simulation of the OT using finite element model.
Field Core Specimen
Magnified View
38 mm in Thicknes
102 mm in Length Fig. 6. Horizontal strain (E11) distribution at maximum opening displacement in non-destructive step.
0.025
Integrated Area (Strain*mm)
0.10
Horizontal Strain
0.02 Crack Length=2.375mm 0.015
Crack Length=7.125mm Crack Length=11.875mm Crack Length=16.625mm
0.01
Crack Length=21.375mm Crack Length=26.125mm
0.005
Crack Length=30.875mm
0.08 0.06
y = 0.1026e-0.06x R² = 0.9962
0.04 0.02 0.00 0
0
5
10
15
20
25
30
35
Crack Length (mm) 0
10
20
30
40
Fig. 8. Plot of covered area under horizontal strain profiles vs. crack length.
Specimen Depth (mm)
Fig. 7. Horizontal strain profiles along the center of field core specimen at different crack lengths.
of the asphalt mixtures. Eq. (3) will be used to estimate the crack growth function in the destructive step. 3.2. Determination of the undamaged tensile properties Fig. 9 presents the free-body diagram of a specimen in the OT. The force equilibrium equation is expressed as,
Z 0
h
rðt; zÞbdz ¼ PVE
ð4Þ
where rðt; zÞ is the viscoelastic stress within the specimen as a function of time t at depth z; b is the width of the specimen; and PVE ðtÞ is the measured viscoelastic force as a function of time t. Since there is no crack initiating in the non-destructive step, the corresponding h is the thickness of the entire specimen.
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Setting that
51 mm
Z sðu0 ; c ¼ 0Þ ¼ 0
Field Core Specimen
(t,z)
eðu0 ; zÞdz
ð11Þ
where sðu0 ; c ¼ 0Þ is the integration area of the horizontal strain profile over the depth at the maximum opening displacement in the non-destructive step, which is represented by the shaded area in Fig. 7. Eq. (10) is then simplified as
H mm
PVE(t)
z-direcon
h
PVE ðtÞ ¼
Fig. 9. Free-Body Diagram of Field Core Specimen.
bE1 t 1m sðu0 ; c ¼ 0Þ ð1 mÞt1
ð12Þ
Taking the natural logarithm on both sides, Eq. (12) can be transformed as The viscoelastic stress rðt; zÞ is further calculated using the constitutive model for the one-dimensional viscoelastic response [17], which is expressed as,
rðt; zÞ ¼
Z 0
t
Eðt sÞ
deðs; zÞ ds ds
ð5Þ
where eðs; zÞ is the linear viscoelastic strain at depth z; s is a timeintegration variable; and Eðt sÞ is the relaxation modulus, which is approximately represented using a power law model, which is shown in Eq. (6) [18].
Eðt sÞ ¼ E1 ðt sÞ
m
ð6Þ
in which E1 and m are the undamaged tensile properties of the asphalt mixture, which will be determined in this section. The reason for using the power law model is to simplify the derivation of the analytical methodology in this study. According to the displacement loading patterns in Fig. 3, Eq. (5) is expanded as a piecewise function separated at each inflection point, which is shown in Eq. (7) [19].
8R t > Eðt sÞ dedðss;zÞ ds ð0 < t < t1 Þ > 0 > > > > R R > > > 0t1 Eðt sÞ dedðss;zÞ ds þ tt Eðt sÞ dedðss;zÞ ds ðt1 < t < 2t 1 Þ > 1 > > < rðt; zÞ ¼ R0t1 Eðt sÞ dedðss;zÞ ds þ Rt2t1 Eðt sÞ dedðss;zÞ ds > 1 > > > > R > t d e ð s ;zÞ > > ð2t1 < t < 3t1 Þ > þ 2t1 Eðt sÞ ds ds > > > : :::
ð7Þ where t 1 is the loading and unloading interval, i.e., 5-s; 0 < t < t1 is the first loading period; t 1 < t < 2t 1 is the first unloading period and 2t 1 < t < 3t 1 is the second loading period. The opening displacement at time t is calculated using Eq. (8).
uðtÞ t ¼ u0 t1
ð8Þ
where uðtÞ is the opening displacement at time t and u0 is the maximum opening displacement in the non-destructive step, i.e., 0.05 mm. Accordingly, the strain at time t is calculated using Eq. (9).
eðuðtÞ; zÞ t ¼ eðu0 ; zÞ t1
ð9Þ
where eðuðtÞ; zÞ is the horizontal strain at time t and depth z and eðu0 ; zÞ is the horizontal strain at time t1 and depth z.
Take the data from the first loading period 0 < t < t 1 as an example to calculate the undamaged properties of asphalt mixture. Substituting the first equation in Eq. (7), and Eq. (9) into Eq. (4) yields Eq. (10).
bE1 t 1m PVE ðtÞ ¼ ð1 mÞt 1
Z 0
h
eðu0 ; zÞdz
ð10Þ
ln
PVE ðtÞt1 E1 ¼ ln þ ð1 mÞ ln t bsðu0 ; c ¼ 0Þ 1m
ð13Þ
Since PVE ðtÞ is the recorded load as a function of time t, the only unknown parameters E1 and m can be calculated from the OT data using a linear regression method. 3.3. Estimation of the crack growth function dc , Two steps are involved to estimate the crack growth function dN including:
I. Calculating the integration area of the horizontal strain profile at each loading interval; and II. Back-calculating the crack length corresponding to each obtained area of the horizontal strain profile using Eq. (3). In the destructive step, the crack propagates with increasing load cycles. The horizontal strain at time t, depth z and crack length c is represented by eðuðtÞ; z; cÞ, which is calculated using Eq. (14).
eðuðtÞ; z; cÞ t ¼ eðud ; z; cÞ t1
ð14Þ
where eðud ; z; cÞ is the horizontal strain corresponding to the maximum opening displacement ud in the destructive step at time t and depth z. Similar to the analysis in the non-destructive step, the measured force can be represented in terms of the undamaged tensile properties E1 and m, loading time interval t 1 , specimen width b and the integration area of the horizontal strain profile of the specimen Sðud ; ci Þ. The only difference is that the intact thickness h reduces with the increasing number of load cycles. Take the first loading period 0 < t < t 1 as an example. Substituting the first equation in Eq. (7), and Eqs. (6) and (14) into Eq. (4) yields Eq. (15), which is used to calculate the integration area of the horizontal strain profile at the first maximum opening displacement Sðud ; c1 Þ.
Pðt 1 Þ ¼
bE1 t 11m Sðud ; c1 Þ ð1 mÞt 1
ð15Þ
where Pðt 1 Þ is the measured force at time t1 . Likewise, the integration area of the horizontal strain profile at the ith maximum opening displacement Sðud ; ci Þ is calculated using Eq. (16).
P½ð2i 1Þt 1 ¼
n o X bE1 Sðud ; ci Þ 2i1 ð1Þn1 ½ðn 1Þt 1 1m þ ðnt 1 Þ1m t 1 ð1 mÞ n¼1 ð16Þ
where P½ð2i 1Þt 1 is the measured force at the ith loading peak. Eq. (16) and the measured E1 and m from the nondestructive characterization are used to determine the integration area of the horizontal strain profile Sðud ; ci Þ at each loading interval. According to Eq. (3),
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the crack length for each load cycle is then back-calculated and presented in Fig. 10. In the destructive step, the crack propagates fast during the first few cycles and the rate of crack growth reduces with the increasing load cycles. A power function is employed to fit the curve of the accumulated crack length against the number of the load cycles. An R-squared value of 0.977 obtained from the curve fitting indicates that the crack growth function can be properly expressed as a power function shown in Eq. (17).
cðNÞ ¼ 6:6233 N 0:2339 R2 ¼ 0:977
2500 2000 1500
Load (N)
1000 500 0 -0.2
-0.1
0
0.1
0.2
0.3
0.4
-500
ð17Þ
-1000
where n is the number of the load cycles; and cðNÞ is the crack length at the Nth cycle.
-1500 -2000
Displacement/Pseudo Displacement (mm)
3.4. Analysis of change of the dissipated pseudo displacement work According to Schapery’s viscoelastic fracture theory [20], dissipated pseudo strain energy or dissipated pseudo displacement work was found to be efficient in characterizing the cracking damage of viscoelastic medium during a strain-controlled or displacement-controlled test [21]. In this study, the dissipated pseudo displacement work is used to quantify the crack propagation in the specimen during the destructive test. The pseudo displacement is calculated using Eq. (18) [22].
uR ðtÞ ¼
1 ER
Z 0
t
Eðt sÞ
duðsÞ ds ds
ð18Þ
where ER is the reference modulus that is assigned as the undamaged modulus E1 in this study; Eðt sÞ is the relaxation modulus; uðsÞ is the displacement as a function of time; and s is a timeintegrated variable. Similar to Eq. (7), Eq. (18) is also expanded as a piecewise function separated by each loading and unloading period, which is shown in Eq. (19).
8 Rt 1 > Eðt sÞads ð0 < t < t1 Þ > > E R R0 > Rt > t1 > 1 1 > Eðt s Þ a d s þ Eðt s Þð a Þd s ðt1 < t < 2t 1 Þ > ER 0 ER t 1 < R R R t 2t 1 u ¼ 1 1 Eðt sÞads þ 1 Eðt sÞðaÞds > ER t 1 > ER 0 R > > t > 1 > þ Eðt s Þ a d s ð2t 1 < t < 3t 1 Þ > ER 2t 1 > : ::: ð19Þ where a is the slope of the displacement curve versus loading time. An example of the load-pseudo displacement hysteresis loop is shown in Fig. 11. The enclosed area of the load-pseudo displacement hysteresis loop represents the dissipated pseudo displacement work, which is used to drive the propagation of the crack within the specimen. Eq. (20) is used to calculate the dissipated pseudo displacement work by integrating the load and pseudo displacement.
Load vs. Displacement at 1st Loading Cycle Load vs. Pseudo Displacement at 1st Loading Cycle Fig. 11. Example of load-pseudo displacement hysteresis loop of a field core specimen.
Z WR ¼
R
tb
PðtÞ ta
du ðtÞ dt dt
ð20Þ
where W R is the dissipated pseudo displacement work in a load cycle ½t a ; t b . As can be seen from Fig. 11, the load-pseudo displacement loop enclosed area is much smaller than the load–displacement loop enclosed area, which indicates that only a small portion of the total work is dissipated for the propagation of the crack, and the remaining work is actually dissipated due to the viscoelastic stress relaxation of the asphalt concrete. Fig. 12 shows the evolution of the cumulative dissipated pseudo displacement work with the increasing number of load cycles. It suggests that the power function is also able to capture the trend of the cumulative dissipated pseudo displacement work with the increasing number of load cycles. Eq. (21) is the fitted power function for the example in Fig. 12.
W RC ðNÞ ¼ 424:88 N0:1193
R2 ¼ 0:9729
ð21Þ
where W RC ðNÞ is the cumulative dissipated pseudo displacement work. 3.5. Determination of the fracture properties of asphalt field cores As mentioned previously, the fracture properties of an asphalt mixture are determined based on the modified Paris’ law, as shown in Eq. (1). Because DJ R represents the work dissipated to propagate cracks in the material, it can be represented by Eq. (22).
DJ R ¼
@W RC @ðc:s:aÞ
ð22Þ
Cumulative Dissipated Pseudo Displacement Work (N*mm)
900
35
Crack Length (mm)
30 25
6.6233x0.2339
y= R² = 0.9772
20 15 10 5
800 700 y = 424.88x0.1193 R² = 0.9729
600 500 400 300 200 100 0 0
0 0
100
200
300
400
500
600
700
50
100
150
200
250
Number of Load Cycles
Number of Load Cycles Fig. 10. Estimation of crack growth function in destructive step.
Fig. 12. Example of evolution of cumulative dissipated pseudo displacement work with increasing number of load cycles.
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where c:s:a is the total crack surface area. Taking the partial derivatives of W RC and c:s:a with respect to the number of the load cycles n, Eq. (22) is expressed as @W RC
@N DJR ¼ @ðc:s:aÞ
ð23Þ
@N
As shown in Fig. 12, the evolution of the pseudo displacement work with the increasing number of the load cycles can be represented as a power function, which is shown in Eq. (24).
W RC ðNÞ ¼ a Nb
cðNÞ ¼ d Ne
ð25Þ
where c and d are regression parameters. Therefore, the crack surface area c:s:a is calculated using Eq. (26).
c:s:aðNÞ ¼ d N e w 2
ð26Þ
where w is the width of the specimen, i.e. 0.076 m. Substituting Eqs. (23)–(26) into Eq. (1) yields:
n ab ðdeÞ N e1 ¼ A NnðbeÞ 2wde
ð27Þ
Comparing both sides of Eq. (27) gives the following: nþ1
ðdeÞ A ¼ ab n
ð28Þ
2w
e1 be
ð29Þ
Based on Eqs. (28) and (29), the fracture properties A and n can be determined from the OT. Table 2 presents the results of A and n calculated by the inputs of the presented example. In order to verify the values of A and n calculated by the proposed approach, Schapery’s estimation method [20] and Luo’s regression equation which relates A0 and n0 [10] are used to calculate the values of A0 and n0 , as shown in Eqs. (30) and (31).
n0 ¼
4. Results and discussions
ð24Þ
where A and b are regression parameters. Likewise, the crack growth function can also be represented by a power function, which is expressed as
n¼
cores have relatively higher air voids than the LMLC asphalt mixtures, which results in a smaller A values [10]. Therefore, the comparison of fracture properties in Table 2 demonstrates that the proposed approach can provide rational results of the fracture properties. After verifying the rationality and comparability of A and n values, the proposed methodology will be applied to evaluate the fracture properties of field-aged asphalt concrete in the next section.
Based on the OT test protocol and methodology introduced in the previous two sections, the test and analysis results are presented in this section as well as the discussions. 4.1. Determination of fracture properties of field cores Based on the methodology elaborated above, the fracture properties of all of the specimens are calculated to investigate the cracking resistance of field-aged asphalt concrete. Fig. 13 presents the relationship between A and n for the tested cores. A linear regression model is used to fit the scattered points, which are shown in Eq. (32).
log A ¼ 2:2045n þ 1:3133;
R2 ¼ 0:9348
ð32Þ
An R-squared value of 0.93 is obtained from the regression model, which indicates a highly linear correlation between n and log A. According to the Paris’ law with the pseudo J-integral, the crack propagation speed is proportional to both A and n. In other words, an asphalt mixture has a lower cracking resistance when A increases or n increases. However, the established relationship between A and n indicates they cannot increase at the same time. In order to quantify the cracking resistance of asphalt concrete by comparing A and n, Luo et al. [10] conducted a sensitivity analysis on the damage density of asphalt mixtures with various groups of A and n. It was found that the change of n is predominant to the resulting damage density, and suggested that n can be used alone to evaluate the cracking resistance of different asphalt mixtures.
30
2 m
ð30Þ
where m is the undamaged tensile property. 0
20
2
log A ¼ 0:93 n þ 5:30 R ¼ 0:91
ð31Þ
-log (A)
0
y = 2.2045x + 1.3133 R² = 0.9348
25
0
The estimation of A and n0 using Eqs. (30) and (31) is also presented in Table 2. It is seen that the values of n calculated by the proposed approach are comparable to the values of n0 estimated by the Schapery’s method. However, the calculated A values using the proposed method is smaller than the estimated A0 values using Luo’s regression equation. The reason is that Luo’s regression equation is based on the statistical analysis of LMLC asphalt mixtures, while the field
15 10 5 0 0
2
4
6
8
10
12
14
n
Fig. 13. Relationship between A and of tested field cores.
Table 2 Examples of comparison of calculated fracture properties using proposed approach and estimation approach. Mixture type
Estimation approach based on Schapery’s method and regression equation Inputs m
H3 E3 F3
0.32 0.35 0.32
Outputs
Proposed approach obtained by OT results Inputs
0
n0
A (mm) 12
7.7 10 2.5 1011 7.7 1012
6.25 5.71 6.25
a 424.9 413.2 364.9
Outputs b 0.12 0.11 0.10
d 6.62 5.65 5.82
e 0.234 0.245 0.221
A (mm)
n 16
3.2 10 2.4 1014 3.1 1015
6.72 5.59 6.44
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4.2. Effect of field aging on fracture properties
35.0
4.3. Impact of WMA technologies on fracture properties In order to clearly investigate the impact of WMA technologies on cracking resistance of asphalt concrete, Fig. 14 is converted to Fig. 16 by changing the legend from aging time to types of asphalt mixture. The n values of the first set of cores demonstrate that the EWMA technology slightly improves the initial cracking resistance, while the FWMA technology provides comparable fracture properties to the HMA field cores. This is because the WMA technology has lower production and paving temperatures, which reduces the oxidation of the asphalt binder and potentially improves the cracking resistance of WMA [28–29]. The reason why the FWMA performed similarly to the HMA is that the injected water inside of asphalt binder also reduces the cracking resistance of WMA at the same time, which may counteract the improvement of cracking resistance due to the decreased mixing and paving temperatures. After 15 months aging, it is found that both EWMA and FWMA have comparable or even higher n values than the HMA. This indicates that the 15 month aged EWMA and FWMA field cores have
12.00 10.00
n
8.00 6.00 4.00 2.00 0.00 HMA
1 Month
FWMA
9 Months
EWMA
15 Months
Fig. 14. Influence of aging time on n value for three types of asphalt field cores.
Air Temperature (°C)
30.0
Paving in December 2011
25.0 20.0
Second set of field cores
15.0
First set of field cores
10.0
Third set of field cores
5.0 0.0 0
1
2
3
4
5
6 7 8 9 Aging Month
10 11 12 13 14 15
Fig. 15. Change of average monthly air temperature in aging period.
12.00 10.00 8.00 n
Fig. 14 compares the cracking resistance of the three types of asphalt field cores with different aging times. The level of test accuracy is shown by the error bar with one standard deviation. As shown in Fig. 14, the average n value increases with the aging time for all the three types of field cores. This indicates that the cracking resistance of asphalt concrete decreases with the aging time, which is consistent with the fact that the aged material is prone to be more brittle and easier to crack. A further observation reveals that the n value increases significantly from the first aging month to the ninth aging month, and then slightly increases from the ninth aging month to the fifteenth aging month. This nonlinear impact demonstrates that there should be other factors influencing the change of cracking resistance of asphalt field cores besides the aging time. Fig. 15 shows the change of average monthly air temperature in the entire aging period. A significant difference among the three set of field cores is that the first set of field cores only experienced the winter climatic condition, while the second and third sets of field cores both experienced the entire summer climatic condition (i.e., 6th month-9th month aging period). Generally, the aging factors on the fracture properties of field cores include geographical location, aging time, air temperature, wind speed, solar radiation etc. [23–26]. Compared to the winter climate, the summer normally has a higher air temperature and solar radiation, which can accelerate the aging of asphalt concrete. Yin et al. [27] concluded that the subjected summer climatic condition is a more important factor than aging time that embrittles the asphalt concrete in the field. In this study, the summer climatic condition is also believed to be the major cause of an accelerated reduction of cracking resistance of field cores.
6.00 4.00 2.00 0.00 1-Month
9-Month
HMA
FWMA
15-Month
EWMA
Fig. 16. Influence of WMA technologies on n value at different aging times.
Table 3 Summary of pavement performance distress in the field sections (After Glover et al. 2013). Mixture type
Observed distresses Longitudinal cracks under wheel-path (%)
Longitudinal cracks under non wheelpath (%)
Fatigue cracks (%)
Transverse cracks (%)
HMA FWMA EWMA
0.8 1.2 1.5
1.2 1.0 1.2
0 0 0
0 0 0
the same or even lower cracking resistance compared to the HMA. Table 3 summarizes the distresses of three types of flexible pavement sections observed in the field after 15 months of service [30]. There is no significant difference between the HMA and WMA sections at this time. This field distress observation is consistent with the trend of the fracture properties of field cores determined using the OT shown in Fig. 16.
5. Summary and conclusions This paper proposes a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the OT. A two-step OT method is devised to determine the fracture properties A and n for asphalt field cores. A total of 27 field cores are investigated in this study in order to quantify the effect of field aging on their fracture properties and develop a better understanding of the impact of WMA technologies on their fracture properties. The major contributions of this paper are summarized as follows: Starting from the mechanical analysis of force equilibrium in the OT specimen, the developed approach combines analytical and numerical analyses to determine the undamaged properties in the nondestructive step, and estimate the crack growth function
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in the destructive step. The trend of crack propagation in the destructive step is found to follow the power function. Based on Schapery’s fracture theory, the dissipated pseudo displacement work is determined to characterize the cracking damage of asphalt field cores in the OT. The power function fits well the evolution of the cumulative dissipated pseudo displacement work with the number of load cycles. Theoretical equations are formulated to calculate the fracture properties A and n. The rationality of the proposed methodology is verified by comparing the results of A and n calculated in this study to those using Schapery’s estimation method. Investigation of the effect of field aging on fracture properties of field cores agree with the results in the published literature [10] that n is a good indicator to evaluate the cracking resistance of asphalt materials. The cracking resistance of field cores significantly reduces from the 1st month to the 9th month, and then slightly decreases from the 9th month to the 15th month. This suggests that the subjected summer climatic condition is a more important factor than the aging time that affects the fracture properties of the material. Comparison of n values of the field cores indicates that the EWMA technology slightly improves the cracking resistance, while the FWMA technology provides comparable fracture properties to the HMA. After 15 months aging, the n value does not exhibit a significant difference between HMA and WMA field cores, which is confirmed by the observations of field distresses where the field cores are taken. Acknowledgement The authors acknowledge the TxDOT for the financial support. Special thanks are to Yasser Koohi from Fugro Consultants, Jeff Perry and Lubinda Walubita from Texas A&M Transportation Institute for their help in this study. References [1] G.R. Rada, D.J. Jones, J.T. Harvey, K.A. Senn, M. Thomas, Guide for conducting forensic investigations of highway pavements. Research Report No. 747, National Cooperative Highway Research Program, Washington, D.C., 2013. [2] H. Wen, Y.R. Kim, Simple performance test for fatigue cracking and validation with WesTrack mixtures, Transp. Res. Rec. 1789 (2002) 66–72. [3] X. Li, M.O. Marasteanu, Using semi circular bending test to evaluate low temperature fracture resistance for asphalt concrete, Exp. Mech. 50 (7) (2010) 867–876. [4] M.P. Wagoner, W.G. Buttlar, G.H. Paulino, Disk-shaped compact tension test for asphalt concrete fracture, Exp. Mech. 45 (3) (2005) 270–277. [5] H. Wen, Characterization of fatigue performance of WesTrack pavement using work potential theory, Road Mater. Pavement 4 (1) (2003) 109–121. [6] Y.R. Kim, J.S. Daniel, H. Wen, Fatigue performance evaluation of WesTrack asphalt mixtures using viscoelastic continuum damage approach. Research Report No. FHWA/NC/2002-004, 2002.
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