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A-1 APPENDIX A. MEASUREMENT OF COMPLEX MODULUS GRADIENT USING DIRECT TENSION TEST The test protocol to measure the complex modulus and modulus gradient include: 1) The materials for testing, containing asphalt field cores and laboratory-mixed-laboratory- compacted (LMLC) mixtures; 2) The configuration and procedure of the direct tension test with a nondestructive monotonically increasing load; and 3) The characteristics of mechanical responses of field cores as well as their comparisons with those of LMLC mixtures. Asphalt Field Cores and LMLC Mixtures The asphalt field cores used in this study include one type of hot mix asphalt (HMA). They are collected from a field project near the Austin Bergstrom airport in Texas. The field asphalt mixtures are fabricated with a PG 70-22 asphalt binder and Texas limestone aggregates. The binder content is 5.2%. The nominal maximum aggregate size is 10 mm (3/8 inch). The detailed mix design and the aggregate gradation can be found in this report (1). The cores are taken at the center of two lanes of a HMA section at 8 months and 22 months after construction. It is reasonable to assume that the collected cores are not damaged by traffic within this aging period. In order to demonstrate the modulus gradient features of field cores, laboratory HMA specimens are also fabricated. The parallel tests are performed between the field and LMLC specimens to demonstrate the differences in the measured data. Two air void contents for the laboratory specimens are chosen. The tested LMLC specimens are obtained only from the center of the compacted cylinder samples for the purpose of having uniform air void distributions through their thicknesses. All of the original cylinder field cores and LMLC mixtures samples are cut into rectangular specimens 102 mm (4 inches) long and 76 mm (3 inches) wide. The thickness of the rectangular specimen varies from 38 to 51 mm (1.5 to 2 inches) dependent on the thickness of the original field core. The thickness of the LMLC specimens is 38 mm (1.5 inches). Then steel studs are glued on the top, center and bottom of the specimens for placing linear variable differential transformers (LVDTs). The rectangular field core specimen preparation is shown in Figure A-1. The air void content, thickness and aging time of each field and LMLC specimen are given in Table A-1. After being cut and trimmed in the laboratory, each rectangular specimen is fixed with six LVDTs, as shown in Figure A-2. The two vertical LVDTs are used to measure the vertical deformations of the top and bottom of the specimen, respectively; another pair attached on the two sides is used to measure the vertical deformations of the center of the specimen. The two horizontal LVDTs are used to measure the lateral deformations of the top and bottom, respectively. This lateral deformation is used to determine the Poissonâs ratio of field cores, which will be discussed in a following study. The gauge length is 50.8 mm (2 inches) for each LVDT.
A-2 Figure A-1. Field Core Specimen Preparation Table A-1. Field Cores and Laboratory Fabricated Mixtures Specimens Tested in Direct Tension Test Material Type Air Void Content (%) Field Aging Time (month) Thickness (mm) HMA Field Cores 6.6 8 38 5.8 8 51 5.5 22 51 5.3 22 38 LMLC HMA 6.3 N/A 38 5.2 N/A 38 (a) (b) Figure A-2. Field Core Specimen with LVDTs and Setup in the MTS
A-3 Direct Tension Test The direct tension test is conducted using the Material Test System (MTS) shown in Fig. A-2b. A nondestructive monotonically increasing load is applied on the rectangular specimens at 10°C, 20°C and 30°C at a ramp rate of 0.020 mm/min, respectively. This MTS is an electrohydraulic servo machine. It includes a load cell and a temperature chamber, and is connected to a desktop for reading, saving and analyzing the test results including the load and strains. The MTS is also equipped with ball joints. To keep the specimens undamaged, the maximum tensile strain is set below 100 microstrains. It takes approximately 2 hours to change the temperature of the specimens from one to another, and it takes approximately 8 hours to finish the entire set of the tests for three temperatures. A new set of specimens are put in the temperature chamber overnight to reach the temperature equilibrium and recover the temperature loss due to opening the chamber for unloading and removing the previous specimens. The direct tension tests conducted on the tested specimens at each temperature are repeated three times in order to avoid the undesired test errors and confirm that the specimens are undamaged during testing. Otherwise, the data cannot be used for analysis. Note that a rest period of 15 min between the two tests is needed to recover the viscoelastic strains after one test. The three repeated test results are shown in Figure A-3, which indicates that a rest period of 15 min is enough and the repeatability is satisfied. (a) Load in Three Repeated Tests (b) Top and Bottom Strains in Three Repeated Tests Figure A-3. Three Repeated Test Results at 10ËC Mechanical Responses of Field Cores and LMLC Mixtures The mechanical responses of the field cores and LMLC specimens are shown in Figures A-4 to A-6. Figure A-4a shows the measured loads applied on the field core specimen when the test temperatures are 10°C and 30°C, respectively. It can be seen that as the temperature increases, the load-time curve becomes smaller and more curved, and the duration of the test is
A-4 shorter. This observation indicates that the use of time-temperature superposition and thermorheologically simple material can be applied to the field specimens. Figure A-4b presents the applied load when the aging times are 8 and 22 months, respectively, it shows that when the aging time is longer, the field core specimens become stiffer. Figure A-5 presents the measured vertical and horizontal strains of the field core specimen calculated from the readings of the deformation of one vertical and one horizontal LVDT attached to the top surface. The vertical deformations are recorded by the four vertical LVDTs attached to the top, center and bottom, whereas the horizontal deformations are recorded by the two horizontal LVDTs attached to the top and bottom surfaces. Note that the vertical strains at the center of the specimen are calculated by averaging the readings from the two LVDTs attached to the two center of both sides. It is shown that as the tensile load increases, the vertical strain increases whereas the horizontal strain decreases. Figures A-6a and A-6b compare the induced vertical strains obtained from the corresponding vertical deformation data for the field core specimen and LMLC specimen, respectively. Under the similar loading, the measured vertical strains in the field and laboratory specimens are obviously different. The three measured vertical strains in the field core specimen (Figure A-6a) have different magnitudes at the three locations, which are closely related to the modulus at each depth. However, the three measured strains for the LMLC specimen in Figure A-6b are almost identical. It is known that the LMLC specimen has an almost uniform modulus across the thickness. Therefore, the difference between three measured strains of the LMLC specimen is minimal. The measured strains at the top, center and bottom of the field core specimens are different, which is due to the non-uniform modulus distribution in the field cores. In general, the strain at the top is smallest and the strain at the bottom is largest, which reflects the modulus distribution. Figure A-6c illustrates that the strain is smaller and increases slower for the field specimen with a longer aging time, which shows the long-term aging effect on the mechanical response. Due to the existence of the modulus gradient, the monotonic load applied at the center of the field core specimen is actually located different from the neutral axis as shown in Figure A-7. It is expected that the neutral axis is closer to the stiffer side than to the softer side. This eccentricity induces a bending moment and corresponding bending strains at these three locations during the testing. Therefore, the measured strains at the top, center and bottom include two parts: the tensile strain and bending strain. The modulus gradient of a field core specimen at a specific loading frequency and temperature is modeled by Eqs. (A-1) and (A-2): 0( ) ( )( ) n d d d zE z E E E d ï ï½ ï« ï (A-1) 0 d Ek E ï½ (A-2) where E (z) is the dynamic modulus in pavement depth z at a specific loading frequency and temperature; Ed and E0 are the dynamic moduli at the top and bottom at the same loading condition, respectively; d is the thickness of the field core specimen; n is the model parameter,
A-5 which presents the shape of the stiffness gradient; and k is the ratio of the modulus at the top to the modulus at the bottom. When z equals to 2 d , the center modulus Ec is obtained. (a) Loads at Different Temperatures (b) Loads at Different Aging Times Figure A-4. Monotonic Loads in Direct Tension Test Figure A-5. Measured Vertical and Horizontal Strains at the Top Surface of Field Core Specimen â100 0 100 200 300 400 500 0 10 20 30 40 Lo ad  (N ) Time (s) 8 Months 22 Months
A-6 (a) Strain at Different Depths of Field Core Specimen (b) Strain of Laboratory Fabricated Specimen (c) Strain at Different Aging Times of Field Core Specimen Figure A-6. Measured Vertical Strains at Top, Center, and Bottom of Tested Specimen â20 0 20 40 60 80 100 0 10 20 30 M ic ro st ra in Time (s) Center Top â20 0 20 40 60 80 100 0 10 20 30 M ic ro st ra in Time (s) Center â20 0 20 40 60 80 0 5 10 15 20 M ic ro st ra in Time (s) 8 Months 22 Months Bottom BottomÂ
A-7 Figure A-7. Illustration of Non-uniform Distributions of Stress, Strain, and Modulus in Field Core Specimen
