Laboratory Validation of an Endurance Limit for Asphalt Pavements (2013)

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5 Beam Fatigue Testing Beams were prepared using vibratory loading applied by a servohydraulic loading machine. A mold was used with inside dimensions larger than the required dimensions of the beam to allow for sawing to achieve standardized specimen dimensions. The mix was compacted using a stress-controlled sinusoidal load to reach a pre-determined density. The beams were brought to the required dimensions of 15 × 2 × 2.5 in. for fatigue testing by sawing ¼ in. from each side. Air voids were measured using the saturated surface-dry procedure (AASHTO T166, Method A). Any specimen with air voids deviating by more than 1 percent from the target value of 7 percent was rejected. The details of beam preparation and verification of air void uniformity within the specimen are presented elsewhere (23). Fatigue tests were performed using the beam fatigue test apparatus shown in Figure 3. Sinusoidal versus Haversine Waveforms Before testing, a pilot study (24) was performed using the PG 64-22 mixture to compare haversine and sinusoidal wave- forms (see Figure 4), especially when incorporating rest periods between load cycles that cause healing of the HMA. Deflection- controlled haversine and sinusoidal flexure beam fatigue test protocols are defined in ASTM D7460 and AASHTO T321, respectively. Figure 5 illustrates what happens (hypothetically) to an HMA beam during the sinusoidal deflection-controlled test and the haversine deflection-controlled test. In the sinusoidal test (Figure 5[a]), the deflection input is sinusoidal, which bends the beam in both directions. The neutral position of the beam does not change during the test and remains in the original position halfway between the two extreme posi- tions. In the haversine test (Figure 5[b]), the deflection input is haversine, which bends the beam with the same peak-to- peak magnitude as the sinusoidal test but in one direction only. Because of the viscous response of the material, creep (permanent deformation) occurs in the beam and the neu- tral position of the beam shifts downward after a few loading cycles. The neutral position is located halfway between the extreme positions and the haversine deflection transitions to a sinusoidal deflection performed on a bent beam. Figure 6 illustrates the deflection input and the stress and strain outputs that occur in the HMA beam during the test. Since the neutral position of the beam does not change in the sinusoidal test, the developed strain and stress are sinusoidal, causing alternating tension and compression in the beam as shown in Figure 6 (a). In the haversine test, the deflection input remains haversine throughout the test. The developed strain and stress pulses start as haversine waveforms caus- ing strain and stress in one direction (compression at the top of the beam and tension at the bottom without reversal). Because of the shifted position of the beam, however, the developed strain and stress pulses immediately change to sinusoidal causing alternating tension and compression with one-half of the magnitude of the stress applied at the begin- ning of the test as shown in Figure 6 (b). At the end of the test, when the load is removed, the beam remains in the bent position showing permanent deformation. The permanent deformation at the center of the beam at the end of the test is equal to one-half of the peak-to-peak deflection during the test. For example, if a 400 peak-to-peak microstrain is main- tained during the test, a peak-to-peak deflection of 0.009 in. is produced and 0.0045 in. of permanent deformation would result at the end of the test. Although this permanent defor- mation is not seen with the naked eye, it produces erroneous fatigue and endurance limit results since the calculations do not match the test conditions. This pilot study observation confirmed the conclusions of Pronk (25, 26). Therefore, it was concluded that the deflection-controlled sinusoidal test (AASHTO T321) is more consistent than the deflection-controlled haversine test (ASTM D7460) since it produces the intended stress and strain waveform. This is par- ticularly important for studies dealing with healing and the endurance limit of HMA, in order to obtain a fair comparison C H A P T E R 2 Developing of Endurance Limit Model Based on Beam Fatigue Tests

6rest periods with a frequency of 10 Hz according to AASHTO T321, while others used a 0.1s sinusoidal loading followed by a rest period. Figure 7 shows the waveform used in the study, which required a software modification in the operating sys- tem of the loading machine. Tests without rest periods were performed up to failure, which occurs when the SR reaches 0.5. Since the tests with rest periods take considerably longer than tests without rest periods, it was decided to run all tests with rest period up to 20,000 cycles only. Extrapolation was then used to predict the SR for the test with rest period at Nf w/o RP. Figure 8 shows the extrapolation used to determine the SR for tests with rest period at Nf w/o RP. The accuracy of the extrapolation was verified by run- ning several tests with a rest period until 200,000 cycles. Data points from the first 20,000 cycles were used to extrapolate up to 200,000 and were compared with actual data. It was found that an exponential function was able to extrapolate the data accurately and this process almost exactly predicted the measured data obtained at 200,000 cycles. Experimental Design The following factors and levels were used during testing for the beam fatigue endurance limit study. of tests with and without rest periods and an accurate assess- ment of the fatigue and healing results. It was also concluded that in the beam fatigue test on HMA, the loading machine controls the deflection, not the strain. Because of the perma- nent deformation that occurs in the material, the strain does not match the deflection. Therefore, the so-called haversine “strain-controlled” test on HMA is technically a haversine “deflection-controlled” test. Based on the results of the pilot study, beam fatigue tests were conducted according to AASHTO T321 test procedure using sinusoidal loading. Some tests were performed without Figure 3. Beam fatigue test apparatus. Time Sinusoidal Haversine D ef le ct io n Figure 4. Haversine and sinusoidal waveforms. Neutral Position Extreme Positions (a) Sinusoidal (AASHTO T321) Extreme PositionsNeutral Positions Extreme Position (b) Haversine (ASTM D7460) First Few Cycles During Test Figure 5. Neutral and extreme positions using sinusoidal and haversine waveform deflection-controlled test on HMA.

7 St re ss o r St ra in St re ss o r St ra in 0 0 St re ss o r St ra in Time Lag Stress Strain or Deflection Time Time Time 0 Stress Strain Deflection First Few Cycles During Test (a) Sinusoidal (AASHTO T321) (b) Haversine (ASTM D7460) Figure 6. Stresses, strains, and deflections versus time for sinusoidal and haversine deflection-controlled tests. Sinusoidal Load Rest Period Sinusoidal Load Portion of Pulse Causing Bottom Tension Up wa rd D ef le ct io n D ow nw ar d D ef le ct io n Figure 7. Deflection-controlled sinusoidal waveform with rest period used in the study.

8was decided to use two replicates in the rest of the study. In the beam fatigue study, the results from a total of 468 tests were analyzed to develop the SR model as discussed in the subsequent section. Model Development Several trials were made to determine the best mathemati- cal form to relate the independent variables to SR. It was found that there was a need for logarithmic transformations for some variables. It was also concluded that the best mathe- matical form to relate SR to rest period was the tangent hyper- bolic (Tanh) function since it was noted during the laboratory tests that there was no large gain in healing from applying a 10s rest period compared to a 5s rest period. This observation agrees with the literature that showed that there is a threshold rest period beyond which no additional healing is gained. In an effort to develop a satisfactory relationship between the SR and the material and testing conditions, several regres- sion models were attempted. Originally, a regression model was developed to relate the SR to all factors used in the study, which are binder content, air voids, binder grade, tempera- ture, applied tensile strain, rest period, and number of loading cycles. Later, the model was simplified using the initial stiff- ness of the mixture as a surrogate for the binder content, air voids, binder grade, and temperature, as all these parameters affect stiffness. This rather innovative approach relates the endurance limit to a basic material property, stiffness. Two main advantages were achieved with this modification. First, the model is simplified. Second, the model is more compat- ible with the AASHTOWare Pavement ME Design software, where the prediction of pavement performance is mainly driven by the stiffness (or dynamic modulus) of HMA. How- ever, care has to be taken when replacing volumetric prop- erties with the material stiffness since air voids and binder content can counteract each other and create the same stiffness but different endurance limits. This problem was minimized in the development of the beam fatigue model in this study by considering the effect of a wide range of stiffness (three binder grades), which reduced the impact of the stiffness effect. The model was further refined by adding more data points. As discussed earlier, the applied strain was pre-selected to reach failure for the test without rest period at a certain number of cycles (Nf w/o RP). This situation resulted in co-linearity between the strain and the number of cycles. To remove the co-linearity in the model, SR data were collected at three different locations along the SR-N relationship for tests with rest period. Two of these points were taken during the test, while the third point was taken at Nf w/o RP. Figure 9 shows the typical SR-N relation- ships for the tests with and without rest period and the loca- tions where data points were taken. Note that the test results with rest period are extrapolated to Nf w/o RP as discussed earlier. 0 0.2 0.4 0.6 0.8 1 1.2 0 20000 40000 60000 St iff n e ss R at io Loading Cycles, N Test without Rest Period Test with Rest Period Extrapolation to Nf w/o RP Nf w/o RP Healing Figure 8. Typical extrapolation to estimate stiffness ratio (SR) (with rest period) at Nf w/o RP (PG 64-22, 40F, 4.2% AC, 4.5% Va, 200 microstrain). 1. Binder grade (3 levels: PG 58-28, PG 64-22, PG 76-16) 2. Binder content (2 levels: optimum ± 0.5%) 3. Air voids (2 levels: 4.5, 9.5%) 4. Strain level (3 levels: L, M, H) 5. Temperature (3 levels: 40, 70, 100°F) 6. Rest period (4 levels: 0, 1, 5, 10s) The criterion for selecting the strain level at each tempera- ture was to reach a fatigue life of approximately 20,000 cycles at the high strain level and approximately 100,000 cycles at the low strain level for tests without rest period (Nf w/o RP). These strain levels were determined from pilot beam fatigue tests conducted at different strain levels at 40, 70, and 100°F. It was clear that a complete factorial design using the previously mentioned factors and levels would be practi- cally impossible considering the time and resources avail- able. Added to the problem is the time it takes to run beam fatigue tests with rest periods. For example, a fatigue test with a 0.1s loading cycle, 5s rest period, and 20,000 load applica- tions takes 28.3 hours, in addition to the time needed for mix preparation, specimen compaction and sawing, and air void determination. Therefore, it was decided to use a six-factor fractional factorial statistical design with partial randomiza- tion that would provide accurate results and require fewer tests (27). This design allows for determining the effects of the main factors and up to three-factor interactions. Table 3 shows the factor combinations used in the beam and uniaxial fatigue tests. Three replicates were tested at each factor combination in the first part of the study. An analy- sis using the PG 64-22 data points was then performed to determine the minimum number of replicates to maintain the required accuracy. The statistical results concluded that the accuracy of the results does not change when using two or three replicates for each factor combination. Therefore, it

9 Beam Fatigue Test X Uniaxial Fatigue Test 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5 4.5 9.5 Strain Level Rest Period (seconds) 0 x x x 1 5 x x x x 10 0 x x x 1 x 5 x x x 10 x 0 x 1 x 5 x 10 0 x x x 1 5 x x x 10 x 0 x x x 1 x 5 x x x x 10 0 1 x 5 10 0 x x x 1 x x 5 x x 10 0 x x x 1 5 x x x 10 x 0 x 1 5 x 10 PG 58-28 4.2 5.2 4.2 5.2 4.2 5.2 Temperature (F) Air Voids (%) 40° PG 76-16 PG 64-22Binder Grade Binder Content (%) High 70° 100° Low Medium High Low Medium High Low Medium Table 3. Factor combinations used for the beam and uniaxial fatigue tests.

10 y = 0.8942x + 0.078 R2 = 0.891 Se/Sy=0.32 N=934 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Pr e di ct ed SR Measured SR Figure 10. Predicted versus measured SR for the beam fatigue SR model. A total of 946 data points was used to build the regression model. Two main statistical software programs were utilized to build the regression model: STATISTICA and Microsoft Excel®. STATISTICA was used to determine the best initial values for the coefficients. An optimization process was then performed using Excel® to minimize the sum of squared error followed by setting the sum of errors equal to zero. The JMP® software (27) was used in developing the model by trying dif- ferent combinations of factors. A statistical procedure (28) was then used to remove the outliers in order to improve the accuracy of the model. Equation 3 shows the final SR model developed from the beam fatigue test results. SR 2.0844 0.1386 log E 0.4846 log( ) 0.2012 log N 1.4103 Tanh 0.8471 RP 0.0320 log E log( ) 0.0954 log E Tanh 0.7154 RP 0.4746 log( ) Tanh 0.6574 RP 0.0041 log N log E 0.0557 log N log( ) 0.0689 log N Tanh 0.259 RP 3 o t o t o t o t                     ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) = − − ε − + + ε − − ε + + ε + where, SR = stiffness ratio Eo = initial flexural stiffness (ksi) et = applied tensile microstrain (the tensile portion of the tension-compression loading cycle, or half peak-to- peak) (10−6 in./in.) RP = rest period (s) N = number of loading cycles The adjusted R2 value of the model was 0.891. Figure 10 shows the predicted versus measured SR values of the model, which indicates an accurate prediction. The figure shows two clusters of data points, where the top cluster represents data with rest period and the bottom cluster represents data with- out rest period. A larger number of tests were performed with rest period since they produce results close to the endurance limit, which is the main outcome of the study. The two clus- ters of data represent a wide range of SRs producing a ratio- nal and stable regression model. By substituting the SR in Equation 3 with 1.0 (complete healing condition), the strain becomes the endurance limit for different values of Eo, N, and RP. Since N is included in the model, it is important to know how changing the value of N affects the endurance limit. A sensitivity analysis study was performed, where SR was plot- ted versus strain and rest period for different Eo values and three values of N (20,000, 100,000, 200,000 cycles). It was concluded that the number of loading cycles has little to no effect on the SR value, especially for rest periods higher than 1s and large values of N. This conclusion validates the assumption that complete healing occurs during the rest period after each load application, which makes the number of load applications redundant when the model is used to define the endurance limit strain. As a result, the endurance limit was calculated at a value of 200,000 cycles in the model. Note that aging is indirectly considered in Equation 3 since aging affects the stiffness of the mix. Estimation of Endurance Limit Based on Beam Fatigue Testing Model The endurance limit was estimated by plotting SR versus strain at rest periods of 1, 2, 5, 10, and 20s. In each case, the endurance limit was obtained as the strain corresponding to an SR value of 1.0, indicating complete healing during the rest period. Figure 11 provides examples of estimating the endurance limits at rest periods of 1 and 5s and SR = 1.0. Figure 12 and Table 4 summarize the endurance limit val- ues obtained from the model for several rest periods and stiff- ness values. The model produced endurance limit values of 22 microstrain to 223 microstrain for the variables analyzed 0 0.2 0.4 0.6 0.8 1 1.2 0 20000 40000 60000 St iff n e ss R at io Loading Cycles, N Test without Rest Period Test with Rest Period Healing Nf w/o RP Figure 9. Selection of data point locations.

11 0 50 100 150 200 250 1 2 5 10 20 En du ra n ce Li m it, µε Rest Period, seconds Eo=3000 ksi Eo=1000 ksi Eo=200 ksi Eo=50 ksi Figure 12. Summary of endurance limit values versus several rest periods and stiffness values using the beam fatigue test model. 0 0.2 0.4 0.6 0.8 1 10 100 St iff ne ss R at io Microstrain Endurance Limits 0 0.2 0.4 0.6 0.8 1 10 100 St iff ne ss R at io Microstrain Log. (Eo=50 ksi) Log. (Eo=200 ksi) Log. (Eo=1000 ksi) Log. (Eo=3000 ksi) 5-sec Rest Period Endurance Limits 1000 1-sec Rest Period 1000 Figure 11. Examples of estimating the endurance limits for several initial stiffness values.

12 (rest period and AC moduli [Eo]). The results show that decreasing the stiffness makes the material more ductile and, therefore, the endurance limit increases. Also, increasing the rest period increases the endurance limit. This means that the endurance limit at larger strains is obtained at longer rest periods in order to allow for complete healing. The endurance limit increased from a range of 22–82 microstrain at 1s rest period to a range of 81–223 microstrain at a 20s rest period. The endurance limit values at rest periods of 10 and 20s were almost the same. This suggests that the threshold rest period to complete the healing is between 5 and 10s for a loading period of 0.1s. Figure 13 shows that the number of loading cycles has little or no effect on the SR value for tests with a rest period, especially at large values of N. Since the endurance limit is obtained at an SR value of 1.0, the number of loading cycles also has little or no effect on the endurance limit. As a result, the endurance limit was calculated at a value of 200,000 cycles in the rest of the study. Rest Period (seconds) Stiffness (ksi) Predicted EL (µ ) EL Range (µ ) 1 3,000 22 22 – 82 1,000 32 200 56 50 82 2 3,000 45 45 – 138 1,000 62 200 96 50 138 5 3,000 66 66 – 187 1,000 90 200 134 50 187 10 3,000 80 80 – 220 1,000 106 200 161 50 220 20 3,000 81 81 – 223 1,000 108 200 164 50 223 Table 4. Endurance Limits (EL) predicted from the beam fatigue test model. Figure 13. SR vs. strain at different values of rest period, stiffness, and number of load repetitions. 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain RP=2 sec, Eo=50 ksi 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain RP=5 sec, Eo=50 ksi 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain RP=2 sec, Eo=1000 ksi 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain RP=5 sec, Eo=1000 ksi 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain N=20000 N=100000 N=200000 RP=2 sec, Eo=3000 ksi 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 SR Microstrain N=20000 N=100000 N=200000 RP=5 sec, Eo=3000 ksi